IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 4, DECEMBER 2007 881

A Single-Stage Three-Phase Grid-ConnectedPhotovoltaic System With Modified MPPTMethod and Reactive Power Compensation

Wu Libo, Zhao Zhengming, Senior Member, IEEE, and Liu Jianzheng

Abstract—Single-stage grid-connected photovoltaic (PV) sys-tems have advantages such as simple topology, high efficiency, etc.However, since all the control objectives such as the maximumpower point tracking (MPPT), synchronization with the utility volt-age, and harmonics reduction for output current need to be consid-ered simultaneously, the complexity of the control scheme is muchincreased. This paper presents the implementation of a single-stagethree-phase grid-connected PV system. In addition to realize theaforementioned control objectives, the proposed control can alsoremarkably improve the stability of the MPPT method with a mod-ified incremental conductance MPPT method. The reactive powercompensation for local load is also realized, so as to alleviate gridburden. A DSP is employed to implement the proposed MPPTcontroller and reactive power compensation unit. Simulation andexperimental results show the high stability and high efficiency ofthis single-stage three-phase grid-connected PV system.

Index Terms—Grid-connected inverters, maximum power pointtracking (MPPT), photovoltaic (PV), solar energy.

I. INTRODUCTION

PHOTOVOLTAIC (PV) systems are solar energy supplysystems, which either supply power directly to an electri-

cal equipment or feed energy into the public electricity grid.Generally, PVs are considered as an expensive method of pro-ducing electricity. However, in stand-alone situations, PVs arethe most economic solutions to provide the required power ser-vice. Moreover, with the development of PV technologies, appli-cations of PVs in grid-connected situations have grown rapidly,indicating that PVs are very attractive to produce environmen-tally benign electricity for diversified purposes [1]–[3].

Power electronic conversion is the key to improve the effi-ciency of PV panels and the system stability in grid-connectedPV systems. One task of power electronic conversion is to con-tinuously adapt the system such that it can draw the maximumpower from the PV panels regardless of weather or load con-ditions. Since the PV panels have a nonlinear voltage–currentcharacteristics, and the insolation and ambient temperature areunpredictable, the maximum power point tracking (MPPT)controller tends to be a nonlinear and time-varying system.Many MPPT techniques have been developed such as the per-turb and observe method [4], [5], the incremental conductancemethod [6], etc. The perturb and observe method is simple for

Manuscript received October 25, 2005; revised June 28, 2006. Paper no.TEC-00363-2005.

The authors are with the State Key Laboratory of Power Systems, De-partment of Electrical Engineering and Applied Electronic Technology, Ts-inghua University, Beijing 100084, China (e-mail: wulibo@tsinghua.org.cn;zhaozm@tsinghua.edu.cn; liujianzheng@263.net).

Digital Object Identifier 10.1109/TEC.2007.895461

implementation, but its accuracy is low because the perturba-tion process would make the operation point of the PV panelsto oscillate around the maximum power point (MPP). Further-more, when insolation changes rapidly, the perturb and observemethod would probably fail to track the MPP. The incrementalconductance method offers good performance under the condi-tions of rapidly changing insolation. However, high complexityof the method requires high sampling accuracy and fast controlspeed, which adds to the cost of the total system.

Generally, a grid-connected PV system has two control loops.The inner loop is a pulse width modulation (PWM) loop, whichmodulates output currents of the inverter, to meet the require-ments of the waveform and phase. The outer loop determines theoutput power of the inverter according to the MPP of PV panels.Conventionally, these two loops are realized respectively in twostages of power conversion [7]. One is a dc/dc converter withMPPT control and the other is a dc/ac inverter. But two stagesmay result in more power loss than that of the single-stage con-version. In single-stage grid-connected PV systems, both loopsare realized simultaneously in one power conversion stage, thus,simplifying the system topology. However, to maintain the si-nusoidal waveform of output currents, the minimum period tochange the reference output power should be half of the gridvoltage period, thus, the outer loop here has a much lower speedthan that of the PWM loop. To maintain the system stability, theMPPT method should be modified to work at low speed.

This paper presents a modified incremental conductanceMPPT method applied in a single-stage grid-connected PV sys-tem [8]. With voltage and current sensors, the controller adopt-ing this method calculates the recent power point of PV panelsand decides the output power of the inverter. To avoid voltagecollapse phenomena, the minimum step length to modify the ref-erence value of the output power varies according to the trackingdirection. However, because the tracking speed is limited by thestep length and the control period, the variable-step method stillcannot assure the stability of the dc-link voltage when there is arapid change of insolation. In the modified method, if the outputpower of PV panels is detected to be decreasing rapidly, the con-troller will presume that a step change of insolation occurs, andthen, reset the reference output power of the inverter accordingto the current PV output power. The control objective of thismethod is to balance the input and output current of the dc-linkcapacitor and maintain its voltage so as to track the MPP formaximizing the energy capture.

Generally, a single-stage grid-connected PV system consistsof voltage and current sensors, a power electronic converter, and

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882 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 4, DECEMBER 2007

Fig. 1. Schematic diagram of the proposed grid-connected PV system. vPV :output voltage of PV panels; iPV : output current of PV panels; iPV U/V /W :output currents of the inverter in three phases; iGRID U/V /W : currents drawnfrom grid in three phases; iLOAD U/V /W : local load currents in three phases;S1−S6 : switching devices in the inverter; C : dc-link capacitor; LU/V /W :inverter output filters.

a control system with a DSP or micro controller unit (MCU).If load current sensors are included, the PV system can alsoserve as a static var generator to compensate reactive power oflocal load. Integration of a reactive power compensation unitin the system can reasonably improve system performance withfew additional costs. The proposed PV system in this paper hasrealized the function of detecting and compensating reactivepower.

The proposed grid-connected PV system consists of PV pan-els, an inverter, a controller, and filters, which will be discussedin Section II. Section III will introduce the electrical character-istics of PV panels and discuss the operation principle of themodified MPPT method. Simulation of the stability will also bepresented to explain the performance of this MPPT method inSection IV. Section V will discuss the implementation of a reac-tive power compensation unit in the system. The experimentalresults and conclusions will be included in the Sections VI andVI1, respectively.

II. OVERALL SYSTEM CONFIGURATION

The proposed three-phase single-stage grid-connected PVsystem consists of PV panels, an inverter, a controller, and filters,which is shown in Fig. 1.

In the proposed grid-connected PV system, output currents ofthe inverter are the control objects of MPPT, PWM, and reactivecompensation. Currents drawn from grid or local load currentsalso need to be sampled for the calculation of local reactiveload.

III. PROPOSED MODIFIED MPPT METHOD

Fig. 2(a) and (b) shows the simulated I−V and P−V char-acteristics of the ideal PV panels, respectively. The series of

Fig. 2. Simulated characteristics of PV panels under different insolation con-ditions. (a) I−V characteristics. (b) P −V characteristics.

curves show the output characteristics under different insola-tion conditions [9], [10].

The output voltage, current, and power of the PV panelsin the grid-connected system are defined as VPV , IPV , andPPV , respectively. When the PV panels operate at the MPP,(1) must be satisfied. In a PV system, see Fig. 2(b), there arethree kinds of operating states, which are discussed herein asfollows.

1) If (2) is true, the PV panels operate in the voltage-sourceregion, and the reference output power of the inverterPREF should be increased to approach the MPP.

2) If (3) is true, the PV panels operate in the current-sourceregion, and PREF should be decreased rapidly to avoid avoltage collapse and to approach the MPP simultaneously.

3) If (1) is true, PREF should be unchanged since the PVpanels operate already at the optimal point.

Also

∂PPV

∂VPV=

∂(VPVIPV)∂VPV

= VPV∂IPV

∂VPV+ IPV

∂VPV

∂VPV= 0 (1)

VPV∂IPV

∂VPV+ IPV

∂VPV

∂VPV< 0 (2)

VPV∂IPV

∂VPV+ IPV

∂VPV

∂VPV> 0. (3)

In the proposed single-stage PV system, if the reference out-put power of the inverter is increased or decreased by a fixedstep length, the method could be called a constant-step MPPT

LIBO et al.: SINGLE-STAGE THREE-PHASE GRID-CONNECTED PV SYSTEM 883

Fig. 3. Simulation of the constant-step MPPT method (steady state). (a) PVoutput power. (b) Inverter output current.

method. Fig. 3 shows the steady-state simulation waveforms ofa single-stage grid-connected PV system with the constant-stepMPPT method. The PV panels in simulation are 300 WP (peakwatt), 23-V open voltage, and 17 V at the MPP. The dc-linkcapacitance is 2200 uF.

Fig. 3 shows that, in a steady state, the constant-step MPPTmethod can balance the input and output current of the dc-linkcapacitor, so as to track the MPP of PV panels. The PV outputpower is very close to the maximum power.

The MPPT control objective in PV systems is to regulatethe actual operating voltage of the PV panels according to thevoltage at MPP, by adjusting the output power of the inverter.In the tracking process, if the operating voltage of PV panels isgreater than the MPP voltage, the system controller will increasethe output power of the grid-connected inverter to pull it down;if the operating voltage of PV panels is less than the MPPvoltage, the system controller will decrease the output power ofthe grid-connected inverter to push it up. However, in the lattercase, if insolation decreases at the same time, after the valueof PREF has been set lower, inverter output power may be stillgreater than the actual PV output power, which will pull downthe dc-link voltage further. From Fig. 2(b), when the operatingpoint of PV panels moves from MPP to its left side, the outputpower will decrease at the same time, which will cause thedc-link voltage to collapse finally.

To avoid a dc-link voltage collapse phenomenon in the PVgrid-connected system, a novel MPPT method with a variable-step method is proposed. The modification of this method fo-cuses on the closed-loop control of power. The modified methodcan fulfill the requirement of high efficiency and high stability.

When the insolation of sunlight is smooth and steady, thetracking process of the modified MPPT method is similar to theconstant-step MPPT method. Both of them track the MPP of PVpanels by increasing or decreasing the reference output power of

Fig. 4. Flow process diagram for determination of PREF in the modifiedMPPT method.

the inverter. The difference between them is that, in the modifiedmethod, the step length is different in the increasing case and thedecreasing case. In the increasing case, it is smaller. Therefore,when PREF exceeds the current maximum output power of PVpanels, the system controller can rapidly decrease it so as tomaintain dc-link voltage, to operate PV panels near its MPP,and to assure the system stability.

However, when there is an insolation disturbance or stepchange of sunlight, decreasing PREF by a large step lengthstill cannot assure the stability of the dc-link voltage.

In the modified method, the system controller samples the PVoutput voltage VPV and current IPV , and then calculates outputpower PPV . If PPV is detected to be decreasing rapidly, thecontroller will presume that a step change of insolation occurs,and the reference value of inverter output power will be resetaccording to the current PV output. This method can keep thesystem operating stably in an insolation step change process.

Fig. 4 is the flow process diagram for determination of PREFin the modified MPPT method. ∆P is the step change thresholdvalue of PV panels’ output power, P1 is the minimum step lengthto modify PREF ,K is a constant with a value greater than 1,and P0 is the PV output power in the previous control period.In the simulation, K is set between 2 and 3.

IV. STABILITY COMPARISON

To test the stability of the proposed modified MPPT method,the simulation results of a single-stage grid-connected PV sys-tem that uses the modified method are compared to the resultsof the constant-step method.

884 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 4, DECEMBER 2007

Fig. 5. Simulation of the dc link voltage collapse process. (a) Step change ofinsolation. (b) The dc-link voltage collapse process.

Fig. 5 shows a simulated dc-link voltage collapse process inthe PV system with the constant-step method. From Fig. 5, whenthere is a negative step change of insolation for 0.1 s, PREF willdeviate from the current MPP of PV panels, which will pulldown the dc-link voltage until the inverter output current isdistorted. The voltage of the dc-link capacitor will rise slowlyafter its input and output currents balance again.

The modified MPPT method is also simulated to test its sta-bility. Circuit parameters are the same as the aforementionedsimulation. Fig. 6 shows the simulation waveforms of a track-ing process during step change of insolation. Fig. 6 indicatesthat systems with the modified method can detect step changeof insolation, modify the reference value of output power, andprevent the dc-link voltage collapses. Simulation results showthat the system can remain stable in case of a 50% step changeof insolation. The high stability of the MPPT method will alsoensure the high efficiency of the system by drawing the max-imum power from the PV panels under different insolationconditions.

V. REACTIVE POWER COMPENSATION UNIT

For three-phase power systems with sinusoidal voltages andsinusoidal currents, quantities such as active power, reactive

Fig. 6. Simulation of tracking process during step change of insolation withthe modified MPPT method. (a) Step change of insolation. (b) dc-link voltage.(c) Output current of inverter after insolation step change.

Fig. 7. Diagram of calculation for output current reference value in the three-phase grid-connected PV system.

power, active current, and reactive current are conventionallydefined on the average concept. But for systems with unbal-anced and distorted currents, average concept is not suitable.The concept of instantaneous reactive power, which has beenestablished by Akagi et al. [11], provides an effective methodto calculate and compensate the reactive power for three-phasesystems.

In the proposed grid-connected PV system, the flowchart forthe calculation of the output current reference value is shown in

LIBO et al.: SINGLE-STAGE THREE-PHASE GRID-CONNECTED PV SYSTEM 885

Fig. 8. Photographs of the experimental system. (a) Inverter in the proposedPV system. (b) PV panels installed in Tsinghua University.

Fig. 9. Experimental waveform of dc-link voltage during a step change ofinsolation.

Fig. 7, which includes both the MPPT algorithm and a reactivepower compensation unit.

In Fig. 7, the detected load currents iLOAD U , iLOAD V , andiLOAD W are transformed into p−q coordinates by the block(Cpq) after the α−β coordinate transformation. The dc compo-nents ip0 and iq0 with extremely low-frequency components areextracted from the currents ip and iq on p−q coordinates by alow-pass filter (LPF). They are then transformed into α−β coor-dinates again by the block Cpq−1 , after which the fundamentalcurrents iF U , iF V , and iF W are obtained by retransforming

Fig. 10. Experimental waveforms of the proposed three-phase grid-connectedPV system. (a) Output voltages and currents without reactive power com-pensation. (b) Output voltages and currents with positive reactive powercompensation. (c) Output voltages and currents with negative reactive powercompensation. (d) Output current with deadbeat algorithm. (e) Currents drawnfrom the grid.

886 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 4, DECEMBER 2007

iF α and iF β into U−V −W coordinates. Finally, the referencecurrents iREF U , iREF V , and iREF W are calculated by block(CAL). The equations are listed as follows:

iREF U = iLOAD U − iF U + iPV UiREF V = iLOAD V − iF V + iPV ViREF W = iLOAD W − iF W + iPV W .

(4)

With the proposed method, it is simple to determine the ref-erence currents of the three-phase grid-connected PV inverterwith minute fluctuations.

VI. EXPERIMENTAL RESULTS

Based on the earlier theoretical analysis, a 300-WP experi-mental system was designed and implemented. Fig. 8 presentsphotographs of the inverter and PV panels in the proposed PVsystem that was installed on the West Main Building, TsinghuaUniversity, Beijing, China.

The experimental waveform of the proposed modified MPPTmethod applied in the single-stage grid-connected PV system isshown in Fig. 9. After a step change of insolation, the MPPTcontroller can maintain the dc-link voltage and keep it close tothe MPP. In Fig. 10, experimental waveforms of the proposedPV system are shown. A deadbeat control algorithm [12] is alsoemployed in the system for PWM generation. The current wave-form of the inverter adopting this deadbeat algorithm is shownin Fig. 10(d). The currents drawn from the grid are included inFig. 10(e) to indicate that there is no reactive power drawn fromthe grid after the compensation.

VII. CONCLUSION

Implementation of a single-stage three-phase grid-connectedPV system is presented in this paper. The novel modified MPPTmethod applied in the system can remarkably improve systemstability during rapidly changing process of insolation. Due to itsimprovement on the dynamic response, the step length of outputpower reference is reduced, which can also increase the steady-state accuracy of the method. A reactive power compensationunit based on the instantaneous reactive power theory is alsorealized in the same system, which can compensate the reactivepower of local load without increasing total system cost.

REFERENCES

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[3] E. V. Solodovnik, S. Liu, and R. A. Dougal, “Power controller designfor maximum power tracking in solar installations,” IEEE Trans. PowerElectron., vol. 19, no. 5, pp. 1295–1304, Sep. 2004.

[4] O. Wasynczuck, “Dynamic behavior of a class of photovoltaic powersystems,” IEEE Trans. Power App. Syst., vol. PAS-102, no. 9, pp. 3031–3037, Sep. 1983.

[5] P. Huynh and B. H. Cho, “Design and analysis of a microprocessor-controlled peak-power-tracking system,” IEEE Trans. Aerosp. Electron.Syst., vol. AES-32, no. 1, pp. 182–190, Jan. 1996.

[6] K. Hussein, I. Muta, T. Hoshino, and M. Osakada, “Maximum photo-voltaic power tracking: an algorithm for rapidly changing atmosphericconditions,” Proc. Inst. Electr. Eng., vol. 142, no. 1, pp. 59–64, Jan. 1995.

[7] A. Lohner, T. Meyer, and A. Nagel, “A new panels-integratable inverterconcept for grid-connected photovoltaic systems,” in Proc. IEEE Int.Symp. Ind. Electron., Warsaw, Poland, vol. 2, Jun. 17–20, 1996, pp. 827–831.

[8] W. Libo, Z. Zhengming, and L. Jianzheng et al., “Modified MPPT strategyapplied in single-stage grid-connected photovoltaic system,” in Proc. 8thInt. Conf. Electr. Mach. Syst. Conf., Sep. 27–29, 2005, vol. 2, pp. 1027–1030.

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[10] C. Kunlun, Z. Zhengming, and Y. Liqiang, “Implementation of a stand-alone photovoltaic pumping system with maximum power point tracking,”in Proc. ICEMS, Aug., vol. 1, pp. 612–615.

[11] H. Akagi, Y. Kanazawa, and A. Nabae, “Instantaneous reactive powercompensators comprising switching devices without energy storage com-ponents,” IEEE Trans. Ind. Appl., vol. IA-20, no. 3, pp. 625–30, May/Jun.1984.

[12] T. Kawabata, T. Miyashita, and Y. Yamamoto, “Dead beat control threephase PWM inverter,” IEEE Trans. Power Electron., vol. 5, no. 1, pp. 21–28, Jan. 1990.

Wu Libo received the B.S.E.E., M.S.E.E., and Ph.D.degrees from Tsinghua University, Beijing, China, in2001, 2003, and 2006, respectively.

His current research interests include power elec-tronics applications, inverter design, and stand-aloneand grid-connected photovoltaic systems.

Zhao Zhengming (M’02–SM’03) was born in Hu-nan, China. He received the B.Sc. and M.Sc. de-grees in electrical engineering from Hunan Univer-sity, Changsha, China, in 1982 and 1985, respec-tively, and the Ph.D. degree from Tsinghua Univer-sity, Beijing, China, in 1991.

He was in the Department of Electrical Engineer-ing, Tsinghua University, where he is currently aProfessor. From 1994 to 1996, he was a Postdoc-toral Fellow at the Ohio State University. He has alsobeen a Visiting Scholar at the University of Califor-

nia at Irvine. His current research interests include power electronics and motorcontrol, high power conversion, motor design and drive, adaptive parameteridentification, solar energy applications, etc.

Liu Jianzheng received the B.S.E.E. and M.S.E.E.degrees from Tsinghua University, Beijing, China, in1985 and 1988, respectively.

He is currently an Associate Professor in the De-partment of Electrical Engineering, Tsinghua Uni-versity. His current research interests include powerelectronics applications, grid-connected photovoltaicsystems, and wind generation systems.