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992 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 4, APRIL 2010

Design and Analysis of a Grid-ConnectedPhotovoltaic Power System

Bo Yang, Wuhua Li, Member, IEEE, Yi Zhao, and Xiangning He, Fellow, IEEE

Abstract—A grid-connected photovoltaic (PV) power systemwith high voltage gain is proposed, and the steady-state modelanalysis and the control strategy of the system are presented in thispaper. For a typical PV array, the output voltage is relatively low,and a high voltage gain is obligatory to realize the grid-connectedfunction. The proposed PV system employs a ZVT-interleavedboost converter with winding-coupled inductors and active-clampcircuits as the first power-processing stage, which can boost a lowvoltage of the PV array up to a high dc-bus voltage. Accordingly,an accurate steady-state model is obtained and verified by the sim-ulation and experimental results, and a full-bridge inverter withbidirectional power flow is used as the second power-processingstage, which can stabilize the dc-bus voltage and shape the outputcurrent. Two compensation units are added to perform in the sys-tem control loops to achieve the low total harmonic distortion andfast dynamic response of the output current. Furthermore, a simplemaximum-power-point-tracking method based on power balanceis applied in the PV system to reduce the system complexity andcost with a high performance. At last, a 2-kW prototype has beenbuilt and tested to verify the theoretical analysis of the paper.

Index Terms—Bidirectional power flow control, compensa-tion units, direct current control, maximum-power-point-tracking(MPPT) method, photovoltaic (PV) system, steady-state model.

I. INTRODUCTION

TODAY photovoltaic (PV) power systems are becomingmore and more popular, with the increase of energy de-

mand and the concern of environmental pollution around theworld. Four different system configurations are widely devel-oped in grid-connected PV power applications: the centralizedinverter system, the string inverter system, the multistring in-verter system and the module-integrated inverter system [1]–[4].Generally three types of inverter systems except the centralizedinverter system can be employed as small-scale distributed gen-eration (DG) systems, such as residential power applications.The most important design constraint of the PV DG system isto obtain a high voltage gain. For a typical PV module, theopen-circuit voltage is about 21 V and the maximum powerpoint (MPP) voltage is about 16 V. And the utility grid voltageis 220 or 110 Vac. Therefore, the high voltage amplification isobligatory to realize the grid-connected function and achieve thelow total harmonic distortion (THD). The conventional system

Manuscript received February 28, 2009; revised July 27, 2009 and August 29,2009. Current version published April 9, 2010. This work was supported by theNational Nature Science Foundations of China (50737002 and 50777055) andby the China Postdoctoral Science Foundation (200902625). Recommended forpublication by Associate Editor R. Burgos.

The authors are with the College of Electrical Engineering, Zhejiang Uni-versity, Hangzhou 310027, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPEL.2009.2036432

requires large numbers of PV modules in series, and the normalPV array voltage is between 150 and 450 V, and the systempower is more than 500 W. This system is not applicable to themodule-integrated inverters, because the typical power rating ofthe module-integrated inverter system is below 500 W [3], [4],and the modules with power ratings between 100 and 200 Ware also quite common [5]. The other method is to use a linefrequency step-up transformer, and the normal PV array volt-age is between 30 and 150 V [3], [4]. But the line frequencytransformer has the disadvantages of larger size and weight.

In the grid-connected PV system, power electronic invertersare needed to realize the power conversion, grid interconnec-tion, and control optimization [6], [7]. Generally, gird-connectedpulsewidth modulation (PWM) voltage source inverters (VSIs)are widely applied in PV systems, which have two functions atleast because of the unique features of PV modules. First, thedc-bus voltage of the inverter should be stabilized to a specificvalue because the output voltage of the PV modules varies withtemperature, irradiance, and the effect of maximum power-pointtracking (MPPT). Second, the energy should be fed from the PVmodules into the utility grid by inverting the dc current into asinusoidal waveform synchronized with utility grid. Therefore,it is clear that for the inverter-based PV system, the conversionpower quality including the low THD, high power factor, andfast dynamic response, largely depends on the control strategyadopted by the grid-connected inverters.

In this paper, a grid-connected PV power system with highvoltage gain is proposed. The steady-state model analysis andthe control strategy of the system are presented. The grid-connected PV system includes two power-processing stages:a high step-up ZVT-interleaved boost converter for boosting alow voltage of PV array up to the high dc-bus voltage, which isnot less than grid voltage level; and a full-bridge inverter for in-verting the dc current into a sinusoidal waveform synchronizedwith the utility grid. Furthermore, the dc–dc converter is respon-sible for the MPPT and the dc–ac inverter has the capability ofstabilizing the dc-bus voltage to a specific value.

The grid-connected PV power system can offer a high voltagegain and guarantee the used PV array voltage is less than 50 V,while the power system interfaces the utility grid. On the onehand, the required quantity of PV modules in series is greatlyreduced. And the system power can be controlled in a widerange from several hundred to thousand watts only by changingthe quantity of PV module branches in parallel. Therefore, theproposed system can not only be applied to the string or multi-string inverter system, but also to the module-integrated invertersystem in low power applications. On the other hand, the non-isolation PV systems employing neutral-point-clamped (NPC)

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YANG et al.: DESIGN AND ANALYSIS OF A GRID-CONNECTED PHOTOVOLTAIC POWER SYSTEM 993

Fig. 1. Proposed grid-connected PV power system.

Fig. 2. High step-up ZVT-interleaved boost converter and its equivalent cir-cuit. (a) ZVT-interleaved boost converter. (b) Equivalent circuit.

topology, highly efficient reliable inverter concept (HERIC)topology, H5 topology, etc. [8]–[14], have been widely usedespecially in Europe. Although the transformerless system hav-ing a floating and nonearth-connected PV dc bus requires moreprotection [10], [15], [16], it has several advantages such as highefficiency, lightweight, etc. Therefore, the nonisolation schemein this paper is quite applicable by employing the high step-upZVT-interleaved boost converter, because high voltage gain ofthe converter ensures that the PV array voltage is below 50 V andbenefits the personal safety even if in high-power application.Fig. 1 shows the proposed grid-connected PV power system.

II. STEADY-STATE MODEL OF HIGH STEP-UP

ZVT-INTERLEAVED BOOST CONVERTER

Fig. 2 shows the ZVT-interleaved boost converter withwinding-coupled inductors and active-clamp circuits, which isproposed by our research team [17]. The winding-coupled in-ductors offer the voltage-gain extension [18]–[20]. The active-clamp circuits realize the ZVT commutation of the main

switches and the auxiliary switches [17]. As shown in Fig. 2(a),S1 and S2 are the main switches; Sc1 and Sc2 are the active-clamp switches; Do1 and Do2 are the output diodes. The cou-pling method of the winding-coupled inductors is marked byopen circles and asterisks. Each coupled inductor is modeledas the combination of a magnetizing inductor, an ideal trans-former with corresponding turns ratio and a leakage inductorin series with the magnetizing inductor. The equivalent circuitmodel is demonstrated in Fig. 2(b), where Lm1 and Lm2 arethe magnetizing inductors; Llk1 and Llk2 are the leakage in-ductors including the reflected leakage inductors of the secondand third windings of the coupled inductors; Cs1 and Cs2 arethe parallel capacitors, including the parasitic capacitors of theswitches; Cc1 and Cc2 are the clamp capacitors; N is the turnsratio n2 /n1 .

The operation principle analysis and the steady-state wave-forms of the high step-up ZVT-interleaved boost converter havebeen discussed in [17]. Compared with the proposed converter,the full-bridge dc–dc converter is also employed commonly as asimilar first stage in the PV system. However, for the high step-up gain applications, the large current ripples of the primary-sideswitches increase the conduction losses, and the secondary-sidediodes need to sustain a high voltage stress. Moreover, as a buck-type converter, a large turns ratio of the transformer is necessaryto obtain a high step-up gain, which induces a large leakageinductance and large commutation energy on the primary-sideswitches. Therefore, the design of the transformer is difficultand the converter’s efficiency is impacted. Furthermore, theresonant-mode converters such as LLC, LCC, and higher orderelement converters are studied and developed, which are attrac-tive for potential higher efficiency and higher power densitythan PWM counterparts. However, most of resonant convert-ers include some inherent problems, such as electromagneticinterference (EMI) problems due to variable frequency oper-ation and reduced conversion efficiency due to circulating en-ergy generation. Moreover, to make practical use of the resonantconverters, the required precise control waveform and difficultovercurrent protection increase the design complexity of thewhole system [21]–[24]. Correspondingly the ZVT-interleavedboost converter has the following three main advantages.

1) Voltage gain is extended greatly by using a proper turnsratio design. As the turns ratio increases, the voltage gainincreases without the extreme duty ratio, which can re-duces the input and output current ripples. Omitting theeffect of the leakage inductance and applying the voltage-second balance to the magnetizing inductor, the voltagegain is given by

M =Vout

Vin=

N + 11 − D

. (1)

2) Voltage stress of the main switches is reduced, as theturns ratio increases. Therefore, the low-voltage and high-performance devices can be used to reduce the switchingand conduction losses. And the voltage spikes are clampedeffectively and the leakage energy is recovered. If theclamp capacitance is assumed large enough and the volt-age ripple on the switches can be ignored when they turn


off, the normalized voltage stress of the main switches isgiven by

Vds =Vout

N + 1. (2)

3) ZVT soft switching is achieved for both main switches andauxiliary switches during the whole switching transition,which means the switching losses are reduced greatly.Diode reverse-recovery loss is greatly reduced becausethe di/dt of the diode current is controlled by the inherentleakage inductor of a coupled boost inductor.

Unfortunately, the leakage inductor of the winding-coupledinductors has great effect on the voltage gain expression anda big error is found in the steady-state model based on (1),especially when the leakage inductance increases to a certainlevel, which brings difficulty to the design of circuit parameters.To derive a more accurate steady-state model of the converter,the leakage inductance of the winding-coupled inductors shouldbe considered, since the leakage inductance strongly influencesthe operation states of the circuit. To simplify the calculation,the following conditions are assumed in reason.

1) The clamp capacitance is large enough, so the voltageripple on the main switches can be ignored and the voltageVds is taken as a constant when they turn off.

2) The magnetizing inductance is much larger than the leak-age inductance, so the magnetizing current ILm is takenas a constant in one switching period.

3) The dead times of the main switches and the correspondingauxiliary switches are ignored.

4) The two interleaved and intercoupled boost converter cellsare provided with a strict symmetry.

Based on the previous assumptions, the partial key waveformsof this converter are shown in Fig. 3, which have reached a steadystate. And the following approximations are given:

∆If ≈ ∆Ir = ∆I (3)

VLk1 ≈ VLk2 = VLk . (4)

The equation of the output voltage is always true by theKirchhoff voltage law

Vout = Vds1 + V ◦n2

+ V ∗n2

(5)

where V ◦n2

and V ∗n2

, respectively, represent the voltage of thesecond winding L1b and the voltage of the third winding L2c .

A. Stage a (Main Switches S1 is OFF and S2 is ON)

Based on the voltage-second balance to the magnetizing in-ductor, the switching voltage of S1 is given by

Vds1 =Vin

1 − D. (6)

From the waveform of iLk1 shown in Fig. 3, it can be foundthat

VLk = VLk1 = Llk1 ×∆If

∆t1= Llk1 ×

∆I

(1 − D)/fs. (7)

Fig. 3. Partial key waveforms of the converter.

As shown in Fig. 2, the voltages on the winding-coupledinductors are decided by

V ◦n1

= VLm1 = Vds1 − VLk1 (8)

V ◦n2

= N × V ◦n1

(9)

V ∗n2

= N × (Vin − VLk2) (10)

where V ◦n1

represents the voltage of the first winding L1a .Therefore, substituting (6), (9), and (10) into (5), the equation

of the output voltage in stage a is obtained

Vout = (N + 1) × Vds1 − 2 × N × VLk

=N + 11 − D

× Vin − 2 × N × Llk1 ×∆I

(1 − D)/fs. (11)

B. Stage b (Main Switches S1 is ON and S2 is ON)

Likewise, from the waveforms shown in Fig. 3, it can be foundthat

Vds1 = 0 (12)

VLk = VLk1 = Llk1 ×∆Ir

∆t2= Llk1 ×

∆I

∆t2. (13)

Considering the polarity of the voltages on the winding-coupled inductors in stage b, the voltage expressions for the


winding-coupled inductors are also obtained by

V ◦n1

= VLm1 = VLk1 − Vin (14)

V ◦n2

= N × V ◦n1

(15)

V ∗n2

= N × (VLk2 + Vin). (16)

Therefore, substituting (12), (15), and (16) into (5), the equa-tion of the output voltage in stage b is obtained

Vout = 2 × N × VLk = 2 × N × Llk1 ×∆I

∆t2. (17)

In addition, from the waveform of iDo1 shown in Fig. 3, thetotal charge through the two output diodes in one switchingperiod is decided by

Q1 = 2QDo1 = (∆t1 + ∆t2) ×∆I

N. (18)

Meanwhile, the charge through the load in one switchingperiod is

Q2 =Vout

R× 1

fs. (19)

Therefore, the charge-conservation equation can be found that

(∆t1 + ∆t2) ×∆I

N=

Vout

R× 1

fs. (20)

Therefore, the (11), (17), and (20) can be solved to obtain theexpression for the steady-state model of the converter.

M =Vout

Vin

= (N + 1)

√[(1 − D)R]2 + 8N 2fsLlkR − (1 − D)R

4N 2 × fs × Llk

(21)

where Llk is the equivalent leakage inductance of the winding-coupled inductors, and Llk = Llk1 = Llk2 , and R is the equiv-alent load of the converter.

As shown in Table I, the results calculated by the two steady-state models and the simulation software PSIM, are comparedto verify the proposed model. From the data in Table I, the max-imum error of the output voltage between the accurate modelbased on (21) and the simulation results is only 0.6%, and thecorresponding maximum error of the model based on (1) reachesup to 43.1%. It is clear that the proposed steady-state model ap-proaches the simulation results closely.

III. CONTROL STRATEGY OF FULL-BRIDGE INVERTER WITH

BIDIRECTIONAL POWER FLOW

The full-bridge inverter shown in Fig. 1 works as avoltage-source PWM (VS-PWM) converter in this paper, whichimplements the bidirectional power flow. By using a direct-current-control strategy, the VS-PWM converter can force theinstantaneous load current to accurately follow the sinusoidalreference, which synchronizes with the utility grid voltage. Andthe high power factor, the low THD and the fast dynamicresponse are achieved. Furthermore, the bidirectional flow of

TABLE ISTEADY-STATE MODEL VERIFICATION

Fig. 4. Control block of two-stage grid-connected PV system.

Fig. 5. Control block of full-bridge inverter with bidirectional power flow.

power facilitates the compensation of the dc-bus and the ac-sidevoltage variations, which helps to stabilize the dc-bus voltagein startup and cloudy situations and improves the stability ofoverall system. Fig. 4 shows the control block of the two-stagegrid-connected PV system. Fig. 5 shows the control block of thefull-bridge inverter with bidirectional power flow.


A. Control of the Bidirectional Power Flow

As shown in Fig. 5, the dc-bus voltage Udc is always con-trolled to keep a constant value Uref with zero error by thevoltage-feedback control loop. Meanwhile, the direction andmagnitude of VS-PWM converter’s output current and powerare decided dynamically by the value of Ue , which is the outputof negative PI regulator in the voltage loop.

If Udc > Uref then Ue is increasing, and the VS-PWM con-verter works as an inverter which transfers the PV array powerto the utility grid. The energy generation of PV power system ispositively correlated with the magnitude of Ue .

If Udc < Uref then Ue is decreasing, and when Ue < 0, theVS-PWM converter works as a PWM rectifier, which draws theenergy from the utility grid to the capacitor of dc bus, maintain-ing the stability of dc-bus voltage. The current in the negativedirection finally approaches a quite small value, which is onlyused to compensate for the switch losses of VS-PWM converter.

The earlier characteristic guarantees that the dc-bus voltageis stabilized to a required value by the back-end VS-PWM con-verter, whether the front-end dc–dc converter works or not.Therefore, it is avoided that the ZVT-interleaved Boost con-verter works in an open-circuit state, on the condition that theback end is started up prior to the front end.

B. Direct Current Control With Compensation Units

As shown in Fig. 5, the load currents iout is detected andcompared with the reference current iref , and the error signalis processed by a PI regulator in the current-feedback controlloop. Main advantages of this direct current control are thelow harmonics to reduce losses in steady state, the fast re-sponse to provide high dynamic performances, and the peak-current protection to reject overload [25], [26]. Generally, thecurrent control loop is designed to have a bandwidth of 2–5 kHz,higher than the voltage loop bandwidth of 200–500 Hz, to as-sure the stability of the proposed inverter control with two PIregulators.

However, the instantaneous power and the dc-bus voltage in-clude a ripple component with the frequency 2ω in the caseof a single-phase inverter. Furthermore, the grid voltage is notan ideal sinusoidal waveform in practice. Therefore, it is hardto achieve low THD of the output current by using the sim-ple direct-current-control strategy in the real grid condition.Accordingly, two compensation units are added to the currentcontrol loop as the feedforward control units. The feedforwardcontrol has little impact on the system’s zeros and poles config-uration, but achieves to track the sinusoidal reference accuratelyand restrain the harmonics distortion of the load current, espe-cially at the current peak.

Compensation coefficient Kd directly processes the magni-tude of reference currents iref , and can counteract the maininfluences of the dc-bus voltage ripple because Kd representsa negative fluctuating feature with the frequency 2ω, comparedwith the dc-bus voltage ripple. Kd is defined as

Kd =Uref

Udc. (22)

TABLE IIP&O ALGORITHM EMPLOYING Ue

The PI regulator in the grid-voltage-feedforward control mul-tiplies the real, defective grid voltage with a proportion gainKf . Its output uc and the output ua of PI regulator in current-feedback loop are together fed to the PWM modulator to pro-duce the drive signals for the inverter switches. Therefore, themodulation wave uout includes the defective component of gridvoltage to compensate grid voltage fluctuation and obtain highlysinusoidal current waveform. The feedforward effect dependson the value of Kf .

In addition, the frequency ω and phase φ of current referenceiref are calculated to synchronize with utility grid voltage ugridin real time by a phase-locked-loop (PLL) system, which isachieved via the digital algorithm of DSP chip in this paper.

IV. SIMPLE MPPT SOLUTION BASED ON POWER BALANCE

Many MPPT solutions are developed to ensure the optimalutilization of PV modules [27]–[29]. The implementations gen-erally involve sensing the output current and voltage of PVmodules, and the MPPT algorithms use the information to max-imize power drawn from the PV modules. Unfortunately, suchrealizations are costly and complex [27], [28].

In this paper a simple MPPT solution is adopted in view ofthe power balance. If omitting the whole system losses, the gen-erated power of the PV array is equal to the output power thatis transferred to the utility grid. Therefore, the rms value of theload currents iout is in proportion to the PV array power, asthe grid voltage is clamped to 220 or 110 V. And as discussedearlier, the magnitude of the load current iout directly dependson the output Ue of the negative PI controller in the voltageloop. Therefore, the majority of MPPT algorithms can be im-plemented by controlling the value Ue rather than the calculatedpower value by multiplying the inputs from voltage and currentsensors, which holds universality.

To verify the previous analysis, as shown in Table II, theperturb and observe (P&O) algorithm of employing the valueUe is applied in this paper. And perturbing the duty ratio Dof the ZVT-interleaved boost converter perturbs the PV arraycurrent and voltage, and consequently, perturbs the PV arraypower. The operating point is then adjusted to maximize PVarray power.

The other advantage is the simple MPPT solution ensures themaximization of the power transferred to the utility grid, but notthe output power from PV array. Although the two are equiva-lent in theory, the former is a real MPPT technique in practicethat converts maximum energy to utility grid, because some


complications, like nonlinearity of the whole system losses andlong-term fluctuation of the utility grid voltage, are eliminated.

V. EXPERIMENTAL RESULTS

A. System Configuration

To confirm the theoretical analysis in the previous sections, a2-kW prototype of the proposed grid-connected PV power sys-tem was built. Two ZVT-interleaved boost converters of 1 kWare connected in parallel via a dc bus through a central inverterof 2 kW to the grid. The lower power dc–dc converters are con-nected respectively to the individual PV arrays, and the centralinverter can expand the power rate and reduce the system cost.The detailed components and parameters used are as follows.

ZVT-interleaved boost converter:Vin : 38–50 V; Vout : 380 V.fs : 50 kHz dead time: ∆td1 = ∆td2 = 250 ns.N = n2 :n1 = 36:18 = 2.S1 and S2 : FQA62N25C.Sc1 and Sc2 : FQA59N25C.Do1 and Do2 : RHRP15120.Cc1 and Cc2 : 2.2 µF.Cs1 and Cs2 : 2.2 nF.Lm1 and Lm2 : 150 µH.Llk1 and Llk2 : 4 µH.Full-bridge inverter:fs : 20 kHz; dead time: 1 µs.Insulated-gate bipolar transistor (IGBT): FGAF40N60.Cdc : 470 µF × 4.Lf 1 and Lf 2 : 1.2 mH.Digital controller:TMS320F2808.

B. Experimental Results

The following experimental results are given at 1 kW powergeneration of each PV array under a specific temperature andirradiance condition, and the total power of the grid-connectedPV system can reaches 2 kW.

Fig. 6 shows the experimental results of the ZVT-interleavedboost converter at 1 kW when the input voltage is 40 V. As shownin Fig. 6(a), the extreme duty ratio is avoided when the voltagegain is extended. Meanwhile, the voltage stress of the mainswitches is reduced to 170 V, far lower than the output voltage380 V, and the low-voltage and high-performance devices canbe used to reduce the conduction losses. The waveforms ofZVT soft switching of the main switch S1 and clamp switchSc1 are, respectively, shown in Fig. 6(b) and (c). It is clear thatthe ZVT of the main switches and the auxiliary switches areachieved during the whole switching transition, which reducesthe switching losses, improves the efficiency and increases thepower density. Fig. 6(d) shows the experimental waveform ofthe turn-OFF current of the output diode Do1 . It is clear thatthe reverse-recovery current is reduced to a small value, andthe reverse-recovery problem is alleviated dramatically by theleakage inductor. The EMI noise is suppressed significantly, andthe losses caused by the reverse recovery are reduced greatly.

Fig. 6. Experimental results about ZVT-interleaved boost converter.(a) Switching voltages of main switch S1 , S2 . (b) ZVT operation for mainswitch S1 . (c) ZVT operation for auxiliary switch Sc1 . (d) Turn-OFF current ofoutput diode Do1 .

Furthermore, to verify the proposed steady-state model ofthe ZVT-interleaved boost converter, the experimental resultsof the output voltage are compared in Table III. It is clear thatthe experimental error values are within 2.5% of the valuescalculated by the accurate model and the simulation software.The errors are induced by the assumptions in modeling.


TABLE IIIEXPERIMENTAL VERIFICATION OF STEADY-STATE MODEL

Fig. 7. Experimental results about full-bridge inverter with bidirectionalpower flow. (a) Output current and dc-bus voltage waveforms in the rectify-ing condition. (b) Output current and dc-bus voltage waveforms in the invertingcondition.

Fig. 7 shows the experimental results of the full-bridge in-verter with bidirectional power flow. The output current and thedc-bus voltage waveforms in the rectifying condition are shownin Fig. 7(a). It is clear that the current is close to zero and thedc-bus voltage is stabilized to 380 V without a very small rip-ple, because no active power is consumed except compensatingfor the IGBTs losses. The output current and the dc-bus volt-age waveforms at 2 kW in the inverting condition are shown inFig. 7(b). It can be clearly seen that the output current is highlysinusoidal synchronized with the grid voltage, which is hardlydeteriorated by the ripple component with the frequency 2ω ofthe dc-bus voltage due to the two compensation units. Fig. 8shows the harmonic spectrum of the output current at 2 kW, andthe measured THD counted till to 50th is 3.384%.

The experimental results of the dynamic response for thesystem under different step source changes are given in Fig. 9.As shown in Fig. 9(a), the power source is changed from 500

Fig. 8. Harmonic spectrum of the output current at 2 kW.

Fig. 9. Experimental results of the system dynamic response under differentstep source changes. (a) Dynamic response under power source change from500 to 1600 W. (b) Dynamic response under power source change from 1600 to500 W.

to 1600 W, and reversely, the power source is changed from1600 to 500 W, as shown in Fig. 9(b). It can be clearly seen thatthe fast and effective responses to the abrupt source changesare achieved due to the direct-current-control strategy with twocompensation units.

Fig. 10 shows the MPPT effect of P&O algorithm by employ-ing the value Ue , when the MPP is changed from 500 to 800 W.The output current waveform in the MPPT process is shown inFig. 10(a), and the responses of output current rms and outputpower rms are shown in Fig. 10(b). It is clear that the outputcurrent and power gradually increase during the MPPT periodand finally reach the steady stage. Therefore, this MPPT methodbased on power balance is practical with a good performance.

Fig. 11 and Table IV show the detailed efficiency data of thewhole system including the maximum efficiency and European


Fig. 10. MPPT effect of P&O algorithm by employing value Ue . (a) Outputcurrent waveform about MPPT effect. (b) Responses of output current and powerabout MPPT effect.

Fig. 11. Measured efficiency of the whole system.

TABLE IVMEASURED EFFICIENCY OF THE WHOLE SYSTEM

efficiency, which were measured by the power analyzer PZ4000from Yokogawa, respectively, when the input voltages wereselected as 40 and 48 V. The maximum efficiency of 93.9%and European efficiency of 92.7% are achieved when the inputvoltage is 48 V.

VI. CONCLUSION

This paper presented a grid-connected PV power system withhigh voltage gain. The proposed PV system employs a highstep-up ZVT-interleaved boost converter with winding-coupledinductors and active-clamp circuits as the first power-processingstage, and high voltage gain is obtained by the turns ratio se-lection of winding-coupled inductors. An accurate steady-statemodel of the converter is obtained and verified by the simulationand experimental results. A full-bridge inverter with bidirec-tional power flow is used as the second power-processing stage,to stabilize the dc-bus voltage and shape the output current. Twocompensation units are added to the system control loops, andthe low current THD and the high dynamic performance areachieved. Furthermore, a simple MPPT method based on powerbalance is applied in the PV system and represents a good per-formance. A 2-kW prototype is built, and experimental resultsconfirm the validity and applicability of the proposed PV system.

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Bo Yang was born in Sichuan, China, in 1981. Hereceived the B.Sc. degree in applied power electronicsin 2004 from Zhejiang University, Hangzhou, China,where he is currently working the Ph.D. degree inelectrical engineering.

His current research interests include photovoltaicpower system, power converter modeling, and digitalcontrol techniques.

Wuhua Li (M’09) received the B.Sc. and Ph.D. de-grees in applied power electronics and electrical engi-neering from Zhejiang University, Hangzhou, China,in 2002 and 2008, respectively.

From September 2004 to March 2005, he wasan Intern, and from January 2007 to June 2008, aResearch Assistant in GE Global Research Center,Shanghai, China. In July 2008, he joined the Col-lege of Electrical Engineering, Zhejiang University,where he is currently a Postdoctoral Fellow. His re-search interests include high frequency dc/dc con-

verters, soft-switching techniques, RF power amplifiers, converter modeling,and digital control.

Yi Zhao was born in Liaoning, China, in 1983. Hereceived the B.Sc. degree in the College of Electricaland Electronic Engineering, Huazhong University ofScience and Technology, Wuhan, China, in 2006. Heis currently working toward the Ph.D. degree with theCollege of Electrical Engineering, Zhejiang Univer-sity, Hangzhou, China.

His research interests include dc/dc converters andphotovoltaic power system.

Xiangning He (M’95–SM’96–F’10) received theB.Sc. and M.Sc. degrees from Nanjing Universityof Aeronautical and Astronautical, Nanjing, China,in 1982 and 1985, respectively, and the Ph.D. degreefrom Zhejiang University, Hangzhou, China, in 1989.

From 1985 to 1986, he was an Assistant Engineerat the 608 Institute of Aeronautical Industrial GeneralCompany, Zhuzhou, China. From 1989 to 1991, hewas a Lecturer at Zhejiang University. In 1991, heobtained a Fellowship from the Royal Society, U.K.,and conducted research in the Department of Com-

puting and Electrical Engineering, Heriot-Watt University, Edinburgh, U.K., asa Post-Doctoral Research Fellow for two years. In 1994, he joined ZhejiangUniversity as an Associate Professor, where he has been a Full Professor withthe College of Electrical Engineering, Zhejiang University, since 1996. He wasthe Director of the Power Electronics Research Institute and the Head of theDepartment of Applied Electronics. He is currently the Vice Dean of the Col-lege of Electrical Engineering, Zhejiang University. His research interests arepower electronics and their industrial applications. He is the author or coauthorof more than 200 papers and one book “Theory and Applications of Multi-levelConverters.” He holds 12 patents.

Dr. He received the 1989 Excellent Ph.D. Graduate Award, the 1995 ElitePrize Excellence Award, the 1996 Outstanding Young Staff Member Award, andthe 2006 Excellent Staff Award from Zhejiang University for his teaching andresearch contributions. He received five Scientific and Technological ProgressAwards from Zhejiang Provincial Government and the State Educational Min-istry of China in 1998, 2002, and 2009, respectively, and five Excellent PaperAwards. He is a Fellow of the Institution of Engineering and Technology (for-merly IEE), U.K.

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