particle swarm optimization algorithm based photovoltaic...

International Journal on Power Engineering and Energy (IJPEE) Vol. (9) No. (4) ISSN Print (2314 – 7318) and Online (2314 – 730X) October 2018

Reference Number: JO-P-0120

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Particle Swarm Optimization Algorithm Based Photovoltaic Maximum Power Point Tracking under Partial Shading Conditions

Gaber El-Saady A. Taha El-Noby A. Ibrahim Department of Electrical Engineering, Faculty of Engineering, Assiut University, Cairo, Egypt

[email protected] Mohamed Amin Moftah

Egyptian Electricity Transmission, Company, Middle Egypt, Electricity Zone, Assiut, Egypt Amany Ali Abo El-Hassan

Electrical Department, Integrated Technical Education Cluster, Assiut, Egypt [email protected]

Abstract- The studies on the photovoltaic PV system are extensively increasing because of a large, secure, and broadly available resource as a future energy supply. However, due to defects in solar cells or environmental conditions changes , partial shading of photovoltaic cells is occurred . Partial shading causes oscillations in output characteristics of the PV (photovoltaic) array and distracts the system to track MPP (maximum power point).Therefore the maximum power point tracking under these condition is not easy and the conventional methods used to track maximum power point is not suitable. In this paper, generalized approximate model of the solar cell is implemented using MATLAB/Simulink software package. In order to track maximum power efficiently from the PV array, evolutionary search technique PSO (particle swarm optimization) algorithm is used via controlling the duty cycle of DC/DC boost converter interfaced with PV system. The duty cycle of the converter is controlled by the proposed MPPT algorithm . The PV system with DC/DC converter is simulated and PSO algorithm is applied to track the maximum power point under partial shading conditions using MATLAB code and Simulink package. The digital simulation results under different operation and environmental conditions is obtained.

Keywords- particle swarm optimization (PSO) algorithm, maximum power point tracking (MPPT), photovoltaic module array, P-V characteristic curves.

I. INTRODUCTION SOLAR Photovoltaic power generation industry is the

world's fastest growing high-tech industry in the 20th century. Photovoltaic (PV) generation is becoming increasingly important as a renewable source since it offers many advantages such as incurring no fuel costs, not being polluting, requiring little maintenance, and emitting no noise, among others.

The V-I and V-P characteristic curves specify a unique operating point at which maximum possible power is delivered.

At the MPP, the PV operates at its highest efficiency. Therefore, many methods have been developed to determine MPPT [1].

The objective of MPPT is to ensure that the system can always harvest the maximum power generated by the PV arrays. However, due to the varying environmental condition, namely temperature and solar insolation, the P- V characteristic curve exhibits a maximum power point (MPP) that varies nonlinearly with these conditions, thus posing a challenge for the tracking algorithm.

To date, various MPP tracking methods have been proposed [2]. These techniques vary in complexity, accuracy, and speed. Each method can be categorized based on the type of the control variable it uses: 1) voltage, 2) current, or 3) duty cycle. For the voltage and current based techniques, two approaches were used. The first one is the observation of MPP voltage VMP or current ISC with respect to the open circuit voltage VOC [3] and short circuit ISC, respectively [4]. The second approach is to obtain the information on the actual operating point of the PV array (i.e., voltage and current) and these points are updated according to the variation in environmental conditions.

However, the major disadvantage of the PV source is the ineffectiveness during low insolation periods or partially shaded conditions. Partial shaded condition is popular and complex in all kinds of PV systems [5]. In the literature, various MPPT algorithms [7]-[9] have been proposed so far. In [8], authors have done comparison of various maximum power point tracking (MPPT) techniques applied to the photovoltaic (PV) systems. To improve the MPPT performance, the conventional perturb and observe (P & O) method based on fuzzy logic (FL) was used in [9]. But with fuzzy logic controller, their effectiveness depends a lot on the knowledge of the user or control engineer in choosing the right error computation and coming up with the rule base table. The neural network (NN) based methods have



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also been implemented for MPPT [11], but large number of data is needed for training the network. Moreover, with change of PV characteristic with time, the NN methods require to be periodically trained to assure accurate MPPT.

An alternative and effective solution is provided by particle swarm optimization (PSO) based method which has fast computational capability and easy to implement due to its simple structure.

In [11], the conventional PSO was implemented for MPPT with various extra coefficients, thus, the computational burden of the algorithm was increased. Moreover, most of the PSO algorithms presented in previous works have been implemented and tested for two-stage PV system where the duty ratios were selected as PSO agents.

This paper proposes a simple PSO based MPPT algorithm for a single-stage photovoltaic system, which is operated with other control. The reactive power control is also considered with maximum real power injection to utilize reactive power capability of inverters and dc-link capacitor connected with PV system. The effectiveness of the proposed method is established by comparing the results with the conventional HC and INC methods. It is found that the modified PSO method tracks the MPP with fast speed and good accuracy.

Fig. 1. (a) Model of the PV cell. (b) Series parallel

combination of the PV array

II. MODELING OF THE PV MODULE AND ARRAY

Single diode model is the most common mathematical representation of the solar cell. In the literature there are other models available which uses additional diodes to represent the recombination effects of charge carriers [6-8]. The two diode model is more accurate in representing solar cell but it takes more computational time. In this work single diode model is considered for simulation of PV system as it is effective and provides a good compromise between simplicity and accuracy [9].

The equivalent circuit of this model is given in Fig.1 and the output current of photovoltaic cell is given below:

(1) here I is the solar cell terminal current, IPV is the solar cell light-generated current, Io is the reverse biased saturation current of diode, V is the solar cell terminal voltage, n is the ideality factor of the diode, and VPV is the thermal voltage. The function of thermal voltage is described as (2) Where,

(2) Where is the numbers of solar cells connected in series, k is the Boltzman constant (1.381 x 10-23 ), T is the operating temperature of the solar cell in unit Kelvin, q is the electron charge (1.602 x 10-19 C).

The external influences, such as solar irradiance and cell temperature will affect the generation of charge carrier in PV module and eventually affect the , as described in (3):

(3) Where is the PV module light-generated current in the nominal condition, k1is the ratio of short-circuit current to temperature coefficient, T is the difference of actual temperature to the nominal temperature.

III. VALIDATION THE MODEL

In order to test the validity of the model a comparison with other experimental data Fig.2 shows the mathematical I-V curve of the MSX-60 solar panel [10] plotted with the experimental data and Fig. 3 shows the P-V curve.

Table.1

PARAMETERS OF THE MSX-60 PV MODULE AT

STC: TEMPERATURE= 25 ,

AIR MASS = 1.5, AND INSOLATION = 1000W/m2



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Fig. 2. I-V model curve and experimental data of the MSX60

solar array at different temperatures, 1000W/m2

` Fig. 3. P-V model curve and experimental data of the MSX60

solar array at different temperatures, 1000W/m2.

IV. SIMULATION OF THE PHOTOVOLTAIC ARRAY

Fig.4 show the photovoltaic model circuits implemented with MATLAB/SIMULINK . The PV module taken for modelling is MSX60 .The developed model is implemented for the above module and evaluated. The evaluation is done using the equations developed in the previous sections . The chosen module provides the output power of 60W maximum nominal and has 36 series arrays.The technical specifications are listed in the table 1.The PV and IV characteristics are modeled and simulated for the chosen module using the developed equations and models.

V. PARTIAL SHADING AND BYPASS DIODE EFFECT

It is not possible to have uniform illumination of PV panel all the time because of buildings or trees shades, atmosphere fluctuation, existence of clouds and daily sun angle changes . Power loss occurs from shade, also current mismatch within a PV string and voltage mismatch between parallel strings. Typically, a crystalline silicon module will contain bypass diodes to prevent damage from reverse bias on partially shaded cells .

The operating principle of a solar cell with a Bypass Diode is such that during normal operation without shade, the Bypass Diode is reverse biased and has high impedance, therefore no current flows through it. This prevents the un-shaded cells

from forcing a current against the reverse biased state . Connection diagram of solar PV module is shown in Fig. 5.

Because of the absorption of the power, the cells would get heated up and cause hot spot problem, which could result into the cracking of the glass shield. To overcome this effect, we use bypass diode across the string of particular cells connected in series (ideally we should use one bypass diode across each cell but it is not feasible). Bypass diode allows the current to flow in one direction. If the power flows toward the sink, bypass diode connected in ant parallel offers the power low impedance path. This prevents the power loss in the panel and prevents the problem like hotspot and shield cracking. [19,20].

Fig. 4. Photovoltaic circuit model built with MATLAB/SIMULINK



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Fig. 5 Connection of Bypass Diode across the module

VI. CHARACTERISTICS OF THE PV ARRAYUNDER PARTIAL SHADING CONDITION

A PV module consists of several PV cells connected in parallel to increase current and in series to produce a higher voltage. Several PV modules are then connected in series/parallel to form a PGS. Under PSC, the P–V curve of PV module will display multiple MPPs because of the bypass diodes. The partial shading effect on PV modules in a PV string is analyzed by performing the simulation for PV string which has 3 series connected PV modules. Simulation model of PV string is shown in Fig. 6.

Different irradiation values are applied to each of the modules by maintaining the temperature value as constant for all the 3 modules . The characteristics of a PV module under PSC with bypass diodes connected at module terminal can be explained as follows. Under PSC, the shaded cells behave as a load instead of a generator and create the hot spot. Therefore, bypass diodes of these shaded cells will conduct to avoid this problem. Since the shaded cells are bypassed, V-I characteristics of PV module under partial shading will be presented as shown in Fig. 7 (a) and multiple peaks in the P–V curve will be presented as shown in Fig. 7 (b).

VII. BOOST CONVERTER

The DC – DC boost converter is used which consists of boost inductor, diode, MOSFET used as a switch, output filter capacitance and resistive load. When supply voltage is given and the switch S closed , inductor current increases . When the switch is opened, both inductor voltage and supply voltage gets discharged through the load. Hence a higher Voltage at the output is obtained than the given input voltage [26].

The circuit diagram of traditional boost converter is shown in Fig. 8. Boost converter is connected between the supply and the load. To maintain constant output voltage a capacitor is connected to the load. The feedback is provided by the controller connected to the output of the boost converter.

Fig. 9. Shows the circuit diagram of boost converter with MPPT. It consists of two main parts such as boost converter and controller. The output of the controller is duty cycle of the converter and it is sent to the comparator that compares the

reference duty cycle of the converter and the error signal so the controller can control the duty cycle . Boost converter is used to convert DC to variable DC source The controller is used to control the output voltage. When the switch is opened the inductor gets charged after closed the switch inductor charge will goes to the diode and the diode only conducted in forward biasing and the capacitor removes the ripple component [27].

VIII. CONVENTIONAL HC METHOD

To obtain the maximum power from the PV modules,

MPPT is normally employed. Over the years, various MPPT methods were proposed; for example, P&O, IC, HC,NN, and FLC [2], [4], [12], [13]–[17], [18]. In particular, the conventional HC method is interesting as the duty cycle of the power converter

Fig. 6 Simulation diagram system

(a)



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(b)

Fig. 7 (a) V-I characteristics of PV module under partial shading. (b) V-P characteristics of PV module under partial

shading.

Fig. 8. Boost converter

Fig. 9. System framework of this presented PSO-based MPP tracker.

can be varied directly [14]. This can be explained with the help of a flow chart as shown in Fig. 10 and Fig. 11 show the typical movement of particles in the optimization process.

The algorithm periodically updates the duty cycle d(k) by a fixed step size with the direction of increasing power. The perturbation direction is reversed P(k) < P(k 1), that indicates that the tracking is not moving toward the MPP. This can be described by the following; equation :

=

(4) A clear advantage of this algorithm is that the MPPT

algorithm does not require proportional (P) or proportional integral (PI) action, which is normally employed to control the duty cycle with reference to voltage or current. In this case, the duty cycle directly feeds the power converter.

IX. PSO-BASED MPPT

A. Elements Used In PSO

Before working with the PSO, we have to know about the elements used in the PSO. First of all, we shall overview the brief concepts of the PSO elements. Particle---We can define the particle as Pi where i=1,2,3,….. Fitness Function---Fitness Function is the function used to find the optimal solution. Usually it is an objective function. Local Best---It is the best position of the particle among its all positions.

Fig. 10. Flowchart of the conventional HC method.

Fig. 11. Movement of particles in the optimization process.

Global Best---The position where the best fitness is achieved among all the particles Velocity Update---Velocity is a vector to determine the



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speed and direction of the particle. Position Update---All the particles try to move toward the best position for optimal fitness. Each particle in PSO updates their positions to find the global Position.

B. PSO MPPT Technique

PSO is one of the swarm intelligence techniques that uses stochastic variables based on population for solving optimization problems. This technique is first introduced by Eberhart and Kennedy in (1995) [19],[22] ,[24] modeled after the behavior of bird flocks [15]. The first work have been used PSO in MPPT of PV-systems have been in 2004 by [25]. Wide range of literatures have been done in same area. PSO are inspired by social swarming behavior of fish schooling or bird’s flocking. PSO evolutionary process, potential solutions, called particles, move about the multi-dimensional search space by following and tracking the current best particle position in the swarm. Each particle in the swarm has mainly two variables

associated with it. These variables are: the position vector , and the velocity vector .

The idea of PSO-based distributed MPPT control algorithm is that regard the multi-module’s voltage output as a multi-dimensional variables and the system's total power output as the objective function. Through the use of particle swarm optimization, the maximum total output power is found, that is, each module finds the maximum power point at the same time, and then solar panels control the output voltage at maximum power point by conventional constant voltage method. This realizes the distributed MPPT of PV generation system and the group control of multi-module. The steps and multi-peak optimization of Particle Swarm Algorithm MPPT are similar, which needn’t repeat here.

In PSO algorithm, assuming that k particles are initialized randomly, each particle is a D-dimension vector, the i-th particle is expressed as (5),

) (5) The i-th particle experiences the best position (present local optimal solution), denoted as (6),

= ) (6) The whole particle swarm experiences best position (present global optimal solution), denoted as (7),

= ) (7) Flying velocity of the i-th particle denoted as (8)

)

(8)

In PSO Particles follow a simple behavior: emulate the success of neighboring particles and its own achieved successes. The position of a particles, therefore, influenced by the best particle in a neighborhood as well as the best solution found by all the particles inthe entire population . The

particle position is adjusted using

(9) is adjusted where the velocity component represents the step size. The velocity is calculated by

(10)

where, is weight coefficient which is general as

[0.4,0.9] to adjust the scope of searching of solution

space, and are learning factors which are general as

, [0,2] to adjust learning step, and are two

random number which are general as , , [0,1] to

increase the ability of searching random[22][23]. Particle velocity in each dimension is limited to a maximum velocity Vmax (Vmax>0) to avoid the fast particle flying velocity which can result in the algorithm premature to convergence to a local optimal solution. If position is defined as the actual duty cycle while velocity shows the perturbation in the present duty cycle, then (9) can be rewritten as

(11) The objective function is defined as

C. Algorithm for PSO

A flowchart of the conventional PSO algorithm is shown in Fig. 12, and the steps are described below: Step 1. Parameter Selection: For the proposed MPPT algorithm, the duty cycle of the converter was defined as the particle position, and the generated output power was chosen to be the fitness value.evaluation function, the position and initial velocity of each particle was randomly initialized in a uniform distribution over the search space. Step 2. Fitness Evaluation: The goal of the proposed MPPT algorithm is to maximize the generated power PPV. After the digital controller output,



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the PWM command according to the position of particle i (which represents the duty cycle command), the PV voltage VPV and current IPV can be measured and filtered using digital finite impulse response filters. These values can then be utilized to calculate the fitness value PPV of particle i. It should be noted that in order to acquire correct samples, the time interval between successive particle evaluations has to be greater than the power converter’s settling time. Step 3. (Update Individual and Global Best Data): Update the fitness values, individual best positions ( ) and global best fitness values ( ) of each particle bycomparing the new calculated fitness values against theprevious ones and replacing the , and corresponding to their positions as necessary. Step 4. (Update Velocity and Position of Each Particle): After evaluating all particles, update the velocities and positions of each particle in the swarm by using the PSO formulas . Step 5. (Convergence Determination): The converge criterion are either locating to optimal solution or reaching the maximum number of iterations. If the convergence criterion is met, the process would terminate ; otherwise, return Steps 2 through 5. Step 6. (Reinitialization): In standard PSO method the converge criterion are either locating to optimal solution or reaching the maximum number of iterations. However in PV systems the fitness value is not constant as it changes with the weather condition and load . Therefore, the PSO must be reinitialized and search again for a new to search the new MPP when the PV module output changed .

X. SIMULATION AND RESULTS

To verify the correctness of the proposed MPPT method, MATLAB simulation model is carried out accordingly. The PV system is consisting of PV array, high step-up DC-DC converter, MPPT controller, and load. In the simulation, the sampling time of the MPPT controller is set to 0.06 s and the

Fig.12. Flowchart of proposed algorithm



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switching time for the MOSFET in the DC-DC converter is 5kHz .

A. MPPT for Partial Shading PV Array and constant temperature

This paper use MPPT controller to track MPP by using two methods P&O and PSO and output duty cycle is adjusted through DC-DC boost converter and implemented using MATLAB/simulink. A variable irradiance is used with

different step size of w/ 2and temperature as well, that will

show a simulation results for current, voltage, duty cycle and power tracked respectively. Simulation results are carried out under non-uniform irradiance with different cases

1000,500,800W/ 2 and 300,400,800,900W/ 2, between

PSO and P&O. As described each PV module consists of one bypass

diodes. Therefore, as shown in Fig.13 three series connected PV modules have maximum 3 peaks (3 bypass diodes) when the PV array is under 3 different levels of solar intensity and four series connected PV modules have maximum 4peaks (4 bypass diodes) when the PV array is under 4different levels of solar intensity.

For the first case, the - curve is shown in Fig.13(a). The

PSO algorithm is used to track the GMPP and the result is as shown in Fig. 14(a) . As shown in the simulation result, For the first case the PSO algorithm begins the initialization by setting the duty cycle of the DC-DC converter to 0.16 and 0.73 in order to ensure that these arch space covers the whole

- curve.After that, the values of duty cycle are mutated and

crossed over; this process keeps on going until the difference

in the power is less than 1%. At = 3 s, the algorithm stop

the searching and remains at the GMPP where the power of that point is 96.7W. Throughout the searching process, the duty cycle is converging to 0.174 . This fulfilled the criteria of the PSO algorithm where all the particles converged to the best solution.

As a comparison, P&O is used to track the GMPP under the same partial shading condition and the result is as shown in Fig.14(b). The P&O starts the perturbation by

setting the duty cycle of the converter to 0.5. At = 0.13 s;

the algorithm started to oscillate around the LMPP instead of GMPP due to its disability to differentiate between the two . Therefore, P&O tracked the LMPP which has the lower power (117W). Another case is simulated to ensure

that the PSO algorithm is able to function well. The -

curve is as shown in Fig.15(a) and the GMPP is at 91.9W. The proposed algorithm tracked the GMPP and remains to operate at the GMPP, but the P&O still failed to track the GMPP in this partial shading condition when it also tracked the LMPP (30W).

B. MPPT for Partial Shading PV Array and variable

temperature

Simulation is carried out based on MATLAB/Simulink

(a)



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(b)

Fig. 13. - curves for PV array under partial shading, solar intensity are (a) 1000W/m2, 500W/m2, 800W/m2and 800W/m2

and (b) 300W/m2, 400W/m2, 800W/m2, and 900W/m2.

(a)

(b)

Fig. 14. Tracking voltage, current, duty cycle, and power for case (1) 1000,500,800 w/ 2. (a) PSO method.

(b) P&O method



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(a)

(b)

Fig. 15.Tracking voltage, current, duty cycle, and power for case (2) 300,400,800,900 w/ 2. (a) PSO method. (b) P&O

method.

platform. Three PV panels of the same ratings are considered to be connected in series. The net voltage contribution of any PV panel depends upon the state of operation of bypass diode connected to it.

This study uses a PV panel having three solar models in series Simulation results are carried out under non-uniform irradiance with different cases

1000,600,800W/ 2.The - curve is as shown in Fig.16

and the PSO algorithm is used to track the GMPP and the result is shown in Fig.17(a) .

As shown in the simulation result the PSO algorithm begins the initialization by setting the duty cycle of the DC-DC converter to 0.44 and 0.6 in order to ensure that the

search space covers the whole - curve and P&O is used

to track the GMPP under the same condition and the result is as shown in Fig.17(b).

Fig. 16. - curves for PV array under partial shading, solar

intensity are (a) 1000W/m2, 600W/m2,and800W/m2 XI. CONCLUSION AND DISCUSSION

The main purpose of this paper is to develop an accurate and system-independent MPPT algorithm for PV under PSC. The standard version of PSO is modified to meet the practical consideration of PV cells operating under PSC. The problem formulation, design procedure, and parameter setting method which takes the hardware limitation into account are described and explained in detail. According to the simulation results of test cases, the proposed method can reach the GMPP in less than 27 iterations, and the averaged tracking efficiency is higher than 99.9%.

Four different shading patterns are also utilized to experimentally validate the correctness of the proposed system. Proposed MPPT algorithm using PSO is very high .



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PSO is a good candidate for MPPT algorithms, as it is easy to implement and converges to the desired solution in a reasonable time. The proposed method requires knowledge only of the number of the series cells; therefore, it is system independent. It is well known that the choice of PSO parameters may have some impact on optimization performance; this aspect will be investigated in the future work.

As a comparison point of view between PSO and P&O its seems that:

A] PSO: 1) Almost zero steady state oscillation 2) High tracking speed and accurate

(a)

(b)

Fig. 17. Tracking voltage, current, duty cycle, and

powerfor1000,600,800 w/ 2 and temperature 27,26,25. (a)

PSO method (b) P&O method.



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3) Ability to track MPP under various environmental conditions

4) Easy hardware implementation using low cost micro-controller

B] P&O:

1) Large amount of power losses and not accurate 2) Tracking efficiency is low if it’s compared

with PSO 3) In hardware implementation, it’s require fast

controller speed & more sensor devices that leading to increase the system cost

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