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Novel Maximum-Power-Point TrackingAlgorithm For Grid-ConnectedPhotovoltaic SystemAbd El-Shafy A. Nafeh aa Electronics Research Institute , Cairo, EgyptPublished online: 10 Dec 2010.

To cite this article: Abd El-Shafy A. Nafeh (2010) Novel Maximum-Power-Point Tracking AlgorithmFor Grid-Connected Photovoltaic System, International Journal of Green Energy, 7:6, 600-614, DOI:10.1080/15435075.2010.529404

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International Journal of Green Energy, 7: 600–614, 2010Copyright © Taylor & Francis Group, LLCISSN: 1543-5075 print / 1543-5083 onlineDOI: 10.1080/15435075.2010.529404

NOVEL MAXIMUM-POWER-POINT TRACKINGALGORITHM FOR GRID-CONNECTED PHOTOVOLTAICSYSTEM

Abd El-Shafy A. NafehElectronics Research Institute, Cairo, Egypt

This paper presents a novel maximum-power-point (MPP) tracking algorithm for photo-voltaic (PV) energy conversion systems. The algorithm is based on utilizing the relationbetween the PV array MPP current and the solar insolation level at different atmosphericconditions. Also, a single-stage grid-connected PV system is proposed to track the MPP of thePV array, using the new algorithm, and to produce a sinusoidal output current in phase withthe utility voltage (i.e., to obtain a unity power factor). The power stage of the proposed sys-tem includes, mainly, a direct current–alternate current inverter, whereas the control stageis based on utilizing both the Proportional Integral (PI) and the P resonant controllers. Theobtained results satisfy the desired performance for the proposed system.

Keywords: Maximum-power-point tracking; PI controller; PR controller; PV energyconversion system; Unity power factor

INTRODUCTION

As the conventional energy sources are dwindling fast, renewable energy sourcesoffer a very promising alternative to the power generated from the fossil and nuclearfuels.

Photovoltaic (PV) energy is the most important energy resource since it is clean,pollution-free, and inexhaustible (Kuo, Liang, and Chen 2001). Also, due to the latestdevelopment in power and digital electronics, the market for small distributed power gen-eration systems, such as PV systems connected to the domestic grid, is increasing rapidly(Teodorescu et al. 2004). However, there is an optimum operating point for any PV array,known as the maximum-power-point (MPP). This MPP varies depending on cell tem-perature and solar insolation level. To extract maximum power from a PV array, a MPPtracking algorithm is necessary. Many MPP tracking algorithms have been reported in lit-eratures (Ahmeda and Miyatake 2008; Altasa and Sharaf 2008; Femia et al. 2008; Floreset al. 2009; Fortunato et al. 2008; Gounden et al. 2009; Gules et al. 2008; Koutroulis,Kalaitzakis, and Voulgaris 2001; Kuo, Liang, and Chen 2001; Liu et al. 2008; Lo, Lee, andWu 2008; Nikraz, Dehbonei, and Nayar 2003; Patel and Agarwal 2008; Sera et al. 2008;Tafticht et al. 2008). These algorithms can be classified into three main categories that

Address correspondence to Abd El-Shafy A. Nafeh, Electronics Research Institute, El-Tahrir St., Dokki,Cairo, Egypt. E-mail: abdelshafyn@eri.sci.eg

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NOVEL MPP TRACKING ALGORITHM 601

include look-up table algorithms, hill-climbing algorithms, and computational algorithms(Nikraz, Dehbonei, and Nayar 2003). The above algorithms require a matching converterbetween the PV array and the load, to match the output characteristics of the PV array tothe input characteristics of the load. The conventional matching converters, in the case ofgrid-connected PV systems, are composed of two converters that are connected in seriesbetween the PV array and the utility line. These converters are the direct current (DC)–DC converter and the DC–alternate current (AC) inverter. The function of the DC–DCconverter is to track the MPP of the PV array according to the various MPP tracking algo-rithms, whereas that of the inverter is to produce an output AC current in phase with theutility voltage (i.e., to obtain a unity power factor) (Kuo, Liang, and Chen 2001; Kuo et al.2003; Nikraz, Dehbonei, and Nayar 2003; Sugimoto and Dong 1997; Yuvarajan, Yu, andXu 2004). However, the efficiency of such series-connected two-stage converters is low.Further, the size, weight, and cost are high.

In this paper, a novel MPP tracking algorithm that is based upon the slope of the PVarray MPP current versus insolation level is presented. Also, a single-stage grid-connectedPV system is proposed and simulated to track the MPP of the PV array and to produce asinusoidal output current in phase with the utility voltage.

PROPOSED MPPT ALGORITHM

A new maximum-power-point tracking (MPPT) algorithm that is able to follow therapid variations in both the insolation level and cell temperature can be developed from thePV array characteristic as follows.

If the internal shunt resistance of the PV array is neglected, the characteristic of thearray can be given as (Kuo, Liang, and Chen 2001):

IPV = Ig − Isat

{exp

[ q

AKT(VPV + IPVRs)

]− 1

}(1)

where

IPV PV array currentVPV PV array voltageIg light-generated currentIsat PV array saturation currentq charge of an electronK Boltzmann’s constantA ideality factor of the p-n junctionT absolute temperature of the PV arrayRs intrinsic series resistance of the PV array

Equation (1) is a non-linear equation of the form IPV = f (VPV , IPV ), which can beput in the form VPV = f (IPV ) as:

VPV = AKT

qln

[Ig − IPV

Isat+ 1

]− IPVRs (2)

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Figure 1 Imp-λ characteristic at a constant array temperature.

Therefore, the array power is given as:

PPV = VPV × IPV

= AKT IPV

qln

[Ig − IPV

Isat+ 1

]− I2

PVRs (3)

If the PV array is operated at constant insolation and temperature values, then the PVarray MPP can be determined from dPPV/dVPV or dPPV/dIPV = 0, which yields:

f (Imp) = AKT

qln

[Ig − Imp

Isat+ 1

]− AKT/q Imp

Ig − Imp + Isat− 2ImpRs = 0 (4)

Using any numerical method (e.g., Newton–Raphson method), Equation (4) can besolved for the MPP current Imp. Thus, the relation between the MPP current Imp and theinsolation level λ, at a certain operating temperature, can be determined to be a straightline passing through the origin and having a slope m, as shown in Figure 1. Hence, thevalue of Imp at the considered operating temperature and at any insolation level can bedetermined from:

Imp |T=cons. = m × λ (5)

Plotting Figure 1 for different array temperatures leads to Figure 2, which indicatesthat by varying the array temperature, only the slope of the linear relation of Figure 1will change, where the value of this slope is indicated to decrease by increasing the arraytemperature and vice versa. Therefore, the value of Imp at any insolation level and arraytemperature can be determined from:

Imp = mT × λ (6)

where mT is the slope of the Imp−λ characteristic at the array temperature T . Thus, forMPP operation of the PV array, at all insolation levels and cell temperatures, the desiredvalue of the PV current I∗

PV must be set to be:

I∗PV = mT × λ (7)

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NOVEL MPP TRACKING ALGORITHM 603

Figure 2 Imp-λ characteristics at different array temperatures.

Figure 3 Block diagram of the proposed MPPT algorithm.

Table 1 The mT data of the PV arrayat different temperatures.

T (◦C) mT (A/W/m2)

0 0.00458710 0.00454620 0.00450430 0.00446440 0.00442750 0.00439560 0.004366

Figure 3 illustrates the block diagram of the proposed MPPT algorithm, where inthis algorithm, offline calculations are utilized to determine the values of mT at differentarray temperatures. The obtained data are either curve fitted or tabulated in a look-up table,to easily calculate the value of mT at any operating temperature T . In this work, the mT

data of the considered PV array are calculated at different operating temperatures and thentabulated as shown in Table 1, where linear interpolation is used to calculate the missingtable data.

SYSTEM DESCRIPTION AND CONTROL

The power stage of a traditional two-stage grid-connected PV system (Kim, Yu, andSong 1996; Kuo et al. 2008; Sugimoto and Dong 1997; Wang and Hu 2004) is composed of

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Figure 4 Configuration of the proposed grid-connected PV system.

the PV array, the DC–DC converter, the DC–AC inverter, and the utility line. The functionof the DC–DC converter is to track the MPP of the PV array and to transfer the DC energyto the inverter, whereas that of the inverter is to convert the input DC energy into an outputAC form and to produce a sinusoidal output current in phase with the utility voltage (i.e., toobtain a unity power factor). Because the DC–DC converter and the DC–AC inverter haveindependent control architecture, the controllers are easy to design. Yet, the efficiency ofthe entire conversion system is low because of using two stages for energy conversion (i.e.,the DC–DC converter and the DC–AC inverter).

The configuration of the proposed grid-connected system is shown in Figure 4,which is a single-stage PV energy conversion system containing a power stage and acontrol stage. The power stage of the proposed system consists mainly of the PV array,the single-phase voltage source inverter (VSI), and the utility line. Whereas, the maincomponents of the control stage are the MPPT algorithm, the MPPT controller, the phase-locked loop (PLL), the AC current regulator, and the pulse-width-modulation (PWM)generator.

The Power Stage

The power stage of the proposed single-stage grid-connected PV energy conversionsystem is shown in the top half of Figure 4. An input DC capacitor Ci filter is utilized

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NOVEL MPP TRACKING ALGORITHM 605

to stabilize the input DC-bus voltage of the inverter and to limit ripples from the PV arraycurrent. Also, an output inductor filter Lo is used to diminish harmonics from the AC outputcurrent of inverter io. The blocking diode DB is used, in this case, to protect the PV arrayfrom the reversal of the PV current. The I-V and the P-V characteristics of the used PVarray, at different insolation levels and cell temperatures, are shown in Figure 5. This PVarray is composed of 40 Applied Energy Group (AEG) PV modules (each module contains20 series-connected monocrystalline silicon solar cells) connected in two parallel strings.Each string consists of 20 series-connected modules.

The single-phase VSI is used to convert the DC power from the PV array to an ACpower for the grid by providing an output AC current that is in phase with the grid voltagevg. At the same time, the VSI is necessary, in this work, to track the MPP of the used PVarray. The differential equation of the inverter is:

VPV (S+A − S+

B ) − (N1/N2) vg = Lodiodt

(8)

where S+A and S+

B are the switching states of the upper transistors in the inverter [resultedfrom the PWM generator (Rashid 2004)], and N1/N2 is the turns ratio of the step-up trans-former, which was assumed an ideal one in this work (Ong 1998). It is to be noted herethat the transformer turns ratio must be chosen carefully. In the proposed system, in orderto supply current to the grid, the minimum PV array MPP voltage Vmp |min in volts mustsatisfy the following inequality (Yilmaz, Ertan, and Leblebicioglu 2004):

N2/N1 × Vmp|min > vg|max + 10 (9)

where vg|max is the peak of the grid voltage in volts. Thus, using the values indicated inFigures 4 and 5 (i.e., for vg|max and Vmp|min , respectively), Equation (9) gives N2/N1 >

2.844. Therefore, in this work, N2/N1 is chosen to be 3.

The Control Stage

The proposed single-stage PV energy conversion system must be controlled so asto supply AC power with a unity power factor to the utility line. At the same time, thesingle-stage conversion system must be operated so as to track the MPP of the PV array.The bottom half of Figure 4 shows the details of the considered control stage.

MPPT of the PV Array. The proposed MPPT algorithm is used to compute thedesired PV current I∗

PV , as indicated in Section II. The MPPT controller is considered tobe a PI controller. This controller uses the input error signal EIPV , which is the differencebetween the desired and actual values of the PV current, to produce the DC referencecurrent commend Im, as follows:

EIPV = I∗PV − IPV (10)

Im = EIPV

(KP + KI

s

)(11)

where KP and KI are the proportional and integral gains of the PI controller, respectively,and s is the complex frequency of the Laplace transform domain.

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(a) I-V characteristics

(b) P-V characteristics

Figure 5 PV array characteristics at different insolation levels and cell temperatures. (a) I-V characteristics;(b) P-V characteristics.

AC Current Regulation. For the AC current regulation of the VSI output currentio, the desired output current i∗o is set to synchronize the injected grid current ig with thegrid voltage vg (to achieve unity power factor), as follows:

i∗o = Im sin ωgt (12)

where ωg is the angular frequency of the grid voltage. The phase angle θg = ωgt can beobtained by the PLL principle to synthesize the grid voltage (i.e., the unit amplitude sine

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NOVEL MPP TRACKING ALGORITHM 607

wave reference signal sin ωgt can be captured from the PLL block). The value of i∗o is thencompared to the actual VSI current io to give an AC current error signal eio, as:

eio = i∗o − io (13)

Linear current regulation of three-phase AC systems is commonly performed usingthe rotating frame d-q PI controller. Using the rotating frame allows the PI controller toact on a DC signal, and therefore provides zero steady-state error at the fundamentalfrequency. However, for single-phase systems (such as the one described here), the d-qtransformations are not directly applicable, and many single-phase systems are forced touse either the classical PI controller or other methods (Nikraz, Dehbonei, and Nayar 2003).Therefore, using the classical PI controller, in this work, will not be able to track the sinu-soidal reference current (i.e., the resulted steady-state error will not be zero). Hence, inorder to get a good dynamic response for io, a stationary frame P+ resonant (PR) currentcontroller (Liserre, Teodorescu, and Blaabjerg 2004; Nikraz, Dehbonei, and Nayar 2003;Teodorescu et al. 2004) is used, as depicted in Figure 4. The transfer function of the PRcurrent controller is defined as:

GPR(s) = Kp + 2 Ki ωc s

s2 + 2 ωc s + ω2o

(14)

where ωc is the high pass filter cut-off frequency, ωo is the fundamental frequency, and Kp

and Ki are the proportional and integral gains of the PR controller, respectively.The output signal from the PR controller is the required modulating signal of the

PWM generator. The PWM generator then alters the modulation index of the PWM signalin such a way that the desired response of io is achieved.

RESULTS AND DISCUSSION

The simulation of the system was designed, in Matlab/Simulink, to verify the per-formance of the proposed grid-connected PV energy conversion system. As the poles ofthe designed control systems can be freely located by adjusting the controller parameters,through trial and error method. Thus, the optimal parameters of the used controllers aretuned, by using the trial and error method, to ensure good dynamic response for the pro-posed system, at insolation level of 1000 W/m2 and array temperature of 25◦C. Theseparameters are indicated in Table 2. The PR controller (i.e., the inner controller) is tunedfirst, and then the PI controller. Noting that the value of the DC reference current com-mend Im is set, during tuning of the PR controller, to be the value of the PV array MPP

Table 2 Optimal parameters of the used controllers.

Controller Parameter Value

PI KP 225controller KI 25PR Kp 2controller Ki 100

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(a) Response of i∗o

(b) Response of io

Figure 6 Optimal response of the inverter output current. (a) Response of i∗o; (b) Response of io.

current at 1000 W/m2 insolation and 25◦C array temperature (since setting the value of Im

controls the level of power flow). The optimal response of the inverter AC output current,using the PR controller, is shown in Figure 6, where Figure 6a is dedicated for i∗o and 6bfor io. Therefore, the adjusted parameters for the PR controller ensure good transient and

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NOVEL MPP TRACKING ALGORITHM 609

(a) Response of the PV current

(b) Response of the PV power

Figure 7 Optimal response of the PV array. (a) Response of the PV current; (b) Response of the PV power.

steady-state response for io. Also, the optimal responses of the PV current (i.e., the con-trolled variable) and the corresponding PV power, using both the PI controller and the PRone, are shown in Figure 7a and 7b, respectively. Thus, Figure 7 indicates, also, that theadjusted parameters for the PI controller ensure good transient and steady-state responsesfor the PV current and the corresponding PV power. At the same time, this figure indicatesthe ability of the proposed system, using the proposed MPP tracking algorithm, to operatethe PV array at its MPP. The MPP tracking capability of the proposed system is illustratedin Figure 8, where Figure 8a and 8b illustrate, respectively, the MPP tracking performance

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(a) During step change in insolation level

(b) During step change in temperature

Figure 8 Performance of the PV current during step changes in atmospheric conditions. (a) During step changein insolation level; (b) During step change in temperature.

of the proposed system during step change in insolation or temperature. Thus, it shown,from Figure 8, that the system is able to rapidly track the different MPPs during insolationvariation than the case of temperature variation. This is due to the high value of the inputcapacitor filter Ci (= 33,000 µF). The array temperature variation requires a significantvariation in the array voltage (which is equal to the capacitor voltage) for MPP track-ing. On the other hand, the array voltage variations are nearly negligible during insolation

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NOVEL MPP TRACKING ALGORITHM 611

(a) During step change in insolation level

(b) During step change in temperature

Figure 9 Performance of the PV voltage during step changes in atmospheric conditions. (a) During step changein insolation level; (b) During step change in temperature.

variations (i.e., for MPP tracking). Figure 9a and 9b confirm the above explanation for thecase of insolation and temperature variations, respectively.

The waveforms of the grid current ig and grid voltage vg are shown in Figure 10,which shows that the two waveforms are in phase with a unity power factor (i.e., thesupplied power to the grid has no reactive component). Also, the harmonic spectrum ofthe injected grid current, which is illustrated in Figure 11, shows that ig has very lit-tle harmonics. It is to be noted that the above results are collected by setting the carrier

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Figure 10 Waveforms of the grid current and grid voltage.

Frequency (HZ)

0

0

1

2

3

4

5

200 400 600 800 1000

Am

plitu

de (A

)

Figure 11 Harmonic spectrum of the grid current.

frequency of the PWM generator at 1 kHz and the output inductor filter Lo of the VSI at1.66 mH.

CONCLUSION

A single-stage grid-connected PV energy conversion system is proposed to overcomethe problems of the conventional two-stage configuration, which is characterized by a lowefficiency and is bulky and expensive. Also, a new MPP tracking algorithm is presented and

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NOVEL MPP TRACKING ALGORITHM 613

utilized to track the MPP of the proposed system. The new algorithm is based on utilizingthe linear relation between the PV array MPP current and the solar insolation level, wherethe slope of this linear relation is found to depend, only, on the value of the PV arrayoperating temperature. The results of the proposed system show that, by fine-tuning ofthe parameters of both the PI controller and the PR one, the desired dynamic response ofthe system is verified. Also, the ability of the proposed system, using the new trackingalgorithm, is indicated to rapidly track the different MPPs of the PV array during stepchange in insolation level or array temperature. Moreover, the waveforms of the injectedgrid current and the grid voltage indicate that the two waveforms are in phase with a unitypower factor; at the same time, the harmonic spectrum of the injected grid current is shownto have very little harmonics.

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