concluding that to date there has been multiple high level feasibility studies indicating ...... The offshore system proposed by Siemens uses series connected diode rectifiers offshore, to ...... [47] H. W. H. Wang and M. Redfern, âThe advantages and disadvantages of using. HVDC to ..... 62, no. 1, pp. 310â321, Jan 2015. 185 ...
Low Frequency AC Transmission for the Integration of Offshore Wind Jonathan Ruddy, ME, BSc
A thesis submitted to University College Dublin in fulfilment of the requirements for the degree of
Philosophiæ Doctor College of Engineering and Architecture School of Electrical and Electronic Engineering
Head of School: Supervisor:
Dr. Andrew Keane Dr. Terence O’Donnell
September 2017
c by Jonathan Ruddy, 2017
All Rights Reserved.
ii
ABSTRACT
Offshore wind farm integration is providing substantial technical and economic challenges in the medium term and the trend for farther shore development in the future is focusing research and industry attention on cost effective transmission alternatives to existing technologies. The majority of offshore wind farms are grid connected via High Voltage AC (HVAC) transmission. Wind farms commissioned farther offshore (>100 km) utilise High Voltage DC (HVDC) transmission for grid interconnection. Low Frequency AC transmission is of significant interest for offshore wind farm integration at a range of 80-180 km. LFAC is an adaptation of HVAC transmission, operated at lower frequency, typically 16.7 Hz. Operating AC cables at a lower frequency reduces reactive power production in the AC cable, allowing more cable capacity for active power transmission at longer distances. The key advantage of LFAC compared to HVDC is the elimination of the requirement for an offshore converter station, thereby reducing offshore complexity and cost associated with offshore wind generation. The motivation of the thesis is to determine the technical, economic and operational feasibility of LFAC transmission as a transmission option for offshore wind. This thesis starts by presenting a comprehensive review of the research to date in LFAC connections, concluding that to date there has been multiple high level feasibility studies indicating positive results for LFAC. However, these have not considered in detail the technical and operational aspects of controlling the LFAC transmission system with a long HVAC cable. Onshore the low frequency must be converted to the grid frequency via an AC-AC frequency converter. Cycloconverters Back to Back (BtB)
iii
VSCs and Matrix converters have been considered as options in the literature, these have been compared and BtB VSCs are selected as the most appropriate choice due to the technical benefits of VSCs. A techno economic analysis is conducted comparing LFAC with both a BtB converter and a cycloconverter to HVDC transmission using capital costs, operational costs and losses. The results find that LFAC is less costly than HVAC and HVDC in the range 50-150 km. An analysis to determine the optimum frequency for LFAC determines that between 100 km and 200 km the frequency lies in the range 17-13 Hz, showing the potential for LFAC. The technical design of the LFAC transmission system is examined, with a particular focus on the control of the offshore grid voltage by the onshore BtB converter. The design and voltage control of the BtB converter is modelled in Simscape Power Systems and validated with a hardware experiment. Next, the design of the offshore voltage ’grid forming control’, is examined and adapted for the connection of a long HVAC cable, operated at low frequency. The impact of using long HVAC cables connected to power electronics on each end and operated at low frequency is examined. Controllers are adapted to control the LFAC voltage considering the impact of the long cable. Simulations are performed on a LFAC test system to examine the influence of controller parameters and the associated design trade-offs between the selection of dq controller time constants and voltage control bandwidth. The LFAC system design and control is then validated in a hardware experiment where the proposed controller operates in a real time, hardware in the loop experiment. Lastly, the relatively new impedance based stability approach for grid tied inverters is outlined applied to determine the harmonic stability of the LFAC grid. The concept of control instability in power electronic grids is then examined with potential for an interaction between the dq control of the onshore VSC and the PLL observed. Mitigation techniques for sub synchronous control interactions in the form of control design are then proposed and implemented. To conclude, LFAC transmission has been found to be a competitive and technically feasible approach for integrating offshore wind. Simulations and hardware experiments have verified the design and control of the system to maintain a stable offshore grid. iv
ACKNOWLEDGEMENTS
A body of work like this over a four year time period is not possible by one person without a lot of amazing support. Firstly I would like to thank my supervisor Dr. Terence O’Donnell for his guidance and advice through the entire project. His attention to detail, deep knowledge of power electronics and patience is second to none and have been invaluable to me. A special thanks must also go to Dr. Ronan Meere who worked tirelessly with me on the LFAC journey from the very beginning and was in all but name a co-supervisor. His technical insights and experience were essential and his attitude made the entire research process a more enjoyable experience. This work was funded by Science Foundation Ireland under Grant No. SFI/09/SRC/E1780, thanks to them for the support. I would like to thank also anyone in the Electrical/Energy Engineering department in UCD who had some hand in this project.
In particular I
have to acknowledge the essential help and expertise of Cathal O’Loughlin who painstakingly produces exceptionally reliable hardware experiments based on the hair brained ideas of the students he helps. To all the PhDs, post-docs and lecturers past and present in UCD Electrical Engineering thank you for all the craic, coffees, lunches, 5-aside soccer, tag rugby and random chats. I have made some amazing friends here which I hope will continue beyond the gates of UCD. Special mentions have to go to a few people, Alison, Conor, Val, Killian, James, Alex, Padraig, Mossy, Paul, Fab, Oli and Peter.
v
A huge thank you to Claire, who when apologetically asked to proof read yet another chapter replied ¨It’s no problem, I enjoy pointing out your mistakes¨. To my family, Mum, Dad, Claire and Declan thank you for the constant love and support that has been there forever. Visiting the safe haven of our home in Donegal always leaves me feeling refreshed and reinvigorated. Finally and most importantly, to Michelle, you have provided me with so much love, care and support over the past four years which I am eternally grateful for. Whenever things got difficult you were always there, and knew exactly what to say and when to say it. We have had some great times over these four years but our journey is just beginning.
vi
CONTENTS
Abstract
iii
Acknowledgements
v
List of Tables
x
List of Figures
xi
Nomenclature
xvi
1 Introduction 1.1 General Introduction . . . . . . . . . 1.2 Offshore Wind Power . . . . . . . . . 1.3 Research Objectives . . . . . . . . . . 1.4 Outline . . . . . . . . . . . . . . . . . 1.5 Publications Arising from this Thesis
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2 Literature Review 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Offshore Wind Transmission Technologies . . . . . . . 2.3 A Brief History of Low Frequency AC . . . . . . . . . . 2.3.1 LFAC for Bulk Power Transmission . . . . . . 2.3.2 LFAC for Offshore Wind Interconnection . . . . 2.4 Low Frequency AC Transmission Design Considerations 2.4.1 Onshore Frequency Converter . . . . . . . . . . 2.4.2 Offshore Infrastructure . . . . . . . . . . . . . . 2.4.3 Grid Connection . . . . . . . . . . . . . . . . . 2.5 Multi terminal Offshore Grid . . . . . . . . . . . . . . . 2.6 Cost of Offshore Transmission System . . . . . . . . . . 2.7 Stability in LFAC Grids . . . . . . . . . . . . . . . . . 2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Outcomes of State of the Art . . . . . . . . . . . . . .
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1 1 2 5 6 8
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9 9 10 12 13 16 17 18 26 31 33 35 37 38 39
3 LFAC Techno-economic analysis 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Offshore Transmission System Design . . . . . . . . . . 3.3 Onshore Frequency Converter Selection . . . . . . . . . 3.4 Losses Modelling . . . . . . . . . . . . . . . . . . . . . 3.4.1 Cable loss . . . . . . . . . . . . . . . . . . . . . 3.4.2 Transformer Loss . . . . . . . . . . . . . . . . . 3.4.3 Cycloconverter Loss . . . . . . . . . . . . . . . 3.4.4 Voltage Source Converter Loss . . . . . . . . . . 3.4.5 Component Reliability . . . . . . . . . . . . . . 3.5 Capital Investment Costs . . . . . . . . . . . . . . . . . 3.5.1 Cable Costs . . . . . . . . . . . . . . . . . . . . 3.5.2 Transformer Costs . . . . . . . . . . . . . . . . 3.5.3 Reactive Power Compensation . . . . . . . . . . 3.5.4 HVAC Platform Costs . . . . . . . . . . . . . . 3.6 Transmission Topology Comparison . . . . . . . . . . . 3.6.1 Component Losses . . . . . . . . . . . . . . . . 3.6.2 Capital Investment Costs . . . . . . . . . . . . . 3.6.3 Converter Reactive Power Requirements . . . . 3.6.4 Discussion . . . . . . . . . . . . . . . . . . . . . 3.7 Optimum Frequency Selection for Varying Transmission 3.7.1 Methodology . . . . . . . . . . . . . . . . . . . 3.7.2 Levelised Cost of Energy . . . . . . . . . . . . . 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .
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4 Modelling and Design of LFAC Transmission 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Modelling Background Information . . . . . . . . . . . . . . . . . 4.2.1 dq Frame Transformation . . . . . . . . . . . . . . . . . . 4.2.2 dq Current Controller . . . . . . . . . . . . . . . . . . . . 4.2.3 Pulse Width Modulation . . . . . . . . . . . . . . . . . . . 4.2.4 Phase Locked Loop (PLL) . . . . . . . . . . . . . . . . . . 4.3 LFAC Transmission Control . . . . . . . . . . . . . . . . . . . . . 4.3.1 DC Voltage Control . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Grid Forming Control . . . . . . . . . . . . . . . . . . . . 4.3.3 Wind Turbine LFAC System . . . . . . . . . . . . . . . . . 4.4 LFAC Offshore System Design . . . . . . . . . . . . . . . . . . . . 4.4.1 PLL and Voltage Controller Design . . . . . . . . . . . . . 4.4.2 Time Domain Simulations . . . . . . . . . . . . . . . . . . 4.5 LFAC Transmission System Initial Scaled Model . . . . . . . . . . 4.5.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Hardware in Loop Real Time Emulation of LFAC Transmission System . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
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42 42 43 44 46 46 48 49 50 51 52 52 53 53 54 54 56 57 59 60 61 61 64 67
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70 70 71 72 73 75 75 78 79 83 86 88 90 92 95 95
. 97 . 102 . 103
5 Operational Design and Voltage control of LFAC transmission 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 LFAC HVAC Cable . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Cable Modelling . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Voltage Controller Design Including HVAC Cable . . . . . . . . . 5.4 Time Domain Simulation of Test System . . . . . . . . . . . . . . 5.5 Hardware Experimentation . . . . . . . . . . . . . . . . . . . . . . 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
104 . 104 . 106 . 107 . 110 . 120 . 124 . 129
6 Impedance Based Stability in LFAC Power Electronic Grids 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Stability Analysis by Impedance Measurement . . . . . . . . . . 6.3 LFAC Impedance Measurement Technique . . . . . . . . . . . . 6.3.1 Impedance Scan of LFAC System . . . . . . . . . . . . . 6.4 Harmonic Stability of Voltage Controlled Inverter . . . . . . . . 6.4.1 Impact of Filter Capacitance . . . . . . . . . . . . . . . . 6.4.2 Impact of Current Control Bandwidth . . . . . . . . . . 6.4.3 Impact of Cable Length . . . . . . . . . . . . . . . . . . 6.5 Analysis of Frequency Coupling . . . . . . . . . . . . . . . . . . 6.6 Current Controlled Inverter Stability . . . . . . . . . . . . . . . 6.6.1 Sub-Synchronous Control Instability . . . . . . . . . . . 6.6.2 Simulation of SSCI . . . . . . . . . . . . . . . . . . . . . 6.6.3 Mitigation of SSCI . . . . . . . . . . . . . . . . . . . . . 6.6.4 Hardware Verification of SSCI . . . . . . . . . . . . . . . 6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
131 . 131 . 134 . 136 . 138 . 143 . 143 . 145 . 148 . 151 . 154 . 155 . 156 . 158 . 161 . 162
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7 Conclusions and Future Work 165 7.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 165 7.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 7.3 Recommendations for Future Work . . . . . . . . . . . . . . . . . . 170 References
171
A Cycloconverter harmonic output 187 A.1 Cycloconverter Output Power Quality . . . . . . . . . . . . . . . . . 187 B Marine Institute data
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C ABB HiPak IGBT Module 5SNE 0800M170100
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D Faults on LFAC grid 191 D.1 LFAC Fault analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 191 D.1.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
ix
LIST OF TABLES
2.1
Comparison of frequency converter options . . . . . . . . . . . . . . 34
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8
System components of LFAC and VSC - HVDC . . . . . . . . . . IGBT switch data . . . . . . . . . . . . . . . . . . . . . . . . . . . Failure rates and MTTR of Offshore Transmission System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AC cable data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transmission system data . . . . . . . . . . . . . . . . . . . . . . Annual Energy Losses . . . . . . . . . . . . . . . . . . . . . . . . Capital Investment Costs (eMillion) . . . . . . . . . . . . . . . . Operation and Maintenance Cost Factors . . . . . . . . . . . . . .
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52 55 55 56 58 62
4.1 4.2 4.3 4.4
Parameters for LFAC transmission system. . . . . . . Calculated parameters for LFAC transmission system. Scaled LFAC transmission system parameters. . . . . Hardware Parameters . . . . . . . . . . . . . . . . . .
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89 90 96 99
5.1 5.2 5.3 5.4 5.5
LFAC transmission cable data at 50 Hz. . . . . . . . . . . Trade offs associated with compensator design choices. . . Parameters for LFAC transmission system. . . . . . . . . . Controller specifications. . . . . . . . . . . . . . . . . . . . Parameters for scaled hardware LFAC transmission system.
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111 120 120 121 125
6.1 6.2
LFAC transmission system parameters for impedance measurements.140 Details of parameters used and the frequencies where minor loop responses are 0 dB below 1500 Hz. . . . . . . . . . . . . . . . . . . 149
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B.1 Wind Speed data from site in Irish Sea . . . . . . . . . . . . . . . . 189
x
LIST OF FIGURES
1.1
Annual onshore and offshore wind installations in Europe 2001-2016.
2.1 2.2 2.3
HVAC offshore transmission topology. . . . . . . . . . . . . . . . . VSC-HVDC offshore transmission topology. . . . . . . . . . . . . Transmission capability curves for 220 kV, 1000A cable at different frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 LFAC offshore transmission topology. . . . . . . . . . . . . . . . . 2.5 36 Pulse Cycloconverter. . . . . . . . . . . . . . . . . . . . . . . . 2.6 Change of harmonic frequency with output frequency for fi = 16.7 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Matrix converter topology. . . . . . . . . . . . . . . . . . . . . . . 2.8 Hexverter topology. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Back to Back Voltage Source Converter. . . . . . . . . . . . . . . 2.10 Comparison of a 50 Hz and the Tall design 16.7 Hz 220 MVA transformer at the offshore platform. . . . . . . . . . . . . . . . . 2.11 State of the art of viable distances for HVAC, LFAC and HVDC transmission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 3.2 3.3 3.4 3.5 3.6 3.7
. 10 . 11 . 15 . 17 . 18 . . . .
20 22 24 25
. 28 . 36
VSC-HVDC and LFAC offshore wind transmission options. . . . . . Cycloconverter efficiency and Line Commutated Inverter efficiency. Offshore Wind Farm layout. . . . . . . . . . . . . . . . . . . . . . . Individual component losses for both LFAC and VSC-HVDC. . . . Total losses for 2010-2013. . . . . . . . . . . . . . . . . . . . . . . . Capital costs of components. . . . . . . . . . . . . . . . . . . . . . . HVAC offshore transmission architecture for the 1-50 Hz wind farm grid connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Conventional transmission architure for VSC-HVDC grid connected wind farm design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 An overview of the power loss and CAPEX/OPEX mechanisms for the comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Component based CAPEX of 4 different operating frequencies for 150 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 LCoE for AC at 1, 10, 16.7 and 50 Hz and HVDC transmission for 200 MW at varying distance from shore. . . . . . . . . . . . . . . .
xi
3
44 49 55 57 58 59 62 62 63 63 65
3.12 Annual CAPEX and OPEX for 10 Hz, 16.7 Hz and HVDC for transmission distances up to 200 km over 20 years. . . . . . . . . . 65 3.13 Selection of optimum frequencies for 10 km transmission intervals up to 300 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21
4.22 4.23 4.24 4.25
4.26 5.1 5.2 5.3
General control of the VSC . . . . . . . . . . . . . . . . . . . . . . 72 dq current controller. . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Schematic diagram of Pulse Width Modulation. . . . . . . . . . . . 75 Implementation of the SRF-PLL. . . . . . . . . . . . . . . . . . . . 76 LFAC Transmission system for offshore wind. . . . . . . . . . . . . 79 DC Bus voltage control scheme . . . . . . . . . . . . . . . . . . . . 80 DC voltage control block diagram implementation. . . . . . . . . . 80 Small signal linearised control block diagram of DC voltage controller. 81 Grid forming control on the LFAC side VSC to maintain the offshore voltage magnitude and frequency. . . . . . . . . . . . . . . . . . . . 83 Voltage control block. . . . . . . . . . . . . . . . . . . . . . . . . . 84 Control block diagram of controlled frequency VSC. . . . . . . . . 85 Wind turbine VSC control. . . . . . . . . . . . . . . . . . . . . . . . 87 LFAC transmission system . . . . . . . . . . . . . . . . . . . . . . . 88 Bode plots of the components of the AC voltage control, including the open and closed loop response. . . . . . . . . . . . . . . . . . . 91 Open Loop bode plots of 50 HZ PLL and 16.7 Hz PLL. . . . . . . . 92 LFAC voltage, current, dq voltage and current and the DC link voltage of the BtB converter connected an offshore resistive load. . . 93 Time domain simulation of controlled power port VSC side. . . . . 94 LFAC transmission system modelled in software. . . . . . . . . . . . 95 Software model and hardware model in red. . . . . . . . . . . . . . 96 LFAC (a) voltage and (b) current at start-up and in response to a (c) power ramp beginning at 0.7s. . . . . . . . . . . . . . . . . . . . 97 (a) Reference Id compared to actual Id in dq controller and (b) reference Vd and controlled Vd in voltage controller of the controlled frequency VSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 LFAC transmission system modelled in hardware. . . . . . . . . . . 98 Picture of hardware setup. . . . . . . . . . . . . . . . . . . . . . . . 99 Hardware (a) voltage d and q components, (b) 3 phase voltage, (c) current, (d) active and reactive power. . . . . . . . . . . . . . . . . 100 (a) Hardware voltage, (b) Vd , (c) Id and (d) Active power response for hardware and simulation, in response to step in power from 500 W to 1000 W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Vd response to step in active power from 500 W to 1000 W for filter with 20 µF, 40 µF and 80 µF capacitor. . . . . . . . . . . . . . . . 102 Steady state pi-model of the cable. . . . . . . . . . . . . . . . . . . 107 Lumped pi-section cable model. . . . . . . . . . . . . . . . . . . . . 109 Multiple pi-section cable model where N is the number of pi-sections.109
xii
5.4
5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 6.1 6.2 6.3 6.4 6.5 6.6 6.7
Frequency response showing resonant frequencies of a 150 km cable with distributed parameter cable model, and multiple pi-section models with 1, 5 and 20 pi-sections. . . . . . . . . . . . . . . . . . Resonant peaks of 220 kV cable combined with LC filter. . . . . VSC connected to filter and cable. . . . . . . . . . . . . . . . . . . Control block diagram including LFAC cable. . . . . . . . . . . . (a) Open loop and (b) closed loop frequency response with cables from 50 km to 300 km. . . . . . . . . . . . . . . . . . . . . . . . (a) Open and (b) closed loop frequency response with updated controller for any cable length. . . . . . . . . . . . . . . . . . . . . Closed loop step response of Equation 5.8 with k = Cf ω and k = (Cf + C)ω. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Closed loop poles of Equation 5.8 for cable lengths from 50 km to 300 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nyquist plot of closed loop small signal system for cable lengths from 50 km to 300 km. . . . . . . . . . . . . . . . . . . . . . . . . Closed loop step response of Equation 5.8 for each Controller in Table 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vd response to voltage reference step from 1 to 1.5 pu. . . . . . . . Vd response to large current step. . . . . . . . . . . . . . . . . . . Voltage, Vdq , Power transferred, Id and VDC from test system simulation for Controller B. . . . . . . . . . . . . . . . . . . . . . LFAC transmission system hardware setup with OPAL RT real time simulator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Picture of hardware setup . . . . . . . . . . . . . . . . . . . . . . Small signal step response of hardware model. . . . . . . . . . . . Response of hardware and software model to step in voltage from 1 pu to 1.5 pu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vd response to power step from 0.3 pu to 1 pu in hardware for three controllers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison hardware and software LFAC Voltage, Vdq , Id , power and VDC during step from 300 W to 1000 W. . . . . . . . . . . . .
. . . .
. 115 . 117 . 118 . 118 . 119 . 121 . 122 . 122 . 123 . 126 . 127 . 127 . 128 . 128 . 129
Small signal representation of (a) voltage source inverter with a load and (b) current source inverter with a load. . . . . . . . . . . . . . . Small signal representation of Zs (s) and ZL (s) to find the stability of the LFAC voltage controlled inverter. . . . . . . . . . . . . . . . Small signal representation of Ys (s) and Yl (s) inverter with a cable and load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single line diagram of impedance measurement circuit setup to find (a) Zs and (b) ZL . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single line diagram of impedance measurement circuit to find (a) YL and (b) Ys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flowchart methodology for determining impedance and admittance. Control schemes of (a) current controlled inverter and (b) voltage source inverter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
110 111 112 113
136 137 137 138 139 139 140
6.8 6.9 6.10 6.11
6.12 6.13
6.14
6.15 6.16
6.17
6.18
6.19 6.20 6.21 6.22 6.23 6.24 6.25 6.26 6.27 6.28 6.29
ZL and Zs for LFAC voltage controlled inverter. . . . . . . . . . . Comparison of directly measured impedance of 150 km cable and wind farm inductance with impedance ZL . . . . . . . . . . . . . . Comparison of directly measured impedance of LC filter with impedance Zs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impedance scans of voltage controlled side with changing filter capacitance compared to wind farm impedance with 100 km cable with current controller bandwidth 2000 rads −1 . . . . . . . . . . . Minor loop responses varying filter capacitance with 100 km cable. Impedance scans of voltage controlled with 11 µF Cf varying current controller bandwidth compared to wind farm impedance with 100 km cable. . . . . . . . . . . . . . . . . . . . . . . . . . . Minor loop responses with varied current controller bandwidth with 100 km cable, unstable for high current controller bandwidth and stable for low current controller bandwidth. . . . . . . . . . . . . Three phase circuit layout for harmonic stability time domain simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage, Current and FFT of Voltage showing harmonic instability for 11µF capacitor and 100 km LFAC cable with a current control bandwidth of 2000 rads1 . . . . . . . . . . . . . . . . . . . . . . . . Voltage, Current and FFT of Voltage showing for 11µF capacitor and 100 km LFAC cable with a current control bandwidth of 1000 rads1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impedance scans of voltage controlled with 4 µF Cf varying current controller bandwidth compared to wind farm impedance with 150 km cable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minor loop responses varying current controller bandwidth with 150 km cable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Source and load impedance for 3 cable lengths using controller design procedure in Chapter 5. . . . . . . . . . . . . . . . . . . . . Voltage, Current and PLL frequency for a 10 Hz 0.01 pu voltage disturbance injection. . . . . . . . . . . . . . . . . . . . . . . . . . FFT of current during a 10 Hz 0.01 pu voltage disturbance showing frequency coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . Source and load admittance showing influence of voltage control bandwidth and PLL bandwidth. . . . . . . . . . . . . . . . . . . . Minor loop response of Figure 6.23 with 8 Hz PLL. . . . . . . . . Voltage, current, power, PLL frequency and FFT of current for unstable case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage, current, power and PLL frequency for case without PLL. PLL open loop response for different PLL bandwidths. . . . . . . Vdq , Id and PLL frequency for two cases with changing PLL bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vdq , Id and PLL frequency for three cases changing voltage control bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiv
. 141 . 141 . 142
. 144 . 144
. 145
. 146 . 146
. 147
. 148
. 149 . 150 . 151 . 153 . 153 . 154 . 155 . 157 . 158 . 159 . 160 . 161
6.30 Voltage, current, power, PLL frequency and FFT of current for stable case with voltage control bandwidth of 220 rad s−1 . . . . . . 162 6.31 Voltage, current, Vdq and power for hardware with voltage control bandwidth reduced to 111.3 rad s−1 . . . . . . . . . . . . . . . . . . 163 A.1 Output voltage of step down cycloconverter . . . . . . . . . . . . . 188 A.2 Harmonic content of step down cycloconverter (50 Hz to 16.67) . . 188 A.3 Harmonic content of step up cycloconverter (16.7 Hz to 50 Hz) . . . 188 C.1 Switching energy per pulse vs collector current of IGBT . . . . . . . 190 C.2 Reverse recovery characteristics vs forward current of IGBT . . . . 190 D.1 Vabc , Iabc , Vdq and active power at the onshore point of connection during a 3 phase fault on the LFAC cable. . . . . . . . . . . . . . . 192 D.2 Vabc , Iabc , Vdq and active power at the onshore point of connection during a fault on phases A and B of the LFAC cable. . . . . . . . . 192 D.3 Vabc , Iabc , Vdq and active power at the onshore point of connection during a fault on phase A of the LFAC cable. . . . . . . . . . . . . 193
xv
NOMENCLATURE
AC
Alternating Current
BtB
Back to Back converter
CAPEX
Capital Expenditure
FCC
Forced Commutated Converter
FFT
Fast Fourier Transform
FFTS
Fractional Frequency Transmission System
HVAC
High Voltage Alternating Current
HVDC
High Voltage Direct Current
IGBT
Insulated Gate Bipolar Transistor
LCC
Line Commutated Converter
LCoE
Levelised Cost of Energy
LFAC
Low Frequency Alternating Current
MMC
Modular Multi-level Converter
MMMxC
Modular Multi-level Matrix converter
OPEX
Operational Expenditure
PCC
Point of Common Coupling
PLL
Phase Locked Loop
PWM
Pulse Width Modulation
SSCI
Sub-Synchronous Control Instability
SSR
Sub-Synchronous Resonance
TOV
Temporary Over Voltage
VSC
Voltage Source Converter xvi
CHAPTER
ONE INTRODUCTION
1.1
General Introduction
Renewable energy sources are playing an ever increasing role in the power system of today. Penetrations of wind, solar, biomass, hydro, tidal and wave power have increased due to a number of factors. The global action on climate change is the primary driver behind these renewable energy sources to remove the reliance on emission heavy fossil fuel based energy sources. In December 2015 195 countries signed up to the Paris Climate Accord agreement within the United Nations Framework Convention on Climate Change (UNFCCC) where each country agrees to make contributions to mitigate global warming [1]. One major part of this commitment is the dependence on fossil fuel based generation. Reducing the use of fossil fuels also has a substantially positive effect on the air and water quality in urban areas near fossil fuel burning stations. Another aspect which has to be considered is the trend in recent years showing that the cost of renewable energy, in particular onshore wind and solar power, has reduced to almost parity with gas powered plants in the UK [2]. This statistic is the one which means renewable energy is here to stay, at least in the short to medium term, as it can be considered competitive with other energy options without requiring subsidies for infrastructure to be built. A number of reasons can be attributed to the reduction in cost. Increased power density and efficiency have brought about 1
economies of scale which improve the cost effectiveness of individual renewable sources. Increased market certainty about the future of renewables has improved investment. Another factor which has to be taken into account is carbon taxes applied to fossil fuel based generation. Renewable energy is still a relatively new industry compared to fossil fuel based generation. The techniques and processes for installing renewables have been refined over the years to increase cost effectiveness and functionality. Onshore wind and solar are the relative ”success stories” so far. To further de-carbonise the energy system other forms of renewable energy must be considered to hedge against the variability of onshore wind and solar generation. This thesis focuses on offshore wind power and in this context there is a need to further reduce the cost of generating energy offshore. LFAC is examined as a potentially viable alternative to HVDC and the feasibility of an LFAC transmission system for offshore wind is determined based both on the economic comparison to HVDC and the technical design and operational viability.
1.2
Offshore Wind Power
Offshore wind is a key enabler to achieving the ambitious European renewable energy targets [3]. Challenges on the availability of land and public opposition to large onshore wind turbines are driving wind power plants offshore. In addition consistently stronger wind conditions offshore create higher capacity factors, making the move offshore more appealing. Many coastal areas have high energy demands, meaning that building offshore wind can locate the energy source closer to the major load centres in some cases. Figure 1.1 [4] shows onshore and offshore wind installations in Europe from 2001 to 2016, from which it can be seen that the proportion of offshore wind to onshore wind has been steadily increasing from 2006. Offshore wind farms enable the use of larger wind turbines to increase power capture. Opposition to unsightly near shore wind farms reduces their attractiveness and therefore offshore wind farms are being planned farther offshore. With the move farther offshore the feasibility is very dependent on reliability and
2
cost, so current research in the area tends to focus on reducing the overall cost of offshore wind and increasing the reliability to reduce offshore wind plant down time. 14,000 ϯϬϭϯ
13,000
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12,000 11,000 10,000 9,000 8,000 Installed Capacity 7,000 (MW) 6,000 5,000 4,000 3,000 2,000 1,000 0
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Offshore 00 00 00 00 Onshore
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Figure 1.1: Annual onshore and offshore wind installations in Europe 2001-2016. Numerous topologies and configurations have been suggested for efficient power transfer from the offshore wind site to the onshore grid. For near shore wind farms (less than 50 km approx.), High Voltage AC (HVAC) transmission at 50 or 60 Hz is sufficient [5] and most of the existing wind farms are built with HVAC transmission [6]. For farther offshore installations, current trends in research and practice point towards the use of High Voltage Direct Current (HVDC) transmission with Voltage Source Converter (VSC) based HVDC transmission being the preferred approach as it displays distinct control and design advantages over traditional Line Commutated Converter (LCC) technology [7]. In such installations the wind farm collector network typically operates at 50 or 60 Hz, which is then converted to HVDC by an offshore converter station for transmission to an onshore converter station. VSC-HVDC is currently considered the market leader for offshore wind integration at distances greater than 60-80 km largely due to its established use in onshore point to point bulk power transfer [8]. The offshore converter station however becomes a concern when the reliability and the cost of the system are 3
considered. Large power electronic converter stations far offshore are costly and difficult to reach if a failure occurs, therefore potentially increasing down time and interruption of supply. Offshore wind farm integration is providing substantial technical and economic challenges in the medium term and the trend for farther offshore development in the future is focusing research and industry attention on cost effective transmission alternatives to existing technologies. A CIGRE general meeting 2014 contribution by Bell et al. [9] indicates that efforts to decrease the amount of complexity offshore could be advantageous to the overall feasibility of an offshore transmission system, stating that due to the high cost of offshore HVDC transmission systems the balance between cost and reliability for an offshore HVDC network will be shifted significantly towards minimisation of the number and size of physical assets and, arguably, away from high continuity of supply. Transmission solutions seeking to minimise the complexity of the offshore network have been proposed in the recent past, both as competitors and complimentary systems to VSC-HVDC. Low Frequency AC (LFAC) transmission, typically at a frequency of 16.7 Hz has been proposed as an alternative to conventional 50 Hz AC or VSC-HVDC [10, 11, 12]. LFAC is an interesting alternative transmission option for offshore wind, primarily due to the extension of AC power transmission distance at lower frequency. Offshore cables operated at low frequencies, usually 16.7 Hz, extend the maximum power transmission distance of the cable from 60-80 km at 50 Hz to 180-200 km. The key advantage of LFAC compared to HVDC is the removal of the offshore power electronic converter station [10, 13]. The elimination of the offshore converter station is based on the assumption that the wind turbines have the ability to produce AC at a lower frequency [10], which is possible with full converter type IV wind turbines. The LFAC transmission cable transmits power at low frequency to the shore where a frequency changing converter converts from low frequency to the grid frequency. This technology reduces the complexity offshore and therefore may reduce the capital investment costs and increase reliability, with the impact of decreasing the overall cost of offshore wind. It should also be noted that other alternative technologies have been presented which aim to 4
reduce offshore infrastructure complexity, reduce the number of conversion steps and increase reliability. These include DC wind turbines connected to a HVDC station [14], DC wind turbines connected to a LFAC transmission system [12] and variable frequency collection grids with HVDC transmission [15]. LFAC has been used in the rail systems in parts of Europe for many years, where in Germany and Norway the trains operate at a frequency of 16.7 Hz and as such has an already established industry base, producing equipment at low frequency, albeit, primarily single phase.
Potential drawbacks to LFAC
transmission include the size of low frequency transformers and inductive elements at low frequency.
1.3
Research Objectives
The feasibility of LFAC for offshore interconnection depends on a thorough investigation of the impact of operating at lower frequency on the components involved and understanding of the technical and economic comparison between the LFAC system and its competitors. In particular this PhD will focus on the offshore aspect of the transmission systems. This PhD aims to uncover the details behind the LFAC transmission system, identify the challenges to implementation of this technology and in the form of a scaled hardware experiment, implement a working LFAC system representing the application of LFAC to offshore wind. The following research questions are posed: • Is LFAC economically feasible compared to the alternative HVDC for offshore wind farms outside of the range of HVAC transmission? • Is 16.7 Hz the most appropriate frequency to use for LFAC transmission considering with modern power electronics the frequency no longer needs to be a fraction of the fundamental 50 Hz? • What components are required for a feasible design of a LFAC transmission system, including component selection and control design?
5
• How is the LFAC grid controlled considering it is a fully power electronic offshore grid with a long HVAC cable and no synchronous machines providing inertia? • What are the implications for harmonic stability when connecting a long HVAC cable operated at LFAC to an onshore BtB converter which controls the offshore grid? • In the fully power electronic AC grid are there any control interactions present causing instability and how can these be mitigated?
1.4
Outline
A review of the literature is conducted in Chapter 2 including an introduction to the transmission options for offshore wind. A review of the previous work conducted on LFAC transmission with a focus on the choice of onshore frequency converter is included. The techno-economic analysis is performed in Chapter 3. Analytical loss models are developed and used to compare HVDC and LFAC for the transmission of offshore wind for wind farms over 100 km from shore. A full techno-economic comparison is performed and a levelised cost of energy analysis is used to determine the optimum frequency to operate LFAC for various transmission distances. Chapter 4 begins the technical modelling of LFAC transmission. The initial control building blocks required are outlined at the outset of the chapter and are used to design the control system for the converters. The component design of LFAC transmission system is also included in this chapter and is incorporated with the control in an initial simulation test and scaled hardware validation. In Chapter 5 the full LFAC transmission system model is developed to include the LFAC cable and the back to back converter. Small signal models are developed to improve back to back converter control from Chapter 4 to allow for the connection of a long HVAC cable. Time domain switching simulations are performed and validated against the small signal models. The impact of control
6
on temporary over voltages in the LFAC cable is the examined and the associated design trade offs are discussed. The chapter concludes with a full scaled hardware experiment verifying the design and control of the LFAC system. Chapter 6 considers the stability of the LFAC transmission system. The simulation models developed in Chapter 5 are used to perform impedance based stability analysis on the LFAC transmission system to determine the harmonic stability. The relatively new impedance based stability approach for grid tied inverters is outlined at the beginning of the chapter and applied thereafter. The concept of control instability in power electronic grids is then examined with potential for an interaction between the dq control of the onshore VSC and the PLL observed. Mitigation techniques for SSCI in the form of control design are then proposed and implemented. Finally in Chapter 7 some conclusions from the thesis are drawn, the contributions are outlined and possible future work is proposed.
7
1.5
Publications Arising from this Thesis
Journal Publications J. Ruddy, R. Meere, T. O’Donnell, ”Low Frequency AC transmission for offshore wind power: A review ”, Renewable and Sustainable Energy Reviews, Volume 56, April 2016, Pages 75-86, ISSN 1364-0321. J. Ruddy, R. Meere, C. O’Loughlin and T. O’Donnell, ”Design of VSC Connected Low Frequency AC Offshore Transmission with Long HVAC Cables”, In review, IEEE Transactions on Power Delivery. J. Ruddy, R. Meere, T. O’Donnell, ”A Comparison of VSC-HVDC with Low Frequency AC for Offshore Wind Farm Design and Interconnection”, Energy Procedia, Volume 80, 2015, Pages 185-192, ISSN 1876-6102. R. Meere, J. Ruddy, P. McNamara, T. O’Donnell, ”Variable AC transmission frequencies for offshore wind farm interconnection”, Renewable Energy, Volume 103, April 2017, Pages 321-332, ISSN 0960-1481. J. Ruddy, C.O’Loughlin, R. Meere, T. O’Donnell, ”Impedance based Harmonic Stability in Low Frequency AC Transmission systems”, In review, Electric Power Systems Research
Conference Publications J. Ruddy, R. Meere, C. O’Loughlin and T. O’Donnell, ”Scaled hardware verification of low frequency AC transmission system for interconnection of offshore wind ”, 5th IET International Conference on Renewable Power Generation (RPG) 2016, London. J. Ruddy, R. Meere and T. O’Donnell, ”Low Frequency AC transmission as an alternative to VSC-HVDC for grid interconnection of offshore wind ”, PowerTech, 2015 IEEE Eindhoven, Eindhoven, 2015, pp. 1-6. 8
CHAPTER
TWO LITERATURE REVIEW
2.1
Introduction
This chapter provides a review of Low Frequency AC (LFAC) transmission, which is of significant interest for offshore wind farm integration at a range of 80-180 km. LFAC is an adaptation of HVAC transmission, operated at lower frequency, typically 16.7 Hz. The key advantage of LFAC compared to HVDC is the elimination of the requirement for an offshore converter station, thereby reducing offshore complexity and potentially increasing the operational life of the offshore wind farm. Design challenges are introduced surrounding the design of the 16.7 Hz transmission transformer and associated offshore platform for this potential transmission technology. A comprehensive review of existing research conducted on LFAC and a discussion centering on the design considerations for offshore LFAC transmission components is presented. The frequency changing converter onshore, offshore LFAC substation and the wind turbine considerations are evaluated in detail. LFAC multi-terminal offshore grids are also considered, as this alternative to HVDC multi-terminal grids may reduce the requirement for multiple offshore converter stations.
9
2.2
Offshore Wind Transmission Technologies
For near shore wind farms, (most of the existing offshore developments) HVAC transmission at a frequency of 50 or 60 Hz is sufficient and can be directly connected to the onshore grid similarly to an onshore wind farm. The HVAC system consists of well-established technology [16].
The HVAC links usually
consist of an AC collecting system platform offshore, an offshore transforming substation and a three phase submarine cable to connect to an onshore substation. Figure 2.1 displays the layout of an AC connected offshore wind farm. The submarine AC cable generates a large reactive current due to the high capacitance of the cable, this reduces the active power carrying capability of the cable, thus limiting the distance that an AC submarine cable can transmit power economically [17]. In general it has been seen that for short distances HVAC connection of offshore wind farms lead to lower losses than the alternatives, as there are no conversion steps, however many other aspects influence the choice of transmission system for example, the number of cables required, reliability, integration to the onshore grid and the overall cost of the transmission architecture [18].
Figure 2.1: HVAC offshore transmission topology. With the trend for offshore wind farms pushing further offshore and into deeper water [4] the transmission system has to be adapted to cope with increased transmission distance to shore. HVDC transmission has been proposed as the solution to integrate large scale offshore wind power from far offshore wind (greater than 50 km) [19, 20, 21, 22]. There is no charging current effect in the DC cable and no resonance between the cables and other AC equipment and therefore the DC 10
link does not have the same maximum distance limitation compared to AC cables [17]. Figure 2.2 shows the HVDC transmission topology, the DC link decouples the offshore wind farm from the onshore grid which has the advantage that faults are isolated in the offshore grid. VSC-HVDC is the preferred choice over the alternative Line Commutated Converter (LCC) HVDC due to the avoidance of commutation failures, independent control over active and reactive power, the ability to connect to weaker grids with a low short circuit ratio, and the faster dynamic response compared to LCC [23]. VSC-HVDC can also easily provide grid support services, where active power control can be used to aid frequency control of the onshore grid and even if there is no active power flow the VSC can provide or absorb reactive power to support the grid voltage [24]. The filtering requirement of the VSC-HVDC system is small especially if the most recent technology based on multi-level converters is used [25].
Figure 2.2: VSC-HVDC offshore transmission topology. Nevertheless VSC-HVDC has the disadvantage of requiring an offshore converter station which increases costs and raises reliability concerns. In an effort to reduce the complexity of the offshore transmission system, and in particular the offshore converter station, there have been proposals to replace the offshore converter with a diode based rectifier, with a VSC remaining onshore [26, 27, 28]. This system has the advantage of utilising robust and reliable power electronics offshore, with high reliability and low maintenance requirements. The offshore system proposed by Siemens uses series connected diode rectifiers offshore, to achieve the required DC voltage [29]. This can enable stepwise installation of the wind farm, with shorter delivery times than conventional VSC-HVDC and the DC
11
platforms offshore, contributing to the economic viability of offshore wind farms on a large scale. Another approach which has been proposed is the use of a single centralised converter which controls the variable frequency and speed of a cluster of windturbines thus eliminating the converter from each turbine. This approach uses a variable voltage and frequency, but fixed voltage to frequency ratio, (V/Hz) wind farm collector grid with a VSC-HVDC connection from offshore to onshore [30, 31]. The disadvantage of this approach is that all turbines in a cluster will have the same speed, determined by the centralised converter, thus the speed of individual turbines may not be optimised for maximum power capture. It has however been shown that the difference between V/Hz and conventional variable speed operation is less than 3% for wind variations below 1 m/s between the wind turbines [31]. For a particular wind site with variable wind speeds which are between the cut in and rated wind speed, the variable frequency system can display distinct advantages in terms of energy production compared to the conventional approach since the variable frequency approach can maximise energy capture below rated speed [32]. Another alternative option is to use a DC collection grid with a HVDC offshore network [33, 34, 35]. This however, does not reduce the requirement for large offshore converters. DC fault clearance is another concern for an offshore DC grid. The currently proposed solutions include DC circuit breakers and redundancy in the cables [36]. These solutions tend to increase the offshore infrastructure requirement and therefore the costs.
2.3
A Brief History of Low Frequency AC
LFAC has been utilised for almost a century in railway systems in Germany, Austria, Switzerland and Norway.
The traction system in these European
countries utilise 16.7 Hz and some train systems in the USA use 25 Hz [37]. In the early 1900s all traction systems were coal based, however prior to the First World War, coal shortages forced train operators to develop electric traction systems. DC drives were the motor of choice for controllable speed, however DC
12
could not be transformed easily and therefore long distance railway lines were not a viable option with DC [38]. Universal motors were then used, however when fed AC at standard distribution frequency the large inductance of the windings made design of large motors impractical. Furthermore, eddy currents induced at standard frequencies caused overheating and reduced efficiency [39]. The solution was to use powerful propulsion motors at lower frequency to reduce eddy current losses and reduce the complexity of the design. The lower frequency was created using a motor generator pair. From this the rail network of 16 2/3 Hz was developed (1/3 of 50 Hz) [38], and was altered slightly to 16.7 Hz during the 1990s for stability purposes. The increased use of static power electronic converters made the transition from 16 2/3 to 16.7 less difficult. Lower frequency also has the advantage that train tracks can have large distances between electrical stations which are advantageous for long railway lines. Countries which utilise low frequency railway lines also have dedicated low frequency power stations for the railway electrification, reducing the need for converters in the traction systems [40].
2.3.1
LFAC for Bulk Power Transmission
HVAC cables have two main limiting factors which limit the power transfer capability of the cable. These are the maximum allowable voltage deviation at the receiving end of the cable, and the cable current carrying capability. Current carrying capability is a combination of the active current and the charging current (reactive current) which depends on the frequency, length and capacitance of the cable [41]. As can be seen from Equation 2.1, at lower frequencies the charging current is reduced, therefore reactive power generated in the cable is reduced, from Equation 2.2, leaving more space for active power, thus increasing the current carrying capability, and the maximum active power calculated by Equation 2.3.
Ic = 2πf lCE
13
(2.1)
Qc = Ic E
PR =
p S 2 − Q2c
(2.2)
(2.3)
Where: E: rated voltage, f: frequency, l: length of cable, C: cable capacitance per unit length, S: apparent power, PR : maximum active power transmission capability. To increase the transmission capability of a cable, the options are to increase the voltage or decrease the inductive reactance of the cable.
If a cable is
operated at lower frequency, its inductive reactance decreases resulting in a reduced voltage deviation across the cable, reduced charging current and therefore reduced generated reactive power. This results in an increase in active power that can be transmitted in the cable PR . Figure 2.3 shows the effect of alternative frequencies on a 220 kV 3 core XPLE subsea transmission cable. It can be seen in Figure 4 that a reduction in frequency provides an increased maximum length that power can be transmitted through an offshore cable. The maximum distance allowed is limited by the voltage deviation constraint at the receiving end. For transmission at 16.7 Hz the maximum distance allowable is almost three times that at 50 Hz. LFAC was first proposed for high power transmission by Xifan Wang in 1994 [42] in the form of a Fractional Frequency Transmission System (FFTS), which uses lower frequency to reduce the reactance of AC transmission system. The motivation behind the FFTS was to transmit hydro resources from the west of China to the large load centres in the east and south coast. At the time the conventionally used DC transmission was deemed too expensive, and the highest voltage HVAC transmission was 550 kV, which limited the distance [42]. FFTS at a frequency of 50/3 Hz was proposed as a solution to this issue. They concluded that FFTS can increase the amount of transmissible power. For example their calculations, which were based on examination of the power-angle curves at different frequencies, indicated that for a 550 kV, 1200 km transmission line at 50
14
Figure 2.3: Transmission capability curves for 220 kV, 1000A cable at different frequencies. Hz the transmission power limit was 850 MW, whereas with FFTS the limit was 1700 MW. In a follow up paper the same group demonstrated a scaled hardware model of the frequency changing converter [43]. A scaled model was produced of a hydro plant, with the generator configured to produce 16.67 Hz (adding extra poles to the generator), connection via LFAC transmission to the load centre 1200 km away, and connecting to the local grid via a frequency changer in this case, a cycloconverter. The analysis concluded that LFAC could reduce the number of lines required, by increasing the maximum power transfer capability of AC cables. It was also concluded that the cycloconverter can change the frequency from 16.67 to 50 Hz; however there were concerns with the low power factor, and the introduction of significant harmonics in the output voltage from the thyristor switching. The feasibility of connecting large scale wind generation a great distance from the load centre is further investigated in Wang et al. [44], via FFTS or LFAC. Again the motivation was to reduce the investment cost required for transmission of vast wind resources 915 km from the biggest load centres. The
15
authors present a specific case study comparing conventional 50 Hz transmission and FFTS to integrate 10,000 MW of wind power. A power flow analysis concludes that the voltage variation of the 50 Hz system spends more time outside the voltage limit of 5% than the variation at FFTS. Therefore the FFTS system can transmit more wind power without curtailment due to voltage constraints. It is interesting to note that a HVDC option is not included in this analysis as this could be the most feasible way of transmitting power such distances. The authors concede that the added cost of larger transformers and the frequency changer may make the system more expensive. Further work considering the power flow in a FFTS system connected to onshore wind farms is presented in [45]. The steady state performance of LFAC with transmission lines and a cyclonconverter as the frequency changing converter is presented in [46]. A range of operating frequencies are examined from 5 to 60 Hz with the conclusion that the lower frequency systems have a superior voltage profile due to the reduced voltage drop, adding to the potential benefits of LFAC for bulk power transmission. It has also been proposed that LFAC may be used to interconnect two grids which operate at different frequencies or voltages, in much the same way as HVDC has done in many cases [47]. Funaki and Matsuura [11] propose LFAC transmission and compare it to both HVAC and HVDC transmission in the form of a feasibility study for interconnecting two grids. The basic operation was demonstrated and confirmed by transient simulation. A control system was implemented based on the swing equation to maintain frequency stability in the simulation. Simulation results indicated that the LFAC system had comparable control compared to a HVDC system in terms of AC power flow control; however the low order harmonics on the output of the frequency converter are a concern.
2.3.2
LFAC for Offshore Wind Interconnection
In recent years the most interesting application of LFAC transmission is for offshore wind interconnection. LFAC is an interesting alternative to HVDC for the interconnection of offshore wind due to the absence of the offshore converter, and the extension of the maximum transmission length for AC cables, thus reducing the 16
cost and complexity of the offshore network [10, 12]. It has been stated in a study of the prospects and challenges for LFAC that 600 MW of power transfer is possible for up to 400 km with existing 245 kV XLPE cables operated at low frequency [48]. Figure 2.4 displays the layout of a LFAC offshore transmission system. The wind turbine, which is assumed to be a full converter, type 4 turbine, produces a low frequency output for the low frequency collection network. The voltage is then stepped up to transmission voltage in a large low frequency transformer. Onshore a frequency converter converts from low frequency to grid frequency. In 2009 Qin et al. [49] proposed LFAC as a solution for offshore wind interconnection, which had previously only been discussed by using conventional HVAC or VSC based HVDC transmission systems. The authors suggest that for short and intermediate distances, between 30 and 150 km, LFAC is competitive in terms of capital costs.
Figure 2.4: LFAC offshore transmission topology.
2.4
Low Frequency AC Transmission Design Considerations
A number of technical challenges need to be overcome before the implementation of LFAC can be realised.
The components required to make up the LFAC
transmission system require careful consideration. A number of different converter types have been proposed in the literature to date. These include the use of a cycloconverter, matrix converter and Back to Back Voltage Source Converter (BtB VSC), all of which are reviewed below. The effect of lowering the frequency
17
from its nominal value (50 or 60 Hz) on the size of the transformers, reactors and wind turbine is also of critical importance to the feasibility of LFAC.
2.4.1
Onshore Frequency Converter
Cycloconverter A cycloconverter is a thyristor based device which uses direct AC-AC conversion to change frequency. The operation of the three phase cycloconverter is to convert AC at a primary frequency to AC at a secondary frequency achieved using a thyristor based 36 pulse converter shown in Figure 2.5. Each phase of the output wave has a positive and negative 6 pulse converter which transforms the three phase input 16.7 Hz wave to each single phase 50 Hz output. The thyristor firing angle in each converter is controlled using the cosine wave crossing method and the firing pulses are produced based on a reference input signal at the desired output frequency [12].
Figure 2.5: 36 Pulse Cycloconverter.
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Most applications of cycloconverters today are frequency step down in the direction of power flow. Examples include train systems [50], ships [51] and the operation of large drills or mills for mining [52]. These applications require the input frequency (50 or 60 Hz) to be stepped down to the frequency required for the application. In contrast to these the application proposed in LFAC systems for offshore wind, requires the cycloconverter to step up the frequency, from 16.7 Hz to 50 Hz. Step down cycloconverters, or naturally commutated cycloconverters use thyristors as power switches. The thyristors are line commutated and therefore there is no requirement for extra commutation circuits. The line commutated cycloconverter typically has a limit on the frequency conversion ratio (output frequency/input frequency) of approximately 0.7, due to the power quality of the produced output voltage waveform [53]. The poor quality of the output waveform can be explained by the presence of sub-harmonics and inter-harmonics in the output voltage. The harmonic spectrum for the naturally commutated cycloconverter can be calculated from Equation 2.4 [54].
foH = |6fi ± (2n + 1)fo |
(2.4)
Where foH is the harmonic frequency, fi and fo are the input and output frequencies of the cycloconverter and n is any positive integer. Figure 2.6 displays the change in harmonic frequency with output frequency of the naturally commutated cycloconverter. It can be seen that for certain fo ratios of (where fi = 16.7 Hz) the order of harmonics can be below the fi desired output frequency, known as sub-harmonics. When the desired output frequency is above the input frequency harmonics occur at frequencies which are not all direct multiples of the desired output frequency. These are known as inter-harmonics. Sub-harmonics and inter-harmonics are difficult to filter from the voltage waveform, and require large and complex filter design. The output frequency to input frequency ratio required for the LFAC system at 16.7 Hz is approximately 3. It can be seen that when stepping up an exact multiple of the
19
Figure 2.6: Change of harmonic frequency with output frequency for fi = 16.7 Hz. input frequency, the frequencies at which the harmonics occur are direct multiples of the desired output frequency. However, the harmonics do occur at low orders, which require large and expensive filters. When the thyristors are replaced by fully controlled devices such as Gate Turn On thyristors (GTOs), power transistors or IGBTs, the frequency range of the output may increase and an output frequency of three times the input is achievable. Cycloconverters with fully controlled switches are known as Forced Commutated Converters (FCC). FCC’s do not generate large sub harmonics or inter-harmonics due to the more complex switching pattern employed. With fully controlled switches the switching frequency may be larger than the input frequency, thus allowing switching to be controlled to eliminate sub harmonics. The FCC however does still have the disadvantage that large low order harmonics are created, which are still difficult to filter from the voltage waveform [53]. In literature the cycloconverter has often been chosen as one of the main options for the frequency changing component of the LFAC system. A robust time domain simulation method and model for the three phase six pulse cycloconverter was presented in [55].
This model has been used in [56] applied to the
LFAC system for remote wind farms. Chen et al. [12] presented a method
20
to design the system components for a LFAC system interconnecting offshore wind. A forced commutated cycloconverter was used in this LFAC topology. The paper presented a case study, connecting 200 MW of wind to an onshore network. The work produced a detailed overview of the LFAC system with a cycloconverter and demonstrated its feasibility; however the economics and the technical characteristics required when connecting to an onshore grid require further study for this type of configuration. The authors conclude that LFAC with a forced commutated cycloconverter appears to be feasible however there are issues with large filtering and complex cycloconverter control to achieve the desired frequency conversion. The main drawback presented in this analysis are the size of the filtering required at the cycloconverter converting which converts 20 Hz to 60 Hz onshore to suppress the low order harmonics. Matrix converter The issue of substantial low order harmonics can be mitigated by using an adaptation of the forced commutated cycloconverter, called the matrix converter. This is a forced commutated converter which uses bi-directional switches to create a variable output voltage with unrestricted frequency. Figure 2.7 displays the matrix converter, which achieves direct AC to AC conversion like the cycloconverter, and therefore does not have any DC link, or require any bulky energy storage elements [57].
The absence of the energy storage elements
makes the matrix converter technology a compact implementation, reducing the environmental footprint of the converter station. Conversely however the absence of DC link has the impact that any disturbance on the input voltage is transferred to the output voltage. For this reason there are protection issues with matrix converters to protect the switches. Matrix converters have been suggested as a replacement for the BtB converter in the wind turbine nacelle [58, 59], in aircrafts and in advanced motor drives [60]. Advantages of matrix converters for this application include size and weight reduction, potential for increased efficiency due to the absence of the DC link and increased reliability from a modular approach [59]. The main disadvantages 21
Figure 2.7: Matrix converter topology. are the large number of devices required for high power operation, the protection issues, complex control, intrinsic limitation of the output voltage, and as yet the unavailability of a fully controllable bilateral monolithic switch [53, 61]. Another disadvantage is the intrinsic limitation on the output voltage; the maximum output voltage is limited at 86.6% of the input voltage. To achieve 100% output voltage the output current of the matrix converter must be 115% of an equivalent BtB converter [61]. It has been proposed that the voltage issues can be overcome by using a multi-level matrix converter or a Modular Multi-level Matrix converter (MMMxC) [62].
The main difference between the matrix converter and the multi-level
matrix converter is that the bi-directional monolithic switches are replaced by four quadrant DC link H-bridge switching cells [53]. These converters can combine the advantages of matrix converters and multi-level converters, with low energy storage
22
and the possibility for high power density and multi-level output waveforms [63] however a disadvantage of this topology is the large number of devices required. Using a MMMxC for the integration of LFAC offshore wind power was proposed by Muira et al. [64] and an updated control strategy for MMMxC in LFAC systems has recently been presented in [65]. In [64] it is shown that in theory the multilevel matrix converter can act as the onshore frequency changer, with active and reactive power control. However, the experiment took place at 1 kW, and the scalability of the system to offshore wind farm power levels was not considered. The power levels considered in the literature for matrix converters are far from the levels required in wind power systems, with the highest reported experiment taking place at 1 MW [59]. The matrix converter and its associated converters are as yet an immature technology. For industrial applications, despite intensive research, it has achieved a very low market penetration compared to the BtB converter [60]. The BtB converter has the advantage of decoupling the input and output voltage via the DC link, and the ability to provide independent control over both active and reactive power. An interesting new topology of AC-AC converter closely related to the MMxC called the Hexverter has been proposed [66]. The Hexverter displays advantages in frequency conversion when there is a significant difference between the input and output frequency [67], which is interesting for LFAC applications. Figure 2.8 displays the proposed topology of the Hexverter [68]. Six modular multilevel branches consisting of series-connected H-bridge modules and a branch inductor connect one phase of system 1 to one phase of system 2. Since there is no DC-link the energy in the branches must be balanced with branch energy control proposed in [69]. A recent paper has proposed a control scheme for the application of Hexverters in LFAC transmission [70]. The authors confirmed the feasibility of applying the Hexverter to LFAC, however future research must be conducted to address the concerns of fault ride through and stability of the LFAC grid controlled by the Hexverter. The MMMxC and the hexverter are interesting alternatives due to the advantages quoted above; further research should identify their competitiveness and scalability to high voltage and high power applications. 23
Figure 2.8: Hexverter topology. Back to Back Voltage Source Converter VSCs are well suited to high power, high voltage applications [71]. The technology is most commonly used in point to point HVDC transmission systems where the converters are placed at either end of a HVDC cable spanning a long transmission distance. The BtB VSC system shown in Figure 2.9 comprises two converter stations built with VSC technology, using IGBT power switches. A review of VSC based transmission, and the operating principles is presented in [72]. In the LFAC topology the offshore low frequency grid and the onshore grid are connected via the two converters with the DC link between them, meaning that there is no offshore converter station. Advantages of the BtB converter include the ability to store energy in the DC link to control power flow and to provide independent control over active and reactive power consumed or generated by the converter. BtB converters will be located onshore, away from the coast with easy access and not dependent on weather conditions which could improve the reliability of the LFAC system compared to a HVDC system with two VSCs. It should be noted
24
that if only unidirectional power flow is to be considered then the BtB converter can be simplified to use less complex control and less expensive switches [10].
Figure 2.9: Back to Back Voltage Source Converter. Olsen et al. [13] explore the potential to integrate a large offshore wind farm via a LFAC point to point connection using an onshore BtB converter for the frequency conversion. They considered this to be achieving the best of both worlds i.e. using LFAC transmission from the offshore wind farm, thus negating the requirement for an offshore converter station, while still being able to meet the transmission distance requirement. At the onshore side the BtB converter maintains the advantages of the HVDC point to point connection, while housing both converters onshore at the same location. The authors establish through Electromagnetic Transient (EMT) simulation that there is an issue with filtering required on the low frequency side of the BtB converter due to a sharp third harmonic resonance, from the natural cable resonant frequency. Simulations have indicated that moving away from the frequency of 16.7 Hz, to around 15 Hz seems to be more favourable in terms of harmonics and stability on the low frequency side of the BtB converter. Recently Jafar et al. [73] discussed the possible implementation of an offshore grid in the North Sea, integrating offshore wind power plants, using LFAC technology for the interconnection between the Netherlands, Germany and Denmark. There is also no requirement for bulky offshore DC breakers and their associated larger footprint, which incidentally are causing research concerns in the area of HVDC offshore grids; however it has been stated that LFAC switchgear and circuit breakers would be larger than the 50 Hz 25
switchgear, and would take three times longer to clear a fault. The authors also concede that there are no LFAC offshore wind integration projects, perhaps due to hesitance in accepting new LFAC technology. It is claimed that the manufacturers have the capacity to increase the ratings of LFAC equipment, but there is no market to do so as yet [73]. BtB MMC designs for LFAC were considered in Tang et al. [74], it was found that each capacitor module is required to be almost 3 times the size a similar MMC operating with a 50 Hz system explained by the lower reactive power capacity requirement of the LFAC side. This increased size contributes to extra costs and footprint of the onshore station. Larger capacitor modules could also require re-design of the MMC converter system as a whole which would make using an MMC for LFAC less attractive from a manufacturers point of view.
To avoid this extra cost and footprint it is proposed that a
2 level converter is used on the low frequency side of the BtB converter. A MMC converter could be used on the grid side of the BtB converter if desired to connect to the 50 Hz system, allowing the BtB converter the advantages of MMC technology including reduced filtering while reducing costs and complexity on the low frequency side. The VSC on the low frequency side is required to establish and maintain the offshore low frequency voltage. AC cables have a resonant frequency associated with the total capacitance and inductance of the cable. LFAC will involve the connection of long cables to the AC side of the VSC, unlike HVDC where the cable is connected to the DC side. Therefore resonance interactions between the cable and the LFAC filter may be a concern.
2.4.2
Offshore Infrastructure
The use of LFAC has important consequences for the offshore infrastructure in addition to the elimination of the offshore converter station already discussed. Most notably the lower frequency implies an increase in size of the transformers and reactors with knock on implications for size of the offshore platforms.
26
AC Transformer Platform Perhaps the most important advantage of the low frequency system is the size of the offshore platform compared to its HVDC counterpart. In the LFAC system, this platform comprises only the AC transformer, and the relevant AC switchgear. Adapting the frequency of the offshore network has considerable knock on effects for the design of offshore network components, in particular the transformers, reactors and the offshore substation. One disadvantage of LFAC is that the low frequency transformer is larger than at 50 Hz. Dominguez-Garc´ıa et al. [75] present a review on the effect of non-standard operating frequencies on the cost and size of offshore components. The AC switchgear with the LFAC solution would be larger than the 50 Hz switchgear, potentially leading to increased manufacturing and installation costs [73]. A 50 Hz transformer may be used at 16.7 Hz if the V/Hz ratio is kept constant [76], however this would have implications for the power level of the transformer and extra transformers would be required to meet the power level of the offshore wind farm. Therefore to keep the same power level, a new transformer should be designed, increasing the core cross-sectional area (Acore ) in order to compensate for the reduced frequency. Assuming all else remains constant the core cross-sectional area is inversely proportional to the frequency according to Equation 2.5 [75].
Acore =
E 4.44f N Bsat
(2.5)
Where: E is the applied voltage, N is the number of turns, Bsat is the saturation flux density and f is the frequency. Equation 2.5 therefore implies a three times increase in core cross-sectional area for a 3 times decrease in frequency. It is worth noting that this increase in core area may not necessarily result in a 3 times increase in overall transformer volume as the other aspect of the volume (winding volume, tank, etc.) do not necessarily increase by the same factor. Wyllie et al. from the University of Warwick in 2015 presented the design of a 16.7 Hz transformer for LFAC applications [77]. The authors remark that the magnetic flux density is not significantly influenced
27
Figure 2.10: Comparison of a 50 Hz and the Tall design 16.7 Hz 220 MVA transformer at the offshore platform. by frequency and therefore the only methods to maintain the voltage is vary the core area or the number of windings, or indeed change both simultaneously. The analysis focused on two LFAC transformer options adapted from a standard 50 Hz transformer for the same power - Wide (core diameter is increased and the number of windings unchanged) and Tall (the core diameter unchanged and vary the number of turns to maintain the voltage). The findings concluded the Tall design, see Figure 2.10, with an increased overall height (m) of 43.5% compared to the 50 Hz standard; results in a lighter transformer of approximately 39% when compared to the Wide design. The core is considerably denser than the windings hence the benefit in reduced overall weight for the Tall design. This outcome aligns with other recent studies from Erlich [48] and an industry study from Vattenfall [78] who claim the transformer for 16.7 Hz operation should be in the range of 2-2.5 times the gross weight of a 50 Hz transformer for the same power. Submarine cables suffer from significant charging currents for long transmission distances and therefore reactive compensation is required at the onshore PCC. The inductance required, Lcomp , to compensate for this is given by Equation 2.6 [75].
The peak charging current of the cable, Ic(peak) given by Equation
2.7, is proportional to the frequency. The peak energy storage, E, in the shunt
28
compensation can be calculated from 2.7. Inserting Equation 2.6 and 2.7 into Equation 2.8, it can be seen that the energy storage requirement and size for the shunt compensation is frequency independent.
Lcomp =
1 C(2πf l)2
(2.6)
√ Ic(peak) = 2 2πCV f l
(2.7)
1 2 E = LIc(peak) 2
(2.8)
Where: f : frequency (Hz), C: cable capacitance per unit length (F/km), l: length of the cable (m). Wind Turbine LFAC may also require a change in the design of the offshore wind turbine due to the increased size of the transformer and the reactor discussed above. Currently the transformer and the converter are housed in the nacelle of the turbine, however under these circumstances, and as the wind turbines themselves get larger, the transformer will get increasingly larger and heavier. It may be more appropriate to house the transformer in the base of the wind turbine, due to space and weight saving requirements in the nacelle of future large offshore wind turbines [79]. The use of LFAC also has implications for the choice of generator used. There are a number of options mentioned in the literature, namely fixed speed, DFIG and PMSG wind generators. A review of different types of wind turbine concepts can be found in [80]. The wind farm modelled in [49] used fixed speed wind turbines directly connected to the grid where the gearbox ratio was lowered to produce the 16.7 Hz output. Simulations showed that the dynamic behaviour of the fixed speed wind turbine was unstable during start-up. The authors concluded that a re-design of the wind turbine generator was required to safely produce 16.7 Hz at turbine output, requiring a larger inertia. This means an increase in the
29
size of the fixed speed machine. If this is combined with the required increase in size of the wind turbine transformer, the space requirement in the wind turbine is dramatically increased. Nguyen et al., [81] explore a DFIG based LFAC transmission system and compared it to a conventional 50 Hz AC system. The authors consider the grid code compliance of the offshore wind farm at the onshore point of connection, in particular the ability to meet the reactive power requirements of the grid code. It was shown in the analysis that for steady state, under variable wind speeds and during a fault, the DFIG has the ability to maintain the standards set by a 50 Hz DFIG, when operated at 50/3 Hz. However, there is a caveat to using the DFIG based wind turbine, similar to using a fixed speed wind turbine, the size and weight of the generator would be considerably larger for lower frequency applications [10]. Future wind turbine systems should seek to minimise size and weight of the generator. It is anticipated that PMSG systems with full conversion will have less weight and less maintenance than DFIGs or fixed speed turbines [82]. It is for these reasons that PMSG wind turbines are suggested as the best option to produce wind power at 16.7 Hz, as they require only a reconfiguring of the full converter and no extra space requirement for the generator and converter compared to standard wind turbines [10, 13, 73, 83]. The only extra space requirement is the wind turbine transformer which scales by the same factor as the AC platform transformer discussed previously. Collection Network Two main collection network options for use with the LFAC transmission have been investigated in the literature. These are the use of an LFAC network, at the same frequency as the LFAC transmission [10, 13, 73], or the use of a DC collection network, and an offshore inverter to produce LFAC [12, 55, 56]. The main motivation behind the use of DC collection networks was to avoid a redesign of the wind turbine to produce low frequency. However this requires an inverter station offshore to produce the low frequency voltage waveform. The 30
offshore inverter may reduce the attractiveness of this type of LFAC transmission system as there is still an offshore conversion stage contributing to the overall cost, reliability and efficiency of the transmission system. The offshore inverter also contributes harmonics to the LFAC transmission system which need to be filtered out before the onshore converter [12]. Zhao et al. 2012 [84] evaluated the reliability and capital costs of different transmission options. They compare power transfer between nominal frequency transmission and LFAC transmission systems connected to different types of DC collection networks. When LFAC transmission is used with a DC collection grid, it is found that in terms of both reliability and costs, the LFAC transmission performs comparably with the HVDC and the conventional AC solutions. It can be concluded that the main driver behind any difference in reliability is the different type of collection network compared (i.e. DC parallel, DC series or AC) and whether an offshore inverter is required. LFAC transmission was not considered with a LFAC collection network in this analysis. Analysis in [85] has found that the issue of reliability is changed somewhat when considering a LFAC offshore collection network, as there is no offshore converter, the overall interruption time is reduced, resulting in a more reliable supply of power from the offshore wind farm. This suggests that a LFAC collection network, despite the knock on implications of size and cost for frequency dependent components should be the preferred design choice for offshore wind farms connected to LFAC transmission.
2.4.3
Grid Connection
An important consideration in the selection of an offshore transmission system is the ability to meet the grid code standards set out by the transmission system operator of the onshore grid. ENSTO-E have produced a draft network code for HVDC connections and DC connected power park modules [86] which outlines the grid code requirements for the interconnection of offshore wind farms to the onshore network. These include active and reactive power control, frequency control, power quality and fault ride through capability [24, 87]. It would be reasonable to expect that LFAC interconnected offshore wind farms must also meet 31
these general grid codes, to the specific requirements of the connected systems Transmission System Operator. There has been extensive work outlining the ability of VSC-HVDC to comply with the grid codes, in particular, frequency response [88, 89, 90, 91, 92, 93] and providing fault ride through capability through decoupling the offshore wind farm and the onshore grid [94, 95, 96, 97]. Therefore it is reasonable to expect that LFAC connected via a BtB VSC converter will also comply with grid code standards as the BtB converter is essentially the same as the HVDC link, without the long DC cable and the offshore converter. Alternatively grid code compliance of the cycloconverter connected LFAC poses a concern which must be considered. Unlike the VSC, the cycloconverter is a passive thyristor based device and does not have independent control over active and reactive power. As the cycloconverter switches at a low frequency, power quality is quite poor and therefore large expensive filters are required to meet power quality standards. It has been shown that cycloconverters generate large low order harmonics by experimental analysis in [43, 49, 98], where in each case the total harmonic distortion was over 20%. Cho et al. [98] perform a deeper analysis of the cycloconverter with more advanced time domain simulations to include harmonic analysis of the voltage waveforms. The harmonic analysis shows large, low order harmonics on the cycloconverter output which would require large filters to eliminate. These filters incur extra costs and land use making the use of a cycloconverter less attractive when power quality issues are considered. The cycloconverter is a direct AC-AC conversion and there is no decoupling of the input and output, leading to protection concerns. Fault ride through of the cycloconverter is also an issue which requires further study. Cycloconverter control has the ability to provide active power control, and control strategies may be developed to provide frequency response based on the system frequency. The onshore converter of an offshore wind farm is required to have control over reactive power for voltage control of the onshore grid at the PCC. An experiment conducted by [43] found that the cycloconverter has a power factor of 0.78 lagging, thereby consuming reactive power. This means that the auxiliary equipment (filters and compensation) must provide this static reactive 32
power for the cycloconverter, and the dynamic reactive power control required to support the grid voltage. The reactive power consumption in the cycloconverter thus requires extra reactive compensation in the form of switched capacitors, SVC or STATCOM. The impact of these extra requirements to meet the grid code standards has a direct impact on the capital investment costs required to make the systems grid code compliant. In Chen et al. [12] for example, the authors simulated a 200 MW transmission system with LFAC connected via a cycloconverter. The cycloconverter receiving power from the offshore wind farm required filters rated at 200 MVAr to supply reactive power to the cycloconverter. With conventional matrix converters there is a greater degree of control over reactive power, however there is some limitation. The reactive power compensation capability is restricted by the topology; the formation of reactive power when active power is zero is not possible. The BtB converter in comparison, due to its inherent energy storage does not have such a restriction, and can provide reactive power at zero output current i.e. when the active power is zero [60]. This is a key advantage when considering the interconnection to a weak network, where control over reactive power and voltage are paramount to stabilising the network. Table 2.1 compares the three converter options, and summarises the main comparison points. Reviewing table 2.1 it is clear that the BtB VSC should be selected as the onshore frequency converter for future LFAC transmission systems.
2.5
Multi terminal Offshore Grid
In the last decade there has been a lot of discussion particularly in Europe about multi terminal offshore grids. In particular the North Sea offshore grid, with its large offshore wind resources, is the most likely candidate for an offshore multi terminal grid [99]. These offshore grids will integrate far offshore wind farms and connect European countries to each other to create power exchange networks. The most common suggested method for achieving multi terminal offshore grids is using VSC-HVDC, where a number of different offshore converters are connected to
33
Table 2.1: Comparison of frequency converter options Cycloconverter
Matrix Converter
Back VSC
Semiconductor
Thyristor
IGBT
Conversion type Power Control
AC-AC P only
Bilateral monolithic switch AC-AC Q control depends on P>0 Small
AC filters
Large (3rd-13th harmonic) Black Start Capability No No Weak System Perfor- Requires strong Good (no commance grid (commuta- mutation) tion failures) Fault ride through ca- Not decoupled Not decoupled pability Power Factor 0.78 lagging Controllable Frequency response Only from Wind Only from Wind farm farm Voltage Control
to
Back
AC-DC-AC Independent P & Q Small (31st35th) Yes Good (no commutation) Decoupled
Controllable From both Wind farm and DC capacitor Needs external OK (limited out- Independent Q equipment e.g. put 0.866 of control SVC input)
each other to form a meshed grid [100, 101]. A major concern with multi terminal HVDC is the clearance of DC faults on this network, if DC circuit breakers are not employed then the entire offshore grid voltage would have to be brought to zero to clear the DC fault [102]. The response of several multi terminal DC networks to DC faults and the impact of the DC circuit breaker have been analysed in [103], and they conclude that successful fault isolation is possible but requires breakers with a fast interruption time and a large reactor. However DC breakers are as yet are an immature technology [36]. The VSC-HVDC multi terminal offshore network requires a large amount of power electronic converters offshore, and therefore there are issues around the reliability of the offshore network, the cost of building and maintaining offshore VSC converters and achieving cost effective DC fault clearing. LFAC could be used as a part of a multi terminal offshore grid [12], utilising the increased AC transmission range to connect offshore wind farms to compliment 34
a larger HVDC multi terminal network. Meshed AC interconnection of offshore LFAC links could easily be performed using existing AC breakers at low frequency and existing expertise in onshore AC networks [10]. Low frequency circuit breakers would have to be designed for the LFAC transmission system, however this is not considered a challenging design issue [10, 73]. It has been suggested that 50 Hz circuit breakers could even be used at lower frequency with the appropriate derating factors [73]. The integration of the LFAC grid to the offshore multi terminal grid could reduce the complexity of such a grid and allow connections up to 200 km using AC transmission rather than DC, negating the requirement for AC-DC conversion. A separate feasibility study would need to be performed to determine the value of this to the offshore grid.
2.6
Cost of Offshore Transmission System
An important comparison metric between potential transmission systems is the overall capital investment costs required, and the impact of operating and maintenance costs. There has been a small amount of work done on evaluating the potential economic benefit of LFAC transmission, and can be used to draw some important conclusions. An economic comparison between transmitting 10 GW of wind power via 50 Hz AC and 16.67 Hz AC from a DFIG wind farm is performed in [44]. The comparison shows that the annual cost of the LFAC system is 17% less than the 50 Hz system. This is due to a number of factors; since the transmission distance is the same in both cases, the lower frequency cable can carry more power, therefore fewer cables are required (two cables compared to five at 50 Hz). The reduced number of cables also means a reduced number of breakers. This significantly contributes to the reduction in cost at lower frequency. Offsetting these are the substation at the receiving end of the line is more expensive because of the cycloconverter converting from low frequency to 50 Hz, and the increased costs of the transformers at lower frequency. Olsen et al. [13] present a specific comparison between AC transmission at 50 Hz, LFAC transmission and HVDC transmission, for a 1200 MW offshore wind
35
farm at varying transmission distances. The analysis found that for distances lower than 125 km, the AC transmission at 50 Hz is the least expensive. This is due to the fact that no converters are required. From 125 km to 200 km it is shown that LFAC is approximately 16% less expensive than VSC-HVDC. This is again primarily due to the absence of the offshore converter. It is also worth noting that the onshore BtB converter in the LFAC topology costs less than two onshore VSC stations. This agrees with the results presented in Hytten et al. [104]. Hytten uses a comprehensive levelised cost of energy calculation tool to obtain the result that LFAC is less expensive than HVDC and HVAC at 50 Hz in the distance range of 140 - 210 km for an offshore wind farm. 60 HVAC
50 40 Frequency 30 (Hz) 20
LFAC
10 HVDC
0 0
50
100 150 Distance to shore (km)
200
250
Figure 2.11: State of the art of viable distances for HVAC, LFAC and HVDC transmission. The potential differences in wind turbine costs at lower frequency have been considered in [85] where a case study compares HVDC transmission with LFAC connected with both a cycloconverter and a BtB converter for a 200 MW offshore wind farm, 100 km from the shore. A techno economic study shows that LFAC with a cycloconverter is the least expensive option for connecting offshore wind; however the cost of correcting grid compliance issues (power quality, provision of reactive power) is not included. It was found that LFAC with a BtB converter is 4.6% more expensive than with the cycloconverter, but it is envisaged that the BtB converter will solve the grid connection issues. Overall it was found that VSC-HVDC was 6% more expensive than LFAC (BtB). This is due again to the removal of the offshore converter however this cost reduction is offset by increased 36
cost of AC cables, more expensive substation and wind turbine transformers, and the cost of the onshore BtB station. It can be concluded that in general, for a medium distance offshore wind farm (50 - 200 km) LFAC transmission can be economically competitive to HVDC. Figure 2.11 displays the state of the art of viable distances for LFAC, HVAC and HVDC transmission according to recent literature.
2.7
Stability in LFAC Grids
The stability of the LFAC transmission system is another critical point to analyse when considering the feasibility of LFAC as an option for the interconnection of offshore wind. There has been little work done in the literature on the various areas of stability. The voltage stability of LFAC transmission lines connected to a cycloconverter was presented in [105] using eigenvalue analysis on a 6 bus LFAC system. Voltage stability is checked at a number of frequencies. It is found that with lower frequency voltage stability is improved due to the reduced reactance and therefore the reduced voltage drop with increased power transfer. Frequency stability of a LFAC system is examined in [106] where the response of a LFAC connected hydro generator is examined during frequency events in the grid. In this specific example control is developed to improve the frequency stability and response of the LFAC transmission lines. In the context of offshore wind the small signal stability of FFTS connected offshore wind is assessed in [107]. Small signal models of DFIG wind turbines, a 100 km transmission cable and a cycloconverter are developed to determine the stability. It has been found that the LFAC grid has lower damping than the equivalent 50 Hz system, making the system less stable. It is proposed to solve the damping issue with additional control on the cycloconverter. The issue of damping is also present in [108] where it was found that for a 200 km transmission cable and BtB converter system the resonant frequency was close to 50 Hz. Large damping filters were used to maintain transmission system stability. These filters are both large and expensive and can have significant losses (1-2%) and consume a
37
large portion of reactive power (50-70% of power). The authors in [108] performed 3 phase simulations and made observations about the stability of the system. It was observed that control interactions may be present in the LFAC system, and that cable resonances may interact with transformers and filters to cause harmonic resonance instability. The paper concludes by proposing a significant amount of future work including reducing the size of damping filters and developing control systems and planning tools to assess and improve system stability.
2.8
Conclusions
This chapter has presented a review of LFAC as a transmission option for offshore wind. LFAC is a practically feasible alternative transmission option and has the potential to decrease the cost of transmitting power from offshore wind. A novel transmission technology which can reduce the cost of offshore wind merits detailed study. The trend in recent years has been towards more expensive and larger wind turbines, which are further offshore and in deeper water, requiring more expensive transmission systems. This characteristic is to be expected as the industry is still in its infancy compared to onshore wind; however it is imperative that the overall cost begins to reduce for further expansion of the industry. In the interests of reducing the cost of energy produced from offshore wind alternative AC transmission options LFAC transmission has been found to be a competitive option for the interconnection of offshore wind farms in the region of 50km-200 km offshore compared to VSC-HVDC. The economic assessments reviewed here are first order approximations, and site specific. However they are indicative of a continuing trend in the analysis that LFAC is competitive at medium distances to shore compared to HVDC. The offshore LFAC grid consists of components has the potential for commercial availability in the near term. Stage-wise installation of the offshore wind farm may become easier with LFAC transmission as a large offshore HVDC converter station is not required to begin exporting power, which could contribute to a reduction in up front capital costs of the offshore wind farm.
38
The frequency conversion stage is performed onshore via either a cycloconverter or a BtB converter. It has been suggested that the conversion could be performed using a matrix converter or MMMxC, however at the power levels required the technology does not exist as yet. The frequency converter is located onshore away from the harsh offshore conditions, improving access for maintenance and thereby reducing downtime. The selection of the onshore frequency converter is a component which has sparked debate, some authors opt for the less expensive thyristor based cycloconverter and others consider the IGBT based BtB converter as the best solution due to the increase in control and power quality produced during the conversion. The cycloconverter is less expensive option alone; however large filters are required to suppress low order harmonics from the cycloconverter and to provide reactive power compensation. Alternatively, the BtB VSC will alleviate the technical concerns when connecting to a mainland grid, with dynamic control over both active and reactive power, and a more sophisticated switching pattern reducing the need for low order harmonic filters. Future work in the area should consider an assessment of LFAC in a meshed offshore network, as there is a significant advantage in reducing the number of converter stations and DC breakers offshore. Additionally, new converter topologies such as the modular multi-level matrix converter may also reduce the footprint of the LFAC system, while achieving similar controlability to the BtB converter.
2.9
Outcomes of State of the Art
Current state of the art literature has been discussed in some detail. The following points detail specific outcomes from the review of the state of the art. • Previous work has examined the feasibility of LFAC in isolation, or compared to HVAC transmission at 50/60 Hz. There is a need for a techno-economic comparison between HVDC, LFAC and 50 Hz AC to determine the crossover distances where each technology becomes more competitive than the other including the use of operation and maintenance costs across the lifetime of an offshore wind farm. 39
• The choice of operating frequency is a factor which deserves further investigation. It has been seen in [105] that reduced frequency as low as 5 Hz improves the voltage profile of LFAC. An examination of the feasible range of operating frequencies is required considering the techno-eonomics. • A number of publications have begun to scratch the surface regarding detailed transient simulations of low frequency AC however no detailed operation and design have been presented using a BtB onshore frequency converter. A number of the transient simulations which have been performed simulate a generator connected to a LFAC transmission line. The LFAC offshore grid is a fully power electronically formed AC grid with no inertia coming from rotating machines. This thesis will improve the knowledge base of LFAC in terms of transient simulation and provide a basis for design of the offshore transmission system. • Connecting long LFAC cables to a converter based system is an issue which appears in the literature. Some publications have performed studies using large AC filters to guarantee stability which generate significant losses. There is a need for a control based solution to the problem of connecting long HVAC cables to the BtB VSC. • The stability of the system is an important aspect to consider. It can be seen from the state of the art that there have been only a few small studies on the stability of LFAC systems. Accounting for the fact that LFAC for the connection of offshore wind requires the use of a long HVAC cable, there is an obvious need for a harmonic stability assessment of LFAC considering interactions between cables and other components and control in the LFAC system. Another important harmonic interacton to consider in a power electronic AC grid is the interaction between multiple layers of controls, and controls of multiple converters potentially causing instability. • There have been a number of small demonstration experiments using LFAC transmission, all of which have used cycloconverter technology. The
40
literature suggests that the most appropriate onshore frequency converter is the BtB VSC. This thesis will build, test and validate the control and design of a LFAC transmission system for offshore wind in hardware, utilising a BtB converter. This thesis addresses these points in the following pages. The next section looks at a techno economic analysis of the LFAC transmission system for offshore wind.
41
CHAPTER
THREE LFAC TECHNO-ECONOMIC ANALYSIS
3.1
Introduction
After reviewing the literature it can be seen that a number of publications have analysed the feasibility of low frequency AC transmission. These publications have primarily chosen one transmission option to analyse. Previous works have studied individually VSC-HVDC [109, 17, 72] and LFAC [12, 56, 42, 10] to understand their technical feasibility. However, there is an absence of a thorough technical and economic analysis of LFAC as a transmission option in the context of the comparison to HVDC, which has become the industry standard for the connection of far offshore wind. This chapter firstly outlines the structure of the proposed offshore transmission options. The LFAC system is then approached in more detail, in particular the impact of lower frequencies on the size of components, and the choices available for the onshore frequency converter. The methodology for power loss and cost calculations is then presented.
A case study in the
Irish Sea is used to assess the transmission configurations in terms of a technoeconomic analysis, to compare the potential technical and economic advantages of Low Frequency AC transmission for offshore wind farms to a VSC-HVDC based solution for a 150 km transmission distance. The Levelised Cost of Energy (LCOE) is used as a metric to determine the cost effectiveness of transmission options over a range of transmission distances, accounting for capital costs, operation and 42
maintenance costs and losses. The chapter then proceeds to explore the extended range of transmission capability for non-conventional AC frequency approaches and determines an optimum frequency for transmission from offshore wind, which is dependent on transmission distance. The question is posed whether 16.7 Hz is necessarily the best frequency. Finally, some techno-economic conclusions are drawn comparing LFAC and VSC HVDC transmission for offshore wind.
3.2
Offshore Transmission System Design
This section will initially assess three configurations, which are displayed in Figure 3.1. A VSC-HVDC transmission with a 50 Hz collection grid, an LFAC transmission with an LFAC collection grid, both at a frequency of 16.7 Hz connected to shore via a cycloconverter. Thirdly, the same LFAC transmission system connected to shore via a BtB VSC. HVAC transmission is not considered here because the distance from the offshore wind farms to shore is assumed to be greater than the maximum distance for 50 Hz AC cables due to the reactive power requirement of AC cables limiting active power transmission. It is assumed here that the LFAC collection grid utilises the same 33 kV AC cables operated at a frequency of 16.7 Hz, the same generator and back to back converters in the wind turbine, as in the 50 Hz collection grid. Full converter wind turbines are used for this analysis and it is assumed that the full converter has the capability to produce AC at a frequency of 16.7 Hz for the LFAC grid [10] . The components required for the lower frequency system are similar to the 50 Hz system, however, the size and cost of the transformers and filtering will increase with reduced frequency [75]. Crucially there is no offshore converter in the LFAC configuration, which reduces capital cost and decreases the amount of power electronics offshore, thereby potentially increasing reliability. Onshore, the frequency changing converter converts from 16.7 Hz to the grid frequency. The cycloconverter option uses thyristor based technology compared to the BtB VSC which uses Insulated Gate Bi-polar Transistors. Cycloconverter connected LFAC configurations therefore like LCC’s require a strong AC grid onshore to
43
enable reliable operation of the thyristors [110]. A number of technical concerns exist with LFAC for offshore wind, principally any inductive equipment will be larger than the 50 Hz equivalent, this includes current transformers and converter reactors, most importantly the increased size of the transformers and switchgear offshore [10]. These may be overcome by redesign of the wind turbine nacelle and the offshore AC substation.
KĨĨƐŚŽƌĞ
ϱϬ,nj ŽůůĞĐƚŝŽŶ'ƌŝĚ
ϱϬ,nj s^ ,sdƌĂŶƐŵŝƐƐŝŽŶ dƌĂĨŽ
KŶƐŚŽƌĞ
s^
'ƌŝĚ ϱϬ,nj dƌĂĨŽ
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>&dƌĂŶƐŵŝƐƐŝŽŶ ϭϲ͘ϳ,nj
LJĐůŽͲ ĐŽŶǀĞƌƚĞƌ
'ƌŝĚ ϱϬ,nj dƌĂĨŽ
ϭϲ͘ϳ,nj ϭϲ͘ϳ,njdƌĂĨŽ ŽůůĞĐƚŝŽŶ'ƌŝĚ
>&dƌĂŶƐŵŝƐƐŝŽŶ ϭϲ͘ϳ,nj
'ƌŝĚ
ϱϬ,nj ĂĐŬƚŽĂĐŬ dƌĂĨŽ s^
Figure 3.1: VSC-HVDC and LFAC offshore wind transmission options.
3.3
Onshore Frequency Converter Selection
One of the important technical concerns is the onshore frequency changing converter. Previous research [56, 12, 11, 111] has focused on using a thyristor based cycloconverter to perform the onshore conversion, due to the fact that the thyristor based cycloconverter may be less expensive than an IGBT based solution. These studies have not adequately discussed issues such as power quality, harmonic filtering and the ability to provide reactive power support to the offshore or onshore grids. 44
Direct AC-AC conversion with a cycloconverter is difficult to achieve from low frequency to a higher frequency, without leading to high levels of low order harmonics which require large filters [53]. Appendix A provides an example of the large low order harmonics present in the cycloconverter [112]. The cycloconverter also suffers from a poor power factor and requires large reactive compensation. In addition to this the commutation of thyristors is vulnerable to disturbances in the onshore grid. It has been suggested that the most appropriate frequency converter is a back to back (BtB) VSC based converter [10, 13, 74] due to the independent controllability of active and reactive power and the ability to establish and control offshore grid frequency. Modular Multi-level Converter (MMC) designs for LFAC were considered in Tang et al. [74], it was found that each capacitor module is required to be 3 times the size a similar MMC operating with a 50 Hz system, contributing to extra costs and footprint of the onshore station. To avoid this extra cost and footprint it is proposed that a 2 level converter is used on the low frequency side of the BtB converter. A MMC converter could be used on the grid side of the BtB converter if desired to connect to the 50 Hz system, allowing the BtB converter the advantages of MMC technology while reducing costs and complexity on the low frequency side. The LFAC offshore grid is a fully power electronic defined grid with no synchronous generator present to establish and maintain the grid voltage and frequency. Therefore, either the wind turbine converters or the onshore power frequency converter must control the voltage. Since the cycloconverter is a thyristor controlled device it cannot control the voltage at the AC terminals. In this case the full converters in the offshore wind turbines would be required to control the grid voltage. This may add additional costs to the wind turbine. In the case where a BtB converter is used onshore, VSC technology has the ability to control the grid voltage. In the following sections both cycloconverter LFAC and BtB converter connected LFAC are considered to determine if economic savings from cycloconverter based LFAC can overcome the technical disadvantages compared to the BtB converter.
45
3.4
Losses Modelling
This section outlines the models required to compute the losses associated with each transmission option. Loss models for each component in Table 3.1 have been developed. Table 3.1: System components of LFAC and VSC - HVDC LFAC
VSC-HVDC
16.7 Hz Wind Turbine Transformers 50 Hz Wind Turbine Transformers 16.7 Hz Collection Network 50 Hz Collection Network 16.7 Hz Transformer 50 Hz Transformer Offshore Converter (VSC) 16.7 Hz Transmission Cable HVDC Transmission Cable Onshore Cycloconverter/ BtB converter Onshore Converter (VSC)
3.4.1
Cable loss
The collection and transmission cables are a key component of the wind farm architecture. The generator to collector transformer cable is rated for 33 kV and the connecting cable to converter rated in this case for 220 kV. The 33 kV cable is tapered with 3 different cross-sectional areas to transmit the power to the offshore substation. The electrical behaviour of the cables is modelled using the standard π equivalent circuit. The charging current of the cable, Ic reduces with decreasing frequency and is expressed using equation 3.1.
Ic = 2πf ClV
(3.1)
Where: f : frequency (Hz), C: capacitance (F), l: length of the cable (m), V : voltage (V) The ohmic losses PΩ per meter are expressed using equation 3.2 PΩ = I 2 RAC Where: I: current per phase (A), RAC : AC resistance (Ω/m)
46
(3.2)
The AC resistance of a cable is composed of the DC resistance and the resistance caused by both the skin and proximity effect respectively. The skin effect is the tendency of AC current to become distributed with the highest current density near the surface of a conductor. At low frequency the skin depth increases and thus increasing the effective cross-section of the conductor. The skin effect multiplication factor for three-core cables can be directly referenced from the IEC60287 standard and is calculated by equations 3.3 and 3.4 [113].
ys =
x4s 192 + 0.8x4s
(3.3)
Where: x2s = ks
8πf × 10−7 RDC
(3.4)
Where: ks = 1 for round conductors, ys : skin effect multiplication factor, RDC : DC resistance. The proximity effect constrains the distribution of currents in conductors in close proximity so that the effective conductor resistance increases. This is due to induced eddy currents in each of the conductors which are proportional to the current. The proximity factor for 3 core cables is expressed by equations 3.5 and 3.6.
yp =
d 2 h d 2 x4p c c 0.312 + 192 + 0.8x4p s s
1.18 x4p 192+0.8x4p
i
(3.5)
+ 0.27
Where: x2p = kp
8πf × 10−7 RDC
(3.6)
Where: yp : proximity effect multiplication factor, kp ≈ 1 for round conductors, dc : diameter of the conductor (mm), s: distance between the conductor axes (mm). The total AC resistance losses can be calculated by equation 3.7.
RAC = RDC 1 + (ys + yp )
47
(3.7)
The dielectric losses for the cable are associated with the dielectric insulation material. The dielectric loss, Wd , for a single phase of a cable under AC operation is expressed by equation 3.8.
Wd = 2πf CV 2 tan δ
(3.8)
Where tan δ: insulation loss factor (0.0004 - XLPE).
3.4.2
Transformer Loss
Both the wind turbine transformer (0.69/33 kV) and the transformer at the offshore platform (33/220 kV) are included to determine the individual contribution of winding and core losses. In the 16.7 Hz case it is assumed that the LFAC transformer is designed, such that the winding losses are the same as in the 50 Hz transformer. The core losses reduce from those in the 50 Hz transformer; this can be observed from the Steinmetz equation (equation 3.9) commonly used to estimate transformer core loss. β Pcoreloss = vt kf α Bpk
(3.9)
Where vt : transformer volume, k: constant, f : frequency, Bpk : peak flux density, α and β: material constants. From literature core loss is quoted as approximately 1/6 of overall transformer loss at 50 Hz [114] with the remaining contribution lost in the windings. Power transformers aim for efficiency in excess of 98.5% for both wind turbine and transmission transformer applications. The transformer design here maintains the same efficiency as a 50 Hz transformer. The standard 50 Hz layout is modified to achieve this design objective. To adapt the transformer for a different frequency requires an increase/decrease in the either the core area or the number of turns, which is evident from reviewing the induced voltage in transformer equation 3.10.
E = 4.44f BN Ac
48
(3.10)
Where, f : frequency, B: magnetic flux density, N : number of turns, Ac : crosssectional area of the core
3.4.3
Cycloconverter Loss
From previous literature comparing cycloconverters and VSCs for mining applications [52] the full load losses of a 32 MW rated cycloconverter are 0.7%. The cycloconverter is a thyristor based device consisting of three 12 pulse thyristor bridges as shown in Figure 2.5. This is similar to a Line Commutated Converter (LCC) which also operates with thyristors and a similar switching pattern. Therefore to determine the cycloconverter losses at fractional loading a comparable LCC efficiency curve is used and adapted to cycloconverter losses at full load [115]. The efficiency vs. load curve shown in Figure 3.2 is used to determine the cycloconverter losses at fractional loading. The cycloconverter efficiency curve starts from 99.3 % at full load and follows the same trend as the LCC curve. The high efficiency of cycloconverters is the reason that many publications have considered it as an option for connecting LFAC transmission to the grid. Similarly in HVDC applications the high efficiency and higher power capability of LCC based HVDC makes LCC a more attractive option than VSC for applications
Efficiency %
where high power bulk transmission is required. 99.5 99.0 98.5 98.0 97.5 97.0 96.5 96.0 95.5 0
20
LCI efficency
40 60 % rated load
80
100
Cycloconverter efficiency
Figure 3.2: Cycloconverter efficiency and Line Commutated Inverter efficiency.
49
3.4.4
Voltage Source Converter Loss
The evaluation of the efficiency of the VSC-HVDC transmission and wind turbine converters is introduced for a 2 level neutral point clamped design.
MMCs
(Modular Multilevel Converters) are increasingly seen as the highest efficiency solution for VSC transmission applications.
However, switching frequencies
substantially lower than 50 Hz, will require MMCs with much larger capacitors and therefore make each module more expensive. In addition 2 level technology can achieve efficiencies close to MMC of approximately 98.3% at 50 Hz [71]. Equations for power loss are derived for the power switches in the converter, based on the average and root mean square of the converter current to estimate the conversion loss in the converter. The specific IGBT and free-wheeling diode device characteristics are obtained from manufactures datasheets for both converters [116]. The conversion losses for VSCs are divided into conduction and switching loss. Conduction losses occur due to device on-state voltage drop across the device by averaging losses in each switch. The switching energy loss is a combination of on-state and turn-off switching loss and depends on the device characteristics, current and switching frequency [117]. Equation 3.11 and 3.12 calculate the switching losses and the conduction losses respectively with Equation 3.13 calculating the total VSC losses.
Psw loss = Kon Ipk (ωsw ) + Kof f Ipk (ωsw ) + Krr Ipk (ωsw )
(3.11)
1 1 m × pf m × pf 2 + + Rc Ipk + + 2π 8 8 3π 1 1 m × pf m × pf 2 UD0 Ipk − + Rd Ipk − 2π 8 8 3π
(3.12)
Pcond loss = Uce0 Ipk
VSCloss = (Pcond loss + Psw loss ) × noswitches
(3.13)
Kon and Kof f are calculated from the slope of the switching energy per pulse vs. collector current curve. Krr is calculated from the slope of a curve of reverse
50
Table 3.2: IGBT switch data Collector-emitter voltage Diode on state resistance Collector-emitter on state resistance Diode on state zero current voltage On state switching energy constant Off state switching energy constant Reverse recovery switching energy constant Power factor Switching frequency Switching frequency Number of switches modulation index
Uce0 Rd Rc UD0 Kon Kof f Krr pf fswitch ωsw noswitches m
1.1 0.0005 0.00182 0.9 0.00047 0.000388 0.00034 0.85 1350 214.86 134 0.856
recovery energy required and forward current. These graphs can be found in the IGBT datasheet [116] and are shown in Appendix C.
3.4.5
Component Reliability
Reliability is an important aspect to consider when comparing technologies to transmit power onshore. Offshore locations can present difficulties for reliable operation. The repair time for offshore components can often be very high due to the difficulties in accessing offshore infrastructure [118]. The reliability analysis in this paper uses the failure rate (λ) and the Mean Time to Repair (MTTR) of the components to calculate the annual unavailability of the offshore wind farm (U) and calculate the Expected Energy Not Supplied (EENS). Table 3.3 outlines the failure rates and MTTR of each of the components considered in the analysis which has been taken from various literature sources [118, 119, 5]. Cycloconverter failure rates were difficult to obtain, the failure rate used here is based on that of a thyristor based line-commutated converter [5]. On the assumption that the different transmission options have no impact on actual wind farm reliability, the wind farm availability is assumed here to be 100% to facilitate a comparison based only on the transmission systems. It is also assumed that for redundancy purposes there is a back-up transformer at each offshore substation.
51
Table 3.3: Components
3.5
Failure rates and MTTR of Offshore Transmission System
Component
λ (failures/yr.)
MTTR (hrs)
Collection network Circuit Breakers Offshore Transformer Transmission Cable VSC Onshore VSC Offshore Cycloconverter Onshore Transformer
0.008 0.032 0.03 0.08 0.05 0.05 0.031 0.02
2160 720 4320 720 50 720 50 1440
Capital Investment Costs
The installation of offshore infrastructure involves a substantial investment and an economic analysis is essential when comparing both transmission technologies. In this thesis published data for capital and operating costs are used - except for the offshore VSC/platform converter and offshore cable related costs which are best estimates from research and industry data. It is important to note that most capital costs are complex to predict with any degree of exact certainty as they are both location and vendor specific.
The costs provided in this
thesis should therefore be taken as best estimates as quoted in literature where available. Capital investment costs are calculated for each component of the LFAC transmission system and the HVDC transmission systems respectively.
3.5.1
Cable Costs
The submarine collection and transmission cables represent a significant portion of the overall costs for the offshore architecture. Cable costs are sourced from relevant literature and from a recent 2014 industry supported research thesis with multiple cost references from numerous commercial and academic sources. The cost figures (e/km) are taken as e1.591 Million/km [75] for AC cables and e1.567 Million/km for DC cables [120].
52
3.5.2
Transformer Costs
Varying the frequency of the transformer changes the volume of bulk magnetic material and copper required and hence directly impacts on price. The cost of the transformer at rated 50 Hz can be calculated from Dicorato et al. [121], using equations 3.14 and 3.15 for LV/MV and MV/HV transformers respectively:
LV/MV Trafo Cost 50 Hz = −153 + 131 Rated Power0.447
MV/HV Trafo Cost 50 Hz = 42.7 Rated Power0.751
(3.14)
(3.15)
Taking 50 Hz as the nominal frequency a cost scaling expression is derived to calculate the cost of the transformer at variable frequency (VF) in equation 3.16: p 0.325fr + 0.22fr + 0.164 3 fr2 Trafo Cost VF = 0.325 + 0.22 + 0.164
(3.16)
Where: fr : is the normalised frequency and is calculated as the ratio between 50Hz 50 Hz and the desired frequency (fr = ). f
3.5.3
Reactive Power Compensation
Since the cable is operated at 16.7 Hz the reactive power requirement is lower than the equivalent 50 Hz cable, however it still exists. The offshore wind farm collection network in the HVDC case also requires reactive power support, as those cables are at 50 Hz. The cost of the shunt reactive compensation for the LFAC cable is quoted as 2/3 the costs of the transformer with equal rating [30]. The cost of the shunt reactance is expressed using equation 3.17:
Number of cables at VF Shunt Reactor Cost VF = 50 Hz cost Number of cables at 50 Hz
53
(3.17)
3.5.4
HVAC Platform Costs
The offshore AC platform is closely tied to the dimensions and size of the offshore transformer mentioned previously, which in turn has a significant impact on its cost. The offshore platform cost is quoted from Ergun et al. [120] and is given by Equation 3.18, in (e/MVA).
Offshore Platform = 120 × 103
Trafo Rated Power −0.413 300
(3.18)
The size and hence the cost of these offshore platforms is highly dependent on the selected frequency for the wind farm. The complex nature of offshore construction and the potentially large size of these platforms is a major challenge to practical implementation. Added costs are included for additional auxiliary equipment.
3.6
Transmission Topology Comparison
The three topologies depicted in Figure 3.1 are compared in terms of energy losses and capital investment costs in this section. An energy capture analysis is performed on a site in the Irish Sea which is approximately 150 km from the Point of Common Coupling (PCC) onshore. Measured wind speed data is utilised to demonstrate the potential of the offshore wind resource in Ireland and also evaluate the performance, in terms of energy capture, of the LFAC system using both a cycloconverter, and a BtB VSC onshore, compared to the VSC HVDC system. The wind data employed for the analysis is provided by the Irish Marine Institute [122]. The wind speed measured at the buoy is taken just above the surface of the water and is converted to the correct hub height (90 m) wind speed for offshore turbines. Four years of measured wind data, with approximately 95% of the total annual data set are used in the energy capture analysis. Appendix B details the data measured at the buoy for the four years 2010-2013 and presents a distribution of wind speeds for each year. A 200 MW wind farm is modelled as seen in Figure 3.3, consisting of 40, 5 MW, Type 4 wind turbines with full
54
conversion capability connected in a radial network. The NREL reference 5 MW wind turbine [123] is used for this analysis. Tables 3.4 and 3.5 outline the cable data and transmission system data used in this comparison. KŶƐŚŽƌĞ W
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Figure 4.18: LFAC transmission system modelled in software.
4.5.1
Simulation
The scaled LFAC transmission system is first modelled in Matlab SimPowerSystems to perform preliminary tests and design verification. Figure 4.18 outlines 95
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sŽůƚĂŐĞ ŽŶƚƌŽů
Figure 4.19: Software model and hardware model in red. the LFAC grid modelled with the BtB converter on the 50 Hz grid side. The sending end (wind farm) is modelled as a full switching model of a VSC, fed from a constant DC source. The BtB converter VSCs are modelled as full switching models. The dq controller time constant (ti ) is selected as 1 ms to achieve a fast inner current response. The parameters of the scaled LFAC transmission system can be seen in Table 4.3. Table 4.3: Scaled LFAC transmission system parameters. Parameter
Value
Offshore Grid Frequency Converter Rated Power DC Voltage DC Capacitor LFAC Converter AC Voltage Interface Reactor (Lf ) LFAC Capacitor (Cf ) PWM Frequency Inverter Resistance ron
16.7 Hz 1500 VA 500 V 60 µF 100 V 33 mH 40 µF 1352.7 Hz 43.3 mΩ
Figure 4.20 shows the voltage and current of the LFAC grid in response to a ramp in active power from 0 to 1 kW. The power ramp takes 0.2 seconds allowing a steady increase in the power. After the initial start-up the LFAC voltage remains steady in response to the power ramp. Figure 4.21 shows the peak value of the LFAC voltage d component (Vd ) following the reference value specified in the voltage controller (Figure 4.11). The output of the voltage controller is a reference dq current for the dq current controller. The d component of this can be seen in Figure 4.21 compared to the actual value. The actual value in the dq 96
controller tracks the reference after the initial power consumption where the DC
(b)
100 50 0 -50 -100 0
0.5
1
1.5
1
1.5
10
Current(A)
(a)
Voltage (V)
link capacitor is charging.
5 0 -5 -10 0
0.5
(c)
Power (W)
Time (s) P
1000
ref
P 500 0 0
0.5
1
1.5
Time (s)
Figure 4.20: LFAC (a) voltage and (b) current at start-up and in response to a (c) power ramp beginning at 0.7s.
(a)
Current (A)
5 I I
0
dref d
-5 -10 0
0.5
1
1.5
(b)
Voltage (V)
Time (s) V
100
V
sd sdref
50 0 0
0.5
1
1.5
Time (s)
Figure 4.21: (a) Reference Id compared to actual Id in dq controller and (b) reference Vd and controlled Vd in voltage controller of the controlled frequency VSC
4.5.2
Hardware in Loop Real Time Emulation of LFAC Transmission System
In this thesis a scaled hardware implementation of a low frequency transmission system has been implemented with a hardware in the loop real time simulation 97
platform, OPAL-RT [136]. The Real Time Digital Simulator (OPAL-RT) is a parallel computer system with multiple input/outputs allowing it to be connected to external hardware and equipment. Input, output or control signals can be directly sent from simulation window to the hardware model to control its operation and the resulting response of the hardware can also be sent back to the simulation space. This is all achieved in real time. System stability, real time response, and performance evaluation of hardware are possible in this real time digital simulator. For this work the control algorithms and PWM are implemented in the OP5600 Series OPAL-RT simulators which are generated from the Matlab/Simulink models. The aspect of the LFAC transmission system which is of interest for hardware experimentation is the formation of the inertia-less, low frequency (16.7 Hz) offshore grid using VSC. This represents a fully decoupled AC grid which must support its own voltage and frequency and enable power transfer to the onshore grid. The LFAC transmission system has been partially constructed in hardware with the software control developed on the RTS Opal-RT OP5600 [136].
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Figure 4.22: LFAC transmission system modelled in hardware. The hardware test in this experiment considers only the LFAC grid, and the inverters which are tied to it. Figure 4.22 displays the schematic of the hardware implementation and a picture of the setup is shown in Figure 4.23. While it is important to consider the DC link control and the interface with the AC grid onshore, the purpose of this experiment is to verify the principle of LFAC transmission, to test the grid forming control and to compare the accuracy of 98
the simulation with hardware results. Later in Chapter 5 the full BtB converter with DC link control is implemented. The same component parameters as the simulation (Table 4.3) are used in the hardware experiment, Table 4.4 provides more information about the OPAL-RT real time system and the inverters in the experiment.
Figure 4.23: Picture of hardware setup.
Table 4.4: Hardware Parameters Parameter
Value
IGBT Chopper/Inverter (Lab-Volt) 8857-1 Opal RT RTS OP5600
Figure 4.24 displays the measured voltage Vdq , 3 phase voltage and current and active and reactive power of the LFAC grid. A voltage step from 100 V to 80 V is implemented to test the voltage controller, and a power ramp from 0 to 1 kW to test power transfer. It can be seen that the voltage controller maintains the voltage at 100 V during the power transfer and tracks the reference voltage closely during the voltage step. The ripple on the dq voltage occurs on two frequency peaks at 118.3 Hz and 151.7 Hz. This is due to the effect of the dq transform on an actual AC voltage ripple component at 135 Hz, which corresponds to the parallel 99
120 V
sd
100
(a)
Vsd ref V
Vsdq (V)
80
sq
60 40 20 0 -20 40
42
44
46
48
50
52
54
56
58
52
54
56
58
52
54
56
58
Time (s)
(b) Voltage (V)
100 50 0 -50 -100 40
42
44
46
48
50
Time (s) 8
(c)
6
Current (A)
4 2 0 -2 -4 -6 -8 40
42
44
46
48
50
Time (s)
P (W), Q(Var)
(d)
1000
P
800
P Q
ref
600 400 200 0 -200 40
42
44
46
48
50
52
54
56
58
Time (s)
Figure 4.24: Hardware (a) voltage d and q components, (b) 3 phase voltage, (c) current, (d) active and reactive power. resonant frequency of the LC load on the controlled frequency VSC. The LC resonance of the LC filter connected to the controlled frequency VSC is designed to be controlled by the current control bandwidth, the ripple is caused by the LC resonance between the controlled power port VSC and the filter capacitor. This ripple component is particularly significant in the step response shown in Figure 4.25. Figure 4.25 compares the simulation and the hardware response for both the voltage controller which controls Vdq and the current controller which controls Idq . The reference power input to the wind farm converter is stepped from 500 W to
100
1000 W in both simulation and in hardware. The results in Figure 4.25 validate the simulation with the hardware. The time constant of the dq controller is 1 ms, it can be seen that Id begins to respond to the step change in around 1 ms, however the overall power response to reach the reference in both simulation and hardware takes 20 ms. 150
(a) Voltage (V)
100 50 0 -50 -100 -150
59.96
59.98
60
60.02
60.04
60.06
60.08
Time (s)
(b)
hardware reference simulation
180
Vsd (V)
160 140 120 100 80 60
59.96
59.98
60
(c)
60.02
60.04
60.06
60.08
Time (s)
8
hardware reference simulation
7
Id (A)
6 5 4 3 2
59.96
59.98
60
60.02
60.04
60.06
60.08
Time (s) hardware reference simulation
1400
Power (W)
(d)
1200 1000 800 600 400
59.96
59.98
60
60.02
60.04
60.06
60.08
Time (s)
Figure 4.25: (a) Hardware voltage, (b) Vd , (c) Id and (d) Active power response for hardware and simulation, in response to step in power from 500 W to 1000 W. The voltage controller in Figure 4.25 responds to a step in active power with 30 ms of distortion on the voltage wave, half the time for one 16.7 Hz wave. Vd in simulation has a settling time of 40 ms and reaches a peak of 180 V before settling back to 100 V. The hardware response is more damped, settling in 20 ms and reaching a peak of 150 V. The extra damping in hardware is due to the effective 101
series resistance of the capacitor, and extra AC resistance of the inductor. Only the DC resistance of the inductor has been accounted for in simulation.
4.5.3
Discussion
For this design in hardware the Total Harmonic Distortion (THD) on the voltage and current is 8% and 7% respectively at power transfer. This high level of THD is mainly due to the parallel resonance of the LC load. It is critical that LFAC transmission systems are designed for an acceptable level of harmonics, (below 4% at power transfer [137]). The ripple on Vdq is concerning as Vdq is an input to the voltage controller (see Figure 4.11) with the impact that the ripple is translated through the controller to the reference dq current for the dq controller. In Figure 4.26 the power step experiment is repeated in hardware for the LC filters with capacitor values of 20 µF, 40 µF and 80 µF. This then changes the corner frequency of the LC load to 195 Hz, 135 Hz and 98 Hz respectively for each value of capacitance. It can be seen that the frequency of the ripple increases with decreased capacitor size, as the corner frequency of the LC load is increased. It is clear increasing the capacitor size will reduce the ripple on the voltage at normal operation at 100 V.
Vsd (V)
160
reference 20 µF 40 µF 80 µF
140 120 100 80 60 59.995
60
60.005
60.01
60.015
60.02
60.025
60.03
60.035
60.04
60.045
Time (s)
Figure 4.26: Vd response to step in active power from 500 W to 1000 W for filter with 20 µF, 40 µF and 80 µF capacitor. Increasing the size of the filtering components will reduce the ripple and therefore the THD of a system; however, there are concerns about the size of the filters at low frequency, and the reactive power consumption which accompanies these large capacitances. The design focus should aim to reduce the filtering size and include more sophisticated damping to reduce the harmonics of the transmission system.
Improved voltage controller design is an aspect worth 102
investigating, by improving the robustness of the controller to the disturbances caused by resonance between filtering and cables. Another point to note is that the minimum size of the inductor must be large enough to provide adequate phase shift to transfer power across the VSC.
4.6
Conclusion
Initially this chapter outlines 3 phase power electronic modelling basics, including dq control, PWM and PLL operation.
Next the VSC control schemes were
introduced and outlined. A scaled hardware design for a LFAC transmission system for offshore wind farm interconnection is then presented. The design and control of the transmission system is verified firstly in software and then with hardware emulation in the laboratory. The simulation and hardware results are comparable on a millisecond time scale in response to voltage steps, power ramps and power steps. The design of an LC filter for LFAC transmission has also been introduced. The LC load’s impact on the voltage ripple of Vdq produced by the Park Transform of harmonics at the corner frequency of the LC filter has also been examined. Figure 4.26 has shown the impact of the changing capacitance voltage control with a VSC. When a long HVAC cable is connected to the VSC, effectively another large capacitance will be placed in parallel with the filter capacitance adding to the size of the load connected to the controlled frequency VSC. This capacitance will have an effect on the control of the offshore voltage in the LFAC transmission system. Chapter 5 applies the information in this chapter to develop the overall design of a LFAC based transmission system connecting offshore wind, considering the impact of the long HVAC cable on the control of the offshore grid voltage with a focus on reducing over voltages.
103
CHAPTER
FIVE OPERATIONAL DESIGN AND VOLTAGE CONTROL OF LFAC TRANSMISSION
5.1
Introduction
In this chapter the system model in Chapter 4 is expanded upon to include the LFAC offshore grid and LFAC cable. The LFAC grid is unique for long distance power transmission in that it is a fully power electronic AC grid. There are no synchronous machines in the grid providing a stable frequency and voltage amplitude, no inertia, and minimal loads offshore providing damping. In this case the power electronic converter must regulate the voltage amplitude and frequency in steady state and in response to disturbances, which due to the lack of damping from any loads offshore will react quicker than in over-damped systems.
In
addition the LFAC system is unusual in that the AC transmission system consists entirely of high voltage AC cables. In LFAC transmission the VSC on the low frequency side is required to establish and maintain the offshore low frequency voltage. AC cables have resonant frequencies associated with the capacitance and inductance of the cable. LFAC will involve the connection of long cables to the AC side of the VSC, unlike HVDC where the cable is connected to the DC side. Therefore resonance interactions between the cable and the LFAC filter may be a concern. Moreover, at low frequency the filter components will be larger than
104
they would in a 50 Hz system and therefore possibly push resonances to lower frequencies. Chapter 4 outlined the modelling of a LFAC system without a cable attached, focusing on the control of the BtB converter onshore, and it’s ability to establish and control the offshore grid voltage amplitude and frequency. This chapter examines the impact of adding a long HVAC cable to the closed loop voltage controlled system. AC cables have a resonant frequency associated with the capacitance and inductance of the cable. Therefore resonance interactions between the cable and the LFAC filter may be a concern. The combination of the large filter inductance and the cable capacitance has the impact of moving the resonant frequency of the combined filter and cable system to lower frequencies. This effect has been seen before in previous publications on LFAC transmission, Canelhas et al. [108] found that for a 200 km transmission cable and BtB converter system the resonant frequency was close to 50 Hz. Large damping filters were used to maintain transmission system stability. These filters are both large and expensive and can have significant losses (1-2%) and consume a large portion of reactive power (5070% of power). With resonant frequencies below the 14th harmonic inductive elements may interact with the resonance to cause a Temporary Over-Voltage (TOV) if there is a disturbance on the system [138, 139]. TOVs cause instability in the voltage which the low frequency side converter is attempting to control. A sustained TOV will cause offshore breakers to trip resulting in disconnection from the onshore system. For any long HVAC cable connected to the onshore system these issues are prevalent. In HVAC (50 Hz) transmission, the offshore wind farm is connected directly to the onshore grid, meaning disturbances are propagated to the onshore system. Conversely in LFAC transmission, the cable is connected to a BtB VSC which decouples the cable from the onshore grid. It is important to analyse the interactions between the cable, the filter and the VSC control and compensate for any issues present with filtering or proper VSC controller design. The key contributions of this chapter are as follows; The characterisation of the impact of connecting a long AC transmission cable to a VSC and filter system.
The application of an adapted VSC voltage control scheme for the 105
connection of long HVAC cables to maintain a stable offshore voltage in an LFAC transmission system. The characterisation of the design trade offs between switching frequency, filter capacitance and controller parameters to minimise the amplitude and duration of TOVs. Novel hardware based verification of the LFAC transmission system design which has not been presented before with a BtB converter onshore. In this chapter, Section 5.2 describes the issue of HVAC cable resonance. Section 5.2.1 outlines and compares the options for long cable modelling to gain accurate results. Section 5.3 examines the addition of a HVAC cable to the voltage control loop, examining the frequency responses of the system to design an adapted voltage controller compensator. In Section 5.4 simulations are conducted to analyse different controller parameters in terms of system stability and response to TOVs. This approach is then validated in Section 5.5 on a scaled hardware model of the LFAC transmission system, with the control operating in real time through a hardware in the loop real time simulation.
5.2
LFAC HVAC Cable
The predominant effect of introducing a long transmission cable is to add a large capacitance, which depending on cable length can create low frequency resonance issues. With longer cables if over voltages occur the frequency of over-voltage can be low, meaning longer duration of over-voltages. Low frequency resonances are often poorly damped [140] and can cause over-voltages to exceed insulation strength of many devices, causing failures and interruption of supply [141]. It is important to note that since there are no loads offshore, resonances are less damped than in onshore grids. Conventional converter control often considers the impedance of the grid it is connected to as a lumped inductance and neglects the impact of the connected HVAC cable, however this large capacitance cannot be neglected. Zhang et al. [135] consider the impact of long HVAC cables on the control of the Wind Turbine Generator (WTG) converter, proposing a new grid modelling method and control architecture to deal with high frequency resonances.
106
In the LFAC case the WTG are connected via a HVAC cable to a large VSC, therefore no synchronous grid is present. VSCs can become unstable due to series resonances which are caused by HVAC cables. In [142] the authors have examined the impact of the VSC controller parameters on system stability, given the connection of different lengths of HVAC cable. Voltage control and current control bandwidth have been proven to impact on system stability, and need to be designed in coordination with the connected system. The authors in [142] only considered the impact of adding cables up to 100 km in length. LFAC cables have the capability to reach up to 250 km, further increasing the problem with low frequency resonance. This low frequency resonance is a problem for LFAC voltage control stability and ability to control TOVs [13].
5.2.1
Cable Modelling
In order to understand the impact of the LFAC transmission cable on the voltage control of the system the cable must be modelled in simulation and in hardware. There are a number of options for cable modelling which can be separated generally into two groups, lumped parameter or distributed parameter models. Distributed parameter cables assume that the attributes of the cable are distributed continuously through the material of the circuit. The distributed parameter model of a cable can be described by Figure 5.1 where Zπ and Yπ are defined by Equations 5.1 and 5.2.
ǀϭ
ŝϭ
ʋ
ŝϮ
ǀϮ
zʋ Ϯ
zʋ Ϯ
Figure 5.1: Steady state pi-model of the cable.
Zπ = zl
sinh(γl) γl
107
(5.1)
Yπ = yl
tanh(γl/2) γl/2
(5.2)
Where l is the length of the cable, z and y are the impedance and admittance per unit length defined by
z(ω) = R(ω) + jωL(ω)
(5.3)
y(ω) = G(ω) + jωC(ω)
(5.4)
and γ is the propagation constant defined by γ=
√
zy
(5.5)
Equations 5.3 and 5.4 highlight the frequency dependent nature of the cable parameters. Reference [143] examines in detail frequency dependent cable modelling including using cascaded pi-sections with multiple parallel branches to more accurately represent the frequency dependent nature of the parameters, with lumped parameter based models. The frequency dependent nature of the parameters is not taken in these models. The effect of the frequency dependence on the parameters at high frequencies is potentially to damp the resonance points. Therefore using multiple pi-sections or a distributed parameter model can be considered the worst case scenario for high frequency cable resonance. For steady state conditions and short cables the single lumped pi-model is an appropriate model [144]. The parameters are combined into a lumped inductance and resistance and the total capacitance is divided equally across either end of the cable. This approximation stems from Equations 5.1 and 5.2 where the hyperbolic functions approach 1 for short cables, typically less than a quarter wavelength. For longer cables the approximation can be corrected by cascading multiple pi-sections together. Figure 5.2 shows the layout of a lumped parameter cable model. Pi models can be connected in series to make a multiple pi model where the total resistance, inductance and capacitance is divided across multiple sections 108
>
Z
'
ͬϮ
'
ͬϮ
Figure 5.2: Lumped pi-section cable model. to more accurately reflect the distributed nature of cables. The layout of this is shown in Figure 5.3. Zϭ
>ϭ
ͬϮ
ZE ͬϮ
ͬϮ
>E ͬϮ
Figure 5.3: Multiple pi-section cable model where N is the number of pi-sections. Figure 5.4 shows the frequency response of a 150 km cable modelled with a distributed parameter cable model, a single lumped pi-section and multiple pisection models with 5 and 10 series connections. The series and parallel resonances of the cable can be clearly seen.
This illustrates the accuracy of using the
different type of models for power system simulation. It can be seen that the distributed parameter model has resonant frequencies distributed evenly along the frequency spectrum. Above 1000 Hz the accuracy of the 5 pi-section model performs considerably worse than the 10 pi-section model. Distributed parameter or multiple (N=20+) pi cable models are the most accurate representation for long cables at high frequencies.
109
Impedance (dB Ω)
60 40 20 Distributed 0 0
N=1
N=5
N=20
500
1000
1500 2000 Frequency (Hz)
2500
3000
500
1000
1500 2000 Frequency (Hz)
2500
3000
Phase (deg)
100 50 0 −50 −100 0
Figure 5.4: Frequency response showing resonant frequencies of a 150 km cable with distributed parameter cable model, and multiple pi-section models with 1, 5 and 20 pi-sections.
5.3
Voltage Controller Design Including HVAC Cable
The standard voltage control design is outlined in Section 4.3.2 where the grid forming control of the VSC is presented. In this section the impact on the voltage control of adding a long HVAC cable to this system is examined. Equations 4.36 to 4.40 show the design procedure for k(s), the voltage controller compensator transfer function. For a case without any long HVAC cable attached the open loop transfer function of the system is given by Equation 5.6 and the compensator gain k is given by 5.7.
l(s) =
h k(s + z) ih s 110
1 ih 1 i ti s + 1 sCf
(5.6)
k = Cf ωc
(5.7)
The HVAC cable affects the voltage at the filter capacitor, which has an impact on the control and stability of the system. If the controller is not designed to compensate for the effect of the long AC cable, then the voltage may not be stable and controlled. In order to determine the component resonant points of the LFAC transmission system a frequency sweep from 1 to 10000 Hz is performed on the LC filter and HVAC cable [139]. Table 5.1 shows the cable parameters [145] used with a filter inductance and capacitance of 85.8 mH and 4.03 µF. Figure 5.5 displays the frequency sweep for 150 and 300 km HVAC cables. To obtain the higher frequency resonant points of the system, the cables are modelled using 20 pi-sections. The lowest frequency peaks represent the first LC resonance of the filter which has been shifted to lower frequency by the presence of the cable. The LC filter resonance is designed to be 270 Hz, however the addition of the cable capacitance reduces this resonance to 88 Hz and 62 Hz for 150 and 300 km cable lengths.
Impedance (ohms)
Table 5.1: LFAC transmission cable data at 50 Hz. Voltage (kV)
R (Ω/km)
X (Ω/km)
C (nF/km)
220
0.046
0.07
198
80
150 km 300 km
60 40 20 0 0 10
1
10
2
10
Frequency (Hz)
3
10
4
10
Figure 5.5: Resonant peaks of 220 kV cable combined with LC filter.
111
These low frequency resonances have the potential to provide significant difficulties in terms of maintaining stability and sustaining harmonic levels below an allowable threshold if the controller is not appropriately designed. From a voltage control compensator design point of view, analysis of the open loop system is performed using a lumped pi model. Using a simplified pi-section to model the cable will represent the first filter LC resonance and the first cable resonance. This simplification aids in the design and understanding of the voltage controller. The simplified cable can be easily added to a small signal analysis to understand the stability of the voltage control within the bandwidth of both the dq and voltage controllers. Chapter 6 will examine more accurately the stability of the LFAC transmission system including more detailed cable models. LF
LC
VSC
CF
Cc
Cc
Figure 5.6: VSC connected to filter and cable. Figure 5.6 shows the layout of the pi cable model connected to the LC filter and VSC. The voltage at the filter capacitor is dependent on the current drawn by the parallel combination of the filter capacitor and the cable equivalent capacitance. Since the cable has an impact on the voltage measured it impacts the structure of the control block diagram, illustrated in Figure 5.7. k(s) is the voltage controller compensator defined by the first part of Equation 5.8. The second block is a representation of the closed loop inner current controller dynamics. The third and fourth blocks are the parallel combination transfer function of the filter capacitor and the first cable capacitance, and the transfer function of the remaining cable components. It follows that Equation 5.8 describes the open loop gain of the controlled frequency VSC system including the cable in the small signal model.
l(s) =
h k(s + z) ih s
ih i 1 ih 1 s2 C c L c + 1 c ti s + 1 s(Cf + Cc ) s2 Cc Lc + 1 + C C+C c f
112
(5.8)
Vdref -
k(s)
1 tis + 1
1 s(Cf+Cc)
s2CcLc+1 s[s CcLc+1 + Cc/(Cf+Cc)]
Vd
2
Figure 5.7: Control block diagram including LFAC cable. The introduction of the HVAC cable adds a complex conjugate pair of poles s 1 + Cc /(Cf + Cc) 1 and double zero at ω = √ at ω = to the open loop Lc Cc Lc Cc system resulting in the dip and peak in the loop response. The cable capacitance in the open loop system will reduce the magnitude of the frequency response, reducing the voltage controller crossover frequency to below the selected crossover frequency ωm , resulting in an inadequate phase margin at the crossover frequency. The closed loop stability of the system depends on the poles of 1 + l(s) where the closed loop system is equal to Equation 5.9. l(s) 1 + l(s)
(5.9)
In order to illustrate the issues with controlling the LFAC voltage while connecting a HVAC cable, the compensator is first designed using the voltage control compensator gain in Equation 5.7. In this analysis the cable parameters in Table 5.1 are used, with filter inductance and capacitance of 85.8 mH and 4.03 µF respectively and the control parameters ti and δm set to 1 ms and 53◦ as previously described in Chapter 4. Figure 5.8 shows the open and closed loop frequency response of Figure 5.7 with the addition of different cable lengths from 50 km to 300 km. This response incorporates one pi-section cable model, the impact of which can be seen in the series and parallel resonance sfor each cable. As expected 1 + Cc /(Cf + Cc) . In the Lc Cc open and closed loop system the magnitude is continually decreasing as frequency the series resonance occurs at the frequency ω =
increases, therefore the impact of extra pi-sections on the frequency response will be at negative magnitudes. The open loop frequency response for the case with no cable verifies a 53◦ phase margin at ωc = 334 rad s-1 indicating that under these conditions the voltage controller will provide a stable response, verified in the 113
closed loop plot. However, increased cable length reduces the crossover frequency below the desired value. It follows that at longer cable lengths with reduced crossover frequencies the reduced phase margin causes the closed loop response positive gains. These have the potential to cause oscillations in the response of the controlled frequency VSC with a cable connected. To reduce overshoot and ensure adequate phase margin of the controlled frequency VSC system the controller gain k must compensate for the reduced magnitude of the frequency response with increased cable length. Reviewing Figure 5.8, the range of the crossover frequencies is not impacted by the cable resonance which is due to the inductance and occurs at much higher frequencies. The cable capacitance has the effect of reducing the magnitude of the open loop plot. The cable capacitance drives the decrease in magnitude, and therefore the decrease in crossover frequency. In order to evaluate the compensator gain an open loop system without the cable inductance effect can be examined. This produces a loop gain defined by Equation 5.10. Since the cable inductance is neglected in this instance the loop gain becomes similar to Equation 5.6 with the total cable capacitance and the filter capacitance added in parallel.
l(s) =
s+z 1 k ti (Cf + C) s + t−1 s2 i
(5.10)
q zt−1 i
(5.11)
ωc =
Where C = 2Cc is the total cable capacitance. The gain crossover frequency (ωc ) is set by Equation 5.11 then the new compensator gain k is obtained from the solution of Equation 5.10, setting l(jωc ) = 0 Equation 5.12 yields the new compensator gain.
k = (Cf + C)ωc
114
(5.12)
50km
100km
150km
200km
Bode Diagram
250km
300km
no cable
Magnitude (dB)
40 20 0 −20 −40 −60
Phase (deg)
0 −45 −90 −135 −180 0 10
1
10
2
10 Frequency (Hz)
3
4
10
10
(a)
Magnitude (dB)
50km
100km
Bode Diagram 150km 200km
250km
300km
0 −20 −40 −60
Phase (deg)
0 −45 −90 −135 −180 0 10
1
10
2
10 Frequency (Hz)
3
10
4
10
(b)
Figure 5.8: (a) Open loop and (b) closed loop frequency response with cables from 50 km to 300 km. Equation 5.12 is used to calculate the compensator gain value incorporating cable length. The open and closed loop response for various cable lengths is shown in Figure 5.9. As required the phase margin is 53◦ and the crossover frequency is 115
about 334 rad s−1 in all cases. This indicates that for any cable length, the voltage controller with a compensator designed as in Equation 5.12 will provide a closed loop response without significant positive gains. Although the plant (i.e. the cable plus filter system) does have an inherent disturbance associated with the cable resonance, the closed loop plot of Figure 5.9 shows that the closed loop system is stable with the new compensator design for cable lengths from 50km to 300 km. This small signal analysis assumes an ideal transformer with a 1:1 turns ratio. When applying Equation 5.12 to a system where the cable is separated from the converter system by a step up transformer the capacitance (C) should be multiplied by the turns ratio squared to account for the real cable impedance seen at the converter terminals. Figure 5.10 compares the closed loop step response of the LFAC small signal model, for a 150 km cable, with both the original voltage controller design developed in Chapter 4 and the voltage controller in Equation 5.12. Comparing these it is clear that the adapted voltage controller design is much better in terms of limiting TOVs and undesirable oscillations. Figure 5.11 shows the effect of increasing cable lengths on the closed loop poles of the system. Figure 5.12 shows the nyquist plots for the 6 cable lengths, verifying the closed loop stability of the system by not encircling the point (-1,0). This analysis has been performed at a fixed power level with varying transmission distance. It is worth noting that increasing the power level for this analysis will lead to different LC filter and cable parameters, however the procedure to design the controller will remain the same. To further improve the response time and overshoot reduction of the of the voltage control the bandwidth can be increased by varying design parameters.
116
50km
100km
Bode Diagram 150km 200km
250km
300km
Magnitude (dB)
40 20 0 −20 −40 −60
Phase (deg)
0 −45 −90 −135 −180 0 10
1
10
2
10 Frequency (Hz)
3
4
10
10
(a)
Magnitude (dB)
50km
100km
Bode Diagram 150km 200km
250km
300km
0 −20 −40 −60
Phase (deg)
0 −45 −90 −135 −180 0 10
1
10
2
10 Frequency (Hz)
3
10
4
10
(b)
Figure 5.9: (a) Open and (b) closed loop frequency response with updated controller for any cable length.
117
1.5
k=(Cf +C) ω
Amplitude
k=Cfω 1
0.5
0 0
0.05
0.1
0.15
0.2 0.25 Time (seconds)
0.3
0.35
0.4
0.45
Figure 5.10: Closed loop step response of Equation 5.8 with k = Cf ω and k = (Cf + C)ω.
6000
50km 100km 150km 200km 250km 300km
Imaginary Axis (seconds−1)
4000 2000 0 −2000 −4000 −6000 −350
−300
−250
−200 −150 −100 −1 Real Axis (seconds )
−50
0
Figure 5.11: Closed loop poles of Equation 5.8 for cable lengths from 50 km to 300 km.
118
1
Imaginary Axis
0.5
50km 100km 150km 200km 250km 300km
0
−0.5
−1 −1
−0.5
0
0.5
1
1.5
Real Axis
Figure 5.12: Nyquist plot of closed loop small signal system for cable lengths from 50 km to 300 km. From Equations 5.8 and 5.12 it can be seen that the bandwidth of the controller is dependent on the required phase margin and on the time constant of the dq current control scheme (ti ) which dictates the placement of the real pole 1/ti . The time constant (ti ) for standard VSC control is typically selected to be between 0.5 and 5 ms. However, the bandwidth of the inner current controller (1/ti ) must be considerably smaller than the switching frequency of the VSC [128]. The selection of the switching frequency is an interesting decision for an LFAC transmission system. Intuitively since the fundamental frequency is 3 times lower, the switching frequency of the VSC on the low frequency side may be lower than the standard for HVDC transmission, preserving the ratio between fundamental and switching frequency. This would reduce switching losses, however reducing the switching frequency decreases the maximum allowable 1/ti , thereby reducing controller bandwidth. This constitutes a design trade off which can be summarised by Table 5.2. Increasing the phase margin improves the damping of the system response to changes in voltage. Using a higher phase margin the damping ratio can be increased to almost 1, however the associated reduction in bandwidth renders this 119
Table 5.2: Trade offs associated with compensator design choices.
fsw ↑ δm ↑
Filter C
max ti
PI bandwidth
Switch damping Losses
↓ -
↑ -
↑ ↓
↑ -
↑
increase impractical. In the context of TOVs a higher bandwidth will increase the speed of the controller in response to disturbances, thereby reducing the magnitude and duration of the TOVs.
5.4
Time Domain Simulation of Test System
The test system used models a 200 MW offshore wind farm connected via a 150 km, 220 kV LFAC cable. The BtB converter is connected at 100 kV and a low frequency transformer steps up to the cable voltage. Table 5.3 shows the parameters used in modelling the LFAC transmission system. Table 5.3: Parameters for LFAC transmission system. Parameter
Value
Filter Inductance (Lf ) Filter Capacitance (Cf ) R Cable Resistance Cable Inductance (Lc ) Cable Capacitance (C) VDC Vsd ref , Vsq ref Switching Frequency (fsw ) Transformer Turns Ratio (n:1)
85.8 mH 4.03 µF 0.27 Ω 0.046Ω/km 0.07 ΩF/km 198 nF/km 400 kV 100 kV, 0 V See Tab. 5.4 2.2:1
Four different sets of compensator parameters are tested, ensuring fast dq control with ti of between 0.5 ms and 1 ms, and appropriate damping with phase margin δm of 45◦ and 53◦ . The switching frequency is selected to be approximately 8 times the bandwidth of the dq controller, and a multiple of the fundamental frequency. Table 5.4 displays the details of the 4 controllers examined. 120
Table 5.4: Controller specifications. Contr- oller
fsw (Hz)
dq time Phase constant Margin (ti )(ms) (δm ) (◦ )
Bandwidth (rad s−1 ) (ωc )
A B C D
2104.2 2104.2 1653.3 1352.7
0.5 0.5 0.75 1
828.4 669.2 446.1 334.6
45 53 53 53
Amplitude
1.5
1
Controller A Controller B Controller C Controller D
0.5
0 0
0.005
0.01
0.015 0.02 Time (seconds)
0.025
0.03
0.035
Figure 5.13: Closed loop step response of Equation 5.8 for each Controller in Table 5.4. Figure 5.13 shows the closed loop step response of the small signal model in Equation 5.8. The higher frequency oscillations which can be seen correspond to the frequency of the complex pole pair at 316 Hz, this resonance can also be verified from the impedance scan for a 150 km cable in Figure 5.5. Simulations are performed to examine each controller in the LFAC transmission test system.
The full switching simulations have been performed in Matlab
Simscape Powersystems [127] modelling the LFAC offshore transmission system as depicted in Figure 4.13. The cable is modelled in simulation using 20 pi-sections as in Figure 5.5. Two tests are carried out to determine the appropriateness of the selected controllers. Equation 5.13 is used to calculate the gain of the voltage controller taking the effect of transforming the impedance across the LFAC transformer (where n is the turns ratio) into account. 121
k = (Cf + n2 C)ωc
(5.13)
1. After 0.5 seconds a voltage step is applied from 1 pu to 1.5 pu. The systems ability to respond to step changes in voltage depends both on the bandwidth and the phase margin of the compensator. 2. After 1.5 seconds a power step from 0 to 1 pu is applied as a disturbance to the system. The objective of the controllers is to maintain the voltage at the desired value (1 pu) in response to the change in power.
1.8
Vd (pu)
1.6 1.4
Controller A Controller B Controller C Controller D Reference
1.2 1 0.8
0.5
0.52
0.54
0.56
0.58
Time (s) Figure 5.14: Vd response to voltage reference step from 1 to 1.5 pu.
Controller A Controller B Controller C Controller D Reference
Vd (pu)
1.3 1.2 1.1 1 0.9
1.5
1.52
1.54
1.56
1.58
1.6
Time (s) Figure 5.15: Vd response to large current step. Figure 5.14 shows the response of each controller to this voltage step. As expected from Figure 5.13 the controller with the largest bandwidth responds the 122
Voltage (pu) Vdq (pu)
1 0.5 0
Current (pu)
1 0.5 0
Power (pu)
1 0.5 0 1.6 1.4 1.2 1 0.8 1.3
Voltage (pu)
1 0 −1 Vdref
Vd
Vq
1.45
1.6 1.75 1.9 Time (s) Figure 5.16: Voltage, Vdq , Power transferred, Id and VDC from test system simulation for Controller B.
fastest. Increased phase margin reduces the overshoot which can be seen in the difference between controller A and B. Comparing the responses in Figure 5.14 the response to a step change in voltage is quick and controlled, with the d component of the voltage returning to the reference value within 30-50 ms for the 4 controllers. This test verifies that the voltage control is stable when responding to a change in the LFAC voltage. Comparing these responses to the small signal step responses it is clear that the real full switching model has a slightly settling time in response to voltage steps than the small signal model suggests (30-50 ms in the simulation compared to 15-30 ms in the small signal model). The main factor contributing to this is the time taken for the converters to respond to the change in voltage. A number of small oscillations can be seen on the step responses, corresponding to the cable series resonance, however these oscillations are decaying. These oscillations will be further analysed in Chapter 6. In Figure 5.15 the voltage controller is responding to an external disturbance, in this case a step increase in current to the controllers caused by a step increase in power. It is clear again that the larger
123
bandwidth controllers provide a more desirable response, responding in 15 - 20 ms to control the voltage. The TOV caused by the disturbance reaches as much as 1.3 pu for 20 ms for Controller D, which may cause stress and failure of protection equipment if not controlled back to the reference value in time. TOV limits have been defined by the Irish Transmission System Operator on HVAC cables at 1.6 pu for the duration of one electrical cycle [146]. These results show each controller to be within this limit. For Controller A the TOV reaches almost 1.15 pu, returning after 20 ms to the desired value. Figure 5.16 shows the LFAC voltage, power and the dq components of voltage and current using controller B for the power step, displaying the overall simulation responses.
5.5
Hardware Experimentation
To verify the design and operation of the LFAC transmission system and the voltage controller design, the LFAC transmission system is built in hardware using the parameters in Table 5.5. The hardware setup is similar to the one described in Chapter 4. In this case the full LFAC transmission system is modelled in hardware, including the LFAC cable, the full BtB converter with DC link capacitor and the 50 Hz AC source. In hardware, the offshore wind farm is modelled as a DC source connected to the grid side converter of a wind turbine. The entire hardware setup schematic is shown in Figure 5.17, outlining the control schemes for each of the three converters, which are operated in real time. The wind farm side converter locks onto the 16.7 Hz grid produced by the BtB converter. The BtB converter is comprised of two 2 kVA VSCs, with a 680 µF capacitor on the DC link. The cable is scaled using Equation 5.14 where kscale is based on the ratio of the base impedance of the hardware system and the real system [147]. kscale =
Zhardware Lhardware Creal = = Zreal Lreal Chardware
(5.14)
The experiment was performed with a 150 km scaled cable modelled with the total inductance and capacitance divided across 5 pi sections. Figure 5.18 displays a
124
picture of the hardware setup, including a picture of a single phase of the cable model. Table 5.5: Parameters for scaled hardware LFAC transmission system. Parameter
Value
Filter Inductance (Lf ) Filter Capacitance (Cf ) Cable Inductance (Lc ) Cable Capacitance R (Inductor) VDC Vsd ref, Vsq ref Switching Frequency (fsw )
33 mH 40 µF 9.21 µH/km 4.79 µF/km 0.126 Ω 500 V 100 V, 0 V 1.3527 kHz B: 669.2 rad s−1 C: 446.1 rad s−1 D: 334.6 rad s−1
Voltage Controller Bandwidth (ωc )
The hardware experiments are performed at a fixed switching frequency of 1352.7 Hz. The voltage controller bandwidth is varied by the parameters B-D in Table 5.5. Controller A has been neglected as the only difference between A and B is phase margin. These voltage controller bandwidths correspond to the ones in Table 5.4. To verify and validate the simulation results in Section 5.4 a simulation of the scaled hardware system is also performed with the parameters in Table 5.5. This allows direct comparison of software and hardware, to validate the design and control. Figure 5.19 shows the small signal closed loop step response with the hardware parameters for each controller. In hardware and software the voltage step test is performed from 1 pu to 1.5 pu. Figure 5.20 shows the voltage step test for two different controller bandwidths (B and D) in both the hardware and software model. It can be seen that generally there is reasonable agreement between the hardware and the software for the voltage step test. The overshoot in voltage of 0.1 pu is 20% of the voltage increase of 0.5 pu. This agrees with Figure 5.19 where the overshoot is also 20%. The hardware and software both have longer settling times than the small signal model, which is due to multiple aspects not modelled in small signal, including the PLL on the wind farm side, the DC link, and the extra cable pi sections causing high frequency harmonics. 125
R
Controlled Power port VSC
PI cable model
L
Controlled Frequency VSC
L
C
Controlled DC Voltage Power Port
50 Hz AC grid
abc
pulses
dq
ρ abc
dq
126
Reference Signal Generator
idref iqref
idq
abc
sdq
iodq ref
sdq
Iabc
PWM mabc
dq ρ
ρ
abc dq
idq
sd
Current Control Scheme
iodq
iqref idref Voltage Control Scheme
abc
PWM mabc ρ2 abc
dq
dq
mdq
idq2
ρ2
PLL Vsdq2 ω
mdq
Current Control Scheme
q
Iabc
pulses
pulses
sdq
sdq
Pref Qref
Virtual PLL
abc
abc
ρ
dq
ρ PLL
mdq
Cf
Iabc ρ
abc PWM mabc
abc
Iabc
Current Control Scheme sdref ref
Pref DC ref DC
iqref2 idref2 DC Bus Voltage Controller
Control in OPAL RT Real Time Simulator Figure 5.17: LFAC transmission system hardware setup with OPAL RT real time simulator.
Cable
VSC s
Filter
OPAL-RT
LFAC Cable
Figure 5.18: Picture of hardware setup
1.4 1.2
Amplitude
1 Controller A Controller B Controller C Controller D
0.8 0.6 0.4 0.2 0 0
0.01
0.02
0.03 0.04 0.05 Time (seconds)
0.06
0.07
Figure 5.19: Small signal step response of hardware model. Figure 5.21 shows the response of voltage controllers B, C and D to a 0.7 pu step in active power from 0.3 pu to 1 pu. It can be seen that Controller B provides the fastest and smoothest response as expected, with controllers C and D responding as in simulation with a TOV of higher amplitude and longer duration (20 - 40 ms). The TOVs observed in hardware are lower than in the high power simulation. This is due to extra resistive damping in the hardware setup from the filter and cable implementations. The duration of the TOVs are similar to those
127
1.6 1.5 Vd (pu)
1.4
B − Hardware B − Software D − Hardware D − Software Reference
1.3 1.2 1.1 1 0.9
0.5
0.51
0.52
0.53 Time (s)
0.54
0.55
0.56
Figure 5.20: Response of hardware and software model to step in voltage from 1 pu to 1.5 pu. in Section 5.4, validating the controller design in the high power simulation, in hardware.
V d (pu)
1.2 Controller B Controller C Controller D Reference
1.1 1 0.9
92
92.05
92.1
92.15
92.2
Time (s) Figure 5.21: Vd response to power step from 0.3 pu to 1 pu in hardware for three controllers. Figure 5.22 displays the voltage, current, and power exported from the wind farm using Controller B for both hardware and software model validating the overall LFAC system design and control in hardware. It can be seen that the hardware and software match each other for a power step event from 0.3 pu to 1 pu. This provides validation in hardware that the control performs as expected in Section 5.4. Comparing the hardware results to the simulation in Figure 5.16 similar responses can be seen in the LFAC grid simulation. The DC link voltage 128
responds much slower and has a smaller amplitude response than in simulation due to a proportionally much larger capacitor being placed in on the DC link in
Voltage (pu) (pu)
1 0.5 0 1
Id
1 0 −1
Vdq (pu)
hardware.
Vd software
Vq software
Vd hardware
Vq hardware
0.5
(pu)
VDC
Power (pu)
0 1 0.5 0 1.1
Software Hardware
1 0.9 1.6
1.8
2 Time (s)
2.2
2.4
Figure 5.22: Comparison hardware and software LFAC Voltage, Vdq , Id , power and VDC during step from 300 W to 1000 W.
5.6
Conclusion
This chapter has presented the design and control of an LFAC transmission system with a focus on accounting for the impact of connecting a long HVAC cable operated at 16.7 Hz to a VSC. The addition of a long HVAC cable causes voltage control instability if the controller is not appropriately designed. The chapter begins by assessing the modelling approaches for HVAC cables. Then presenting a VSC AC voltage control scheme which is adapted from the one outlined in Chapter 4 to compensate for the addition of a long HVAC cable. The control of the onshore BtB converter in an LFAC transmission system has been developed 129
in a small signal analysis to provide a stable offshore voltage. The proposed controller design is tested in simulation on an LFAC test system with various parameters accounting for design trade offs between controller time constants, phase margin and switching frequency. Comparing the time domain simulations to the small signal analysis shows good agreement between both methods. The design of the LFAC transmission system and the controller design have been validated in a scaled hardware test setup, where the results are comparable to the small signal results and a scaled down simulation of the hardware. This direct verification of simulation and hardware experiment allows validation of the scaled up simulations which incorporate all the components of the LFAC transmission system. It is also worth noting that alough in this case the application is Low Frequency transmission, this chapter provides an approach to design voltage controllers for any long HVAC cable connected to a controlled frequency VSC. In both the hardware experiment and simulation high frequency cable harmonics were observed. In Chapter 6 the harmonic stability of the system will be examined with particular attention paid to the influence of controller parameters on stability.
130
CHAPTER
SIX IMPEDANCE BASED STABILITY IN LFAC POWER ELECTRONIC GRIDS
6.1
Introduction
Until now this thesis has considered the techno-economic aspects of LFAC transmission, the design and operation of an LFAC transmission system and its ability to control the voltage in the offshore grid, particularly in response to disturbances.
Power electronic grids provide advantages over traditional
grids including full controllablity and improved efficiency. However, they also introduce new challenges. High frequency switching introduces harmonics which may interact with higher frequency resonances [148], also power converter control interactions may exist between converter controls and between control and passive components. These interactions can affect the power system in any frequency range from sub synchronous, to high order harmonics. As seen in Chapter 4 filter components can also affect the oscillations observed in the grid. In Chapter 5 the impact of converter control on oscillations in the system can also be seen. In the LFAC case the combinations of the converter controls, filter impedances, cable impedance and wind farm control and impedance means that there are many areas for potential harmonic instability. This chapter presents techniques which feed back into the design process in the planning phase of an inverter based grid. In
131
an inverter based grid with no synchronous machines interactions between devices and controllers are a concern. In an offshore grid this is a particularly important problem for utilities to understand. Since the offshore wind farm will be developed by a third party developer and the offshore station by a vendor, it may be difficult to obtain accurate EMT simulation data, including sensitive control schemes to enable utilities to study this effect in the planning phase. In HVDC connected wind farms it has been observed that the combination of the offshore wind farm and the HVDC converter station in an offshore network can cause sub synchronous resonance (SSR) between the converter controls and the wind turbine controls, known as Sub Synchronous Control Interactions (SSCI). SSCI can be defined as interactions between a power electronic device (such as an HVDC link, SVC, wind turbine etc.) and a series compensated system, or interactions between two power electronics based systems (HVDC link and wind farm or FACTS device) [149]. Planning for large power electronic grids, in particular HVDC connected offshore wind generation generally use positive sequence models to perform initial planning studies, which are not accurate at capturing SSCI. Therefore in planning it is important to perform three phase EMT simulations to determine the stability of a system across a range of frequencies [150]. The first real experience with inverter dominated offshore grids has been BorWin1, a HVDC connected offshore wind farm in the North Sea [151]. Stability problems due to interaction of converters and grid resonances were observed and caused significant outages. These phenomena were not considered during planning phase of BorWin1, however in the intervening years there has been an industry wide focus on identifying these stability problems in inverter dominated grids [151, 152]. These problems are of significant interest to a LFAC system due to the presence of very long HVAC cables. Analysing the stability of grids with high penetrations of power electronics is a difficult task for power system planners. In generic power systems state space models are developed to determine stability, where the dynamics are primarily dictated by rotating machines. However, with power electronics the fast dynamics of controllers and non linearity’s require more detailed state space 132
modelling of loads and the network to understand their dynamic response to the much smaller system time constants [148]. An approach to overcome this limitation is the Component Connection Method (CCM) where the power system components and network dynamics are separately modelled by a set of vectormatrix equations [153]. CCM is a particular form of state space analysis which reduces state equations to lessen the computation burden. The separation allows the interactions and critical parameters to be more easily determined [148]. A state space approach to stability in power electronic grids would require full detail of the dynamics of the mechanical and electrical subsystems involved in the wind farm. In a real system this may not be applicable due to the complexity of wind turbine control and the unavailability of data about these subsystems [152]. EMT simulations use time domain simulations to determine the response of the grid in various grid scenarios. Accurate EMT simulations require full knowledge of the control schemes, component parameters and proprietary information from the vendor of both the wind farm and the inverters. Where possible EMT simulations should be used to verify stability or instability detected by these stability analysis approaches. An approach which can overcome some of the previously mentioned approaches is the impedance based stability analysis of power electronic converter systems, where the stability of the system is predicted at the PCC based on the ratio of input and output impedance of the converter and grid system [154]. In contrast to the state space approach which examines the eigen-properties of the state matrix, the impedance measurement predicts system stability based on the ratio of the output and load impedance. Since models provided by vendors may not provide access to detailed converter control and PLL dynamics this approach allows system planners to determine the stability of power electronic systems even ¨ in cases where parts of the models are black boxes¨. This chapter will investigate the interactions in LFAC transmission system for offshore wind based on the system design presented by the authors in Chapters 4 and 5. The interactions will be examined by impedance analysis. The key contributions of this chapter are the application of the relatively new impedance based stability analysis approach on the LFAC transmission system. 133
This approach accurately predicts the harmonic stability of the LFAC grid in the presence of long HVAC cables by examining harmonic interactions between the onshore BtB converter and the LFAC cable resonances. The introduction of Sub Synchronous Control Interaction (SSCI) in the form of an interaction between the dq control of the onshore VSC and the PLL at the offshore wind turbines. Mitigation techniques for SSCI in the form of control design are proposed and implemented.
6.2
Stability Analysis by Impedance Measurement
Impedance based analysis provides a practical tool for the assessment of stability in power electronics based power systems. The impedance measurement approach separates the system into source and load subsystems and examines the interaction between the two subsystems [154]. The impedances in general are composed of contributions from the converter controllers and the actual physical impedances. The impedance can be measured in the abc (positive and negative sequence) frame [155, 152, 148, 156], or dq domain [157, 158, 159] which may have advantages from the perspective of control analysis. Reference [157] proves mathematically the relationship between the two domains and shows that both can be viewed equally as a method for stability analysis. A disadvantage of using dq impedance models is that the stability analysis requires use of the generalised Nyquist stability criterion and the dq impedance matrix manipulation is complicated [156]. An assumption present in the majority of sequence impedance analysis to date is that the positive and negative sequence impedances of the inverters are decoupled from each other. This is true if the inner current and voltage control loops of the inverters have symmetric structures and equal parameters and if there is no PLL or the PLL has a low enough bandwidth that it’s effect is negligible. Under these conditions impedance measurement for stability has been used to determine the harmonic stability between HVDC converters and offshore wind farms [160, 161] and the stability of systems with multiple power electronic inverters [148, 157, 162]. 134
A comparison of the state space approach and the impedance based approach can be found in [163], concluding that both methods are applicable for the determination of system stability.
The advantages of the impedance based
approach are that the impedance data is measured data from the real system and can potentially be measured on-line [164]. Impedance measurement is a more straightforward approach for power system planners than eigenvalue analysis or CCM as the unavailability of proprietary information from vendors is not a critical issue, provided accurate impedance data is supplied, or there is the ability to take measurements. A disadvantage of the impedance approach is that the stability is not global [163], meaning the impedance approach must consider all possible subsystems. Recent advances in the impedance scan technique have used the impedance based approach and system identification to determine the eigenvalues of the system. This is used as an extension on the impedance measurement approach to provide more complete information about the system and perform eigenvalue analysis [165]. The basis of the impedance measurement based stability criteria is to split the system into a source and load subsystem. The source subsystem of a voltage controlled inverter consists of a Thevenin equivalent circuit with an ideal voltage source in series with an output impedance (Zs (s)).
The load subsystem is
modeled by its load impedance (ZL (s)). Figure 6.1a depicts the equivalent small signal circuit of voltage controlled inverter, typical of a grid forming inverter, for impedance based analysis [154]. For current controlled inverter (grid feeding inverter) based system the source subsystem consists of a Norton equivalent circuit with an ideal current source in parallel with an output admittance (Ys (s)). The load subsystem is modeled by its input admittance (YL (s)). Figure 6.1b displays the equivalent small signal circuit of a current controlled inverter. In Figure 6.1 Gcl (s) is the closed loop reference to output transfer function which controls the dynamics of the inverters. Equations 6.1 and 6.2 derive the closed loop transfer functions of the inverter small signal systems in Figure 6.1. On the assumption that Gcli (s) and Gclv (s) are independently stable the stability of the output of both the voltage controlled 135
ZS(s)
I1(s)
I2(s) +
𝐺𝑐𝑙𝑣 𝑠
+ _ -
V2(s)
𝑉2∗ (𝑠)
+ YS(s) V1(s)
ZL(s) 𝐺𝑐𝑙𝑖 𝑠
_
𝐼1∗ (𝑠)
(a)
YL(s)
_
(b)
Figure 6.1: Small signal representation of (a) voltage source inverter with a load and (b) current source inverter with a load. inverter and the current controlled inverter is dependent on the minor loop Ys (s) Zs (s) and . Based on these minor feedback gains the stability feedback of ZL (s) YL (s) of the system can be determined. 1 I1 (s) = Gcli (s) ∗ I1 (s) 1 + Ys (s)
(6.1)
1 V2 (s) = Gclv (s) ∗ V2 (s) 1 + Zs (s)
(6.2)
YL (s)
ZL (s)
The source and load impedances and admittances can be found by injecting perturbations at the connection point between the subsystems (PCC). The resulting impedances across a frequency range can be examined to identify potentially unstable frequencies for a wide range of operating conditions.
6.3
LFAC Impedance Measurement Technique
Figure 6.2 represents an extension of Figure 6.1a where the load impedance is replaced by the LFAC cable, the LFAC transformers and the impedance of the current controlled inverter. Figure 6.3 display the small signal representation of the setup to determine the stability of the current controlled inverter, showing the components of the load admittance. The stability of each inverter is assessed separately using the appropriate circuit setup.
136
Zc(s)
I1(s)
Zcable(s)
I2(s)
+
+
V1(s)
𝐺𝑐𝑙𝑖 𝑠 𝐼1∗ (𝑠)
ZL(s)
ZS(s)
∗ + _ 𝐺𝑐𝑙𝑣 𝑠 𝑉2 (𝑠)
V2(s)
_
_
Figure 6.2: Small signal representation of Zs (s) and ZL (s) to find the stability of the LFAC voltage controlled inverter.
I1(s) +
+ 𝐺𝑐𝑙𝑖 𝑠 𝐼1∗ (𝑠)
V1(s) Ys(s) _
V2(s) Ycable(s)
∗ YC(s) + _ 𝐺𝑐𝑙𝑣 𝑠 𝑉2 (𝑠)
_
YL(s)
Figure 6.3: Small signal representation of Ys (s) and Yl (s) inverter with a cable and load. In both cases the load subsystem (ZL (s) and YL (s)) includes the LFAC transmission cable and the LFAC transformers. Similar to Figure 6.1 the stability Zs (s) of the LFAC transmission system depends on the minor loop feedback of ZL (s) Ys (s) and for each inverter. Figure 6.4 shows the single line diagrams of the YL (s) circuit setup to obtain the impedance measurement. Figure 6.4 shows the setup used to obtain Zs and ZL . Figure 6.5 displays the circuit setup used to determine Ys and YL . For both voltage controlled inverter cases (Figures 6.4a and 6.5b) the subsystem is connected to a stiff current source, at 1 pu, corresponding to full loading, at the fundamental frequency of 16.7 Hz (ω0 ). A current perturbation is added at a disturbance frequency of ωd and an amplitude of 0.01 pu to maintain the small signal integrity of the model. The voltages and currents at the input perturbation can be measured and a Fast Fourier Transform (FFT) performed on them to identify the voltage and current components at ωd . 137
Is
1pu ω=ω0
0.01pu ω=ωd
I2
If
+
+
Vs
V2
_
_
ZLf Voltage Controlled Inverter
ZCf
VDC
mV abc
(a)
Current Controlled Inverter
I1
Zcable
0.01pu IL ω=ωd
+
+
V1
VL
_
_
mi abc
+
VDC
Z Lf
_
+ _ 1pu
ω=ω0
(b)
Figure 6.4: Single line diagram of impedance measurement circuit setup to find (a) Zs and (b) ZL . Similarly for the current controlled inverter side (Figures 6.4b and 6.5a) the subsystem is connected to a stiff voltage source and a voltage perturbation is added at ωd and the impedance or admittance is calculated from the measured voltages and currents. Figure 6.6 displays a flowchart of the methodology for performing the impedance measurement to calculate the admittance or impedance as required. Figure 6.7 outlines the control schemes used in this analysis for the current controlled inverter and the voltage controlled inverter. Detailed design of of the current and voltage control blocks can be found in Chapter 4. The parameters used in this analysis are outlined in Table 6.1. In this analysis the transformers are assumed ideal with a step up and down ratio of 2.2:1 and the system is modelled as in Chapter 4 and 5 using an average model of converters. All wind farm inverters are lumped into one inverter to simplify the system.
6.3.1
Impedance Scan of LFAC System
Figure 6.8 shows the positive sequence load and source impedance (Zs and ZL ) of the voltage controlled inverter in the LFAC system. 138
As seen in Figures
Current Controlled Inverter
I1
0.01pu IL ω=ωd
+
VDC
Z Lf
_
+ _ 1pu
ω=ω0
mi abc
(a)
Is + 1pu ω=ω0
0.01pu ω=ωd
Zcable
I2
If +
Vs
V2
_
_
ZCf
ZLf Voltage Controlled Inverter
VDC
mV abc
(b)
Figure 6.5: Single line diagram of impedance measurement circuit to find (a) YL and (b) Ys .
Set ωd frequency array of length n
For n=[1:end]
Simulate with disturbance ωd(n)
Save Is, Vs or IL,VL
Perform FFT and calculate Impedance/ Admittance
No End n?
Yes
Plot Impedance/ Admittance vs. ωd
Figure 6.6: Flowchart methodology for determining impedance and admittance. 139
V2, If
V2, I2
V1, I1
V1, I1 ρ
abc
PLL
dq idq idq ref
ρ Vsdq
dq 0 ref
mdq Current Control Scheme
V2dq Reference Angle Vdq ref
i2dq
abc dq
dq
abc ωPLL
abc
abc
mi abc
mV abc
V2dq
dq
If dq
mdq
Current Control Scheme
idq ref Voltage Control Scheme
(a)
(b)
Figure 6.7: Control schemes of (a) current controlled inverter and (b) voltage source inverter. Table 6.1: LFAC transmission system parameters for impedance measurements. Parameter
Value
Voltage Controller Bandwidth Voltage Controller Kp , Ki Current Controller Bandwidth Current Controller Kp , Ki Filter Inductance (Lf ) Filter Capacitance (Cf ) Cable Inductance Cable Capacitance Cable Length Transformer turns ratio VDC Vsd ref , Vsq ref Id reference
334.2 rads−1 0.0113, 1.2628 1000 rads−1 85.77, 181.82 85.8 mH 4.03 µF 222.8 µH/km 198 nF/km 150 km 2.2:1 400 kV 100 kV, 0 V 1000 A
6.4a and 6.7b the voltage controller source impedance is composed of a voltage controller, an inner current controller, a voltage controlled VSC and an LC filter. The load impedance (Figure 6.4b) is composed of the LFAC cable, the wind farm inductance, the current controlled wind farm inverter and its control. The impedances shown here are 3 phase positive sequence impedance scans, in other words they are in the abc frame. The controllers however, as can be seen in Figures 6.7a and 6.7b operate in the dq frame. In order to give some insight into the origin of the impedance curves and as a form of validation the impedance scans are compared to the physical impedances of the cable, transformers and filters connected to an open circuit, without the
140
Magnitude (dB) Phase (deg)
60 40 20 0 1
2
10
ZS ωc: 669 rad s−1
180 90 0 −90 −180
3
10
1
10
ZS ωc: 334 rad s−1
ZL
2
10
3
10 Frequency (Hz)
10
Figure 6.8: ZL and Zs for LFAC voltage controlled inverter. influence of converter control. In Figure 6.9 the ZL is compared the impedance of the cable, transformers wind farm inductance and VSC, without the influence of the controllers. It can be clearly seen from Figure 6.9 that the impedance scan matches the physical impedance outside of the bandwidth of the current control loop. Within the current control bandwidth the impedance rises as frequency approaches zero, which is expected for a current controlled inverter. For an ideal current controller the impedance at the fundamental frequency is equal to the unloaded cable impedance, as at this frequency the controller allows no disturbance current. The first LC resonance associated with Lf and the cable capacitance falls within the current control bandwidth and is therefore not present in the impedance
Magnitude (dB)
measurement as it has been controlled out. 60 40 20 Current Controller Bandwidth
0
1
Phase (deg)
10 180 90 0 −90 −180
ZL
10
2
Impedance of Lf & Cable
1
10
10
3
Unloaded Cable impedance
2
10 Frequency (Hz)
10
3
Figure 6.9: Comparison of directly measured impedance of 150 km cable and wind farm inductance with impedance ZL .
141
Similarly Figure 6.10 displays the impedance of Zs compared to the impedance of the LC filter.
At frequencies above the current controller bandwidth the
impedance is dominated by the capacitor in the LC filter. Again within the current control bandwidth the current controller dominates the dynamic impedance. The influence of the voltage controller can be seen where Zs tends to go to zero at the fundamental, 16.7 Hz. This is due to the integrator in the voltage controller and the fact that at the fundamental frequency in the abc frame, the dq component is at 0 Hz. Therefore 1/s becomes infinite, implying infinite gain which results in zero impedance. Below the fundamental frequency the frequency in the dq frame is negative which is treated the same as the equivalent positive one by the voltage controller and the impedance from zero to the fundamental mirrors the impedance from the fundamental to twice the fundamental. For example, a disturbance at ωd = 5 Hz, corresponds to -11.7 Hz in the dq frame. The voltage controller responds in the same way as for 11.7 Hz. Converting this back to the abc frame
Magnitude (dB)
gives the same response as ωd = 28.4 Hz. 60 40 20 0
Current Controller Bandwidth
Voltage Controller Bandwidth 1
Phase (deg)
10 180 90 0 −90 −180
10
ZS impedance measurement
1
10
2
10
3
Impedance of LC filter
2
10 Frequency (Hz)
10
3
Figure 6.10: Comparison of directly measured impedance of LC filter with impedance Zs . Figure 6.8 shows the impact of changing the voltage control bandwidth on the source impedance. The control bandwidth is changed from 334 rad s−1 to 669 rad s−1 . It can be seen that in the lower frequency range the impedance is slightly reduced with a higher voltage control bandwidth. Outside of the current control bandwidth the impedance returns to the physical impedance of the LC filter.
142
6.4
Harmonic Stability of Voltage Controlled Inverter
Harmonic instability in power electronic grids can be caused by a combination of factors.
These include fast inner current or voltage controllers and high
frequency switching harmonics interacting with passive elements in the grid such as capacitors, filters or underground cables [156]. The aspects of interest in a LFAC grid are the current and voltage controllers of the onshore voltage controlled inverter, the LC output filter and the LFAC cable. The stability of the current controlled inverter will be assessed later in the chapter. In this harmonic analysis the stability of the voltage controlled inverter is analysed by examining the minor loop response of ZL and ZS . The load impedance consists of the LFAC cable and the wind farm current controlled inverter. It is assumed in this harmonic stability analysis that the PLL bandwidth at the wind turbines is low enough that it does not cause any sequence or frequency coupling at frequencies above 100 Hz, which are the frequencies of interest for harmonic instability. The parameters used in the following analysis are the same as Table 6.1 unless otherwise stated in Table 6.2.
6.4.1
Impact of Filter Capacitance
Initially the current controller bandwidth for the voltage controlled inverter is set to 2000 rads−1 . Figure 6.11 displays the load and source impedances for the voltage controlled inverter with a 100 km cable. To illustrate the effect of filter parameters, in Figure 6.11 the filter capacitance Cf is changed from 4 µF to 11 µF. This has the impact of decreasing Zs above the LC corner frequency and therefore causing Zs and ZL to cross at more points, increasing the chance of the system becoming unstable when connected to the load subsystem which includes the LFAC cable. Figure 6.12 shows the minor loop response of both scenarios. ZS The minor loop magnitude is the ratio of and the phase is the difference of ZL the angles at the given frequency. For the minor loop response and therefore
143
Magnitude (dB)
60 40 20 0 1
10
Phase (deg)
180
10
Zs Cf: 11 µF
90
2
3
10 ZL 100 km
Zs Cf: 4 µF
0 −90 −180 1
2
10
3
10 Frequency (Hz)
10
Figure 6.11: Impedance scans of voltage controlled side with changing filter capacitance compared to wind farm impedance with 100 km cable with current controller bandwidth 2000 rads −1 . the inverter to be stable, when the minor loop magnitude is equal to 0 dB, i.e. |ZS | = |ZL |, the phase must be greater than -180◦ .
Magnitude (dB)
60 40
10
20
5
0
0
−20
−5
−40 1 10
2
3
10
10
1370
1450
Phase (deg)
180 −178
90 0
−180
−90
Minor Loop Cf: 11µF
−180
Minor Loop Cf: 4µF 1
10
−182
2
10 Frequency (Hz)
3
10
1370
1450
Figure 6.12: Minor loop responses varying filter capacitance with 100 km cable. It can be seen from the minor loop plot that the combined impedance crosses 0 dB at the frequencies and phases outlined in Table 6.2 and that the 11 µF capacitor 144
causes an instability at 1372 Hz. Decreasing the capacitance to 4 µF increases the impedance Zs , thereby increasing the minor loop response and removing the instability.
Impact of Current Control Bandwidth
Magnitude (dB)
6.4.2
60 40 20 0 1
10
Phase (deg)
180
10
Zs Low control BW
2
Zs High Control BW
3
10
ZL 100km
90 0 −90 −180 1
10
2
10 Frequency (Hz)
3
10
Figure 6.13: Impedance scans of voltage controlled with 11 µF Cf varying current controller bandwidth compared to wind farm impedance with 100 km cable. Figure 6.13 displays the impedance of the system again with a 11 µF capacitor. The impact of changing the current controller bandwidth is shown for two bandwidths, low (1000 rads−1 ) to high (2000 rads−1 ) for the voltage controlled inverter. It can be clearly seen in Figure 6.14 that the minor loop with high current controller bandwidth is unstable at a frequency of 1372 Hz and is stable for all frequencies with a low current control bandwidth. This shows the impact control parameters can have on harmonic stability. The minor loop response does cross 0 dB at other frequencies, however the phase in those cases is not below -180◦ . The frequencies at which the minor loop responses are equal to 0 dB and the corresponding phase angles are outlined in Table 6.2. Time domain simulations are performed to verify the harmonic stability analysis. The simulations are performed on the LFAC transmission system which 145
Magnitude (dB)
40
Minor loop high BW Minor loop low BW
20
2
0
0
−20
−2 1
2
10
Phase (deg)
4
10
10
−4
3
1370
1390
1370
1390
−176
180 90
−180
0 −184
−90 −180 1
2
10
3
10 Frequency (Hz)
10
Figure 6.14: Minor loop responses with varied current controller bandwidth with 100 km cable, unstable for high current controller bandwidth and stable for low current controller bandwidth. has been outlined in Section 4.4 and Figure 5.17. The offshore wind farm is connected to shore via a LFAC cable. Onshore the BtB converter consists of the voltage controlled inverter on the LFAC side and a DC voltage controlled power port on the 50 Hz side. The inner current and outer voltage controllers are as outlined in Figures 6.7a and 6.7b and the DC voltage controller is designed as in Figure 4.6 and average models of the converters are used. Figure 6.15 shows the three phase circuit setup used to perform the simulations. Switches
DC Source
Current Controlled Inverter
Lwf
Cable Model
Lf Cf
mi abc
Voltage Controlled Inverter
Controlled DC Power Port
mv abc
mvdc abc
LF_50
50 Hz AC grid
Figure 6.15: Three phase circuit layout for harmonic stability time domain simulations. Initially the LFAC cable is not connected to the BtB converter. The voltage controller brings the AC voltage at the terminals of the VSC to 100 kV. At t = 0.3 s the switches are closed, LFAC cable is switched into service and the offshore
146
wind farm is connected to the onshore grid. This is done to allow any startup transients to dissipate and show that the system has no harmonic instability without the cable connected. Figure 6.16 displays the results of the unstable case in Figure 6.14. The LFAC voltage and current at the voltage controlled inverter terminals is shown, with the FFT of each below. The FFT is taken for the first 10 cycles (0.6 s) after the cable is switched in. The minor loop plot crosses 0 dB at 1370 Hz with a phase of -182◦ indicating that the voltage controlled inverter will be unstable. It can be seen from Figure 6.16 that the system is unstable and has a large high frequency harmonic instability at 1370 Hz. Less significant harmonic components can be seen in the current at the other points where the source and load impedance cross
100 0 −100
Current Mag (% of (kA) fundamental)
Mag (% of fundamental)
Voltage (kV)
each other.
0.3 20 10 0 0
0.35
500
1000
0.4 Time (s)
0.45
1370 2000 Frequency (Hz)
0.5
2500
3000
2 0 −2 0.3 60 40 20 0 0
0.35
500
1000
0.4 Time (s)
1370 2000 Frequency (Hz)
0.45
0.5
2500
3000
Figure 6.16: Voltage, Current and FFT of Voltage showing harmonic instability for 11µF capacitor and 100 km LFAC cable with a current control bandwidth of 2000 rads1 . Figure 6.17 shows the response of a stable LFAC system for the case with lower current control bandwidth in Figure 6.14 without any harmonic instability present. The cable is connected and after a brief transient normal operation begins and the offshore wind farm is connected to the grid. It can be seen from the FFT of the current that there are harmonic components in the initial transient at all the frequencies which the source and load impedance cross in Figure 6.13. 147
Voltage (kV)
Current Mag (% of (kA) fundamental)
Mag (% of fundamental)
100 0 −100 0.3 10 5 0 0
0.35
500
1000
0.4 Time (s)
0.45
1500 2000 Frequency (Hz)
0.5
2500
3000
2 0 −2 0.3 10 5 0 0
0.35
500
1000
0.4 Time (s)
1500 2000 Frequency (Hz)
0.45
0.5
2500
3000
Figure 6.17: Voltage, Current and FFT of Voltage showing for 11µF capacitor and 100 km LFAC cable with a current control bandwidth of 1000 rads1 . Table 6.2 summarises the responses shown in Figures 6.13 - 6.19, outlining the parameters changed and the responses observed at the stability points.
6.4.3
Impact of Cable Length
It has been seen in Figures 6.13 and 6.11 that increasing current control bandwidth and filter capacitor size in isolation can have an adverse effect on stability. However, using the design method developed in Chapter 4 and 5 the harmonic stability of the system is improved. Using this method the impedances in Figure 6.18 are obtained. The current controller bandwidth is varied as in Figure 6.13 however the combination of a filter capacitance designed in Chapter 4 has increased the stability of the voltage controlled inverter. This can be seen by the minor loop response in Figure 6.19 in which the phase does not cross -180◦ for either case. Figure 6.20 shows the source and load impedance when the controller has been designed for the specific cable length as in Chapter 5 with a current control bandwidth of 1000 rads−1 .
Interestingly increasing the cable length appears
to have a positive impact on harmonic stability in the LFAC case. For longer cables the resonant frequencies decrease to below or close to the current controller bandwidth, meaning that the source impedance is higher at the cable resonant
148
Table 6.2: Details of parameters used and the frequencies where minor loop responses are 0 dB below 1500 Hz. Zs Current Control BandWidth, (Kp , Ki )
Figure
|
ZL
Zs | = 0 dB ZL
Frequency (Hz)
Angle (degrees)
100 km
689 830 1351
-174 -20 -177 -172 -28 -182
Cf
Cable Length
11 µF
1000 rad s−1 (85.78, 181.8)
6.12, 6.14
2000 rad s−1 (171.54, 363.6)
11 µF
100 km
700 818 1370
6.12
2000 rad s−1 (171.54, 363.6)
4 µF
100 km
1450 1525
-168 -45
6.19
2000 rad s−1 (171.54, 363.6)
150 km
1000 1461 1525
-90 -155 -35
6.19
1000 rad s−1 (85.78, 181.8)
150 km
1020 1461 1525
-90 -155 -35
Magnitude (dB)
6.14
4 µF
4 µF
60 40 20 0 1
2
10
Phase (deg)
180
ZS High Control BW
10
ZS Low Control BW
3
10
ZL 150 km
90 0 −90 −180 1
10
2
10 Frequency (Hz)
3
10
Figure 6.18: Impedance scans of voltage controlled with 4 µF Cf varying current controller bandwidth compared to wind farm impedance with 150 km cable.
149
Magnitude (dB)
60 40 20
Minor loop high BW Minor loop low BW
0 −20 −40 1 10
2
3
10
10
Phase (deg)
180 90 0 −90 −180 1 10
2
10 Frequency (Hz)
3
10
Figure 6.19: Minor loop responses varying current controller bandwidth with 150 km cable. frequencies therefore Zs and ZL do not cross at frequencies where the combined phase is close to -180◦ . Higher frequency resonances for longer cables tend to be more damped than lower frequency resonances meaning that the load phase at higher frequencies is not close to 90◦ . This means the minor loop will not cross -180◦ . To conclude it is clear that control parameters, particularly current control bandwidth can have a negative effect on harmonic stability by varying the source impedance ZS . The voltage control bandwidth has little impact on harmonic stability as it’s influence is at lower frequency. In the LFAC system ZL will generally not change at high frequencies as it is only influenced by cable length. To mitigate harmonic stability issues ZS can be adapted, either by varying the filter components, or the controller bandwidths. A proportional resonant filter could help mitigate harmonic stability issues however perfect knowledge of the resonant frequencies is required and the movement of resonant frequencies due to changes in grid conditions must be taken into account. It is important when designing LFAC transmission systems that accurate harmonic studies are performed in the planning phase. Since all the control parameters may not always be known the
150
Magnitude (dB) Phase (deg)
60 40 20 0 90
ZS 100 km
ZL 100 km
0
Phase (deg)
Magnitude (dB)
−90 60 40 20 0 90
ZS 150 km
ZL 150 km
Z 200 km
Z 200 km
0
Magnitude (dB)
−90 60 40 20 0
S
Phase (deg)
90
L
0 −90 1
10
2
10 Frequency (Hz)
10
3
Figure 6.20: Source and load impedance for 3 cable lengths using controller design procedure in Chapter 5. impedance scan approach provides system planners with an effective method to determine potential harmonic resonances occurring in the system.
6.5
Analysis of Frequency Coupling
The basis behind the accuracy of the impedance measurement approach in the previous section where a single perturbation is injected is that the positive and negative sequences are decoupled [155, 152, 148, 156]. The positive and negative sequences can only be considered decoupled if inverter control schemes for current and voltage controller have symmetrical structures and equal parameters and if there is no PLL present, or the PLL has sufficiently low bandwidth so as to not effect the impedance measurement [157, 152, 166]. These couplings although they
151
can be very small are important to the stability of the converter and should be taken into account [166]. Sources of sequence and frequency coupling in converter based systems are listed below [157]: • The presence of a PLL. • Current controllers with unequal control structures or parameter values in both the d and q channels (i.e Kd 6= Kq ). • External DC link voltage control systems on one of the converters. • Active and Reactive power controllers. In the LFAC system the only possibility for frequency coupling is the PLL, as the controller parameters and schemes are the same for each d and q channel of the control. The DC link control is on the onshore side of the BtB converter and has been removed from the impedance analysis and replaced by a constant DC source. The active and reactive power set points are provided by a fixed current reference. To illustrate the presence of frequency couplings a 10 Hz voltage disturbance is added to the system in Figure 6.4b. Figure 6.21 shows the voltage, current and measured PLL frequency resulting from the disturbance. The magnitude of the disturbance is at 0.01 pu and cannot be clearly seen on Vabc and Iabc however it can be seen on the PLL frequency which has a minor oscillation at 6.7 Hz, verifying the presence of the disturbance in Vabc . The FFT of the current in response to the disturbance is shown in Figure 6.22. As expected there is a component of current at 10 Hz. Added to this there is another component at 23.4 Hz. This can be explained by the frequency coupling effect. For a 10 Hz positive sequence ωd the dq component is 10 − 16.7 = −6.7 Hz, hence the 6.7 Hz disturbance in the PLL. When the dq is translated back to the abc frame it now has two frequency components due to the frequency coupling effect of the PLL. Therefore it has components at positive sequence −6.7 + 16.7 = 10 Hz and negative sequence −6.7 − 16.7 = −24.4 Hz. The PLL introduces a non-linearity into the system, resulting in two frequency outputs for one disturbance frequency input. 152
For disturbance frequencies in
Voltage (pu) Current (pu) PLL Frequency (rad/s)
1 0 −1 1 0 −1
106
104.9 104 1
1.25
1.5 Time (s)
1.75
2
Figure 6.21: Voltage, Current and PLL frequency for a 10 Hz 0.01 pu voltage disturbance injection.
Current (A)
8 6 4 2 0 0
5
10
16.7 Frequency (Hz)
23.4
30
Figure 6.22: FFT of current during a 10 Hz 0.01 pu voltage disturbance showing frequency coupling. the dq frame within the bandwidth of the PLL there will be two frequency components in the output measurement. Therefore it is clear that to create an accurate impedance plot at frequencies below approximately 100 Hz is not possible with the previous method [166]. Adapted methods for accurately measuring the impedance with two disturbance injections to capture the coupling effect and accurately predict the stability of the inverter at lower frequencies have very recently been developed [152, 157]. These methods determine where the coupled frequency will occur and inject a secondary disturbance to obtain the response at the coupling frequency. They then use complex matrix manipulation to determine the impedance at one disturbance frequency and generate positive, negative and coupling sequence (p-n and n-p) impedances. Developing these complex impedance scan techniques and applying them to frequency and sequence coupled 153
systems including PLLs is an ongoing and relatively young research topic which will become increasingly important in inverter based power systems. Although the stability at lower frequencies cannot be accurately predicted the impedance scan technique developed in the previous sections may still be used to accurately predict the stability of the current controlled inverter at higher frequencies.
6.6
Current Controlled Inverter Stability
Figure 6.23 show the source and load admittance of the current controlled inverter system which has the PLL included in the source admittance. Figure 6.24 show the minor loop of the admittance’s in Figures 6.23 which is equal to the ratio of the admittance and the combination of the phase angles. It can be clearly seen from the combined phase in Figure 6.24 in the high frequency range that the current controlled inverter has no stability issues resulting from the LFAC cable.
Magnitude (dB)
0
−50
−100 1
10 YS 8Hz PLL
10
YL ωc: 334 rad s−1
YS 4 Hz PLL
180 Phase (deg)
2
10
3
YL ωc: 145 rad s−1
90 0 −90 −180 1
10
2
10 Frequency (Hz)
10
3
Figure 6.23: Source and load admittance showing influence of voltage control bandwidth and PLL bandwidth. The factors which effect the source admittance in the lower frequency range are the PLL, the current controller and the inductive filter. The effect of the
154
Magnitude (dB)
0 −50 −100
1
2
Phase (deg)
10
10
10
3
180 0 −180 1
10
2
10 Frequency (Hz)
10
3
Figure 6.24: Minor loop response of Figure 6.23 with 8 Hz PLL. PLL is to cause a decrease in the source impedance resulting in an increased admittance [167]. As seen in the previous section increasing current controller bandwidth decreases impedance, thereby increasing admittance.
The factors
which impact the load admittance are the voltage and current controllers and the LFAC cable. Decreasing the voltage control bandwidth decreases the load admittance. Although this method is not accurate in the lower frequency range as it does not take into account the frequency coupling, it has some merit in distinguishing frequency ranges which may be of interest for further study. It can be seen from Figure 6.23 that the effect of higher PLL bandwidth and lower voltage control bandwidth moves the YS and YL closer to each other at low frequencies. This suggests that there is potential for oscillations at very low or sub synchronous frequencies. The following sections will examine the sub synchronous stability of the current controlled inverter using detailed three phase simulations with average models of inverters.
6.6.1
Sub-Synchronous Control Instability
The interaction studied here is a sub synchronous resonance caused by an interaction between the voltage controller on the onshore BtB converter and the PLLs in the offshore wind turbine which have the task of locking onto the grid voltage and providing the angular information of the three phase grid. The PLL is also regulating the output q component of the voltage to zero by changing
155
the angle, meaning that it has an indirect impact on the voltage it is measuring through control of the converter at the wind turbine. The trade-offs discussed in Chapters 4 and 5 where increasing the current controller bandwidth has knock on effects on increasing the PWM frequency are also an issue here. There is a minimum ratio required between the current controller bandwidth and the PWM bandwidth. Likewise it has been observed that there is a ratio between the voltage controller bandwidth and the PLL bandwidth. If the voltage controller bandwidth is too close to the PLL bandwidth interactions can occur when disturbances are present in the system [158, 168]. A typical disturbance could be a fault, or a sudden increase or decrease in power or voltage. If the voltage controller does not control the phase voltage to a stable steady state value after a disturbance before the PLL control picks up the disturbance, then the PLL will begin to oscillate, changing its angle to regulate Vq to zero. The system then becomes unstable if the voltage controller is unable to regain control of the voltage after the PLL has begun to oscillate. The stability of the PLL is affected by a few factors including increased current level and decreased grid impedance [169]. Weaker AC systems are more reliant on control and therefore the possibility for control instability is greater in weak AC systems [150].
6.6.2
Simulation of SSCI
Simulations are performed on the LFAC transmission system to identify SSCI oscillations occurring due to interactions between the PLL at the wind farm and the outer voltage controller of the onshore BtB converter. The simulation is first performed with the PLL design in Chapter 4 with a 8.75 Hz PLL bandwidth. This corresponds to almost half of the fundamental frequency of the LFAC system. Considering a case where the inner current converter control time constant ti is be set to a value of 2.3 ms, resulting in an open loop current controller bandwidth of 435 rad s−1 . Following the design criteria for the BtB converter grid forming control, from Equation 4.39 the voltage control bandwidth is calculated to be 145 rad s−1 . The ratio of voltage controller bandwidth to PLL bandwidth is 2.63:1.
156
In simulation the wind farm is connected and the voltage is increased to 100 kV.
(rad/s)
1 0 −1 0 1 0 −1 0 1.5 1 0.5 0 0
0.5
1
1.5
2
2.5
0.5
1
1.5
2
2.5
0.5
1
1.5
2
2.5
0.5
1
1.5
2
2.5
120 100 0
Mag (% of Fundamental)
ωPLL
Power (pu)
Current Voltage (pu) (pu)
Active power is then increased from 0 to 1 pu and the responses are observed.
20 10 0 0
5
11.7
Time (s)
16.7 21.7 Frequency (Hz)
30
40
Figure 6.25: Voltage, current, power, PLL frequency and FFT of current for unstable case. Figure 6.25 displays the results of this initial simulation showing instability in the voltage and current. It can be seen that the PLL begins to oscillate at 5-6 Hz. There is a large sub synchronous oscillation in the voltage and current with components at 12-14 Hz and 20-22 Hz confirmed by the FFT of the current in Figure 6.25. This controller design in isolation will work adequately for a LFAC transmission system however when a PLL with a relatively high bandwidth is adopted at the wind turbines interactions can occur. To verify that the oscillation seen in Figure 6.25 is indeed a control interaction and not a problem with the stability of the individual converters on either end, the PLL is removed from the wind farm side. Figure 6.26 shows the simulation without a PLL. It can be seen that the converter
157
Voltage (pu)
1 0 −1 0 1 0 −1 0
1
1.5
2
2.5
0.5
1
1.5
2
2.5
1 0.5 0 0
0.5
1
1.5
2
2.5
120 100 0
0.5
1
1.5
2
2.5
10
20 30 Frequency (Hz)
40
50
(rad/s)
Mag (% of Fundamental)
ωPLL
Power (pu)
Current (pu)
0.5
20 10 0 0
Time (s)
Figure 6.26: Voltage, current, power and PLL frequency for case without PLL. control is stable and the voltage and current are both stable, therefore proving the PLL is involved in the instability seen in Figure 6.25.
6.6.3
Mitigation of SSCI
Typical solutions which can be adopted are to increase the bandwidth of the voltage controller, thereby decreasing the likelihood that the PLL will pick up the disturbance in time to begin to oscillate. Another proposed solution is to decrease the PLL bandwidth significantly so that it is unresponsive to the changes in voltage. Increased PLL bandwidth may be desirable for applications where an accurate frequency measurement is required to provide a response, such as in the provision of frequency response. For example where the offshore wind farm is required to provide a power response based on a frequency reduction during a frequency event onshore. For instance, if the PLL was required to follow the grid frequency closely to provide frequency response from the wind turbines for the
158
onshore grid, limiting the bandwidth of the PLL would limit the effectiveness of this approach. Decrease PLL Bandwidth Figure 6.27 displays the open loop frequency responses of the PLL varying the bandwidth. The bandwidth of each PLL can be seen however it is clear that the crossover frequency is not clearly defined. The PLL design has a significant flat portion along the line at 0 dB, particularly in the 55 rad s−1 case. Beyond this frequency the closed loop gain is below 0 dB. The negative spike at 33.4 Hz is due to the design to eliminate the double pole at the 3rd harmonic in the abc reference frame, which corresponds to the 2nd harmonic in the dq reference frame, as designed in Chapter 4.
Magnitude (dB)
50
−1
55 rad s
PLL
−1
25 rad s
PLL
0 −50
Phase (deg)
−100 0 −90 −180 −270 0 10
1
2
10
10
10
3
Frequency (rad/s)
Figure 6.27: PLL open loop response for different PLL bandwidths. In Figure 6.28 the dq voltage, current and PLL frequency are shown for two simulations where the PLL bandwidth is changed from 55 rad s−1 to 25 rad s−1 . All other parameters including voltage control bandwidth are the same as Figure 6.25. It can be clearly seen that decreasing the PLL bandwidth (thereby increasing the ratio of voltage controller bandwidth to PLL bandwidth) increases the stability of the system.
159
(pu)
(pu)
Id
Vdq
1.5 1 0.5 0 −0.5 0 2
(rad/s)
1
1.5
1 0 0
ωPLL
0.5
2
55 rad s−1 PLL 0.5
1
0.5
1
2.5
3
25 rad s−1 PLL
1.5
2
2.5
1.5
2
2.5
120 100 0
Time (s)
Figure 6.28: Vdq , Id and PLL frequency for two cases with changing PLL bandwidth. In the case with the highest PLL bandwidth, the same case as Figure 6.25, the PLL and the dq components oscillate at approximately the crossover frequency of the PLL. The crossover frequency is 55 rad s−1 (8.75 Hz) however the oscillation occurs at 4.5 Hz. This is due to the flat nature of the PLL open loop response around the designed crossover frequency and how close the PLL bandwidth is to the fundamental frequency, causing the closed loop response to reduce very quickly at the crossover frequency. When this unstable oscillation is translated from the dq frame to the abc frame the oscillation manifests itself at two frequencies, one at the fundamental plus the oscillation frequency in the dq frame and one at the oscillation frequency minus the fundamental. This can be seen in Figure 6.25 where the oscillations occur around 12-14 Hz (4.5-16.7) and 20-22 Hz (4.5+16.7). Increase Voltage Control Bandwidth In Figure 6.29 the PLL bandwidth remains at 55 rad s−1 and the voltage controller bandwidth is adjusted. It can be clearly seen that once the ratio of voltage controller bandwidth to PLL bandwidth is above 3:1 the stability of this system can be ensured.
160
(pu)
(pu)
Id
Vdq
1.5 1 0.5 0 −0.5 0 2
(rad/s)
1
1.5
2
2.5
0.5
1
1.5
2
2.5
1 0 0
ωPLL
0.5
120
ωc = 145 rad s−1
ωc = 165 rad s−1
ωc = 220 rad s−1
100 0
0.5
1
Time (s)
1.5
2
2.5
Figure 6.29: Vdq , Id and PLL frequency for three cases changing voltage control bandwidth. In Figure 6.30 the voltage controller bandwidth is increased to 220 rad s−1 so that the ratio of voltage control bandwidth to PLL bandwidth is now 4:1. It can be seen that for the same simulation the system remains stable during the power increase and the PLL frequency remains constant at the fundamental frequency.
6.6.4
Hardware Verification of SSCI
The SSCI observed in the previous section can be recreated in the hardware system presented in Chapter 5 (Figure 6.31) by reducing the voltage control bandwidth of the BtB converter to 111.3 rad s−1 . This significantly reduces the ratio between voltage controller bandwidth and PLL bandwidth to almost 2:1. The PLL is not unstable at higher voltage controller bandwidths because the current level is not at its maximum, to protect the hardware equipment from the oscillations. It can be seen that the PLL and Vdq oscillate at approximately 5.5 Hz. This oscillation can then be clearly seen on the hardware voltage and current. It should be noted that this scenario in the context of LFAC transmission is unlikely as decreasing the voltage control bandwidth so far is unrealistic. However
161
Voltage (pu) Current (pu) Power (pu)
ωPLL Mag (% of Fundamental) (rad/s)
1 0 −1 0 1 0 −1 0 1.5 1 0.5 0 0
120 100 0 20 10 0 0
5
0.5
1
1.5
2
2.5
0.5
1
1.5
2
2.5
0.5
1
1.5
2
2.5
0.5
1
1.5
2
2.5
21.7 30 Frequency (Hz)
40
50
11.7
16.7
Time (s)
Figure 6.30: Voltage, current, power, PLL frequency and FFT of current for stable case with voltage control bandwidth of 220 rad s−1 . for 50/60 Hz systems with higher bandwidth PLLs (200 rad s−1 approx), SSCI between PLLs and voltage controllers is a real concern. The analysis in the previous section would suggest a minimum ratio of 4:1 for voltage controller bandwidth to PLL bandwidth in power electronic based AC grids. This requires a voltage control bandwidth of 800 rad s−1 . It is therefore imperative that the design choices made at the beginning of projects consider the entire connected system and be aware of the potential for control interaction issues.
6.7
Conclusions
This chapter has examined in detail the stability of a LFAC transmission system via impedance analysis and 3 phase simulations. The concept of impedance scan analysis for stability analysis in a power electronic converter dominated system is introduced. The impedance scan methodology is used to determine the harmonic 162
Voltage (pu)
1 0 −1
Vdq (pu)
Current (pu)
91.9 1
92.1
92.2
92.3
92.4
92.5
92.6
92.7
92.8
92
92.1
92.2
92.3
92.4
92.5
92.6
92.7
92.8
0 −1 91.9 1.5 1 0.5 0 91.9
Power (pu)
92
Vdref 92
92.1
92.2
92.3
92
92.1
92.2
92.3
92.4
Vd
92.5
92.6
92.7
92.8
92.4 92.5 Time (s)
92.6
92.7
92.8
Vq
1 0.5 0 91.9
Figure 6.31: Voltage, current, Vdq and power for hardware with voltage control bandwidth reduced to 111.3 rad s−1 . stability of the LFAC transmission system.
The impact of different control
parameters and filter sizes on stability is examined. It is found that decreasing the magnitude of the voltage controlled inverter source impedance by increasing either the current controller bandwidth or the filter capacitor size can have an adverse effect on harmonic stability. It is also found that shorter LFAC cables are more susceptible to harmonic instability than longer cables since with the longer cables the resonant points are at lower frequency and therefore usually within or close to the current controller bandwidth. This causes the source and load impedance scans not to intersect at any frequency where the combined phase may be close to -180◦ . The obvious caveat is that longer cables require significantly more reactive power compensation. Using single perturbation impedance scans for SSCI analysis is found to be inaccurate for determining SSCI events due to the mirror frequency coupling introduced by the non-linearity of the PLL. The stability of the current controlled 163
inverter is then assessed with three phase simulations. The control interaction between the voltage controller and the PLL is explored. It is confirmed that the ratio between the PLL bandwidth and the voltage controller bandwidth is an important ratio to keep in mind when designing these systems. This becomes particularly important when different vendors may be designing the onshore and offshore parts of the system. It is found that reducing PLL bandwidth increases the stability of the system however this may not always be desirable. A trade off exists within the entire design process. As seen in Chapter 5 the current controller bandwidth must be significantly lower than the PWM frequency and the PLL bandwidth must be at least 4 times lower than the voltage controller bandwidth. It is also shown that the instability in the PLL occurs at approximately the crossover frequency of the PLL. This oscillation is then transformed from the dq to the abc frame into two frequency components. The impact the voltage controller bandwidth on stability of the PLL can clearly be seen in Figure 6.17 where the bandwidth is increased to 220 rad s−1 . It is clear there is no substitute for having complete knowledge of the system and performing detailed 3 phase simulation studies and eigenvalue analysis for a range of disturbance scenarios to determine stability issues. However as mentioned this may not always be the case. Impedance based stability analysis can be used in practice as a practical approach to determine the stability of an inverter based system, where complete information of system parameters is not always available. A major problem for installers of offshore wind farms is the black box nature of the PLL and the control around both the wind turbine and the large substation converters. Models will be provided by the manufactures however it is not always possible that accurate PLL bandwidth, or voltage/current controller parameters will be known. It is important for system planners to determine the sub synchronous stability and the harmonic stability of the system in the design stage, so that controls can be adjusted to mitigate these issues.
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CHAPTER
SEVEN CONCLUSIONS AND FUTURE WORK
7.1
Summary and Conclusions
As outlined in Chapter 1, in 2016, offshore wind capacity in Europe consisted of 12,631 MW, with the majority of this connected to onshore grid via HVAC transmission as it is located close to the shore. The industry standard for connecting wind farms from farther offshore is VSC HVDC. HVDC transmission requires an offshore VSC converter station to convert to DC for power transmission. This converter station is large and expensive to build and to maintain. As an alternative, LFAC transmission has been proposed. The key advantage of LFAC compared to HVDC is the removal of the offshore power electronic converter station. This thesis has examined in detail the feasibility of LFAC transmission as a transmission option for offshore wind. In Chapter 2 a review of the past work on LFAC transmission has been summarised. The review concludes that there has been several initial feasibility assessments performed on LFAC transmission, however the literature was lacking an in depth technical analysis of LFAC transmission. In the literature there is a split between researchers proposing the use of a cycloconverter or a BtB VSC based converter as the onshore frequency converter. The differences between the two converter types are addressed and other options such as matrix converters are examined. It is found that the BtB converter is the preferred choice for the 165
onshore frequency converter with it’s associated advantages including independent control over active and reactive power, fault ride through capability and reduced filtering requirement. In Chapter 3 analytical loss models are developed and used to compare HVDC and LFAC for the transmission of offshore wind for wind farms over 100 km from shore. It is found that compared to HVDC the removal of the offshore substation generates significant cost savings for LFAC transmission.
However these are
somewhat offset by the increased cost of transformers and the AC cable. A LCoE analysis including the operation and maintenance costs is used to comprehensively compare HVDC and LFAC at different frequencies to determine the optimum frequency to operate LFAC for various transmission distances. It is concluded that for distances of 100-200 km offshore, lower frequencies in the range 10-20 Hz can have decreased LCoE compared to HVDC. In Chapter 4 the in-depth technical modelling of LFAC transmission is introduced. The initial control blocks including the dq control, PWM and PLL operation. Next the VSC control schemes are introduced and outlined. These include the dq current control scheme, the AC voltage control scheme and the DC voltage control scheme. The design of the LFAC transmission system on a component by component basis is presented and initial simulations are performed to verify the operation of the controllers. A scaled hardware design for an LFAC transmission system for offshore wind farm interconnection is then presented. The design and control of the transmission system is verified firstly in software and then with hardware emulation in the laboratory. It is concluded that the simulation and hardware results are comparable on a millisecond time scale in response to voltage steps, power ramps and power steps validating the accuracy of the simulations and hardware. In Chapter 5 the full LFAC transmission system model is developed to include the LFAC cable and the BtB converter. The LFAC system is an unusual system in that it is a power electronic converter based system with a long HVAC cable connecting the offshore wind farm to shore. Small signal models are developed to improve the BtB converter control from Chapter 4 to account for the connection of 166
a long HVAC cable. The proposed controller design is tested in simulation on an LFAC test system with various parameters accounting for design trade offs between controller time constants, phase margin and switching frequency. The design of the LFAC transmission system and the controller design have been validated in a novel scaled hardware test setup. This direct verification of simulation and hardware experiment shows validation of the scaled up simulations which incorporate all the components of the LFAC transmission system. It is concluded that this control scheme and design, although they are applied to LFAC in this case could have applications in any power electronic grids, like microgrids or offshore AC networks connected to HVDC systems. In Chapter 6 impedance based stability analysis is performed on the LFAC transmission system to determine the harmonic stability. The relatively new impedance based stability approach for grid tied inverters is outlined at the beginning of the chapter and applied thereafter. The method accurately predicts the stability of the LFAC system with different control parameters and filter sizes. It is concluded that in some cases increasing the current controller bandwidth is enough to make the system unstable. It is also found that shorter LFAC cables are more susceptible to harmonic instability than longer cables since with the longer cables the resonant points are at lower frequency and therefore usually within or close to the current controller bandwidth. It is a clear conclusion that small changes in control and component parameters may have a large impact on stability if the system is already close to becoming unstable. Therefore it is clearly important in planning to use the techniques outlined in Chapter 6 to determine the load impedance before designing the source control and filtering. Knowledge of the load impedance scan will provide information for the design of the source impedance profile. The concept of control instability in power electronic grids is then examined with potential for an interaction between the dq control of the onshore VSC and the PLL observed. Mitigation techniques for SSCI in the form of control design are then proposed and implemented. It is concluded that in this system the PLL bandwidth must be at least 4 times lower than the voltage controller 167
bandwidth to avoid SSCI. A clear technical conclusion from this thesis is the potential for stability issues in fully power electronic grids, if they are not designed in a coordinated way, or if new power electronic devices are connected to the system without detailed knowledge of the characteristics of the system being connected. The problems of sub synchronous control interaction and harmonic stability can be avoided with adaptation of converter controls, provided the potential issues are studied. This project has considered the feasibility of LFAC as a transmission option for offshore wind and no conclusion would be complete without addressing that overall point. It is the authors conclusion that LFAC is an economically viable and technically feasible alternative to HVDC for transmission of offshore wind in the range of 100-200 km. LFAC uses proven AC components where expertise from onshore AC systems can be utilised in offshore transmission systems. The converter technology required is the same converter technology as for HVDC, with a slightly adapted topology. The largest barrier the author sees is the supply chain of LFAC components, in particular the offshore LFAC transformer. Manufacturers should have no difficulty producing these, however unless a wind farm developer requests LFAC transmission the components will not be produced. Developers may then opt to choose the more ”available” option of HVDC.
7.2
Contributions
The following are the contributions arising from this thesis. • The collection and critical assessment of the literature surrounding LFAC to assess the work done in previous projects is presented as a contribution. A comprehensive review of the technology, the progress to date and the prospects did not previously exist in the literature. • The techno economic analysis to assess the viability of LFAC transmission as a competitive transmission option compared to HVDC and the assessment of the optimum transmission frequency for LFAC is a contribution to the
168
literature. Previous publications assessed independently LFAC and HVDC and did not include operation and maintenance costs in the analysis. • The full design of an LFAC transmission system including design of the components and the control required is established. Detailed full switching simulations for the LFAC transmission system with a BtB onshore converter are used to test the design. This had not previously been presented in a detailed manor for LFAC with a BtB converter. • The LFAC voltage control of the BtB converter is designed to account for the connection of a long HVAC cable. The key contributions are: 1) The characterisation of the impact of connecting a long AC transmission cable to a VSC and filter system on the VSC voltage control scheme in an LFAC transmission system. 2) The characterisation of the design trade offs between switching frequency, filter capacitance and controller parameters to minimise the amplitude and duration of over voltages during disturbances. • The hardware based verification of the LFAC transmission system design which has not been presented before for a LFAC system with a BtB converter onshore. • The impedance based converter stability analysis applied to the LFAC system. This approach accurately predicts the harmonic stability of the LFAC grid in the presence of long HVAC cables by examining harmonic interactions between the onshore BtB converter and the LFAC cable resonances. The impact of control and system components on stability is also examined. Impedance based stability analysis had not previously been used to determine stability in LFAC grids. • The examination of SSCI in power electronic LFAC grids in the form of an interaction between the dq control of the onshore VSC and the PLL at the offshore wind turbines has not previously been presented for LFAC. Mitigation techniques for SSCI in the form of control design are proposed and implemented. 169
7.3
Recommendations for Future Work
The recommendations for future work arising from this thesis can be divided into two parts: 1) Future work in the development of LFAC transmission and 2) Future work in the development and control of power electronic based grids. 1) In the LFAC transmission system a detailed analysis of the different types of frequency converter topologies including BtB MMC, 2 level VSCs, hexverters and matrix converters would be interesting. The extension of LFAC to multi-terminal is an interesting research area, since the connections are AC the extension to multi terminal is easier than with as DC breakers are not required. This provides an initial advantage to LFAC over HVDC. The issue of the control and operation of a multi-terminal LFAC grid is an interesting topic for further research in the context of an interconnected offshore grid. Another aspect of importance is the fault handling of the LFAC grid. Fault ride through strategies and control need to be developed to ensure that the LFAC system meets the onshore grid codes. The provision of ancillary services such as frequency and voltage support from an LFAC offshore grid is an interesting aspect for further study depending on the requirements of the onshore grid. 2) The interactions between the wind turbines is something which has not been studies in this thesis. Developing this work to determine the stability of individual wind turbines within an LFAC grid could be an interesting piece of future work. An extension of the impedance based stability analysis for power electronic grids in general with a focus on using double injection techniques to accurately predict the stability at lower frequencies where frequency coupling is an issue. An analysis of PLL stability and the effect of different types of PLL on the stability of a power electronic grid is an interesting extension of this work.
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185
Appendix
186
APPENDIX
A CYCLOCONVERTER HARMONIC OUTPUT
A.1
Cycloconverter Output Power Quality
Figure A.1 shows the output of a step down cycloconverter, changing the frequency from 50 Hz to 16.7 Hz. The poor quality and large harmonic content of the produced output wave can be clearly seen. Figure A.2 shows the magnitude of the harmonic order of the harmonic content, with a Total Harmonic Distortion (THD) of 15.24%. Figure A.3 shows the harmonic content of a step up version of the 36 pulse naturally commutated cycloconverter, the THD in this case is 32.57%. It is clear with cycloconverters, especially when stepping up the frequency from the input, that the low order harmonics are substantial. These low order harmonics require significantly large filters to provide a clean and stable output voltage.
187
Figure A.1: Output voltage of step down cycloconverter
Figure A.3: Harmonic content of step up cycloconverter (16.7 Hz to 50 Hz)
Figure A.2: Harmonic content of step down cycloconverter (50 Hz to 16.67)
188
APPENDIX
B MARINE INSTITUTE DATA
Table B.1 shows the Marine Institute wind speed data used in Chapter 3 [122]. Table B.1: Wind Speed data from site in Irish Sea Year
2013
2012
2011
2010
Wind count Normalspeed ised (m/s) count
count
Normalised count
count
Normalised count
count
Normalised count
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
7 70 109 198 390 481 486 623 753 835 823 763 635 518 471 466 341 219 145 110 74 60 38 25 19 8 5 0 1
7.07 70.70 110.09 199.99 393.91 485.82 490.88 629.25 760.55 843.38 831.26 770.65 641.37 523.20 475.72 470.67 344.42 221.20 146.45 111.10 74.74 60.60 38.38 25.25 19.19 8.08 5.05 0.00 1.01
14 67 155 237 361 397 510 648 607 667 636 663 607 509 425 329 286 155 133 81 80 46 16 8 4 5 6 2 0
16.02 76.68 177.40 271.25 413.16 454.37 583.69 741.64 694.71 763.38 727.90 758.80 694.71 582.55 486.41 376.54 327.33 177.40 152.22 92.70 91.56 52.65 18.31 9.16 4.58 5.72 6.87 2.29 0
0 53 182 189 526 320 766 441 469 974 494 1000 369 364 703 292 516 164 142 187 65 83 31 12 12 0 0 0 0
0.00 55.58 190.85 198.19 551.56 335.55 803.23 462.43 491.79 1021.34 518.01 1048.60 386.93 381.69 737.17 306.19 541.08 171.97 148.90 196.09 68.16 87.03 32.51 12.58 12.58 0.00 0.00 0.00 0.00
0 40 97 166 459 291 753 399 458 1022 469 1045 413 349 542 179 279 94 81 103 23 27 8 6 4 5 4 0 1
0.00 47.89 116.13 198.74 549.52 348.39 901.50 477.69 548.32 1223.55 561.49 1251.09 494.45 417.83 648.89 214.30 334.02 112.54 96.97 123.31 27.54 32.32 9.58 7.18 4.79 5.99 4.79 0.00 1.20
Total
8673
8760
7654
8760
8354
8760
7317
8760
189
APPENDIX
C ABB HIPAK IGBT MODULE 5SNE 0800M170100
The switching energy and reverse recovery constants are calculated from the following graphs in the IGBT datasheet [116]. Kon and Kof f are calculated from the slopes of Eon and Eof f respectively in Figure C.1. Krr is calculated from the slope of Erec in Figure C.2.
Figure C.2: Reverse recovery characteristics vs forward current of IGBT
Figure C.1: Switching energy per pulse vs collector current of IGBT
190
APPENDIX
D FAULTS ON LFAC GRID
D.1
LFAC Fault analysis
To further test the LFAC transmission system stability under likely grid conditions a fault analysis is conducted to test the response of the system to faults in the offshore cable. The system is simulated with the parameters in Table 6.1. A number of faults are applied to the receiving end of the LFAC cable. The faults last for two 16.7 Hz cycles. It is worth noting that two cycles in 16.7 Hz lasts 0.12 seconds, compared to 0.04 seconds for two 50 Hz cycles. It is therefore important that the system has the ability to recover quickly, with the increased length of time under fault conditions compared to a 50 Hz system. Figure D.1 shows a 3 phase fault applied at the receiving end of the LFAC cable, the fault lasts for 0.12 seconds. This is the most severe type of fault expected on the system. Once the fault is cleared the controller takes approximately 0.14 seconds to return to a controlled stable state. For the duration of the recovery the voltage is at 2 pu. In this case some controlled fault ride through may need to be established to make the system robust to a 3 phase fault. Once the fault recovers there is a large surge of power as the system returns to transmitting full power. Figure D.2 shows a 2 phase fault applied at the receiving end of the LFAC cable, the fault lasts for 0.12 seconds. After the fault is cleared the LFAC system returns to a controlled state in under one cycle. 191
0 −200
Current (kA)
Voltage (kV)
200
20 0
Power (MW)
dq Voltage (kV)
−20
300 200 100 0 −100
0 −2000 −4000 0.5
0.875
1.25 Time (s)
1.625
2
200 0 −200
Current (kA)
Voltage (kV)
Figure D.1: Vabc , Iabc , Vdq and active power at the onshore point of connection during a 3 phase fault on the LFAC cable.
20 0
Power (MW)
dq Voltage (kV)
−20
300 200 100 0 −100
0 −2000 −4000 0.5
0.875
1.25 Time (s)
1.625
2
Figure D.2: Vabc , Iabc , Vdq and active power at the onshore point of connection during a fault on phases A and B of the LFAC cable. Figure D.3 shows a single phase fault applied at the receiving end of the LFAC cable, the fault lasts for 0.12 seconds. Similar to a two phase fault the system deals well with the fault and after the fault is cleared the system becomes stable after less than half a cycle. There is also a much lower initial spike in current feeding the fault as expected for a single phase to ground fault. When a fault is applied to the onshore system the LFAC controlled system continues to feed power to the onshore grid through the DC link. The DC link 192
Voltage (kV)
200 0 −200
Current (kA)
10 0
dq Voltage (kV)
−10 300 200 100 0 −100
Power (MW)
500 0 −500 0.5
0.875
1.25 Time (s)
1.625
2
Figure D.3: Vabc , Iabc , Vdq and active power at the onshore point of connection during a fault on phase A of the LFAC cable. responds to an onshore fault by increasing initially and then decreasing the voltage. However the LFAC side remains stable and connected, verifying that even with disturbances on the onshore grid and on the DC link the LFAC grid will remain controlled.
D.1.1
Conclusion
A fault on the LFAC system lasts longer than a fault on a 50 Hz system which is potentially a problem for a LFAC system, however it is anticipated that the LFAC system connected to a BtB converter with appropriate fault ride through control and braking resistors in place fault ride through of a LFAC transmission system should not be an issue.
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