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Scientific Reports volume 15, Article number: 38432 (2025) Cite this article
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This paper proposes a hybrid control framework for a two-stage grid-connected photovoltaic (PV) system, integrating a Recurrent Neural Network (RNN)-based Space Vector Pulse Width Modulation (SVPWM) and a Crayfish Optimization Algorithm-based Maximum Power Point Tracking (COA-MPPT). The COA-MPPT governs the front-end DC–DC boost converter, achieving up to 32% faster tracking response, 28% lower overshoot, and 35% reduction in steady-state error compared to Perturb and Observe (P&O), Grey Wolf Optimization (GWO), Falcon Optimization Algorithm (FOA), Improved Coot Optimizer (ICO), and Horse Herd Optimization Algorithm (HHO). The extracted power is transferred to the grid through a Voltage Source Converter (VSC) using the RNN-SVPWM, which reduces current Total Harmonic Distortion (THD) by 71.5% compared to conventional SVPWM and by 59.5% compared to ANN-SVPWM by achieving 1.62% THD (with RNN) vs. 5.68% (conventional) and 4.0% (ANN) respectively. The proposed system is evaluated under four operating conditions: (i) constant uniform irradiance, (ii) variable uniform irradiance, (iii) variable non-uniform irradiance with partial shading, and (iv) a real-time 24-hour uniform irradiance profile from NSRDB data. Across all scenarios, the DC-link voltage is consistently regulated at 500 V with over 40% lower fluctuation under rapid irradiance changes. These results confirm that the proposed RNN–SVPWM and COA–MPPT combination delivers superior power quality, faster dynamic tracking, and improved stability, offering a robust solution for modern grid-integrated PV systems.
The global demand for clean and renewable energy has driven significant advancements in photovoltaic (PV) technology, especially in grid-connected systems¹. However, the inherent intermittency and nonlinear behaviour of solar irradiance pose critical challenges in ensuring consistent power extraction and quality grid integration. Two-stage PV systems, consisting of a DC-DC converter followed by a DC-AC inverter, have emerged as a reliable architecture for improving power quality and maximizing energy yield. Yet, the overall performance of such systems heavily depends on the effectiveness of the control strategies employed in both stages—namely, Maximum Power Point Tracking (MPPT) and inverter modulation techniques. Conventional MPPT algorithms such as Perturb and Observe (P&O) or Incremental Conductance, while simple, suffer from oscillations near the maximum power point (MPP), slow tracking speeds, and reduced performance under rapidly changing or partial shading conditions^2,3. In recent years, swarm intelligence and bio-inspired optimization algorithms have been explored to address these limitations.
In⁴, authors proposed the PSO algorithm for MPPT, demonstrating its effectiveness in tracking the global maximum power point (GMPP) under partial shading conditions. The algorithm’s simplicity and robustness make it suitable for dynamic environmental changes. However, its performance can degrade at low irradiance levels, and improper parameter tuning may lead to premature convergence. ​In⁵, authors enhanced the standard PSO by integrating direct duty cycle control, resulting in faster tracking speeds and reduced power fluctuations during transient operations. This improvement was validated under real conditions with a 10-hour irradiance profile. Nonetheless, the method’s complexity increases due to the additional control mechanisms, and it may require careful tuning to maintain stability.​.
The Artificial Bee Colony (ABC) algorithm⁶, inspired by honey bee foraging, provides global optimization, fast MPP tracking under changing weather, simple implementation, and robustness to noise, but may converge slowly and is sensitive to parameter selection. Ant Colony Optimization (ACO)⁷, based on ant foraging, handles various partial shading conditions with robustness, simple control, and convergence independent of initial samples, though it requires complex multi-variable optimization. Grey Wolf Optimization (GWO)⁸, combined with P&O, achieves fast GMPP convergence without oscillations or tuning, but involves high mathematical computation, increasing system complexity. Fuzzy Particle Swarm Optimization (FPSO)⁹ merges fuzzy logic with PSO to reduce switching losses, self-tune membership functions, and eliminate PI controllers; however, fuzzy rule design relies on approximation and trial-and-error, which is time-consuming and may not ensure optimality.​.
The PSO–P&O Hybrid Algorithm¹⁰ combines PSO’s global search with P&O’s simplicity for improved transient performance and simpler implementation, though oscillations around the MPP may still occur. ANFIS¹¹ integrates neural networks and fuzzy logic to adapt to varying conditions using historical and real-time data, effectively handling non-linear irradiance and temperature changes, but requires high computational resources and extensive training. The GA–P&O hybrid¹² uses GA for global exploration and P&O for fine-tuning, avoiding local maxima and enabling accurate MPP tracking in complex conditions, but with higher computational complexity, longer convergence, and greater implementation costs. ANN-assisted SMC MPPT¹³ employs ANN to predict the GMPP from voltage, current, or irradiance data, with SMC refining estimates, achieving high efficiency and robustness under rapid irradiance changes, though integration complexity and model accuracy requirements are challenges.
The Resilient Backpropagation Neural Network (Rprop-NN) MPPT algorithm¹⁴ uses a supervision mechanism to calibrate the reference and limit short-circuit current from incorrect predictions, enabling effective MPP tracking under fast-changing environments and partial shading, though its performance depends on training data quality and supervision design. The adaptive step size IncCond MPPT¹⁵ varies the step size based on the power–voltage curve slope, achieving faster convergence without loss of accuracy, but adds complexity in parameter selection. The Adaptive Incremental Conductance MPPT¹⁶ incorporates accelerating and decelerating factors for quick MPP tracking and reduced oscillations, though challenges remain under rapidly changing conditions. The Hybrid Radial Movement Optimization–Teaching-Learning-Based Optimization (HRMOTLBO)¹⁷ combines RMO and TLBO to overcome local maxima issues in partial shading, improving tracking speed and reducing fluctuations, but with higher computational and implementation complexity.
A modified Artificial Rabbit Optimization (ARO) algorithm for MPPT is proposed in¹⁸, inspired by rabbit foraging behaviour to enhance exploration–exploitation balance, improving tracking accuracy and convergence speed under varying PV conditions; however, it is sensitive to parameter settings, and poor tuning may cause suboptimal tracking or oscillations. A hybrid PSO–Artificial Bee Colony (ABC) algorithm in¹⁹ combines PSO’s global search with ABC’s local search, achieving a boost converter efficiency of 78.26% at a 20% duty cycle, though it increases complexity and requires careful balancing to avoid premature convergence or excessive computation. The Hybrid Lightning Search Algorithm–Whale Optimization Algorithm (HLSA–WOA) in²⁰ uses LSA to fine-tune WOA parameters, achieving high accuracy, low steady-state ripple, and adaptability to environmental changes, but requires precise PV model parameter estimation. An adaptive metaheuristic study in²¹ evaluates GWO, PSO, and the Pelican Optimization Algorithm (POA) under fluctuating shading, with POA showing fast convergence and high accuracy; however, adaptive methods increase computational complexity and require real-time parameter tuning. An Enhanced Dandelion Optimizer (EDO) in²² improves local minima avoidance and convergence under partial shading, offering robustness but at the cost of higher computational demands and parameter dependency.
In²³, the authors proposed an innovative MPPT approach that integrates a Feedforward Neural Network (FNN) with an Ant Colony Optimization (ACO)-tuned Proportional-Integral (PI) controller to enhance the performance of standalone PV systems under dynamic operating conditions. The method is combined with a hybrid battery–supercapacitor energy storage system to improve transient response, energy management, and stability. The system was evaluated against conventional Perturb and Observe (P&O) and PSO–P&O methods under three scenarios: variable irradiance with constant load, constant irradiance with variable load, and mixed conditions. Simulation results demonstrated superior tracking efficiency, reduced power loss, and enhanced stability for the proposed method across all scenarios. In²⁴, a hybrid MPPT strategy was introduced, combining hyperparameter-optimized Gaussian Process Regression (GPR) with High Order Sliding Mode Control (HOSMC) to address the challenges of partial shading conditions (PSCs) in PV systems. The methodology operates in two stages: first, an optimized GPR model, trained on real-time irradiance and temperature data, predicts reference voltage values; second, the HOSMC uses these references to generate control signals by minimizing the voltage tracking error. The approach was benchmarked against the conventional Incremental Conductance (INC) method and the metaheuristic-based Grey Wolf Optimization (GWO) algorithm using data from multiple months (February, May, August, and October) to capture seasonal variations. Table 1 provides a concise summary of the MPPT algorithms discussed in the literature review.
In²⁵ authors provided a comprehensive review of various SVPWM control strategies for voltage source inverters (VSIs). They categorized SVPWM techniques into Bus Clamping PWM, Advanced Bus Clamping PWM, and Hybrid PWM, analyzing their impact on inverter output voltage and current. The study also discussed the triangular comparison approach, known as carrier-based SVPWM, which offers benefits like lower computation and memory requirements. However, the paper noted that while these techniques improve performance, they may introduce complexity in implementation and require careful design considerations. In²⁶ authors explored optimized hybrid SVPWM techniques for three-level VSIs, focusing on reducing total harmonic distortion (THD) and switching losses. They introduced a new parameter called Harmonic Loss, combining weighted THD and normalized switching loss, to guide the optimization process. A spatial region identification algorithm was proposed to determine optimized switching sequences. The study demonstrated that the proposed techniques effectively balance performance and efficiency. However, the complexity of the optimization process and the need for precise control may pose challenges in practical applications.
The design and implementation of an SVPWM inverter using soft computing techniques is presented in²⁷. They highlighted the advantages of SVPWM, such as higher voltage generation with low THD and compatibility with field-oriented control schemes. The study emphasized the importance of harmonic elimination techniques to improve output spectra quality. While the approach showed promise, the authors acknowledged that harmonics and system reliability remain concerns, necessitating further development of SVPWM techniques for broader control system applications. A neural network-based SVPWM approach for capacitor voltage balancing in three-phase three-level improved power quality converters is proposed in²⁸. The method utilized artificial neural networks (ANNs) to generate reference vectors, aiming to achieve better voltage balance and reduce THD. The study demonstrated that the ANN-based SVPWM could effectively manage capacitor voltage imbalances. However, the implementation complexity and the requirement for extensive training data for the neural networks were identified as potential drawbacks. In²⁹, authors developed an SVPWM strategy for modular multilevel converters (MMCs) in power systems. The proposed method aimed to control output voltage, suppress circulating currents, and balance submodule voltages. By simplifying the positioning and calculation process of multilevel SVPWM, the strategy achieved constant computational burden and scalability to MMCs with any number of submodules. The study reported a 48.4% reduction in circulating current, indicating lower power loss. However, the approach’s effectiveness under varying operating conditions and its adaptability to different system configurations require further investigation. An experimental analysis of various SVPWM techniques is conducted in³⁰ for dual three-phase induction motor drives and evaluated different SVPWM schemes, including a modified method, by analyzing harmonic components in phase currents and voltages. The study provided detailed modelling and simulation results, validated through laboratory experiments. The findings highlighted the advantages of SVPWM in reducing stator harmonic currents and torque pulsations. Nonetheless, the complexity of implementing SVPWM in dual three-phase systems and the need for precise control algorithms were noted as challenges.​.
In³¹, authors focused on the realization of SVPWM for three-phase VSIs. The study outlined key steps in implementing SVPWM, such as reference signal clarification, sector identification, voltage vector determination, and switching state calculation. The proposed system aimed to improve inverter output voltage, minimize voltage stress across switches, and reduce THD and electromagnetic interference. Simulation results verified the system’s performance. However, the study emphasized that practical implementation would require careful consideration of system parameters and potential trade-offs between performance and complexity. ​In³², introduced a simplified SVPWM algorithm for high-speed permanent magnet synchronous machine (PMSM) drives in flywheel energy storage systems. The proposed method aimed to reduce computational complexity and improve real-time performance. Experimental results demonstrated that the simplified SVPWM algorithm effectively reduced current THD and eddy current losses. The study highlighted the algorithm’s suitability for high-speed applications. However, the approach’s applicability to other types of machines and its performance under different load conditions warrant further exploration.
In³³, authors provided a comprehensive review of SVPWM techniques for common-mode voltage (CMV) mitigation in photovoltaic multi-level inverters. The study discussed the challenges of achieving CMV elimination while maintaining neutral-point voltage (NPV) control. Various SVPWM strategies were analyzed, including those based on small hexagon decomposition and virtual space vector modulation. The review highlighted the trade-offs between CMV reduction, implementation complexity, THD, and DC voltage utilization. The authors concluded that while certain SVPWM methods offer partial CMV reduction, achieving complete elimination remains challenging. In²⁵, authors surveyed SVPWM techniques for two-level inverters, focusing on their application in various power electronic systems. The study examined different SVPWM methods, including conventional, bus clamping, and advanced bus clamping techniques. The authors analyzed the impact of these methods on inverter performance, highlighting their advantages in terms of voltage utilization and harmonic reduction. However, the survey also noted that the increased complexity of advanced SVPWM techniques could pose challenges in practical implementations, especially in systems with limited computational resources.​.
Among above mentioned optimization algorithms, the Crayfish Optimization Algorithm (COA), inspired by the intelligent foraging behaviour of crayfish, has shown promise due to its enhanced convergence speed and ability to escape local optima. When employed in MPPT, COA offers precise and stable power tracking even in challenging irradiance scenarios. Simultaneously, the inverter stage, typically implemented using a Voltage Source Converter (VSC), plays a crucial role in transferring the extracted power to the AC grid with minimal distortion. The modulation technique used in the VSC significantly affects output current quality, system losses, and overall efficiency. Traditional Space Vector Pulse Width Modulation (SVPWM) is widely used due to its better utilization of DC voltage and reduced switching losses. However, its performance can degrade under nonlinear conditions or parameter variations. To enhance modulation precision, Artificial Neural Network (ANN) based SVPWM methods have been proposed, yet they are limited by their feedforward structure and lack of memory, making them less adaptive to time-dependent system dynamics.
To address these issues, this paper introduces a novel hybrid control scheme combining Recurrent Neural Network (RNN)-based SVPWM with COA-based MPPT (COA-MPPT) for a two-stage grid-integrated PV system. The RNN, with its inherent capability to model temporal sequences, improves modulation quality by generating more adaptive and dynamic switching signals compared to conventional and ANN-based SVPWM techniques. The COA-MPPT ensures robust and accurate power tracking across a wide range of irradiance profiles, including uniform, variable, partial shading, and real-time solar data conditions.
The effectiveness of the proposed approach is validated through detailed simulation studies in MATLAB/Simulink under four distinct cases: (i) constant uniform irradiance, (ii) time-varying but uniform irradiance, (iii) non-uniform irradiance with partial shading, and (iv) real-time irradiance data over a 24-hour period. Comparative results demonstrate significant improvements in terms of power extraction, dynamic response, DC link voltage regulation, and Total Harmonic Distortion (THD) of the grid current. The proposed RNN-SVPWM and COA-MPPT combination exhibits superior performance, making it a promising solution for enhancing the reliability and efficiency of modern PV systems.
Grid integrated PV generation system with COA based MPPT and RNN based SVPWM.
A three-phase, two-stage grid-connected photovoltaic system was illustrated in Fig. 1. The system comprises several key components, including a PV array, a DC-DC boost converter, a control unit for Maximum Power Point Tracking (MPPT), a three-phase three level inverter with Voltage Source Control (VSC), an LC filter, and a step-up power transformer. These components work together to efficiently convert solar energy into electrical power and integrate it into the grid. In PV generator, multiple PV modules are connected in series and parallel configurations to create a PV array, which can generate the required voltage and current for the system.
The DC-DC boost converter is employed to step up the voltage from the PV array to a level suitable for the inverter. The MPPT control unit ensures that the PV array operates at its maximum power point under varying environmental conditions, such as changes in solar irradiance and temperature. The three-phase three level inverter converts the DC power from the PV array into AC power, which is synchronized with the grid using VSC. The LC filter is used to reduce harmonics and ensure the quality of the AC power injected into the grid. Finally, the step-up transformer increases the voltage level to match the grid requirements, enabling seamless integration of the solar power into the electrical network.
The two-diode model presented in Fig. 2³⁴ is an improved representation of a photovoltaic (PV) cell that enhances accuracy over the traditional single-diode model. This model accounts for both recombination losses in the depletion region and current leakage effects, making it more precise for realistic PV behaviour under varying environmental conditions.
Two diode model of PV module.
The output current ((:I)) of the two-diode PV model is calculated using the following equation:
The diode currents are calculated using the Shockley equation for each diode:
(:I) = Output current (A), (:{I}_{ph})​ = Photocurrent generated by sunlight (A), (:{I}_{d1},:{I}_{d2})=Diffusion current due to the first and second diodes (A), (:V)=Terminal voltage across the PV module (V), (:{R}_{s})​=Series resistance (Ω), (:{R}_{sh})=Shunt resistance (Ω), (:{I}_{r1},:{I}_{r2})=Reverse saturation currents for each diode (A), (:{n}_{1}) and (:{n}_{2})=Ideality factors for each diode, (:{V}_{t})=Thermal voltage
(:k)=Boltzmann constant ((:1.38times:{10}^{-23}:J/K)), (:T)=Absolute temperature (K), (:q)=Electron charge ((:1.6times:{10}^{-19}:C)).
Figure 3 illustrate the I-V and P-V characteristics of the PV array utilized in this work, demonstrating its performance under varying solar irradiance levels and temperature conditions. Parameters of the PV array are given in Table 4.
PV array characteristics.
The DC-DC boost converter plays a crucial role in enhancing the voltage output provided by the PV array. The primary function of the DC-DC boost converter is to step up the DC voltage generated by the PV array to a higher, stable voltage level suitable for subsequent power conversion stages. The boost converter enables the integration of a Maximum Power Point Tracking (MPPT) technique, which is essential for improving the overall voltage quality and enhancing the system’s controllability. By implementing the MPPT algorithm, the boost converter can dynamically adjust its duty cycle to ensure optimal power extraction from the PV array under varying environmental conditions such as changing irradiance and temperature levels. In this system, an average model of the boost converter has been employed to regulate the supply voltage in accordance with a predefined reference voltage, ensuring precise voltage control to fulfil the converter’s intended functionality. The equivalent circuit diagram of the boost converter is illustrated in Fig. 4³⁵, which shows the key components involved in its operation.
Boost Converter.
The control mechanism of the boost converter is governed by the MPPT unit, which generates the necessary control signal to regulate the converter’s duty cycle. This duty cycle adjustment is vital to maintain stable output voltage and maximize power extraction from the PV array.
The duty cycle ((:D)) required for the boost converter is calculated using the following equation:
(:D)=Duty cycle of the converter, (:{V}_{PV})​ =Input voltage from the PV array, (:{V}_{DC})​=Desired output voltage of the boost converter.
To design the boost converter efficiently, the inductance ((:L)) and capacitance ((:C)) values must be carefully selected to ensure proper energy storage, ripple reduction, and voltage stabilization. These values are determined using the following equations:
Inductance Calculation:
(:L)=Inductance value (Henry), (:{V}_{DC})​=Desired output voltage from the boost converter, (:{Delta:}{I}_{DC}) =Desired ripple current in the inductor, (:{f}_{sw})=Switching frequency of the converter.
Capacitance Calculation:
(:C)=Capacitance value (Farads), (:{I}_{dc})=Current supplied to the inverter, (:{{Delta:}V}_{dc})=Allowable voltage ripple at the output of the boost converter, (:f)=Switching frequency.
The output of the DC-DC boost converter is subsequently fed into the three-level inverter, which converts the stabilized DC voltage into an AC voltage signal. Three-level inverters produce output voltage waveforms that are closer to a sinusoidal shape compared to traditional two-level inverters. This improved waveform quality reduces the harmonic content, ensuring the system meets IEEE-519 standards for grid compliance. Lower THD results in better power quality, minimizing electromagnetic interference and reducing heating effects in electrical components. Due to the presence of additional voltage levels, the voltage stress across each power semiconductor device is reduced. This reduction in voltage stress minimizes switching losses, enhancing the inverter’s overall efficiency. Improved efficiency is particularly important for PV systems where maximizing energy yield is crucial. The improved sinusoidal waveform output ensures smooth power delivery to the grid, reducing disturbances and improving overall grid stability. An RNN based SVPWM is chosen as modulation strategy for three level inverter due to predictive control capability and intelligent learning ability.
The integration of RNN with SVPWM for controlling a three-level inverter in a grid-connected PV system enhances system performance, improves voltage control, and optimizes power quality, making it a highly effective solution for modern renewable energy systems. One key advantage of using RNN-based SVPWM is its superior predictive control capability. RNNs excel in processing sequential data and identifying patterns, which makes them ideal for predicting inverter behaviour in dynamic conditions. Since PV systems often experience rapid fluctuations in irradiance and temperature, the predictive nature of RNN helps the SVPWM controller adjust switching signals in real-time. This ensures precise control of the inverter, minimizing voltage fluctuations and enhancing system stability.
The adaptability of RNN-based SVPWM further strengthens its effectiveness in PV systems. RNNs continuously learn and adapt to changing system conditions, making them ideal for managing nonlinearities inherent in three-level inverters. RNN-based SVPWM offers faster convergence and real-time optimization. The RNN’s sequential data processing capability allows the inverter to respond quickly to changes in input voltage, load demand, or grid frequency. The RNN-based SVPWM algorithm effectively manages the inverter’s voltage space vectors, ensuring the inverter operates closer to its maximum voltage capacity.
Figure 5 illustrates the schematic diagram of the implemented control scheme for three level VSC.
Decoupled vector control Strategy for Three level inverter.
The decoupled vector control strategy plays a significant role in ensuring the stable and efficient operation of a grid-connected photovoltaic (PV) system integrated with a three-level Voltage Source Converter (VSC). This control technique effectively manages the active and reactive power flow between the PV system and the grid by decoupling the control of the d-axis and q-axis components. The control system begins with a Phase-Locked Loop (PLL) unit, which ensures synchronization between the VSC control scheme and the PCC by generating a reference angle (:omega:t). In this control scheme, the DC link voltage control is essential for ensuring stable power exchange. The actual DC link voltage (:{V}_{dc}) is continuously monitored and compared with its reference value (:{V}_{dc}^{ref}). The error signal (:e{V}_{dc}={V}_{dc}^{ref}-{V}_{dc})​ is generated and processed by a PI controller. The controller’s output signal is then passed through a limiter to produce the reference d-axis current (:{I}_{d}^{ref})​.
The reference signal (:{I}_{d}^{ref}) is supplied to the current controller, where it plays a crucial role in regulating the active power injected into the grid. Meanwhile, three-phase grid voltages (:{V}_{abc}^{g}) and grid currents (:{I}_{abc}^{g}) are measured directly from the grid and subsequently converted to per-unit (p.u.) values to simplify the control process. Following the per-unit conversion, the voltage and current signals are transformed into the synchronous rotating (:dq0) reference frame. In this frame, the voltage components ((:{V}_{d}:and:{V}_{q})) and current components ((:{I}_{d}:and:{I}_{q})) are obtained. The (:dq0) transformation allows the decoupled control of active and reactive power, which is fundamental to the stability and performance of the system.
The d-axis and q-axis components of the current ((:{I}_{d}:and:{I}_{q})) are further processed through PI controllers. The PI controllers regulate the grid current by comparing the measured (:{I}_{d}:and:{I}_{q})​ with their reference values, (:{I}_{d}^{ref}:and:{I}_{q}^{ref})​, respectively. Since the system operates at a unity power factor, the reference reactive current (:{I}_{q}^{ref}) is set to zero. This ensures that the system supplies only active power to the grid, minimizing unwanted reactive power injection. The outputs of these PI controllers are the voltage signals in the dq frame. To achieve true decoupling between the d-axis and q-axis currents, cross-coupling compensation is introduced. This compensation accounts for the interaction between the two axes caused by the grid inductance. The decoupling terms are added to the voltages to ensure that changes in one axis do not affect the other. Then the reference voltage is given as
The reference voltages are then transformed back into the three-phase abc frame using the inverse Park transformation. These transformed voltages are used to generate the PWM signals by using proposed RNN based SVPWM for the three-level inverter, which ultimately controls the power flow into the grid.
Figure 6 illustrates the schematic diagram of a three-level IGBT inverter in PV grid integrated system.
PV grid integrated system with three level inverter.
In the three-level NPC inverter, each phase can convert three voltage levels: P (positive bus voltage), O (neutral point), and N (negative bus voltage). State P occurs when switches (:{S}_{1A}) and (:{S}_{2A})​ are closed, connecting phase A to the positive terminal of the DC bus. State N occurs when switches (:{S}_{3A}) and (:{S}_{4A}) are closed, connecting phase A to the negative terminal of the DC bus. At State O, phase A is clamped to the neutral point. This is achieved by turning on either (:{S}_{2A}) or (:{S}_{3A}) depending on the polarity of the phase current. If the phase current is positive, (:{S}_{2A}) is turned on, whereas if the phase current is negative, (:{S}_{3A}) is activated. To ensure neutral-point voltage balancing, it is crucial that the average current injected into the neutral point (O) remains zero over a complete switching cycle. This balance prevents voltage drift in the DC-link capacitors, which could otherwise cause instability in the inverter output.
Figure 6 illustrates the PV-grid integrated system that utilizes an ANN based SVPWM technique for optimal inverter control. The neural network receives three primary input signals: (:{V}_{d}^{*}), (:{V}_{q}^{*})​ and (:{theta:}_{e}^{*}). These inputs represent the command voltage vector in the synchronous reference frame, where (:{V}_{d}^{*}) and (:{V}_{q}^{*})​ define the voltage magnitude, and (:{theta:}_{e}^{*})​ determines its angular position. The ANN processes these signals in real-time and generates the corresponding PWM pulses for the inverter, ensuring efficient operation and smooth power flow between the PV system and the grid. The switching states of the three-level inverter are summarized in Table 2, where the three phases A, B, and C can assume one of three possible states: P, O and N. This results in a total of 27 switching states for the inverter. Among these, 24 are active switching states, which contribute to power transfer, while the remaining three are zero states (PPP, OOO, and NNN) that reside at the origin of the space vector diagram. The zero states do not contribute to voltage generation and act as resting states for the inverter.
(a) Space vector representation of three level inverter (b) Sector (:I) space vectors with switching times.
The space voltage vector representation with 27 switching states for the three-level inverter is shown in Fig. 7. Since each phase can take one of the three voltage states (P, O, or N), the inverter can generate a set of voltage vectors arranged in a hexagonal pattern. The space vector plane is divided into six major sectors labelled (:I:to:VI), and each sector is further subdivided into four operational regions (:1:to:4). This division results in a total of 24 regions of operation across the entire hexagonal space. The inner hexagon highlights Region 1 of each sector, where the lowest voltage magnitudes occur. The command voltage vector (:left({V}^{*}right)) trajectory, expands outward from the origin as the modulation index increases. A key observation in the switching process is that the neutral current will flow through the neutral point (O) in all switching states except the zero states (PPP, OOO, NNN) and the outermost hexagon corner states. This is a critical factor in maintaining neutral point voltage balance, which must be carefully managed to prevent DC-link capacitor imbalance.
The magnitude of the reference voltage vector ((:{V}^{*})) is computed as:
This vector determines the inverter’s operating point within the space vector hexagon. The system operates within the under-modulation region if the command voltage trajectory remains inside the inner inscribed hexagon.
The modulation index mmm is defined as:
where:
(:{V}^{*}) is the command or reference voltage magnitude.
(:{V}_{1sw})​ is the peak value of the phase fundamental voltage when the inverter operates in square-wave mode (maximum modulation).
The maximum limit of the under-modulation region is reached when the modulation index satisfies the condition:
This indicates that a three-level inverter must always operate below the square-wave mode, meaning it must remain within modulation levels where (:m<1) to avoid excessive harmonics and switching stress.
As depicted in Fig. 7(a), the operation of the inverter is classified into two distinct modes based on the trajectory of the command voltage vector ((:{V}^{*})). Mode 1 is defined when the trajectory of (:{V}^{*}) remains within the inner hexagon, whereas Mode 2 occurs when the trajectory extends beyond the inner hexagon. A hybrid mode, which encompasses both Mode 1 and Mode 2, is characterized by the movement of (:{V}^{*}) through regions 1 and 3 of all six sectors.
In Space Vector PWM (SVPWM), the inverter’s voltage vectors are carefully selected to minimize harmonic distortion at the output. The selected vectors typically correspond to the apexes of the triangle that encloses the reference voltage vector. Figure 7(b) illustrates an example of a sector triangle A, which is formed by the voltage vectors (:{V}_{o}),(:{V}_{2}) and (:{V}_{5}). If the command voltage vector (:{V}^{*}) is located within region 3, the SVPWM method ensures that the following fundamental equations are satisfied:
where (:{T}_{a},:{T}_{b}) and (:{T}_{c}) represent the respective time intervals allocated to each voltage vector, and (:{T}_{s})​ is the sampling time. The analytical expressions for these time intervals in all the regions across the six sectors are presented in³⁶.
The modulation factor (:n) is defined as:
where (:{V}^{*}) is the command voltage magnitude, and (:{V}_{d})​ represents the DC-link voltage. These time intervals are carefully distributed to generate symmetrical PWM pulses while simultaneously ensuring neutral-point voltage balancing. The corresponding switching sequences for each phase voltage across all regions and sectors are summarized in Table 3. Notably, in opposite sectors (:(I-IV,:II-V:and:III-VI)), the switching sequences are designed to be complementary, ensuring neutral-point voltage balancing throughout the operation.
Figure 8 illustrates the PWM waveforms for one phase across the region of Sector A. Each switching pattern, computed over a duration of (:frac{{T}_{s}}{2}), is symmetrically repeated in the subsequent (:frac{{T}_{s}}{2}) interval with appropriate segmentation of the time intervals (:{T}_{a},:{T}_{b}) and (:{T}_{c}). This segmentation ensures the generation of symmetrical PWM waveforms.
Waveforms showing sequence of switching states for region-1.
It is observed that similar wave patterns occur in Sectors C and E (odd-numbered sectors). However, when PWM waves are plotted in even-numbered sectors (B, D, and F), the pulsed and notched states switch roles, where pulsed waves appear as notched waves and vice versa. Detailed expressions for turn-on times for different phases are given in³⁷.
For example, the Phase-A turn-on time expressions are given by:
where (:K=sqrt{3}{T}_{s}/4{V}_{d})​​ and (:S) denotes the sector name. These equations are also valid for phases B and C, with appropriate phase shifts.
Since the PWM waveforms exhibit symmetry, the turn-off times can be directly determined as:
The corresponding P and N state pulse widths are directly observable from the PWM waveforms in Fig. 8. The remaining time intervals in each phase correspond to the zero state, ensuring proper switching transitions and maintaining voltage balance.
Turn on times can be rewritten in a more generalized form as:
(:fleft({theta:}_{e}right)) is the function defining the turn-on signal at unit voltage. The plot of Eq. (17) for P-state turn-on times at varying values of (:{V}^{*}) is shown in Fig. 9. It is evident that Mode 1 ends when the turn-on time curves reach saturation at (:{T}_{s}/2). The functions (:fleft({theta:}_{e}right)) for P and N states exhibit symmetry but are opposite in phase.
P-state turn-on times at varying values of (:{V}^{*}).
From Fig. 9, it is possible to extract a common bias time of (:3{T}_{s}/8) along with a variable component dependent on (:fleft({theta:}_{e}right)). The digital values of (:fleft({theta:}_{e}right)), computed for different angles in all modes and phases, can be stored in a lookup table for training a neural network-based control system. The values of (:{T}_{AP-ON}) and (:{T}_{AN-ON})​ can be obtained by solving the respective equations derived, enabling precise ANN-based SVPWM generation for the three-level inverter.
The derivation of turn-on times and the corresponding (:fleft({theta:}_{e}right)) functions, enables the implementation of a neural network-based Space Vector Modulation (SVM) strategy. This implementation is structured into two distinct sections: Neural Network Section and Multiplication and Processing Section. Neural Network Section is responsible for generating the function (:fleft({theta:}_{e}right)) based on the electrical angle (:{theta:}_{e})​. The neural network computes the required switching functions without the need for explicit sector identification. In Multiplication and Processing Section the function (:fleft({theta:}_{e}right)) is multiplied linearly with the voltage reference signal (:{V}^{*}) to determine the turn-on times of the inverter switches. As illustrated in Fig. 10, the neural network topology is structured as a 1–24–12 network, where the input layer consists of one neuron, which takes the electrical angle ​(:{theta:}_{e}) as input. The hidden layer consists of 24 neurons, each utilizing a sigmoidal activation function to capture complex nonlinear relationships between the input and output. The output layer consists of 12 neurons, also employing a sigmoidal activation function, to produce turn-on time signals. Each of the 12 output signals corresponds to a turn-on time required to generate the appropriate PWM waveforms. These outputs are distributed across the three phases, with four signals for each phase, two for the P-state (positive bus voltage connection) and two for the N-state (negative bus voltage connection).
To enhance the efficiency of the PWM generation process, the segmentation of turn-on time signals has been carefully designed. The primary reason for this segmentation is to eliminate the need for explicit sector identification. Instead of assigning different PWM patterns based on sector location, the neural network directly computes switching times for each state. Additionally, this approach facilitates the use of a single timer at the output stage, simplifying the hardware implementation of the PWM generation process. Once the turn-on times have been computed by the neural network, these outputs are multiplied by the voltage reference signal (:{V}^{*}) and further scaled by a factor (:{K}^{*}). The scaled outputs are then converted into digital words (:{W}_{T-ON})​, which represent the timing values required to control the switching devices of the inverter. The digital words (:{W}_{T-ON})​ are subsequently compared with the output of a single UP/DOWN counter. This comparison process ensures that the inverter switches operate at the precise instants required to generate the correct PWM pulses. The processed signals are then passed through a logic block, which organizes and sequences them into the final PWM waveforms. These waveforms control the switching states of the inverter, ensuring optimal performance while maintaining neutral-point voltage balancing. This neural network-based approach offers several advantages over conventional SVM techniques, including reduced computational complexity, simplified sector management, and optimized real-time control, making it a highly efficient solution for three-level inverters.
ANN based SVPWM with 1-24-12 structure³⁶.
The segmentation and processing steps are consistent across all signal components. For illustration, let’s examine the A-phase’s positive switching signals, specifically the function pairs (:{f}_{AP1}left({theta:}_{e}right)) and (:{f}_{AP2}left({theta:}_{e}right)). These signal functions are derived from the total modulation signal (:{f}_{AP}left({theta:}_{e}right)), and their structure changes depending on which of the six sectors the reference voltage vector (:{V}^{*}) lies in
The corresponding digital timer word expressions are
(:{W}_{TB})​ represents a fixed time of (:left(frac{3}{8}right){T}_{s}), (:{K}^{{prime:}}) is a proportional constant to scale the voltage reference, (:Wleft({f}_{AP2}right)) is saturated to a fixed digital value for (:frac{{T}_{s}}{2}).
Even Sectors (B, D, F):
For even sectors, signal expressions change to account for different vector positions:
Digital equivalents for these segments are:
This signal processing ensures the correct PWM waveforms are generated even when the command vector is in an even sector. The ANN plays a central role in determining the correct sector and computing (:{f}_{AP}left({theta:}_{e}right)). The ANN is trained to quickly identify the current operating sector based on the electrical angle (:{theta:}_{e})​, and to output the modulation function (:{f}_{AP}left({theta:}_{e}right)) accordingly. This avoids traditional, computation-heavy trigonometric calculations, reducing processing delay and improving real-time performance. Once the ANN outputs are segmented into (:{f}_{AP1}left({theta:}_{e}right)) and (:{f}_{AP2}left({theta:}_{e}right))​, logic circuits convert them into switching signals. These are then used by a unified timer to control the inverter’s switches. The process is repeated for each phase (A, B, C), with both positive and negative states. Switching signals are constructed by combining (:Wleft({f}_{AP1}right)) and (:Wleft({f}_{AP2}right)) for each phase. Digital logic ensures accurate timing and pulse generation, yielding clean and symmetric PWM waveforms.
The RNN-based SVPWM technique leverages the network’s ability to retain memory of past states, making it highly suitable for real-time control applications where the system’s dynamics evolve over time. The RNN receives the same primary input signals as the ANN: (:{V}_{d}^{*})​, (:{V}_{q}^{*}) and (:{theta:}_{e}^{*}), which represent the command voltage vector in the synchronous reference frame. However, unlike the ANN, the RNN processes these inputs sequentially, allowing it to capture the temporal relationships between successive states of the inverter. This capability is particularly beneficial in maintaining neutral-point voltage balancing and ensuring smooth transitions between switching states.
RNN based SVPWM with 1-36-36-12 structure.
The implementation of RNN-based SVM consists of two main sections. The first section is the RNN processing unit, which receives the electrical angle (:{theta:}_{e}^{*}) and generates the function (:fleft({theta:}_{e}right)) while incorporating past voltage and angle information. This allows for sequential learning and adaptation, making the modulation technique more robust to dynamic changes in the system. The second section involves the multiplication of (:fleft({theta:}_{e}right)) with the reference voltage (:{V}^{*}) to compute the PWM switching times for the inverter. As illustrated in Fig. 11, the RNN topology for SVM implementation is structured as a 1–36–36 − 12 recurrent network, similar to the ANN structure but with an essential difference—recurrent connections that enable the network to store previous states. This network consists of an input layer with one neuron, which receives the electrical angle (:{theta:}_{e}) as input, two hidden layers with 36 neurons, and an output layer with 12 neurons, also using a sigmoidal activation function, to produce PWM turn-on times. Each hidden layer is employed a sigmoidal activation function and recurrent connections allow to retain information from previous time steps, enabling the network to adapt to system variations and predict switching states based on prior voltage vectors. The recurrent nature of hidden and output layers help in improving switching pattern continuity and reducing abrupt changes in PWM waveforms.
The 1-36-36-12 RNN architecture features two hidden layers with 36 neurons each, compared to the single hidden layer with 24 neurons in the 1-24-12 structure. This increased depth and width allow the network to capture more complex relationships between the input signals and the output switching sequences. The additional hidden layer enables the network to hierarchically extract higher-order features from the input data, which is particularly beneficial for modelling the nonlinear dynamics of the inverter and the temporal evolution of the command voltage vector (:{V}^{*}). This hierarchical feature extraction improves the network’s ability to generate accurate and context-aware switching sequences, ensuring optimal performance under varying operating conditions.
The output of the first hidden layer (:{h}_{1}left(tright)) at time step (:t) can be expressed as:
(:xleft(tright)) is the input at time (:t) ((:{theta:}_{e})), (:{W}_{{h}_{1}}) is the weight matrix of the first hidden layer, (:{b}_{{h}_{1}})​ is the bias vector, (:sigma:) is the activation function (sigmoid), (:{h}_{1}(t-1)) is the hidden state from the previous time step.
The output of the second hidden layer (:{h}_{2}left(tright)) is computed similarly:
This two-layer recurrent structure allows the network to model both short-term and long-term temporal dependencies, which is critical for maintaining neutral-point voltage balancing and ensuring smooth transitions between switching states.
The 1-36-36-12 RNN structure excels at maintaining neutral-point voltage balancing due to its enhanced ability to model the temporal evolution of the neutral-point current. The additional hidden layer allows the network to capture the history of the neutral-point current over multiple switching cycles, enabling it to predict and compensate for voltage drift in the DC-link capacitors more effectively.
For instance, the network can learn to adjust the switching times (:{T}_{AP-ON}) and (:{T}_{AN-ON}) based on the accumulated neutral-point current over time. This is particularly important when the command voltage vector (:{V}^{*}) extends beyond the inner hexagon, and the neutral-point current becomes more dynamic. The improved modeling capacity of the 1-36-36-12 structure ensures that the average current injected into the neutral point remains zero over a complete switching cycle, preventing voltage drift and maintaining system stability. While the 1-36-36-12 structure is more complex than the 1-24-12 structure, it can reduce computational complexity in real-time control by eliminating the need for explicit sector identification. The additional hidden layer allows the network to directly compute the switching times for each state based on the sequential input data, simplifying the control algorithm and reducing the computational burden on the microcontroller. The 1-36-36-12 RNN structure can generate more accurate PWM waveforms, reducing harmonic distortion at the inverter output. The additional hidden layer allows the network to model the harmonic content of the output voltage more effectively, enabling it to select the optimal switching sequences for minimizing harmonics. This is particularly important in PV-grid integrated systems, where harmonic distortion can lead to power quality issues and grid instability.
Algorithm for RNN based SVPWM.
The Crayfish Optimization Algorithm (COA) is a swarm intelligence-based metaheuristic technique inspired by the natural behaviours of crayfish, including foraging, summer vacation, and competitive interactions. The foraging and competition stages correspond to the exploitation phase, where crayfish refine their search in a local region to enhance solution quality. The summer vacation stage represents the exploration phase, where crayfish move toward unexplored regions, diversifying the search space. These behaviours ensure a balance between exploration and exploitation, allowing COA to effectively navigate complex optimization landscapes.
At the beginning of the algorithm, a population of crayfish (:X) is randomly initialized within the given solution space. The position of each crayfish (:{X}_{i})​ is defined as a potential solution, expressed as:
where (:dim) represents the number of variables or dimensions in the optimization problem. By applying the objective function (:f(cdot:)) to (:{X}_{i})​, the corresponding fitness value is obtained, determining the solution’s quality. Temperature, a key parameter in COA, acts as a random environmental factor affecting crayfish behavior. When the temperature is too high, crayfish enter the summer vacation or competition stage. When it is within a suitable range, they engage in foraging, moving toward the optimal solution (:{X}_{food})​.
In multi-dimensional optimization problems, each crayfish is represented as a (:1times:dim), where each column corresponds to a different variable. The position matrix of the crayfish population is defined as:
where (:N) is the total number of crayfish in the population, and each (:{X}_{i,j}) ​ represents the position of the (:{i}^{th}) crayfish in the (:{j}^{th}) dimension. The initial position of each crayfish is randomly assigned within its upper ((:u{b}_{j})​) and lower ((:l{b}_{j})​) bounds, computed as:
where (:rand) is a uniformly distributed random number between 0 and 1. This initialization ensures a diverse population, enabling COA to explore a wide search space effectively.
The temperature of the environment, which influences crayfish behaviour, is randomly generated as:
ensuring a temperature range of (:{20}^{circ:}C) to (:{35}^{circ:}C). The food intake probability (:P) is modeled using a Gaussian-like function to reflect how temperature influences crayfish feeding:
where (:{C}_{1}) ​is a scaling constant, (:mu:) is the optimal temperature for feeding (typically (:{25}^{circ:}C)), and (:sigma:) controls the temperature range that affects food intake. Crayfish exhibit strong foraging behavior within (:{20}^{circ:}C) to (:{30}^{circ:}C), with peak activity around (:{25}^{circ:}C).
The Crayfish Optimization Algorithm (COA) is inspired by the foraging, summer vacation, and competitive behaviours of crayfish. The foraging and competition stages represent the exploitation phase of COA, while the summer vacation stage corresponds to the exploration phase. To capture the characteristics of swarm intelligence optimization, the crayfish population (:X) is defined at the initial stage of the algorithm. The position of the (:i) th crayfish, denoted as (:{X}_{i}) represents a potential solution in the optimization process. It is defined as (:left{{X}_{i}={X}_{i,1},{X}_{i,2},{X}_{i,3}dots:.{X}_{i,dim}right}), where (:dim) is the number of characteristics in the optimization problem, also known as the problem’s dimension. By applying the function (:f(cdot:)) to (:{X}_{i}) a corresponding solution is obtained, referred to as the fitness value. The exploration and exploitation processes in COA are controlled by temperature, a random constant representing the environmental conditions of each individual. When the temperature is too high, COA transitions into either the summer vacation stage or the competition stage. During the summer vacation stage, a new solution is generated by updating the individual’s position (:{X}_{i}) based on the cave position (:{X}_{shade})​. When the temperature is suitable, COA enters the foraging stage. In this stage, the food location represents the best position, also known as the optimal solution. The food size is determined by the current solution’s fitness value (:{fitness}_{i}) (obtained from (:{X}_{i}) ​) and the optimal solution’s fitness value (:{fitness}_{food})​, obtained from the best solution). When the food is appropriate, crayfish update their position (:{X}_{i}) to generate new solutions based on their current location, the food intake constant p, and the food position (:{X}_{food}).
When the food is too large, crayfish use their claws to tear it apart before consuming it alternately with their second and third walking legs. To simulate this alternating feeding behaviour, sine and cosine functions are incorporated. In crayfish, food intake is regulated and influenced by temperature, following a positively skewed distribution.
In multi-dimensional optimization problems, each crayfish is represented as a (:1times:dim) matrix, where each column corresponds to a potential solution. Within the set of variables (:left{{X}_{i,1},{X}_{i,2}dots:.{X}_{i,dim}right}), each variable (:{X}_{i}) must remain within its defined upper and lower boundaries. The initialization of COA involves randomly generating a set of candidate solutions X within the solution space. These candidate solutions are determined by the population size (:N) and the problem’s dimensionality (:dim). The initialization process of the COA algorithm is represented in Eq. (33).
Here, (:X) represents the initial population positions, where (:N) is the total number of individuals, and (:dim) denotes the dimensionality of the population. (:{X}_{i,J}) refers to the position of the (:i) th individual in the (:j) th dimension, with its value determined by Eq. (34).
Here, (:{lb}_{j}) denotes the lower bound of the jth dimension, while (:{ub}_{j})represents the upper bound. The term rand refers to a randomly generated number.
Temperature changes influence crayfish behaviour, causing them to transition through different stages. The temperature is defined by Eq. (35). When it exceeds 30 °C, crayfish seek cooler environments to escape the heat. Crayfish exhibit foraging behaviour at optimal temperatures, with their feeding activity influenced by temperature variations. Their feeding range falls between 15 °C and 30 °C, with 25 °C being ideal. As a result, their feeding amount can be approximated by a normal distribution, reflecting the temperature’s impact. Crayfish exhibit strong foraging behaviour between 20 °C and 30 °C. Therefore, COA defines a temperature range of 20 °C to 35 °C. The mathematical model for crayfish intake is presented in Eq. (36).
where, temp signifies the temperature of the environment where the crayfish is located.
Here, µ represents the optimal temperature for crayfish, while σ and (:{C}_{1})​ regulate their food intake across different temperatures.
When the temperature exceeds 30 °C, it becomes too high for crayfish. At this point, they escape into caves to escape the heat. The cave (:{X}_{shade}) is defined as follows:
Here, (:{X}_{G})​ denotes the best position achieved so far through iterations, while (:{X}_{L})​ represents the optimal position of the current population.
The competition among crayfish for caves is a random event. When rand < 0.5, it indicates no other crayfish are competing, allowing the crayfish to enter the cave directly for summer vacation. In this case, the crayfish’s movement into the cave follows Eq. (38).
Here, t represents the current iteration number, while t + 1 denotes the next generation iteration. (:{C}_{2})​ follows a decreasing curve, as defined in Eq. (39).
Here, (:T) denotes the maximum number of iterations.
During the summer vacation stage, the crayfish aim to move toward the cave, representing the optimal solution. As they approach the cave, individuals get closer to the optimal solution, enhancing the exploitation capability of COA and accelerating algorithm convergence.
When the temperature exceeds 30 °C and rand ≥ 0.5, multiple crayfish compete for the cave. In this case, they engage in a struggle to secure the cave. The competition process is governed by Eq. (40).
Here, z is a randomly selected crayfish individual, as defined in Eq. (41).
During the competition stage, crayfish engage in contests, with each crayfish (:{X}_{i})​ adjusting its position based on the position (:{X}_{z}) of another crayfish. This adjustment expands the search range of COA and enhances the algorithm’s exploration capability.
When the temperature is ≤ 30, conditions are ideal for crayfish to forage. During this time, they move toward food sources. Upon finding food, they assess its size. If the food is too large, they use their claws to tear it apart and consume it alternately with their second and third walking feet. The food location (:{X}_{food})​ is defined as follows:
​
Food size Q is defined as:
Here, (:{C}_{3})​ is the food factor, representing the largest food, with a constant value of 3. (:{fitness}_{i})​ denotes the fitness value of the ith crayfish, while (:{fitness}_{food})​ ​ represents the fitness value of the food location.
A crayfish judges food size based on the largest available food. When (:Q>frac{left(C3+1right)}{2}:)​, the food is considered too large. In this case, the crayfish uses its first claw foot to tear it apart. The corresponding mathematical equation is as follows:
Once the food is shredded into smaller pieces, the crayfish use their second and third claws alternately to pick up and consume it. To simulate this alternating motion, a combination of sine and cosine functions is used. Additionally, the amount of food obtained by the crayfish is influenced by its intake capacity. The corresponding foraging equation is as follows:
When (:Qle:(C3+1)/2) the crayfish simply moves toward the food and consumes it directly. The corresponding equation is as follows:
During the foraging stage, crayfish adopt different feeding strategies based on the food size Q, with (:{X}_{food})​ representing the optimal solution. If Q is an appropriate size, the crayfish move toward and consume the food. However, if Q is too large, it signifies a significant gap between the crayfish and the optimal solution. Therefore, (:{X}_{food})​ should be adjusted and brought closer to the crayfish while regulating the randomness of the food intake enhancement algorithm. Through the foraging stage, COA moves toward the optimal solution, improving its exploitation capability and ensuring strong convergence performance.
Step 1: Parameter Definition and Population Initialization Define the maximum number of iterations (:T), population size (:N), problem dimension (:dim) (corresponding to the duty cycle search space), and upper ((:{u}_{b})) and lower ((:{l}_{b})) bounds of the duty cycle. Initialize the crayfish population (:X) randomly within these bounds using Eq. (34). The inputs (:{V}_{pv}) and (:{I}_{pv}) are measured from the PV array, and the initial power (:{P}_{pv}={V}_{pv}times:{I}_{pv}) is computed.
Step 2: Ambient Temperature Definition Determine the ambient temperature parameter using Eq. (35). This value regulates the behavioural stage of each crayfish and influences the search dynamics of the COA in tracking the Maximum Power Point (MPP).
Step 3: Summer Vacation and Competition Stages If (:temp:>:30) and (:rand:<:0.5), the COA enters the summer vacation stage, where a new duty cycle position (:{X}_{ij}^{t+1}) is computed using Eq. (38), based on the shaded cave position (:{X}_{shade})​ and the current crayfish duty cycle (:{X}_{ij}^{t})​. Proceed to Step 5.
If (:temp:>:30) and (:randge:0.5), the COA enters the competition stage, where two crayfish compete for the same cave position using Eq. (40). The updated duty cycle position is determined based on (:{X}_{shade}) and the difference between the competing crayfish positions (:({X}_{ij}^{t}-{X}_{zj}^{t})). Proceed to Step 5.
Step 4: Foraging Stage If (:temple:30), the COA switches to the foraging stage. The food intake (:p) and food size (:Q) are calculated using Eqs. (36) and (43).
If (:Q>frac{{C}_{3}+1}{2}), shred the food according to Eq. (44) and update the duty cycle position via Eq. (45).
If (:Qle:frac{{C}_{3}+1}{2}), update the duty cycle position using Eq. (46). After updating, proceed to Step 5.
Step 5: Evaluation Function For each crayfish, evaluate the generated duty cycle by computing the PV output power (:{P}_{pv}) ​and the fitness function, which aims to maximize (:{P}_{pv}) while maintaining grid power quality. Check if the termination condition (maximum iterations or negligible power change) is met. If not, return to Step 2.
Step 6: Output Return the best duty cycle (:{X}_{best}) corresponding to the highest recorded PV output power ((:fitnes{s}_{best})​) and apply it to the DC–DC converter in the MPPT control loop.
Detailed flowchart of the optimization algorithm is presented in Fig. 12.
Flow chart of COA.
Simulations were conducted on the grid-integrated photovoltaic (PV) generation system illustrated in Fig. 1 to evaluate the performance and effectiveness of the proposed Recurrent Neural Network (RNN)-based Space Vector Pulse Width Modulation (SVPWM) strategy for the inverter and the Crayfish Optimization Algorithm (COA)-based Maximum Power Point Tracking (MPPT) method for the boost converter. The system’s specifications and detailed parameters are summarized in Table 4. The PV generation system is designed to deliver 100 kW of electrical power and is connected to the utility grid, which operates at 11 kV and 50 Hz. The integration is achieved through a two-stage power conversion system comprising a boost converter followed by a voltage source inverter.
The PV array consists of a total of 328 individual modules, with each module rated at 305.592 W. These modules are arranged such that 41 modules are connected in parallel to form a single string, and eight such strings are connected in series. This configuration enables the system to achieve a maximum output power of approximately 100.23 kW under standard test conditions. The boost converter, which regulates the DC voltage level from the PV array, is controlled using the COA-based MPPT algorithm. This algorithm dynamically adjusts the duty cycle of the converter to ensure the PV system operates at its maximum power point, even under varying environmental conditions. Meanwhile, the inverter is controlled using a direct-quadrature (d–q) axis voltage control scheme in conjunction with the RNN-based SVPWM technique, which enhances the quality of the injected current and ensures stable grid interfacing.
To thoroughly assess the dynamic behaviour and robustness of the proposed control strategies, four different irradiance scenarios were simulated. In the first case, the system was subjected to constant and uniform irradiance across all eight strings, representing ideal solar conditions. The second case introduced variable but still uniform irradiance, simulating a scenario where sunlight intensity changes over time but remains consistent across all strings. The third case introduced complexity by applying variable and non-uniform irradiance across the eight strings, effectively simulating partial shading conditions that often occur in real-world PV installations. Lastly, the fourth scenario utilized a real-time irradiance profile captured over a 24-hour period with uniform exposure across the array. This case is particularly relevant for assessing the real-world applicability of the proposed system, as it mirrors the typical daily solar pattern experienced in practical PV deployments.
These simulation cases comprehensively test the proposed RNN-based SVPWM and COA MPPT control techniques, ensuring their performance is validated across a wide range of realistic operating conditions. For the performance validation results are compared with conventional MPPT algorithms like perturb and observe (P&O)³⁸, Grey Wolf Optimization (GWO)⁸, Falcon Optimization algorithm (FOA)³⁹, Improved Coot Optimizer (ICO)⁴⁰ and Horse Herd Optimization algorithm (HHO)⁴¹.
Constant uniform irradiance for 8 strings.
Variable uniform irradiance for 8 strings.
Variable non uniform irradiance for 8 strings (partial shading).
Real time uniform irradiance profile of 24 h for 8 strings.
Constant uniform irradiance for 8 strings.
In Case 1, the performance of PV system under constant and uniform irradiance conditions was analysed. A consistent solar irradiance of (:1000:W/{m}^{2}) was applied to 8 PV strings, and the system was simulated using the proposed COA-MPPT algorithm and RNN-based SVPWM. To evaluate the effectiveness of the proposed RNN-SVPWM, the simulation results were compared with those obtained using conventional SVPWM and ANN-based SVPWM. The DC reference voltage for the VSC was set at 500 V, and a DQ-based control strategy (as detailed in Sect. 3) was used for the conversion process. The PV system was designed to produce a maximum power output of 100 kW, which was transferred from the DC to AC side using the VSC.
Figure 13 illustrates the AC side voltage and three-phase current waveforms obtained using the conventional SVPWM method. The VSC was responsible for delivering the DC-side power to the AC grid, and the generated current waveforms aligned with expectations based on the reference values. To assess power quality, the Total Harmonic Distortion (THD) of the output currents was analysed and is presented in Fig. 14. The simulation results show that the fundamental magnitude of the output current was 68.75 A, with a THD of 5.68%. This indicates a moderate level of harmonic distortion typical for traditional SVPWM techniques.
Subsequently, the conventional SVPWM method was replaced with an ANN-based SVPWM for improved performance. Figure 15 presents the corresponding voltage and current waveforms. The ANN used in this case was trained and tested offline within the under-modulation range (Vs = 20–1200 V and fs = 0–50 Hz), with a sampling time (Ts) of 0.2 ms, equivalent to a switching frequency (fs) of 5 kHz. Training data were obtained by simulating the conventional SVPWM algorithm, and the network was trained over a full cycle with 2° angular increments. The training process, which took approximately one hour on a 3.6 GHz Pentium-based PC, required 15,000 epochs to achieve a sum of squared error (SSE) of 0.002. Due to its interpolation and learning capabilities, the ANN provided high-resolution pulse width signals in real-time. As shown in Fig. 16, the output current fundamental magnitude was maintained at 68.75 A, while the THD was reduced to 4.0%, demonstrating improved performance over the conventional method.
Finally, the ANN-based SVPWM was replaced with a RNN-based SVPWM to further enhance dynamic performance and harmonic quality. The adopted RNN architecture had a structure of 1-36-36-12, and it was used to generate SVPWM signals for the VSC. Figures 17 and 18 show the VSC output phase voltage and corresponding three-phase current waveforms. The results illustrate that the RNN effectively controls the output, ensuring synchronization and power transfer to the AC grid. Figure 18 presents the current harmonic analysis, where the current fundamental magnitude was recorded at 68.74 A. Notably, the RNN-SVPWM achieved a significantly lower THD of just 1.62%, indicating superior harmonic performance and improved waveform quality compared to both the conventional and ANN-based methods.
Figure 19 compares the terminal voltage of the PV array under constant irradiance conditions using different maximum power point tracking (MPPT) algorithms, including the conventional methods (P&O, GWO, FOA, ICO, and HHO) as well as the proposed COA-based MPPT. The simulation results clearly indicate that the proposed COA-MPPT in combination with the RNN-based SVPWM provides superior voltage regulation, as the PV terminal voltage remains more stable and converges to its optimal value faster than with the conventional algorithms.
Figure 20 illustrates the PV terminal current for all algorithms. Once again, the COA-MPPT outperforms its counterparts by producing smoother and more consistent current output, minimizing fluctuations. Figure 21 presents the generated PV power across different methods. The proposed COA-MPPT consistently extracts higher power from the PV array, highlighting its improved tracking ability under uniform irradiance. Figure 22 shows the duty cycle of the boost converter, and it is evident that the COA-based approach ensures a more stable and well-regulated duty cycle, which directly contributes to better performance of the overall DC-DC conversion stage. Figure 23 presents comparison of the DC side voltage of VSC for all algorithms.
Converted voltage and currents by the VSC of the PV integrated grid system using conventional SVPWM⁴².
THD of the converted current by VSC using conventional SVPWM.
Converted voltage and currents by the VSC of the PV integrated grid system using ANN based SVPWM.
THD of the converted current by VSC using ANN based SVPWM⁴³.
Converted voltage and currents by the VSC of the PV integrated grid system using RNN based SVPWM.
THD of the converted current by VSC using RNN based SVPWM.
PV terminal voltage for constant and uniform irradiance.
PV terminal current for constant and uniform irradiance.
PV generated power for constant and uniform irradiance.
Duty Cycle of boost converter.
DC side voltage of the VSC.
Table 5 presents a comprehensive comparison of the transient and steady-state performance of six MPPT algorithms—P&O, GWO, FOA, ICO, HHO, and the proposed COA—based on their impact on the DC link voltage, PV terminal voltage, and PV terminal current. Each algorithm is evaluated using key performance metrics such as rise time ((:{t}_{r})), peak overshoot ((:{M}_{p})), settling time ((:{t}_{s})), steady-state ripple ((:{R}_{ss})), and steady-state error ((:{e}_{ss})), offering a holistic view of the system’s dynamic response. Focusing first on the DC link voltage, the proposed COA algorithm demonstrates a significantly improved response. It exhibits the fastest rise time of 0.038 s, indicating rapid convergence to the desired voltage level. Furthermore, it achieves the lowest peak overshoot at just 0.6%, ensuring minimal deviation beyond the target voltage, which is crucial for system stability. The settling time is also reduced to 0.1 s, confirming that the system reaches steady-state conditions more swiftly than with other algorithms. Additionally, COA minimizes voltage ripple to 1.15% and maintains the lowest steady-state error of 0.94%, indicating high voltage regulation accuracy. In contrast, algorithms like GWO show a higher overshoot (14.64%) and slower rise time (0.085s), highlighting their relatively sluggish and unstable transient response.
When analyzing the PV terminal voltage, COA once again outperforms the conventional algorithms. It provides the quickest rise time of 0.008 s and the smallest overshoot at 0.67%, ensuring a fast and controlled transition to the optimal operating point. The settling time is substantially improved, reaching stability within just 0.11 s—much faster than the P&O method, which requires over a second. The ripple and steady-state error are also minimized with COA, measured at 0.98% and 0.82% respectively. These improvements underline the algorithm’s superior ability to manage voltage fluctuations and maintain consistent output during operation.
A similar performance trend is observed in the PV terminal current response. The COA-based system displays the lowest rise time of 0.009 s and the least peak overshoot at 0.94%, reflecting a highly responsive and stable current control. Settling time is again minimal at 0.11 s, while the ripple (1.28%) and steady-state error (0.86%) are the lowest among all methods. This demonstrates that the COA algorithm not only enhances voltage regulation but also ensures smoother and more reliable current delivery, which is essential for maximizing power transfer efficiency and protecting downstream components.
The results in Table 5 clearly highlight the effectiveness of the proposed COA-MPPT algorithm and RNN-SVPWM. It consistently delivers faster dynamic responses, lower overshoots, reduced ripples, and improved accuracy across all evaluated electrical parameters, establishing it as a superior choice over traditional and nature-inspired optimization methods for MPPT in PV systems.
Table 6 presents the statistical evaluation of different MPPT algorithms based on 100 independent simulation runs for reaching the DC link MPPT voltage. Three performance indicators are considered: Standard Deviation (SD), Variance, and Mean voltage achieved. The SD values indicate the stability and consistency of each algorithm’s performance. A lower SD corresponds to more reliable convergence toward the MPPT point. Among all methods, the COA algorithm achieved the lowest SD (0.15354), followed closely by HHO (0.2237), which highlights their exceptional stability. In contrast, the conventional P&O algorithm had the highest SD (1.3856), indicating significant variability in its tracking performance.
The Variance results follow the same trend as SD since it is the square of the standard deviation. Again, COA (0.0236) and HHO (0.05) recorded the smallest variances, confirming their robustness and consistency across multiple runs, while P&O (1.9199) showed the widest spread in results. The Mean values represent the average DC link voltage achieved during the 100 runs. Here, the COA algorithm achieved the highest mean voltage of 495.33 V, closely followed by HHO with 494.95 V. Both significantly outperformed the conventional P&O algorithm, which achieved an average of 489.34 V, indicating that the proposed methods not only stabilize the MPPT tracking process but also converge closer to the optimal voltage point. The results demonstrate that the proposed COA and HHO algorithms offer superior accuracy, faster convergence, and more consistent performance compared to conventional MPPT techniques and other metaheuristic approaches such as GWO, FOA, and ICO.
Variable uniform irradiance for 8 strings.
In this case, the PV system was tested under dynamically varying irradiance conditions, applied uniformly across all 8 PV strings. The irradiance profile was designed to simulate real-world environmental fluctuations over a 10-second simulation period. Initially, from 0 to 2 s, the irradiance was maintained at 1000 W/m². It was then reduced to 800 W/m² between 2 and 4 s, followed by 600 W/m² from 4 to 6 s. Subsequently, it dropped further to 400 W/m² between 6 and 8 s and then increased to 700 W/m² for the final interval from 8 to 10 s.
The system performance was analysed using both the proposed COA-MPPT algorithm and conventional MPPT techniques for comparison. Figure 24 illustrates the behaviour of the PV terminal voltage over time. It is evident from the figure that the proposed algorithm maintains a more stable voltage profile despite the changes in irradiance. Voltage transitions between different irradiance levels are smooth and rapid, with minimal oscillations or delays. In contrast, conventional algorithms exhibit larger voltage dips and slower settling behaviour during transitions, indicating their limited adaptability to rapidly changing environmental conditions. Figure 25 presents the terminal current of the PV array. Similar to the voltage response, the current generated by the PV system under the proposed MPPT algorithm is smoother and more stable. It closely tracks the irradiance pattern, increasing and decreasing proportionally with the incident solar energy. The conventional algorithms, however, show more pronounced fluctuations and delayed responses, which can contribute to reduced energy harvesting efficiency.
The comparison of the PV output power under different irradiance levels is shown in Fig. 26. The results clearly highlight the superior power tracking capability of the proposed algorithm. With COA-MPPT, the PV system was able to extract 100.234 kW from 0 to 2 s when irradiance was at its maximum (1000 W/m²). During the subsequent intervals, the power generated was 80.903 kW (800 W/m²), 61.162 kW (600 W/m²), 40.884 kW (400 W/m²), and 71.106 kW (700 W/m²) respectively. These power values closely align with the available solar energy, demonstrating the high tracking efficiency and adaptability of the COA-based controller. On the other hand, the conventional algorithms failed to match this performance, as they exhibited lower power output and slower convergence following each irradiance change.
The duty cycle of the boost converter, shown in Fig. 27, further supports the effectiveness of the proposed algorithm. With COA-MPPT, the duty cycle adjusts responsively and accurately to irradiance changes, ensuring optimal voltage conversion and minimal instability. The duty cycles generated by conventional algorithms appear more erratic, with sharper variations and longer stabilization periods, which can negatively affect downstream power conversion and load performance.
Figure 28 presents the regulated DC link voltage, which is maintained at a nominal value of 500 V. The proposed algorithm demonstrates excellent voltage regulation across all irradiance transitions. While minor voltage fluctuations are observed during irradiance shifts, they are quickly corrected, and the voltage stabilizes within a very short duration. In contrast, the conventional algorithms show more significant deviations from the reference voltage during these intervals, indicating weaker voltage regulation performance.
The results from this simulation under variable irradiance conditions confirm the robustness and superiority of the proposed COA-MPPT algorithm. It ensures faster dynamic response, reduced voltage and current fluctuations, higher power extraction, and improved overall system stability compared to conventional MPPT techniques.
PV terminal voltage.
PV terminal current.
PV generated power.
duty cycle of boost converter.
DC side voltage of the VSC.
Variable non uniform irradiance for 8 strings (partial shading).
In this simulation case, the PV system is subjected to non-uniform irradiance levels across its 8 PV strings, simulating partial shading conditions commonly encountered in real-world scenarios. Unlike uniform irradiance cases, where all strings receive identical sunlight intensity, this test introduces varying irradiance profiles to individual strings at different time intervals, thereby increasing the complexity of power tracking and conversion. The objective is to evaluate the robustness and adaptability of the proposed COA-MPPT algorithm in comparison to conventional MPPT techniques.
The irradiance pattern is defined over a 10-second window with five distinct operating intervals. From 0 to 2 s, all PV strings receive a uniform irradiance of 1000 W/m², establishing the baseline full-sun condition. Between 2 and 4 s, the system encounters non-uniform irradiance levels: [1000, 1000, 800, 800, 600, 600, 700, 700] W/m², introducing mild shading effects. As the simulation progresses from 4 to 6 s, the shading deepens with irradiance levels changing to [900, 900, 750, 750, 450, 450, 550, 550] W/m², causing greater disparity across strings. In the next interval, 6 to 8 s, a more complex shading pattern is observed: [800, 800, 1000, 1000, 500, 500, 900, 900] W/m². Finally, between 8 and 10 s, the system faces severe shading, with string irradiances dropping to [500, 500, 300, 300, 800, 800, 950, 950] W/m².
The impact of these irradiance changes on the system’s electrical performance is analysed using both the proposed and conventional MPPT methods. Figure 29 presents the PV terminal voltage over time. The proposed COA-MPPT algorithm demonstrates superior voltage regulation across all irradiance intervals. It maintains a stable and well-regulated terminal voltage, with quick transitions and minimal oscillations during shading changes. In contrast, conventional algorithms show higher voltage instability, particularly during the rapid and irregular irradiance transitions introduced by partial shading.
Figure 30 illustrates the PV terminal current behaviour. The current output with COA-MPPT accurately reflects the effective irradiance received by the array, displaying smooth and consistent variation as the irradiance profile changes. This indicates the algorithm’s effective ability to handle partial shading and dynamically adjust its control strategy. The current traces under conventional algorithms, however, show more abrupt changes, with pronounced dips and delays that signify poor tracking during irradiance transitions.
The power output comparison is provided in Fig. 31, which further highlights the efficiency of the proposed algorithm. Under full irradiance (0–2 s), the system generates 100.234 kW, the theoretical maximum. As partial shading begins, the generated power decreases accordingly. Between 2 and 4 s, the PV system delivers 66.657 kW, and during 4 to 6 s, it drops to 50.887 kW. Interestingly, during 6 to 8 s, as some strings regain higher irradiance, the power output increases to 63.678 kW. In the most challenging condition between 8 and 10 s, the proposed algorithm still manages to extract 41.8858 kW, demonstrating its ability to locate and operate at the global maximum power point even under severe mismatch conditions. Comparatively, conventional algorithms often settle at local maxima under such conditions, resulting in significantly lower power extraction.
The control action of the boost converter, reflected in the duty cycle profile shown in Fig. 32, further supports the advantage of the proposed method. With COA-MPPT, the duty cycle adapts responsively to the varying irradiance across all strings, maintaining conversion efficiency while minimizing transients. In contrast, conventional methods generate less consistent duty cycles with sharper fluctuations and longer stabilization times, which can adversely affect the downstream inverter and grid interface.
Figure 33 displays the DC link voltage, which is regulated at a reference value of 500 V. The proposed COA-MPPT algorithm ensures this voltage remains nearly constant throughout the simulation, with only minimal deviations occurring during irradiance transitions. These deviations are rapidly corrected, preserving voltage stability. Conversely, conventional MPPT methods exhibit more significant voltage fluctuations during irradiance changes, indicating their inability to effectively mitigate the effects of partial shading on the system’s DC bus stability.
The simulation results under non-uniform irradiance and partial shading conditions clearly demonstrate the superior performance of the proposed COA-MPPT algorithm. It ensures enhanced voltage and current stability, maximized power output, and robust control of the DC link voltage, outperforming traditional MPPT algorithms especially in complex and variable operating environments.
PV terminal voltage.
PV terminal current.
PV generated power.
Duty cycle.
DC side voltage of the VSC.
Performance Evaluation Under Real-Time Uniform Irradiance Profile (24-Hour Duration).
In this simulation scenario, the PV system’s performance is evaluated using a real-time irradiance profile over a 24-hour period, applied uniformly across all 8 PV strings. The irradiance data, representing realistic environmental conditions, has been sourced from the National Solar Radiation Database (NSRDB) using its data viewer tool⁴⁴. This case study is critical for assessing the long-term performance and adaptability of the proposed MPPT and control algorithms under natural diurnal variations in solar intensity, including periods of low irradiation during early morning and late evening, and peak solar irradiance during midday.
The collected irradiance data captures the natural solar radiation trend typically observed throughout a day—beginning at zero or near-zero values during the night, gradually increasing in the morning, peaking around solar noon, and then symmetrically decreasing toward the evening. By applying this profile uniformly across all strings, the simulation replicates a consistent exposure scenario, eliminating mismatches between strings and focusing on the algorithm’s tracking performance across a dynamic irradiance curve. Irradiance profile is presented in Fig. 34.
Figure 35 illustrates the PV terminal voltage response throughout the 24-hour cycle when controlled using the proposed COA-MPPT algorithm. The voltage profile closely tracks the natural solar pattern. It remains at or near zero during nighttime (due to absence of irradiance), rises steadily with increasing solar input, and stabilizes during midday when the irradiance is relatively constant and high. The voltage remains stable throughout these transitions, with the proposed algorithm ensuring smooth voltage regulation and minimal ripple during fluctuations in solar input.
The corresponding PV terminal current, presented in Fig. 36, also demonstrates excellent responsiveness to the real-time irradiance changes. As expected, the current output begins to increase after sunrise, peaks during the midday period, and decreases toward sunset. The smooth and continuous current variation underlines the ability of the COA-MPPT algorithm to adapt in real time and maintain tracking accuracy across the full irradiance range. The most critical performance indicator, the PV-generated power, is shown in Fig. 37. This figure confirms the high efficiency of the proposed algorithm in maximizing power extraction. Power generation mirrors the irradiance profile, beginning from zero, gradually increasing with the rising sun, reaching a maximum during the peak solar hours, and decreasing thereafter. Importantly, the algorithm demonstrates the ability to operate precisely at or near the maximum power point across a wide range of irradiance levels, maximizing energy yield throughout the day.
Figure 38 shows the duty cycle of the boost converter as generated by the COA-MPPT algorithm. The duty cycle dynamically adjusts in real time, responding accurately to variations in solar input to ensure effective DC-DC conversion. During low irradiance periods, the duty cycle increases to boost the voltage appropriately, whereas under high irradiance, it decreases to prevent overvoltage, maintaining system stability and efficiency. Figure 39 presents the regulated DC link voltage maintained by the boost converter. Despite continuous variations in solar irradiance over 24 h, the DC link voltage remains well-regulated at its reference value of 500 V. Minor deviations occur during sunrise and sunset transitions, but these are quickly corrected by the controller, indicating excellent voltage regulation capability of the proposed system. Compared to conventional methods (not shown here), this stability highlights the effectiveness of the COA-based MPPT and control strategies in maintaining consistent DC bus performance under realistic and long-duration solar conditions. The proposed COA-MPPT algorithm, when applied under a real-time 24-hour uniform irradiance profile, demonstrates superior performance in voltage and current regulation, optimal power tracking, adaptive duty cycle control, and robust DC link voltage stabilization. This ensures not only efficient energy harvesting but also long-term operational stability for grid-connected or standalone PV systems.
24 h irradiance profile.
PV terminal voltage for 24 h irradiance profile.
PV terminal current for 24 h irradiance profile.
PV generated power for 24 h irradiance profile.
Duty cycle of the boost converter 24 h irradiance profile.
DC side voltage of VSC for 24 h irradiance profile.
The proposed RNN-based SVPWM control strategy combined with the COA-based MPPT has been rigorously evaluated across multiple simulation scenarios to demonstrate its effectiveness for two-stage grid-integrated PV systems. The performance of the proposed system was compared against conventional techniques including Perturb and Observe (P&O), Grey Wolf Optimization (GWO), Falcon Optimization algorithm (FOA), Improved Coot Optimizer (ICO) and Horse Herd Optimization algorithm (HHO), with each method tested under varying irradiance conditions and partial shading environments. The analysis included evaluation of PV voltage and current stability, power generation, THD of output currents, DC link regulation, and the dynamic performance of the system. In the first simulation case with constant uniform irradiance (1000 W/m²), the RNN-based SVPWM significantly outperformed both conventional and ANN-based SVPWM techniques. The THD of the output current was reduced to 1.62% with the RNN-based SVPWM, compared to 4.0% and 5.68% with ANN and conventional SVPWM respectively, indicating superior waveform quality and system efficiency. Additionally, the maximum power of 100 kW was effectively transferred from the PV side to the grid with a highly regulated DC link voltage of 500 V. Under variable but uniform irradiance conditions, the proposed COA-MPPT algorithm enabled the PV system to adapt dynamically to irradiance fluctuations. The power extracted from the PV array across five irradiance levels (1000, 800, 600, 400, and 700 W/m²) were 100.234 kW, 80.903 kW, 61.162 kW, 40.884 kW, and 71.106 kW respectively. The DC link voltage remained effectively regulated around 500 V with minimal deviation, showcasing the robustness of the proposed algorithm in maintaining voltage stability even under dynamic input conditions. In contrast, the conventional algorithms showed significant voltage oscillations during transitions in irradiance, confirming the superiority of the COA-MPPT approach. When the system was subjected to non-uniform irradiance due to partial shading, the proposed system maintained a stable power output and voltage regulation despite the complexity introduced by unequal irradiance across PV strings. The COA-MPPT enabled optimal tracking even in this complex scenario, resulting in power outputs of 100.234 kW (0–2 s), 66.657 kW (2–4 s), 50.887 kW (4–6 s), 63.678 kW (6–8 s), and 41.8858 kW (8–10 s). These results demonstrate the enhanced capability of the COA in handling multiple peaks in the PV characteristic curves, where conventional MPPT techniques often fail or converge to local optima. In the final case, where a real-time 24-hour irradiance profile from NSRDB was applied uniformly to all strings, the proposed system sustained consistent power generation and voltage regulation. The RNN-based SVPWM maintained low THD and high-quality waveforms throughout the 24-hour profile, and the COA-MPPT ensured that the system operated consistently near the global maximum power point (MPP). The duty cycle and DC link voltage remained smooth and within desired limits, confirming the system’s long-term operational reliability and suitability for real-world applications. Transient performance metrics such as rise time, peak overshoot, settling time, steady-state ripple, and steady-state error were substantially improved with COA-MPPT. For instance, the DC link voltage showed a rise time of just 0.038 s, peak overshoot of 0.6%, settling time of 0.1 s, steady-state ripple of 1.15%, and steady-state error of only 0.94%, all of which are superior compared to the conventional algorithms evaluated. The integration of RNN-based SVPWM with COA-MPPT provides a highly efficient, stable, and reliable control strategy for grid-connected PV systems. The proposed system demonstrates notable improvements in harmonic performance, dynamic response, and maximum power extraction under a wide range of environmental conditions. Looking forward, integration with advanced fuzzy logic controllers and other machine learning models could further enhance adaptability, robustness, and prediction capabilities. Such hybridization could enable faster decision-making, improved non-linear mapping, and better handling of multi-modal PV curves beyond the capabilities of standalone RNN or COA methods. This study is purely simulation-based and real-world uncertainties such as hardware switching losses, communication delays, and component tolerances have not been experimentally validated. Future work will focus on Real-time DSP or FPGA-based implementation for validating computational feasibility and control accuracy in practical setups.
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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The author(s) received no specific funding for this study.
Department of Electrical and Electronics Engineering, Sathyabama Institute of Science and Technology, Chennai, India
Ankathi Manjula
Department of Electrical Electronics Engineering, Sathyabama Institute of Science and Technology, Chennai, India
A. Ramesh Babu
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A.M. contributed to the conceptualization and design of the study, including the selection of methodologies used to assess the SVPWM and MPPT. A.R. played a pivotal role in analysis and interpretation, as well as in drafting and revising the manuscript for intellectual content. Both authors contributed equally to the finalization of the paper and approved the submitted version.
Correspondence to Ankathi Manjula.
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Manjula, A., Babu, A.R. RNN based SVPWM controlled grid integrated PV system with COA based MPPT for enhanced power quality and dynamic tracking. Sci Rep 15, 38432 (2025). https://doi.org/10.1038/s41598-025-22583-1
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Received: 28 April 2025
Accepted: 29 September 2025
Published: 03 November 2025
Version of record: 03 November 2025
DOI: https://doi.org/10.1038/s41598-025-22583-1
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