C I C E D 5th International Conference on Electricity Distribution Shanghai, 5-6 Sept 2012

Paper CP0191

Paper No CP0191 1/6

RREESSEEAARRCCHH OONN DDEESSIIGGNN FFOORR TTHHEE GGRRIIDD CCOONNNNEECCTTIIOONN CCOONNVVEERRTTEERR OOFF AACC PPEELL

Chengzhi Wang1, Yun Liu2, Xudong Zou3, Jun Xie1, Yunzhao Li1, Dejun Shao1, 1Huazhong Branch of State Grid Corporation of China, Production Technology Department,

Wuhan, Hubei, China, wisewangzhi@163.com 2 Institute of Geophysics & Geomatics, China University of Geosciences, Wuhan, Hubei, China, Ida095757@163.com 3 College of Electric & Electronics Engineering, Huazhong Uninversity of Science and Technology,

Wuhan, Hubei,China, xdzou@mail.hust.edu.cn

ABSTRACT

The AC power source can be tested by the PEL (Power Electronic Load) expediently and economically. The GCC(Grid-Connection Converter) of the PEL should send back the recycling energy to the utility grid with high power factor and low harmonics components. Considering that the single phase PEL can be widely used to test the single phase or three phase power source, the single phase PEL is analyzed in the paper. The paper gives the electrical model and the control scheme based on the GCC’s circuits, and analyzes the harmonic components based on the structure and the function of the PEL. The effects of the notch filter, low-pass filter and mean filter are compared, and the mean filter has been chosen to filter the harmonics components mixed with the dc voltage, for its perfect steady-state characteristics. Large inertia links such as DC capacitor with large capacity and means filter deteriorate the dynamic characteristics, a small signal model based on active power balance is constructed, and feedforward control strategy is applied to ensure the whole system with perfect dynamic response when the input voltage, input current and grid voltage flicker fluctuate. The improved repetitive controller is employed to ensure the inner current loop with zero-errors track characters and hold the GCC with near unity power factor. The experimental and simulation results show that the analysis in the paper is right and the new control scheme is effective. The conclusion can be applied in the control strategy of GCCs, which are used in the distributed power supply system such as Photovoltaic power generations.

KEY WORDS

power electronic load; grid connect converter; mean filter; dc ripple; feedforward control;

1 INTRODUCTION

With the rapid development of economy, all kinds of power sources have been applied in every respect of production and people’s daily life. The stern ex-factory and field tests for them are essential to guarantee quality. A great number of components, such as resistances, inductances and capacitors are used in traditional tests.

These ways not only waste a lot of test energy, but also take a lot of time for workers to fix and modulate the test circuit.

1L2L

C

11T

12T

13T

14T

11D

12D

13D

14D

21T

22T

23T

24T

21D

22D

23D

24D

1dci2dci

_dc ci

1i

2isi2r1r

Input Simulation Converter Output Grid Connection ConverterDC Bus

1P 2P

dcP

Fig.1 Circuit of the PEL

Single phase PEL can be widely used to test single phase or three phase power source by different electrical connection. So the research is based on the single phase PEL. Fig.1 shows that the single phase PEL consists of three parts, including SC (simulation converter), DC link, and GCC(Grid Connection Converter). SC can simulate linear load R, RL, RC and nonlinear load by adjusting the current values, power factor, creast factor and other parameters. GCC sends back the recycling energy to the utility grid with little loss, high power factor and low current THD. DC link hold a constant voltage to ensure that the SC and GCC work properly. Many researches focus on the reference generator[1] and current reference tracing[2]. However, how to enhance the quality of the feedback energy and how to keep the operation of SC and GCC in a state of balance are ignored. The paper constructs the control scheme of GCC based on the circuit equation, analyzes producing mechanism, distributing regulation of the harmonics in the dc bus voltage and the impact on the feed backing current. The mean filter is applied in the controller to eliminate a wide range of harmonics in the dc voltage control loop. According to the instantaneous power and active power balance, the small signal model of the whole system is constructed. The feedforward control of the input current reference and ac voltage can optimize the dynamic state characteristics of the whole system. Current control loop based on repetitive control enhances the quality of the recycling energy. The experimental and simulation results testify the conclusion in the paper.

2 MODEL AND CONTROL BLOCK OF GCC

From the Fig.1, we can get the equation:

2 2

22 2 2s a b

diL u u i r

dt

1 2 _dc

dc dc dc c

duC i i i

dt (1)

The transfer function of the current control loop can be expressed as[3][4]:

C I C E D 5th International Conference on Electricity Distribution Shanghai, 5-6 Sept 2012

Paper CP0191

Paper No CP0191 2/6

2 2

2 2

2 2 2 2

( ) ( ) 1( )

( ) ( ) ( )L a b

i s i sG s

u s u s u s L s r

(2)

The transfer function of the dc voltage control loop can be expressed as:

_

( ) 1( )

( )dc

dcdc c

U sG s

i s Cs (3)

The control block diagram can be shown in Fig.2

2S

2i 2dci 1dci

_dc ci1/ Csdcu

*

dcu

2u

su

2 2

1

L s r

DC VoltageController

ReferenceGenerator

CurrentController

Fig.2 Control block diagram of the GCC

3 SPECTRAL ANALYSIS OF DC LINK VOLTAGE RIPPLE Dc bus voltage fluctuates with the pulsation of the energy, for the reason that the input and the output voltage are both alternating current. Spectral analysis of dc link voltage ripple is essential, because the harmonics will affect the output current reference through the dc voltage control loop. If SC simulates the linear loads, φ means the input power factor, the input voltage and current can be respectively expressed as 1 1 1sinu U t

1 1 1sin( )i I t , [ , ] (4) The output voltage and current can be expressed as

2 2 2sin( )u U t 2 2 2sin( )i I t

(5) θ indicates the phase angle of the input and output voltage, the output power factor is set as 1. Equ.(4) can be derived from tellegen theorem[5]

2 11 1 1 1 1 1

1

2in

diP u i i r L i

dt

2 22 2 2 2 2 2

1

2out

diP u i i r L i

dt

2( )

2dc

in out

d uCP P

dt (6)

Put (4)and (5) into (6), thus the dc voltage can be expressed as

21 1 1 1 1 1

0 1 1

1 1 1[ sin(2 2 ) sin(2 )8 4dc

dc

U I r t U I tCU

22 2 2 2 2 2

2 2

1 1sin(2 2 ) sin(2 2 )

4 8U I t I r t

2 2

2 2 1 12 1cos(2 2 ) cos(2 2 )]

4 4

L I L It t (7)

If the test power source frequency is equal to the grid frequency, 1 2 ＝ , second harmonic will be the main

harmonic in the dc voltage. If the SC simulates the nonlinear loads or the frequency of the test power source is different from the frequency of the grid, the harmonics components will be very complex. Nolinear current is odd harmonic function. It is the sum of fundamental wave and odd harmonics[6], which can be expressed as equ.(8):

1 1 1sin( ) sin( )s n n ni I t I t

2 1

sin( )n n nn k

I t

0,1,2k (8)

Put (4), (5) and (8) into (6), thus the dc voltage can be expressed as

2

sin( )dc dcn n nn k

U U t

1,2,k (9)

The dc voltage harmonic is the sum of the even harmonic. If the frequency of the test power source is different from the frequency of the grid, 1 2 , based on the

intermodulation theory[7][8], the dc voltage harmonics include odd times of input voltage frequency harmonics

12n , odd times of output voltage frequency harmonics

22n and intermodulation production 1 22 2n n

harmonics.

4 FILTER USED IN THE DC BUS VOLTAGE CONTROLLER DESIGN DC bus voltage includes a great number of harmonics, filter must be used to reduce the effects of harmonics on the output current reference. The characteristics of depressing the harmonics in the dc voltage control loop of digital notch filter, low-pass filter and mean filter [9-13]are compared in this paper. When the SC simulates linear load, and the tested power source frequency is equal to the grid frequency, the dc voltage harmonics components will be simple, notch filter can be used to depress the harmonics. But when SC simulates nonlinear load or input power frequency is different from the grid frequency, the harmonics components will be rich. Notch filter can not depress the wide band harmonics. Low-pass filter may do this. But it will be hard for the digital low-pass filter to realize in the digital control system based on DSP or single-chip, for the reason that its parameter number will be very small if its cut-off frequency is low enough and its order is high enough. Mean filter is applied in the control system, due to its terrific steady characteristics of reducing the times harmonics and the interharmonics. The digital mean filter is also easy to design, because its parameter is large enough. The Block diagram of the mean filter is shown in

Fig.3. dcu is the voltage of the dc bus, sf is the sample frequency of the system, ZOH1 is its zero order holder, fNET is the grid frequency, ZOH2 is its zero order holder.

( )dcu k is the sampling value of dc voltage, UDC means

C I C E D 5th International Conference on Electricity Distribution Shanghai, 5-6 Sept 2012

Paper CP0191

Paper No CP0191 3/6

the average of the ( )dcu k .

Equ.(10) can be obtained from the figure

1

1( )

K N

DC dcK

U u KN

(10)

Discrete equation of equ.(10) can be expressed as:

1

10

( )( ) ( ) ( )

NKdc

DC dcK

u zU z z u z F z

N

(11)

The mean filter is a rectangular window FIR filter, it can be expressed as:

11 ( )2

10

sin( )1 1 2( ) ( )sin( )

2

NN jj j KR

K

N

F z W e e eN N

(12)

N means the width of the rectangular window

s

NET

fN

f (13)

Digital cut-off frequency can be expressed as 2 /c c sf f (14) Put (13) and (14)into (12), thus mean filter can be expressed as:

2

12( )( )

22

sin( )1 2( )

sin( )2

c sfs s NET

fc NET

c s

c

s

f ff f

fj

j fR f

f

W e eN

12( )( )

2sin( )1

sin( )

fsf cc NET

NETs

c

s

ffj

fff

f

eN

If c NETf Kf , ( ) 0cjRW e (15)

The FIR mean filter can also be designed as IIR filter[10][11]. It is a sliding window filter, which can be expressed as:

1( ) ( 1) ( ( ) ( ))DC DC dc dcU K U K u K u K N

N (16)

Discrete transfer function of the filter is

2 1

( ) 1 1( )

( ) 1

NDC

dc

U z zF z

u z N z

(17)

Its frequency characteristics are similar to the FIR filter. Fig.4(a) shows the effects of the filters, such as 100Hz north filter, 25Hz low-pass filter, and mean filter on the signal mixed with 40V dc voltage and 20V 100Hz ac voltage. Small dotted line, dotted line and solid line respectively show the filtered signals through north filter, low-pass filter, and mean filter. Fig.4(b) shows the effects of the filters on the signal mixed with 40V dc voltage and 20V 75Hz ac voltage. Excellent harmonic suppression characteristics of the mean filter can be seen from the maps.

: 0.02 /t s DIV

10/

VDIV

Signal

Using Notch

Filterc

Using Low-pass

Filter

Using Mean

Filter

(a) Signal mixed with 100Hz ac voltage

: 0.02 / DIVt s

10/

VDIV

Signal Using Low-pass

Filter

Using Mean

Filter

Using Notch

Filter

(b) Signal mixed with 75Hz ac voltage

Fig.4 Effect of the mean filter

5 FEEDFORWARD CONTROL

Mean filter and DC bus capacitors with large capacity are both big inertia links. They can enhance the quality of the feedback current and dc bus voltage, but damage the dynamic characteristics of the whole system. The feedforward control scheme of the input current reference and ac voltage is presented to stimulate the system response and lower overshoot[14-19]. The active power in SC, GCC and DC bus link can be expressed as:

21 1 1 1 1

1cos( )

2rms rms INrmsP u i i r

22 2 2 2 2

1

2rms rms rmsP i i i r 21

2dc DCP CU (18)

u1rms and i1rms are the valid values of the input voltage and current, Φ means input power factor. i1INrms means the valid values of the fundamental input current. When SC simulates the linear load, i1rms = i1INrms . When SC simulates the nonlinear load, considering that r1 is very small, the loss caused by the harmonics can be ignored.

i1rms is close to i1INrms. dcU means the average value of

the dc bus voltage. If the loss of the whole system is ignored, input power

is equal to the output power in a steady state, 1 2P P .

When the parameters such as: input voltage, input current and grid voltage change, the power balance of the whole system will be destroyed. The power change of the whole system can be expressed as

C I C E D 5th International Conference on Electricity Distribution Shanghai, 5-6 Sept 2012

Paper CP0191

Paper No CP0191 4/6

1 1 2 2 dcP P P P P (19)

Since the parameter can be expressed as the sum of the steady-state value and the variation, equ.20 can be obtained:

1 1 1rms rms rmsu U u , 1 1 1rms rms rmsi I i

2 2 2rms rms rmsu U u , 2 2 2rms rms rmsi I i (20)

DC bus energy changes when the average value of the dc bus voltage changes, it can be expressed as:

2 21 1( )

2 2dc DC DC DC DC DCP C U U CU CU U (21)

Put (20),(21)into (18) and (19), thus the small signal equation of the system can be obtained if the high order term is ignored:

1 1 1 1 1( cos ) cosDC DC rms rms rms rms rmsCU U U I r i I u

2 2 2 2 2( )rms rms rms rms rmsU I r i I u (22)

Equ.(22) can also be expressed as:

1 1 1 1( ) ( )DC vi rms vv rmsC U G s i G s u

2 2 2 2( ) ( )vv rms vi rmsG s u G s i (23)

Fig.5 can be derived from the equ.(23), it is the small signal model with feedforward control. Fvi1(s)、Fvv1(s) and Fvv2(s) are feed forword transfer function of the input current valid value, input voltage valid value and output voltage valid value respectively.

+

-

*DCU

( )iG s

1

Cs

1( )vvG s2 ( )vvG s1( )viG s

2 ( )viG s

1( )viF s

2 ( )vvF s

1( )vvF s

( )dcG s

1rmsi1rmsu 2rmsu

Fig.5 Small signal model with feedforward control

Disturbance can be reduced by feedforward control link. The feedforward transfer function can be expressed as:

1 1 1 11

2 2 2 2

( ) cos( )

( ) ( )vi rms rms

vii vi rms rms

G s U I rF s

G s G s U I r

2 2 22

2 2 2 2

( )( )

( ) ( )vv rms

vvi vi rms rms

G s I rF s

G s G s U I r

1 11

2 2 2 2

( ) cos( )

( ) ( )vv rms

vvi vi rms rms

G s IF s

G s G s U I r

(24)

6 DESIGN FOR THE CURRENT CONTROL LOOP

It is difficult for traditional P or PI controller to meet the need for the stability and the static precision. Amended repetitive controller can trace the reference current with nearly zero gain and zero phase shift[20-22]. S(z) is a compensator which modifies the magnitude and the phase in low and medium frequency band of the system. Repetitive controller can ensure the system terrific steady characteristics. To make up for the shortage of the repetitive controller with dynamic characteristics, the traditional P controller is connected with the repetitive

controller in a paralleled connection. Fig.6 shows the bode map of the current control loop. Solid line means the bode map of the current control loop using PI controller, while dotted line means the one using amended repetitive controller. It can be seen from the figure that amended repetitive controller can ensure the feedback current with high factor and low harmonics if the output current reference is suitable.

Fig.6 Bode map of the current loop with repetitive

controller or PI controller

7 EXPERIMENTAL RESULTS

To testify the effectiveness of the proposed control scheme, a single-phase 10KVA PEL prototype is constructed. The grid voltage is 220V, frequency of the grid is 50Hz, DC voltage reference is 400V, sampling frequency is 12800Hz, input inductance is 1mH, output inductance is 3mH, and the capacity of the DC capacitor is 4700uF.

2U2I 2U

2I

200V/div45A/div T:2.5ms/div

(a)Using PI controller (b)Using Amended Repetitive Controller Fig.7 Waveforms of ac voltage and current of the grid connection converter when PEL operates in full load

Waveforms of the feedback currents are compared in figure 7, when SC simulates the resistance load and works in constant current mode. Fig.7(a) and (b) show the feedback current of the GCC and grid voltage, when the system use the traditional PI controller and amended repetitive controller respectively. The power factors are -0.875 and -0.993. Amended repetitive controller improves the power factor of the output current. Fig.8 shows the feedback current waveform and its spectral analysis, when SC simulates the nonlinear load with crest factor as 3.0. Fig.8(a), (c),(e) show the output current waveforms when the notch filter, low-pass filter or mean filter is applied in the controller respectively. Fig.8 (b), (d),(f) show the spectral analysis of the

C I C E D 5th International Conference on Electricity Distribution Shanghai, 5-6 Sept 2012

Paper CP0191

Paper No CP0191 5/6

feedback currents. The total harmonic distortions are 17.63%, 9.7% and 5.14%, the power factors are 0.974, 0.995 and 1.0. Since the amended repetitive controller is used in all these controllers, the feedback power factor is close to unity. As far as filtering effect is concerned, mean filter has the best filtering effect, the low pass filter is better than the notch filter.

90V/div18.5A/div T:5ms/div18.5A/div

1u

2i

1i

(a)Using notch filter (b)output current spectral analysis

90V/div18.5A/div18.5A/div

T:5ms/div

2i

1i1u

(c)using low pass filter (d) output current spectral analysis

90V/div18.5A/div T:5ms/div18.5A/div

1u

2i

1i

(e)mean filter (f) output current spectral analysis

Fig.8 Effect of the mean filter in experiments

dcU :50V/div 2I :46.5A/div T:40ms/div

dcu

2i

Fig.9 Ac components in dc voltage when the frequency of the input source is different from the grid’s frequency Fig.9 shows the waveforms of the feedback current and the ac component in dc voltage, when the frequency of the tested power source is 60Hz. The dc voltage includes 10Hz, 20Hz, 100Hz,110Hz,120Hz harmonics in terms of the intermodulation theory, but the mean filter can reduce all these harmonics signal well, so it is qualified for the

feedback current reference. The system using mean filter can not remain steady when the input current reference suddenly changes. Fig.10 shows the influence of the feedforward control, when the valid value of the input current reference suddenly increases from 5A to 46A. Fig.10(a) shows the waveforms of grid voltage, input current, feedback current and dc voltage, when the feedforward control parameter is set small. The system can work for a short time, but the oscillation is very serious. The system can not work steadily if the feedforward controller is not added to the whole control system.Fig.10(b) shows that the system can keep stable and the overshoot of the dc voltage is very small when the parameter is set properly. Experimental results show that the feedforward controller is useful and efficient.

450V/div92A/div92A/div

100V/divT:50ms/div

(a)with small feedforward parameter

450V/div92A/div92A/div

100V/div

T:50ms/div

(b)with proper feedforward parameter

Fig.10 Effect of the feedforward control in experiments

8 CONCLUSION

The paper constructs the circuit model and the whole control system, and gives the design process of the controller. The presented control can ensure the system an excellent steady state and dynamic characteristics. 1)The harmonics of the dc bus voltage will be very rich, when the SC simulates nonlinear loads with high crest factor. So it is very important to depress the wide band harmonics. 2)Digital mean filter has the best filtering effect comparing to the notch filter and low pass filter. It enhances the quality of the feedback current. 3)Small signal equations are constructed based on the active power balance of the whole system. Feed forward

C I C E D 5th International Conference on Electricity Distribution Shanghai, 5-6 Sept 2012

Paper CP0191

Paper No CP0191 6/6

control of the input voltage, input current and grid voltage can optimize the dynamic characteristics of the whole system. 4)Current controller using amended repetitive control can trace the current reference with nearly zero steady state errors. It significantly improves the quality of the feedback current. 5)Simulation and experimental results testify the conclusion in this paper.

REFERENCE

[1] Zhao Jianfeng, Pan Shifeng, Wang Xun. "High Power Energy Feedback AC Electronic Load and Its Application in Power System Dynamic Physical Simulation"[J].TRANSACTIONS OF CHINA ELECTROTECHNICAL SOCIETY, 2006, 21(12): 35-39.

[2] LI Chunlong, SHEN Songhua, LU Jialin,et al. "Digital Control With Compensation of Delay for PWM Rectifier" [J].Proceedings of the CSEE, 2007, 27(7): 94-97.

[3] Chengzhi Wang, Yunping Zou, Fen Li, et al. " Research on the filters used in the PWM VSR"[C]. Applied Power Electronics Conference and Exposition, Austin, TX, USA, 2008: 1353-1357.

[4] Wang Chengzhi, Zou Yunping, Jia Kai, Li Fen. " Research on the Single-Phase Rectifier" [J]. Power Electronics. 2008.42(1):69-71.．

[5] Qiu Guanyuan. 2010, Electrical Circuit ( Fourth Edition). Higher Education Press, Beijing, China, 96-99.

[6] Zheng Junli, Yin Qiheng, Yang WeiLi. 2009, Signals and Systems ( Second Edition). Higher Education Press, Beijing, China, 95-97.

[7] Li Qionglin, Liu Huijin, Zhang Zhenhuan, et al. " Interharmonic Analysis in the AC/DC/AC System Based on Intermodulation Theory" [J].Proceedings of the CSEE,2007,27(34):107-114.．

[8] Li Qionglin, Liu Huijin, Li Zhimin, et al. "Analysis on Interharmonics Generation in the Asynchronous Interconnection HVDC System " [J]. Southern Power System Technology, 2008,2(2):49~57.．

[9] Zou Yunping, Li Xiao. 1994, Signal Conversion and Processing, Huazhong University of Science and technology press . Wuhan, China.353-403.

[10] Zou Yunping, Lin Hua. 2003, Signal and System Analysis. Science Press. Beijing, China. 313-316.

[11] Cheng Peiqing, 2001, Digital Signal Processing Tutorial(Second Edition). Tsinghua University Press,

Beijing, China. 344-355. [12] Luo Huan. Active Power Current Detection and

Realization Based on Fryze Power Definition[D]. Wuhan：Wuhan University,2004.．

[13] Zhang Junming. Study on Harmonic Currents Detecting Methods in Active Power Filters[D]. Wuhan：Wuhan University,2004.．

[14] Li Shijie, Li Yaohua, Chen Rui. "Study of the Optimum Feed-forward Control Strategy in Back-to-back Converter System"[J]. Proceedings of the CSEE, 2006, 26(22):74-79.．

[15] Salomonsson, D. Sannino, "A. Comparative Design and Analysis of Dc-Link -Voltage Controllers for Grid-Connected Voltage-Source Converter"[C]. IEEE Industry Applications Conference, 2007, New Orleans, LA. IAS’2007: 1593-1600.

[16] P. Antoniewicz, M. Jasinski, M.P. Kazmierkowski. "AC/DC/AC Converter with Reduced DC Side Capacitor Value"[C]. IEEE EUROCON’2005, Belgrade, Serbia and Montenegro: 1481-1484.

[17] Somkun, S. Sehakul, P. Chunkag, V. "Novel control technique of single-phase PWM rectifier by compensating output ripple voltage"[C]. IEEE ICIT’2005:969-974.

[18] Hyosung Kim,Seung-Ki Sul. "Compensation voltage control in dynamic voltage restorers by use of feed forward and state feedback scheme"[J]. IEEE Transaction on Power Electronics, 2005,20(5):1169-1177.．

[19] Zhang Hui, Liu Jinjun, Huang Xinming, et al. "Modeling and Analysis of DC Link Voltage Control for Universal Power Quality Controllers"[J]. Transactions of China Electrotechnical Society, 2007, 22(4): 144-149.．

[20] Chengzhi Wang, Yunping Zou, Kai Jia, et,al. "Research on the power electronic loas based on the repetitive controller"[C]. Applied Power Electronics Conference and Exposition, Austin, TX, USA, 2008: 1735-1740.

[21] Wei Xueliang, Dai Ke, Fang Xin, Kang Yong. "Performance Analysis and Improvement of Output for Three Phase Shunt Active Power Filter"[J]. Proceedings of CSEE, 2003.27(28):113-119.．

[22] Kai Zhang, Yong Kang, Jian Xiong, Jian Chen. "Direct Repetitive Control of SPWM Inverter for UPS Purpose"[J]. IEEE Transactions on Power Electronics, 2003, 18(3):784-792.