# Improved Performance Analysis of PV Array Model Using Flower Pollination Algorithm and Gray Wolf Optimization Algorithm

Authors: J. Jayaudhaya; K. Ramash Kumar; V. Tamil Selvi; N. Padmavathi
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The efficiency of a photovoltaic (PV) system under partial shading conditions (PSCs) is primarily determined by how the PV panels are connected to the load. Various PV system architectures have been developed to improve power processing capability and thus power conversion efficiency. In this article, a central and string architecture are considered, and the performance characteristics are obtained using optimization techniques such as gray wolf optimization (GWO) and flower pollination algorithm (FPA) in MATLAB/Simulink. The simulation results show that the performance characteristics of string architecture obtained using the GWO algorithm outperform central architecture with both GWO and FPA.


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## Body

## 1. Introduction

The demand for electricity in the home and industry is increasing all the time. Nonrenewable energy sources are best replaced with renewable energy sources such as fuel cells, wind energy, solar energy, and biogas in [1-5]. Solar energy has more advantages than other sources because it is nonpolluting, requires less maintenance, has no fuel costs, and is readily available. The output power of a photovoltaic panel is primarily determined by lighting, temperature, and panel construction. During shading conditions, a portion of the PV panel is shaded by trees, dust, castles, and high-rise structures [6, 7], and as a result of these shading conditions, the panel produces less output power as well as several peak powers [9]. As a result, extracting maximum power (MP) under partial shading conditions is complicated.An optimization technique is required to obtain the peak output power of a PV panel under shaded conditions. Various optimization techniques based on convergence time and equipment implementation have been developed and tested over the years. The most commonly used traditional approaches are perturb and observe (P&O) and incremental conductance (IC) [9]. Despite their ease of use and simplicity, these methods are unable to find the exact local and global peaks under shading conditions. Fuzzy logic (FL) and artificial neural network (ANN) are combined in [10] to improve the performance of the solar panel. Following that, several approaches to swarm intelligence (SI) [11] are proposed and implemented. Because of the lack of mutation and crossover processes, PSO is used in [12, 13], resulting in a longer convergence time and poor local search capabilities.In [14, 15], the flower pollination algorithm (FPA) and simulated annealing are combined to improve search performance and convergence rate. In [16], the gray wolf optimization (GWO) and flower pollination algorithms are only implemented for central architecture. Grouped beetle antennae search (GBAS) is a new technique used in [17-19] to identify the PV cell characteristics in three different models. GA-FPA is used in [20] to evaluate convergence speed and accuracy. Maximum power tracking of photovoltaic (PV) systems is one of the most important characteristics in PV panels, according to [21]. To achieve maximum power tracking, proper modeling of solar cells is required.The main key contributions of this article are given as follows:(i)
Central and string architecture of PV panel are selected for the case study(ii)
FPA and GWO algorithms are used for analyzing the case study(iii)
Comparison is made between the performance characteristics of central and string architecture using FPA and GWO(iv)
From the results, the best architecture with suitable algorithm is concluded(v)
The performance of the proposed model is validated with help of the MATLAB/Simulink software platformThis article is structured as follows: Section1 clearly addresses the introduction and goal of the work. Section 2 describes the literature review. Section 3 describes the architecture of central and string solar PV panels that employ various algorithms. The simulation results were described in Section 4. Section 5 discusses and concludes the performance of the PV array central and string architectures.


## 2. Literature Survey-Related Work

Nonuniform irradiance significantly reduces the power output of a solar array [22]. The shading pattern, array arrangement, and physical positioning of modules all have an impact on PV array output power reduction. Figure 1 shows a PV array/string module. Reconfiguration strategies are frequently used to mitigate the effects of partial shading [23]. The proposed work will use the GWO and FPA to optimize efficiency by minimizing partial shading effects and increasing the system’s output power. The advantage of solar photovoltaic (PV) technology is that it directly converts sunlight into power. As a result, it is strongly recommended when compared to other renewable energy sources [24, 25]. In addition to that reconfiguration DC-DC strategy, there are 2 various methods: (i) isolated and (ii) nonisolated. Hence, solar PV MOPE is possible with nonisolated switching converter [26]. The several nonisolated DC-DC converter topologies using traditional MPP algorithms [27], as well as associated characteristics such as construction, efficiency, switching frequency, and losses, were evaluated. In the suggested analysis, several reconfiguration techniques and procedures are investigated. Under varied partial shade situations, static reconfiguration methods were employed to examine the Sudoku and enhanced Sudoku reconfiguration approaches for a 9 × 9 total cross-Tied PV array [28]. Sudoku and enhanced Sudoku patterns are used to modify the physical location of modules in the TCTPV array while maintaining their electrical connections [29]. Intelligent hybrid-based optimization strategies are developed to reduce partial shading losses across the entire array by uniformly dispersing shade [30]. Improved squirrel search algorithm is implemented in [31] and demonstrated improved tracking efficiency and time. Maximum power point tracking with restructured butterfly optimization method for  partial shading patterns, uniform shading, solar intensity, and load variation conditions [32]. Figure 1 depicts three types of PV constructions: PV array, PV string, and irregular sub-array. The proposed work here focuses on PV central array-type and string-type architecture.Figure 1
Architecture for the PV string and PV array.


## 3. Architecture of the PV Panel and Optimization Techniques

### 3.1. Architecture of the PV Panel

Mismatch between shading conditions occurs, resulting in current variation from one panel to the next. Because of the lower output power of the PV panel, it is difficult to harvest the peak power. Different architectural methods are used and analyzed to obtain the peak power (PP), and increase panel conversion and tracking efficiency [33]. In this paper, the central and string architectures are used for this analysis.In the proposed work, four to twenty PV solar panels are connected in series, and the output of the series-connected PV panels is fed into a boost converter. Then, it is connected to a DC load, as shown in Figure2(a). As shown in Figure 2(b), six to twenty (n) PV panels are considered for this analysis in this PV string architecture. It is divided into two strings, with each PV string connected to a DC to DC boost converter that provides peak power point tracking control for each individual string as shown, with the string voltage and string current of each PV panel measured. MPP is done at the string level in string architecture. As a result, tracking efficiency in string architecture is higher than in central architecture under shading conditions. Figure 3 depicts proposed control architectures for both the central and string modules. The proposed converter operates intermittently for both the source and the load. The closed-loop system is controlled by both optimizations. The optimization controller is used to tune the reference output voltage and input voltage based on the execution results of duty cycle values under different irradiation conditions. Figure 4 is executed with four different modules, namely, 8, 10, 14, and 18 PV shaded-unshaded modules, and the proposed system is executed with individual eight-module operating control output under different optimization algorithms.Figure 2
(a) Architecture for central. (b) PV string architecture.
(a)(b)Figure 3
Proposed overall PV module with GWO/FPA.Figure 4
Proposed shaded and unshaded PV. (a) 8 modules, (b) 10 modules, (c) 14 modules, and (d) 18 modules.
(a)(b)(c)(d)


### 3.2. DC-DC Converter Implementation

Most solar PV systems use DC-DC power converters to convert DC electricity from one voltage level to another. These can also be used to boost the efficiency of solar PV systems. In general, PV systems have a lower energy conversion yield, as well as poor stability and irregular characteristics. As a result, the MPPT algorithm is required to ensure that all available solar PV power is utilized. Furthermore, when used in conjunction with an MPPT, the converter achieves load matching and supplies full power. The most significant issue affecting solar PV systems is the variable availability of sun irradiance levels. Several power electronic DC-DC converters are used to overcome this challenge and maintain a constant output voltage.A step-up converter, also known as a boost converter, is a DC-DC power converter with an output voltage greater than the input voltage. It is a type of SMPS that includes at least two semiconductor switches (a diode and a transistor) and at least one energy storage component, such as a capacitor, inductor, or both in combination, as shown in Figure3. In comparison with other converters, this traditional converter is well suited for the proposed central and string PV architectures, as well as having a simple switching strategy [34]. Capacitor filters are frequently connected to the converter’s output to reduce output voltage ripple. Table 1 shows a proposed converter comparison.Table 1
Traditional converter topology comparison.
ParametersBuckBoostBuck-boostOutput voltageVinDVin(1/1-D)Vin(D/1-D)Number of switches111Number of diodes111Number of magnetic components111Input current rippleLargeLargeLargeEfficiencyLowLowMediumCalculation of output power of boost converter = input power of converter - (Ploss_converter) input power of the converter = output power of PV array = 400 W.Hence, output power of boost converter = (400–42.12.) W.Hence, efficiency of the converter estimation = (400–42.12)/400 = 90%.Power losses in a boost converter are due to the following contributors:(1)
Conduction loss of IGBT(2)
Turn on and turn off losses of IGBT(3)
Gate charge or input capacitance loss(4)
Output capacitance loss(5)
Diode loss(6)
Inductor loss


#### 3.2.1. Conduction Loss

(1)PlossRon=IC2×Ron,where IC is the collector current.


#### 3.2.2. Turn On and Turn Off Loss

(2)Plosstrisetfall=12⋅trise+tfall⋅IRMS⋅VCE⋅FSW,where trise is rise time, tfall is fall time, IRMS is RMS current, VCE is collector to emitter voltage, and FSW is switching frequency.


#### 3.2.3. Gate Charge or Input Capacitance Loss

(3)Plossgatecharge=12Qgtotal⋅VGE⋅FSW,where Qg total is total gate charge and VGE is applied gate to emitter voltage.


#### 3.2.4. Output Capacitance Loss

(4)Ploss_Co=12VCE2FSW,where Co is output capacitance of the IGBT.


#### 3.2.5. Diode Loss

(5)Plossdiode=IRMSDIODE×VF,where IRMS DIODE is the RMS current through the diode while VF is the forward voltage of the diode.


#### 3.2.6. Inductor Loss

(6)Plossinductor=IRMS_INDUCTOR2×RDC,(7)efficiency=output poweroutput power+total losses.


#### 3.2.7. Calculation of Boost Converter Losses

IRMS of IGBT = Ic of IGBT = 5 A; Ron = 0.01 Ω; trise(tr) = 68 ns; tfall(tf) = 65 ns; VCE = 230 V; Fsw = 10 kHzQgtotal = 257nc; VGE = 15 V; Co = 260pF; IRMS of diode = 7A; VF = 0.7 V, IRMS of inductor = 7A; RDC = 0.1 ΩPlossRon = 52 ∗ 0.01 = 0.2500 WPloss_trsie_tfall = 0.5 ∗ (68 × 10–9+65 × 10–9) ∗ (5∗230) ∗ (10 × 103) = 0.7647 WPloss_gatecharge = 0.5 ∗ 257 × 10–9 ∗ 15 ∗ (10 × 103) = 0.0193 WPloss_Co = 0.5 ∗ 260 × 10–12 ∗ 2302 ∗ (10 × 103) = 0.0688 WPlossIGBT = PlossRon + Ploss_trsie_tfall + Ploss_gatecharge + Ploss_Coes = 0.25 + 0.7647 + 0.0193 + 0.0688 = 1.1028 WPlossdiode = 7∗0.7 = 4.9 WPlossinductor = 7^2 ∗ 0.1 = 4.9 WPloss_converter = Plossdiode + Ploss IGBT + PlossinductorHence, the converter losses (Ploss_converter) = 4.9 + 1.1028 + 4.9 = 10.9 W


### 3.3. MPP Implementation

MPPT is a photovoltaic (PV) power converter algorithm that constantly adjusts the impedance seen by the solar array to keep the PV device running (or) close to the peak power point of the PV panel under varying conditions such as changing solar irradiance, temperature, and load. The P&O (perturb and observe) and INC (incremental conductance) techniques are considered traditional because they have been around for decades [35]. This study investigates the concept of MPP methods, which significantly improve the efficiency of a solar PV system. In tracking rapidly changing irradiation conditions, the INC algorithm outperforms the P&O approach. In the P&O approach, the voltage never reaches a precise value; rather, it fluctuates around the MPP. As a result, the INC technique produces the MPP faster and more accurately than P&O because it does not drift and is the most efficient in rapidly changing conditions.The incremental conductance method requires only two sensors to compute the PV system’s output voltage and current: voltage and current sensors. A source’s output voltage is normally positive. The goal of this algorithm is to find the voltage operating point at which the conductance equals the INC. The maximum power point is calculated by the INC algorithm by comparing the incremental conductance (I/V) with the array conductance (I/V). When these two are equal (I/V = I/V), the output voltage is equal to the MPP voltage. The controller keeps this voltage until the irradiation increases, at which point the procedure is repeated. The INC algorithm is predicated on the assumption that at full power, P/V = 0 andP = VI. Maximum power is sensed from both types of architecture like PV central type and PV string. The estimated maximum power sends it through converter and as usual gives the reference current to the optimization controller.


## 3.1. Architecture of the PV Panel

Mismatch between shading conditions occurs, resulting in current variation from one panel to the next. Because of the lower output power of the PV panel, it is difficult to harvest the peak power. Different architectural methods are used and analyzed to obtain the peak power (PP), and increase panel conversion and tracking efficiency [33]. In this paper, the central and string architectures are used for this analysis.In the proposed work, four to twenty PV solar panels are connected in series, and the output of the series-connected PV panels is fed into a boost converter. Then, it is connected to a DC load, as shown in Figure2(a). As shown in Figure 2(b), six to twenty (n) PV panels are considered for this analysis in this PV string architecture. It is divided into two strings, with each PV string connected to a DC to DC boost converter that provides peak power point tracking control for each individual string as shown, with the string voltage and string current of each PV panel measured. MPP is done at the string level in string architecture. As a result, tracking efficiency in string architecture is higher than in central architecture under shading conditions. Figure 3 depicts proposed control architectures for both the central and string modules. The proposed converter operates intermittently for both the source and the load. The closed-loop system is controlled by both optimizations. The optimization controller is used to tune the reference output voltage and input voltage based on the execution results of duty cycle values under different irradiation conditions. Figure 4 is executed with four different modules, namely, 8, 10, 14, and 18 PV shaded-unshaded modules, and the proposed system is executed with individual eight-module operating control output under different optimization algorithms.Figure 2
(a) Architecture for central. (b) PV string architecture.
(a)(b)Figure 3
Proposed overall PV module with GWO/FPA.Figure 4
Proposed shaded and unshaded PV. (a) 8 modules, (b) 10 modules, (c) 14 modules, and (d) 18 modules.
(a)(b)(c)(d)


## 3.2. DC-DC Converter Implementation

Most solar PV systems use DC-DC power converters to convert DC electricity from one voltage level to another. These can also be used to boost the efficiency of solar PV systems. In general, PV systems have a lower energy conversion yield, as well as poor stability and irregular characteristics. As a result, the MPPT algorithm is required to ensure that all available solar PV power is utilized. Furthermore, when used in conjunction with an MPPT, the converter achieves load matching and supplies full power. The most significant issue affecting solar PV systems is the variable availability of sun irradiance levels. Several power electronic DC-DC converters are used to overcome this challenge and maintain a constant output voltage.A step-up converter, also known as a boost converter, is a DC-DC power converter with an output voltage greater than the input voltage. It is a type of SMPS that includes at least two semiconductor switches (a diode and a transistor) and at least one energy storage component, such as a capacitor, inductor, or both in combination, as shown in Figure3. In comparison with other converters, this traditional converter is well suited for the proposed central and string PV architectures, as well as having a simple switching strategy [34]. Capacitor filters are frequently connected to the converter’s output to reduce output voltage ripple. Table 1 shows a proposed converter comparison.Table 1
Traditional converter topology comparison.
ParametersBuckBoostBuck-boostOutput voltageVinDVin(1/1-D)Vin(D/1-D)Number of switches111Number of diodes111Number of magnetic components111Input current rippleLargeLargeLargeEfficiencyLowLowMediumCalculation of output power of boost converter = input power of converter - (Ploss_converter) input power of the converter = output power of PV array = 400 W.Hence, output power of boost converter = (400–42.12.) W.Hence, efficiency of the converter estimation = (400–42.12)/400 = 90%.Power losses in a boost converter are due to the following contributors:(1)
Conduction loss of IGBT(2)
Turn on and turn off losses of IGBT(3)
Gate charge or input capacitance loss(4)
Output capacitance loss(5)
Diode loss(6)
Inductor loss


### 3.2.1. Conduction Loss

(1)PlossRon=IC2×Ron,where IC is the collector current.


### 3.2.2. Turn On and Turn Off Loss

(2)Plosstrisetfall=12⋅trise+tfall⋅IRMS⋅VCE⋅FSW,where trise is rise time, tfall is fall time, IRMS is RMS current, VCE is collector to emitter voltage, and FSW is switching frequency.


### 3.2.3. Gate Charge or Input Capacitance Loss

(3)Plossgatecharge=12Qgtotal⋅VGE⋅FSW,where Qg total is total gate charge and VGE is applied gate to emitter voltage.


### 3.2.4. Output Capacitance Loss

(4)Ploss_Co=12VCE2FSW,where Co is output capacitance of the IGBT.


### 3.2.5. Diode Loss

(5)Plossdiode=IRMSDIODE×VF,where IRMS DIODE is the RMS current through the diode while VF is the forward voltage of the diode.


### 3.2.6. Inductor Loss

(6)Plossinductor=IRMS_INDUCTOR2×RDC,(7)efficiency=output poweroutput power+total losses.


### 3.2.7. Calculation of Boost Converter Losses

IRMS of IGBT = Ic of IGBT = 5 A; Ron = 0.01 Ω; trise(tr) = 68 ns; tfall(tf) = 65 ns; VCE = 230 V; Fsw = 10 kHzQgtotal = 257nc; VGE = 15 V; Co = 260pF; IRMS of diode = 7A; VF = 0.7 V, IRMS of inductor = 7A; RDC = 0.1 ΩPlossRon = 52 ∗ 0.01 = 0.2500 WPloss_trsie_tfall = 0.5 ∗ (68 × 10–9+65 × 10–9) ∗ (5∗230) ∗ (10 × 103) = 0.7647 WPloss_gatecharge = 0.5 ∗ 257 × 10–9 ∗ 15 ∗ (10 × 103) = 0.0193 WPloss_Co = 0.5 ∗ 260 × 10–12 ∗ 2302 ∗ (10 × 103) = 0.0688 WPlossIGBT = PlossRon + Ploss_trsie_tfall + Ploss_gatecharge + Ploss_Coes = 0.25 + 0.7647 + 0.0193 + 0.0688 = 1.1028 WPlossdiode = 7∗0.7 = 4.9 WPlossinductor = 7^2 ∗ 0.1 = 4.9 WPloss_converter = Plossdiode + Ploss IGBT + PlossinductorHence, the converter losses (Ploss_converter) = 4.9 + 1.1028 + 4.9 = 10.9 W


## 3.2.1. Conduction Loss

(1)PlossRon=IC2×Ron,where IC is the collector current.


## 3.2.2. Turn On and Turn Off Loss

(2)Plosstrisetfall=12⋅trise+tfall⋅IRMS⋅VCE⋅FSW,where trise is rise time, tfall is fall time, IRMS is RMS current, VCE is collector to emitter voltage, and FSW is switching frequency.


## 3.2.3. Gate Charge or Input Capacitance Loss

(3)Plossgatecharge=12Qgtotal⋅VGE⋅FSW,where Qg total is total gate charge and VGE is applied gate to emitter voltage.


## 3.2.4. Output Capacitance Loss

(4)Ploss_Co=12VCE2FSW,where Co is output capacitance of the IGBT.


## 3.2.5. Diode Loss

(5)Plossdiode=IRMSDIODE×VF,where IRMS DIODE is the RMS current through the diode while VF is the forward voltage of the diode.


## 3.2.6. Inductor Loss

(6)Plossinductor=IRMS_INDUCTOR2×RDC,(7)efficiency=output poweroutput power+total losses.


## 3.2.7. Calculation of Boost Converter Losses

IRMS of IGBT = Ic of IGBT = 5 A; Ron = 0.01 Ω; trise(tr) = 68 ns; tfall(tf) = 65 ns; VCE = 230 V; Fsw = 10 kHzQgtotal = 257nc; VGE = 15 V; Co = 260pF; IRMS of diode = 7A; VF = 0.7 V, IRMS of inductor = 7A; RDC = 0.1 ΩPlossRon = 52 ∗ 0.01 = 0.2500 WPloss_trsie_tfall = 0.5 ∗ (68 × 10–9+65 × 10–9) ∗ (5∗230) ∗ (10 × 103) = 0.7647 WPloss_gatecharge = 0.5 ∗ 257 × 10–9 ∗ 15 ∗ (10 × 103) = 0.0193 WPloss_Co = 0.5 ∗ 260 × 10–12 ∗ 2302 ∗ (10 × 103) = 0.0688 WPlossIGBT = PlossRon + Ploss_trsie_tfall + Ploss_gatecharge + Ploss_Coes = 0.25 + 0.7647 + 0.0193 + 0.0688 = 1.1028 WPlossdiode = 7∗0.7 = 4.9 WPlossinductor = 7^2 ∗ 0.1 = 4.9 WPloss_converter = Plossdiode + Ploss IGBT + PlossinductorHence, the converter losses (Ploss_converter) = 4.9 + 1.1028 + 4.9 = 10.9 W


## 3.3. MPP Implementation

MPPT is a photovoltaic (PV) power converter algorithm that constantly adjusts the impedance seen by the solar array to keep the PV device running (or) close to the peak power point of the PV panel under varying conditions such as changing solar irradiance, temperature, and load. The P&O (perturb and observe) and INC (incremental conductance) techniques are considered traditional because they have been around for decades [35]. This study investigates the concept of MPP methods, which significantly improve the efficiency of a solar PV system. In tracking rapidly changing irradiation conditions, the INC algorithm outperforms the P&O approach. In the P&O approach, the voltage never reaches a precise value; rather, it fluctuates around the MPP. As a result, the INC technique produces the MPP faster and more accurately than P&O because it does not drift and is the most efficient in rapidly changing conditions.The incremental conductance method requires only two sensors to compute the PV system’s output voltage and current: voltage and current sensors. A source’s output voltage is normally positive. The goal of this algorithm is to find the voltage operating point at which the conductance equals the INC. The maximum power point is calculated by the INC algorithm by comparing the incremental conductance (I/V) with the array conductance (I/V). When these two are equal (I/V = I/V), the output voltage is equal to the MPP voltage. The controller keeps this voltage until the irradiation increases, at which point the procedure is repeated. The INC algorithm is predicated on the assumption that at full power, P/V = 0 andP = VI. Maximum power is sensed from both types of architecture like PV central type and PV string. The estimated maximum power sends it through converter and as usual gives the reference current to the optimization controller.


## 4. Optimization Approach

The generation of peak power under PSC is a significant challenge for PV arrays/strings [36]. In this proposed work, the optimization algorithms FPA and GWO are chosen to obtain the best duty value for a DC-DC boost converter in order to obtain MP from a PV array under PSC.


### 4.1. Gray Wolf Optimization (GWO) Algorithm

The GWO algorithm is used to optimize the positions of a group of wolves or particles (N) moving toward a prey or goal. Gray wolves are divided into three distinct leadership groups: alpha (α), beta (β), and delta (δ). The alpha, as the leader, decides on prey hunts, sleeping locations, and waking times. These are the rules that the beta must abide by. If the alpha wolf dies or matures, the beta wolf assumes leadership. Steps involved in the hunting process are as follows:(a)
Finding the prey(b)
Following the prey(c)
Encountering the preyIn order to update the wolves’ position, below equations are used:(8)d⟶α=C⟶∗X⟶α−X⟶,d⟶β=C⟶∗X⟶β−X⟶,d⟶δ=C⟶∗X⟶δ−X⟶,(9)X⟶1=X⟶α−A∗d⟶α,X⟶2=X⟶β−A⟶∗d⟶β,X⟶3=X⟶δ−A⟶∗d⟶δ.A⟶ and C⟶ values are estimated as follows:(10)A⟶=2a⟶.r⟶1−a⟶,(11)C⟶=2r⟶2.a⟶ varies from 2 to 0, and random vectors are r1 and r2.(12)X⟶n+1=X⟶1+X⟶2+X⟶33.Here,X (n + 1) is the global best duty value.


### 4.2. Flower Pollination Algorithm

The main objective of a flower is reproduction via pollination, in which the pollen transfer takes place between flowers by pollinators like insects, birds, bats, and other animals. Flower pollination algorithm is applied to select best pollen gamete from a group of pollen gamete (N) carried by pollinators to perform pollination, which is the main objective.The global pollination is given by(13)Xi,n+1=Xi,n+LXi,n−G,where Xi,n is the pollen i at iteration n, G is the current best solution among all solutions at the current iteration, and L is the strength of the pollination; its value is expressed as(14)L≈λΓλsinπλ/2/π∗1/S1+λ.Standard gamma function is Γ (λ), and λ = 1.5 is used.The local pollination can be given as(15)xi,n+1=xi,n+εxp,n−xq,n,where xp,n and xq,n are randomly chosen pollen of the same type of plant from different flowers and ε is [0, 1].Flower pollination algorithm is included to get the best duty (D) of a group of flowers (N) moving toward a desired duty called best duty (G), which is decided based on fitness variable which is maximum power of PV panel. The simulation of FPA is performed by developing the MATLAB code which calls Simulink PV model as a function in an iteration. The iteration involves passing the duty from code to the Simulink PV model and getting the power from the model to code. The best duty at the end of kth iteration is the best duty (D) optimized in this search process.


### 4.3. Algorithm Steps of Flower Pollination Algorithm

Steps of flower pollination algorithm are shown as follows:Step 1: choose N flowers for duty andk iterations for optimization process.Step 2: allow maximum powerPmax to be fitness variable. Select the initial Pmax.Step 3: choose initial best duty. The best duty of the flower is the objective determined by the fitness variable as shown in Figure5.Step 4: select upper limit and lower limit for duty.Step 5: generate duty for each flower.Step 6: choose a switch probability factor to switch between local and global pollination.Step 7: run the simulation with nth duty of ith flower and get powerPi, n.Step 8: check whetherPi,n is greater than Pmax.Step 9: if yes, then set the value asPi, n as Pmax and corresponding duty as Pbest.Step 10: if no, then generate a random number, and if it is greater than switch probability factor, then choose global pollination; otherwise choose local pollination.Step 11: update the duty of ith flower by either global or local pollination equation.Step 12: repeat the above six steps for all flowers one by one to complete the iteration.Step 13: increase the iteration count and repeat the above procedure fork iterations.Step 14: the Pbest for duty and corresponding Pmax are updated in all the iterations.Step 15: the value of Pbest at the end of k iterations is the optimized duty for maximum power.Figure 5
Flowchart of FPA optimization.


### 4.4. GWO Algorithm Steps

The following steps are used to track the best PWM duty to extract the maximum power from PV system under PSC (refer Table2):Step 1: choose an initial group of wolves (N) and the number of iterations (k).Step 2: allow maximum power (Pmax) to be an objective or fitness variable.Step 3: the variable to achieve the goal is the wolves’ PWM duty.Step 4: set the upper and lower limits for PWM duty.Step 5: PWM duty should be generated for each wolf.Step 6: create an initial fitness power for each wolf, sort them in descending order, and assign the first three highest values as alpha, beta, and delta. Set the power that corresponds to alpha toPmax and the duty to Gbest.Step 6a: begin the nth iteration by running simulation with each wolf’s PWM duty and obtaining power,Pn,i for the nth iteration for all the wolf.Step 7: sort the powerPn in descending order and I in ascending order.Step 8: using the first three highest power levels, update the alpha, beta, and delta.Step 9: if the power corresponding to alpha is greater thanPmax, then at the nth iteration, set this power as Pmax and the corresponding duty as Gbest.Step 10: calculate the difference between the current PWM duty cycle and the corresponding alpha, beta, and delta duty cycles for the next iteration and take the average of this difference. As shown in Figure6, this average value is used to determine the PWM duty for the next iteration.Step 11: repeat the previous iteration with a different PWM duty.Step 12: the PWM duty (Gbest) is updated during iterations.Step 13: after “k” iterations, iterations are terminated. The desired duty for MPP is the value of Gbest at the end of “k” iterations.Table 2
Parameter settings of proposed GWO/FPA.
Standard parameters of optimization algorithmsParameterGWO valueFPA valueMaximum iteration number50100Population size1050Number of decision variables5—Stopping criteria100 iterations200 iterationsSwitching probability—0.8Figure 6
Flowchart of GWO algorithm.The flowchart of the GWO algorithm is shown in Figure6.


## 4.1. Gray Wolf Optimization (GWO) Algorithm

The GWO algorithm is used to optimize the positions of a group of wolves or particles (N) moving toward a prey or goal. Gray wolves are divided into three distinct leadership groups: alpha (α), beta (β), and delta (δ). The alpha, as the leader, decides on prey hunts, sleeping locations, and waking times. These are the rules that the beta must abide by. If the alpha wolf dies or matures, the beta wolf assumes leadership. Steps involved in the hunting process are as follows:(a)
Finding the prey(b)
Following the prey(c)
Encountering the preyIn order to update the wolves’ position, below equations are used:(8)d⟶α=C⟶∗X⟶α−X⟶,d⟶β=C⟶∗X⟶β−X⟶,d⟶δ=C⟶∗X⟶δ−X⟶,(9)X⟶1=X⟶α−A∗d⟶α,X⟶2=X⟶β−A⟶∗d⟶β,X⟶3=X⟶δ−A⟶∗d⟶δ.A⟶ and C⟶ values are estimated as follows:(10)A⟶=2a⟶.r⟶1−a⟶,(11)C⟶=2r⟶2.a⟶ varies from 2 to 0, and random vectors are r1 and r2.(12)X⟶n+1=X⟶1+X⟶2+X⟶33.Here,X (n + 1) is the global best duty value.


## 4.2. Flower Pollination Algorithm

The main objective of a flower is reproduction via pollination, in which the pollen transfer takes place between flowers by pollinators like insects, birds, bats, and other animals. Flower pollination algorithm is applied to select best pollen gamete from a group of pollen gamete (N) carried by pollinators to perform pollination, which is the main objective.The global pollination is given by(13)Xi,n+1=Xi,n+LXi,n−G,where Xi,n is the pollen i at iteration n, G is the current best solution among all solutions at the current iteration, and L is the strength of the pollination; its value is expressed as(14)L≈λΓλsinπλ/2/π∗1/S1+λ.Standard gamma function is Γ (λ), and λ = 1.5 is used.The local pollination can be given as(15)xi,n+1=xi,n+εxp,n−xq,n,where xp,n and xq,n are randomly chosen pollen of the same type of plant from different flowers and ε is [0, 1].Flower pollination algorithm is included to get the best duty (D) of a group of flowers (N) moving toward a desired duty called best duty (G), which is decided based on fitness variable which is maximum power of PV panel. The simulation of FPA is performed by developing the MATLAB code which calls Simulink PV model as a function in an iteration. The iteration involves passing the duty from code to the Simulink PV model and getting the power from the model to code. The best duty at the end of kth iteration is the best duty (D) optimized in this search process.


## 4.3. Algorithm Steps of Flower Pollination Algorithm

Steps of flower pollination algorithm are shown as follows:Step 1: choose N flowers for duty andk iterations for optimization process.Step 2: allow maximum powerPmax to be fitness variable. Select the initial Pmax.Step 3: choose initial best duty. The best duty of the flower is the objective determined by the fitness variable as shown in Figure5.Step 4: select upper limit and lower limit for duty.Step 5: generate duty for each flower.Step 6: choose a switch probability factor to switch between local and global pollination.Step 7: run the simulation with nth duty of ith flower and get powerPi, n.Step 8: check whetherPi,n is greater than Pmax.Step 9: if yes, then set the value asPi, n as Pmax and corresponding duty as Pbest.Step 10: if no, then generate a random number, and if it is greater than switch probability factor, then choose global pollination; otherwise choose local pollination.Step 11: update the duty of ith flower by either global or local pollination equation.Step 12: repeat the above six steps for all flowers one by one to complete the iteration.Step 13: increase the iteration count and repeat the above procedure fork iterations.Step 14: the Pbest for duty and corresponding Pmax are updated in all the iterations.Step 15: the value of Pbest at the end of k iterations is the optimized duty for maximum power.Figure 5
Flowchart of FPA optimization.


## 4.4. GWO Algorithm Steps

The following steps are used to track the best PWM duty to extract the maximum power from PV system under PSC (refer Table2):Step 1: choose an initial group of wolves (N) and the number of iterations (k).Step 2: allow maximum power (Pmax) to be an objective or fitness variable.Step 3: the variable to achieve the goal is the wolves’ PWM duty.Step 4: set the upper and lower limits for PWM duty.Step 5: PWM duty should be generated for each wolf.Step 6: create an initial fitness power for each wolf, sort them in descending order, and assign the first three highest values as alpha, beta, and delta. Set the power that corresponds to alpha toPmax and the duty to Gbest.Step 6a: begin the nth iteration by running simulation with each wolf’s PWM duty and obtaining power,Pn,i for the nth iteration for all the wolf.Step 7: sort the powerPn in descending order and I in ascending order.Step 8: using the first three highest power levels, update the alpha, beta, and delta.Step 9: if the power corresponding to alpha is greater thanPmax, then at the nth iteration, set this power as Pmax and the corresponding duty as Gbest.Step 10: calculate the difference between the current PWM duty cycle and the corresponding alpha, beta, and delta duty cycles for the next iteration and take the average of this difference. As shown in Figure6, this average value is used to determine the PWM duty for the next iteration.Step 11: repeat the previous iteration with a different PWM duty.Step 12: the PWM duty (Gbest) is updated during iterations.Step 13: after “k” iterations, iterations are terminated. The desired duty for MPP is the value of Gbest at the end of “k” iterations.Table 2
Parameter settings of proposed GWO/FPA.
Standard parameters of optimization algorithmsParameterGWO valueFPA valueMaximum iteration number50100Population size1050Number of decision variables5—Stopping criteria100 iterations200 iterationsSwitching probability—0.8Figure 6
Flowchart of GWO algorithm.The flowchart of the GWO algorithm is shown in Figure6.


## 5. Simulation Results and Discussion

In this section using simulation performance of PV central, string architecture is estimated. Analyzed FPA and GWO algorithms using MATLAB files were created for proposed algorithms. Proposed GWO/FPA has generated the respective model to identify the overall duty cycle of the converter in order to get the peak power under PSC conditions. The solar panel parameters are presented in Table3. P-V characteristics are presented in Figure 7, and the outcome specifications of GWO/FPA are shown in Tables 4 and 5. It shows the optimization procedures for algorithm measurements. The load resistance values are 3.75 ohm and 4.5 ohm, respectively. Figure 8 shows a Simulink model of central architecture.Table 3
Specification of the PV panel.
DescriptionValuesPV power rating (W)400 WPeak power (Pmax)240 WOpen-circuit voltage (Voc)20 VVoltage at maximum power (Vmp)15 VShort-circuit current (Isc)20 ACurrent at maximum power (Imp)16 AIrradiance (W/m2)1500 W/m2Number of cells (n) per modules24Figure 7
PV array P-V characteristics under PSC.Table 4
Simulation output measurements of central architecture PV.
Fig. no.Pmax (W)AlgorithmVPV (V)IPV (A)PPV (W)V0 (V)Output current (A)Output power (W)Efficiency (conversion) (%)Efficiency (tracking) (%)Figures9 and 10960FPA and GWO (uniform)58.8716.64946.657.9915.4692197.2998.60Figures11 and 12827.3FPA and GWO (nonuniform)56.9314.03798.658.5313.01778.497.4396.53Table 5
Simulation output measurements of string architecture PV.
Fig. no.Pmax (W)AlgorithmVPV (V)IPV (A)PPV (W)V0 (V)IO (A)PO (W)Conversion efficiency (%)Tracking efficiency (%)Figure13829.3GWO (shading condition)30.8826.86829.332.9821.99749.690.42100Figure14960GWO (uniform irradiation)29.632.4958.934.5123.01871.190.8499.88Figure15960FPA (uniform architecture)33.6625.05843.133.9122.61792.694.0287.82Figure16829.3FPA (shading condition)32.8424.4801.433.0422.03752.693.9196.6Figure 8
Simulink model of central architecture with uniform irradiance of 20 PV module.Figure9 shows that GWO simulation output for uniform irradiances that the power is extracted from the PV array, while there is no shade output power which is 960 W. When there is shaded part, the power collected is only 827.3 W. It consists of four PV panels connected in series, and converter duty cycle is 0.09. The converter output is connected to a DC load. The fixed STC temperature in all four PV panels is 25°C and remains constant. Each PV panel has varied different irradiations 1000 W/m2 to 800 W/m2.Figure 9
GWO simulation output for uniform irradiance conditions.From the simulation, it is concluded that the power extracted from the PV array is 946.6 W, the convergence time is more in FPA, and at the same time it does not reach the steady-state value. The best duty value obtained from the flower pollination algorithm is 0.09. The simulation results of PV array under shading condition are presented in Figure10. From Figures 11 and 12, it is noticed that power reaches a steady-state value at time t = 0.155 sec in GWO algorithm. FPA does not reach a steady-state value, but it extracts a power from the PV array. Using an optimization algorithm power extracted from the PV array is 796.6 W, and the power obtained from the PV array from the P-V characteristics is 827.3 W. Figure 13 shows GWO simulation under shading condition using PV string architecture. Duty cycle of the converter is 0.09, and the maximum output power is 892.3 W.Figure 10
FPA simulation output for uniform irradiance conditions.Figure 11
FPA simulation output for central architecture under shading condition.Figure 12
GWO simulation output for central architecture under shading condition.Figure 13
GWO simulation under shading condition using PV string architecture.From the results, it is noticed that power reaches a steady-state value at timet = 0.155sec in GWO algorithm. FPA does not reach a steady-state value, but it harvested a maximum power from the PV array. Using GWO algorithm, maximum power extracted across the load is 796.6 W and the power obtained from the PV array from the P-V characteristics is 827.3 W. In PV string architectures, each string consists of two PV panels and the irradiance value is 1000 W/m2 and 800 W/m2.Total numbers of strings are two, and it is connected in parallel. Using string architecture, uniform and shading conditions are simulated and the simulation outputs are given in Figure14. It is noticed that at t = 0.18 sec output power reaches a final value and the peak power is 829.3 W presented in Figure 14. The power obtained from PV panel is 959 W under uniform irradiance condition, and it reaches steady-state value at t = 0.23 sec. The maximum power obtained from the load is 843.1 W, and the power is not reaching the steady-state value as shown in Figure 15. Figure 16 shows that PV array under partial shading condition of FPA. Table 6 shows that the PV panel power obtained is extraordinarily compared to other methods. Comparison of FPA to reach the steady-state value is better performance to other optimization. Table 7 shows different PV structures with uniform and un-uniform shading conditions. Figure 17 indicates the simulated power and duty with respect to time using GWO and P&O methods.Figure 14
String architecture using GWO under uniform conditions.Figure 15
PV string architecture using FPA under uniform condition.Figure 16
PV string architecture using FPA under shading condition.Table 6
Output measurements using PV string converter under uniform and shading conditions.
Pmax (W)AlgorithmArchitectureVPV (V)IPV (A)PPV (W)V0 (V)IO (A)PO (W)Conversion efficiency (%)Tracking efficiency (%)Irradiance960GWOString29.632.4958.934.5123.01871.190.8499.88UniformFPA33.6625.05843.133.9122.61792.694.0287.82829.3GWO30.8826.86829.332.9821.99749.690.42100PSCFPA32.8424.4801.433.0422.03752.693.9196.6Table 7
Measurements from central and string converter under uniform and shading condition with GWO and FPA.
Pmax (W)AlgorithmArchitectureTracking efficiency (%)Irradiance960GWOPV central98.60UniformFPA827.3GWO96.53PSCFPA960GWOPV string99.88UniformFPA87.82829.3GWO100PSCFPA96.6Figure 17
The GWO and P&O power and duty with respect to time [10].Table8 presents the simulation results obtained from central and string architecture using various optimization techniques with irradiance value 1000 W/m2, 800 W/m2, 600 W/m2, and 400 W/m2. From these results, it clearly found that proposed GWO has proficient performance over the other methods.Table 8
Measurements from central and string architecture under partial shading condition with GWO, FPA, RDPSO, and PSO.
Algorithms and architectureVPV(V)VO (V)IPV (A)IO (A)PPV (W)PO (W)Converter efficiency (%)Tracking efficiency (%)PSOCentral55.263.847.9716.38444040893.0395.71String37.3338.448.7867.688326.1295.597.7381.72RDPSOCentral54.1363.498.0556.349436.0403.592.7795.71String37.0838.019.6528.446355.732197.7382.37FPACentral59.1563.7213.8111.59816.8739.690.5485.08String37.0838.009.5528.346350.732091.2480.9GWOCentral63.5665.937.3176.593465.1435.193.5498.72String37.3338.58.7877.699326.1296.497.7382.47


## 6. Conclusion

The performance of central and string architecture of PV panel under nonshading and partial shading conditions is examined in this research. Optimization techniques such as FPA and GWO are used to examine the PV array conversion and tracking efficiency. The proposed algorithms are incorporated with MPP approach. Literature review is presented for two different PV architectures, based on the analysis which is more suitable for maximum power extraction from source to load. The performance analysis of two different optimization algorithms is validated with simulation results. From the observations, the GWO algorithm for the string architecture achieves faster convergence and tracks the maximum power from PV panel than the GWO and FPA for central architecture.



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*Source: 5803771-2022-08-05.xml*