[ieee 2013 iv international conference on power engineering, energy and electrical drives (powereng)...

A Soft Computing MPPT for PV System Based on Cuckoo Search Algorithm

Jubaer Ahmed, Zainal Salam Faculty of Electrical Engineering

Universiti Teknologi Malaysia 81310 Johor Bahru, Malaysia

Email: [email protected], [email protected]

Abstract— This paper presents a novel approach to determine the maximum power point (MPP) in Photovoltaic (PV) System using the Cuckoo Search (CS) algorithm. In CS, three samples of voltage are generated randomly over the span of the PV voltage. Based on the Le’vy distribution, the voltage samples are directed towards the best solution and on the basis of power comparison, the best position is found. The algorithm is simulated using MATLAB and compared to the conventional P&O method. It exhibits very fast convergence with zero steady state oscillation. In addition, it tracks the MPP perfectly when PV system is subjected to rapid changes of atmospheric condition.

Keywords- MPPT, Cuckoo Search, Le’vy Flight, Convergence speed, Rapid tracking

I. INTRODUCTION Solar power is considered one of the most important

renewable energy (RE) sources of the future. Besides the abundance of the sun, photovoltaic (PV) system is easy to install, almost maintenance free and environmentally friendly. One of the most economical ways of increasing efficiency of PV system is to ensure it is operated at the maximum power point (MPP). This can be achieved by employing a MPP tracker (MPPT). Since the relation between the power and voltage/current in PV cell is highly non-linear, MPPT algorithms needs to track the MPP with the following constraints: (1) convergence speed, (2) steady state condition, (3) adaptability with changing atmosphere as irradiance or temperature and (4) compatibility with abnormal condition such as partial shading [1].

Conventional MPPT operates by sensing the current and voltage of the PV array; the power is calculated and accordingly the duty cycle of the converter is adjusted to match the MPP. Among them, Perturb and Observe (P&O) [2], Incremental Conductance (IC) [3] and Hill Climbing (HC) [4] are the most popular. One of the major problems of these methods is their incompatibility with the rapid change in the irradiance and temperature. Besides, P&O and HC oscillate around MPP that cause huge loss in power during operation. None of these techniques are capable of handling partial shading condition.

To overcome this problem MPPT based on soft computing (SC) techniques, for example Artificial Neural Network [5], Fuzzy logic Controller [6], Genetic algorithm [7], Differential Evolution [8] and Particle Swarm Optimization [9] are attracting considerable interests. Recently, there are several works on a SC method known as “Cuckoo Search (CS)”. Compared to other SC techniques, CS is proven (in other applications) to be more robust, has better convergence and exhibits higher efficiency. Despite these advantages, the use of CS for MPPT has not been reported anywhere in the literature. Hence, this paper proposes the application of CS for MPPT.

II. PV MODELING To investigate the performance of a PV system, first, a

model for the PV module needs to be developed. A simplified cell model is presented in Fig. 1.

The Current from the PV cell can be presented in (1)

( )V IRsI I IPV d Rp

+= − − (1)

Where, light generated current is given in (2)

_( ( )) GI I K T Tpv IPV STC STC GSTC= + − (2)

Note that IPV_STC is the light generated current in standard test condition (STC), i.e. temperature T=298 K and irradiance G=1000 w/m2. KI is the short circuit current coefficient, which is usually provided by the manufacturer. The diode current can be written as in (3)

exp 11 ( ( ) )V IRSI Iod VT

+= − (3)

Figure 1. Simplified PV panel Modeling

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Where diode saturation current is expressed in (4)

_1 13 exp( ) [ ( )]o STC

qET gSTCI Io T k T TSTC= − (4)

In (4), Io_STC is the saturation current under STC, q is the charge of electron, Eg is the band gap energy of the fabrication material and k is the Boltzmann constant. Based on this equation the P-V curves for the PV cell at STC are shown in Fig. 2.

III. CUCKOO SEARCH

A. Cuckoo Behaviour Cuckoo Search (CS) was first proposed by [Yang &

Deb][10]. The algorithm emulates the aggressive reproduction strategy of cuckoo birds. It is observed that several species of cuckoos perform brood parasitism [10], i.e. by laying their eggs in other birds’ (host birds) nests. Usually three types of brood parasitism are seen (1) intraspecific, (2) cooperative and (3) nest takeover. Some cuckoo species as ‘Tapera’ are intelligent enough to mimic the shape and color of host bird that increases the reproduction probability. It is also presented in [11] that cuckoos lay their eggs at some specific time so that their eggs hatch some time earlier than the host bird’s own. After early hatching, cuckoos destroy some host bird’s eggs to increase the chance of their chicks getting more food. It is also a common phenomenon that host birds discover the cuckoo’s eggs and destroy these. Sometimes they abandon their nest completely and go elsewhere to build a new nest.

B. Le’vy Flight Searching for a suitable host bird’s nest is an important

part of cuckoo’s reproduction method. Normally, the search for nest is similar for a search for food, which takes place randomly or in a quasi-random form. In general, while searching for food, animals choose directions or trajectories that can be modeled on certain mathematical functions. One of most common model is the Le’vy flight. A recent study by Reynolds and Frye [12] shows that that fruit flies or Drosophila melanogaster, explore their landscape using a series of straight flight paths punctuated by a sudden 90 degree turn, leading to a Le’vy flight style. Such behavior is

adopted in meta-heuristic search algorithm for optimization problem [13].

In CS, nest searching steps of cuckoo is determined by Le’vy Flight. Mathematically, a Le’vy flight is a random walk where step sizes are extracted from levy distribution according to a power law in (5), i.e.

y t λ−= (5) Where, 1 < <3. Thus (5) has an infinite variance. Fig.3 is showing an example of le’vy flight in a two dimensional plane.

C. Cuckoo Search Algorithm

Yang and Deb [10] have used three idealized rules for CS based on cuckoo’s brood parasitic behavior: (1) each cuckoo lays one egg at a time and places it in a randomly chosen nest, (2) the best nest with high quality of eggs will carry over to the next generation and (3) the number of available nests is fixed and the egg laid by a cuckoo is discovered by the host bird with a probability of Pa, where 0 < Pa <1. If the cuckoo’s eggs are discovered, host bird can abandon its nest or destroy cuckoos’ eggs. Either way a new nest will be generated with a probability of Pa of fixed number of nest. Based on these three rules, the CS algorithm can be summarized in a pseudo code below: Begin Objective function ( )f x , 1 2( , ..... )T

nx x x x= ; Generate initial population of n host nest, ( 1, 2,......., )ix i n= ; While(t< Max Generation or stop criterion) Get a cuckoo randomly by levy flight Evaluate its quality/fitness, if Choose a nest among n (say, j) randomly If (

i jf f> ) Replace j by the new solution End A fraction(Pa) of worst nest occurs; Worst nests are abandoned and new nests are built; Keep the best solutions; Rank the solutions and find the current bests; End while Post process of results and visualization; End

Figure 3. A Le’vy Flight

Figure 2. P-V and I-V curve at STC

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When generating a new solution ( 1)tx + for a cuckoo, a le’vy flight is performed as in (6), i.e.

( 1) ( )t tx x le vyi i α λ+ ′= + ⊕ (6) Where, > 0 is the step size which is related to the constraint of the optimization problem. Based on the constraints it is important to tune the value of to get desired step size. The product ⊕ means entry wise multiplication. The value of le’vy ( ) is found from le’vy distribution given in (7), i.e.

, (1 3)Le vy u t λ λ−′ ≈ = < < (7) In the context of MPPT algorithm, the structure of CS algorithm in (6) is in the same form of the hill climbing (HC) method. This similarity, of course, does not include the step size from le’vy flight. However, there are several significant features [14] that allow for CS to be much more robust than HC: (1) CS is a population based algorithm like GA and PSO but it exhibits elitism in selection procedure like harmony search, (2) in CS, the randomization is much more efficient as the steps sometimes get bigger because of levy flight which provide faster convergence and (3) the number of parameters for tuning in CS is two; this is less than GA and PSO where the tuning parameters are three and above .

IV. MPPT DESIGN USING CS

A. MPPT Algorithm Considering fixed number of nest (n) initially population is

generated as voltage, 1 2, ,......,i nV V V V= and initial step size 0α .

Voltages are applied in the PV panel and the power is found as the fitness value. The maximum value among the fitness is considered as the current best. Then le’vy flight is performed and new nests are generated as in (8)

( 1) ( )t tV V le vyi i α λ+ ′= + ⊕ . (8)

Where, ( )0 x xibestα α= − . A simplified scheme of le’vy distribution is presented in [x] as (9)

( ) ( ) 0.010 1( )( )us x x Le vy x xi ibest best

vα λ

β′= − ⊕ ≈ −

(9)

where =1.5, u=random(1, n)×� and v=random(1, n). The variable � is defined in (10)

(1 ).sin( . / 2)11(( ). .2 )22

1

β π βββ β

β

φ Γ +−+Γ

= (10)

Where, Γ denotes the integral gamma function. New fitness values are tested through PV panel. Afterwards, probability of discovered worst nests is applied and such nests are destroyed

while keeping the better nests. New nest are generated in place of worst nest. Values of fitness are tested again and current best is selected. Iteration continues until all nests reach at the maximum power point.

B. Simulation In the simulation, the direct duty cycle control method

MPPT [15] is utilized. The CS MPPT algorithm is tested on a DC-DC buck-boost converter. The circuit is shown in Fig.4. Two sensors are used to measure the voltage and current of the PV array. Using the CS algorithm, the reference value of the duty cycle is computed. This value is directly fed to the input in the PWM generator. This PWM signal adjusts the duty cycle of the MOSFET. The common parameters for the tested PV system are given in Table I.

TABLE I. LIST OF PV PANEL PARAMETERS

Panel Parameters Value Short Circuit current 7.5 amp Open Circuit voltage 20.7 v Maximum current 6.6 amp Maximum voltage 16.7 v Temperature coefficient of current 0.00033 amp/C Temperature coefficient of voltage -0.084 v/C Number of cells in series inside panel 36 Number of panels in series 20 Number of panels in parallel 1 To evaluate the performance of the proposed CS MPPT, the standard P&O algorithm is also developed for the same simulated conditions. The P&O is used as a benchmark because it is the most commonly used MPPT in the PV industry.

V. RESULTS

A. At STC The performance of the algorithms (P&O and CS) are

compared at STC, i.e. T=25 C and G=1000 w/m2. The simulation is carried out for 1 sec. The results are shown in Fig. 5 up to 200 ms. From the figure, it can be observed that MPP tracking time for CS, i.e. the time taken to track the MPP from the initial condition, is 22 ms. On the other hand, the P&O tracks at 45 ms. Furthermore, at steady state, the P&O oscillates around MPP, while the CS keeps tracking the exact MPP point. This is an added advantage as the power losses

Figure 4. Simulation Circuit

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associated to power oscillation for CS is almost nil at steady state, leading to a higher MPPT efficiency. In the case of voltage and current waveforms, shown in Figs. 6 and 7 respectively, the P&O keeps on oscillating in steady state but CS sticks on Vmpp and Impp. However, it can be observed that initially CS exhibits much higher power fluctuations as the algorithm starts to check for random samples in different region (in transient). Nevertheless, since the samples get closer to MPP in very quick succession, the power loss associated to this fluctuation is not a big issue.

As the P&O keeps on oscillating around MPP presented in Fig. 5, it looses energy at an average rate of 3 mJ/sample. As 20 panels are in series, energy loss per sample per panel is 0.15 mJ. Since the simulation is designed as 1 ms per sample, which makes energy loss 0.15 J/sec/panel (0.136% of the panel capacity), which is really huge when PV panel is operating for long period of time. In case of CS power loss tends to zero at steady state.

B. Rapid Atmospheric Change

The CS is tested to verify its performance under rapid atmosphere changes. In the simulation, the irradiance and temperature are changed abruptly at every one second. The test patterns for the atmospheric conditions are shown in Table II.

TABLE II. TEST CONDITION FOR RAPID CHANGES

Temperature( C) Irradiance(w/m2) MPP(W) 25 1000 2205 35 1200 2504 20 800 1769 45 1400 2675 15 600 1295

It is clear from Fig. 8 that CS is quite capable of tracking MPP under drastic changes in environmental conditions. However, the initial convergence times are not constant; they vary from 20 to 100 ms. This is to be expected due to the random nature of CS algorithm. Furthermore, it can be observed that after

Figure 7. Combined Current Graph of P&O and CS

Figure 6. Combined Voltage Graph of P&O and CS

Figure 5. Combined Power Graph of P&O and CS

Figure 8. Rapid Tracking of CS

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steady state is reached, CS sticks to the MPP without any further fluctuation.

VI. CONCLULSION In this paper a novel MPPT algorithm is proposed based on cuckoo search algorithm. Following the cuckoos natural behavior and le’vy flight distribution, MPP is tracked very efficiently. It is confirmed from the simulation result that this algorithm converges faster than P&O. Besides, it exhibits zero oscillation at steady state, thus saves a large amount of power. Additionally this algorithm can track MPP successfully when atmospheric condition changes very rapidly.

ACKNOWLEDGMENT The authors would like to thank Universiti Teknologi Malaysia and the Ministry of Higher Education Malaysia for providing the facilities and nancial support (Research University Grant No.2423.00G40 to conduct this research.

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