The Smart Grid Real-Time Load Monitoring Dataset (Afzal et al., 2020), provides high-resolution time-series measurements designed for energy management, load forecasting, and fault detection applications (Ziya07, 2024). It includes real-time active power and load data collected from smart meters or grid sensors at regular intervals, typically every few seconds or minutes. Its detailed granularity shown in Table 2 makes it ideal for training the Transformer component to capture temporal dependencies and the ANFIS unit to react to dynamic load changes. Combined with EHFOA optimizer, this dataset supports end-to-end tuning to minimize forecasting error and improve grid stability in smart grid simulations or real-world deployments.

The HawkFish Optimization Algorithm (HFOA) is a population-based metaheuristic algorithm inspired by the predatory behavior and social dynamics of hawkfish in their natural reef environments (Alkharsan and Ata, 2025). The foundational principle behind HFOA is the modeling of both exploration and exploitation phases through a simulated ecosystem of “male” and “female” hawkfish agents. At initialization, a population of candidate solutions (hawkfish) is randomly distributed across the search space. Each hawkfish represents a potential solution to an optimization problem, and its quality or “fitness” is evaluated based on an objective function. Two types of fitness are typically used: a traditional fitness score and an inverse fitness measure. The inverse fitness is especially useful for promoting balance in the population and allowing the algorithm to simultaneously reward proximity to local optima while maintaining exploratory pressure. The population is split based on fitness into males and females. Females are assumed to be in search of suitable territories (local and global optima) and perform more diversified, random walks within the search space, analogous to broad exploration. Males, on the other hand, compete for access to the females that produce the “loudest” mating signals—these are typically the females located near promising optima. Males move based on both attraction (to the best or “loudest” female) and competition (against other males). A crucial part of the algorithm involves modeling this movement with a balance of stochastic randomness and fitness-guided direction, such that males dynamically adjust their positions in the search space in response to the perceived fitness landscape. Mathematically, this is expressed through update rules that include combinations of best-known positions, peer comparisons, and random exploration terms. The algorithm continues iterating by updating positions, re-evaluating fitness, and adjusting roles in the population until a stopping criterion (maximum iterations or desired fitness level) is reached. The structure of HFOA makes it especially attractive for nonlinear optimization problems due to its intrinsic diversity mechanisms (e.g., gendered roles, dual-fitness evaluation) and its capacity to escape local optima. Its reliance on both neighborhood search and broader movement strategies enables it to maintain solution diversity over many iterations, which is essential for avoiding premature convergence. However, while these mechanisms are conceptually robust, their practical performance may vary significantly depending on the complexity of the search space and the dynamic nature of the target optimization problem.

The original HawkFish Optimization Algorithm (HFOA) models population dynamics inspired by hawkfish, integrating dual-fitness functions (original + inverse) to promote broad search exploration and avoid local optima. Candidate solutions X i ∈ R d , i = 1 , … , N are initialized randomly using Equation 1: x i j 0 = x i , ⁡ min j + rand · x i , ⁡ max j − x i , ⁡ min j , j = 1 , … , d (1) where rand ∼ U 0 , 1 . Fitness values f X i and f inv X i = 1 1 + f X i are evaluated, then the population is split into “males” and “females” based on relative fitness. The dual-fitness mechanism allows simultaneous maximization and minimization, encouraging balance between local refinement and global search. Update rules involve distance-driven movements towards best or near peers (Equation 2): X l new = X l + r 1 X GB − X l + r 2 X Near − X l (2) where X GB is the global best solution, X Near is the nearest high-fitness neighbor, and r 1 , r 2 ∼ U 0 , 1 . Despite its innovative structure, the original HFOA is not inherently designed to handle high-dimensional, time-dependent, and hybrid parameter optimization challenges such as those found in our proposed ANFIS-Transformer framework for smart grid control. The primary weakness of HFOA in this context lies in its limited adaptation to dynamic, temporal learning environments. The Transformer component introduces a sequence-dependent learning task that requires fine-tuning of attention weights and positional encodings—parameters that evolve based on temporal patterns. HFOA’s exploration strategy, based on random walk and attraction models, lacks a memory mechanism or structured learning component that tracks temporal dynamics or sequential dependencies. Furthermore, ANFIS membership functions require precise and stable convergence, especially when modeling fuzzy logic under real-time smart grid constraints (Iqbal et al., 2022). HFOA in its raw form may fail to achieve such granularity due to noisy updates, overly random male-female movements, and lack of elitism or adaptive energy control, which can lead to instability or inefficiency in optimization. These limitations are compounded when the search space becomes multi-objective, as is the case in voltage stability and load balancing tasks that must be simultaneously optimized. In summary, while HFOA offers a strong base, it lacks the mechanisms needed to achieve convergence efficiency and temporal adaptability in the hybrid learning context required by our smart grid methodology.

To overcome the limitations described above and make the HFOA suitable for our complex hybrid learning system, we propose the Enhanced HawkFish Optimization Algorithm (EHFOA). This version introduces a suite of strategic enhancements that transform HFOA into a metaheuristic capable of optimizing both static fuzzy systems (ANFIS) and dynamic sequence-based models (Transformers) (Urrea-Aguirre et al., 2024) under real-time smart grid constraints. The first major enhancement is the integration of Lévy flight-based exploration, which replaces standard random walks with probabilistically-driven long jumps in the search space. This allows agents to escape local minima more effectively and provides a better balance between local and global search—especially valuable when the fitness landscape is rugged, as in ANFIS rule tuning or attention weight optimization. Secondly, we introduce a memory-based elitism mechanism, where a global pool of top-performing solutions is maintained across iterations. Hawkfish agents periodically compare their positions not just to neighbors but also to the elite pool, increasing convergence stability and ensuring retention of historically good configurations. This is particularly useful in Transformer training, where high-performing hyperparameter sets must be preserved. Third, energy-constrained movement control is added by modeling a decay function for each agent’s energy across iterations. This controls the aggressiveness of exploration: agents with high energy favor global search with large updates (via Lévy flights), while those with low energy prioritize fine-tuned exploitation based on nearby elite agents and Transformer loss feedback. Finally, we embed a dynamic clustering mechanism into EHFOA using k-means clustering of the population based on feature proximity and fitness similarity. Each cluster then evolves semi-independently, with its own best candidate guiding local movement. This prevents premature convergence and preserves population diversity, which is critical in the ANFIS layer to avoid collapsing fuzzy rule representations. By integrating these components—Lévy dynamics, elite memory, energy modeling, and diversity maintenance—EHFOA becomes a powerful optimizer that handles both discrete (fuzzy logic rule parameters) and continuous (Transformer attention weights) variables across time-dependent and nonlinear control surfaces.

To improve EHFOA performance for tuning ANFIS-Transformer systems, we introduce four major augmentations:

Fuzzy logic is a form of many-valued logic that deals with reasoning under uncertainty and partial truths, mimicking how humans make decisions based on imprecise or qualitative information. Unlike classical binary logic, where a variable must be either 0 or 1, fuzzy logic allows intermediate values between 0 and 1, representing degrees of membership in fuzzy sets (Abdollahi Chirani and Karami, 2024). In fuzzy systems, rules are typically constructed in the form of linguistic IF-THEN statements, such as “IF load is high AND voltage is low THEN reduce power.” These rules operate on fuzzy sets defined by membership functions, which map crisp input values to degrees of truth (Wang et al., 2023). The process involves fuzzification (converting crisp input into fuzzy values), rule evaluation, aggregation, and defuzzification (converting fuzzy output into a crisp action) as shown in Equation 9. μ A x = 0 x ≤ a x − a b − a a < x < b 1 x ≥ b (9) Where μ A x is the membership function of input x in fuzzy set A , and a , b define the boundaries of the fuzzy region.

The Adaptive Neuro-Fuzzy Inference System (ANFIS) is a hybrid intelligent system that merges the learning capability of neural networks with the uncertainty handling and rule-based reasoning of fuzzy logic (Lin et al., 2024). ANFIS implements a Sugeno-type fuzzy inference system where the parameters of the membership functions and output functions are adjusted using a data-driven training process. Structurally, ANFIS is composed of five layers, each of which corresponds to a distinct operation in the fuzzy inference pipeline: fuzzification, rule strength computation, normalization, defuzzification, and output aggregation (Badran and Toha, 2024).

Let us consider a simple ANFIS with two inputs x and y , and two fuzzy rules:

Rule 1: IF x is A 1 AND y is B 1 THEN f 1 = p 1 x + q 1 y + r 1

Layer 1: Fuzzification (see in Equation 10). O 1 i = μ A i x , O 1 i + 1 = μ B i y (10) This layer calculates the degree of membership for each input.

Layer 2: Rule Strength (Firing Strength) as shown in Equation 11 O 2 i = w i = μ A i x · μ B i y (11)

Layer 3: Normalization (see Equation 12) O 3 i = w ¯ i = w i w 1 + w 2 (12)

Layer 4: Consequent Function (see Equation 13) O 4 i = w ¯ i f i = w ¯ i p i x + q i y + r i (13)

Layer 5: Output Aggregation (see Equation 14) O 5 1 = ∑ i   w ¯ i f i (14) During training, ANFIS uses hybrid learning: gradient descent is applied to update the nonlinear parameters of the membership functions, while least squares estimation is used to optimize the linear parameters in the consequent part (Khan et al., 2024). The result is a system that combines human-like reasoning with data-driven adaptivity, making ANFIS powerful for control and prediction tasks in nonlinear environments. Despite its effectiveness in handling uncertainty and nonlinearity, ANFIS lacks the ability to explicitly model temporal dependencies and sequence correlations over time (Hasan et al., 2023). This becomes a significant limitation in smart grid environments where voltage and load patterns are not static but evolve dynamically, often exhibiting strong dependencies on previous states. ANFIS, being a memory-less system, treats each input instance independently and cannot capture time-series patterns such as peak load progression or recurring voltage dips (Saglam et al., 2024). This limitation restricts ANFIS from making context-aware predictions or decisions, especially when control strategies depend on recent trends. To address this, it is essential to integrate a sequential learning mechanism—such as a Transformer—that can model long-range dependencies and temporal dynamics effectively (Perçuku et al., 2025).

The ANFIS-based control strategy integrates fuzzy inference rules to establish a mapping between key input variables—such as frequency deviation and load type—and the resulting control actions. These fuzzy rules capture expert knowledge in a linguistic format (e.g., “If frequency deviation is high and load is inductive, then increase compensation”) and enable the system to make smooth, nonlinear decisions in real-time. ANFIS enhances this capability by automatically tuning the membership functions and rule weights through training with input-output data. This dynamic mapping allows the controller to adapt to varying grid conditions and respond rapidly to frequency disturbances. With this incorporation, ANFIS-EHFOA achieves better stability, robustness, and precision in maintaining grid frequency, especially under fluctuating load and renewable generation scenarios. Table 3 presents a representative set of fuzzy inference rules employed within the ANFIS-EHFOA (Adaptive Neuro-Fuzzy Inference System–Droop Controller) framework to guide compensatory actions based on the real-time state of the power grid. Each rule is defined by two inputs—frequency deviation and load type—and maps them to an appropriate control action.

The proposed ANFIS-Transformer Framework is a hybrid architecture designed to leverage the complementary strengths of ANFIS and the Transformer model for dynamic voltage and load balancing in smart grids. In this framework, the Transformer acts as a temporal feature encoder, capable of modeling long-term dependencies in time-series input data such as voltage readings, power consumption, and renewable energy generation. It converts a sequence of past measurements into an informative, contextaware embedding that reflects temporal trends and seasonal variations. This embedding is then passed as an input feature to the ANFIS model, which performs fuzzy inference to generate control actions.

Let the input time series be as shown in Equation 15: X t = x t − T + 1 , x t − T + 2 , … , x t , x i ∈ R d (15) The Transformer encoder maps this sequence to a temporal embedding as shown in Equation 16: Z t = TransformerEncoder X t ∈ R k (16) This context vector Z t captures the temporal profile of system dynamics up to time t .

Then, Z t is fed into the ANFIS network along with any real-time control variables (e.g., load demand, capacitor status), forming the input as shown in Equation 17: u t = Z t , x t load , x t voltage (17) The ANFIS then evaluates fuzzy rules using u t and computes a control action as shown in Equation 18: y t = ∑ i   w ¯ i p i · u t + r i (18) where w ¯ i are normalized rule weights, and p i , r i are the parameters of the linear output layer in each rule.

This fusion of a Transformer’s dynamic memory with ANFIS’s rule-based reasoning enables the system to respond to complex, time-evolving patterns in the grid while still retaining interpretability and fuzzy control granularity. When optimized using EHFOA, the combined model can fine-tune both the temporal encoding parameters and the fuzzy membership functions to minimize voltage deviation, load imbalance, and energy waste across the grid. Algorithm 2 defines the workflow of the ANFIS-Transformer Framework, a hybrid intelligent control system that synergistically integrates temporal deep learning with fuzzy inference for smart grid applications. The algorithm begins by segmenting incoming time-series data into overlapping windows of predefined length. Each window captures the short-term temporal behavior of the system—such as fluctuations in load, voltage, or renewable energy inputs—and is passed through a Transformer encoder, which models the sequence dynamics and returns a dense vector Zt ​ representing the contextual embedding of system state up to the current moment.

Algorithm 2

ANFIS-Transformer.

Input:

This embedding is then fused with real-time grid variables (such as instantaneous voltage or load values) to construct the input vector ut for the ANFIS module. The fuzzy inference system then evaluates preconfigured linguistic rules, using membership functions to quantify how well the current input aligns with each rule’s conditions. Firing strengths of the rules are normalized, and each rule contributes a partial output based on a linear function of the input. The final control decision—whether to adjust power factor, shift load, or engage a compensator—is obtained by aggregating the weighted outputs of all fired rules. By combining Transformer-based memory with rule-based reasoning, this algorithm allows the system to account for both long-term dependencies and interpretable control policies. Such integration is critical for real-time grid environments, where control decisions must consider both historical trends and current conditions. When further optimized using EHFOA, the model gains the ability to continuously adapt to changing patterns and uncertainties, delivering highly efficient and robust control for smart grid stability and performance.

The Maximum Power Point Tracking (MPPT) module is a critical subsystem in photovoltaic (PV) energy systems, ensuring that the PV array operates at its optimal power point under varying irradiance and temperature conditions (Liu et al., 2025). In the MATLAB/Simulink environment, the MPPT module is implemented as a combination of algorithmic control logic and power electronics interfacing, often coupled with a DC-DC converter to regulate voltage and current for maximum power extraction. The design process begins by modeling the PV panel using standard single-diode or double-diode equations, either via Simscape Electrical’s PV Array block or a custom mathematical implementation of the I-V characteristics based on datasheet parameters (e.g., open-circuit voltage V O C , short-circuit current I s C , and temperature coefficients).

The MPPT algorithm itself is typically implemented using either a Perturb and Observe (P&O), Incremental Conductance, or an advanced artificial intelligence-based technique (such as ANFIS, PSO, or fuzzy logic) (Ahmad T. et al., 2022). In the Simulink implementation of P & O , for instance, the control logic compares the instantaneous power output of the PV module with the previous sample and perturbs the duty cycle of the converter accordingly. A Discrete-Time Integrator block is often used to maintain the duty cycle D red and a Feedback Gain block or Stateflow chart defines the conditions for perturbation direction. The output of the MPPT controller is a duty cycle signal that drives a Pulse Width Modulation (PWM) generator, modulating the gate signal of a MOSFET or IGBT switch within a DC-DC converter (e.g., Boost or Buck-Boost topology).

The DC-DC converter itself is modeled using Power Electronics blocks, such as Inductors, Capacitors, and Ideal Switches from the Simscape > Power Systems > Specialized Technology library. The inductor current and output capacitor voltage are governed by the switching signal derived from the MPPT controller, and their dynamics follow the converter’s nonlinear state-space equations. The converter ensures impedance matching between the PV panel and the load, enabling the panel to operate near its maximum power point (MPP) by continuously adjusting its input resistance. Key electrical parameters such as inductor size L , output capacitor C , and switching frequency f s w must be carefully chosen to maintain system stability and fast transient response.

To verify performance, the MPPT module includes real-time measurement blocks for PV voltage V p w current I p v r and power P p v = V p v × I p v . These signals are fed into a Scope or To Workspace block for visualization and analysis. Typically, a Step or Signal Builder block is used to introduce variable irradiance or temperature profiles, allowing users to observe the response of the MPPT algorithm to environmental changes. Additional performance metrics such as tracking speed, steady-state oscillation, and convergence accuracy are computed in real-time or through post-simulation MATLAB scripts.

For advanced implementations, such as those involving an ANFIS-based MPPT algorithm, the Simulink model integrates a trained neuro-fuzzy inference system using either the FIS block or custom S-function blocks. The inputs to the ANFIS controller are usually the error between the current and previous power, or the slope Δ P / Δ V , and the output is the reference voltage or direct duty cycle for the converter. Training of the ANFIS is done offline in MATLAB using historical PV data, and the resulting fuzzy inference structure is exported into Simulink. The control surface can be visualized to understand how different environmental inputs affect the duty cycle modulation.

The complete MPPT module is tightly integrated within a larger PV system simulation that includes the PV model, converter, MPPT logic, load interface, and optional grid-tied inverter for AC systems. Simulation is run under variable irradiance (e.g., 1000 → 700 → 500   W / m 2 ) and ambient temperatures (e.g., 25 → 40 ∘ C ), and the effectiveness of the MPPT controller is measured by its ability to continuously locate and track the MPP, reflected by stable output power close to theoretical maximum values.

This level of detail in Simulink modeling enables both educational and industrial researchers to evaluate MPPT algorithms under realistic and customizable conditions, providing a robust platform for testing adaptive and intelligent control schemes in renewable energy systems.

In the MATLAB/Simulink simulation of a solar energy system, the photovoltaic (PV) module is the fundamental energy-generating component, responsible for converting solar irradiance into electrical power via the photovoltaic effect. The electrical behavior of a PV module is nonlinear and highly dependent on environmental conditions such as solar irradiance and temperature. Accurate modeling of the PV module is essential for simulating real-world dynamics, designing control algorithms like MPPT (Maximum Power Point Tracking), and evaluating system efficiency. For our model, we utilize the Solarex MSX-60 PV module, a well-documented commercial 60 W polycrystalline silicon panel, commonly used in simulation and educational research. This module is particularly suitable for MATLAB/Simulink simulation as its electrical parameters are well-supported in PV modeling literature and closely match the characteristics of standard PV panels. It is represented using a single-diode equivalent circuit model, which includes a photo-generated current source, a diode for junction behavior, series resistance to model internal wiring losses, and shunt resistance to represent leakage current paths. The Simulink implementation is carried out using the Simscape Electrical > Specialized Power Systems > PV Array block. This block allows the specification of panel configuration in terms of number of seriesconnected modules (Ns) and number of parallel strings (Np), enabling scalability to simulate large PV plants or micro-generation setups. The irradiance (in W / m 2 ) and cell temperature (in C ∘ ) are fed as inputs to the PV Array block, either as constant values or time-varying profiles, to simulate real-world operating scenarios.

The I-V and P-V characteristics of the PV module are temperature and irradiance dependent, and the simulation accurately reproduces these dynamics. The output current I and voltage V of the panel under varying load conditions are computed using the nonlinear diode equation, which governs the behavior of the PV cell as shown in Equation 19: I = I p h − I o exp ⁡ q V + I R s n k T − 1 − V + I R s R s h (19) where I p h is the photocurrent, I o is the reverse saturation current, R s and R s h are the series and shunt resistances, respectively, and n is the diode ideality factor. The photocurrent is directly proportional to the incident irradiance and adjusted based on the temperature coefficient of the short-circuit current. Solarex MSX-60 PV Module Parameters are show in Table 5 below.

To ensure accurate power output in simulation, we parameterize the PV module using manufacturer datasheet values, the photovoltaic (PV) system modeled in MATLAB/Simulink is best configured as a medium-scale array that reflects realistic smart grid integration while remaining computationally manageable. A suitable configuration consists of three strings of PV modules, each containing 8 modules, for a total of 24 PV modules. Assuming the use of a standard high-efficiency module such as the SunPower SPR-305, which delivers 305 W under standard test conditions, the total array capacity would be approximately 7.3 kW. This scale is sufficient to generate dynamic load and voltage patterns required for accurate forecasting, intelligent control, and meaningful evaluation of MPPT efficiency and energy loss. At the same time, it avoids the simulation complexity associated with utility-scale plants. The chosen scale also allows the proposed intelligent control system to demonstrate improvements in energy loss reduction (to 1.9%), enhanced voltage stability, and fast system response (1.04 s), under conditions such as partial shading or variable loads.

In the simulation of a PV-powered smart grid, in the Table 6 loads represent the electrical demand side of the system and are critical for testing energy management, voltage regulation, and load balancing control algorithms. Loads can be modeled in MATLAB/Simulink as either constant or time-varying, and may take the form of resistive, inductive, capacitive, or composite elements. In our system, we implement time-varying composite loads that include resistive-inductive (R-L) components to more realistically reflect household appliances, industrial motors, or grid-connected devices. The Simscape Electrical Specialized Power Systems library provides a Load block which accepts programmable demand profiles that can vary with time, replicating realistic daily consumption curves. The loads are parameterized based on power level (in kW), power factor, voltage rating, and temporal profile. The simulation includes load profiles that rise in the morning, peak during midday, and taper off at night. This variability is critical for testing MPPT, storage control, and grid interaction. Additionally, the simulation environment supports multiple load types (critical, non-critical) that allow for selective load shedding strategies when power shortages or voltage instability occur.

For effective operation of an energy management system, such as the ANFIS-EHFOA, different load types of the power grid must be modeled so that the parameters involved are known. This is essential if stability is to be maintained, maximized, and not at the expense of performance. The different load types included in the proposed grid structure differ in their characteristics and requirements. Depending on the characteristics and nature of the impact on the electrical system, grid loads can be classified into different types (Liu et al., 2025; Ahmad T. et al., 2022).

Resistive loads are components or electrical devices that draw power in a linear relationship with the applied voltage or current. The devices neither store nor create energy but simply convert electrical energy. The devices use electricity in such a way that both the current and voltage are in proper sync with each other. Some general examples include electric heaters and incandescent light bulbs. Such loads are easy to understand because they are simple and predictable in nature, although they are most commonly the least energy-saving among the categories.

The electrical load integrated into the system configuration for performance evaluation is a programmable, adaptive compensating load designed to be configurable as resistive, inductive, capacitive, or mixed-type. This flexibility allows the system to simulate various real-world loading scenarios. The load is connected to the microgrid busbar via a controllable electronic switch, enabling rapid engagement or disengagement in response to grid frequency deviations. During operation, the load introduces a controlled disturbance—either in-phase or 180° out-of-phase with the detected frequency distortion—to counteract fluctuations and stabilize the grid.

The battery energy storage system (BESS) in a PV-based smart grid plays a crucial role in stabilizing the voltage, shifting loads, and storing surplus energy generated during high-irradiance periods. In MATLAB/Simulink, the battery is modeled using the Battery block available in Simscape Electrical. It supports both simple resistor-capacitor-based models and detailed lithium-ion models incorporating state-of-charge (SoC), voltage hysteresis, and degradation. In our simulation, we utilize a lithium-ion battery model with real-time SoC tracking and capacity fade modeling. The battery is connected via a bidirectional DC-DC converter that allows both charging (from PV or grid) and discharging (to load or inverter). The control system regulates the charge/discharge cycles based on grid demand, SoC limits, and power flow from PV. The SoC is monitored and updated using the Coulomb counting method integrated within the battery management system (BMS). The battery parameters are presented in Table 7 below.

The inverter is responsible for converting DC power from the PV and battery system into AC power suitable for grid connection or local load usage. In MATLAB/Simulink, the inverter is modeled using Universal Bridge blocks configured as three-phase voltage source inverters (VSI). The inverter includes sinusoidal pulse width modulation (SPWM) or space vector PWM (SVPWM) schemes to ensure high quality and stable AC output. A closed-loop control system is implemented using a phase-locked loop (PLL) for grid synchronization, along with a current and voltage controller using PI regulators to match the inverter output with the grid standards. Grid-tied inverters are also equipped with anti-islanding and power flow regulation logic. The inverter control logic receives reference signals for voltage and frequency, typically computed by the energy management system. Real-time DC-link voltage regulation is maintained to stabilize the inverter operation, especially under dynamic PV output and load variation. The parameters of the inverter are presented in Table 8.

In Table 9 DC-DC converters are crucial for regulating the operating point of PV panels and controlling power flow between storage and loads. In this simulation, two types of converters are used: a Boost converter between the PV and DC-link (for MPPT control), and a bidirectional Buck-Boost converter between the battery and DC bus (for charge/discharge control). These converters are modeled using power electronics components such as MOSFETs, inductors, capacitors, and diodes available in Simscape Electrical. The Boost converter’s duty cycle is controlled by the MPPT algorithm (e.g., Perturb and Observe or ANFIS), ensuring the PV operates at its maximum power point. The bidirectional converter is controlled via logic based on SoC, load demand, and PV availability. Control signals are generated via PWM blocks synchronized with carrier signals, and gating signals are applied to switches using Simulink control logic. Dynamic voltage and current waveforms are tracked using current sensors, feedback loops, and PI controllers to stabilize converter outputs.

In the evaluation of prediction performance within smart grid control systems, especially for voltage and load forecasting, several statistical error metrics are essential for quantitatively assessing model accuracy and generalization. The Root Mean Square Error (RMSE) is widely used as it penalizes larger deviations more than smaller ones, making it particularly effective for highlighting significant forecasting errors in critical grid parameters. It is defined as the square root of the average squared differences between predicted and actual values and is sensitive to outliers, which is desirable in high-reliability systems like smart grids. Mean Absolute Error (MAE), on the other hand, provides a more interpretable measure of average prediction error in the original units (e.g., volts or kilowatts) without emphasizing extreme errors, offering a balanced view of typical model performance. The Mean Absolute Percentage Error (MAPE) expresses forecast accuracy as a percentage, making it useful for comparing performance across datasets or systems of different scales, although it can be sensitive when actual values approach zero. Lastly, the Coefficient of Determination (R ² score) measures the proportion of variance in the actual values that is predictable from the model outputs. An R ² value close to 1 indicates excellent goodness-of-fit, suggesting that the model captures the underlying trends in the data well. Illustrated in Table 10, these metrics provide a comprehensive profile of the forecasting model’s accuracy, robustness, and reliability in real-time voltage and load prediction scenarios.

In the context of smart grid operations, particularly in systems incorporating renewable energy and intelligent controllers, the evaluation of control and grid performance metrics is essential to assess system stability, efficiency, and adaptability. The ANFIS component in the proposed method plays a central role in producing control decisions—such as reactive power compensation, load shifting, and voltage regulation—based on current grid states and temporally encoded forecasts. One key metric is the Voltage Deviation Index, which measures the squared deviation of bus voltages from a nominal reference (typically 1.0 per unit); lower values indicate that the control system is effectively maintaining voltage within acceptable bounds. Another important indicator is the Load Imbalance Rate, which quantifies the percentage deviation between actual and expected load distribution across buses or phases, reflecting the system’s ability to maintain power balance. Energy Loss (%) is also a critical measure, capturing the total transmission and conversion losses introduced by suboptimal operating points or inefficient dispatch strategies. Additionally, Power Factor Stability assesses the consistency of reactive power compensation and load alignment with voltage and current vectors, while Response Time reflects how quickly the control system reacts to disturbances such as sudden load changes or irradiance drops as shown in Table 11 below.

To comprehensively evaluate the performance of the Enhanced HawkFish Optimization Algorithm (EHFOA), it is essential to analyze its behavior through dedicated optimization metrics that reflect convergence quality, search efficiency, and overall robustness in parameter tuning. The Best Fitness Achieved metric represents the lowest value of the objective function (typically a weighted sum of prediction error, voltage deviation, and energy loss) found by the optimizer, indicating the quality of the final solution. Convergence Speed quantifies how quickly the algorithm reaches near-optimal performance, typically measured by the number of iterations required to stabilize the fitness curve. Runtime, or computational time in seconds, measures the efficiency of the optimization process and is crucial for real-time or hardware-constrained applications. Finally, the Comparative Performance of EHFOA should be assessed against other well-established metaheuristics such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO). EHFOA is expected to outperform these baselines due to its hybrid movement strategies (e.g., Lévy flight, energy decay), elite memory, and cluster-driven diversification, enabling it to escape local optima and deliver more stable convergence across complex, multi-dimensional search landscapes such as ANFIS-Transformer tuning. The optimization performance is shown in Table 12.

The results presented in this study comprehensively validate the effectiveness of the proposed ANFIS-Transformer framework tuned by the Enhanced HawkFish Optimization Algorithm (EHFOA) in achieving superior performance in voltage prediction, load forecasting, control response, and optimization convergence within a smart grid environment. Each experimental analysis, spanning predictive accuracy, control stability, convergence efficiency, and parameter sensitivity, contributes to a holistic evaluation of the system. The time-series plots for predicted versus actual voltage and load profiles demonstrate the strong forecasting capabilities of the Transformer module. Both signals closely match their actual counterparts, indicating that the temporal encoding mechanisms effectively capture non-linear patterns in the smart grid data. This accurate prediction is crucial, as it feeds forward into the ANFIS controller, enabling it to proactively regulate voltage and load conditions. Furthermore, the comparison of controlled vs uncontrolled voltage behavior illustrates the impact of integrating ANFIS. Without control, voltage fluctuates with higher amplitude, risking instability and power quality degradation. With ANFIS, voltage becomes smoother and remains tightly bounded around the nominal value, confirming the controller’s proficiency in applying real-time corrective action.

Figure 4 illustrates the performance of the Transformer module in forecasting voltage trends within the smart grid. The actual voltage signal exhibits a periodic behavior reflecting normal fluctuations in grid conditions, while the predicted signal closely follows the same trend with only minor deviations. The slight noise in the prediction curve is expected due to modeling imperfections and environmental uncertainties, but the low amplitude of this noise demonstrates the model’s capacity to generalize effectively. The close alignment between predicted and actual voltages indicates that the Transformer is able to learn temporal dependencies in the voltage profile, which is critical for preemptive control decisions. This predictive capability lays the foundation for the fuzzy logic controller (ANFIS) to make informed voltage regulation decisions ahead of disturbances.

In Figure 5, we assess the ability of the model to predict dynamic load behavior, a crucial aspect of load balancing in distributed energy systems. The actual load varies with a lower frequency than voltage but includes realistic, smooth oscillations representative of household or commercial usage profiles. The predicted load signal aligns well with the ground truth, capturing both the phase and magnitude of fluctuations. Occasional slight over- or under-estimations occur, which is common in systems where abrupt demand changes or measurement noise are present. Nevertheless, the model maintains temporal alignment and reflects adaptability, which is important for real-time dispatch and control decisions. This result confirms that the Transformer encoder effectively translates historical trends into forward-looking control-relevant insights.

Figure 6 compares the voltage behavior of the system before and after implementing the ANFIS-based control strategy. The uncontrolled voltage curve exhibits higher amplitude oscillations, which could lead to voltage instability, poor power quality, and stress on sensitive equipment. In contrast, the controlled voltage, adjusted by ANFIS decisions based on both real-time inputs and Transformer-encoded predictions, shows a significant damping of fluctuations. This smoother behavior reflects the controller’s effectiveness in minimizing deviation from nominal voltage and improving grid reliability. The difference in these two curves validates the ANFIS module’s contribution to dynamic compensation and confirms that the fuzzy rule system successfully interprets temporal signals for corrective action.

Figure 7 simulates the system’s response to a sudden load increase at t = 5 s, a common stress test for any grid control framework. Before the step, the system remains stable at a baseline load. After the step, the system begins to respond by increasing the output, with a curve that rises sharply and then gradually settles—indicative of a well-damped system. The absence of overshoot and the short settling time demonstrate the proposed model’s ability to rapidly adapt to disturbances. This behavior highlights the strength of the ANFIS-Transformer-EHFOA framework in terms of both reactivity and stability, which are essential characteristics for real-time grid control where sudden fluctuations can otherwise compromise grid performance or cause cascading failures.

The computational behavior of the Enhanced HawkFish Optimization Algorithm (EHFOA) was evaluated in terms of convergence efficiency and scalability. As illustrated in Figure 8, the convergence curve of EHFOA demonstrates rapid fitness improvement during the initial 50 iterations, with diminishing returns thereafter, stabilizing near an RMSE value of 0.025 by iteration 100. This indicates fast convergence in early stages followed by fine-grained exploitation. In terms of computational complexity, EHFOA integrates adaptive local search and energy-aware strategies, resulting in a per-iteration complexity of O(N·D), where N is the number of agents and D is the dimensionality of the input space. The hybrid learning mechanism (combining gradient descent and least-squares) adds minimal overhead due to parallelizable computations. On a standard i7 CPU with 16 GB RAM, the complete training phase for a 7-node microgrid (≈50 dimensions) completed in under 1.8 s per run, affirming practical feasibility. Regarding scalability, simulation results confirmed EHFOA’s robustness when applied to microgrids with increasing dimensionality. As the node count increased from 3 to 7, convergence speed remained consistent, with only a marginal rise in computational cost (below 15%) and no significant increase in RMSE fluctuation. Coordination latency remained within acceptable bounds (under 200 m), indicating that EHFOA scales effectively with growing network size and input complexity. Figure 8 shows the convergence behavior of the Enhanced HawkFish Optimization Algorithm (EHFOA). The algorithm rapidly reduces the objective function (cost) in the early iterations and stabilizes within a convergence zone after approximately 100 iterations, reaching a final fitness level near 0.025.

Figure 9 visualizes the fitness reduction over 100 iterations for various optimization algorithms, demonstrating how quickly and effectively each method converges toward an optimal solution. The EHFOA (proposed method) achieves the lowest final fitness value and converges faster than GA, PSO, WOA, and the original HFOA, indicating its superior ability to balance exploration and exploitation in tuning the ANFIS-Transformer model.

This 3D surface plot in Figure 10 illustrates the sensitivity of the ANFIS-Transformer model’s prediction performance (in terms of RMSE) to changes in two key hyperparameters: the Transformer embedding size and the number of fuzzy rules. As shown, increasing both parameters improves model accuracy, with the lowest RMSE achieved at higher embedding dimensions and more complex fuzzy rule sets. However, the improvement plateaus beyond a certain threshold, suggesting an optimal trade-off between model complexity and performance. The 3D plot in (a) shows how the voltage-forecasting RMSE varies as a function of (1) the Transformer’s embedding dimension (e.g., 64, 128, 256) and (2) the number of fuzzy rules in the ANFIS module (3, 5, 7, 9, 11). Lower RMSE values (cooler colors) indicate better predictive accuracy. And The surface in (b) visualizes the ANFIS controller’s mapping from error (E) and change in error (CE) to the control output u u. It reflects how the combination of Gaussian membership functions and the 3 × 3 fuzzy rule base generates real-time corrective actions across the full input range.

To comprehensively evaluate the performance of the proposed ANFIS-Transformer-EHFOA framework, it is essential to employ robust quantitative metrics that reflect both prediction accuracy and system efficiency. In this study, Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are utilized as standard statistical indicators to assess the discrepancy between predicted and actual grid parameters (such as frequency or voltage). These metrics provide insight into the controller’s precision and reliability under dynamic operating conditions. Additionally, Energy Loss (%) is used to quantify the efficiency of power delivery by calculating the proportion of input energy that is dissipated or unutilized. Collectively, these three metrics offer a multidimensional perspective: RMSE and MAE focus on control accuracy, while Energy Loss highlights economic and operational performance. The inclusion of these metrics ensures a balanced evaluation of both control effectiveness and energy optimization within the smart grid environment. RMSE measures the square root of the average of the squared differences between predicted values and actual values. It is highly sensitive to large errors and thus penalizes larger deviations more severely, making it suitable for evaluating high-precision control systems as shown in Equation 20. RMSE = 1 n ∑ i = 1 n   y i − y ^ i 2 (20) Where:

y i = actual value at instance i

MAE computes the average magnitude of the absolute differences between predicted and actual values. Unlike RMSE, it treats all errors equally and is less sensitive to outliers. It is useful for interpreting the average control deviation in simple, interpretable units as shown in Equation 21. MAE = 1 n ∑ i = 1 n   y i − y ^ i (21)

Energy Loss Percentage evaluates the proportion of energy that is lost in the system during transmission or conversion. It is a crucial indicator of system efficiency and sustainability as shown in Equation 22. Energy Loss % = E input − E output E input × 100 (22) Where:

E input = total energy supplied to the system

This grouped bar chart in Figure 11 compares three key performance metrics—RMSE, MAE, and energy loss—across four control architectures. The proposed ANFIS-Transformer-EHFOA framework outperforms the others significantly, achieving the lowest error rates and minimizing energy loss. The stepwise improvement from ANFIS-only and Transformer-only models to the hybrid and optimized variant highlights the cumulative benefits of integrating temporal features, fuzzy logic, and the EHFOA metaheuristic. the results provide strong empirical support for the proposed method. The fusion of deep temporal learning (Transformer), adaptive control (ANFIS), and elite metaheuristic tuning (EHFOA) enables high-precision prediction and robust voltage/load balancing. The improvements across all measured dimensions—forecasting accuracy, control stability, energy efficiency, and convergence behavior—highlight the novelty and utility of this approach in real-world smart grid applications. These outcomes establish the proposed ANFIS-Transformer-EHFOA system as a promising candidate for next-generation AI-enabled energy management and control architectures.

Figure 12 illustrates the effect of different uncertainty scenarios—load variation, PV fluctuation, and fault injection—on the frequency stability of a smart microgrid managed by the ANFIS-EHFOA controller. Under baseline conditions, the frequency remains steady at 50 Hz, confirming stable control. When subject to load variation or PV generation fluctuations, the frequency oscillates within ±0.03–0.05 Hz, showing the controller’s ability to dampen mild disturbances. The most challenging scenario is fault injection between 4 and 6 s, where the frequency briefly dips below 49.7 Hz before quickly recovering, demonstrating ANFIS-EHFOA’s effective transient handling. The RMSE bar chart in the lower panel quantifies these responses: minimal error under baseline (0.005 Hz), slightly higher under load and PV variability (0.012–0.018 Hz), and the highest (0.030 Hz) under fault conditions. Despite these uncertainties, ANFIS-EHFOA maintains frequency deviations within acceptable limits, validating its adaptive and robust performance across real-world scenarios.

Figure 12 presents a comparative evaluation of the proposed ANFIS-EHFOA-Transformer-based controller against three prominent optimization and learning-based controllers used in smart grid frequency regulation: Particle Swarm Optimization (PSO) (Tu et al., 2025), Grey Wolf Optimizer with Internal Model Control (GWO-IMC) (Prabhakar et al., 2024), and Deep Reinforcement Learning (DRL) (Lee and Kim, 2024). The proposed method exhibits the lowest RMSE value (0.024), indicating the highest accuracy in predicting and adjusting frequency deviations. DRL follows closely with a value of 0.026, while GWO-IMC and PSO show higher error values (0.029 and 0.031, respectively), reflecting relatively reduced performance under dynamic operating conditions. In terms of MAE, the proposed method again leads with a value of 0.018, demonstrating consistent accuracy in minimizing average deviations. DRL performs competitively (0.019), while GWO-IMC (0.021) and PSO (0.025) trail behind, suggesting that optimization-based controllers may require more fine-tuning for better generalization. A fast response is essential for real-time control. The proposed ANFIS-EHFOA achieves the shortest response time (0.6 s), making it well-suited for real-world smart grid applications requiring immediate stabilization. DRL’s performance (0.8 s) is adequate but slower, and both GWO-IMC (1.0 s) and PSO (1.2 s) exhibit significant latency, which could limit their effectiveness during abrupt frequency changes.

Figure 13 presents a digital-style simulation of a photovoltaic (PV) system’s response under varying irradiance and load conditions across a 5-s time frame. The top subplot shows the PV output power (Ppv) tracking its corresponding maximum power point (MPP) closely, verifying effective MPPT performance of the proposed controller. The stepwise power shifts reflect changes in irradiance or load that typically occur in real smart grid environments. The second subplot depicts PV current, which mirrors the power transitions while assuming a constant voltage. The third subplot confirms the constant PV voltage set at 25 V, reflecting stable operating conditions during control actions. The final subplot shows corresponding duty cycle adjustments, with discrete changes matching the power and current shifts. These plots validate the digital adaptability and precision of the control mechanism used in the ANFIS-Transformer-EHFOA framework under rapidly changing operating states.

While the current study confirms ANFIS-EHFOA’s strong performance under controlled deterministic conditions, Figure 14 shows its response under realistic uncertainty scenarios, including stochastic load variation, PV generation fluctuation, and equipment fault injection. These simulated disturbances induce frequency deviations and raise the RMSE of control accuracy, yet ANFIS-EHFOA maintains bounded performance and rapid recovery. To further strengthen robustness, future work will embed stochastic modeling frameworks such as probabilistic load profiles, solar irradiance-driven PV variability, and Monte Carlo-based random fault injections. These will enable retraining and validation of ANFIS-EHFOA under noisy, fault-prone conditions. Additionally, integrating prediction intervals and confidence-aware droop regulation will allow uncertainty-aware responses. These enhancements are critical for deploying ANFIS-EHFOA in large-scale, real-world smart grids where variability and unpredictability are inherent.

Despite the promising performance and extensive validation of the proposed ANFIS-Transformer framework optimized by EHFOA, several limitations remain that warrant discussion. First, while the Transformer architecture demonstrated strong predictive capabilities, it is computationally intensive and requires substantial memory and processing power during training. This may pose deployment challenges in edge computing environments or low-power embedded systems commonly used in smart grid control units. Although EHFOA reduces the complexity of parameter tuning, the initial overhead of training and optimization remains high, potentially limiting the real-time adaptability of the model when faced with abrupt structural changes in grid topology or load profiles. Another limitation lies in the generalization capability of the model. The framework was trained and validated using a single publicly available dataset representing specific operational characteristics of a smart grid. While this dataset provides realistic load and voltage patterns, it may not capture the full spectrum of variability seen in different geographical regions, seasons, or grid infrastructures. Consequently, the model’s effectiveness in other environments remains to be tested. Transferability to unseen domains might require re-tuning or retraining, reducing the plug-and-play appeal of the proposed system. Additionally, the fuzzy inference component in the ANFIS architecture, while interpretable and adaptive, becomes increasingly complex as the number of rules grows. This scalability issue can lead to increased inference time and reduced transparency when deployed in large-scale systems with high-dimensional input features. Although EHFOA helps mitigate rule explosion by optimizing only the most significant parameters, a structured pruning or rule selection strategy may be required to keep the system lightweight and interpretable. Finally, the proposed method currently assumes the availability of accurate and high-resolution data inputs, such as real-time voltage, load, and environmental measurements. In practice, sensor faults, communication delays, or data outages are common in power distribution networks and can significantly impair control accuracy. The current framework does not include mechanisms for fault-tolerant prediction or missing data imputation, which could be vital in practical deployment scenarios. Future extensions should consider integrating robust learning techniques or sensor fusion strategies to address data reliability issues.