Dynamic Particle Swarm Optimization Algorithm Based Maximum Power Point Tracking of Solar Photovoltaic Panels

8/18/2019 Dynamic Particle Swarm Optimization Algorithm Based Maximum Power Point Tracking of Solar Photovoltaic Panels

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Dynamic Particle Swarm Optimization Algorithm

based Maximum Power Point Tracking of Solar

Photovoltaic Panels

Duy C. Huynh, Thoai N. Nguyen

Power Systems Dept.University of Technology

Vietnam National UniversityHochiminh, Vietnam

[email protected]

Matthew W. Dunnigan

Electrical, Electronics & ComputerEngineering Dept.

Heriot-Watt UniversityEdinburgh, United [email protected]

Markus A. Mueller

Institute for Energy SystemsThe University of EdinburghEdinburgh, United [email protected]

Abstract —This paper proposes a novel application of a dynamic

particle swarm optimization (PSO) algorithm for determining a

maximum power point (MPP) of a solar photovoltaic (PV) panel.

Solar PV cells have a non-linear V-I characteristic with a distinctMPP which depends on environmental factors such as

temperature and irradiation. In order to continuously harvest

maximum power from the solar PV panel, it always has to be

operated at its MPP. The proposed dynamic PSO algorithm is

one of the PSO algorithm variants, which modifies the

acceleration coefficients of the cognitive and social components in

the velocity update equation of the PSO algorithm as linear time-

varying parameters to improve the global search capability of

particles in the early stage of the optimization process and direct

the global optima at the end stage. The obtained simulation

results are compared with MPPs achieved using other algorithms

such as the standard PSO, and Perturbation and Observation

(P&O) algorithms under various atmospheric conditions. The

results show that the dynamic PSO algorithm is better than the

standard PSO and P&O algorithms for determining and trackingMPPs of solar PV panels.

Keywords—solar photovoltaic panel; maximum power point

tracking; particle swarm optimization algorithm

I. I NTRODUCTION

Energy is absolutely essential for our life. Recently, energydemand has greatly increased all over the world. This hasresulted in an energy crisis and climate change. The researchefforts in moving towards renewable energy can solve these problems. Compared to conventional fossil fuel energysources, renewable energy sources have the following major

advantages: they are sustainable, never going to run out, freeand non-polluting. Renewable energy is the energy generatedfrom renewable natural resources such as solar irradiation,wind, tides, wave, etc. Amongst these sources, solar energy isone of the most important renewable sources and is widelyused. The sun radiates an amount of energy onto the earth’ssurface everyday which is enough to provide the energydemand of humans. Additionally, most of the renewable energysources such as wind energy, tide energy, wave energy, etc.originate from solar energy.

Solar energy is popularly used to provide heat, light andelectricity. One of the important technologies of solar energy is photovoltaic (PV) which converts irradiation directly to

electricity by the photovoltaic effect [1]. However, the solar PVgeneration panels have two main problems. Firstly, theconversion efficiency of solar PV cells is very low (9% to17%), especially under low irradiation conditions. Secondly,the amount of electric power which is generated by solar PV panels changes continuously with various weather conditions.In addition, the V-I characteristic of the solar cell is non-linearand varies with irradiation and temperature [2]. But in general,there is always a unique point on the V-I or V-P curve which iscalled the Maximum Power Point (MPP). This means that thesolar PV system will operate with maximum efficiency and produce a maximum output power. The MPP is not known onthe V-I or V-P curve, but it can be located by search algorithmssuch as the Perturbation and Observation (P&O) algorithm [3]-

[4], the Incremental Conductance (IC) algorithm [5]-[6], theConstant Voltage (CV) algorithm [7]-[8], the Artificial Neural Network (ANN) algorithm [9]-[10], the Fuzzy Logic (FL)algorithm [11]-[12], the Particle Swarm Optimization (PSO)algorithm [13]-[14]. These existing algorithms have severaladvantages and disadvantages concerned with simplicity,convergence speed, extra hardware and cost. This paper proposes a dynamic Particle Swarm Optimization (PSO)algorithm for searching a MPP on the V-I characteristic of thesolar PV panel. The simulation results using the dynamic PSOalgorithm are compared to using the standard PSO and P&Oalgorithms and confirm the effectiveness and benefit of the proposed algorithm.

The remainder of this paper is organized as follows. Themathematical model of solar PV panels is described in SectionII. A novel proposal using the dynamic PSO algorithm is presented in Section III. The simulation results then follow toconfirm the validity of the proposed algorithm in Section IV.Finally, the advantages of the new proposal are summarizedthrough comparison with several related existing approachessuch as the standard PSO and P&O algorithms.


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II. SOLAR PHOTOVOLTAIC PANELS

A solar PV panel, Fig. 1 is used for generating electricity.Then, a simple equivalent circuit model for a solar PV cellconsists of a real diode in parallel with an ideal current sourceas in Fig. 2 [1].

Figure 1. Solar PV panel

Figure 2. Simple equivalent circuit model of a solar PV cell

The mathematical model of a solar PV cell is described by

the following set of equations:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−= 10

kT

qV

sc e I I I (1)

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ += 1ln

0 I

I

q

kT V scoc (2)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−=×= 10

kT

qV

sc eVI VI I V P (3)

where I is the current of the solar PV cell (A)

V is the voltage of the solar PV cell (V)

P is the power of the solar PV cell (W)

I sc is the short-circuit current of the solar PV cell (A)

V oc is the open-circuit voltage of the solar PV cell (V)

I 0 is the reverse saturation current (A)

q is the electron charge (C), q = 1.602 × 10-19 (C)

k is Boltzmann’s constant, k = 1.381 × 10-23 (J/K)

T is the panel temperature (K)

It is realized that the solar PV panels are very sensitive toshading. Therefore, a more accurate equivalent circuit for asolar PV cell is presented to consider the impact of shading aswell as account for the losses due to the module’s internalseries resistance, contacts and interconnections between cells

and modules, Fig. 3 [1].

Figure 3. More complex equivalent circuit model of a solar PV cell

Then, the V-I characteristic of a solar PV cell is written asfollows:

( )

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−=

+

p

skT

IRV q

sc R

IRV e I I I

s

10 (4)

where R s and R p are the resistances used to consider the impactof shading and losses. Although, the manufactures try tominimize the effect of both resistances to improve their products, the ideal scenario is not possible.

Two important points of the V-I characteristic that must be pointed out are the open-circuit voltage, V oc and the short-

circuit current, I sc. The power generated is zero at both points.The V oc is determined when the output current, I of the cell iszero ( I = 0) whereas the I sc is determined when the outputvoltage, V of the cell is zero (V = 0). The maximum power isgenerated by the solar PV cell at a point of the V-Icharacteristic where the product (V×I ) is maximum. This pointis known as the MPP and is unique.

Figure 4. Important points in the V-I and V-P characteristics of a solar PV

panel

It is obvious that two important factors which have to betaken into account in the electricity generation of a solar PV

I sc

I d

I V

+

–

D Load R p

R s

I pPV

+

–

Sun

+

–

I V

Load

I sc

I d

I V

+

–

D Load

I sc

V oc

C u r r e

n t ( A )

Voltage (V)

P o w

e r W

MPP

0


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panel are the irradiation and temperature. These factorsstrongly affect the characteristics of solar PV panels. As aresult, the MPP varies during the day. If the operating point isnot close to the MPP, significant power losses occur. Thus, it isessential to track the MPP in all conditions to ensure that themaximum available power is obtained from the solar PV panel.This problem is entrusted to the maximum power pointtracking (MPPT) algorithms through searching and

determining MPPs in various conditions. This paper proposesthe dynamic PSO algorithm for searching MPPs which is presented in more detail in the next part.

III. DYNAMIC PARTICLE SWARM OPTIMIZATIONALGORITHM BASED MAXIMUM POWER POINT TRACKING

The standard PSO algorithm is a population-basedstochastic optimization method which was developed byEberhart and Kennedy in 1995 [15]. The algorithm wasinspired by the social behaviors of bird flocks, colonies ofinsects, schools of fishes, and herds of animals. The algorithmstarts by initializing a population of random solutions called particles and searches for optima by updating generations

through the following velocity and position update equations.

The velocity update equation is as follows:

( ) ( ) ( ) ( )( )( ) ( )( )k k r c

k k r ck wk

i

i i i i

x gbest

x pbest vv

−+

+−+=+

22

11

1 (5)

The position update equation is as follows:

( ) ( ) ( )11 ++=+ k k k i i i v x x (6)

where

( )k i v is the k th current velocity of the ith particle.

( )k i x is the k th current position of the ith particle.k is the k th current iteration of the algorithm, nk ≤≤1 .

n is the maximum iteration number.

i is the ith particle of the swarm, N i ≤≤1 .

N is the particle number of the swarm.

Usually, vi is clamped in the range [-vmax, vmax] to reduce thelikelihood that a particle might leave the search space. In caseof this, if the search space is defined by the bounds [- xmax, xmax]then the vmax value will be typically set so that vmax = mxmax,where 0.1 ≤ m ≤ 1.0 [16].

( )k i pbest is the best position found by the ith particle(personal best).

( )k gbest is the best position found by a swarm (global best, best of the personal bests).

c1 and c2 are acceleration coefficients called cognitive andsocial parameters respectively; the c2 regulates the step size inthe direction of the global best particle and the c1 regulates thestep size in the direction of the personal best position of that

particle; c1 and c2 ∈ [0, 2].

r 1 and r 2 are two independent random sequences which are

used to affect the stochastic nature of the algorithm, r 1 and r 2∈ U(0, 1). w is called an inertia weight [17].

It is obvious that the standard PSO algorithm is one of thesimplest and most efficient global optimization algorithms,especially in solving discontinuous, multimodal, and non-convex problems. However, for local optima problems, the particles sometimes become trapped in undesired states duringthe evolution process which leads to the loss of the explorationabilities. Because of this disadvantage, premature convergencecan happen in the standard PSO algorithm which affects the performance of the evolution process. This is one of the majordrawbacks of the standard PSO algorithm. In order to improvethe performance of the standard PSO algorithm, the variant ofthe standard PSO algorithm, known as the dynamic PSOalgorithm was proposed [18]-[19]. This is one of the standardPSO algorithm variants with time-varying accelerationcoefficients of the cognitive and social components. For mostof the population-based optimization techniques, it is desirableto encourage the individuals to wander through the entiresearch space without clustering around local optima during the

early stages of the optimization, as well as being important toenhance convergence towards the global optima during thelatter stages [19]. The acceleration coefficients of the cognitiveand social components in the velocity update equation are oneof the parameters which help the algorithm to satisfy therequirements above in the early and latter stages. Themodification of the acceleration coefficients is to improve theglobal search capability of the particles in the early stage of theoptimization process. The algorithm then directs particles to theglobal optima at the end stage so that the convergencecapability of the search process is enhanced. To achieve this,large cognitive and small social parameters are used at the beginning and small cognitive and large social parameters areused at the latter stage. The mathematical representation of this

modification is given as follows [19]:

( ) ( ) ( ) ( ) ( )( )( ) ( ) ( )( )k k r k c

k k r k ck wk

i

iiii

x gbest

x pbest vv

−+

+−+=+

22

11

1 (7)

where

( ) ( ) initial initial final cn

k cck c 1111 +−= (8)

( ) ( ) initial initial final cn

k cck c 2222 +−= (9)

c1(k ) and c2(k ) are the time-varying acceleration coefficients.

c1initial and c1final are the initial and final values respectively ofthe cognitive parameter.

c2initial and c2final are the initial and final values respectively ofthe social parameter.

The dynamic PSO algorithm is applied for determiningMPPs. The position and velocity of the ith particle are updatedusing (6) and (7) respectively. The velocity update equationuses the time-varying acceleration coefficients. The coefficientc1(k ) is set to decrease linearly during a run with c1initial = 2.5


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and c1final = 0.5 whereas the coefficient c2(k ) is set to increaselinearly with c2initial = 0.5 and c2final = 2.5.

The initial positions and velocities of the ith particle areinitialized as random sequences which represent values as{V mppi , I mppi }. These values are updated using (6) and (7) withthe velocity vector {vVmppi , v Imppi } respectively.

In this application, the other parameters of the standard

PSO and dynamic PSO algorithms are set as follows: theinertia weight, w is set to 0.9; the two independent randomsequences, r 1 and r 2 are uniformly distributed in U(0,1). In this

application, the fitness function, ( ) I V f , depends on ( ) I V , and obtains its maximum at MPPs(V mpp, I mpp), where

( )( )

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−=

+

p

skT

IRV q

sc R

IRV V eVI VI I V f

s

1, 0 (10)

IV. SIMULATION R ESULTS

Simulations are performed using MATLAB/SIMULINKsoftware for determining MPPs of the solar PV panel, BP-MSX-120. The specifications and parameters of BP-MSX-120are listed in Table I [20]. The standard PSO and dynamic PSOalgorithms are applied for determining MPPs in which the particle number of a generation is set to 50 and the maximumiteration number is set to 200. Fig. 5 are the V-I and V-Pcharacteristics of the solar PV panel, BP-MSX-120 fordifferent irradiation values, G=(1000 to 5000)W/m

2 at thetemperature, T 0C =25 0C and Fig. 6 is for different temperaturevalues, T

0C =(25 to 100)

0C at the irradiation, G=1000 W/m

2.

The solar PV panel provides a maximum output power at aMPP with V MPP and I MPP . The MPP is defined at standard testcondition (STC) of the irradiation, 1000 W/m2 and moduletemperature, 25

0C but this condition does not exist in the most

of the time. Thus, the output power of the solar PV panel will be less than the maximum output power. Figs. 5-6 show thatthe output voltage and current are affected by the variations inthe irradiation and temperature. However, under anyatmospheric condition, there is a unique maximum point on theV-I or V-P curve, at which the solar PV panel operates withmaximum efficiency and produces maximum output power.Table II shows that the tracking efficiency of MPPs is lowwhen using the standard PSO algorithm due to its drawbackswhereas it is better when using the dynamic PSO and P&Oalgorithms, Fig. 9. Table III shows the tracking ability of MPPsof the standard PSO, dynamic PSO and P&O algorithms.

The efficiency produced by the new algorithm are always

higher than 95% and higher than the efficiencies achievedwhen using the standard PSO and P&O algorithms. This showsthat the dynamic PSO algorithm is better than the standard PSOand P&O algorithms for searching MPPs of solar PV panels.

Figs. 7-8 are the best fitness of the standard PSO anddynamic PSO algorithms versus the iteration step number thatshow the convergence capability of each algorithm. It can berealized easily that there is a basic difference between thestandard PSO and dynamic PSO algorithms. That is a changeof the acceleration coefficients as time-varying variables in thevelocity update equation of the dynamic PSO algorithm. This

results in a significant improvement in the convergence valueof the dynamic PSO algorithm. The convergence value of thestandard PSO algorithm is 0.194 whereas that of the dynamic

PSO algorithm is 2.568×10-6. The standard PSO algorithmconverges to the best fitness faster than the dynamic PSOalgorithm in Figs. 7-8, however this does not mean that thestandard PSO is better than the dynamic PSO algorithm. Thestandard PSO algorithm became stuck in a local optimum

during the search process and resulted in prematureconvergence. The standard PSO algorithm converges at the13th iteration step whereas the dynamic PSO algorithmconverges at the 64th iteration step respectively.

V. CONCLUSION

In this paper, a novel application of the dynamic PSOalgorithm has been proposed for determining MPPs of a solarPV panel. The dynamic PSO algorithm modifies theacceleration coefficients of the cognitive and socialcomponents in the velocity update equation of the PSOalgorithm as linear time-varying parameters with largecognitive and small social parameters in the early part for

enhancing the global search capability and small cognitive andlarge social parameters at the end stage to improve theconvergence of the algorithm. The simulation results of thetracking efficiencies obtained using the dynamic PSOalgorithm are compared with the results achieved using thestandard PSO and P&O algorithms. The results confirm thevalidity of the proposed application. The tracking efficiencies produced by the proposal are always higher than 95% andhigher than the efficiencies obtained using the standard PSOand P&O algorithms of a solar PV panel.

TABLE I. SPECIFICATIONS AND PARAMETERS OF THE SOLAR PV PANEL, BP-MSX-120

Maximum power, P max 120 WVoltage at P max, V MPP 33.70 V

Current at P max, I MPP 3.56 A

Short-circuit current, I sc 3.87 A

Open-circuit voltage, V oc 42.10 V

Panel series resistance, R s 0.47 Ω Panel parallel (shunt) resistance, R p 1365 Ω Standard test condition of irradiation, G 1000 W/m2

Standard test condition of temperature, T 25 0C

TABLE II. TRACKING EFFICIENCY OF THE MPPS OF THE SOLAR PV PANEL USING THE STANDARD PSO, DYNAMIC PSO AND P&O ALGORITHMS

Tracking efficiency of the MPPs (%)Case

No.

G

(W/m2)

T

(0C) Standard

PSO

Dynamic

PSO

P&O

1 1000 25 88.75 99.91 94.78

2 1000 50 89.27 99.94 97.57

3 2000 25 79.28 97.32 90.72

4 2000 50 79.85 99.02 92.23

5 3000 30 94.75 97.80 91.77

6 3000 40 98.03 97.50 91.90

7 4000 30 83.12 98.59 88.93

8 4000 40 88.70 99.34 92.77

9 5000 35 83.83 98.62 95.64

10 5000 45 92.41 99.74 95.71


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0 10 20 30 40 50

0

5

10

15

20Voltage-Current (V-I)

Voltage (V)

C u r r e n t ( A )

0 10 20 30 40 500

200

400

600

800Voltage-Power (V-P)

Voltage (V)

P o w e r ( W )

Figure 5. V-I and V-P characteristics of the solar PV panel, BP-MSX-120

for different irradiation values, G=(1000 to 5000)W/m2 at the temperature,

T

0

C=25

0

C

0 10 20 30 40 500

2

4

6Voltage-Current (V-I)

Voltage (V)

C u r r e n t ( A )

0 10 20 30 40 500

50

100

150Voltage-Power(V-P)

Voltage (V)

P o w e r ( W )

Figure 6. V-I and V-P characteristics of the solar PV panel, BP-MSX-120

for different temperature values, T 0C =(25 to 100)0C at the irradiation,

G=1000 W/m2

1 20 40 60 80 100 120 140 160 180 2 000

0.19

0.2

0.21

0.22

0.23

0.24

0.25

Iteration step number

B e s t f i t n e s s

Figure 7. Best fitness versus the iteration step number of the standard PSO

algorithm

1 20 40 60 80 100 120 140 160 180 2000

0.05

0.1

0.15

0.2

0.25

Iteration step number

B e s t f i t n e s s

Figure 8. Best fitness versus the iteration step number of the dynamic PSO

algorithm

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10Case

T r a c k i n g e f f i c i e n c y ( % )

Standard PSO

Dynamic PSO

P&O

Figure 9. Tracking efficiency of the MPPs of the solar PV panel using the

standard PSO, dynamic PSO and P&O algorithms

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[10] R. Ramaprabha, V. Gothandaraman, K. Kanimozhi, R. Divya and B. L.Mathur, “Maximum power point tracking using GA-optimized artificial

1000 W/m2

2000 W/m2

3000 W/m2

4000 W/m2

5000 W/m2

o

o

o

o

o

1000 W/m22000 W/m23000 W/m24000 W/m2

5000 W/m2

MPP1

MPP2

MPP3

MPP4

MPP5

25 0C50 0C

75 0C

1000C

25 0C

50 0C75 0C

1000C


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neural network for solar PV system”, 1st Int. Conf. Elect. Energy Syst., ICEES 2011, pp. 264-268, 2011.

[11] S. J. Kang, J. S. Ko, J. S. Choi, M. G. Jang, J. H. Mun, J. G. Lee and D.H. Chung, “A novel MPPT control of photovoltaic system using FLCalgorithm”, 11th Int. Conf. Control, Automat. and Syst., ICCAS 2011, pp. 434-439. 2011.

[12] V. Padmanabhan, V. Beena and M. Jayaraju, “Fuzzy logic basedmaximum power point tracker for a photovoltaic system”, Int. Conf. Power, Signals, Controls and Comput., EPSCICON 2012, pp. 1-6, 2012.

[13]

Md. A. Azam, S. A. A. Nahid, M. M. Alam and B. A. Plabon,“Microcontroller based high precision PSO algorithm for maximumsolar power tracking”, Int. Conf. Inform., Electron. and Vision, ICIEV2012, pp. 292-297, 2012.

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TABLE III. OBTAINED V MPP , I MPP AND P MPP OF THE SOLAR PV PANEL USING STANDARD PSO, DYNAMIC PSO AND P&O ALGORITHMS

Theoretical values Standard PSO algorithm Dynamic PSO algorithm P&O algorithmCase

No.

G

(W/m2)

T

(0C) V MPP(V)

I MPP(A)

P MPP

(W)

V MPP

(V)

I MPP

(A)

P MPP

(W)

V MPP

(V)

I MPP

(A)

P MPP(W)

V MPP

(V)

I MPP

(A)

P MPP

(W)

1 1000 25 33.70 3.56 120.00 30.42 3.50 106.47 33.67 3.56 119.87 32.77 3.47 113.71

2 1000 30 33.72 3.57 120.38 30.53 3.52 107.47 33.70 3.57 120.31 32.90 3.57 117.45

3 2000 25 35.31 7.06 249.29 30.50 6.48 197.64 35.01 6.93 242.62 32.87 6.88 226.15

4 2000 30 35.77 7.11 254.32 30.91 6.57 203.08 35.62 7.07 251.83 33.80 6.94 234.57

5 3000 30 35.84 10.66 382.05 31.45 11.51 361.99 36.03 10.37 373.63 34.04 10.30 350.61

6 3000 40 36.72 10.74 394.37 32.19 12.01 386.60 36.76 10.46 384.51 34.75 10.43 362.44

7 4000 30 36.18 14.17 512.67 32.43 13.14 426.13 36.31 13.92 505.44 34.59 13.18 455.90

8 4000 40 36.36 14.27 518.86 33.99 13.54 460.22 36.87 13.98 515.44 35.11 13.71 481.36

9 5000 35 36.09 17.82 643.12 33.57 16.06 539.13 36.43 17.41 634.25 35.78 17.19 615.06

10 5000 45 37.31 17.93 668.97 35.67 17.33 618.16 37.11 17.98 667.24 36.03 17.77 640.25

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Dynamic Particle Swarm Optimization Algorithm Based Maximum Power Point Tracking of Solar Photovoltaic Panels