An improved intelligent technique for maximum power point tracking under partial shading conditions of photo voltaic system

Abstract

A novel technique is presented for Maximum Power Point Tracking (MPPT) based photovoltaic (PV) system in partial shadow conditions for harvesting maximum power. In this paper, a hybrid technique is developed, which combines Black Widow Optimization (BWO) with Recurrent Neural Network (RNN). To train the data set and provide a control signal for the converter, an RNN is used. After fitting the training data sets, the suggested method achieved maximum power by utilizing BWO based on the control parameters. This proposed method minimizes the difference between actual and average power. Using an optimization technique, the main goal of this proposed strategy is to obtain peak power harvest under various conditions, including partial shading, while minimizing error function, With the help of MATLAB/Simulink software, the conclusions are revealed under various partial shading conditions. For each category, the observed results are evaluated at various time intervals. The proposed method is also compared to other techniques such as the Ant Colony Optimization (ACO)-RNN system, Particle Swarm Optimization (PSO)-RNN system, and Gravitational Search Algorithm (GSA)-RNN system. The proposed system is 36.11% faster than GSA with RNN, 39.47% faster than PSO, and 42.5% faster than ACO with RNN in terms of tracking speed. Significantly, the proposed work is 0.87% more efficient than the other models in terms of obtaining maximum power. In terms of obtaining maximum power, the proposed work BWOA-RNN is more effective than other methods.

Keywords

Partial shading maximum power point tracking (MPPT)photovoltaic (PV)black widow optimization (BWO)recurrent neural network (RNN)gravitational search algorithm (GSA)ant colony optimization (ACO)and particle swarm optimization (PSO)

1 Introduction

1.1 Background

The most major factors for developing renewable energy resources worldwide are rapidly expanding energy demands, diminishing non-renewable supplies, and substantial engagement in the environmental implications of conventional energy sources [1 –3]. Also, it is crucial to discover a track to increase the renewable resources extensively to attain zero-scale fossil-fuel based energy production in future [4 –8]. The solar photovoltaic (PV) system is the most significant one, and the use of PV is increased because of its eco-friendly nature, immense power resources, and unpolluted operation. Due to power electronic converters and the low price of set –up, PV systems have become more popular in recent years [9]. Specifically, the transmission of energy from photoelectric cell arrays covers significant attention due to PV generator exposing a V-I characteristic for the nonlinear region, and its high potential power varies because of its temperature and solar insolation. At a particular stage of solar isolation, the PV generator provides maximum power at its unique operating point. To achieve high utilization of PV system, it is essential to connect the PV generator with the load so that the high potential power point of PV system has coexisted with equilibrium operating point [10, 11].

Generally, the overall efficiency of PV systems is between 11–28% [12]. For attaining, high efficiency, it is essential to keep the PV system running at its maximum power point level. Maximum power point tracking (MPPT) is used in conjunction with a DC-DC boost converter [13, 14]. MPPT stands for maximum potential power extraction from a PV system. There are various kinds of MPPT techniques available, but some of them are mostly used because of their significant performance, such as Perturb, Observe (P&O) and Hill climbing (HC) & Incremental Conductance [15]. Moreover, these techniques are easy to implement but cannot work under the condition of partial shading because these techniques are failed to provide a clear difference between the local peak and the global peak of P-V curves. But partial shading condition permits solar irradiation to easily influence the partially shaded part, which leads to the shading heaviness of PV cell array [16, 17].

Greatest power point tracking, essentially tries to collect a maximum power attainable from the PV array, is one technique that has been commonly used for this purpose. Changes in irradiance or temperature have a direct impact on the supply of electricity to the grid in grid-connected PV systems, causing oscillations throughout the maximum power available and forcing a MPPT algorithm to shift a system back to its MPPT PV systems have a single operation point, current and voltage— a point that allows the most power to be extracted at any temperature and irradiance level [18]. PV modules with power converters can harvest as much electricity as possible. [18 –20]. MPPT techniques have been proposed multiple times in recent years. Others can obtain the MPP without knowing the technical specifications of the PV panel [20, 21]. The constant voltage method [22, 23], constant current method [8], curve fitting on the module using irradiance & temperature data [10], look-up table, which maps MPP points for different situations [24 –26], artificial intelligence with a neuron training period [27], and current scan [24, 26] are some of the methods that use technical data as from panel. The perturbation and observation technique (P&O), on the other hand, specifies increases or reductions in PV panel voltage depending on measured power. [24 , 27–30] and incremental inductance [26 , 31–33], and which does not need any knowledge of the panel’s technical features.

However, due to this partial shading condition, the output power of PV cell arrays is extremely reduced and leads to decreased efficiency, increasing configuration complexity, and increasing the system’s cost. But in the case of uniform irradiance, the PV array characteristics curve produces high potential power and may be sensed by any of the MPPT methods [34, 35]. However, the PV system does not receive uniform irradiation for the whole day. At the time of non-uniform irradiation, under partial shading conditions, the MPPT methods failed to control multiple maxima of the system because of the existence of a diode [36 –38]. Other straightforward methodologies include fragmentary short-out current, partial open-circuit voltage, swell connection control, sliding control, and numerical, graphical technique. MPPT techniques based on delicate registering systems (short circuit) such as Genetic Algorithm (GA), Artificial Neural Network (ANN) strategy, Particle Swarm Optimization (PSO) calculation, Artificial Bee Colony (ABC) calculation, and Ant Colony Optimization (ACO) strategy are expected to alleviate a few issues that exist in conventional strategies [16 , 34–51]. To overcome this issue, an optimized MPPT method is employed widely. PV energy is environmentally friendly, has a simple design that requires little maintenance, and its key benefit is that it can be installed as a stand-alone system with outputs ranging from microwatts to megawatts. They’re used in power plants, water pumps, distant buildings, residential solar systems, communication systems, satellite and spacecraft, reverse osmosis facility, and even megawatt-scale power plants as a consequence. The demand for photovoltaics is growing every year due to its wide range of applications.

The foremost contribution of the proposed methodology is given as follow:

In this work, the intelligent technique with a maximum power point tracking-based PV system is used under partial shading conditions to track the system’s maximum power.

The hybrid optimization technique, namely BWO-RNN, is included in the proposed work to harvest the maximum energy and analyze the efficiency of the photovoltaic cell.

The proposed strategy is validated with the existing techniques to display the superiority of the proposed research. While comparing with the current approach, the proposed approach oscillation is significantly less, and it gives effective performance because it has better tracking speed.

1.2 Existing works relating to MPPT

Various approaches for tracking maximum power from PV differ by their characteristics, techniques used, and structure. This section describes the literature survey for tracking the maximum power under different partial shading conditions. Shyni P Naira et al. [23] presented an MDA-RNN technique, a hybrid approach of MPPT with RNN, and a Modified Dragonfly Algorithm for extracting extreme power from the high penetrating hybrid renewable energy system. It was used to harvest maximum capacity from a hybrid renewable energy system and trace its duty cycle. In addition, levy flight and PSO algorithms were utilized to enhance the producing power of renewable energy sources and reduce the losses in the generator. However, this new approach failed to describe complex topology.

Hassan M.H. Farh, et al. [24] suggested an approach of conventional PSO for tracking maximum global peak (GMP) under the condition of partial shading of PV system but failed to track the dynamic GMP. A hybrid technique of MPPT and PSO was presented for tracking the dynamic GMP under the condition of time-invariant partial shading. Additionally, a deep recurrent neural network was utilized to observe dynamic GMP under the condition of time-variant partial shading. Jira Gosumbonggot et al. [25] discussed, the maximum power of the PV system’s power-voltage curve features were described using a global maximum power point approach that used the shade detection condition and slope trend. The authors also demonstrated this method for power electronics switching devices including DC-DC synchronous converters and interleaved boost converters.

Moreover, J. C. Teo et al. [26] evaluated photovoltaic string which was formed by series-connected photovoltaic elements, to examine the effect on the critical point and partial shading. Here, the author utilized various shading heaviness and shaded elements to examine the P-V characteristics curve. When the darkened element irradiance reached a critical point, the photovoltaic strings were unexpected to shading heaviness. Based on the shadowy element’s number, the crucial point has differed. In this presented work, the critical point for various sizes of photovoltaic string and shaded elements’ numbers in the photovoltaic string were determined by utilizing the equations which were formulated in this work.

Kemal Aygül et al. [27] implemented the BOA on the maximum power point tracking (MPPT) of the PV model, which comes under the partial shading condition to enhance tracking speed. On the PV panel, the proposed BOA was used to simulate 3 different types using a PV model. Additionally, the author utilized particle swarm optimization (PSO), Gravitational search algorithm (GSA), and grey wolf optimization (GWO) to rectify the problems which make the MPPT a difficult process. The final experimental results showed that the presented algorithm was performed efficiently by attaining a high level of accuracy and offered the best tracking speed compared with other algorithms implemented in existing research works.

Furthermore, Xiaoshan Zhang et al. [28] established the Memetic Reinforcement Learning (MRI) with Partial Shading Condition (PSC) for PV system, which was dependent on the MPPT and utilized to produce the solar power. Reinforcement Learning (RL) integrated the memetic computing structure to recover the MRL searching ability. Here the global information is exchanged among various agents with the help of the virtual population. The optimum quality was enhanced by utilizing local search for each memeplex. Also, Majad Mansoor et al. [29] presented a hybrid technique of MPPT controller with the optimization algorithm of Harris Hawk to extract the high potential power of the PV system under all the environment circumference conditions. Then the presented approach was compared with some techniques such as dragonfly optimization algorithm (DFOA), cuckoo search (CS), perturb and observe algorithm (P&O), and grey wolf optimization (GWO) based on the criteria of PS, complex-PS (CPS) and fast varying irradiance.

Additionally, Priyadharshi et al. [30] presented the PSO with ANFIS technique based on MPPT under fluctuating irradiance conditions. Here, the author analyzed PV enhancement, maximum power point tracking, zero ripple output with MPPT function, and zero steady-state error.Pervez et al. [31] demonstrated a Maximum power point tracking based on Gravitational Search Algorithm (GSA) in solar PV. The authors explained the maximum power point tracking under partial shading conditions to extract the maximum power from PV. The author described the metaheuristic algorithm with the conventional perturb and observe method. Babes et al. [32] investigated a nature-inspired MPPT controller for photovoltaics based on Ant Colony Optimization (ACO) and an ANN algorithm. It was designed to address the shortcomings of the existing MPPT method when solar irradiation varies.

The research gaps based on the existing methods towards the development of maximum power tracking under partial shading conditions of photovoltaic system are:

Random oscillations were addressed by MPPT management of PV systems, however overall energy gathering efficiency was not increased. It was difficult to create low-cost hardware implementation in certain ways. Some factors failed to ensure the best answer, which was extremely complex, while using the optimization technique. The dynamic global maximum peak was not tracked, and a new Artificial Intelligence complex topology could not be described. There was a loss of power and a reduction in safety under some switching scenarios. In addition, the controller’s design was complicated, cost more than other systems, and failed to track peak energy in specific partial shadow scenarios. A new methodology, the hybrid optimization technique BWO-RNN as shown in Table 1, is developed to overcome these issues and harvest optimum energy efficiency.

Table 1
A new methodology, the hybrid optimization technique

Author Year Methodology Advantage Disadvantage Dataset

Nair, S.P, Mary Linda 2019 MPPT in hybrid solar and wind energy system combined MDA-RNN. Maximum power is tracked from wind and solar energy source More expensive, large in size voltage, power, current.

Farh H.M, Eltamaly, Ibrahim 2019 Dynamic global power extraction deep RNN and improved PSO. Improve PV system performance, high efficiency, power quality and reliability Maximum power is generated from PV in nonuniform condition also PV irradiance, temperature, Duty ratio.

Gosumbonggot. J, Fujita.G 2019 PV partial shading detection and global MPPT with irradiance and temperature variations. Better performance in terms of tracking speed and average harvested power as compared to another methods. This method needs extra switches in order to reconfigure the PV array to achieve maximum power. PV current and voltage.

Teo, J.C, Tan, R.H, Mok, V.H, Ramachandramurthy 2018 Impact of partial shading on PV characteristics max power of PV string. The stress on the energy storage charge controller could be reduced by eliminating unnecessary reconfiguration. PV panel size is large, high cost Irradiance, temperature, PV voltage, current.

Aygul k, cikan M, Demirdelen T and Tumay M 2019 Butterfly optimization based MPPT of PV system under partial shading condition. Good accuracy, fast tracking speed PV cell efficiency remains between 11 and 28%. The dependence of PV on temperature and solar radiation is another disadvantage. –

Zhang X, Li.s, He,T, Yang, B 2019 MPPT design for PV system with partial shading based on memetic reinforcement learning. High safety, pollution free, less maintenance, noise free. In the presence of multiple MPPs, such strategies have the disadvantage of being easily trapped at a local maximum power point (LMPP). –

Priyadarshini N, Padmanaban S, Holm-Nielson,J.B 2019 Estimation of hybrid ANFIS-PSO based for PV grid integration under fluctuating sun irradiance. This method combined the advantages of hysteresis and SVPWM simultaneously. Uncertainities, nonlinear. PV voltage,PV current, duty ratio, PWM.

Mansoor M, Mirza A.F, and Ling.Q 2020 HHO based MPPT control for PV system under partial shading condition. Scalability, free of noise and fast installation Slow convergence at MPP. Current, voltage, Duty cycle, power.

Pervez I, Sarwar A, Tayyab M and Sarfraz.M 2019 In PV-based generating systems, GSA-based MPPT is used. enhance the amount of electricity production using solar PV Classical algorithms cannot solve the purpose efficiently –

Babes,B.Boutaghane A and Hamouda.N 2021 For a PV fueled arc welding equipment, a novel nature-inspired MPPT control based on ACO-ANN has been developed. modern arc welding is to develop an economical and efficient AWPS with unity power factor (PF) Voltage fluctuations and low power factor (PF varies from 0.4). PV voltage and current.

Author	Year	Methodology	Advantage	Disadvantage	Dataset
Nair, S.P, Mary Linda	2019	MPPT in hybrid solar and wind energy system combined MDA-RNN.	Maximum power is tracked from wind and solar energy source	More expensive, large in size	voltage, power, current.
Farh H.M, Eltamaly, Ibrahim	2019	Dynamic global power extraction deep RNN and improved PSO.	Improve PV system performance, high efficiency, power quality and reliability	Maximum power is generated from PV in nonuniform condition also	PV irradiance, temperature, Duty ratio.
Gosumbonggot. J, Fujita.G	2019	PV partial shading detection and global MPPT with irradiance and temperature variations.	Better performance in terms of tracking speed and average harvested power as compared to another methods.	This method needs extra switches in order to reconfigure the PV array to achieve maximum power.	PV current and voltage.
Teo, J.C, Tan, R.H, Mok, V.H, Ramachandramurthy	2018	Impact of partial shading on PV characteristics max power of PV string.	The stress on the energy storage charge controller could be reduced by eliminating unnecessary reconfiguration.	PV panel size is large, high cost	Irradiance, temperature, PV voltage, current.
Aygul k, cikan M, Demirdelen T and Tumay M	2019	Butterfly optimization based MPPT of PV system under partial shading condition.	Good accuracy, fast tracking speed	PV cell efficiency remains between 11 and 28%. The dependence of PV on temperature and solar radiation is another disadvantage.	–
Zhang X, Li.s, He,T, Yang, B	2019	MPPT design for PV system with partial shading based on memetic reinforcement learning.	High safety, pollution free, less maintenance, noise free.	In the presence of multiple MPPs, such strategies have the disadvantage of being easily trapped at a local maximum power point (LMPP).	–
Priyadarshini N, Padmanaban S, Holm-Nielson,J.B	2019	Estimation of hybrid ANFIS-PSO based for PV grid integration under fluctuating sun irradiance.	This method combined the advantages of hysteresis and SVPWM simultaneously.	Uncertainities, nonlinear.	PV voltage,PV current, duty ratio, PWM.
Mansoor M, Mirza A.F, and Ling.Q	2020	HHO based MPPT control for PV system under partial shading condition.	Scalability, free of noise and fast installation	Slow convergence at MPP.	Current, voltage, Duty cycle, power.
Pervez I, Sarwar A, Tayyab M and Sarfraz.M	2019	In PV-based generating systems, GSA-based MPPT is used.	enhance the amount of electricity production using solar PV	Classical algorithms cannot solve the purpose efficiently	–
Babes,B.Boutaghane A and Hamouda.N	2021	For a PV fueled arc welding equipment, a novel nature-inspired MPPT control based on ACO-ANN has been developed.	modern arc welding is to develop an economical and efficient AWPS with unity power factor (PF)	Voltage fluctuations and low power factor (PF varies from 0.4).	PV voltage and current.

1.3 Problem statement

From the literature survey, it is found that the methodologies adopted by the authors offered several challenges. Some of them are identified as follows:

Failed to describe a new Artificial Intelligence complex topology; the dynamic global maximum peak was not tracked.

Improved PSO was succeeded in tracking dynamic global maximum peak, but steady-state oscillations existed, and it took a long time to follow the maximum global peak due to the searching process at every change.

The MPPT control of PV systems tackled the problems of random oscillations, but the overall energy harvesting efficiency was not improved.

In some switching conditions, there was power loss and also a decrease in safety. Also, the design of the controller was complex, more expensive than other methods, and failed to track maximum power in some partial shadow conditions.

In some approaches, hardware implementation was tough to design with low cost. Using the optimization algorithm, some parameters failed to ensure the optimal solution, which was highly complex.

In order to overcome these problems and harvest maximum energy efficiency, a new methodology, namely the hybrid optimization technique BWO-RNN, is proposed.

2 Modelling of PV system

The photovoltaic depends on isolation, temperature, and cluster voltage, which is essential to use MPPT to change the working voltage close to a large-scale power station under different partial shading conditions. The structure of the proposed model is a combination of BWO and RNN, which control other parameters, as given in Fig. 1. The PV system is connected with load via DC-DC boost converter, and the control signal for the converter is provided by optimization techniques (RNN and BWOA). MPPT changes the working voltage close to the maximum output voltage under different partial shading conditions. It’s also used in conjunction with RNN to get maximum power, with the RNN training the data set to create a converter’s control signal.

Fig. 1

Structure of the proposed model.

It is a well-known fact that the PV panel converts the light into electricity using semiconducting materials. The DC-DC converter must adapt the load to meet the voltage and current of both the solar panel under various operating situations and maintain a steady output voltage. The MPPT controller adjusts the DC-DC converter’s duty cycle (D) with PV switching. The equivalent circuit of each block is described in the next section.

2.1 Equivalent circuit of PV

The equivalent circuit of the PV cell is shown in Fig. 2. There are mainly three components: parallel diode, series resistors, current source. The number of PV cells in series (n_s) and number of PV cells in parallel (n_p) are achieved based on voltage and current requirements. The module’s output is fixed based on the combination of series and parallel PV cells [33]. It is possible to express the affinity between output current and voltage [34, 35].

Fig. 2

PV cell equivalent circuit.

$i_{pv} = n_{p} i_{g} - n_{p} i_{s} (\exp [\frac{Q}{{akt}_{c}} (\frac{v_{pv}}{n_{s}} + \frac{r_{s} i_{pv}}{n_{p}})] - 1)$ (1)

Where

i_pv is PV current,

The generated photo current i_g is represented as solar irradiation, as follows $i_{g} = (i_{sc} + K_{i} (t_{c} - t_{ref})) \frac{s}{1000}$ (2)

where,

i_sc is short circuit current,

t_c is convergence time,

t_ref is reference time.

Based on the subsequent relationship, i_s represents the variation in PV cell saturation current with temperature: $i_{s} = i_{RS} {[\frac{t_{c}}{t_{ref}}]}^{3} \exp [\frac{{Qe}_{g}}{ak} (\frac{1}{t_{ref}} - \frac{1}{t_{c}})]$ (3)

2.2 Equivalent circuit of DC-DC converter

The corresponding circuit of a DC-DC boost converter is shown in Fig. 3. Initially, switch sw₁ is in the closed position, and switch sw₂ is in the open position. The inductor current (I_l) is now growing from zero. The inductor current is supplied to the load and the capacitor is charged when switch sw₂ is closed and switch sw₁ is opened. In the steady condition, the ON-OFF state of switches sw₁ and sw₂ is substantially reliant on the maximum output voltage v_o. Formula (4) Formula (6)

Fig. 3

Equivalent circuit of DC-DC Boost Converter.

$\frac{v_{o}}{v_{in}} = \frac{1}{1 - D_{duty}}$ (4) $\frac{v_{o}}{v_{in}} = \frac{t_{rise}}{t_{fall}} + 1$ (5) $D_{duty} = \frac{t_{rise}}{t_{rise} + t_{fall}}$ (6)

Where,

D_duty is duty cycle,

t_rise –period for raising inductor current when switch sw₁ is in closed condition.

t_fall –time for decreasing inductor current when switch sw₁ is in open condition?

2.3 Load (Grid and DC load)

Solar PV systems are divided into two types: grid-connected and stand-alone. The power conditioning unit in grid-connected PV systems transforms the DC power generated by the PV array into AC power according on the utility grid’s voltage and power quality standards. A three-phase grid-connected PV system is examined in this paper. The DC electricity from the panels is converted into AC power via a power converter. When needed, the transformer enhances the inverter’s AC output voltage. The performance is measured using a single resistive load (DC load). The load refers to networked appliances that are powered by an inverter or the grid.

3 Proposed BWO algorithm

The Black Widow Optimization Technique (BWOA) is a meta-heuristic optimization algorithm for solving complex optimization problems. It is considered as part of developed algorithms due to its parameters. The parameters of BWOA are similar to GA and considered to be one of the best-performing methods. It has some benchmarks that mimic natural evolution like selection, reproduction, and mutation. The BWOA also replicates the bizarre mating behavior of black widow spiders. This method differs from the established algorithm in that it provides greater performance in complex problems. Darwin’s natural selection theory defines the inspired BWOA as drop with modification, the notion of changing species through time and formation of new ones. Because BWO balances the exploration and exploitation phases, it enables speed convergence and avoids local optima in a variety of optimization problems with several local optima. Figure 4 displays the flowchart of BWOA comprehensively.

Fig. 4

Flowchart of BWOA.

The following are the major phases in the explanation of BWOA:

Step 1: Initialization of Population

A population comprises many widows of size M, each of which is represented by an array of 1 × M_var signifying that issue’s solution. The array is written as widow= (X₁, X₂, …… , X_{M
_var}), where M_var is an optimization problem. M_var also indicates how many threshold values the method requires, with X_i being the i–th potential solution.

The fitness function F of each widow in the set (X₁, X₂, …… , X_{M
_var}) is evaluated to obtain a widow fitness. Then fitness= F (widow) which may be written as fitness = F (X₁, X₂, … . . , X_{M
_var}). In the suggested strategy, F may be adjusted using the fitness function. An optimization technique starts with seeding a population of spiders in a M_pop × M_var at random. Randomly selected pairs of parents undertake the procreating and mating processes, During or after the mating procedure, a black male widower consumes the female black widow.

Step 2: Process of Procreation

That spider pairings have nothing in common. In nature, each couple begins to mate in its web in order to reproduce the next generation independently of the others. Approximately 1000 eggs are produced with each mating, although some of the spider offspring survive and are stronge. During the procreation stage, an array termed alpha I is constructed using an array of random numbers that is as long as a widow. The value of alpha (α_i), Equation (7), and Equation (8) are then used to create children, with X₁ and X₂ representing parents and Y₁ and Y₂ representing offspring, respectively. A crossover result was evaluated & kept. $Y_{1} = α_{i} \times X_{1} + (1 - α_{i}) \times X_{2}$ (7) $Y_{2} = α_{i} \times X_{2} + (1 - α_{i}) \times X_{1}$ (8)

Step 3: Process of Cannibalism

The process of cannibalism is divided into three categories. There is sibling cannibalism, sexual cannibalism, and another type of cannibalism in which baby spiders eat their mothers. Female spiders devour male spiders during or after mating in sexual cannibalism. Spiders eat their siblings in sibling cannibalism. The new population is graded and saved in a variable named Pop₂ after the cannibalism operation.

Step 4: Process of Mutation

Mute_Pop . is in charge of the mutation process. A random number of people are chosen from the population and modified. Each of the suggested solutions has two members of the array randomly switched. After the mutation procedure, the new population was graded and recorded in a variable named Pop₃. Then, a migration of Pop₃ and Pop₂, which may be sorted to obtain the optimal M_var dimension threshold values, creates a new population.

After completing the preceding steps, the BWOA is ready to give RNN with training data. The completed training dataset is used to train the RNN, which is explained in detail in the next section.

3.1 RNN for training process

3.1.1 Structure

Figure 5 shows the RNN’s structure, that is made up of four layers: the hidden layer, the input layer, the context layer, as well as an output layer. The hidden layers acquire information from the output for context neurons, sometimes known as memory units, because they preserve the past outputs for hidden neurons. The RNN’s inputs are as v_pv, i_pv, v_WT, and i_WT respectively. Every layer’s basic procedure is examined, and the learning process oversees RNN training.

Fig. 5

Structure of RNN.

3.1.2 Process of the supervised learning process

After initializing the RNN process, the system must be trained using a supervised learning method. This algorithm’s formulation is equal to the backpropagation algorithm. The RNN parameters $ω_{JK}^{3}$ , $ω_{J}^{2}, ω_{IJ}^{2}$ are used in the training pattern. The basic goal of the supervised learning method is to minimize the error function (E), which is expressed as E^*. $E^{*} = \frac{1}{2} {(V_{dc}^{*} - V_{MPPT}^{*})}^{2}$ (9)

Where

$V_{dc}^{*}$ is dc current,

$V_{MPPT}^{*}$ is MPPT voltage.

The erroneous term was delivered as well as the weight $ω_{JK}^{3}$ was changed in RNN using the following Equation (layer 1) $δ_{K}^{*} = \frac{\partial E^{*}}{\partial O_{K}^{3}} = [- \frac{\partial E^{*}}{\partial e_{m}^{*}} \frac{\partial e_{m}^{*}}{\partial O_{K}^{3}}]$ (10)

Following that, the weight $ω_{JK}^{3}$ is adjusted according to the quantity. $Δ ω_{JK}^{3} = [- \frac{\partial E^{*}}{\partial O_{K}^{3}} \frac{\partial O_{K}^{3}}{\partial {net}_{K}^{3}}] = δ_{K} O_{J}^{2}$ (11)

After that, you may update the weight by $ω_{JK}^{3} (n + 1) = ω_{JK}^{3} (n) + η_{JK} Δ ω_{JK}^{3} (n)$ (12)

The weights $ω_{J}^{2}$ and $ω_{IJ}^{2}$ in Layer 2 are modified and used the Equation below. This layer is where the multiplication happens. $Δ ω_{J}^{2} = - \frac{\partial E^{*}}{\partial ω_{J}^{2}} = [- \frac{\partial E^{*}}{\partial O_{K}^{3}} \frac{\partial O_{K}^{3}}{\partial O_{J}^{2}} \frac{\partial O_{J}^{2}}{\partial ω_{J}^{2}}] = δ_{K} ω_{JK}^{2} p_{J}^{2}$ (13) $Δ ω_{IJ}^{2} = - \frac{\partial E^{*}}{\partial ω_{IJ}^{2}} = [- \frac{\partial E^{*}}{\partial O_{K}^{3}} \frac{\partial O_{K}^{3}}{\partial O_{J}^{2}} \frac{\partial O_{J}^{2}}{\partial ω_{IJ}^{2}}] = δ_{K} ω_{JK}^{2} o_{IJ}^{2}$ (14)

The weights $ω_{J}^{2}$ and $ω_{IJ}^{2}$ have different updating rules, $ω_{J}^{3} (n + 1) = ω_{J}^{3} (n) + η_{J} Δ ω_{J}^{3} (n)$ (15) $ω_{IJ}^{3} (n + 1) = ω_{IJ}^{3} (n) + η_{IJ} Δ ω_{IJ}^{3} (n)$ (16)

The learning rates for training parameters $ω_{J}^{2}$ and $ω_{IJ}^{2}$ are η_J and η_IJ, respectively; the training parameters are $ω_{J}^{2}$ , $ω_{IJ}^{2}$ , and $ω_{JK}^{3}$ . This study determines a learning calculation that regulates the mistake to achieve a zero scale.

When the operation is finished, the RNN was ready to send the control signal towards the converter. A BWOA system will assist with dataset preparation for something like the framework. The dataset is constructed to use the RNN and reducing the fluctuation in power at different periods. The orientation of the RNN method is determined by both forward and backward passes. The well-prepared system is obtained as from neural system’s control output. The duty cycle is then provided to the system through MPPT and the converter via pulse. The load may gather maximum power from the PV panel in the proposed approach. The execution of the proposed system is carried out, and the observed optimized parameter is discussed in the following sections.

3.2 Simulink model

The virtual implementation of the proposed method with a load-connected PV system along with partial shadow conditions is performed using Intel CPU (R) Core (TM) with three processors, 8GB RAM, and MATLAB/Simulink (R2015a). Figure 6 shows the proposed model where PV is connected with the grid through converter and inverter.

The hybrid technique is used to control different sorts of load-connected PV systems to stretch the most extreme output control. The proposed system uses the voltage and current quantities as data. When the parameters setting is finished, BWOA are regulated to make a superior control beat of the converter. Further, simulation parameters required for the system are shown in Table 2.

Fig. 6

MATLAB/Simulink system of the proposed model with the grid.

Table 2

Required parameters for simulation

Parameters	Symbol	Value
Output Voltage of PV	V_o	360V
Capacitor	C1	0.1F
Capacitor	C2	1e-5F
Switching Frequency	f_s	8000Hz
Inductor	L_in	5e-3 H

4 Results and discussion

The system’s output must improve on improving the suggested PV model with MPPT to produce a controlled identity again for DC-DC boost converter. The implementation of the proposed model is validated for random solar irradiance, and the PV power control depends on the MPPT technique. In this technique, implementation is estimated from variable conditions using solar irradiance and temperature. The proposed system is connected with the grid to analyze the performance. Under Partial Shading Conditions, the shadow covers some diodes of the PV system. The idiomatic phenomena of the experiments are implemented as given below.

Performance metrics:

PV Voltage: PV voltage is the energy produced by a single PV cell. Each PV cell creates open-circuit voltage, typically referred to as VOC. $Voc = \frac{nkT}{q} (\frac{Il}{Io} + 1)$

Where

Vocisopencircuitvoltage,

PV Current: Solar cells, often known as photovoltaics (PV), are semiconductor devices that convert sunlight into direct current (DC) power. PV cells are electrically connected together to form modules and arrays that may charge batteries, run motors, and power a variety of electrical loads. $I = Ipv - Io [\frac{U + IRs}{enVT}] - \frac{U + IRs}{Rsh}$

where

Io is output current,

IRs is series resistance current,

Rsh is shunt resistance.

PV Power:

Solar panel watts × average hours of sunlight ×75%

4.1 Case 1: Stable irradiance and stable temperature

The stable irradiance and temperature are given as inputs to PV, and the value of irradiance and temperature are considered 1000wb/m² and 25C, respectively. The simulated results may be seen in Fig. 8, which compares the voltage, current, & power of the PV system for various MPPT controllers. In Fig. 7 (a), GSA with RNN technique attained a PV voltage and took 0.18 seconds to reach 358 V. Further, PSO with RNN takes 0.19 seconds to gain, and ACO with RNN takes 0.2 seconds.

Fig. 7

Performance analyses with different controllers (a) PV voltage (b) PV Current (c) PV Power.

Similarly, GSA with RNN takes 0.18 seconds to reach 6.53A, PSO with RNN takes 0.19 seconds, and ACO with RNN takes 0.2 seconds to get 6.50 A. The power of the proposed system takes 0.115 seconds to reach 2358 W, and other techniques offer some glitches to reach the peak of the power. The PV voltage for the proposed controller takes 0.115 seconds to get 360 V, the current takes 0.115 seconds to reach 6.55A, and the power is acknowledged at 2358 W. The proposed system is showing an improvement in convergence compared with existing controllers.

Figures 8(a) and (b) represent a comparison of the voltage-current curve and power-voltage curve for the proposed BWOA -RNN methodology and existing approaches such as GSA-RNN, PSO –RNN, ACO –RNN. The proposed model displays better characteristics compared with other techniques.

Fig. 8

Characteristics curve of (a) PV Voltage, and (b) PV Power.

4.2 Case 2: Stable irradiance and partial temperature

In this case, the irradiance is taken as 1000wb/m^2, and the temperature values vary based on the duration. The simulated results are shown in Fig. 9, which compares the PV system’s voltage, current, and power for different MPPT controllers. The temperature of 25°C and duration of 0 to 0.3 seconds are taken and in the proposed method, the voltage reaches 360 V. Now, the temperature is changed to 32°C for the duration of 0.3 to 0.6 seconds, and the voltage is reduced to 350 V. Further changing of temperature to 40°C for the period of 0.6 to 1 second, voltage reduced to 340 V. Significantly, the proposed method takes less time, about 0.115 seconds, to reach the settling point. On the other hand, the existing techniques take more than 0.115 seconds, as recorded in the observed images. Figure 9 (ii) represents the PV current plot, and the current values are drastically reduced up to 6.55 A during the initial stage. Also, PV current plot clearly shows that the proposed approach takes 0.115 seconds to reach the setting point, whereas existing methods take more than 0.115 seconds. Figure 9 (iii) represents the PV power plot and replicates the same trend to reach the desired power of 2358 W.

Fig. 9

Performance analyses with different controllers (i) PV voltage (ii) PV Current (iii) PV Power.

Figure 10 illustrates the simulation outcome of PV voltage and PV power characteristics curve. Figure 10 (a) exemplifies comparing the voltage-current plot for proposed (BWOA-RNN) with the existing approaches such as GSA- RNN, PSO –RNN, and ACO –RNN. Figure 10 (b) compares the power–voltage plot for the proposed with the existing approaches. Further, the magnified plot is presented for both voltage and power to illustrate the effectiveness of both methods.

Fig. 10

(a) Characteristics curve of PV Voltage, (b) Characteristics curve of PV Power.

4.3 Case 3: Partial irradiance and stable temperature

In this case, different irradiance and constant temperature are given to PV as an input. The different irradiance values are 1000wb/m², 400wb/m² and 800wb/m². The irradiance values are changed for the different time limits. Specifically, 25 degrees Celsius is given as an input temperature range. Figure 11 (i) represents the PV voltage plot; for the 0 to 0.3 seconds, the irradiance value is 1000wb/m²; for the duration of 0.3 to 0.6, the irradiance value is changed to 400. At last, for the time of 0.6 to 1 seconds, the irradiance value is set as 800wb/m². When applying the irradiance value as 1000, the proposed approach reaches 360 V in 0.115 seconds, whereas the existing system takes from 0.16 to 2 seconds. Further, applying irradiance values as 800 and 400, the proposed approach reaches 350 V and 360 V, respectively. Figure 12(b) represents the PV current plot. The proposed method gets 6.55 A in 0.115 seconds. The settling point for the proposed approach is faster than the existing approach. There must be a fluctuation in the current ranges when varying the irradiance value. Figure 11 (iii) represents the PV power plot, and it reaches 2358 W in 0.115 seconds at the time of 0.3 and 0.6 seconds, but there are fluctuations because of changing the irradiance value.

Fig. 11

(i) Performance analysis of PV Voltage, (ii) Current, and (iii) Power.

Fig. 12

Characteristics curve (a) PV Voltage, and (b) PV Power.

Figure 12 illustrates the simulation outcome of the characteristics curve of I-V and P-V, which mimics the behavior of cases 1 and 3, i.e., the proposed (BWOA –RNN) method performed well compared with existing approaches such as GSA- RNN, PSO –RNN, and ACO –RNN.

4.4 Case 4: Partial irradiance and partial temperature

In this case, different irradiance and various temperature values are given to the PV as an input. The different irradiance values are 1000wb/m², 400wb/m² and 800wb/m² and the temperature values are 25, 32, and 40-degree Celsius. Further, the irradiance and temperature values are changed for different time limits. Figure 13 (a) represents the PV voltage plot; for the 0 to 0.3 seconds, the irradiance value is 1000wb/m² and the temperature range is 25-degree Celsius; for the duration of 0.3 to 0.6, the irradiance value is changed to 400, and the temperature is adjusted to 32-degree Celsius. At last, for the time of 0.6 to 1 seconds, the irradiance value is set as 800wb/m² and the temperature is set as 40-degree Celsius. When applying the irradiance value as 1000, the proposed approach reaches 360 V in 0.115 seconds, whereas the existing procedure takes from 0.16 to 2 seconds. When irradiance values like 800 and 400, the proposed system comes 340 V. Figure 13 (b) represents the PV current plot. The proposed method gets 6.55A in 0.115 seconds. The settling point for the proposed approach is faster than the existing approach. When varying the irradiance value and the temperature, there must be a fluctuation in the current ranges. Figure 13 (c) represents the PV power plot. The proposed approach reaches 2358 W in 0.115 seconds at the time of 0.3 seconds represented in the plot.

Fig. 13

Performance analyses (a) PV Voltage, (b) Current, (c) Power.

The magnified segments in Fig. 14 warrant the proposed methodology’s effectiveness over other compared approaches.

Fig. 14

Characteristics curve (a) PV Voltage, and (b) PV Power.

4.5 Comparative analysis

From Table 3–6, it is observed that the overall performance of the proposed model shows more excellent results significantly and outperformed another existing model, notably, increased voltage, current, and power, and decreased convergence time for all three parameters. It shows similar trends during partial temperature change and irradiance with different configurations.

Table 3
Stable irradiance and Stable temperature: 1000 wb/m² and 25°C

Methods Voltage (V) Time(s) Current (A) Time (s) Power (W) Time (s)

ACO-RNN 356 0.18 312.43751 0.24 8.652035 0.14

PSO-RNN 357 0.16 312.43753 0.22 8.652036 0.12

GSA-RNN 358 0.14 312.43754 0.20 8.652038 0.1

BWOA-RNN(Proposed) 360 0.115 312.43755 0.18 8.652042 0.08

Methods	Voltage (V)	Time(s)	Current (A)	Time (s)	Power (W)	Time (s)
ACO-RNN	356	0.18	312.43751	0.24	8.652035	0.14
PSO-RNN	357	0.16	312.43753	0.22	8.652036	0.12
GSA-RNN	358	0.14	312.43754	0.20	8.652038	0.1
BWOA-RNN(Proposed)	360	0.115	312.43755	0.18	8.652042	0.08

Table 4

Stable irradiance and partial temperature: 1000 wb/m² and 25°C up to 0.3 seconds, 32°C for (0.3–06) seconds, and 40°C for (0.6–1) seconds

Methods	Voltage (V)			Time(s)			Current (A)			Time(s)			Power(W)			Time(s)
	25°C	32°C	40°C	25°C	32°C	40°C	25°C	32°C	40°C	25°C	32°C	40°C	25°C	32°C	40°C	25°C	32°C	40°C
ACO-RNN	356	350	339.89	0.18	.321	0.63	312.4327	–60.57	–68.73	0.24	0.34	0.643	8.652035	–2.586	–3.235	0.14	0.34	0.643
PSO-RNN	357	350.58	339.97	0.16	.32	.0.289	312.4341	–60.58	–68.79	0.22	0.33	0.636	8.652036	–2.638	–3.324	0.12	0.33	0.636
GSA-RNN	358	350.673	340.00	0.14	0.317	0.28	312.4366	–60.586	–60.7952	0.2	0.32	0.622	8.652038	–2.678	–3.386	0.1	0.32	0.622
BWOA-RNN (Proposed)	360	351.002	340.27	0.115	0.315	0.23	312.4385	–60.61	–60.805	0.18	0.31	0.6103	8.652042	–2.73	–3.410	0.08	0.31	0.6103

Table 5

Variable irradiance and variable temperature: 1000wb/m², 400wb/m², and 800wb/m² and 25°C

Methods	Voltage (V)			Time(s)			Current (A)			Time(s)			Power(W)			Time(s)
	1000wb/m²	400wb/m²	800wb/m²	1000wb/m²	400wb/m²	800wb/m²	1000wb/m²	400wb/m²	800wb/m²	1000wb/m²	400wb/m²	800wb/m²	1000wb/m²	400wb/m²	800wb/m²	1000wb/m²	400wb/m²	800wb/m²
ACO-RNN	356	350	354.89	0.18	.321	0.63	312.4302	–75.52	74.830	0.24	0.34	0.643	8.652035	–3.3736	3.7363	0.14	0.34	0.643
PSO-RNN	357	350.58	354.93	0.16	.32	.0.289	312.4304	–75.58	74.85	0.22	0.33	0.636	8.652036	–3.3737	3.7364	0.12	0.33	0.636
GSA-RNN	358	350.673	355.00	0.14	0.317	0.28	312.43045	–75.83	74.900	0.2	0.32	0.622	8.652038	–3.3738	3.7365	0.1	0.32	0.622
BWOA-RNN	360	351.002	355.27	0.115	0.315	0.23	312.4306	–76.14	75.005	0.18	0.31	0.610	8.652042	–3.3739	3.7366	0.08	0.31	0.610
(Proposed)

Table 6

Partial irradiance and partial temperature: 1000wb/m² –25°C, 400wb/m² –32°C, and 800wb/m²–40°C

Methods	Voltage (V)			Time(s)			Current (A)			Time(s)			Power(W)			Time(s)
	1000wb/m²-25°C	400wb/m²-32°C	800wb/m²-40°C	1000wb/m²-25°C	400wb/m²-32°C	800wb/m²-40°C	1000wb/m²-25°C	400wb/m²-32°C	800wb/m²-40°C	1000wb/m²-25°C	400wb/m²-32°C	800wb/m²-40°C	1000wb/m²-25°C	400wb/m²-32°C	800wb/m²-40°C	1000wb/m²-25°C	400wb/m²-32°C	800wb/m²-40°C
ACO-RNN	356	350	348.1005	0.18	.321	0.63	312.4302	–110.304	74.83002	0.24	0.34	0.643	8.652035	–4.32641	0.8324	0.14	0.34	0.643
PSO-RNN	357	350.58	348.1006	0.16	.32	.0.289	312.4304	–110.306	74.85	0.22	0.33	0.636	8.652036	–4.32642	0.83245	0.12	0.33	0.636
GSA-RNN	358	350.67	348.1007	0.14	0.317	0.28	312.43045	–110.304	74.9006	0.2	0.32	0.622	8.652038	–4.32643	0.8326	0.1	0.32	0.622
BWOA-RNN	360	351.00	348.1012	0.115	0.315	0.23	312.4306	–110.314	75.0054	0.18	0.31	0.6103	8.652042	–4.32646	0.8331	0.08	0.31	0.6103
(Proposed)

The proposed method is compared to existing techniques such as the Ant Colony Optimization (ACO)-RNN system, Particle Swarm Optimization (PSO)-RNN system, and Gravitational Search Algorithm (GSA)-RNN system. Existing methods are tracking minimum power ACO with RNN (8.652035), PSO with RNN (8.652036), and GSA with RNN (8.652038) in terms of tracking minimum power. The suggested technique BWOA-RNN (8.652042) is more efficient than other ways in terms of obtaining maximum power.

When the temperature rises, conventional approaches reduce the voltage, current, and power, resulting in a sustainable irradiance & partial temperature situation. In addition, this proposed technology reduces voltage, current, & power. The proposed method is superior to the existing method. The proposed model is much simpler, taking only 0.115 seconds. In addition, when compared to other models, the proposed approach extracted the most electricity from the PV system. As a result, this BWOA –RNN may be used to track maximum capacity from photovoltaic systems on a large scale.

Consolidating the inferences, the convergence time of the proposed model is relatively more minor, about just 0.115 seconds. Also, the proposed scheme harvested maximum power from the PV system compared to other models. Therefore, this BWOA –RNN can be employed for a large-scale approach to track maximum capacity from the Photovoltaic system.

5 Conclusions

The enhanced approach for obtaining more electricity from the PV panel for various atmospheric situations is provided in this research paper. BWOA was used to improve the RNN, and then the RNN was created as a computational dataset based on the PV model current, power, and voltage. The controller modifies the output based on the proposed approach to categorize the control signal in order to extract more energy from the PV. Simulation results show that the proposed method (BWOA–RNN) extracts more energy and reduces convergence time compared to existing approaches such as GSA–RNN, PSO–RNN, and ACO–RNN. The proposed system is 36.11% quicker than GSA with RNN, 39.47% faster than PSO, and 42.5% faster than ACO with RNN in terms of tracking speed. Significantly, the proposed approach is 0.87% more efficient than the other models in terms of obtaining maximum power. Consolidating the results, the suggested model’s convergence time is relatively short, around 0.115 seconds. As a result, the proposed method performs better under partial shadowing conditions and may be used to a large-scale system.

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