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Three-Phase Grid-Connected PV System With. Active And Reactive Power Control Using dq0. Transformation. Mateus F. Schonardie, Adriano Ruseler, Roberto ...
Three-Phase Grid-Connected PV System With Active And Reactive Power Control Using dq0 Transformation Mateus F. Schonardie, Adriano Ruseler, Roberto F. Coelho and Denizar C. Martins Federal University of Santa Catarina, Department of Electrical Engineering, Power Electronics Institute [email protected], [email protected], [email protected], [email protected]

Abstract- This paper presents a three-phase grid-connected photovoltaic generation system with unity power factor for any situation of solar radiation. The modelling of the PWM inverter and a control strategy using dq0 transformation are proposed. The system operates as an active filter capable of compensate harmonic components and reactive power, generated by the loads connected to the system. An input voltage clamping technique is proposed to control the power between the grid and photovoltaic system, where it is intended to achieve the maximum power point operation. Simulation and experimental results are presented to validate the proposed methodology for grid connected photovoltaic generation system.

I.

In order to achieve the maximum power point (MPP) operation an input voltage clamping technique is proposed for the inverter. To validate the proposed methodology some simulation and experimental results are presented.

INTRODUCTION

The works on photovoltaic distributed generation systems, such as photovoltaic solar cells connected to the power grid, has increased in the last decades due to need of supplying the world rise demand for electric power. Several papers have been published with varied topologies and control strategies for three-phase systems [1], [2], [3], [4], [5], [6], [7]. There are some advantages that have been motivating grid-connected photovoltaic system applications, which are: • Reduction in the costs of the PV panels [8]. • Operation does not pollute the atmosphere [9]. • Capability to supply AC loads and inject active power, from the photovoltaic system to the grid, relieving the grid demand (distributed generation system). The researches developed in this area have shown another great advantage, which is the possibility to accomplish a reactive power control originated from linear and non-linear loads also connected to the system [10]. This fact is so attractive, since a single system is able to realize two different functions as energy generation to supply AC loads and active power filter. Following this research line, this work presents a threephase PWM inverter modeling and a control strategy using dq0 transformation to be employed in a grid-connected photovoltaic generation system (Fig. 1). The proposed system also operates as an active power filter capable of compensate harmonic components and reactive power, generated by the other loads. Therefore, the control strategy permits the operation near unity power factor to any solar radiation, UPS function for any kind of load and control of the energy flux between the photovoltaic panels and the grid.

Fig. 1. Proposed three-phase power photovoltaic system.

II.

MODELLING CONVERTER

A. The three-phase converter The converter proposed in this work is a three-phase bidirectional DC-AC converter with PWM modulation using six power switches. The simplified electrical diagram of the converter is shown in Fig. 2. The bi-directional characteristic of the converter is very important in this proposed photovoltaic system, because it allows the processing of active and reactive power from the generator to the load and vice versa, depending on the application. Thus, with an appropriate control of the power switches it is possible to control the active and reactive power flow.

Fig. 2. Bi-directional DC-AC PWM converter.

B. Current control modeling The converter modelling is relatively simple and is accomplished through dq0 transformation. The modelling for the current control is obtained considering the AC output.

When the circuit is observed from the AC output, it is possible to make some initial considerations that result in a simplified circuit [11], shown in Fig. 3. The line voltages are presented in (1) considering L1=L2=L3=L, R1=R2=R3=R and D are the duty cycle.

C. Voltage control modeling The purpose of this model is to accomplish the active input voltage clamping Vi(t). This active clamping allows controlling the power flow between the grid and the PV system and possibility to realize the Maximum Power Point Tracking (MPPT) of the PV panels. The MPP algorithm is based on the constant voltage method that is achieved by keeping the voltage in the PV terminals constant and close to the MPP [12], [13], as per Fig. 4.

Fig. 3. Simplified circuit from AC output.

dI12 (t )  V12 (t ) = L ⋅ dt + D12 (t ) ⋅ Vi + R ⋅ I12 (t )  dI 23 (t )  + D23 (t ) ⋅Vi + R ⋅ I 23 (t ) V23 (t ) = L ⋅ dt  V (t ) = L ⋅ dI 31 (t ) + D (t ) ⋅ V + R ⋅ I (t ) 31 i 31  31 dt

(1)

Applying dq0 transformation and developing the equations system (1), it is possible to find the differential equations (2), which describe the currents behavior in axis d and q.

 dI d (t ) R ⋅ I d (t ) 3 V p Vi = ω ⋅ I q (t ) + ⋅ − ⋅ Dd (t ) −  dt L 2 L L (2)  dI ( t ) R ⋅ I ( t ) V q q i  = −ω ⋅ I d (t ) − ⋅ Dq (t ) −  dt L L The direct axis current depends on the quadrature axis current and vice-versa. In order to decouple this dependence, a new duty cycle was defined and it is presented in (3).

ω⋅L   D 'd (t ) = Dd (t ) − V ⋅ I q (t )  i   D ' (t ) = D (t ) + ω ⋅ L ⋅ I (t ) q d  q Vi

(3)

If Dd (t ) and Dq (t ) were isolated in (3), it is possible to rewrite (2) as follow:

 dI d (t ) R ⋅ I d (t ) 3 V p Vi = ⋅ − ⋅ D 'd (t ) −  dt 2 L L L  ( ) ⋅ ( ) dI t R I t V q q  = − i ⋅ D 'q (t ) −  dt L L

Observing the MPP points (MPP Line), it is possible to notice that the voltage values vary very little even when the intensity of the solar irradiation suffers great alterations. Concern to the temperature, fortunately, the region in Brazil, which this system is implemented, the temperature has no important variation during the day. So, the experimental tests showed that this MPP technique can be used, in this case, without any problem. With the voltage clamped in a value “inside” of the MPP Region, when a variation of the solar irradiation happens, the intensity of the PV cell current also change, however the output voltage of the PV cell will not be altered. Thus, it is necessary to obtain the transfer function of input voltage Vi as functions of axis d and q currents. The control voltage across capacitor Ci is obtained considering the DC input shown in Fig 2. The equivalent circuit in dq0 axis seen by the DC side is shown in Fig. 5.

(4)

Developing these equations, it is obtained the differential equations that show the behavior of the currents in axis d and q as functions of the duty cycles. So, the transfer functions used in the design of the current controllers are shown in (5).

Vi  id ( s )  d ' ( s) = − s ⋅ L + R  d  i (s) Vi  q =−  d 'q ( s ) s ⋅ L +R 

Fig. 4. Example of the current and voltage characteristics of a PV cell.

(5)

Fig. 5. Equivalent circuit seen by the DC side.

In this equivalent circuit, I(t) represent the current supplied by PV panels (7) and Ii(t) represents the input inverter current (8). The transfer function between the voltage vi(s) and the input current of the inverter ii(s) is shown in (9). I (t ) = I Ci (t ) + I i (t ) (7)

I i (t ) = I d (t ) ⋅ Dd (t ) + I q (t ) ⋅ Dq (t )

(8)

vi ( s ) 1 =− iCi ( s ) s ⋅ Ci

(9)

Developing and substituting appropriately the equations, it is possible to obtain the desired voltage control modelling. The equations vi(s) as function of currents in axis d and q are shown in (10) and (11), respectively.

vi ( s ) 1 = id ( s ) s ⋅ Ci

 3 Vp  ⋅ ( − K ⋅ L ⋅ s ) − 2 ⋅ K ⋅ R + ⋅  (10) 2 Vi  

vi ( s ) 2 Q =− ⋅ iq ( s ) 3 Vi ⋅ V p

 L⋅ s + 2⋅ R  ⋅   s ⋅ Ci 

acquired through sensors. In the line currents it is applied dq0 transformation. A. Current control strategy To control the currents of the axis d, the current Id(t) and the reference currents Idref1(t) and Idref2(t) are used, according to Fig. 7. The sign Idref2(t) represents the current load Idc(t) alternate portion of the direct axis d and it is obtained through a high-pass filter (Fig. 8) [14]. This is necessary to compensate possible power unbalances in the system, and it has negative sign so that the power flows in opposition to the load.

(11)

Where: L, R - Equivalent resistances and inductances Ci - Input capacitor Vp - Voltage peak of grid Vi - Input voltage id, iq - Currents in the axis d and q P - Active power Q - Reactive power

K= III.

Fig. 7. Block diagram of the current control in the d axis.

Fig. 8. Idref2(t) obtaining.

2

P 3 V p ⋅ Vi IMPLEMENTATION OF THE CONTROL METHODOLOGY

Fig. 6 shows the diagram of the control methodology and the modulation of the proposed three-phase grid-connected PV system. The practical implementation of this control strategy has been implemented with DSP (Digital Signal Processing) and a zero cross detector circuit to make the synchronism method with the grid. As can been seen from Fig 6, the inverter output currents (I1, I2 and I3) and the load currents (I1c, I2c and I3c) are

To control the currents of axis q (Fig. 9), a reference signal Iqc(t) is used to compensate the reactive power caused by the load connected to the system.

Fig. 9. Block diagram of the current control in the axis q.

In the output of both controls (d and q axis) its necessary to accomplish a uncoupling in order to obtain the duty cycles dd(t) as function of id(t) and dq(t) as function of iq(t).

Fig. 6. Diagram of the control system.

B. Voltage control strategy The voltage in the capacitor Ci is compared with the reference voltage Viref and the error signal enters in the voltage controller resulting in the signal Idref1(t) (Fig. 10).

B. Simulation Results Several numerical simulations of the proposed system were accomplished for different situations of load connected in this system (linear and non-linear). The most important parameters of the converter are shown in Table 2. TABLE II

Parameters P = 12.6 kVA Fig. 10. Diagram of the voltage regulator

This signal Idref1(t) is used as one of the references in the current control loop of the direct axis d, guaranteeing that voltage Vi(t) keeps clamped at the desired value, as shown in Fig. 11.

Fig. 11. Block diagram of the voltage control.

IV.

SIMULATION AND EXPERIMENTAL RESULTS

A. PV array design To validate the proposed methodology for grid-connected PV generation system, a 12 kilowatts PV array was design using Kyocera KC50, connected in a proper series-parallel configuration. Table 1 shows the main characteristics of the PV array, that was design to 700 Volts photovoltaic output voltage and 18 Amperes of current. The equivalent circuit simulated is shown in Fig. 12.

SIMULATION PARAMETERS Description - Converter Power

Vi= 700 V

- Input Voltage (DC)

Vout= 220 V

- RMS Output Voltage (grid)

fr= 60 Hz

- Grid Frequency

fs = 20 kHz

- Commutation Frequency

R = 0.57 Ω

- Output inverter equivalent resistor

L = 1.92 mH

- Output inverter equivalent inductance

Ci= 2.7 mF

- Input Inverter capacitor

The simulation with linear loads was done and good results were obtained to several load parameters. However, to show a better performance of the system proposed, only the results considering non-linear loads connected to the system are presented. The performance of the reactive power compensation and harmonics current elimination is better observed when non-linear load tests are done. The non-linear load presented in this work is a three-phase bridge rectifier with RC output, shown in Fig. 13. Fig. 14 presents the three grid currents and the input voltage Vi(t) behavior for several situation of abrupt variations of the current supplied by the PV panels. It is seen that the grid input currents always has a sinusoidal shape.

TABLE I

PV ARRAY SPECIFICATIONS USING KYOCERA KC50 PANELS Total peak power 12.6 kW Number of series strings panels - Ns 42 Number of paralel – Np 6 Number of PV panels 252 Corrent peak 18 A Voltage in maximum power 701.4 V Corrent: short circuit 18.6 A Voltage: open circuit 903 V

Fig. 13. Non-linear load simulated

In the proposed photovoltaic array modeling, the DC voltage source represents the open circuit voltage of all series photovoltaic modules, while de diode imposes its semiconductor characteristic.

Fig. 14. Three grid currents and the input voltage. Fig. 12. PV Array simulated circuit.

Fig. 15 shows in the phase 1 the grid voltage, grid current,

load current, output inverter current and input voltage Vi(t) behavior, when a variation of the current supplied by the PV panels occurs at the instant t=150ms. Even with non-linear load, the grid currents are sinusoidal and the voltage control maintains the desired level of 700V. The grid input current waveform is sinusoidal and is 180° out of phase to the grid voltage. This situation means that the grid is receiving energy.

Fig. 17. Current spectrum harmonic: Grid and load in the phase 1.

Fig. 15. Grid voltage and current (phase 1), Load current and output inverter current (phase1); and Input voltage.

Fig. 16 shows the behavior of the current and voltage in phase 1 of the grid, when an abrupt variation of the current supplied by PV panels occurs. In this case the energy supplied by the PV panels becomes null at the instant t=300ms and it returns to the nominal value at instant t=450ms. In the absence of energy supplied by the PV panel, the converter only acts as an active power filter. The inverter output current and the PV current are also shown in Fig. 16. Even with this abrupt variation, the power factor in phase 1 is very high in both cases; i.e., when there is solar irradiation (grid receiving energy) and in the periods when there is no energy supplied by the PV panels.

Fig. 18 shows the active power flux in the: grid, load, PV array and converter, for verifying the control strategy performance for several solar conditions. At the same figure it is possible to observe that the load active power remains constant and can be supplied by PV array or by the grid. The grid active power is negative when the grid is receiving energy.

Fig. 18. Active Power: Grid, load, PV and converter to several solar conditions.

Fig. 16. Current and voltage in the phase 1 – PV current and output current inverter of phase 1.

To prove the structure operation as active power filter, Fig. 17 shows the grid and load current harmonic spectrum in the phase 1. It was verified that using the control strategy, the harmonic components of the grid current are eliminate.

C. Experimental Results To demonstrate the feasibility of the discussed PV system, a prototype was designed and implemented following the specifications presented in Tables 1 and 2. The PV array was design to 500 Volts photovoltaic output voltage.. Fig. 19 depicts in the phase 1 the utility voltage (VUtility), the Non-linear load current (IL) and utility current (IS) with the system operating just in the active power line conditioning mode (cloudy day or night). The THD of IS is 2.8% for a load crest factor of 2.8, and the PF=0.97. Fig. 20 shows the utility voltage and the utility current in the phase 1, with the system only supplying power to the utility grid (THD = 2.5% and PF = 0.98). In this case no load is connected in the PV system. Fig. 21 presents the performance of the utility voltage and utility current (THD = 2.8% and PF = 0.978) with a 50% of non-linear load connected between the PV system and the commercial electric grid.

It is important to emphasize that for both situations the power factor is always high and the currents present low harmonic distortion. Due to a little variation of the temperature in the region where the PV panels is implemented, an input voltage clamping technique is used to assure the maximum power point (MPP) of the PV panels. To validate the structure operation some simulation and experimental results were presented and they show the viability of the proposed model, as well as the control strategy used for the PV systems. Fig. 19. Utility current (IS), Load current and utility voltage (VUtility) (Ch1 and Ch2 20A/div and Ch2 50V/div).

ACKNOWLEDGMENT The authors would like to thanks the CNPq and FINEP by the financial support. The authors also wish to thank the engineer Marcio Silveira Ortmann for their support during the experimental tests. REFERENCES [1] [2]

Fig. 20. Utility current (IS) and utility voltage (VUtility) with no load. (Ch1 10A/div and Ch2 50V/div).

[3]

The efficiency curve of the whole system is shown in Fig. 22.

[4]

[5]

[6] [7] [8]

Fig. 21. Utility current (IS) and utility voltage (VUtility) with 50% of nonlinear load. (Ch1 5A/div and Ch2 50V/div).

[9]

Fig. 22. Efficiency curve of the whole system.

[10]

V.

CONCLUSION

This paper has presented in a simple way the modelling and the control strategy using dq0 transformation of a three-phase PWM inverter to be employed in a grid-connected photovoltaic generation system. The main focus of this work is to realize a design of a dual function system that would provide solar generation and works as an active power filter, compensating unbalances of power and the reactive power generated by other loads connected to the system.

[11] [12] [13] [14]

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