1

Improvement of the Maximum Power PointTracker for Photovoltaic Generators

with Particle Swarm Optimization Techniqueby Adding Repulsive Force among Agents

Vanxay Phimmasone∗, Tsugio Endo∗, Yuta Kondo∗ and Masafumi Miyatake∗∗Department of Engineering & Applied Sciences, Sophia University, Tokyo 102-8554, Japan

Abstract— This paper deals with Maximum Power PointTracking (MPPT) control of photovoltaic generators. Photovoltaic(PV) generation systems need maximum power point trackerbecause the PV power output depends on the operating terminalvoltage and current. Further, the PV array exhibits two ormore MPP’s under partial shading condition and hence findingthe MPP using conventional techniques is a difficult task. Toovercome the difficulty, finding the MPP, the authors improvethe MPPT with Particle Swarm Optimization (PSO) techniqueby adding a kind of “repulsion term” to the equation ofPSO algorithm. The term enables to improve the response tovarious types of insolation change. This results in lower cost,higher overall efficiency and also the algorithm is simple. Theimproved PSO-MPPT algorithm is verified through simulativeand experimental studies. It is proved this algorithm is superior tothe original PSO-MPPT methods by evaluating generated powerand electrical energy.

Index Terms— Maximum Power Point Tracker, Multidimen-sional optimization, Photovoltaic array, Particle Swarm Opti-mization.

I. INTRODUCTION

Clean and renewable energy source such as photovoltaic(PV) power generation is expected as one of the key tech-nologies to mitigate global warming. It is possible to use thePV power in distributed generation, transportation and mobileapplications. Since the PV sources exhibits non-linear v − icharacteristics their power output mainly depends on the natureof the connected load. Hence direct load connection to the PVsystem results in poor overall efficiency. As the solar panelsare still expensive life cycle cost minimization is essential. Toachieve some of these goals direct connected PV systems arereplaced by a PV systems having an intermediate maximumpower point tracker.

The power produced by a PV module depends on the solarirradiance and temperature. It is important to find the optimaloperating voltage of PV arrays in order to increase the effi-ciency of PV generators. To achieve this, various conventionalMaximum Power Point Tracking (MPPT) algorithms [1]-[2]have been proposed and used to extract maximum power fromPV arrays under varying atmospheric conditions. However, allthe above MPPT schemes are suitable under ideal conditionsand are not able to extract true maximum power under partial

V

I

maximum area

maximum power

variation of irradiance

Fig. 1. I-V characteristics of a solar cell.

shading conditions.

If a PV array is partially shaded by the shadow of building,tree etc, realization of MPPT is a difficult task. If the moduleswith different optimal current, caused by uneven insolation,are connected in series-parallel, local maximum power points(MPPs) often appears in the power -vs- voltage characteristics.This is due to the fact that the optimal current of each PVmodule is nearly proportional to the insolation falling onit. Under these conditions the conventional MPPT controllermay track to a local MPP instead of global MPP. Hence, thegenerated power may be reduced and PV system efficiencywill decrease.

Several research groups have been made attempts in theglobal MPPT realization by evolving different algorithms[3]-[5]. However, most of them use lengthy calculations, on-linesensed data or special circuit configurations. The authors madean attempt to simplify the MPPT algorithm and to track globalMPP under partial shading conditions. The author’s aim is torealize a power-tracking scheme that will have the followingsalient features:

1) Finding the global MPP to maximize the generatedpower from the PV source

2) Simplicity in the algorithm and it should use the con-ventional circuit configuration

3) Applicable to large scale PV system, resulting fromseries parallel combination of the solar cells.

The authors tested the proposed MPPT controller [7]-[8] with

unshaded module shaded module totalV V V

III

V

P=VI

+ =

Fig. 2. Characteristics of PV modules connected in series.

Particle Swarm Optimization technique. It worked almostvery well, however, in some conditions, it was found thattrackability of the global MPP is not enough.

In this paper, the authors propose to add a kind of “repulsionterm” to the equation of PSO algorithm that determines themagnitude of voltage shift. The term enables to improve theresponse to various types of insolation change.

II. CHARACTERISTICS OF PHOTOVOLTAIC ARRAY

A PV module is composed of several solar cells connectedin series-parallel to get the desired voltage/ current andshielded with glass to protect against environmental changes.The v − i characteristics of a PV cell is shown in Fig. 1.The current is almost proportional to solar insolation. Most ofthem also have a by-pass diode and reverse blocking diode. Atypical PV generation system is composed of several modulesconnected in series-parallel to meet the load power demand.

Here, a PV system consisting of two modules connectedin series is considered. Let us assume that one module isfully illuminated, while the second one is partially shaded.Under this condition the current flowing through the twomodules is same, since the modules are connected in series, butcurrent generated by the second module is less than the fullyilluminated module. Under this condition the excess currentflows through the by-pass diode. The v − i characteristics ofindividual module as well as the PV total system is shownin Fig. 2. It can be seen that, Fig. 2, there are two MPPs.If the number of modules increases, the characteristics underuneven insolation are complicated and generate two or moreMPPs. Under such cases it becomes difficult to realize theMPPT using the conventional methods. Furthermore, if theglobal MPP can be found, each module is not operated at theoptimal condition, because the optimal current is inherentlydifferent at different insolations.

If the PV system is divided into number of small arraysand each small array is controlled with its own converterthen the power loss due to partial shading can be minimized.

DC

DC

DC

DC

DC

AC

MPPT controller

MPPT controller

grid / load

sensor

sensor

Fig. 3. Multiple arrays controlled by multiple controllers.

DC

DC

DC

DC

DC

AC

MPPT controller

grid /load

sensor

Fig. 4. Multiple arrays controlled by a single controller.

However, this scheme requires more number of voltage andcurrent sensors as shown in Fig.3. In order to reduce the costas well as to have fewer problems with controlling scheme thenumber of sensors should be less. To this direction authorshave proposed a new scheme, shown in Fig.4, where-in asingle pair of voltage and current sensors is sufficient to realizethe MPPT scheme. The detailed MPPT control technique ofthis new scheme is discussed in the next section.

pbesti

gbestsk−1i

ski

sk+1i

vk+1iv

ki

Fig. 5. Movement of a PSO agent.

III. PARTICLE SWARM OPTIMIZATION APPLIED TO MPPTCONTROL

A. Particle Swarm Optimization

The authors proposed a Particle Swarm Optimization(PSO)[6] technique to solve the problems involved in theMPPT control discussed in the preceding sections. The PSOmethod is a simple and effective meta-heuristic approach thatcan be applied to a multivariable function optimization havingmany local optimal points. The PSO uses several cooperativeagents and each agent shares the information attained by eachindividual during the search process. In the method, each agentmoves in the search space with a velocity, vk

i , according toits own previous best solution and its group’s previous bestsolution. The velocity and position update can be describedby the following equations.

vk+1i = wvk

i + c1r1 (pbesti − ski ) + c2r2 (gbest − sk

i ) (1)

sk+1i = sk

i + vk+1i (2)

where w is the momentum factor; c1 and c2 are positiveconstants; r1 and r2 are the random numbers and their valuesare in between (0-1). The variable pbesti is used to memorizethe best position that the i-th agent has found so far. It isupdated like (3) if the condition (4) is satisfied,

pbesti = ski (3)

f(ski ) > f(pbesti) (4)

here f is the objective function that should be maximized. Thevariable gbest is used to memorize the best position achievedamong all the all agents. During the process of optimizationthe agents’ movement appearance is illustrated in Fig. 5.

B. Original Way of Applying PSO to MPPT

In case of constant bus voltage applications only one currentsensor is sufficient for tracking the maximum power from theseveral individual PV modules. It can be called a multidimen-sional MPPT control as shown in Fig. 6. The terminal voltageof the individual PV systems are grouped and represented inthe form of N - dimensional row vector as (5).

sk = [V k1 , V k

2 , · · · , V kN ] (5)

V1V2

P(V1, V2)

Fig. 6. An image of multidimensional function.

where N is the size of the row vector and it indicates thenumber of PV arrays. The velocity variable v can be writtenas

vk = [V k1 − V k−1

1 , V k2 − V k−1

2 , · · · , V kN − V k−1

N ] (6)

The objective function f is the generated power P , which isthe summation of power generated by each array. The outputvoltage vector s changes in the following order and measuresthe power P (s).

· · · → sk1 → sk

2 → · · · → skM

→ sk+11 → sk+1

2 → · · · → sk+1M → · · · (7)

where M is the number of agents.The authors modified the PSO algorithm in order to apply

it to the MPPT control. In real-time operation, the objectivefunction f often changes due to environmental as well aselectrical load changes. Under such cases the agents must bereinitialized so as to search the new MPP again. The agentsare reinitialized whenever the following two conditions aresatisfied.

|vi+1| < Δv (8)

|P (si+1) − P (si)|P (si)

> ΔP (9)

The equations (8) and (9) represents agents convergencedetection and sudden change of insolation, respectively.

As already reported in [7], the experimental result of theoriginal PSO-MPPT showed that the global MPP on the 2 di-mensional searching plane could be tracked within one secondeven under partially shaded conditions. The typical waveformof the response is shown in Fig.7. However, the originalPSO-MPPT had a shortcoming of inappropriate response ingradual change of insolation. Therefore, the authors intendedto improve the original PSO-MPPT.

C. Improvement of PSO by Adding Repulsion Term

In the proposed method that is an improvement of theoriginal PSO method, the magnitude of voltage shift for each

D1

D2

P[W]

0

0.5

10

0.5

1

125

250

375

500

0

unshaded partially shaded

1 2 3 4 5t [s]

Fig. 7. Transient response of output power and duty cycles of two boost choppers for two PV arrays.

TABLE I

PARAMETERS OF THE PSO.

PSO agentsM 3 N 2

PSO coefficientsw 0.4c1 0.8 c2 1.2

conditions of initializationΔv [V] 0.8 ΔP 0.15

agent is determined by the following equation that repulsiveterm is added as the 4th term,

vk+1i = wvk

i + c1r1 (pbesti − ski ) + c2r2 (gbest − sk

i )− c3r3 (centk − sk

i )/(|centk − ski | + d)3, (10)

where c3 and r3 are a positive constant and a random numberwhose value is in between (0-1). The function “cent” is thecenter of all agents described as the following equation,

centk =M∑

i=1

ski

M. (11)

The constant d is a small number and needed to avoid the 4thterm divided by zero in centk = sk

i . If the 3 agents convergeto around the center of the agents, the 4th term is getting largeto diverge the agents. It is effective especially in frequent andgradual insolation changes, e.g. cloudy conditions.

IV. EXPERIMENTAL SYSTEMS

The PSO algorithm parameters used in this paper aretabulated in Table I which were determined by trial anderror method using simulations. They were re-tuned after theprevious paper[7]. The appropriate number of agents M wasalready discussed in [9]. Fixed values were used for the agents’initial positions and they are given in Table II.

The configuration of the experimental system is shown inFigs 8 and 9. Two PV arrays, which consist of six PV modules

Electronic Load

gate controller

MPPT controller

D1 D2I

gate signalPV1 PV2

3 φ IPM

current sensor

Fig. 8. Circuit configuration of the experimental system.

TABLE II

INITIAL POSITION OF AGENTS.

agent V1 [V] V2 [V]1 0.2Vop 0.2Vop

2 0.8Vop 0.5Vop

3 0.5Vop 0.8Vop

Vop : open circuit voltage of the array

(Fuji Electric Co. ELR-615-160Z) connected in series-parallel,connected to an electronic load via two boost choppers. Theterminal voltages of the individual PV arrays were to becontrolled by their respective choppers. Rated output powerand voltage of each PV array was about 300 W and 50 Vrespectively. Actually, two legs of a three phase IntelligentPower Module (IPM) was used to realize the two boostchoppers. Digital Signal Processor (DSP TMS320C32) baseddata acquisition was used to generate the PWM gate signalsand to realize the proposed MPPT control scheme. A currentsensor was inserted in the load circuit. It measures the totalpower generated by the two arrays including converter loss.

1Ax

1Ay

1Az

1Bx

1By

1Bz

2Ax

2Ay

2Az

2Bx

2By

2Bz

PV2PV1

Fig. 9. Connection of PV modules and numbering.

PSO-Bideal value

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

time [s]

pow

er [W

]

Fig. 10. An example of simulation waveform.

The control program was developed in C/C++ environment,which will be compiled and downloaded on to the DSPplatform. An electronic load was set for constant batteryvoltage of 100 V. Inductance of the smoothing reactor was 60[mH]. The output voltage vector s changed after every 0.05seconds and followed the sequence of control as described by(7).

The relation between array voltage V and duty ratio of thechopper D is written as (12) because the output voltage waskept 100 V constant by the electronic load in this system.

D = 1 − V

100(12)

In this paper, only one array PV1 was used because theproposed method was compared with the simple Hill Climbingmethod which can control only one array.

V. RESULTS AND DISCUSSION

A. Several Types of MPPT Controllers to be Compared

In order to discuss the effectiveness of the proposed method,the following MPPT controllers were assumed.

HIL: The simplest hill climbing method was used. Themethod involves moving the operating voltage byone step and then examining the change in generatedpower. If the power increases, the operating pointmoves in the same direction, else it is moves in theopposite direction. The step size of voltage was setto 1.2 V and the required control cycle time is 0.1 s.

PSO-A: The original PSO method was used. It has theinitializing function shown in (8)-(9). Repulsive termis NOT implemented. The method will respond tostepwise insolation change quickly.

frequency of sinusoidal insolation change [Hz]

ener

gy e

xtra

cted

rat

io [%

]

PSO-A

PSO-C

PSO-B

HIL

PSO-APSO-C

PSO-B

HIL

Fig. 11. Frequency characteristics.

PSO-B: One of the proposed PSO method was used. Repul-sive term was used, but initialization was NOT fullyimplemented in order to reduce the loss in gradualand frequent insolation change. If the condition ofinitialization was satisfied, the method only reset therecorded values of output power at pbest, withoutinitializing agents’ positions. In this case only, thevalue of ΔP was 0.05.

PSO-C: The other proposed PSO method was used. Bothrepulsive term and initialization are implemented.The method will have both advantage of PSO-A andB.

B. Simulation

It is not easy to generate identical gradual insolation changein each experiment. Therefore, as the first step, the MPPTcontrollers was compared with simulations. The I − V char-acteristic of an array used in the simulations is

I = −8.66 × 10−5 exp(0.18V ) + 4.92pins, (13)

where the units of I and v are [A] and [V] respectively andpins [kW/m2] shows the power of insolation. The equation isbased on the measured characteristic. The other conditions insimulations are the same as that in experiments shown in theprevious section.

In the simulations, uniform solar insolation was assumed.The insolated power pins was changed like sinusoidal waveshown in Fig. 10,

pins(t) = 0.75 + 0.25 cos(2πft)[kW/m2], (14)

where f was the frequency of insolation change. The valuef is changed to scan the characteristic of frequency response.Since the response time constant is 1 second and more asshown in Fig. 7, the range of f is set between 0.0001 [s] and1 [s].

Each MPPT was evaluated with extracted energy divided bytheoretically maximum energy. It is named “energy extractedratio.”

The frequency responses calculated with simulation resultswere plotted in Fig. 11. From the results, the original PSO-A is not suitable for gradual insolation change, because the

0 100 200 300 400 500 600

0 100 200 300 400 500 600

0

10

20

30

40

50

60vo

ltage

[V]

02040

100120140160

6080

pow

er [W

]

180200

time [s]

time [s]

Fig. 12. Array voltage and power of PSO-A in the experiment.

0 100 200 300 400 500 600

0 100 200 300 400 500 6000

10203040506070

volta

ge [V

]

02040

100120140160

6080

pow

er [W

]

180

time [s]

time [s]

Fig. 13. Array voltage and power of PSO-C in the experiment.

energy extracted ratio is the lowest between f = 0.01[Hz]and 1[Hz]. One of the proposed method PSO-B is the best inthe simulations, but it should be noted that PSO-B cannotrespond to stepwise insolation change because of omittinginitialization. The other proposed method PSO-C is moreimproved than PSO-A and can also respond to stepwiseinsolation change. But, from Fig. 11, it is found that there maybe still more room to raise energy extracted ratio as PSO-Band HIL methods.

C. Behavior of Operating Point in Experiments

The improved PSO-MPPT algorithm was also verifiedthrough experimental studies. A cloudy day was chosen toprove the behavior of operating point under gradual andfrequent change of insolation. Waveforms of the experimentalresults in gradual and frequent insolation changes for PSO-Aand C are shown in Figs 12 and 13, respectively. It is provedthat the proposed method PSO-C could keep small fluctuation

to adapt gradual insolation change and initialize the positionof agents in some points to respond faster insolation change.On the other hand, PSO-A could not move the operating pointbecause the conditions of initialization shown in (8) and (9)was not satisfied against gradual change of insolation.

VI. CONCLUSIONS

The novel MPPT algorithm using PSO technique was im-proved to control operating point appropriately under condi-tions of gradual and frequent insolation change. It is provedfrom simulation and experiments that the added term of repul-sion force was working well. The authors are still improvingthe proposed method and intend to apply the method in thispaper to multidimensional array voltage control.

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