An Active Filter Enabled Power Architecture for

IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS

1

An Active Filter Enabled Power Architecture for Oscillating Wave Energy Generation Samir Hazra, Student Member, IEEE, and Subhashish Bhattacharya, Senior Member, IEEE

Abstract—This paper proposes an active filter enabled power architecture to harness oscillating power from wave energy converter (WEC). The power architecture consists of a diode rectifier and a dc-dc converter to extract active power and the partiallyrated active filter to supply harmonic and reactive power. The proposed power conversion system is cost-effective compared with a conventional, fully-rated power converter in generating oscillating power from the WEC, using both squirrel-cage induction generator (SCIG) and permanent magnet synchronous generator. Analytically, it is shown that the low switching frequency of the active filter is adequate to absorb the harmonic current generated due to the diode rectification. Overall system modeling and control strategy are described for the SCIG based system. The feasibility of the proposed system is validated through experimental implementation with an emulated WEC. A design guideline of the proposed system for high power applications is elaborated.

CEAN wave is an emerging renewable energy source [1], [2]. Among the various types of wave energy converters (WECs), a moving flap-type WEC is of particular interest. Because, the flap-type WEC can be installed at near-shore locations, the resulting system can be more cost-effective than deep sea installation of a buoy [3]. The WEC, swung back and forth by the oscillating speed of the sea wave, as shown in Fig. 1, is capable of converting wave energy into useful mechanical energy [3]. A typical ocean wave profile obtained from [4] is shown in Fig. 2. A hydraulic system can be used

O

Paddle type WEC

Index Terms—Wave energy conversion system, Active filter, Switching frequency, Squirrel-cage induction generator, Field oriented control.

G

Sub-sea cable

Generator

Power conversion station Dc collector PCU

GSC

PCU

ESS

Grid

Land

G

Fig. 1: Overall system configuration with moving flap type WEC.

a, b, c d, q vs , v f , v g vdcf , vrec , vout is , if , io , ic , ig imr ψr ωrm ωr , ωsl , ωe θe rs , rr Ls , Lr , Lm Lls , Llr Pgen , Paf , Pout Qgen , Qaf , Qout

Three stationary phases Two synchronously rotating phases Stator, active filter and grid voltage Active filter, diode rectifier output and grid side dc bus voltage Stator, active filter, diode rectifier, filter capacitor and grid current Rotor flux equivalent magnetizing current Rotor flux-linkage Rotor speed (mech-rad/s) Rotor, slip and synchronous speed (elecrad/s) Position of synchronous reference frame with respect to ph-a axis Stator and rotor resistance Stator, rotor and magnetizing inductance Stator, rotor leakage inductance Generator, active filter and boost converter output active power Generator, active filter and diode rectifier input reactive power I. I NTRODUCTION

S. Hazra, and S. Bhattacharya are with NSF FREEDM Systems Center, North Carolina State University, Campus Box 7571, Raleigh, NC 27695-7571 (shazra,[email protected]).

Speed (p.u.)

N OMENCLATURE 1 0.5 0 −0.5 0

10

20

30

40

50

Time (s) Fig. 2: Typical ocean wave profile [4].

for power generation, as described in [3]. However, hydraulic system can be more complex and expensive for scaled-up highpower installations. Coupling a generator with the shaft of the flap can simplify the system of power generation. The generator can be coupled through a gear or directly to the shaft. As shown in Fig. 1, the power conversion station (PCS) can be installed on the shore to minimize the complexities and cost of the maintenance. Sub-sea power cables can run from each generator to individual power conversion unit (PCU). A speed-up gear can enable the generator to run at higher speed, resulting in a smaller generator size. However, the proposed power conversion architecture is independent of the speed and the size of the generator. The average to peak ratio of the available power from the WEC is around 0.1 to 0.2 as analyzed in [5], [6]. However, the power conversion system using a back to back converter as shown in Fig. 3, must be designed for the maximum power rating of the generator. A permanent magnet synchronous generator (PMSG) or a squirrel-cage induction


2

ias

Paddle type WEC

SCIG

Sub-sea cable

vdcf vaf

Cdcf

vout

iL

iaf vas

iao

iag vag

Lb Cout

vrec Lf Cf iac Boost converter Passive filter Diode rectifier Power conversion unit (PCU)

Charging unit Active filter

Lg Grid side converter (GSC)

Grid

Fig. 4: Proposed power conversion circuit, marked portion is dedicated to a single WEC.

generator (SCIG) based system using a fully-rated power converter structure, are reported in [7]–[10]. A PMSG based power architecture can be realized with the diode rectifier and subsequent boost converter, as reported in [8]. However, the presence of harmonics in the generator current due to diode rectification, increases the power loss in the generator and the harmonic content in the torque. A dual stator winding WEC

Filter

MSC

GSC

Transformer

Machine Gear

Grid

Fig. 3: Fully-rated back to back power converter based energy conversion system.

induction generator (DSWIG) can generate power with a lower rated power converter as reported in [11]–[16] by splitting the power into two wingdings. The winding connected to the power converter, provides the reactive power to the generator, while the other winding generates the active power through diode rectification. With diode rectification, the power loss of the generator increases due to the presence of the lower order harmonics in the winding current. Moreover, with double winding architecture, the utilization of the generator is poor. For a particular power factor x, the percentage of over-design of VA rating of the generator can be given as, p Percentage of overdesign = (x + 1 − x2 − 1)%. (1) With a power factor of even 0.9, the generator needs to be designed for VA rating of 1.34 p.u., which translates to 34 % over-design. Also, six sub-sea cables from each generator must be laid to transport the power to the PCS. Therefore, the DSWIG can not offer a cost-effective solution for wave energy conversion system. A fractionally rated, active filter based SCIG operation in a stand-alone system is reported in [17]. The power converter supplies both reactive power and lower order harmonic current to make the generator winding current sinusoidal. The system is designed for a stand-alone application, where the power generation is dependent on the external loading. In this work, an active filter based power architecture is proposed, as shown in Fig. 4, to generate oscillating power from the WEC. The active filter supplies the reactive power

to the SCIG and absorbs the harmonic current generated due to the diode rectification. The diode bridge and subsequent dcdc converter, control the active power. The architecture can be applied to either the SCIG or the PMSG. Because of the zero magnetizing current requirement of the PMSG, the rating of the active filter for PMSG is lower compared with SCIG. Analytically, it is shown that the switching frequency of the active filter can be lower in the case of higher inductance of the generator. Essentially, the inductance of the low speed, high torque generator used in wave energy conversion system, is higher. The overall control system, for starting and steady state operation is designed. A detailed design method of all the components of the system is elaborated to provide guidelines for the high power system design. II. P OWER A RCHITECTURE As shown in the overall system configuration in Fig. 1, each power conversion unit (PCU) extracts power from the generator and delivers to a common dc collector. A grid side converter (GSC) dispatches the power to the grid. By integrating multiple PCUs from WECs, installed at different locations, a natural averaging can be achieved, resulting in a lower GSC rating. Additionally, an energy storage system (ESS) integrated at the dc collector can absorb the power oscillation, resulting in a further reduction of the GSC rating. In this work, the design, control and validation of one such PCU is reported. The architecture of the PCU with grid tied converter is shown in Fig. 4. The active filter provides the necessary reactive power to the generator. The output of the generator is rectified by the diode rectifier and the dc current of the rectifier is controlled by the dc-dc boost converter to generate desired active power. Although, the diode rectification produces harmonic current at the input side of the rectifier, the active filter is controlled suitably to absorb the harmonics to maintain the generator current sinusoidal. An L-C filter is used at the output of the active filter to reduce the dv/dt of the converter voltage, applied on the long sub-sea cable connecting the generator. Without the L-C filter, long sub-sea cable can cause voltage spikes at the generator terminal, bearing current and other common-mode related problems, as reported in [18], [19]. A central charging unit is used to charge the dc bus of the active filter, at the start of the system and at the low speed of


the WEC, where the dc voltage is collapsed due to insufficient power generation. The volt-ampere (VA) rating of the charging transformer is very low, since a small amount of charging energy is required. When the speed of the generator is reached to a sufficient value, by employing suitable control, the dc bus voltage of the active filter is further built-up and regulated by drawing a small amount of active power from the generator itself. Once the dc voltage is higher than the charging unit output, the charging unit is disconnected due to the reverse biasing of the diode bridge. III. S YSTEM M ODELING AND C ONTROL S TRATEGY The objectives of the control strategy are, (a) to supply the necessary reactive power to the generator, (b) to control the active power by the dc-dc converter, (c) to absorb the lower order harmonic current to keep generator current, is , sinusoidal, and (d) to prevent the exchange of active power with the active filter, except for that supplying for the converter loss. In order to achieve the objectives, the generator current, is , is directly controlled by the active filter. The current control scheme is implemented in the rotor flux reference frame with indirect field oriented control (IFOC) scheme [20]. The control scheme is shown in Fig. 5. The rotor field position is computed from the d and q-axis currents and the measured rotor speed. i∗mr

hψ

imr ∗ vdcf

his

vdsf f ∗ vds dq

ids hvf i∗ qs iqs

vdcf

ids

i∗ds

1/τr

αβ

his ∗ vqs

vqsf f imr

abc ids

dq

iqs iqs

τr imr

maf mbf modulator m cf

αβ

αβ

αβ

ωsl

ωe

abc

ias ibs ics

θe

ωr

3

by the control effort. The active power generated by the diode rectifier and boost converter combination, is also seen as the disturbance in the q-axis current control. A. Current Dynamic Model The d-q current dynamics of the SCIG in the rotor flux reference frame, with stator voltage, vs as input, are given in (2) and (3). vds

=

vqs

=

(rs + σLs p)ids − ωe σLs iqs ,

(2) Lm (rs + σLs p)iqs + ωe σLs ids + ωe ψr , (3) Lr

where, σ is the leakage factor and is expressed as σ =1−

kl

i∗L

vdsf f = −ωe σLs iqs , vqsf f = ωe σLs ids + ωe

d

The rotor flux (ψr ) equivalent current, imr is estimated and controlled by the d-axis component of the generator current. The active power is controlled by the control of rectifier output current, iL , which is reflected in the generator q-axis current. The boost converter current reference is set in proportion (kl ) to the generator speed, ωrm . The active component of the generator current, iqs , is controlled to regulate the dc bus voltage of the active filter, vdcf . Since the dc bus of the active filter is floating, a small amount of active power is drawn accounting for the converter loss and rest of the active power of the generator is channeled through the diode rectifier. The lower order harmonics due to diode rectification is seen as the disturbance components for the current controller design in both d-q axes and are rejected

(5)

In order to control the generator current by the active filter, the current dynamics is modified to include the L-C filter dynamics at the output of active filter. A simplified singlephase equivalent circuit of the system is depicted in Fig. 6. The generator back e.m.f. is es and the active filter voltage is vf . The load current, which is controlled by the boost converter, is considered to be a current stiff load, io . Lf and rf are the filter inductance and its resistance. σLs and rs are the generator inductance and its resistance. Cf is the switching filter. The Lf − Cf filter at the generator terminal, forms an L-C-L resonant circuit with generator inductance, σLs . vf

is Lf

rf

iL (b) Fig. 5: Control architecture of the power conversion unit. (a) Active filter control, (b) Boost converter current control.

Lm ψr , Lr

the transfer function of the current controller design in both axes becomes 1 Gis vs (s) = . (6) rs + σLs s

if

hiL

(4)

By setting the coupling terms in (2) and (3) as feed-forward quantities as

(a) |ωrm |

L2m . Ls Lr

Lsw Switching filter

rs

vs σLs

Rd

Csw

es

io ic

Cf

Fig. 6: Simplified circuit of the system.

Although, an active damping scheme can be implemented [21] to damp the resonance initiated by the active filter step voltage, it can not damp the resonance due to the disturbance from either the rectifier or the generator. A passive damper, Rd , can be used in series with the filter capacitor, Cf , but it reduces the attenuation of the filter. Therefore, the switching filter, can be modified with an additional Lsw − Csw tank in parallel with the damping resistor, Rd , as reported in [22]. The Lsw − Csw tank provides the low impedance path to the switching ripple current and high impedance at other frequencies, forcing resonant current to flow through Rd to get damped. However,


vf

g1

es

io

if

ic

g2

vs

g3

is

Fig. 7: Block diagram of the overall open loop system.

The block diagram of the system dynamics is shown in Fig. 7. The active damping coefficient is considered to be kd . The transfer functions g1 , g2 , and g3 can be expressed as, g1

=

g2

=

g3

=

If (s) 1 = (7) Vf (s) − Vs (s) − kd Ic (s) rf + Lf s Vs (s) 1 Lsw Csw Rd s2 + Rd = + (8) Ic (s) Cf s Lsw Csw s2 + Rd Csw s + 1 Is (s) 1 = (9) Vs (s) − E(s) rs + σLs s

From the block diagram in Fig. 7, the modified current dynamics of Is is derived as, Is (s) =

g1 g2 g3 Vf (s) 1 + g1 g2 + g1 kd + g2 g3 g2 g3 − Io (s) 1 + g1 g2 + g1 kd + g2 g3 g3 + g1 g2 g3 + g1 g3 kd − Es (s) 1 + g1 g2 + g1 kd + g2 g3

−50 −100

Gis vf 0 Gis vf 1 Gis vf 2

−150 −45

is

vs

(10)

In (10), the coefficient of Vf is the modified control transfer function, Gis vf , to control the generator current by the active filter voltage. The coefficient of Io and Es are the disturbance transfer functions, Gis io and Gis es respectively. The frequency response of the open loop control transfer function, Gis vf , is plotted in Fig. 8. Note that the modified switching ripple filter provides good damping while ensuring good attenuation at the switching frequency of the active filter. Classical P-I controller (his ) is designed using control transfer function, Gis vf , to directly control the generator current, is , by the active filter voltage, vf . The selection of the bandwidth of the closed loop system is discussed in the next section. B. Selection of Control Bandwidth and Switching Frequency The active filter is widely used at the point of common coupling (PCC) where a non-linear load is connected to the grid. In most cases, the load current is measured to extract the harmonic content, and the harmonic compensation is performed with the feed-forward control [22]–[25]. The bandwidth requirement of the current control in feed-forward method is high, because the delay between the load current harmonics and the compensating current of the active filter needs to be minimized. Therefore, the switching frequency of the active filter is also higher depending upon the order of the harmonic compensation. Harmonic elimination by source current measurement can also be performed by a feedback control method, as reported in [26]. In [26], the current control bandwidth is assumed to be

Phase (deg)

kd

0 Magnitude (dB)

the active damping still can be implemented in combination with the passive damping, to reduce the size of the Rd and the corresponding power loss.

4

−90 −135 −180 −225 −270

103

104 Frequency (Hz)

Fig. 8: Frequency response of the control transfer function Gis vf = Is (s)/Vf (s). Gis vf 0 : Cf is the switching ripple filter without any damping, Gis vf 1 : Cf with the Lsw − Csw tank and passive damper Rd = 22 Ω, Gis vf 2 : Cf with the Lsw − Csw tank, passive damper Rd = 22 Ω and active damping, kd = 3.

infinitely high to consider the active filter as a current source for the analysis of the filter behavior. In this work, to reduce the switching frequency of the active filter, control of the source current, which is the generator stator current, is considered. In this section, the requirement of the bandwidth and the switching frequency to control the generator stator current, is analyzed. From the block diagram in Fig. 7, the current dynamics of If is derived as, If (s) =

g1 + g1 g2 g3 Vf (s) 1 + g1 g2 + g1 kd + g2 g3 g1 g2 + g1 kd + Io (s) 1 + g1 g2 + g1 kd + g2 g3 g1 g2 g3 + g1 g3 kd − Es (s) 1 + g1 g2 + g1 kd + g2 g3

(11)

The harmonic current sharing through the generator and the active filter in open loop, can be termed as Gis io and Gif io , which are coefficients of Io (s) in (10) and (11) respectively. By varying leakage inductance (Lls ), the current sharing is shown in Fig. 9. The open-loop system of active filtering is essentially the V/f control of the generator without any current control, as reported in [27]. The harmonic current through the generator decreases with the increase in generator inductance. This shows that the higher generator leakage inductance helps in harmonic current compensation. The block diagram of the closed loop system to control generator current, is shown in Fig. 10. In closed loop system, the harmonic current sharing between generator and active filter is derived as, Is (s) −g2 g3 = Io (s) 1 + g1 g2 + g1 kd + g2 g3 + g1 g2 g3 his

(12)

If (s) g1 g2 + g1 kd + g1 g2 g3 his = Io (s) 1 + g1 g2 + g1 kd + g2 g3 + g1 g2 g3 his

(13)

The current sharing in closed loop system, is plotted in Fig. 11, at different current control bandwidth. At frequencies below


C. Active Filter Dc Bus Voltage Dynamic Model

1.2 Gis io , 5mH Gif io , 5mH Gis io , 0.5mH Gif io , 0.5mH

Absolute magnitude

1.0 0.8

Neglecting the power loss in the active filter, the power balance yields, 3 vdcf idcf = − (vqf iqf + vdf idf ), (14) 2 where, vdcf and idcf are the active filter dc bus voltage and current, respectively. The voltage dynamics of the dc bus is,

0.6 0.4

dvdcf dt The kirchhoff’s current law gives,

0.2 0 101

102

103 104 Frequency (Hz)

105

106

Fig. 9: Variation of harmonic current sharing between generator and active filter with different generator leakage inductances. Generator leakage inductance, Lls is considered to be 5 mH and 0.5 mH and the passive filter inductance, Lf = 1 mH.

if

vf g1

his vs

is

es

io ic

vs

g2

g3

idcf = Cdcf

(15)

if = is + io + ic ,

(16)

Combining (14) to (16), the dc bus bus dynamics is derived as, Cdcf

kd i∗s

5

is

dvdcf 3 =− (vqf (iqs + iqo + iqc ) dt 2vdcf + vdf (ids + ido + idc )) 3 = − (mqf (iqs +iqo +iqc )+mdf (ids +ido +idc )) 4 (17)

Fig. 10: Closed-loop block diagram of the generator current control.

where, mqf and mdf are the q and d-axis modulation indexes. By linearizing (17), the small signal model is derived as, resonance frequency (2.3 kHz), the harmonic content in the generator current gradually decreases with the increase of control bandwidth. In the frequency range above resonance, the control bandwidth has no effect on the harmonic compensation and the harmonic current in the generator decided by the open loop currant sharing, which depends on the generator leakage inductance. Therefore, the higher leakage inductance of the generator helps in harmonic compensation, and allows to use lower closed loop current control bandwidth. Due to lower control bandwidth, lower switching frequency of the active filter can be adequate. Here, the current controller, his is designed to have closed loop bandwidth of 500 Hz and the converter switching frequency is chosen to be 10 kHz.

dv˜dcf 3 = − Mqf ˜iqs dt 4 3 − Mqf ˜iqo + ˜iqc + Mdf ˜ids + ˜ido + ˜idc 4 +m ˜ qf (Iqs + Iqo + Iqc )+ m ˜ df (Ids + Ido + Idc ) (18)

Since the active filter dc bus voltage is controlled by the q-axis generator current, the control transfer function is derived from the coefficient of ˜iqs in (18). Other components of (18), are considered to be the disturbances in the voltage controller design. The control transfer function is given as, Gvf =

10 0 −10

Vdcf (s) 3 Mqf =− Iqs (s) 4 Cdcf s

(19)

where, Mqf varies with the speed of the generator. The voltage controller, hvf is designed to ensure the stability of the voltage control over the entire range of variation of the speed [28].

−20 Magnitude (dB)

Cdcf

−30 −40

D. Boost Converter Control

−50

The boost converter controls the current at the output of the diode rectifier. The dynamic model of the rectifier output current is given as,

−60 −70 −80 −90

−100 101

Gif io ,OL Gif io ,100Hz Gif io ,500Hz Gif io ,1000Hz

102

Gis io ,OL Gis io ,100Hz Gis io ,500Hz Gis io ,1000Hz

103

104

105

Frequency (Hz) Fig. 11: Harmonic current sharing between generator and active filter with different bandwidth of generator current controller. Open loop (OL) and closed loop cases with bandwidth of 100 Hz, 500 Hz, and 1000 Hz are plotted. Generator leakage inductance, Lls = 5 mH and the passive filter inductance, Lf = 1 mH.

diL 1 = (vrec − (1 − d)Vout ) dt Lb

(20)

where vrec is the diode rectifier output voltage and d is the duty cycle of the boost converter. The grid side dc bus voltage, Vout is assumed to be constant. By linearizing, the current dynamic model is given as, d˜iL 1 ˜ out ). = (˜ vrec + dV dt Lb

(21)


Driving Motor Drive unit 208V 60Hz

Generator

IM

ias , ibs iL

Cdcf = 100µF Vdcf = 450V

1:2

Generator data: Vs = 220V, Is = 11A, Power = 3hp, N = 1200rpm, rs = 0.5Ω, rr = 0.35Ω, Lm = 65mH, Lls = Llr = 5mH

is

IM

6

iL

if

Cout = 5850µF Vout = 400V ig

Grid

Lb = 5mH

120V 60Hz

Lg = 5mH Lf = 1mH Cf = 4.7µF

208V 60Hz

Lsw = 1mH Csw = 0.27µF Rd = 22Ω

Fig. 14: Schematic diagram of experimental setup.

TABLE I: Closed Loop Control Bandwidth

Hence, the transfer function for the inductor current controller design can be given as GiL =

IL (s) Vout = D(s) Lb s

Controller

Bandwidth

PLL (hP LL ) Grid Current Control (hig ) Output voltage control (hvo ) Active filter dc bus voltage control (hvf ) Generator flux control (hψ ) Generator current control (his ) Boost current control (hiL )

(22)

A P-I controller, hiL is designed to track the varying reference of the boost inductor current to generate oscillating power.

100 Hz 500 Hz 15 Hz 50 Hz 50 Hz 500 Hz 600 Hz

E. Grid Side Converter Control The GSC is controlled to dispatch the generated power to the grid by regulating the dc bus voltage, Vout . The inverter is connected to the grid through an L-filter. The control scheme shown in Fig. 12, is implemented in the synchronously rotating reference frame (d-q), with q-axis aligned with the voltage vector by a phase locked loop (PLL). hig

i∗dg

vdgf f ∗ vdg

idg ∗ vout

vout

hvo i∗qg

θ

dq αβ

hig

iqg

αβ

∗ vqg

vqgf f

abc

idg dq iqg αβ

P LL

abc

Grid filter GSC

Boost converter Drives

vag vbg vcg

modulator

αβ

Oztek control board and interface circuit

Active filter mag mbg mcg

iag ibg icg

Fig. 12: Grid side converter control architecture.

F. Bandwidth of Control Design The bandwidth of closed loop system for all the controller implemented in the system are given in TABLE I. The bandwidth of phase lock loop (PLL) is chosen to be 100 Hz to avoid tracking of the lower order harmonics present in the grid voltage. High bandwidth of boost converter current control is chosen to minimize the impact of the ripple voltage of the rectifier output on the inductor current.

Generator terminal filter Generator

Motor Fig. 13: Experimental setup.

Fig. 13. A drive is used to control the motor to emulate a WEC by controlling the speed of the motor, to track the oscillating speed. A circuit diagram of the experimental set-up with detailed rating of each component is given in Fig. 14. The active filter and boost converter are switched at 10 kHz. The control algorithm is implemented onto a DSP, TMS320F28335 platform. For simplicity, the oscillating speed of the WEC is chosen to be a single sinusoid with a period of about 8.5 s, which is the dominant period of the real sea wave oscillation, shown in Fig. 2. The experimental system is tied to the threephase grid as shown in Fig. 4 and Fig. 14. B. Start-up Sequence

IV. S IMULATION AND E XPERIMENTAL R ESULTS A. Experimental Set-up The proposed power architecture is validated with a motorgenerator based experimental test bed. An induction motor emulates the dynamics of the WEC [29]. Another induction machine is used to generate power from the WEC. The developed hardware setup and its components are shown in

The start-up and operation of the system is performed in a logical sequence. • Step1: Emulation of the WEC is started by the driving motor control. • Step2: The grid side dc bus is pre-charged, and subsequently the GSC is modulated in synchronism with the grid to regulate the dc bus voltage.


• •

Step3: The active filter dc bus is pre-charged, and the controls are activated. Step4: Loading of the generator is initiated in proportion to the generator speed, by enabling the control of the boost converter.

7

Vdcf Voltage build-up

iaf

Ch1 Ch5 ωrm

Voltage build-up

Vdcf

ωrm

Loading starts

iaf

Dc voltage collapsed to charging unit voltage

Ch3

Second power cycle

Ch6 Ch7

Ch1 Ch4

ias

Ch2 Ch4

First power cycle

iao

ids iqs

ias

Ch2 Ch5 Dc bus pre-charge

iao

Ch3 Loading starts

Fig. 16: Voltage build-up and current dynamics at the start of the power cycle. Scale: Ch1, iaf : 20 A/div, Ch2, ias : 20 A/div, Ch3, iao : 20 A/div, Ch4, ωrm : 41.89 rad/s/div, Ch5, vdcf : 250 V/div, Ch6, ids : 10 A/div, Ch5, iqs : 20 A/div.

Vdcf

Fig. 15: Start-up and operation of the system. Scale: Ch1, iaf : 20 A/div, Ch2, ias : 20 A/div, Ch3, iao : 20 A/div, Ch4, ωrm : 41.89 rad/s/div, Ch5, vdcf : 100 V/div.

iaf Ch1

Start-up and power generation over the wave cycles is shown in Fig. 15. At the start, the dc bus of the active filter is pre-charged to the charging unit voltage. Subsequently, the dc bus voltage is built and regulated at the reference value. As shown in Fig. 15, in the first power cycle, the load is not applied and the generator is operated to generate only the small power required to keep the dc bus voltage regulated. The active filter supplies the necessary reactive power. Towards the end of the first power cycle, the power from the generator is negligible at low speed, causing the dc voltage to collapse to the charging unit voltage. In the next power cycle, the voltage is again built-up to the reference value and subsequently, loading of the generator is initiated to generate active power. The active filter supplies both the reactive and harmonic power in this power cycle. The power generation cycle is repeated to generate oscillating power from the WEC. The current dynamics during the voltage build-up is shown in Fig. 16. The flux component of the current, ids , is undisturbed during the voltage build-up and the power component of the current, iqs , changes to charge the dc bus. This confirms the robust implementation of vector control algorithm. The subsequent generation is initiated by the control of the boost converter. It can be seen that the harmonic current is compensated by the active filter instantaneously. C. Steady-State Results The steady-state results with the generator operating around 1200 rpm, is shown in Fig. 17. The active filter supplies the harmonic current and the generator stator current is free of harmonics. The terminal voltage of the generator is also sinusoidal with a small switching ripple.

ias Ch2

Ch5 Ch3

iao

vabs Ch7

Fig. 17: Power generation (3 kW) and harmonic compensation at 1200 rpm. Scale: Ch1, iaf : 50 A/div, Ch2, ias : 50 A/div, Ch3, iao : 20 A/div, Ch5, vdcf : 100 V/div, Ch7, vabs : 500 V/div.

The dc bus voltage of the active filter exhibits oscillation with two distinct frequencies. The low frequency is lower than the fundamental frequency of the generator stator current. The induction generator used for the experiment is made from a doubly-fed induction generator by shorting its rotor terminals. Investigation showed that the brush contact resistance of the three phases is unequal, which causes unbalanced air gap power in the generator. The frequency of the ac component of the unbalanced power is twice of the slip frequency. The instantaneous ac active power due to unbalanced generation, flows into the dc bus of the active filter, forcing the dc voltage to oscillate [25]. It can be seen in Fig. 15 that the frequency of the dc voltage oscillation increases from the first to second power cycle, due to increase in loading and corresponding slip frequency.


The results of a simulation study with an unbalanced rotor resistance is given in Fig. 18, where the dc bus voltage oscillation is seen. With a balanced rotor resistance, the low frequency dc bus oscillation is not present, as shown in Fig. 19. To minimize the low frequency oscillation, a high bandwidth voltage controller (50 Hz) is designed. However, the controller generates an oscillating stator current to reduce the oscillating active power. This particular problem will not occur with the SCIG, because of the balanced rotor resistances of the rotor cage. The high frequency oscillation of the dc voltage is due to the high frequency ac active power, generated due to the lower order harmonic current of the active filter [25].

8

Vout ωrm iag Ch1 vag

Ch4 Ch2 Ch5 iao

vabs (V)

iao (A)

ias (A)

iaf (A) Vdcf (V)

Ch3 480 460 440 420 20

Fig. 20: Grid side converter operation results. Scale: Ch1, iag : 10 A/div, Ch2, vag : 200 V/div, Ch3, iao : 20 A/div, Ch4, ωrm : 41.89 rad/s/div, Ch5, vout : 100 V/div.

0 −20 20 0

Vout

−20 20

ωrm

0

iag

−20 400 200 0 −200 −400

Ch1 Ch4 0

0.02

0.04 0.06 Time (s)

0.08

0.10

vag

Ch2 Ch5

Fig. 18: Power generation and harmonic compensation; an unbalanced rotor resistance is considered.

iao Ch3

vabs (V)

iao (A)

ias (A)

iaf (A) Vdcf (V)

The results of the GSC operation are shown in Fig. 20 Fig. 21. The GSC delivers oscillating power to the grid at unity power factor. Fig. 21: Grid side current and voltage during full loading (3 kW) of the generator. Scale: Ch1, iag : 10 A/div, Ch2, vag : 200 V/div, Ch3, iao : 20 A/div, Ch4, ωrn : 41.89 rad/s/div, Ch5, vout : 100 V/div.

480 460 440 420 20

D. Active and Reactive Power

0 −20 20 0 −20 20 0

−20 400 200 0 −200 −400 0

0.02

0.04 0.06 Time (s)

0.08

0.10

Fig. 19: Power generation and harmonic compensation; balanced rotor resistance is considered.

Instantaneous active and reactive power at different points of the circuit are estimated from the measured current and voltages. Active power at the output of the generator, active filter, and boost converter is estimated. Reactive power into the generator, out of the active filter and into the diode rectifier is estimated. The equations used for power estimation are given in (23). 3 3 Px = (vdx idx + vqx iqx ) , Qx = (vdx iqx − vqx idx ) (23) 2 2 where, x is the general location of the power estimation. The active power at different points of the system is shown in Fig. 22. The power generated by the generator reaches a maximum of 3 kW. The dc active power of the active filter is negligible. Only a small amount of ac active power is exchanged with the dc bus of the active filter. The reactive


9

Paf Pgen

Ch1

Pgen

Ch2

Ch2 Pout

Pout Ch3

Paf

Ch1

Ch3 ωrm Ch4

Fig. 22: Active power flow at different point of the system with sinusoidal wave speed. Scale: Ch1, Paf : 500 W/div, Ch2, Pgen : 1 kW/div, Ch3, Pout : 1 kW/div.

power of the generator as shown in Fig. 23, is completely supplied by the active filter. The reactive power is increased with the loading of the generator due to additional voltage drop across the leakage inductance of the generator and a small amount of reactive power due to diode rectification. Since, the instantaneous reactive power of the generator is a vector product of d-q voltage and currents, the sign of the Qx changes in the negative direction of generator rotation. Because, in the estimation in (23), the scalar multiplication is considered, it becomes negative in the reverse direction, though the reactive power is actually flowing into the generator in both direction of rotation. Experiment is also conducted with the emulated

Qaf (Ch1) Qgen (Ch2)

Qout

Ch1 Ch2 Ch3 Start of generation

Fig. 23: Reactive power flow at different point of the system with sinusoidal wave speed. Scale: Ch1, Qaf : 1 kVA/div, Ch2, Qgen : 1 kVA/div, Ch3, Qout : 1 kVA/div.

WEC driven with the wave profile given in Fig. 2. The active power output of the generator, boost converter and active filter are shown in Fig. 24.

Fig. 24: Active power flow at different point of the system with wave data mentioned in [4]. Scale: Ch1, Paf : 1 kW/div, Ch2, Pgen : 1 kW/div, Ch3, Pout : 1 kW/div, Ch4, ωrm : 209.44 rad/s/div.

Paf Ch1 Pgen (Ch2)

Pout (Ch3) Ch2 Ch3

Fig. 25: Power flow through active filter, when step load is applied by boost converter control. Scale: Ch1, Paf : 1 kW/div, Ch2, P gen: 1 kW/div, Ch3, Pout : 1 kW/div.

E. Slew Rate of Power Control The slew rate of the generating power is determined by the application of a step load from zero to the full rating at the rated speed of the WEC. With a step load command, i∗L , generator and active filter output is shown in Fig. 25. The generator power is around 2 kW and the peak of the transient power of the active filter is 1 kW. Since, the bandwidth of the boost converter current control (600 Hz) is higher than the bandwidth of the dc voltage control (50 Hz), the voltage controller is not able to reject the high bandwidth load disturbance, resulting in the transient power flow from the active filter. To stop the active power flow from the active filter, the inductor current reference is ramped appropriately. With voltage control bandwidth of 50 Hz, the disturbance frequency can be maximum of around 5 Hz, which translates to 130 ms of


rise time. In the experiment, load with ramp rate of 30 kW/s, which translates to the application of the rated load (3 kW) over 100 ms, is applied. The result given in Fig. 26, shows that the active power flow from the active filter is minimized to zero. Since the power cycle of the wave energy is around 5 s, the power control bandwidth of 5 Hz is adequate to generate power by tracking the WEC movement.

10

For peak power of 500 kW and a power factor of 0.9, the active filter full-load VA rating can be computed from (27) as 285 kVA. With a terminal voltage of 460 V, the current rating of the active filter is 358 A. The dc bus voltage can be 800 V, requiring 1200 V insulated gate bipolar transistor (IGBT). The current rating of each IGBT module is 358 A. B. Dc-dc Boost Converter The power output of the generator and terminal voltage are proportional to the speed. Therefore, the diode rectifier output current, iL , is proportional to the rectifier output voltage, Vrec .

Paf

IL = kVrec

Ch1

(28)

Neglecting the non-idealities, the rms current of the boost converter active switch can be expressed as, r √ Vout − Vrec Isw = DIL = kVrec . (29) Vout

Pgen (Ch2)

The maximum of the switch rating can be found from (29) by taking the derivative of the expression of Isw with respect to Vrec and equating it to zero. ! r dIsw d Vout − Vrec = kVrec = 0 (30) dVrec dVrec Vout

Pout (Ch3) Ch2 Ch3

Fig. 26: Power flow through active filter, when ramp load with ramp rate of 30 kW/s, is applied by boost converter control. Scale: Ch1, Paf : 1 kW/div, Ch2, P gen: 1 kW/div, Ch3, Pout : 1 kW/div.

V. S CALED - UP S YSTEM D ESIGN In this section, the design considerations of the proposed power architecture for the WEC with a maximum generated power of 500 kW is considered. The terminal voltage of the generator, VLL , is chosen to be 460 V. The rating of the components for the fully-rated converter system and the proposed architecture are computed and compared. Both SCIG [30] and PMSG are considered as the generator for comparison. A. Active Filter For generated peak power, Pgen , the VA rating of the generator is, Pgen Sgen = (24) p.f. The reactive power of the SCIG, which is supplied from the active filter is p p 1 − p.f.2 2 Qgen = Sgen 1 − p.f. = Pgen . (25) p.f. The VA rating of the harmonic power generated due to the diode rectification is, Qh = 0.3Pgen The total VA rating of the active filter becomes, p q 1 − 0.91p.f.2 2 Qaf = Q2gen + Qh = Pgen . p.f.

(26)

(27)

p

Vout − Vrec −

1 Vrec √ =0 2 Vout − Vrec

(31)

Solving (31), the input and output voltage relation and the corresponding duty cycle at the maximum switch current are given as, 2 1 Vrec = Vout , D = . (32) 3 3 The expression of the maximum rms value of the switch current derived from (29) and (32) as, 2 Isw,max = √ kVout 3 3

(33)

The proportionality constant k can be found from the rated Vrec and Pgen of the generator. The expression of Vrec and Pgen can be given as, √ 3 2 Vrec = VLL (34) π 2 Pgen = Vrec IL = kVrec

(35)

At rated operating condition, the diode rectifier output voltage is computed from (34) as 621 V. The constant, k is found from (35), considering Pgen to be 500 kW as, k=

Pgen = 1.29654 2 Vrec

(36)

The maximum rms value of the switch current now can be computed from (33), considering Vout as 400 V, to be 400 A. The switching frequency of the boost converter can be decided to limit the peak to peak ripple current in the inductor, ∆ILpp . The expression of ∆ILpp is ∆ILpp =

Vrec DTs Lb

(37)


11

TABLE II: Summary of Design Comparison

Components Power Converter Dc bus voltage Power Devices (IGBT) Switching Frequency Inductor

SCIG - 460V, 500kW, p.f., 0.9 Full Converter Proposed 556 kVA 3-ph VSI 285 kVA 3-ph VSI, 500 kW dcdc converter, Diode Rectifier 800 V Both dc bus 800 V 1200V, 698A ×6 1200V, 358A ×6 for AF and 1200V, 400A for dc-dc 10kHz AF 10kHz, dc-dc 5kHz

PMSG - 460V, 500kW, p.f., 1.0 Full Converter Proposed 500 kVA 3-ph VSI 150 kVA 3-ph VSI, 500 kW dcdc converter, Diode Rectifier 800 V Both dc bus 800 V 1200V, 628A ×6 1200V, 188A ×6 for AF and 1200V, 400A for dc-dc 10kHz AF 10kHz, dc-dc 5kHz

1mH, 698A ×3

1mH,628A ×3

1mH, 358A ×3 and 1mH, 805A

By replacing Vrec from (28), it can be written as, ∆ILpp =

IL DTs kLb

∆ILpp DTs = IL kLb

(38)

2) Active Filter Dc Bus Capacitor: Only the ac active power generated due to harmonics, circulates in the dc bus of the active filter. The capacitance of the dc bus is selected to have acceptable voltage ripple due to the ac active power.

(39) D. Comparison with Conventional Fully-rated Converter

Note from (39) that the percentage ripple current is proportional to the duty ratio, D. Once the inductance is fixed, the percentage ripple current decreases at the higher load, since the duty ratio decreases due to the higher input voltage. If the switching frequency of the boost converter is chosen to be 5 kHz, to limit the ripple current to 5 %, the inductance can be computed from (39) as, Lb = 0.003085D

1mH, 188A ×3 and 1mH, 805A

(40)

With full load duty ratio of 0.22375, the required inductance can be computed to be 0.69 mH. Here, for the comparison of the designs, the inductance value is chosen to be 1 mH. C. Passive Component Design 1) L-C Filter: The resonant frequency of L-C filter must be higher than the frequency of the harmonic current to be compensated. The switching frequency of the converter must be at least 4 to 5 times higher than the resonant frequency [31]. The ratio of σLs /Lf provides the uncompensated attenuation that can be utilized at the higher harmonic frequency beyond the resonant frequency. The capacitor needs to be smaller in size to minimize the fundamental current through it. Assuming a generator leakage inductance of 10 mH, the filter inductance is chosen to be 1 mH. The filter capacitance is chosen to be 4.7 uF, resulting in the resonant frequency of 2.3 kHz. To provide passive damping and to absorb the switching frequency ripple, two parallel paths are provided [22] in series with Cf . The resistance of the passive damper Rd needs to be at least 10 times lower than the Lsw −Csw branch, except at the switching frequency, so that the lower order harmonic current passes through the damping resistor and the switching ripples current passes through the Lsw − Csw branch. The switching ripple filter Lsw − Csw is designed to match its resonance with the switching frequency. Values of Csw and Lsw of 0.27 uF and 1 mH respectively, are used in the experiment. The value of the Rd also needs to be very low compared with the impedance of Cf in the working range of the fundamental frequency such that the fundamental voltage does not appear across the damping resistor to cause higher power loss.

The fully-rated and active filter enabled topologies are compared for both SCIG and PMSG based systems and presented in TABLE II. Due to lower rating of the IGBT modules of the active filter, substantial amount of cost saving can be achieved. In the active filter based topology, the line inductor current rating is also quite low compared with the fully-rated converter. Hence, the cost of the total passive component can also be lowered. If the proposed topology is applied to the PMSG, the active filter needs to supply only the harmonic power, resulting in more cost-effective system. VI. C ONCLUSION In this work, a power architecture enabled by a partiallyrated active filter is proposed to generate oscillating power from the wave energy converter. The low cost design of the active filter, by operating at reduced switching frequency, is analyzed. System modeling and control ensures the instantaneous absorption of the harmonic current by the active filter, resulting in a sinusoidal generator current. A comprehensive experimental validation is performed to validate the functioning of the proposed architecture. A guideline for the design of a high power system with the proposed architecture is elaborated. A comparison of the proposed architecture with the traditional fully-rated converter is performed, which shows the proposed technology to be more cost-effective. Application of the proposed topology to the PMSG yields more benefit in terms of the cost and efficiency of the power conversion compared with that of the SCIG. R EFERENCES [1] B. Czech and P. Bauer, “Wave energy converter concepts: design challenges and classification,” IEEE Ind. Electron. Mag., vol. 6, no. 2, pp. 4–16, Jun. 2012. [2] A. V. Jouanne, T. K. A. Brekken, T. Lettenmaier, E. Amon, S. Moran, and A. Yokochi, “Advancing the wave energy industry,” IEEE Potentials, vol. 34, no. 1, pp. 41–47, Jan 2015. [3] L. Cameron, R. Doherty, A. Henry, K. Doherty, J. Vant Hoff, D. Kaye, D. Naylor, S. Bourdier, and T. Whittaker, “Design of the next generation of the oyster wave energy converter,” in Proc. IEEE Int. Conf. on Ocean Energy (ICOE), vol. 6, Bilbao, Spain, 2010. [4] P. Jacobson, “Mapping and assessment of the united states ocean wave energy resource,” Electric Power Research Institute, CA, USA, Tech. Rep., Dec. 2011.


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Samir Hazra (S12) received the B.E. (Hons.) degree in power engineering from Jadavpur University, Kolkata, India, in 2005; and the M.Tech. degree in electrical engineering from the Indian Institute of Technology, Kanpur, India, in 2008. He is currently working toward the Ph.D. degree at the National Science Foundation (NSF) funded Engineering Research Center, Future Renewable Electrical Energy Delivery and Management (FREEDM) System Center, North Carolina State University, Raleigh, NC, USA. From 2005 to 2006, he worked in SIEMENS, Kolkata, and from 2008 to 2011, he was in R& D of TVS Motors Company Ltd., Hosur, India, working as a Power Electronics and Control Engineer. His research interests include the application of wide band-gap power device, medium voltage high power converter, motor drives, energy storage, and renewable energy integration.

Subhashish Bhattacharya (M85, SM13) received B.E. (Hons.) from IIT Roorkee, India in 1986, M.E. from IISc, Bangalore, India in 1988, and Ph.D. from University of Wisconsin-Madison in 2003, all in Electrical Engineering. He worked in the FACTS & Power Quality Group at Westinghouse (later part of Siemens Power T& D) during 1998-2005. He joined the Department of Electrical and Computer Engineering at North Carolina State University (NCSU) in August 2005, where he is the ABB Term Professor, and also a founding faculty member of NSF ERC FREEDM systems center (www.freedm.ncsu.edu), Advanced Transportation Energy Center [ATEC] (www.atec.ncsu.edu) and DOE NNMII PowerAmerica. A part of his PhD research on active power filters was commercialized by York Corp. for their air-conditioner chiller application. His research interests are Solid-State Transformers, MV power converters, FACTS, Utility applications of power electronics and power quality issues; high-frequency magnetics, active filters, and application of new power semiconductor devices such as SiC for converter topologies.