An Improved Control Strategy for Grid Connected

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 4, JULY 2008 1899

An Improved Control Strategy for Grid-ConnectedVoltage Source Inverters With an LCL Filter

Guoqiao Shen, Dehong Xu, Member, IEEE, Luping Cao, and Xuancai Zhu

Abstract—A novel current control strategy based on a new cur-rent feedback for grid-connected voltage source inverters with anLCL-filter is proposed in this paper. By splitting the capacitor ofthe LCL-filter into two parts, each with the proportional divisionof the capacitance, the current flowing between these two parts ismeasured and used as the feedback to a current regulator to stabi-lize and improve the system performances. Consequently, the V–Itransfer function of the grid-connected inverter system with theLCL-filter is degraded from a third-order function to a first-orderone, therefore the closed-loop current feedback control system canbe optimized easily for minimum steady-state error and currentharmonic distortion, as well as the system stability. The character-istics of the inverter system with the proposed controller are inves-tigated and compared with those using traditional control strate-gies. Experimental results are provided, and the new current con-trol strategy has been verified on a 5 kW fuel cell inverter.

Index Terms—Current control, harmonic distortion, intercon-nection, inverters, LCL-filter.

I. INTRODUCTION

TRADITIONALLY, L-filter is used as the interface betweenthe grid network and the grid-connected voltage source

inverters (VSIs). With the L-filter, high switching frequencymust be used to obtain high dynamic performance and suffi-cient attenuation of harmonics caused by the pulsewidth mod-ulation (PWM) method. In contrast, the alternative LCL formof low-pass filter offers the potential for improved harmonicperformance at lower switching frequencies, which is a sig-nificant advantage in higher-power applications [1]. However,the systems incorporating LCL filters are of third order, andthey require more complex current control strategies to maintainsystem stability and are more susceptible to interference causedby grid voltage distortion because of resonance hazards and thelower harmonic impedance to the grid.

When the reference current is a nonsinusoidal signal, a hys-teresis or predictive controller is often deemed a viable solution[2]. While the hysteresis controller is simple and robust, it hasmajor drawbacks in variable switching frequency, current errorof twice the hysteresis band, and high-frequency limit-cycle op-eration [3]. The performance of the predictive controller, on theother hand, is subject to the accuracy of the plant model as wellas the accuracy of the reference current prediction [4].

Manuscript received January 3, 2007; revised March 28, 2007. Published June13, 2008. This work was supported in part by the Delta Power Electronic Tech-nology and Education Foundation. Recommended for publication by AssociateEditor J. Espinoza.

The authors are with the Institute of Power Electronics, College ofElectrical Engineering, Zhejiang University, Hangzhou 310027, China(e-mail: [email protected]; [email protected]; [email protected];[email protected]).

Digital Object Identifier 10.1109/TPEL.2008.924602

Current feedback Proportional Integrate (PI) control with gridvoltage feed-forward is commonly used in stationary referenceframe for current-controlled inverters. But these solutions havetwo main drawbacks: inability of the PI controller to track a si-nusoidal reference without steady-state error and poor distur-bance rejection capability. This is due to the definite controlloop gain required for system stability at the LCL-filter reso-nance frequency. Grid voltage feed-forward is often used to geta good dynamic response, but this leads in turn to the increaseof the grid-voltage background harmonics in the current wave-form because of the imperfect compensations [5], [6].

The rotating synchronous frame PI controller for current con-trol is widely used in three phase inverters to obtain a zerosteady-state error [7], [8]. The limitation consists of significantcomputation arising from the need for multiple reference framesfor harmonic currents attenuations, and its inability of directlyuse in single phase inverters.

Proportional resonant (PR) controller gained a large popu-larity in recent years in current regulation of grid-tied systems[9]–[12]. It introduces an infinite gain at a selected resonantfrequency for eliminating steady-state error at that frequency.However the harmonic compensators of the PR controllersare limited to several low-order current harmonics, due to thesystem instability when the compensated frequency is out ofthe bandwidth of the system [12]. Passive damping method isoften used to maintain the system stability, but it is limited bycost, the value of the inductors, losses, and degradation of thefilter performance [13], [14].

This paper proposes a new control strategy for grid-connectedVSI with an LCL-filter, here, referred as LCCL. The LCCLstrategy “split” the capacitor of LCL-filter into two parts, and thecurrent flowing between these two parts is measured and usedas the feedback of a current controller. In this way, without anydamping resistor, the inverter control system is degraded fromthird-order to first-order, as a first-order system with L-filter.Consequently, the control loop gain and bandwidth can be in-creased and many existent current control methods can be im-plemented to minimize steady-state error and current harmonicdistortion. The characteristics of the inverter system with theproposed LCCL controller are investigated and compared withthe traditional strategy. The new current control strategy hasbeen experimentally verified on a 5 kW DSP controlled fuel cellinverter.

II. SYSTEM STRUCTURE AND CHARACTERISTICS

Fig. 1 shows a system topology for a 5 kW grid-connectedVSI inverter for fuel cell generation. The topology comprisesof a proton exchange membrane fuel cell (PEMFC) system,a dc–dc converter with three-level regulated dc output inter-facing the fuel cell output to the inverter dc side, a half-bridge

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1900 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 4, JULY 2008

Fig. 1. System topology for the grid-connect fuel cell inverter.

single-phase PWM inverter, a low-pass LCL-filter connectingthe inverter output to the grid through a static transfer switch,and a current controller to regulate the inverter.

The LCL-filter is mainly used to achieve decreased switchingripple with only a small increase in filter hardware comparedwith the L-filter. It has the following components:

(1)

(2)

(3)

here, is the inverter side inductance, is the grid side in-ductance of the filter, is the line inductance of the grid, andtheir equivalent series resistors (ESR) are , , and re-spectively. is the capacitance of the LCL-filter.

For the purpose of current control, three transfer functions aregiven as

(4)

(5)

(6)

where is the inverter output current, is the grid sidecurrent, and is the inverter output voltage. For comparingwith an L-filter (with inductance ), we assume

, , and neglect ESR of the inductor. From (1)–(6),the transfer function from inverter output voltage to inverter cur-rent, and grid current, i.e., and , can beexpressed as

(7)

(8)

In order to demonstrate the characteristic of the filter, Fig. 2shows the bode plots of the transfer function of the

Fig. 2. Bode plots of the transfer function of the LCL-filters/� ��.

TABLE ILCL-FILTER PARAMETERS

filter in four cases of component parameters that are listed inTable I. Though all the filters in four cases have a constant totalvalue of inductance, i.e., the same filter cost and size, but theLCL-filter (case 2–4) has more attenuation to the high frequencyswitching ripple, 60 dB per decade, compared with the L-filter(case 1), and the LCL-filter gets the maximum attenuation whenthe inverter side inductance is equal to the grid side inductance,as shown in the case 3.

However, system incorporating LCL filter is of third order,and there exists a peak amplitude response at the resonant fre-quency of the LCL-filter, it requires more carefully design ofLCL-filter parameters and current control strategy to maintainsystem stability.


SHEN et al.: IMPROVED CONTROL STRATEGY FOR GRID-CONNECTED VSIS 1901

Fig. 3. Bode plots of the transfer function of the filters: (a) � �� and (b)� ��.

The most popular method is to insert a damping resistor inthe capacitor shunt branch of the LCL-filter [13]. Then, the (3)should be modified to

Fig. 3 shows the bode plots of the transfer functionand of the filter with a passive damping

and without a passive damping. The damping resistor is 10 ,and the other filter parameters are set as case 3 of Table I. Notethat the high frequency amplitude attenuation in the transferfunction is 20 dB per decade only when the passivedamping is introduced.

As shown in Fig. 3, the damped filter has more attenuationon the resonant frequency, but it has less attenuation in thehigh frequency region, 20 dB per decade less than that of thenon-damped filter. This will make the damping filter a seriousproblem to match the EMI standards for high power con-verters with a lower switching frequency. IEEE Std.519-1992recommended that the harmonics higher than 35th should belimited to be less than 0.3%. Hence, if the switching ripplein the inverter side inductance is designed to be 10% of the

Fig. 4. Block diagrams of the conventional current control: (a) with the invertercurrent feedback �� and (b) with the grid current feedback �� .

rating, more than 30 dB additional attenuation is required inthe transfer function at the switching frequency.Consequently, with the damped filter, the inverter switchingfrequency must be about 30 times higher than the grid sideresonant frequency, whereas with non-damped filter, it can beno more than six times. So, for a given switching frequency ofthe grid-connected inverter, with passive damping method, thefilter size and cost will be raised, and the system bandwidthwill be decreased.

III. PRINCIPLE AND ANALYSIS OF CONTROL STRATEGIES

A. Conventional Control Strategies

Conventionally, the inverter current or the grid current is usedas a feedback of the current controller to regulate the current in-jected into the grid. The block diagrams of two typical conven-tional current controllers are shown in Fig. 4. Where, is the in-verter current reference, is the current regulator determinedby the special control strategy, is the combination of in-verter gain (equal to ) including the PWM switching delay,

is the grid voltage and is defined as the noise voltages,such as the dead time effect of the PWM inverter. The invertercurrent or the grid current is introduced to the current con-troller through a feedback proportional gain ( ). is the

transfer function of the LCL-filter, given by (4) for theinverter current feedback, in Fig. 4(a) or (5) for the grid currentfeedback, in Fig. 4(b).

Then, the control loop gain for the system of Fig. 4 can bederived as

(9)

The steady-state error can be described as

(10)



Fig. 5. Bode plots of the open-loop transfer function under conventional con-trol without current regulators.

The gain of the PWM inverter can be expressed approxi-mately as

(11)

where is the time of PWM control delay.Fig. 5 shows the bode plots of the open-loop transfer func-

tion under the conventional current feedback control strategieswithout current regulators, where the parameters of the filter aregiven as the case 3 of Table I, 0.023, 400 V, andis assumed to be 100 s.

If a PI current regulator is used, for example, then can bedefined as

(12)

For the purpose of the system stability, the proportional gainis limited due to the peak amplitude existing at the reso-

nant frequency of the non-damped LCL-filter in the open-looptransfer function, as shown in Fig. 5. Hence, the control loopgain for the traditional strategy is quite small, and the systemoutput is not able to track a sinusoidal reference without steady-state error.

B. Proposed Control Strategy

The proposed new control structure is shown in Fig. 6. Bysplitting the capacitor of the LCL-filter into two parts, i.e.,and , the current between and , which is indicated as

, is used as the current feedback to control the inverter.Assume and , then the feedback

current can be expressed as

(13)

Fig. 6. Block diagrams of the proposed current control: under LCCL control.

or

(14)

Here, is the total current of the filter capacitors. From (13)and (14), it should be noted that the new control strategy takesthe sum of the grid current and partial capacitor current as thecurrent feedback, instead of which contains no capacitor cur-rent or which contains full capacitor current. In other words,the weighted average of the inverter current and the grid currentis used as the feedback in the proposed new control strategy. Bysplitting the capacitor of the LCL-filter, only one current sensoris required to obtain the weighted average of the inverter currentand the grid current. Now, the LCL-filter is in form of L-C-C-L,so this control strategy is named as LCCL method in short.

The third-order transfer function from to current canbe derived, and expressed as (15). There are three poles and twozeros in this function

(15)

When the value of is selected to satisfy the condition pre-sented as

(16)

Equation (16) can be represented as

(17)

After substituting (16) in (15), is degraded fromthird-order to first-order

(18)

Note that the two zeros counteract two poles in function, and (18) is similar to the transfer function of

L-filter. However, the switching ripple current injected into thegrid is still attenuated by a third-order LCL-filter.

In a word, the proposed LCCL control strategy splits the ca-pacitance in the LCL-filter into two parts with a proportion pre-sented as (17), then measures and takes the current between thetwo parts of the capacitor as the feedback for current control.



Fig. 7. Bode plots of the open-loop transfer function under the LCCL controlwithout current regulators (different ESR values are listed in Table II).

For the steady-state precision of grid current control, the refer-ence of the current control should be modified by adding thegrid frequency current of the second capacitance in LCL-filter,that is, .

Equation (9) and (10) are valid under the proposed LCCLcontrol strategy, but the transfer function, , is givenby (18) instead. Consequently, the peak amplitude existing at theresonant frequency of the LCL-filter is cancelled in the controlloop gain now. Also, the PI current regulator may be appliedin the LCCL control strategy, but this time the value can beincreased to a larger value to improve the system performance.

Considering the ESRs of inductor in LCL-filter, if they areproportional to the corresponding inductances, e.g., as

(19)

then the two zeros counteract two poles in com-pletely, (17) should be modified to

(20)

If the ESR of inductor mismatches (19), zeros can not coun-teract poles completely, but the counteracting effect will existfor rational ESR values. Fig. 7 shows the bode plots of theopen-loop transfer function under the LCCL control strategiesfor three cases of ESR value listed in Table II. The parametersof the filter are given as the case 3 of Table I, 0.023,400 V, 100 s, and the current regulator is not included. Itis shown that the LCCL control is still effective in case of mis-matched ESR values of inductors.

TABLE IILCL-FILTER WITH DIFFERENT ESRS OF INDUCTOR

Fig. 8. Bode plots of loop transfer function for different current feedback con-trols.

TABLE IIIPI PARAMETERS AND RESULTS FOR DIFFERENT CONTROL STRATEGIES

C. Design of the Current Controllers

The merits of the LCCL control strategy can be demonstratedby a comparison of current controller designs for the system.

If PI regulators are selected for the current controllers, forexample, the bode plots of the loop transfer function under dif-ferent control strategies are shown in the Fig. 8, with the PIparameters listed in Table III. All the control strategies have aphase margin more than 30 , but the proportional gains of thePI regulators are quite different to maintain the system stability.The loop gains, error attenuations at the fundamental frequency,and the bandwidth are also calculated and listed in Table III.Fig. 9 shows the low order harmonics attenuations obtained by(10) for corresponding control strategies. Obviously, the loopgain and the cross-over frequency with new control strategy ismuch higher than those with conventional control strategies, re-sulting in minor steady-state error and a better dynamic responsein close-loop control.

If the Proportional Resonant (PR) controller with harmoniccompensations (HC) is to be introduced, it should firstly baseon a proportional or PI system to maintain system stability [11],



Fig. 9. Attenuation of the low order harmonics for different current feedbackcontrols.

Fig. 10. Experimental result with � feed-back, no voltage feed-forward(� � 0.8, � � 8 A).

[12], [15]. Only the LCCL control strategy can provide a suffi-cient bandwidth for harmonic compensations of PR to attenuatethe predominant low order harmonics in the current spectrum,as shown in Fig. 8. Otherwise a passive damping must be in-troduced to expend the bandwidth of the proportional systemwith LCL-filter, and that will in return degrade the switchingfrequency harmonic attenuation in case of a lower switching fre-quency, as mentioned in Section II of this paper.

IV. EXPERIMENTAL RESULTS

A 5 kW DSP controlled prototype is built to verify the pro-posed LCCL control strategy for the grid-connected fuel cellinverter, as shown in Fig. 1. The circuit parameters are:

input voltage: 400 Vdc and 400 Vdc;output: AC 220 V/50 Hz, 5 kW;switching frequency: 16 kHz.

Parameters of the LCL-filter are selected as the case 3 inTable I.

The experimental results are shown in Figs. 10–17. InFigs. 10–13, the grid current is shown on the top, and the gridvoltage is shown on the bottom with 210 V/div. The current inFigs. 10 and 12 are 12 A/div, and it is 24 A/div in Figs. 11 and13.

Fig. 10 shows the experimental result with the grid currentfeed-back and without voltage feed-forward, in the case of

0.8. The grid current is not stable, and is markedly lagged

Fig. 11. Experimental result with � feed-back and grid voltage feed-forward(� � 0.8, � � 23 A).

Fig. 12. Experimental result with proposed control strategy (� � 2.8, � �

8 A).

Fig. 13. Experimental result with proposed control strategy (� � 2.8, � �

23 A).

to the grid voltage. Fig. 11 shows the experimental result withthe grid current feed-back and grid voltage feed-forward con-trol, in the case of 0.8 with a little damping. Though thegrid current is nearly in phase with the grid voltage, the currentwave form is badly distorted.



Fig. 14. Experimental results of THDs of the grid currents.

Fig. 15. Experimental results of power factor for different strategies.

Fig. 16. THD results with different grid side inductances.

Fig. 12 and Fig. 13 show the experimental results with theproposed control strategy, in the case of 2.8, and novoltage feed-forward are introduced. When the grid current

23 A, as shown in Fig. 13, the current total harmonicdistortion (THD) is 3.49%, the third order harmonic current is2.7%, the power factor is 0.995. It should be noted that the gridbackground voltage has a THD of 5.75% and up to 5.6% thirdharmonic at the same time.

Fig. 17. Experimental results of power factor with different grid side induc-tances.

From Figs. 10–13, we can see that the new proposed cur-rent control strategy is effective for minor steady-state error andgood harmonic compensation.

Fig. 14 shows the experimental results of the grid currentTHD and the power factor generated. Curve 1 is the systemoutput under traditional grid current feedback with grid voltagefeed-forward control, and 0.8. Curve 2 are the resultsunder the proposed LCCL control strategy without voltage feed-forward, and 2.8. It is shown that, as the grid current in-creases, the current THD decreases and the new control strategypresents a less distortion.

Fig. 15 shows the experimental results of the power factorof the inverter. Curve 1 is the system output under traditionalgrid current feedback with grid voltage feed-forward control,and 0.8. Curve 2 and 3 are the results under the proposedLCCL control strategy, without or with voltage feed-forward,and 2.8. The grid voltage feed-forward can efficientlyimprove the power factor of the output, but for the grid currentmore than half rating, grid voltage feed-forward can be omittedunder the proposed LCCL control strategy.

Generally, the grid impedance is not easy to be evaluated ex-actly. This is a big problem for most of the grid current controlstrategies. Figs. 16 and 17 show the experimental results withvaried grid side inductances under LCCL control, with the samecontrol parameters and without grid voltage feed-forward. Thegrid side inductance rating is treated as 1.51 mH in controllerdesign. While the grid side inductance is varying from 70% to125% of the rated value, the inverter control system is stableand of good performance. So, it is proved that inverter with theproposed control strategy can robustly response to the variety ofthe grid.

V. CONCLUSION

A novel control strategy for grid-connected voltage sourceinverters (VSI) with an LCL-filter is proposed. By splitting thecapacitor of LCL-filter into two parts proportionally, a new cur-rent feedback control is introduced. In this way, the inverter con-trol system can be degraded from third-order to first-order, theopen loop gain and the bandwidth can be increased, and the



close-loop control system can easily optimized for minimumsteady-state error and current harmonic distortion.

Compared with the traditional strategies, the new controlstrategy has the superiority of simple, low cost and size, highefficiency, and its adaptability to single-phase or three-phase in-verters. Thus, the new current control strategy is more attractiveto grid-connected PV, fuel cell, and wind generation systems.

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Guoqiao Shen was born in Hangzhou, China, in1968. He received the B.S. degree in electrical engi-neering and M.S. degree in power electronics fromthe Department of Electrical Engineering, ZhejiangUniversity, Hangzhou, China in 1990, and 1993,where he is currently pursuing the Ph.D. degree.

From 1993 to 2002, he was with the Zheda Hi-TechDevelopment Co., Ltd., Hangzhou, where he was aDesign Engineer on power supply and a R&D Man-ager. His areas of interests include power convertersfor renewable energy systems, power quality, digital

control, and energy storage technology.

Dehong Xu (M’94) was born in Hangzhou, China, in1961. He received the B.S., M.S., and Ph.D. degreesfrom the Department of Electrical Engineering, Zhe-jiang University, Hangzhou, China, in 1983, 1986,and 1989, respectively.

Since 1989, he has been a faculty member at Zhe-jiang University, where he is currently a Professorin the Department of Electrical Engineering. Hewas a Visiting Professor with the Department ofElectrical Engineering, University of Tokyo, Tokyo,Japan, from 1995 to 1996, and with the Center of

Power Electronics System, Virginia Polytechnic Institute and State University,Blacksburg, from June to December 2000. His research interests includehigh-density power conversion, fuel cell power generation system, powerquality, and SMES.

Dr. Xu is a Vice Chairman of the Chinese Power Supply Society and a ViceChairman of the Chinese Power Electronics Society.

Luping Cao was born in Huzhou, China, in 1982.He received the B.S degree in electrical engineering,from the Department of Electrical Engineering, Zhe-jiang University, Hangzhou, China, in 2005 where heis currently pursuing the M.S. degree.

His research interests include current control andislanding detection for distributed systems.

Xuancai Zhu was born in China in 1980. He re-ceived the B.S degree from the College of Electricaland Electronic Engineering, Huazhong Universityof Science and Technology, Wuhan, China, in 2003and is currently pursuing the Ph.D. degree in theDepartment of Electrical Engineering, ZhejiangUniversity, Hangzhou, China.

His research interests include high efficiencypower converter and fuel cell distributed powersystems.


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An Improved Control Strategy for Grid Connected