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A novel optimization of the particle swarm based maximum power point tracking for photovoltaic systems under partially shaded conditions

Received Jan 14, 2020 Revised May 28, 2021 Accepted Jul 19, 2021 When the irradiance distribution over the photovoltaic panels is uniform, the pursuit of the maximum power point is not reached, which has allowed several researchers to use traditional MPPT techniques to solve this problem Among these techniques a PSO algorithm is used to have the maximum global power point (GMPPT) under partial shading. On the other hand, this one is not reliable vis-à-vis the pursuit of the MPPT. Therefore, in this paper we have treated another technique based on a new modified PSO algorithm so that the power can reach its maximum point. The PSO algorithm is based on the heuristic method which guarantees not only the obtaining of MPPT but also the simplicity of control and less expensive of the system. The results are obtained using MATLAB show that the proposed modified PSO algorithm performs better than conventional PSO and is robust to different partial shading models.


INTRODUCTION
Photovoltaic (PV) is alternative source of clean and renewable energy of high importance to environmental friendliness and low maintenance cost [1], [2]. The output characteristics of the photovoltaic generators are not linear because they always vary according to the solar irradiance and the temperature of the module. However, it is reported in the literature for a system of uniformly shaded photovoltaic panels. That the performance of perturb and observe(P&O) algorithm in the detecting the MPP is very efficient [3], [4]. But in the case of partial shading, this algorithm will not achieve its goal. Since the P-V curve has multiple peaks; evolutionary optimization technique such as Particle Swarm Optimization (PSO) could be used to detect MPP techniques where conventional algorithms fail to converge under partial shading [5], [6]. In this paper we will propose an improved maximum power point tracking (MPPT) method for the PV system using a modified PSO algorithm. Particle swarm optimization (MPSO) algorithm is adopted in detecting the global MPP of a partially shaded PV array [7], [8]. The results obtained from this algorithm will be compared to the Perturb and Observe for the single peak characteristics of the P-V. A similar comparison is made for the multi-peak characteristic of P-V between MPSO and MP&O of a partially shaded PV array. The rest of the paper is organized as follows. In Section 2, the circuit model of PV cell and characteristic of PV array are presented. The studied PV array system under partially shaded is illustrated in Section 3. MPP Results are presented and discussed in Section 5. At the end, conclusion is given in Section 6.

MODELING OF A PV ARRAY WITH UNIFORM IRRADIATION
The photovoltaic panel consists of several solar cells. Energy production can be increased by connecting the PV in series or in parallel. The circuit of a photovoltaic cell is shown in Figure 1. The output PV current depends on the temperature and solar irradiation. The equations given below are used to describe the modeling of the single PV module [9], [10]. The current (Iph) is given by: Then (1) becomes: The panel in parallel and panel in series form a photovoltaic field. The generator voltage V1, the current I1 and the power P1 under uniform irradiation can be obtained from the voltage Vpv and the current Ipv of the PV module as follows: Where: Nss and Npp are respectively the series and parallel number of PV modules in the array. The solution of (5) is obtained, for a grid of values of the current I, by using the bisection method in order to solve the f(VPV)=0 in the interval [0 Voc] where:

MODELING OF A PV ARRAY UNDER PARTIAL SHADING
For verify the capability of an algorithm used to detect the global MPP of a partially shaded PV array, it is important to have a physical PV array assembly or its theoretical model [11], [12]. The challenge in such Int J Pow Elec & Dri Syst ISSN: 2088-8694  studies is the need for simulating an enormous Ns and Np connected PV modules simultaneously, because each PV unit might be subjected to a different irradiance level. Of which a high computational time and therefore oftentimes becomes challenging to simulate and study these systems. A method to model the power peaks of partially shaded PV systems using empirical equations is available in the literature [13], [14]. It estimates the current IPV, voltage VPV and power PPV of the possible peaks shaded partially PV systems. The system under study is composed of 10×10 PV modules operating under the shading scenario depicted in. Figure 2 shows the effect on the characteristics of the PV array under partially shading. When the shaded modules receive an irradiation level of G = 0.1 kW/m 2 , the I-V and P-V characteristics are obtained. We can see from this figure that the P-V curve is formed of three different hills with three maximum power points, two local maximums and one global maximum. The standard characteristics of the PVs used are shown in Table 1. The simulation is performed using the one diode model for the solar panel. The simulation is carried out using the one-diode model for the solar panel. Initially each module receives a uniform irradiance of 1000W/m 2 . Four configurations of C 1 , C 2 , C 3 and C 4 with, uniform irradiation, light shading, medium shading, hard shading, is shown in Figure 3, were used in all simulations of the different shaded modules with an irradiation of 1000W/m 2 resulting in three peaks represented in the maximum power points Pm 1 , Pm 2 , Pm 3 as indicated in the Table 2.  In addition, the variation in the irradiations of the shaded modules changes the position of the global MPP. But the latter remains at its maximum VAm, when G = 0.2 kW/m 2 . Figure 4 show V-I, P-V curves of the PV array for different shaded modules with irradiation 0.1 kW/m 2 , the increase of power is increasing with different irradiation of a partially shaded PV array is shown in Figure 5 with different shaded modules irradiation level.  Configuration C2  1000  -7998  900  -7572  900  -7325  800  1710  4725  7043  800  1629  2970  6569  700  1710  4530  6485  700  1596  2759  5768  600  1710  4307  5890  600  1560  2542  4951  500  1710  4086  5321  500  1531  2327  4110  400  1710  3865  4700  400  1490  2209  3263  300  1710  3645  4102  300  1450  1891  2388  200  1710  3426  3498  200  1423  1691  1530  100  1710  3208  2891  100  1375  1477  685  Configuration C3 1000

BASICS OF MODIFIED P&O, MODIFIED PSO
In this article we have compared the modified PSO method and the modified P&O method. The performance of PSO modified is evaluated in comparison with P&O modified [15], [16]. Brief overviews of these methods are presented in this paper to facilitate the following discussion.

Modified P&O
The solution that we proposeto overcome this problem is to scan by varyingthe value of the duty cycle D while saving the maximum value of the passing power. This will detect the true MPP [17], [18]. c. If there is shading (shad = 1): A cyclic report program close to the global MPP is started. It assigns to the duty cycle D values ranging from 0 to 0.9 with a step of 0.1, then saves the value that gives the greatest power in the variable D_PM. This therefore allows us to be injected to the operating point in the vicinity of the overall MPP. d. When D_PM is found the variable shad is reset to 0 and D_PM is assigned to D in order to restart the conventional P & O algorithm with an initial operating point in the vicinity of the global MPP.

MPP detection using PSO
PSO was first introduced in [19], [20], which isan effective method for multimodal function global optimization and swarm intelligence optimizationsearchguide produced by cooperation and competition among particles in swarm. we firstly give the solution vector definition with NPparticle duty ratiois shown in Figure 6. The position of the individual particleis calculated with [21], [22].
Where; : particle i velocity at iteration k,i: number of particle, : weighting function, C 1 : cognitive coefficient, C 2 : cognitive coefficient, r 1 , r 2 : random parameter,[0,1], : current position vector, : best position found by particle I, : global best positions by particle in the group A linearly decreasing inertia weight from maximum value to minimum value, as reflected in (10), is used to update the inertia weight as (10) w H , w L.
Wherek H is the maximum number of iterations and k is the iteration number. The fitness function of PSO algorithm for tracking GMPP can be expressed as (11): To start the optimization process, a vector of duty cycles areinitialized and the algorithm transmits the duty cycles to the power converter. These duty cycles (representedbyS i in (11) serve as the initial particles in the first iteration. All particles are heading towards their local bestposition [23]. Among these particles, one of them is the global best . It gives the best fitness value. Aftercalculating the velocity, which serves as a perturbation to the voltage, a new position of the voltage is found. Through successive iteration all particles move towards global best position. As the particles approach theMPP, they get closer to the position. Correspondingly, the factor and factor in velocity termmoves towards zero. Eventually a zero velocity is achieved and the voltage position remains almostunchanged. Under this condition, the PV system reaches at MPP [24], [25].

RESULTS AND DISCUSSION
To compare the performance of conventional P&O and PSO during partial shading, we introduced PV modules (A, B, C and D) in series. Consequently, there exists only one MPP at 8KW, as shown by Curve 1 of Figure 7. After a period of one second, the modules A, B, C and D are irradiated (partial shading) with 1000 W/m2, 800 W/m 2 and 300W /m 2 respectively, therefore, several 4.077KW peaks, 5.243KW and 1.744KW are generated which are shown by curve 2 in Figure 7. Figure 8 shows that the P&O algorithm is quickly trapped by the 1.744KW peak which is indicated by the arrows produced by moving the operating point from curve 1 to curve 2. Always in the PV system, the offset between the global and local peak is 40 W, or about 14% of the peak power, as well a loss of power considered to be very large are illustrated in Figure 8. In the Figures 9 (a)

CONCLUSION
In this paper, a study of the partial shading effect on the modified particle swarm optimization (PSO) MPPT controlled PV array solar system has been presented and the modified perturb and observe (P&O). The power loss due to the inability of the PSO MPPT algorithm to track the maximum available power has been calculated for a 100 module PV array using a moderate then a severe shading configuration. The results obtained indicate, this PSO MPPT algorithm should be modified to take into account the partial shading effect for a low insolation level. The proposed MPPT method tracks the global MPP for the two shading configurations and under the four given shading levels. The principal objective of this paper is to present the MPPT method based modified PSO algorithm for extraction of GMPP for PV system. The suggestedmodified PSO technique could be performed appropriately during PSC, pointed the GMPP for achieving a better compare with modified P&Omethod during PSC. The simulation results operation for PV system. The suggested algorithm also made to depict that modified PSO is more effectual, has high convergence rate and less ripple, tracking efficiency of modified PSO is remarkable as matched to conventional modified P&O algorithm. So, modified PSO algorithm is matchless in its performance. In this paper MPSO based MPPT and simulation results under normal and partially shaded conditions are presented. The PV curves show multiple peaks under partially shaded conditions. Results show that MPSO algorithm with high accuracy can track the real peak power point under different irradiation and temperature as well as partially shaded conditions. In addition, MPSO has a better time response and also their convergence speed is higher than other algorithms. It overcomes the weaknesses of conventional direct control method particularly in partial shading conditions. results have shown that the proposed method outperforms the conventional method in terms of tracking performance under ten different irradiance conditions, including various patterns for partial shading.