Power Harvested Maximization for Solar Photovoltaic Energy System Under Static and Dynamic Conditions

Abstract

Photovoltaic (PV) systems are increasingly recognized as a viable renewable energy source due to their clean, abundant, silent, and environmentally friendly nature. However, their efficiency is significantly influenced by environmental conditions, necessitating advanced control strategies to ensure optimal power extraction. This study aims to enhance the performance of PV systems by developing and evaluating maximum power point tracking (MPPT) algorithms capable of operating effectively under both uniform irradiance and partial shading conditions (PSCs). Specifically, two metaheuristic algorithms—Particle Swarm Optimization (PSO) and Cuckoo Search Optimization (CSO)—are modeled, implemented, and tested for tracking the global peak power (GPP) in various static and dynamic scenarios. Simulation results indicate that both algorithms accurately and efficiently track the GPP under static uniform and PSCs. Under dynamic conditions, while both the PSO and CSO can initially locate the GPP, they fail to maintain accurate tracking during subsequent intervals. Notably, CSO exhibits reduced oscillations and faster response time compared with PSO. These findings suggest that while metaheuristic MPPT methods are effective in static environments, their performance in dynamic conditions remains a challenge requiring further enhancement.

1. Introduction

As the global energy demand continues to escalate due to population growth and technological advancement, solar energy has emerged as one of the most viable solutions to the energy crisis [1]. Its abundance, cost-effectiveness, and scalability make it particularly suitable for addressing the long-term energy needs of both developed and developing countries. The photovoltaic (PV) industry has witnessed significant growth worldwide, fueled by extensive research and development efforts aimed at improving efficiency, accessibility, and affordability. As a result, PV systems have become instrumental in improving energy access in underprivileged areas, contributing to socio-economic development and reducing reliance on fossil fuels. However, PV technology faces challenges due to the nonlinear power–voltage curve, which is influenced by environmental factors such as temperature and irradiance. The power–voltage characteristic of a PV array illustrates the relationship between output power generated and voltage under specific solar irradiance and temperature circumstances. The maximum power point (MPP) represents the peak achievable power output. On the curve, the MPP is the operating point where the product of voltage and current is at its peak. At this key point, the PV panel delivers the highest possible power to the load. Operating at the MPP ensures that the PV panel extracts the maximum energy from the available sunlight, enhancing the efficiency of the system. Additionally, accurate maximum power point tracking (MPPT) increases the total energy generated over a given period, directly impacting the system’s overall productivity. MPPT enables the PV system to adapt dynamically to changing environmental conditions (e.g., cloud cover or shading) to maintain high efficiency. If the PV system operates away from the MPP (e.g., at lower or higher voltages), (1) the panel will produce less power than its potential, (2) energy losses will occur, which reduces system efficiency, and (3) over time, suboptimal operation can lead to increased operational costs and reduced system lifespan. To ensure continuous operation at the MPP, the implementation of an MPPT controller is essential. While classical MPPT techniques effectively manage uniform radiation, PSCs cause multiple peaks in the power–voltage characteristic, including a single global peak power point (GPP) alongside several local maxima [2]. Recent advancements in MPPT techniques have extended their application to emerging fields such as transportation electrification. For instance, ref. [3] proposed a fault-tolerant power-sharing strategy with a novel MPPT method for parallel PV converters in electric airplanes, demonstrating improved reliability and efficiency under fault conditions. This highlights the growing need for robust and adaptable MPPT solutions in specialized applications, motivating the exploration of advanced algorithms to address broader PV system challenges, particularly under PSCs.

Several recent studies have focused on improving MPPT techniques to enhance the efficiency and adaptability of PV systems under varying climatic and shading conditions. In [4], an improved perturb and observe (P&O) algorithm was introduced, wherein a reference voltage is calculated as a function of irradiance and temperature to reduce steady-state oscillations and enhance dynamic response. This method is paired with a non-isolated DC–DC converter that achieves a high voltage gain with a single switch, ensuring simplicity and feasibility for PV applications. Similarly, ref. [5] presents a modified P&O algorithm that dynamically adjusts the perturbation step size to reduce oscillations and improve convergence speed without requiring additional sensors. The proposed technique achieved an average steady-state efficiency of 99.8% and significantly reduced tracking time compared with conventional methods. Furthermore, ref. [6] introduces a hybrid MPPT strategy that integrates Particle Swarm Optimization (PSO) with conventional methods such as P&O and incremental conductance (IC). The hybrid approach dynamically adjusts the perturbation step size in response to changing solar irradiance, eliminating the limitations of fixed step sizes in traditional methods. In [7], an enhanced adaptive step-size P&O algorithm is presented, optimized for operation under various levels of partial shading. The results reveal the significant limitations of conventional methods like P&O and IC under partial shading, underscoring the need for advanced control strategies. These studies collectively demonstrate a shift toward intelligent MPPT algorithms that improve accuracy, response time, and reliability, especially under dynamic environmental conditions. Consequently, optimizing global peak power tracking in PV power systems under uniform and partial shading conditions is crucial for improving overall system performance in terms of power output, reliability, efficiency, and power quality [8,9].

Partial shading conditions can greatly affect the performance of PV energy systems, prompting the development of various mitigation strategies. These strategies are broadly classified into soft-computing (artificial intelligence and bio-inspired) and hybrid MPPT approaches for mitigating the shading effects on PV applications, both of which play essential roles in minimizing the impact of shading on PV system efficiency [10]. Ref. [11] proposed a method capable of tracking not only the global peak but the sum of all available peaks using an interleaved boost converter (IBC). This approach significantly outperforms conventional boost converter techniques, enhancing system performance in terms of power quality, mismatch losses, and overall energy extraction under certain partial shading scenarios. Furthermore, the stability of DC-bus voltage plays a crucial role in the reliability and efficiency of standalone PV systems. Voltage ripple and instability, especially under rapid load or irradiance changes, can degrade the effectiveness of MPPT techniques. To address these issues, ref. [12] introduced a novel hybrid optimization method combining the salp swarm algorithm and PSO (SSA-PSO) with a direct sliding mode controller. This intelligent control strategy maintains stable output and robust MPPT performance even in the absence of a battery storage system. In [13], a detailed classification of PV-MPPT approaches categorized them into classical MPPT, soft-computing MPPT, hybrid MPPT approaches, and hardware solutions. Classical MPPT techniques like perturb and observe, constant voltage, and incremental conductance rely on simpler algorithms and are effective under uniform conditions but struggle under partial shading. Soft-computing algorithms leverage artificial intelligence and bio-inspired algorithms, including artificial neural networks, fuzzy logic control, genetic algorithm, and particle swarm optimization, providing higher accuracy and efficiency in tracking the GPP under complex conditions like partial shading. In [14,15], soft-computing techniques, including PSO and modified current sensorless methods, proved effective in managing partial shading circumstances. These approaches provide robustness, flexibility, and reliability, making them well suited for overcoming the challenges associated with partial shading in PV energy systems. On the other hand, hybrid techniques integrate conventional and soft-computing approaches to balance simplicity with accuracy, such as combining ANN with P&O or FLC to overcome individual limitations and enhance performance [16].

Conversely, hardware solutions such as module-based and array-based approaches require physical modifications to PV systems to minimize the adverse effects of partial shading. Several studies have reviewed various mitigation strategies, encompassing both hardware and computational approaches. For instance, one study investigated hardware-based shading mitigation methods in PV grid-connected energy systems, focusing on module and array reconfiguration to enhance performance [17]. Another review examined the theoretical aspects of reverse breakdown phenomena in PV cells and explored multiple approaches to mitigate partial shading effects [18]. Implementing hardware-based solutions often necessitates extra components and intricate system modifications. While these approaches can effectively address shading issues, soft-computing approaches are increasingly preferred because of their superior ability to track the GPP under partial shading with higher accuracy and adaptability [16].

Collectively, the literature underscores the challenges encountered due to partial shading circumstances and the diverse mitigation strategies employed to optimize PV system performance. Soft-computing algorithms offer a dynamic and efficient alternative, complementing hardware-based methods in enhancing energy extraction in PV applications. Given the critical issue for robust shading mitigation techniques, this study is structured around four key objectives, detailed as follows:

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Model and design the power and control circuits of the photovoltaic energy conversion system under static and dynamic environments.

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Apply and compare two advanced metaheuristics-based MPPT techniques, Cuckoo Search Optimizer and Particle Swarm Optimization, to optimize, simulate, and follow the global maximum power output of the PV energy system in both static and dynamic environments. These algorithms are selected for their proven efficiency and robustness in handling the challenges of non-linear and multi-modal optimization problems such as those arising under partial shading in PV energy systems. CSO is known for its superior convergence speed and ability to escape local optima, while PSO excels in simplicity, adaptability, and achieving high accuracy. By leveraging the strengths of these methods, this study aims to provide a detailed comparative analysis of their performance in maximizing PV system efficiency.

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Investigate the performance of the proposed photovoltaic energy conversion system under both time-variant and -invariant PSCs.

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Analyze and compare the effectiveness of the selected metaheuristic-based MPPT techniques in terms of global power tracking, convergence time, and oscillations around the steady state.

2. Solar Photovoltaic Power System Description Under Study

Figure 1 depicts the photovoltaic (PV) power system in which the PV modules are interconnected through the boost converter to the DC load. The system consists of three series-connected PV modules (249 W each) exposed to varying irradiance levels (Ir1, Ir2, Ir3), a boost converter, and an MPPT controller employing CSO and PSO algorithms. Voltage (V_pv) and current (I_pv) are measured using high-precision voltage and current sensors, respectively, positioned at the PV array’s output. The voltage sensor measures the array’s output voltage across the terminals, while the current sensor, placed in series with the array, captures the output current, enabling real-time computation of the power–voltage (P-V) characteristic. Both sensors are interfaced with an MPPT controller. A signal-conditioning circuit with a low-pass filter minimizes noise from environmental variations and the boost converter’s switching transients, which consist of an inductor (L), diode (D), capacitor (C_out), and switch. The MPPT controller processes the data, calculates instantaneous power (P = V_pv × I_pv), and adjusts the boost converter’s duty cycle (D) using the CSO and PSO algorithms to track the MPP.

In the scenario in which the series PV modules have the same irradiances as inputs, the I-V and P-V for one PV module is shown in Figure 2.

Table 1. The PV module specifications under study.

Parameter	Value
Module Type	Polycrystalline
Configuration	Single-sided
Pmax (W)	249 W
VOpen.circuit (V)	36.5 V
Cells (number of each module)	60
IShort.circuit (A)	8.83 A
Vmax (V)	30.2 V
Imax (A)	8.30 A
ILight.generated (A)	8.83 A
IDiode saturation (A)	1.0132 × 10−10
Diode factor of ideality	0.94812

provides the specifications of the Tata TP250MBZ PV module.

Table 2. The specifications of the DC–DC boost converter.

Parameter	Value
fSwitching	f
Inductor	L
Output capacitor	Co
Input capacitor	Cin
Load	R
Imax (A)	8.30 A
ILight.generated (A)	8.83 A
IDiode saturation (A)	1.0132 × 10−10
Diode factor of ideality	0.94812

presents the specifications of the boost converter. The converter is adjusted based on the computed D [19], enabling efficient following of the global peak power by dynamically adjusting its operation.

3. Maximum Power Point Tracking Algorithms

The maximum power point tracking (MPPT) system is an essential component in solar photovoltaic (PV) power systems, designed to maximize energy extraction by continuously regulating the operational point of the PV power system. Its primary function is to guarantee that the system consistently operates at its optimal power point. Various MPPT techniques have been developed to improve PV system efficiency, with the choice of an appropriate method depending on factors like accuracy requirements, computational capabilities, and environmental circumstances [19]. In this research, the Cuckoo Search Optimizer (CSO) and Particle Swarm Optimization (PSO) are applied, which are highly effective techniques for maximizing the power harvested from the PV energy systems due to their adaptability and robustness. CSO, inspired by the brood parasitism behavior of cuckoo birds, excels in global search capabilities, making it particularly effective in navigating complex, multi-modal P-V curves under partial shading circumstances. PSO, inspired by the social behaviors of swarms, combines simplicity and fast convergence, efficiently tracking the MPP even under dynamic irradiance changes. Both methods significantly improve energy extraction by addressing limitations of conventional techniques such as slow convergence or susceptibility to local maxima, thereby improving the efficiency and reliability of PV power systems. Their complementary strengths make them invaluable for advancing renewable energy technologies. More detailed information for both CSO and PSO is provided in the following sections.

3.1. The Cuckoo Search Optimizer (CSO)

The CSO constitutes a nature-inspired approach drawing inspiration from the reproductive strategies observed in certain cuckoo species, particularly those employing brood parasitism tactics. Brood parasitism involves the practice of depositing eggs in the nests of other birds. The methodology of CSO is governed by the following principles [20,21]:

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The cuckoo introduces eggs sequentially, placing one egg at a time in a nest chosen at random.

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Nests containing superior-quality eggs are retained and may be passed on to subsequent generations.

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To enhance the chances of the hatchlings receiving more nourishment, the cuckoo may eliminate some of the host bird’s eggs.

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Upon detecting an unfamiliar egg, the host bird faces a decision point. It may either eliminate the cuckoo’s eggs or abandon the nest entirely, opting to construct a new one elsewhere, with a probability denoted as Pa.

The utilization of the CSO for tracking the global peak in PV power systems involves a series of well-defined steps. In this study, the CSO is employed for simulation purposes, following the outlined procedure:

Step 1: The parameters of CSO for searching the GPP are initially established, with a focus on defining the converter duty ratio (D_i, where i = 1, 2 … n) and the Lévy multiplication factor (L_m) as the selected parameters.

Step 2: The duty ratios (D_i) are sequentially applied to the converter, and the corresponding power is computed. The GPP and duty ratio are retained as the current best sample. The new D samples are generated using the Lévy flight, using the following:

$$D_i^{k+1}=D_i^k+L_m\left({\displaystyle \frac{u}{{\left|v\right|}^{\frac{1}{\beta }}}}\right)\left(D_{best}^k-D_i^k\right)$$

(1)

In this process, β is set to 1.5, while L_m represents the Lévy scaling factor. The variables u and v are randomly drawn from a normal distribution.

Step 3: The updated duty ratios are applied to the boost converter, and the corresponding power output is recorded. The duty ratio that yields the highest power is designated as the new optimal candidate. Furthermore, a fraction of samples is randomly discarded based on a probability factor (Pa), mimicking the natural behavior of a host bird detecting and eliminating foreign eggs. New random samples are then introduced to replace the discarded ones, and their power outputs are evaluated. The most effective candidate is selected by comparing the recorded power values.

Step 4: Once the stopping condition is met, the CSO algorithm concludes, identifying the optimal duty cycle as the final output corresponding to the global peak power (GPP).

These steps outline the systematic application of the CSO for GPP tracking in PV energy systems, encompassing the parameter definition, sample generation, power measurement, and termination criteria. The approach integrates the unique characteristics of the CSO, such as Lévy flights and random sample replacement, to effectively track the GPP in PV systems under dynamic circumstances. The pseudo code of CSO for tracking the GPP in PV systems is illustrated in

Table 3. Pseudo code of CSO for following the global peak in PV energy systems.

1	Initialize the population of host nests (solutions) within the search space (n, β, Pa, k, itermax, Dmin, Dmax).
2	Assess the fitness of each nest using the objective function, which in this case is the PV energy system’s power output under varying environmental circumstances.
3	Update the best solution: Identify the best solution (nest) based on the fitness evaluation.
4	Generate new solutions: Employ the cuckoo’s random walk behavior to generate new candidate solutions using the following equation: $${\mathrm{D}}_{\mathrm{i}}^{\mathrm{k}+1}={\mathrm{D}}_{\mathrm{i}}^{\mathrm{k}}+{\mathrm{L}}_{\mathrm{m}}\left({\displaystyle \frac{\mathrm{u}}{{\left|\mathrm{v}\right|}^{\frac{1}{\mathsf{\beta }}}}}\right)\left({\mathrm{D}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}^{\mathrm{k}}-{\mathrm{D}}_{\mathrm{i}}^{\mathrm{k}}\right)$$ where β = 1.5, Lm is the Lévy multiplication coefficient, and u and v are randomly estimated from the normal distribution function.
5	Evaluate new solutions: Evaluate the fitness of the new candidate solutions.
6	Replace solutions: Replace the host nests with the new solutions based on a predefined selection criterion. If rand > pa, apply step 7; otherwise, apply step 4.
7	Destroy nests: With a probability of Pa, certain nests are destroyed, and new random nests are generated to replace them. Evaluate the fitness of all new nests.
8	Update the best solution: Identify the best solution (nest) based on the fitness evaluation.
9	Check for the termination criteria: If the stopping condition are met, stop the algorithm and output the GPP. Otherwise, go to step 4.
	Initialize the population of host nests within the search space (CSO parameters: n, β, Pa, k, itermax, Dmin, Dmax).

. On the other hand, Figure 3 shows a flowchart that outlines the CSO-based MPPT process for a PV system, starting with the initialization of duty cycles and parameters. Duty cycles are iteratively updated using the Lévy flight equation, and power outputs are evaluated to identify the GPP. The algorithm ensures efficient global search, reduced oscillations, and adaptability to dynamic conditions. After completing iterations, the best duty ratio corresponding to maximum power is output.

3.2. Particle Swarm Optimization (PSO)

The PSO is a metaheuristic algorithm inspired by the social behavior of bird flocks or fish schools employed for maximizing the power harvested from the PV power systems. PSO initializes a population of particles (solutions), which iteratively adjust their positions in the search space based on individual and group experiences to locate the GPP. This method effectively handles non-linear and multi-modal P-V curves, including partial shading, by dynamically optimizing the operating voltage. Its simplicity, adaptability, and high convergence speed make it a robust choice for PV MPPT applications.

The tracking of the global peak (GP) is contingent upon the manipulation of particle position and velocity strategically adjusted to discern the optimal trajectory of the GP rather than converging onto a local peak (LP). The updated position of a particle, denoted as $D_i^{k+1}$, can be expressed mathematically as follows [22,23]:

$$D_i^{k+1}=D_i^k+v_i^{k+1}$$

(2)

The particle velocity $v_i^{k+1}$ is determined through the utilization of the current position $x_i^k$, particle velocity $v_i^k$, and global best position (G_best) using [22,24,25]:

$$v_i^{k+1}={\omega v}_i^k+c_1{r}_1\left(P_{best,i}-D_i^k\right)+c_2{r}_2\left(G_{best}-D_i^k\right)$$

(3)

In the above equations, ω represents the inertia weight governing the exploration region, while c₁ and c₂ denote the acceleration coefficients [26,27].

The PSO algorithm begins the GPP search by generating a set of duty cycles (D_i) and applying them to the boost converter. The corresponding output voltage and current are then used to compute the initial personal best (P_best) and global best (G_best) values. Subsequently, the duty cycles are updated iteratively based on the position and velocity update from Equations (2) and (3), refining the search for the optimal operating point.

The pseudo code of PSO for tracking the global peak in photovoltaic systems is illustrated in

Table 4. Pseudo code of PSO for tracking the global peak in photovoltaic systems.

1	Initialize the population of particles within the search space, each with a position and velocity; i.e., define PSO coefficients ω, c1, and c2 for the global peak search, sequentially send duty ratios, and ascertain the corresponding power.
2	Evaluate the fitness of each particle using the objective function representing the PV system’s power output under varying environmental conditions.
3	Update the best solution for each particle and the global best solution based on the fitness evaluation.
4	Update the velocity and position of each particle using the following: For particle i: $${\mathrm{v}}_{\mathrm{i}}^{\mathrm{k}+1}={\mathsf{\omega }\mathrm{v}}_{\mathrm{i}}^{\mathrm{k}}+{\mathrm{c}}_1{\mathrm{r}}_1\left({\mathrm{P}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t},\mathrm{i}}-{\mathrm{D}}_{\mathrm{i}}^{\mathrm{k}}\right)+{\mathrm{c}}_2{\mathrm{r}}_2\left({\mathrm{G}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-{\mathrm{D}}_{\mathrm{i}}^{\mathrm{k}}\right)$$ $${\mathrm{D}}_{\mathrm{i}}^{\mathrm{k}+1}={\mathrm{D}}_{\mathrm{i}}^{\mathrm{k}}+{\mathrm{v}}_{\mathrm{i}}^{\mathrm{k}+1}$$ where ω is the inertia weight, c1 and c2 are acceleration factors, r1 and r2 are random values, ${\mathrm{P}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t},\mathrm{i}}$ is the particle i best position, and ${\mathrm{G}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}$ is the global best position.
5	Check for the termination criteria: If the stopping criteria are met, stop the algorithm and output the GPP. Otherwise, go to step 3.

. On the other hand, Figure 4 presents the flowchart that illustrates the PSO-based MPPT process for a PV energy system. It begins with the initialization of particles, velocities, and parameters followed by iterative updates of duty cycles and velocities based on fitness evaluations. The algorithm identifies the best individual and global fitness values to maximize PV power output. The process continues until all iterations are completed, after which the optimal duty cycle is output.

4. Simulation Results and Discussion

The proposed PV power system, connected via a boost converter to the DC load, was implemented using MATLAB/Simulink. The MPPT algorithms employed to track the GPP output were the CSO and PSO. To assess the performance of these two metaheuristic MPPT techniques, numerical simulations were performed under both uniform and PSCs considering static and dynamic scenarios. A comprehensive analysis of the results is provided, highlighting the performance characteristics of the CSO and PSO in these varying environments. The following sections present the key findings of the results for the CSO and PSO methods under static and dynamic environmental conditions in both uniform and partial shading.

Scenario 1: Static Uniform Circumstances

In the scenario of uniform conditions, the PV array receives an equal amount of sunlight, leading to a single MPP. In this scenario, the three PV modules receive identical irradiance levels (1000, 1000, 1000) as a uniform condition, producing an output power and output voltage value of 749 W and 92.5 V at the MPP. Figure 5 indicates the PV output power tracked by the CSO and PSO under these uniform irradiance conditions. The figure demonstrates that both CSO and PSO successfully identify the unique peak power (749 W and 748 W, respectively). However, the CSO outperforms the PSO by exhibiting significantly reduced oscillations and requiring less tracking time (0.6 s) to reach the peak power compared with the PSO, which exhibits higher oscillations and a longer tracking time (1.6 s).

Table 5. Scenario 1: Comparisons of the PSO and the CSO under static uniform conditions.

Cases	Scenario #1
Theoretical values	Irradiance (W/m2)	[1000,1000,1000]
	PMPP (W)	749.34
	VMPP (V)	92.9
PSO results	PPV (W)	748
	VPV (V)	92.1
	Tracking time (s)	1.6
	PSO Efficiency	99.59%
CSO results	PPV (W)	749
	VPV (V)	92.5
	Tracking time (s)	0.6
	PSO Efficiency	99.73%

introduces a comparison of the performance metrics of CSO and PSO under static uniform circumstances.

Scenario 2: Static or Time-Invariant Partial Shading

In the presence of static PSCs, the three modules of the PV are exposed to distinct irradiance levels. This variation results in the formation of multi-peaks on the P-V curve consisting of a single global maximum alongside several local maxima. In this scenario, the solar irradiance levels applied to the modules of the PV are [1000,900,800], leading to multi-peaks with a theoretical GPP value of 637.9 W at a maximum power point voltage (V_MPP) of 95.5 V, as demonstrated in the power–voltage characteristic in Figure 6. The figure also presents the PV-generated power tracked by the CSO and PSO under these non-uniform irradiance conditions. While both CSO and PSO successfully identify the global peak power (637.9 W) and voltage (95.5 V), the CSO method demonstrates superior performance by exhibiting fewer oscillations and a shorter tracking time (0.48 s) compared with the PSO, which shows significant oscillations and a longer tracking time (1.7 s).

Scenario 3: Dynamic Uniform Conditions

In dynamic PSCs, the three PV modules are exposed to the same values of uniform irradiances (1000, 1000, 1000) for a specific interval [0 to 2 s], leading to GPP with a theoretical maximum power and output voltage of 749.3 W and 92.9 V, as illustrated in Figure 7 (P-V curve). Subsequently, the irradiance levels were adjusted to [850,850,850] for the time interval between 2 and 4 s, resulting in a shift to another GPP with theoretical GPP and output voltage values of 638.4 W and 92.8 V, respectively. The major objective of this case is to investigate if the PSO and CSO technique can follow the new GPP or stick to the first GPP. Figure 7 shows the obtained findings of the PV-generated power and the output voltage captured by the CSO and PSO under dynamic uniform conditions. Figure 7 shows that the CSO succeeded in tracking the first GPP with fewer oscillations, and it requires a shorter tracking time to detect the global peak of 749 W. After changing the irradiances to [850,850,850], the CSO technique sticks to the previous position and cannot track the new GMPP at the new place. Figure 7 shows that the PSO can track the first global maximum, with notable oscillations and high tracking time, to detect the global maximum power of 746 W. After changing the irradiances (time variant) to [850,850,850], the PSO technique sticks to the previous position and cannot track the new GMPP at the new place.

Table 6. Scenario 3: Comparisons of the PSO and the CSO under dynamic uniform conditions.

Cases	Scenario #3
Theoretical values	Time	(0–2.0 s)	(2.0–4 s)
	Irradiance (W/m2)	[1000,1000,1000]	[850,850,850]
	PMPP (W)	749.3	638.4
	VMPP (V)	92.9	92.8
PSO results	PPV (W)	746	525
	VPV (V)	92.5	76.4
	PSO Efficiency	98.8%	91.6%
CSO results	PPV (W)	749	593
	VPV (V)	92.5	82.4
	PSO Efficiency	99.55%	93.3%

presents a comparative analysis of the results obtained, evaluating the efficiency of each technique and its capability to follow the maximum power in the shortest possible time.

Scenario 4: Dynamic Partial Shading Conditions

Figure 8 indicates the generated power obtained using the CSO and PSO algorithms under dynamic PSCs. In this scenario, the solar PV modules experience time-dependent variations in irradiance, initially set at [1000,900,800] for the time interval of 0 to 2 s. This variation leads to multiple local power peaks and a single GPP, with corresponding power and output voltage values of 637.9 W and 95.5 V. Subsequently, the irradiance levels shift to [1000,400,900] for the next interval, from 2 to 4 s. This change signifies a transition to a different PSC, causing the formation of a new GPP with generated power and output voltage of 460.1 W and 62 V, respectively, due to the fluctuating irradiance distribution over time. Figure 8 shows that the CSO can track the first GPP with fewer oscillations around the steady state, and it requires a shorter tracking time to detect the global peak power, 637.5 W. After changing the irradiances to PSC2 [1000,400,900], the CSO technique sticks and cannot track the new GMPP of the new PSC2. Figure 8 shows that the PSO can track the first global peak power at irradiances (PSC1) of [1000,900,800] with notable oscillations, and it requires more tracking time to detect the peak power, 637.7 W. After changing the irradiances to PSC2 [1000,400,900], the PSO technique sticks and cannot track the new GMPP of the new PSC2.

Table 7. Scenario 4: Comparisons of the PSO and the CSO under dynamic partial shading circumstances.

Cases	Scenario #4
Theoretical values	Time	(0–2.0 s)	(2.0–4 s)
	Irradiance (W/m2)	[1000,900,800]	[1000,400,900]
	PMPP (W)	637.9	460.1
	VMPP (V)	95.5	62
PSO results	PPV (W)	637.7	332
	VPV (V)	95.5	69.3
	PSO Efficiency	99.9%	72.2%
CSO results	PPV (W)	637.5	333
	VPV (V)	95.5	68.8
	PSO Efficiency	99.9%	72.2%

shows the results obtained in terms of the efficiency of each technique and the effectiveness of each technique in extracting maximum power within the shortest time and a comparative analysis between them.

5. Conclusions

This study aims to model, design, optimize, simulate, and track the GPP of a photovoltaic energy system under uniform and non-uniform (partial shading) conditions; both static and dynamic circumstances have been covered. The two metaheuristic MPPT algorithms, PSO and CSO, have been applied for tracking the GPP under static and dynamic uniform irradiance and partial shading. The results obtained proved that both the PSO and CSO techniques can follow the GPP efficiently and accurately under static uniform and partial shading circumstances. But they failed to follow the GPP under dynamic uniform and non-uniform circumstances. This means that these metaheuristic MPPT algorithms cannot deal with dynamic or time-variant conditions, whether under uniform or non-uniform irradiances. Although they performed well in tracking the GPP, the PSO takes more time to search for the GMPP, and the oscillations of the PSO are higher than those of the CSO. Therefore, the CSO algorithm performed well in comparison with the PSO in terms of GPP tracking, tracking time, and oscillations around the maximum power. The main concluding remarks from this study can be summarized as follows:

• In static uniform conditions, both CSO and PSO effectively tracked the single peak, with CSO demonstrating faster tracking than PSO. For example, CSO attained a PPV of 743.66 W (99.55% efficiency), outperforming PSO’s 738.5 W (98.8% efficiency). Moreover, PSO showed greater oscillations around the GPP compared with CSO, indicating CSO’s superior stability during steady-state operation.
• Under static PSCs, the power–voltage curve displayed a single GPP alongside multiple local peaks. Both algorithms successfully tracked the GPP, but CSO surpassed PSO with quicker tracking and reduced oscillations. In this scenario, both achieved 636.9 W (99.9% efficiency), though CSO’s faster convergence and lower oscillation profile were notable.
• In dynamic uniform conditions, CSO and PSO initially tracked the GPP effectively, but they could not adjust after subsequent irradiance shifts.
• In dynamic PSCs, both algorithms tracked the GPP at first, but they were unable to follow the new GPP following changes in irradiance.

In summary, CSO and PSO are adept at handling static irradiance conditions, whether uniform or non-uniform (PSCs), successfully tracking the global power in scenarios with a single GPP (uniform conditions) or a GPP with multiple local peaks (static PSCs). They can effectively differentiate between global and local peaks, capturing the global one with precision. However, when conditions change dynamically over time, both CSO and PSO struggle to adapt to the new GPP, whether under uniform or PSC scenarios. This reveals their limitation in managing dynamic or time-varying conditions, whether uniform or PSCs, without specific enhancements. Such shortcomings lead to significant energy and efficiency losses, resulting in substantial time and cost impacts. We aim to address these challenges in future research by exploring potential solutions. Moreover, future work will include experimental validation on a commercial MCU, assessing real-time performance, memory usage, and control stability to ensure practical deployment in PV systems.