Powering the Future: A Review of PV and Wind Turbine Technologies from Component Modeling to System Coordination

Abstract

The integration of photovoltaic (PV) and wind turbine (WT) systems into modern power grids demands not only accurate component-level models but also a holistic understanding of their coordinated operation. This review bridges the gap between low-level device physics and high-level system coordination, offering a dual perspective often overlooked in existing surveys that treat generation and management separately. We systematically analyze PV models, from single-diode equivalent circuits to data-driven approaches, and WT models, ranging from aerodynamic and mechanical representations to simplified electrical equivalents suitable for stability studies. Critically, we then shift focus to the system level by examining energy management systems (EMS) that enable hybrid PV–WT coordination. Unlike prior reviews that emphasize either component accuracy or dispatch strategies alone, this paper highlights the emerging synergy between hybrid PV–WT modeling and EMS architectures. By identifying mismatches between model fidelity and EMS requirements, this review maps a pathway towards more integrated hybrid renewable systems. The discussion synthesizes key trade-offs in scalability, uncertainty handling, and real-time feasibility, underscoring that true potential is unlocked only through intelligent integration of component models and control architectures.

1. Introduction

The global energy landscape is undergoing a profound transformation driven by the need to mitigate climate change, reduce dependence on fossil fuels, and enhance energy access and security [1]. In response, governments worldwide have introduced new regulations and policies aimed at promoting renewable energy sources (RES) technologies, enhancing energy efficiency, and establishing conservation plans alongside supporting legislation. The advantages of renewable energy sources include the use of freely available resources, namely solar and wind, as fuel, together with low operating and maintenance expenses, and the absence of natural resource depletion. Among renewable energy sources, solar and wind power have emerged as the two dominant pillars, accounting for the majority of new generation capacity installed annually worldwide [2]. This growth is underpinned by decades of technological learning and manufacturing scale-up, which have steadily driven down the levelized cost of solar electricity. As shown in Figure 1, the PV costs dropped significantly over the last 50 years [3].

Photovoltaic (PV) systems and wind turbines (WTs) offer complementary characteristics: solar irradiance exhibits diurnal and seasonal patterns, while wind availability often peaks during different hours or seasons, making their hybridization particularly attractive for smoothing power output and improving overall system reliability [4]. As a result, hybrid PV–WT installations, ranging from small off-grid microgrids to large utility-scale renewable plants, have become a mainstream solution for modern power systems [5]. These technologies are applied not only in microgrids but also in fields. For instance, long before the widespread grid integration of PVs, the technology found one of its first practical applications in water pumping, with pioneering experiments conducted in the Soviet Union during the mid-1960s, and it is still widely used for pumping applications [6,7,8].

Despite the maturity of PV and WT technologies as standalone systems, their effective integration into hybrid configurations poses nontrivial challenges that span multiple temporal and spatial scales [9]. At the component level, accurate modeling is essential for predicting energy yield, designing power converters, and implementing maximum power point tracking (MPPT). The literature on PV modeling is extensive, encompassing equivalent-circuit models (e.g., single-diode, double-diode), empirical models, and more recently, data-driven approaches based on machine learning [10,11]. Similarly, wind turbine modeling spans aerodynamic representations (blade element momentum theory), mechanical drivetrain dynamics, and various generator-converter topologies (fixed-speed, doubly-fed induction generators, permanent magnet synchronous generators) [12,13]. Each model type involves trade-offs among accuracy, computational cost, and parameter availability, choices that have significant downstream consequences.

To ensure transparency and reproducibility of this review, the literature search was conducted directly on the platforms of the major publishers in this field: Elsevier (ScienceDirect), IEEE (IEEE Xplore), MDPI, Springer, Wiley, Taylor & Francis, and other additional publishers. The search covered the period 1994 to 2026. The distribution by publisher is shown in Figure 2.

The initial search yielded 756 records. After duplicate removal, screening, and eligibility assessment, 142 articles were included. Three thematic keyword groups were used: PV models, such as “single-diode”, “parameter extraction”, “neural network”, WT models, such as “BEM”, “power curve”, and EMS, such as “MPC”, “reinforcement learning”, “rule-based”. Inclusion criteria required peer-reviewed English articles presenting original modeling or EMS contributions for PV, WT, or hybrid systems. After duplicate removal (n = 118), title/abstract screening led to additional papers (n = 320) removal, and full-text eligibility assessment papers with insufficient modeling detail or no EMS relevance (n = 176) were also removed. The remaining 142 articles were included in the qualitative synthesis, as shown in Figure 3. These were classified into four thematic categories corresponding to the section structure of this review: PV models, WT models, EMS architectures, and simulation tools.

At the system level, the focus shifts from individual components to coordinated operation. Energy management systems (EMS) are responsible for dispatching power among PV arrays, wind turbines, storage units, and loads while satisfying technical constraints, economic objectives, and grid code requirements [14]. EMS strategies range from simple rule-based logic (e.g., state-of-charge thresholds) to advanced optimization methods (e.g., linear programming, model predictive control) and emerging reinforcement learning approaches [15]. Critically, the performance of any EMS depends not only on the control algorithm itself but also on the underlying models used for prediction, state estimation, and constraint formulation. A mismatch between component model fidelity and EMS requirements can lead to suboptimal decisions, instability, or excessive computational burden—a problem rarely addressed in existing reviews.

Existing survey papers tend to fall into three categories. The first focuses exclusively on PV or wind turbine modeling, with little attention to system coordination [16,17]. The second reviews EMS architectures for hybrid renewable systems but treats component models as black boxes, often assuming simplified linear or lookup table representations without critically examining their limitations [18,19]. The third category addresses hybrid systems from a techno-economic sizing perspective yet again and deemphasizes the dynamic coupling between model choice and control strategy [20]. Consequently, a systematic bridge between component modeling and system coordination is not addressed properly. This gap is increasingly problematic as hybrid systems adopt more sophisticated control methods (e.g., stochastic MPC, learning-based policies) that explicitly rely on model structure and uncertainty characterization.

This review paper directly addresses that gap. We provide a unified examination of PV and WT models alongside EMS architectures, with a specific focus on how model decisions affect coordination outcomes. Our contribution is threefold: (i) a comparative analysis of PV and WT models organized by fidelity, parameter accessibility, and computational suitability for EMS applications; (ii) a structured review of EMS strategies categorized by their underlying model requirements (from model-free to model-based); and (iii) a critical discussion of mismatches, trade-offs, and future directions, including hybrid modeling (physics + machine learning) and real-time coordination under uncertainty.

The remainder of this paper is organized as follows. Section 1 (this section) has introduced motivation and scope. Section 2 reviews photovoltaic models, from equivalent circuits to empirical and data-driven approaches. Section 3 covers wind turbine models, including aerodynamic, mechanical, and electrical representations. Section 4 examines energy management systems at the system level, linking control objectives to model fidelity. Section 5 provides a discussion of key trade-offs, gaps, and future research directions. Section 6 concludes the paper.

2. PV Systems Models

Photovoltaic cells convert sunlight directly into electricity through the photovoltaic effect. The performance, cost, and degradation characteristics of a PV module are strongly influenced by the semiconductor material and manufacturing technology employed [21]. Understanding these technological differences is essential for selecting appropriate component models, as each technology exhibits distinct current-voltage curve shapes, temperature coefficients, and spectral responses. Several main PV technologies are available:

• Monocrystalline Silicon (Mono-Si): Monocrystalline cells are fabricated from a single silicon crystal ingot, typically using the Czochralski process. These cells feature a uniform dark appearance and rounded edges. Mono-Si technology offers the highest efficiency among commercial silicon-based PV cells, typically ranging from 18% to 22%, due to the absence of grain boundaries that impede electron flow [22].
• Polycrystalline Silicon (Poly-Si): Polycrystalline cells are manufactured by melting multiple silicon fragments and casting them into ingots, resulting in a characteristic blue, speckled appearance. The presence of grain boundaries reduces efficiency compared to monocrystalline silicon, with typical values ranging from 15% to 18% [23].
• Thin-Film Technologies: Thin-film solar cells are fabricated by depositing one or more layers of photovoltaic material onto a substrate such as glass, plastic, or metal. The most common thin-film technologies include amorphous silicon (a-Si), cadmium telluride (CdTe), and copper indium gallium selenide (CIGS). Thin-film cells offer advantages in low-cost manufacturing and performance under diffuse light conditions and high temperatures, though their efficiencies are generally lower [24].
• Bifacial Panels: Bifacial solar panels capture sunlight on both the front and rear sides, utilizing reflected and diffused light from the ground and surrounding surfaces. This design can increase energy yield by 5% to 30%, depending on installation conditions [25].
• Emerging Technologies: Emerging PV technologies include perovskite solar cells and organic photovoltaics. Perovskite cells have achieved rapid efficiency gains exceeding 25% in laboratory settings, but face challenges related to long-term stability. These technologies often exhibit complex current-voltage behavior with significant hysteresis [26].

Accurate modeling of photovoltaic systems is fundamental to predicting energy yield, designing power electronics, implementing maximum power point tracking, and evaluating grid integration performance. PV models span a spectrum from simple empirical representations to complex physical equivalent circuits and, more recently, data-driven architectures, Figure 4. The choice of model directly impacts simulation accuracy, computational cost, parameter identification complexity, and ultimately, the effectiveness of higher-level energy management systems that rely on these models for forecasting and optimization. This section provides a structured classification of PV models, organizing them by their underlying principles. Rather than exhaustively cataloging every variant, we focus on model families most relevant to hybrid renewable energy system studies, highlighting their mathematical formulations, key parameters, calibration requirements, and practical limitations in the context of system-level coordination.

2.1. Empirical/Black-Box PV Models

Empirical or black-box models represent photovoltaic systems using purely data-driven relationships without explicit knowledge of internal physical parameters such as diode ideality factors, series resistance, or recombination losses. These models treat the PV system as an unknown nonlinear function that maps inputs (irradiance, temperature, voltage) to outputs (current, power) based solely on measured I-V or P-V data [27]. The primary advantage of empirical models lies in their ability to approximate complex behaviors without requiring detailed physical characterization of the PV cell or module. However, their accuracy is fundamentally limited by the quality, quantity, and representativeness of training data, and they typically lack extrapolation capabilities outside the range of measured conditions.

From an EMS perspective, empirical models offer low computational overhead and rapid evaluation, making them attractive for real-time applications, but their static or quasi-static nature may fail to capture dynamic phenomena such as partial shading transients, bypass diode switching, or thermal hysteresis. Furthermore, black-box models provide no direct insight into physical degradation mechanisms, limiting their long-term reliability for system optimization.

2.1.1. Lookup Table (LUT) Models

Lookup table models pre-store current or power values for discrete combinations of irradiance and temperature, typically derived from manufacturer datasheets or experimental measurements. During operation, the model retrieves the output corresponding to the nearest grid point, often employing linear or bilinear interpolation between entries. The primary appeal of LUT models is their simplicity and deterministic execution time, making them suitable for embedded controllers with limited computational resources.

However, LUT models suffer from several fundamental limitations. First, discretization errors arise from finite table resolution; finer tables reduce error but increase memory requirements and calibration effort. Second, interpolation between points assumes linearity in a fundamentally nonlinear system, leading to systematic inaccuracies near the maximum power point knee region. Third, LUTs cannot adapt to cell aging, soiling, or manufacturing variations without complete recalibration. Fourth, as noted in comparative studies of PV parameter extraction, approximation-based methods (which include LUT approaches) tend to produce incorrect estimation of the simulation current, and the root mean square error (RMSE) compared to more accurate analytical or numerical methods such as the Lambert W or Newton–Raphson approaches [28]. These inaccuracies, while acceptable for rough energy yield estimation, can propagate into EMS optimization errors when used for economic dispatch or battery scheduling.

2.1.2. Polynomial Regression (PR) Models

Polynomial regression models fit low-to-mid-order polynomials to measured I-V or P-V data, expressing output power or current as a polynomial function of irradiance, temperature, and sometimes voltage. These models range from simple univariate quadratic fits to multivariate polynomial surfaces with cross-terms. Regression models were additionally employed to predict solar power output. The following equation represents a basic regression model for PV power [29]:

$$P_{out}=k_1·G+k_2·G^2+k_3·G·T_{amb}+k_4·G·v$$

(1)

where:

• P_out—is the output power, W,
• G—is the solar irradiance, W/m²,
• k_n—are regression coefficients,
• T_amb—is the ambient temperature, °C,
• v—is the air speed at 10 m above grade, m/s.

The primary advantage of polynomial regression is its analytical tractability: polynomial expressions are differentiable, continuous, and computationally trivial to evaluate—properties that align well with gradient-based optimization methods commonly used in EMS. In [30], authors demonstrated that multivariate polynomial regression could achieve greater accuracy compared to conventional analytical methods for modeling photovoltaic-thermal (PVT) systems, while maintaining minimal model complexity suitable for control applications. Similarly, authors in [31] employed exponential polynomial regression models to forecast daily PV power generation using daylight duration as the primary predictor, achieving a standard residual error of 0.3022 kWh.

Nevertheless, polynomial regression has well-documented drawbacks. High-degree polynomials are prone to Runge’s phenomenon (oscillatory behavior at interval boundaries), necessitating careful order selection. Extrapolation beyond the training range is notoriously unreliable, as polynomial tails diverge rapidly. Furthermore, polynomial models assume a fixed functional form that may not capture abrupt changes due to partial shading, cloud edge effects, or bypass diode activation.

2.1.3. Artificial Neural Networks (ANN)

Artificial neural networks represent the most flexible and powerful class of black-box PV models. ANNs learn nonlinear input-output mappings from extensive datasets without requiring an explicit mathematical functional form. Common architectures applied to PV modeling include multilayer perceptron (MLP), recurrent neural networks (RNN), long short-term memory (LSTM), gated recurrent units (GRU), and convolutional neural networks (CNN).

ANNs excel at capturing complex, nonlinear relationships, including temperature-dependent efficiency variations, spectral effects, and partial shading patterns that are difficult to model analytically. In [32], the authors provide a comprehensive state-of-the-art review of five advanced ANN architectures for PV power forecasting, concluding that bidirectional GRU and LSTM offer higher forecasting accuracy, whether used as a standalone model or in a hybrid configuration. They also note that hybrid and upgraded metaheuristic algorithms have demonstrated exceptional performance when applied to standalone and hybrid ANN models.

For PVT systems integrated with phase change materials (PCM), authors in [33] reviewed ANN applications and found that MLPs can achieve high accuracy for stage limits when the models reach a steady situation, while recurrent networks like LSTM explain the dynamic behavior characteristics of the thermal responses adequately.

However, ANNs carry substantial practical burdens. They require large, high-quality training datasets covering the full operational envelope, including rare events such as extreme temperatures or soiling conditions. Architecture selection (number of layers, neurons, activation functions) remains more art than science, often requiring extensive hyperparameter tuning. Overfitting is a persistent risk, particularly with limited data. Finally, the “black-box” nature of ANNs limits interpretability: it is difficult to diagnose why a model failed or to guarantee physically plausible outputs (e.g., negative power at zero irradiance) without explicit constraints.

From an EMS perspective, the computational demands of ANNs, particularly during training, may be prohibitive for embedded real-time applications, though inference (forward pass) is typically fast.

2.2. Physical/Gray-Box PV Models

Equivalent-circuit models, also referred to as physical or gray-box models, represent the photovoltaic cell as a network of ideal electronic components that mirror the underlying semiconductor physics. Unlike black-box approaches, these models incorporate explicit circuit elements, current sources, diodes, and resistors, each corresponding to a specific physical phenomenon within the cell. The photocurrent source represents electron-hole generation by incident photons, the diodes model the p-n junction behavior, series resistance accounts for bulk and contact resistances, and shunt (parallel) resistance captures leakage currents due to manufacturing imperfections or material impurities.

The primary advantage of equivalent-circuit models lies in their interpretability: each parameter has a physical meaning, enabling diagnosis of degradation mechanisms, prediction of performance under varying conditions, and extrapolation beyond measured data ranges. Furthermore, these gray-box models strike a balance between the complete opacity of black-box methods and the prohibitive complexity of full numerical device physics simulations.

However, the parameter estimation problem for equivalent-circuit models is inherently challenging [34]. As noted in comprehensive surveys, the characteristic equation of the single-diode model is transcendental, meaning no closed-form analytical solution directly relates current and voltage without iterative or approximate methods. This mathematical property transforms parameter extraction into a non-convex optimization problem, requiring careful selection of numerical, analytical, or metaheuristic techniques. Moreover, the increased accuracy of more complex models (double-diode, triple-diode) comes at the cost of additional unknown parameters, exacerbating identifiability issues and computational demands.

From an EMS perspective, equivalent-circuit models are preferred for dynamic studies, MPPT design, and grid integration analyses where physical consistency and extrapolation capability are essential. Nevertheless, the computational burden of iterative parameter extraction and the propagation of parameter uncertainty into EMS optimization decisions remain significant practical concerns.

2.2.1. Single-Diode Model (SDM)

The single-diode model is the most widely adopted equivalent-circuit representation in PV literature, offering an optimal compromise between accuracy and complexity. The model consists of five key parameters: photocurrent I_ph, diode reverse saturation I_sat, diode ideality factor a, series resistance R_s, and shunt resistor R_sh, Figure 5.

The governing equation expresses the output current I_o as a function of terminal voltage V_o [35]:

$$I_o=I_{ph}·n_p-I_D·n_p\left(e^{{\displaystyle \frac{q\left(V_o+R_s{I}_o\right)}{akT{n}_s}}}-1\right)-n_p{\displaystyle \frac{q\left(V_o+R_s{I}_o\right)}{n_s{R}_{sh}}}$$

(2)

where:

• I_o—is the output current, A,
• I_ph—is the light-generated current, A,
• I_d—is the diode reverse saturation current, A,
• q—is the electron charge, 1.602 × 10⁻¹⁹ C,
• a—is the ideality factor,
• k—is the Boltzmann constant, 1.381 × 10⁻²³ J/K,
• V_o—is the output voltage, V,
• T—is the temperature, K,
• R_s—is the series resistance, Ω,
• R_sh—is the shunt resistance, Ω,
• n_s—is the number of cells connected in series,
• n_p—is the number of cells connected in parallel.

The SDM captures the primary current-voltage characteristics of PV cells with remarkable fidelity across most operating conditions. Its five parameters correspond to distinct physical phenomena: I_ph scales linearly with irradiance, I_o and a describe recombination in the space-charge region, while R_s and R_sh account for ohmic losses and leakage paths, respectively. The model’s popularity stems from its tractable parameter space (only five unknowns) and the availability of numerous extraction methods ranging from analytical approximations to sophisticated metaheuristic algorithms [36].

The SDM is the preferred choice for EMS applications requiring a balance between physical interpretability and computational feasibility. Its five-parameter structure enables temperature and irradiance corrections essential for forecasting and real-time optimization. However, the need for iterative current calculation can become a bottleneck in embedded EMS implementations with stringent timing constraints.

The SDM is widely used in the literature; in [37], the authors investigated the PV power supply of a centrifugal pump system with the help of a single-diode model in MATLAB/Simulink (R2018a) environment. The model allows for the simulation of the properties of a specific PV module (SunPower SPR-415E; SunPower Corporation, San Jose, CA, USA) with a nominal output power of approximately 400 W, Figure 6. The model helps to estimate the energy yield and compare it to the pumping system’s consumption demand.

2.2.2. Double-Diode Model (DDM)

The double-diode model (DDM) extends the SDM by incorporating a second diode in parallel with the first, providing a more accurate representation of recombination phenomena within the solar cell, as shown in Figure 7.

The physical justification for the DDM lies in the distinct recombination mechanisms occurring in different regions of the cell. The first diode D₁ represents recombination in the bulk neutral regions via the Shockley-Read-Hall mechanism. The second D₂ accounts for recombination in the space-charge region (depletion layer) where carrier concentrations are lower [38]. At high irradiance levels (typical operating conditions), the ideality factor for the first diode dominates, and the DDM effectively reduces to the SDM. However, at low irradiance, such as dawn, dusk, or cloudy conditions, space-charge recombination becomes proportionally significant, and the DDM achieves superior accuracy.

The DDM’s seven-parameter space is considerably more challenging than the SDM’s five-parameter problem. The increased dimensionality exacerbates identifiability issues; multiple parameter combinations can produce nearly identical I-V curves, making physical interpretation ambiguous. Furthermore, metaheuristic algorithms often require more iterations and careful hyperparameter tuning to avoid premature convergence to suboptimal solutions [39].

The DDM is most relevant for EMS applications that must operate accurately under variable irradiance conditions, such as microgrids in regions with frequent cloud cover or hybrid systems where PV forecasting during low-light periods is critical. The computational overhead of iterative current calculation or Lambert W function evaluation may, however, limit real-time applicability. Reduced-order approximations of the DDM represent an active research area for embedded EMS deployment.

2.2.3. Tripple-Diode Model (TDM)

The triple-diode model represents the most detailed equivalent-circuit formulation commonly found in the literature, incorporating three parallel diodes to capture recombination phenomena across multiple regions of the PV cell. The physical rationale for the third diode is the modeling of grain boundary effects and additional recombination centers present in polycrystalline and thin-film technologies. While SDM and DDM were originally developed for monocrystalline silicon cells, emerging PV technologies, including polycrystalline, perovskite, and thin-film, exhibit more complex recombination behavior that may benefit from additional circuit elements.

In [40], the authors proposed a novel, scalable triple-diode-based generalized PV model implemented in MATLAB/Simulink. Their model offers the flexibility to represent SDM, DDM, or TDM configurations by including nine or fewer parameters, enabling inclusive comparison across model complexities. Validation against nine commercial PV modules under standard test conditions yielded modeling errors ranging from 0.2% to 7.31%, demonstrating accuracy comparable to or superior to widely referenced practical models. Furthermore, scalability was verified by modeling a 100 kW PV array under hot climatic conditions (Jodhpur, Rajasthan, reaching 50 °C ambient temperature), where the model correctly simulated a 13.26% average output power reduction.

A comparative study in [41] evaluated SDM, DDM, and TDM for fitting I-V curves of perovskite solar cells using a hybrid PSO-SQP optimization algorithm. Their results indicate that the TDM exhibited better performance in capturing the I-V characteristics of PSCs with greater precision and fewer iterations, surpassing both the SDM and DDM. However, the authors noted a critical caveat: for all three models, the extracted ideality factors deviated from the conventional range expected for single-junction cells. Constraining ideality factors within this physically plausible range compromised fitting accuracy, suggesting that the physical interpretation of the model parameters that are commonly accepted for single junction semiconductor cells is not applicable for PSCs. This finding underscores a broader concern: increased model complexity does not guarantee physically meaningful parameters, and validation should consider both curve-fitting metrics and parameter plausibility.

The TDM is generally too computationally intensive for real-time EMS applications, given the nine-parameter optimization and iterative current calculation. However, its value lies in offline applications such as technology assessment, degradation studies, and the development of reduced-order models for specific cell types.

2.3. Approximate Models

Approximate PV models deliberately sacrifice a degree of accuracy in exchange for computational speed, analytical tractability, or ease of implementation. These models are particularly valuable in applications where absolute precision is less critical than rapid evaluation, convex optimization guarantees, or minimal parameter requirements. Common use cases include preliminary system sizing, real-time EMS with limited computational resources, educational demonstrations, and optimization problems where the non-linearities of full equivalent-circuit models would render the problem intractable.

The fundamental trade-off across all approximate models is between fidelity and simplicity. While these models may introduce systematic errors, sometimes exceeding 10–15% near the maximum power point, they enable closed-form analytical solutions, reduce simulation time by orders of magnitude, and allow the use of linear programming or quadratic programming techniques that guarantee global optimality [42].

2.3.1. Ideal Current Source (ICS) Model

The ideal current source model represents the simplest possible PV abstraction, neglecting all diodes and resistances [43]. In this model, the PV generator is treated as a current source whose output current depends only on irradiance, remaining constant regardless of terminal voltage until the open-circuit voltage is approached, at which point the current drops abruptly to zero. The short-circuit current scales linearly with irradiance, meaning that at half the standard irradiance, the current is also halved, while the open-circuit voltage is typically assumed constant or only weakly dependent on temperature [44].

This model captures only the most basic PV behavior: current proportional to irradiance, independent of voltage until open circuit [45]:

$$I_{ph}={\displaystyle \frac{G}{1000}}\times \left[I_{Lref}+\alpha \left(T_c-25\right)\right]$$

(3)

where:

• I_Lref—is the short circuit current, A,
• α—is the current-temperature coefficient, A/°C,
• T_C—is the cell temperature, °C.

It completely ignores the exponential diode characteristic, the voltage-dependent current roll-off, and the existence of a maximum power point distinct from the short-circuit and open-circuit conditions. As a result, the model cannot predict power output for any operating point other than short circuit, making it essentially useless for maximum power point tracking or power flow analysis. Despite these limitations, the ideal current source model finds occasional use in extremely high-level system studies where PV is aggregated with other sources and only annual energy yield estimates are required. Some very early microgrid sizing tools employed this model, assuming the PV array always operates at its maximum power point, which the model cannot represent [46]. Contemporary applications are limited to educational contexts or first-order feasibility checks.

The ideal current source model is unsuitable for any EMS application requiring dispatch decisions based on actual PV power availability. Its only possible use is in preliminary system sizing where worst-case or average irradiance conditions suffice, and even then, a simple fixed derating factor applied to nameplate capacity would be more accurate.

2.3.2. Linear Approximation (LA) Model

Linear approximation models replace the nonlinear exponential current-voltage relationship of PV cells with piecewise linear or globally linearized representations. These models are motivated by the desire to embed PV systems into linear programming, quadratic programming, or mixed-integer linear programming EMS formulations, where convexity and linearity guarantees enable efficient solution using commercial solvers such as CPLEX 22.1.2, Gurobi 13.0.2, or open-source alternatives.

The simplest linearization replaces the entire current-voltage curve with a single straight line connecting the short-circuit point (zero voltage, short-circuit current) and the open-circuit point (open-circuit voltage, zero current) [47]. This linear relationship implies a constant negative slope, meaning the PV behaves like a fixed resistor. The corresponding power becomes a quadratic function of voltage, reaching its maximum at exactly half the open-circuit voltage, with maximum power equal to one-quarter of the product of short-circuit current and open-circuit voltage. For typical crystalline silicon cells, where the fill factor ranges from 0.7 to 0.85, this linear approximation overestimates the true maximum power point voltage and underestimates maximum power.

To improve accuracy while retaining linearity, researchers have developed piecewise linear models that partition the current-voltage curve into multiple linear segments [48]. A common approach uses three segments: a shallow-slope region near short circuit, a steep-slope region near the maximum power point, and a near-vertical region approaching open circuit. Each segment is represented by a simple linear equation of the form current equals slope times voltage plus intercept, with each equation valid only within a specific voltage range.

Linear approximation models are valuable for EMS formulations that require convexity or linearity guarantees, such as real-time dispatch using linear programming, unit commitment with PV uncertainty represented via linear chance constraints, and coordinated control of PV-storage systems where quadratic costs are acceptable. However, users must compensate for systematic underestimation of PV power at the maximum power point, typically by scaling the linear model or incorporating a correction factor derived from offline simulation.

2.3.3. Fractional Open-Circuit Voltage (FOCV) Model

The fractional open-circuit voltage method is one of the simplest and most widely implemented approaches for maximum power point tracking in small-scale PV systems [49]. Rather than modeling the full current-voltage curve, this method exploits an empirical observation: for most PV technologies, the maximum power point voltage is approximately a fixed fraction of the open-circuit voltage across a wide range of operating conditions. This fraction, typically denoted as k, generally ranges from 0.71 to 0.80 depending on cell technology. For crystalline silicon cells, the commonly cited value is approximately 0.76, while for thin-film technologies such as amorphous silicon or CIGS, the fraction may be lower, typically between 0.70 and 0.75, due to different recombination characteristics [50].

In practical implementation, the fractional open-circuit voltage method operates as follows. First, the system periodically disconnects the PV array from the load or briefly opens the circuit. Second, it measures the open-circuit voltage, which requires only a simple voltage measurement and no current sensing. Third, it calculates the target maximum power point voltage by multiplying the measured open-circuit voltage by the fixed fraction k. Fourth, it adjusts the power converter duty cycle to regulate the PV voltage at this calculated target. Finally, it resumes normal operation until the next sampling interval.

The primary advantage of the fractional open-circuit voltage method is its extreme simplicity: no current sensor is required, the control law involves only a single multiplication, and convergence is instantaneous because there is no perturbation or iteration. This makes the method particularly attractive for very low-cost microcontrollers, energy harvesting applications, and systems where the power loss during periodic open-circuit voltage measurement is acceptable.

The fractional open-circuit voltage method is unsuitable as a PV model for EMS applications because it does not provide a continuous power-versus-voltage relationship needed for dispatch optimization. Instead, it is a control technique for local maximum power point tracking. In hierarchical EMS architectures, the local maximum power point tracking controller implementing this method reports available power to the supervisory EMS as a scalar value, which the EMS treats as a parameter rather than as a variable.

2.4. PV Simulation Tools

Beyond component-level mathematical modeling, practical implementation of PV systems for planning, sizing, and energy yield assessment requires specialized simulation tools. These software platforms translate the physical and empirical models described in Section 2.1, Section 2.2 and Section 2.3 into user-friendly interfaces that enable engineers, researchers, and system designers to predict energy production and optimize system configurations [51]. The choice of simulation tool significantly impacts design outcomes, as different software packages employ varying algorithms for irradiance transposition, temperature modeling, shading analysis, and inverter efficiency calculations.

2.4.1. MATLAB/Simulink for PV Systems

In scientific literature, MATLAB/Simulink is the prevailing simulation tool because it is a high-fidelity, equation-based simulation environment widely used for research and development of PV systems, particularly for MPPT algorithm design, power electronics integration, and dynamic system studies [52]. The software includes a built-in PV array block within the Simscape Electrical (2026a) toolbox and supports custom implementation of single-diode and double-diode models. For hybrid renewable energy systems, MATLAB/Simulink enables co-simulation of PV arrays alongside wind turbines, battery storage, and grid interfaces, making it a preferred platform for academic research.

2.4.2. PV*SOL

PV*SOL premium 2026 is a professional system-based simulation tool for detailed design and financial analysis of grid-connected PV systems, including building-integrated and off-grid configurations. It distinguishes itself through advanced 3D shading analysis capabilities, enabling accurate modeling of complex rooftop installations with nearby obstructions. The authors in [53] conducted a comparative validation study and found that PV*SOL exhibited the lowest error among seven software tools when validated against real-world data from an 84.5 kW solar plant.

2.4.3. Helioscope

A web-based simulation platform, Helioscope (https://helioscope.aurorasolar.com/), has a cloud-native PV design known for its intuitive user interface and rapid 3D modeling capabilities. The platform excels at detailed shade analysis using 3D scene reconstruction and supports both fixed-tilt and single-axis tracking systems. Helioscope is particularly popular among commercial solar installers and project developers due to its rapid simulation turnaround time and professional report generation [54].

2.4.4. Solarius PV

A comprehensive system-based simulation tool, Solarius PV 18.0., is offering integrated design, shading analysis, and financial reporting for residential, commercial, and utility-scale PV systems. The tool features a built-in 3D modeling environment for accurate shading assessment and supports a wide range of module and inverter databases [55]. In validation studies, Solarius PV demonstrates among the lowest errors compared to real-world performance data, indicating high credibility for accurate energy yield prediction.

2.4.5. HOMER Pro

A specialized simulation and optimization tool, HOMER Pro 3.18.4, is optimized for hybrid renewable energy systems, including PV-wind-diesel-battery configurations, with a strong focus on techno-economic analysis for off-grid and grid-connected applications [56]. The software performs thousands of iterative simulations across different system configurations to identify the least-cost combination meeting specified reliability constraints. The main feature is that HOMER Pro uniquely bridges component modeling and system-level EMS design, making it particularly relevant for hybrid PV-wind system studies.

2.4.6. SolarGis

A simulation tool, SolarGis 2.7.1, specializes in solar resource assessment and PV performance modeling. It is distinguished by its high-resolution satellite-derived irradiance database [57]. The platform’s core strength lies in its long-term time series of global horizontal, direct normal, and diffuse horizontal irradiance, derived from geostationary satellite observations. SolarGis is widely used by project developers and financiers for bankable energy yield reports, often in conjunction with other detailed simulation tools.

An overview of the mentioned simulation tools for photovoltaic systems is presented in

Table 1. PV Simulation Tools Comparison.

Simulation Tool	Modeling Approach	Key Strengths
MATLAB/Simulink	Equation-based (custom models).	Flexibility, custom MPPT, co-simulation with other tools.
PV*SOL	3D ray-tracing.	High accuracy, advanced 3D shading.
Helioscope	Cloud-native 3D modeling.	Web-based, rapid layout.
Solarius PV	3D modeling + economic analysis.	High accuracy, integrated reporting.
HOMER Pro	Iterative optimization.	Multi-source optimization, energy management focus.
SolarGis	Satellite-derived irradiance.	High-resolution resource data, high-accuracy simulation

.

3. Wind Turbine Models

Wind turbines convert the kinetic energy of moving air into electrical energy through rotating machinery. Unlike photovoltaic systems, which have no moving parts, wind turbines encompass a wide range of mechanical and electrical architectures that significantly influence their modeling requirements, control complexity, and grid integration characteristics. There are several main types of wind turbine technologies:

• Horizontal Axis Wind Turbines (HAWTs): Horizontal axis wind turbines are the most common configuration for utility-scale wind power generation, characterized by a rotor with two or three blades rotating about a horizontal axis aligned with the wind direction [58]. HAWTs require a yaw mechanism to orient the rotor into the wind and typically operate at higher tip-speed ratios, achieving power coefficients of 0.45 to 0.50.
• Vertical Axis Wind Turbines (VAWTs): Vertical axis wind turbines feature a rotor that rotates about a vertical axis, with common designs including Darrieus (lift-type) and Savonius (drag-type) configurations [59]. VAWTs are omnidirectional, requiring no yaw mechanisms, and offer advantages in urban environments and floating offshore applications due to lower center of gravity and reduced mechanical complexity. However, their aerodynamic efficiency is generally lower than that of HAWTs, and they exhibit highly unsteady loading. VAWTs are less common in large-scale hybrid systems but appear in distributed and small-scale applications.

Variable-speed wind turbines dominate modern installations, enabling higher energy capture and reduced mechanical loading by allowing the rotor speed to vary with wind speed [60]. Variable-speed operation is typically achieved through power electronic converters, which decouple the generator from the grid frequency. Two primary configurations exist:

• Doubly-Fed Induction Generators (DFIGs): DFIGs use a wound-rotor induction generator with the stator connected directly to the grid and the rotor connected via a partial-scale power converter [61]. This configuration offers variable-speed operation at reduced converter cost and size and enables independent control of active and reactive power [62]. DFIGs are sensitive to grid disturbances and require careful protection against voltage dips.
• Permanent Magnet Synchronous Generators (PMSGs): PMSGs use a full-scale power converter that decouples the generator completely from the grid, allowing variable-speed operation over a wider range [63]. The absence of slip rings and gearboxes in direct-drive configurations reduces maintenance requirements, and PMSGs offer better low-voltage ride-through capability compared to DFIGs. The full-scale converter increases initial cost but provides greater grid support capabilities, including synthetic inertia and reactive power control [64].

Wind turbine modeling presents fundamentally different challenges than photovoltaic systems, primarily due to the conversion of mechanical energy from moving air into electrical energy through rotating machinery. Unlike PV cells, which have no moving parts and respond almost instantaneously to irradiance changes, wind turbines exhibit complex multi-physics dynamics spanning aerodynamic forces and electrical generator characteristics across timescales from milliseconds to seconds. These dynamics are further complicated by the stochastic and spatially distributed nature of wind resources, including turbulence, shear, wake effects, and gusts [65]. Consequently, wind turbine models span a broad spectrum from highly detailed aerodynamic simulations to simplified lookup table or constant power models.

The choice of wind turbine model fidelity has profound implications for simulation accuracy and computational cost. Overly detailed models may be computationally prohibitive for optimization, while overly simplified models may fail to capture critical phenomena such as wake-induced power deficits in wind farms. This section provides a focused classification of essential wind turbine models, Figure 8.

3.1. Power Capture Models

Aerodynamic models describe how a wind turbine extracts kinetic energy from the moving air mass and converts it into mechanical torque on the rotor shaft. This conversion process is governed by the fundamental physics of fluid flow around the turbine blades, and the accuracy of the aerodynamic model directly determines the fidelity of the entire wind turbine representation.

The fundamental equation governing wind turbine power capture expresses the electrical power output as a function of wind speed, turbine geometry, and efficiency factors. The electrical power extracted by a wind turbine is given by the product of the available kinetic power in the wind and two efficiency terms: the aerodynamic power coefficient and the generator efficiency. This relationship is captured by the well-known wind turbine power equation [66]:

$$P_{WT}={\displaystyle \frac{1}{2}}\cdot {\rho \cdot A}_{WT}\cdot V^3\cdot C_{WT}{\cdot \eta }_g$$

(4)

where:

• P_WT—is the wind turbine, W,
• ρ—is the air density, kg/m³,
• A_WT—is the wind turbine rotor’s swept area with radius R, m²,
• V³—is the wind speed, m/s,
• C_WT—is the power coefficient that represents the turbine’s aerodynamic efficiency,
• η_g—is the efficiency of a generator coupled to WT’s shaft directly or through a step-up gearbox.

This fundamental equation forms the basis for nearly all wind turbine models used in power system analysis and EMS applications, from the most detailed aerodynamic simulations to the simplest constant power approximations. Among the two most relevant aerodynamic modeling approaches are the blade element momentum theory and the simplified power coefficient lookup tables. Blade element momentum theory represents the highest fidelity among these, combining momentum conservation principles with local airfoil aerodynamics to predict the power coefficient from first principles without relying on precomputed lookup tables. Simplified power coefficient lookup tables, which store precomputed values of C_WT as a function of tip-speed ratio and blade pitch angle, are the most common choice for EMS applications because they evaluate the complete power equation in a single table lookup, avoiding iterative calculations.

3.1.1. Blade Element Momentum (BEM)

Blade element momentum theory is the industry-standard aerodynamic model for wind turbine design and performance analysis, balancing reasonable computational cost with sufficient physical accuracy. The theory combines two complementary approaches: momentum theory, which considers the overall momentum balance of the air flowing through the rotor disk, and blade element theory, which considers the local lift and drag forces on individual blade segments [67]. By solving these two formulations iteratively until convergence, blade element momentum theory predicts the axial and tangential induction factors, from which the power capture and thrust force can be calculated [68].

The key challenge in blade element momentum theory is that the momentum and blade element components are coupled through the induction factors, which are not known a priori. The theory, therefore, requires an iterative solution procedure: the induction factors are guessed initially, the blade element calculations are performed, the resulting forces are used to update the induction factors via the momentum equations, and the process repeats until the induction factors stabilize. Under certain operating conditions, such as turbulent wake or heavily loaded rotor states, the standard momentum equations become invalid, and empirical corrections must be applied to ensure convergence. In [69], authors combine the BEM method with PGD to optimize the blade profile of a horizontal axis wind turbine, achieving a 21.7% improvement in the power coefficient for the turbine compared to a 20 kW reference baseline.

3.1.2. Simplified Power Coefficient (SPC) Lookup Table

The simplified power coefficient lookup table model represents the most common and practical aerodynamic model for many applications. Rather than solving the iterative blade element momentum equations online or performing computationally expensive computational fluid dynamics simulations, this model precomputes the power coefficient C_WT for a range of operating conditions and stores the results in a lookup table [70]. The tip-speed ratio is defined as the ratio of the blade tip speed to the wind speed. The blade tip speed is the product of the rotor rotational speed and the blade radius. A low tip-speed ratio indicates that the rotor is turning slowly relative to the wind, while a high tip-speed ratio indicates fast rotation. The power coefficient C_WT is a strong function of this tip-speed ratio, typically rising from zero at standstill to a maximum at an optimal tip-speed ratio, then gradually decreasing as the rotor spins too fast and encounters increased drag. For modern three-bladed horizontal-axis wind turbines, the optimal tip-speed ratio typically falls between 6 and 8, where the power coefficient reaches its maximum value of 0.45 to 0.50 [71].

The blade pitch angle is the angle between the blade chord line and the plane of rotation. Most large wind turbines employ active pitch control, where the blades can be rotated about their longitudinal axis to adjust aerodynamic forces. In [72,73], the authors propose a two-stage power stabilization control framework for floating offshore wind turbines that integrates field data fusion forecasting with adaptive pitch regulation to mitigate wind-wave coupling perturbations, achieving a 95% reduction in wind power ramp events and a 43.6% reduction in power slope variability.

At wind speeds below rated, the blades are typically set to a fine pitch angle, often zero degrees, to maximize power capture. At wind speeds above rated, the blades are pitched toward feather, reducing the angle of attack and deliberately spilling excess aerodynamic power to prevent generator overload. The power coefficient lookup table, therefore, becomes a two-dimensional array, with tip-speed ratio as one dimension and blade pitch angle as the other.

The primary advantage of the lookup table model is its computational efficiency [74,75]. Evaluating the fundamental power equation with a table lookup requires only a few microprocessor operations and can be executed in microseconds, making it suitable for real-time EMS optimization involving hundreds of turbines. Additionally, the model retains physical interpretability because it is directly derived from blade element momentum theory and respects the fundamental physics captured in the power equation. The lookup table also naturally handles the nonlinear relationship between wind speed and power, including the cut-in, rated, and cut-out regions of the turbine operating curve.

3.2. Reduced Order Models

Simplified and reduced-order wind turbine models deliberately sacrifice aerodynamic and mechanical detail to achieve computational speed, analytical tractability, and low parameters. While the full aerodynamic models described in Section 3.1 are essential for turbine design and detailed simulation studies, they are generally too computationally intensive to embed directly within EMS optimization loops that must solve dispatch problems in seconds or minutes [76]. Simplified models bridge this gap by representing the wind turbine as a static or quasi-static power source whose output depends primarily on wind speed, with all internal dynamics, including blade pitch response, generator transients, and drivetrain oscillations, either neglected or aggregated into simple empirical relationships [77].

3.2.1. Constant Power (CP) Model

The constant power model is one of the simplest possible representations of a wind turbine, treating the turbine as a dispatchable power source with a fixed maximum power output. In this model, the wind turbine is assumed to be capable of delivering constant power P_WT, up to its rated capacity, whenever wind conditions permit [78]. The control system receives either a forecasted time series of expected power output for day-ahead scheduling or a real-time measurement for intra-day dispatch, and the underlying wind speed, aerodynamic efficiency, and generator dynamics are entirely abstracted away.

The primary justification for the constant power model is that modern wind turbines with fast pitch control and power electronics can regulate their output to a commanded setpoint with high accuracy and rapid response [79]. From the perspective of an EMS operating on minute-to-hour timescales, the wind turbine appears as a controllable power source that can track a dispatch signal, subject to the constraint that the requested power cannot exceed the instantaneous available power determined by wind conditions. Many grid codes now require wind farms to provide dispatchable power, meaning they must be able to curtail output to a specified level below the available power [80].

The limitations of the constant power model become apparent in several scenarios. First, during above-rated wind speeds, the turbine’s pitch control system actively limits power to the rated value, and the constant power model correctly captures this behavior. However, during below-rated operation, the available power varies with the cube of wind speed according to Equation (4), and a constant power assumption would be grossly inaccurate if the forecast error is large. Second, the model ignores the turbine’s inertial response, which can provide temporary power support during frequency disturbances, a capability increasingly valued by grid operators. Third, the constant power model cannot represent the reactive power capability of modern wind turbines, which can provide voltage support even when active power is curtailed. Fourth, the model assumes perfect tracking of the dispatch signal, whereas real turbines have ramping limits and minimum power thresholds [81].

3.2.2. Linearized Small-Signal (LSS) Model

The linearized small-signal model represents a wind turbine as a linear transfer function relating small perturbations in wind speed to small perturbations in power output around a nominal operating point. This model is derived by taking the first-order Taylor series expansion of the nonlinear power equation around a specific operating condition, such as a particular wind speed, rotor speed, and pitch angle [82]. The resulting linear model captures the local dynamic response of the turbine to small disturbances, such as wind gusts or grid frequency deviations, and is widely used in stability studies and control system design.

The LSS model reveals several important dynamic properties of wind turbines. First, the model includes the inertial response, which describes how the turbine’s rotating mass provides temporary power support during frequency disturbances. This inertial response appears as a lead-lag transfer function that can be tuned by the generator controller [83]. Second, the model captures the pitch actuator dynamics, which limit how quickly the turbine can reduce power during above-rated wind conditions. Third, the model includes the drivetrain torsional modes, which are lightly damped oscillations that can affect power quality and mechanical loads.

The linearized small-signal model is primarily relevant for studies that require assessment of wind turbine contribution to grid frequency response or small-signal stability. For example, when a hybrid PV-wind system operates in islanded mode [84], the linearized models of all generators can be combined to analyze the overall system’s stability margin and design appropriate controllers. However, for routine dispatch optimization and scheduling, the linearized model is unnecessarily complex, and the simpler lookup table or constant power models are preferred.

3.3. Software Tools for Wind Turbine Simulation

Wind turbine simulation tools span a wide spectrum from flexible equation-based environments for control design to high-fidelity aerodynamic solvers and dedicated controller frameworks. Unlike PV simulation tools that focus primarily on energy yield prediction, wind turbine software must address the multi-physics nature of rotating machinery, including aerodynamics, structural dynamics, and control systems. This subsection reviews four essential software tools often used in the literature for wind turbine simulation: MATLAB/Simulink (R2026a), OpenFAST 5.0, AMR-Wind 3.7.0, and ROSCO 2.10.4.

3.3.1. MATLAB/Simulink for Wind Turbine Systems

Like for PV systems, this simulation environment is widely used for wind turbine control system design, power converter modeling, and grid integration studies [85]. The software includes specialized blocks for simplified generator modeling, enabling maximum power point tracking implementation and grid synchronization studies without the computational burden of detailed aerodynamic models. For educational and research applications, Simulink models support both induction and synchronous generators, advanced control strategies, and scalable architectures for various wind farm sizes [86]. Its primary limitation is the lack of native high-fidelity aerodynamic models, requiring users to implement custom blade element momentum formulations or couple with external tools.

3.3.2. OpenFAST (FAST)

The industry-standard open-source wind turbine simulation tool OpenFAST was developed by the U.S. National Renewable Energy Laboratory (NREL). It builds upon the legacy FAST v8 code, integrating aerodynamics, hydrodynamics, control systems, and structural dynamics to enable comprehensive coupled nonlinear aero-hydro-servo-elastic time-domain simulations of wind turbines [87]. OpenFAST supports various configurations, including land-based, fixed-bottom offshore, and floating offshore turbines, and is widely used for reference turbine designs such as the IEA 3.4 MW, 10 MW, 15 MW, and 22 MW models. The platform fosters an open-source developer community with robust software engineering, unit testing, and multi-platform build capabilities, making it the foundation for most wind turbine research and development workflows.

3.3.3. AMR-Wind

This tool is a high-fidelity computational fluid dynamics solver developed by NREL for modeling wind farm aerodynamics and atmospheric boundary layer interactions. The solver features adaptive mesh refinement (AMR) capabilities, enabling blade-resolved simulations of wind turbines with unprecedented detail while managing computational cost through dynamic mesh refinement [88]. AMR-Wind is a core component of the ExaWind software stack, which couples it with Nalu-Wind 2.4.0 (near-body flow solver), TIOGA 1.3.0 (overset grid assembly), and OpenFAST (structural dynamics) to enable large-scale simulations of entire wind farms with blade-resolved turbines [89]. The solver is designed for high-performance computing environments, with simulations scaling to hundreds of millions of cells on GPU-accelerated supercomputers.

3.3.4. Reference Open Source Controller (ROSCO)

ROSCO is NREL’s reference controller framework that facilitates the design and implementation of wind turbines and wind farm controllers for fixed and floating offshore turbines. The framework includes a large set of modular controllers and advanced functionalities, including yaw control, individual blade pitch control, and floating platform feedback, that can be combined based on the intended application [90]. ROSCO integrates directly with OpenFAST, enabling representative dynamic simulations with controller models, and supports a Python 3.14.3-based toolbox that allows generic controller tuning without requiring aeroelastic simulations or linearized state-space models [91]. The framework has been used to provide reference controllers for many recent reference turbines, including the IEA 3.4 MW, 10 MW, 15 MW, and 22 MW designs, enabling comparison of controller capabilities across different turbine models.

An overview of the described simulation tools for wind turbines and their advantages is presented in

Table 2. Wind Turbine Simulation Tools Comparison.

Simulation Tool	Primary Application	Key Strengths
MATLAB/Simulink	Control design, grid integration.	Flexibility, MPPT, education.
OpenFAST	Aero-hydro-servo-elastic simulation.	Industry standard, multi-physics.
AMR-Wind	High-fidelity CFD, wake modeling.	Blade-resolved, HPC scalability.
ROSCO	Controller design and tuning.	Open reference, OpenFAST compatible.

.

4. Energy Management System for Hybrid PV–WT

While previous Section 2 and Section 3 were focused on component-level models for PV arrays and wind turbines, this section shifts attention to the system level, where energy management systems coordinate multiple generators, storage devices, and loads to achieve reliable, economical, and sustainable operation [92]. An EMS is the decision-making core of a hybrid renewable energy system, responsible for dispatching power among available sources, managing energy storage, scheduling grid interactions, and responding to forecast uncertainties [93]. The performance of any EMS is fundamentally constrained by the fidelity and structure of the underlying component models: a highly simplified constant power PV model enables fast linear programming but cannot capture voltage-dependent curtailment, while a detailed single-diode model provides physical accuracy at the cost of solving nonlinear equations that may be prohibitive in real-time optimization scenarios. EMS architecture can be organized into three broad categories:

• Rule-based;
• Optimization-based;
• Learning-based.

It is important to keep in mind that mismatches between EMS requirements and component model fidelity lead to suboptimal outcomes: overly simple models may cause constraint violations or missed economic opportunities, while overly complex models may render the EMS computationally intractable for real-time deployment, as in Figure 9.

4.1. Rule-Based EMS

One of the most commonly used approaches in practice is rule-based EMS that relies on deterministic if-then-else logic, state machines, or look-up tables to make dispatch decisions without solving an optimization problem in real time [94]. Common rules can include simplified logical statements like: “If battery state of charge (SOC) exceeds 80 percent and load is low, curtail PV output” or “If wind power exceeds load and battery is full, sell to grid”, Figure 10. These rules are typically derived from engineering heuristics, operator experience, or offline simulation studies [95].

This type of EMS requires simplified, low-fidelity component models. The low computational cost of these models enables real-time implementation on embedded hardware, even though the EMS control decisions are made on slower timescales consistent with power system dynamics. The constant power model for wind mentioned in Section 3.2.1 is sufficient because the EMS only needs to know whether available renewable power exceeds the load or not. It is not necessary to know the precise shape of the I-V curve or the aerodynamic power coefficient [96]. The power versus wind speed lookup tables described in Section 3.2.2 may be used to improve accuracy when rules depend on specific wind speed thresholds. The low computational cost of rule-based EMS makes it compatible with simple PV models such as the ideal current source mentioned in Section 2.3.1 for very basic systems, though this is rarely advisable due to the model’s poor accuracy [97].

The primary advantages of a rule-based energy management system are extreme simplicity, deterministic behavior, and minimal computational requirements. Rule-based EMS can be implemented on an industrial-grade microcontroller with a decent amount of available memory. However, rule-based EMS is inherently suboptimal because the rules are static and do not adapt to changing electricity prices, weather forecasts, or battery degradation. Performance degrades significantly as system complexity increases, such as multiple wind turbines, different PV orientations, and time-varying tariffs, because the number of possible rules grows combinatorially [98].

Rule-based EMS is common in small off-grid systems, educational microgrids, and backup power systems where cost and simplicity outweigh optimality [99]. In a hybrid PV-wind context, rule-based EMS is often used as a fallback when communication or computation fails, or as a baseline for comparing more advanced EMS.

In [100], the authors propose an enhanced rule-based (ERB) energy management for an islanded microgrid comprising PV, wind turbine, ESS, and diesel generator, incorporating a day-ahead load shifting mechanism to maximize renewable energy utilization, achieving reductions of 2827.96 in operational costs, 87.87 in greenhouse gas (GHG) emissions costs, and 1742.77 kW in power losses compared to other rule-based EMSs. In [101], the authors propose a rule-based energy management system for a remote area hybrid energy system comprising solar PV, battery, electrolyzer, hydrogen tank, and fuel cell, achieving optimal component sizing and energy coordination with a minimum levelized cost of electricity of 0.2743 USD per kWh while reliably meeting a maximum load of 20 kW.

4.2. Optimization-Based EMS

Another energy management system is optimization-based. This EMS formulates the dispatch problem as a mathematical program that minimizes a cost function, for instance, operating cost, fuel consumption, battery degradation, or subject to system constraints, such as power balance, generation limits, ramp rates, state of charge bounds [102]. The optimization is solved at regular intervals, with the solution providing setpoints for generators, storage, and grid exchange until the next update. Common formulations include linear programming, quadratic programming, mixed-integer linear programming, and model predictive control [103].

Optimization-based EMS requires component models that are differentiable, convex, or linearizable to enable efficient solution algorithms. The choice of PV and wind turbine models directly determines the optimization class and solver feasibility:

• Linear programming (LP) EMS requires linear component models. The constant power approximation for PV and wind is ideal because power appears as a simple parameter [104]. The globally linearized PV model discussed in Section 2.3.2 can also be used if the EMS optimizes voltage setpoints, but the quadratic power function becomes a linear constraint only with additional binary variables [105];
• Quadratic programming (QP) EMS can accommodate convex quadratic cost functions, such as penalizing deviations from a dispatch schedule or modeling inverter efficiency as a quadratic function of power [106]. The piecewise linear PV model can be reformulated as a quadratic program with convex constraints. For wind, the power versus wind speed lookup table discussed in Section 3.2.2 can be approximated as a quadratic function around the nominal operating point;
• Model predictive control (MPC) EMS solves a receding-horizon optimization at each time step, requiring a dynamic model of the system [107]. For PV, the single-diode model mentioned in Section 2.2.1 can be used if simplified to an explicit form to avoid iterative solves [108]. For wind, a linearized small-signal model around the current operating point enables linear MPC formulations. However, nonlinear MPC that retains the full single-diode or blade element momentum models is rarely used in practice due to computational intractability.

Using overly complex models, such as double-diode PV or blade element momentum wind, in optimization-based EMS is almost never justified because the additional accuracy is lost in the presence of forecast errors, while the computational cost may increase by orders of magnitude [109]. Conversely, using overly simple models, such as ideal current source PV, can lead to constraint violations, as the EMS may assume power can be drawn at any voltage when it actually cannot.

Optimization-based EMS can approach globally optimal operation if the model and forecasts are accurate, and can handle complex constraints, time-varying tariffs, and multiple objectives simultaneously. However, it requires solving an optimization problem at each step, which demands sufficient computational resources and may suffer from convergence issues for non-convex formulations. The accuracy of optimization-based EMS is fundamentally limited by the accuracy of renewable generation forecasts and component models.

In [110], the authors propose a linear programming framework for modeling distribution network characteristics and market-clearing processes for flexible loads and distributed renewable energy resources providing reserve and reactive power compensation, demonstrating that the Nash equilibrium between utility and customers can be approximated by a linear program when customers are numerous and infinitesimal, with market prices revealed as marginal costs for the utility.

A nonlinear model predictive control is implemented in a MATLAB R2025a-TRNSYS 18 co-simulation environment, in [111] for a hybrid renewable energy system combining wind turbines, photovoltaic arrays, and hydrogen storage, such as electrolysis, compressed-gas storage, and proton exchange membrane (PEM) fuel cell, achieving a 34.6% reduction in hydrogen consumption, halving state-of-charge variance, and 37% increase in H₂/O₂ co-production rate compared to a deterministic single-step strategy.

Optimization-based EMS is standard in grid-connected microgrids, islanded systems with multiple generators, and systems participating in energy markets [112]. For hybrid PV-wind systems, LP, QP, and MPC formulations with piecewise linear PV models and wind lookup tables are quite common in the literature.

4.3. Learning-Based EMS

Reinforcement learning-based (RL) EMS trains an agent, such as a neural network, to make sequential dispatch decisions by interacting with an environment, either simulated or real, and learning from rewards [113]. Unlike optimization-based EMS that solves a model explicitly at each time step, reinforcement learning-based EMS learns a policy that maps system states, including load, renewable generation, battery state of charge, time of day, and electricity price, directly to control actions. Common algorithms include deep Q-networks, proximal policy optimization, and soft actor-critic [114].

Reinforcement learning-based EMS has different model requirements (Figure 11) depending on the training approach:

• Model-free reinforcement learning does not require explicit component models during online operation because the policy is learned offline and deployed as a neural network that outputs actions given observations. However, training requires synthetic data from a simulation environment that accurately represents PV and wind behavior. This simulation environment typically uses a constant power model for computational speed during training, because millions of training episodes must be simulated. Some studies use the power versus wind speed lookup table to capture nonlinearities without increasing the simulation significantly [115];
• Model-based reinforcement learning learns or uses an explicit model of the environment to plan actions, then interacts with the real system to refine the model. In this case, the model requirements mirror those of optimization-based EMS: the component models must be differentiable to enable gradient-based planning. The simplified single-diode PV model and linearized wind model are suitable because they are differentiable and computationally efficient [116].

In [117], the authors propose a novel RL EMS for predicting renewable energy generation and load demand, integrated into a two-level optimization dispatch framework with dynamic pricing-based demand response for grid-connected microgrids, achieving mean absolute error (MAE) reductions of 1.6391 kW for loads, 0.3027 kW for wind turbines, and 0.761 kW for photovoltaic. A reinforcement learning optimization framework with a parameterized action space for Net-Zero Energy Buildings integrating solar photovoltaic, biomass power generation, and battery storage is proposed in [118]. It is shown that the system can achieve a 4% improvement in off-grid operational performance and a 90% increase in battery operation time within the safe range compared to the baseline model, without additional computational burden.

In [119], the authors propose a novel multi-criteria sizing approach for hybrid renewable energy systems (HRES) based on deep reinforcement learning (DRL), where the DRL agent is guided by a reward function integrating three essential performance metrics, such as levelized cost of energy (LCOE), renewable energy fraction (REF), and loss of power supply probability (LPSP), along with a penalty function to discourage reliance on external sources such as diesel generators and the public grid. The proposed approach was tested on three distinct demand profiles using hourly data over one year and benchmarked against particle swarm optimization and multi-objective particle swarm optimization (MOPSO). Results demonstrate that DRL significantly outperforms all benchmark methods in economic efficiency, achieving LCOE reductions of 21.33–30.09% compared to PSO, and 27.89–30.27% compared to MOPSO, while maintaining system reliability and promoting greater autonomy and renewable usage.

By interacting with the environment, the agent in reinforcement learning learns the best course of action. A policy is a mapping between states and the probability of choosing each feasible course of action. A program agent can be conceptualized as a decision-maker or action-taker that learns via recurrent trial and error and is characterized by a reward system that aims to maximize the overall reward over a long period of time. The reward serves as a means of expressing how successfully the agent is progressing. In order to attain the intended performance, reward shaping is crucial. The benefits of reinforcement learning algorithms can be summed up as follows: (1) they may be instructed offline, retrieving optimal solutions for the entire optimization horizon, which eliminates the necessity to iterate during online operation for all of these reasons, RL is appropriate for sequential decision-making in a dynamic setting, particularly when combined with deep learning for enhanced scalability and efficient feature extraction from data; (2) in contrast to techniques based on mathematical modeling, reinforcement learning can learn without a precise representation of the environment by interaction with the environment through trial and error.

Reinforcement learning-based EMS can, in principle, use any PV or wind model during training, including high-fidelity models, for instance, double-diode equivalent circuits. However, the computational cost of training increases linearly with the simulation time per episode, so practical implementations overwhelmingly use the simplest possible models to reduce training time from weeks to hours. The gap between the simple models used for training and the complex physical behavior of real PV and wind systems is a source of the “simulation-to-real” gap that limits reinforcement learning deployment in practice. It can handle high-dimensional state and action spaces, learn non-intuitive strategies, and adapt to changing conditions through continuous learning. However, it requires extensive training data, either from simulation or real operation, lacks formal performance guarantees, and may exhibit unsafe behavior during exploration. The trained policy is a black-box neural network, making it difficult to interpret or certify. The simulation-to-real gap, where a policy trained on simplified PV or wind turbine models fails when deployed on real hardware, remains a significant challenge.

With growing real-world deployment in building microgrids, EV charging stations, and community energy systems, RL-based EMS is an active research area. For hybrid PV-wind systems, reinforcement learning-based EMS is particularly attractive when weather forecasts are unreliable or when the system has multiple conflicting objectives, such as cost, emissions, and battery lifetime.

To guide the selection of an appropriate EMS for a given hybrid PV-wind application,

Table 3. Key characteristics of the discussed EMS approaches.

Feature	Rule-Based	Optimization-Based	Learning-Based
Decision Logic [120]	If-then-else rules	Mathematical programming	Neural network
Optimality	Suboptimal	Near optimal	Training-dependent
Computational Cost [121]	Very low	Medium to high	High
Training Required [122]	No	No	Yes
Handling Uncertainty [123,124]	Poor	Good	Good
Real-Time Feasibility [125]	Excellent	Good (if solver fast)	Excellent
Implementation Complexity [126]	Low	Medium to high	High
Typical Application [127]	Small off-grid systems	Grid-connected microgrids	Complex grid-connected microgrids

summarizes the key characteristics of the three main architectural approaches discussed in this section. The comparison highlights fundamental trade-offs between optimality, computational cost, interpretability, and implementation complexity, providing a high-level reference for system designers.

To explicitly describe the matching relationships between component models and EMS requirements,

Table 4. Model-EMS Adaptation Matrix: Mapping component models to EMS architectures.

Component	Model Type	Example Model	Best EMS Match	Accuracy	Param. Availability	Comput. Complexity
PV	Empirical/Black-Box	ANN-based PV	Learning-based	High	Low (needs training)	High (train)
PV	Equivalent-Circuit	Single-diode	Optimization (MPC)	High	Moderate (extraction)	Medium (iterative)
PV	Simplified	Constant power	Rule-based, LP	Low	Very low	Very low
PV	Simplified	Piecewise linear	QP		Low	Low
WT	Simplified	Constant power	Rule-based, LP	Moderate	Very low	Very low
WT	Simplified	Power vs. wind speed lookup	Optimization, LP	Moderate	Low	Very low

maps the PV and WT models discussed in Section 2 and Section 3 to the three EMS architectures presented in this section.

4.4. Energy Storage Constraints in EMS

The practical performance of a hybrid PV-WT system depends critically on how energy storage constraints are modeled within the EMS. While the previous subsections focused on PV and WT models, this subsection addresses the key storage-related constraints that influence EMS selection and operational decisions across the three EMS architectures.

• State of Charge Constraints: SOC bounds represent the most fundamental storage constraint, typically expressed as minimum and maximum limits to prevent over-discharge and over-charge. In rule-based EMS, SOC thresholds trigger simple actions, such as “if SOC < 0.2, stop discharging”. In optimization-based EMS, SOC appears as linear inequality constraints that can be hard constraints (infeasible if violated) or soft constraints with penalty weights. In learning-based EMS, SOC limits are typically learned from reward functions that penalize boundary violations [128].
• Battery Degradation Costs: Cycling and calendar aging reduce battery lifetime, adding an implicit cost to each charge/discharge cycle [129]. Degradation can be modeled as a linear cost per kWh cycled, a convex function of depth of discharge, or a more complex electrochemical model. Rule-based EMS typically ignores degradation or uses simple cycle counters. Optimization-based EMS can incorporate degradation as a quadratic or linear term in the objective function [130]. Learning-based EMS can learn degradation patterns from historical data and optimize for lifetime extension.
• Charging/Discharging Efficiency: Round-trip efficiency (typically 85–95%) means that charging losses exceed discharging gains. This asymmetry creates a preference for storing energy only when necessary. In optimization-based EMS, efficiency appears as a linear transformation between charging power and stored energy. In learning-based EMS, efficiency is implicitly learned from state transition data [131].
• Multi-Time Scale Strategies: Storage operates across multiple timescales: fast regulation (seconds to minutes), load following (minutes to hours), and energy arbitrage (hours to days). Hierarchical EMS architectures separate these timescales: a day-ahead optimization schedules SOC trajectories, while a real-time EMS tracks them with adjustments. The choice of EMS architecture determines which timescales are explicitly modeled [132].

Systems with simple storage (small batteries, low cycling) can use rule-based EMS with SOC thresholds. Systems with significant storage and degradation costs require optimization-based EMS with degradation penalties. Systems with complex multi-time scale operation, such as grid arbitrage plus frequency regulation, may benefit from learning-based EMS or hierarchical optimization.

5. Discussion

Advancing the sustainability of hybrid renewable energy systems necessitates a dual transition: improving the accuracy and reliability of component-level models while enabling effective system-level coordination through intelligent energy management systems. This review has examined the critical nexus between these goals, focusing on photovoltaic and wind turbine models and their integration within EMS architectures. While the individual modeling of PV and wind systems has reached considerable maturity, their effective coordination under variable weather conditions and dynamic grid requirements introduces significant challenges that cannot be resolved by component improvements alone. Addressing this mismatch requires a holistic understanding of how model fidelity choices propagate through to EMS performance.

Comprehensive reviews of PV parameter extraction [133] and wind turbine modeling [134] are available, but they do not address system-level coordination. Conversely, surveys of EMS for hybrid renewable systems [135] treat component models as black boxes without examining how model fidelity affects control performance. To the best of our knowledge, no prior work has systematically bridged component modeling and EMS coordination, which constitutes the contribution of the present review.

A central observation from this review is the pronounced disparity between the maturity of individual component models and the relative scarcity of systematic guidance on matching model complexity to EMS requirements. As detailed in Section 2 and Section 3, component-level research is highly advanced. Significant progress has been made in empirical and equivalent-circuit PV models, starting from single-diode to data-driven approaches [136,137], aerodynamic and simplified wind turbine models [138], and a wide array of simulation tools for both technologies. Section 4 discussed a broad spectrum of EMS architectures, from rule-based logic to optimization-based formulations and reinforcement learning agents. However, publications that systematically address the coupling between specific model choices and EMS performance, for example, how using a constant power PV model instead of a single-diode model affects the optimality or feasibility of a linear programming dispatch, remain limited. The field is thus at a critical level where the priority must shift from isolated model development to holistic model-EMS co-design, where the real-world trade-offs between accuracy, computational cost, and scalability can be fully confronted.

The synergy between component models and EMS, when properly matched, reveals the true potential for system-level efficiency gains. A key finding is that the value of a high-fidelity model is fully unlocked only when paired with an EMS that can exploit its information content. For instance, a detailed single-diode PV model presented in Section 2.2.1 captures the full current-voltage curve, enabling EMS to perform voltage-based curtailment or reactive power support. However, this fidelity is wasted if the EMS employs a simple rule-based strategy that only requires the maximum power point. Conversely, a sophisticated model predictive control EMS can leverage the explicit relationship between wind speed, tip-speed ratio, and power coefficient from an SPC lookup table introduced in Section 3.1.2, but it requires a wind model that provides differentiable forecasts, something a simple constant power model cannot offer. The role of BEM models in wind farms further highlights this interdependence [139]. An EMS that ignores wake effects will systematically overestimate power output from downstream turbines, leading to dispatch decisions that violate power balance constraints [140]. The EMS must, therefore, incorporate not just individual turbine models but also their aerodynamic interactions.

The EMS architecture itself must be chosen with explicit awareness of the available component models. The three EMS categories described in Section 4, rule-based, optimization-based, and learning-based, provide a necessary framework for matching control strategy to model fidelity and system complexity. Rule-based EMS may suffice for small-scale, battery-buffered hybrid systems where simple state-of-charge thresholds and constant power renewable models ensure basic reliability [141]. However, for larger systems with multiple PV arrays and wind turbines, or for grid-connected systems participating in energy markets, more advanced strategies become essential. Optimization-based EMS, particularly linear and mixed-integer linear programming, can exploit piecewise linear PV models and wind lookup tables to achieve near-optimal dispatch while respecting physical constraints. Predictive EMS and reinforcement learning-based EMS, as discussed in Section 4.2 and Section 4.3, can perform look-ahead optimization or learn adaptive policies from historical data. They can, for example, schedule battery charging to coincide with forecasted wind ramps, curtail PV output to avoid negative electricity prices, or modulate hydrogen electrolyzer operation to follow renewable generation. This transforms the hybrid system from a collection of independent generators into a coordinated, flexible asset, a paradigm shift crucial for high renewable penetration.

Hierarchical EMSs with primary, secondary, and tertiary layers align best with simplified component models, such as constant power or lookup tables, because each layer tolerates model simplifications. Distributed EMS, requiring communication between generators, works well with moderate-fidelity models. Decentralized EMS, with no communication, requires the simplest models, such as constant power for low-cost embedded implementation. High-fidelity iterative models, such as single-diode PV and BEM wind, are typically confined to centralized hierarchical EMS, while low-fidelity models enable distributed or decentralized architectures.

Stochastic methods for wind-solar coordination, including probabilistic forecasting, scenario-based optimization, robust optimization, and chance-constrained programming, are essential for real-time operation under uncertain weather conditions [142]. However, these methods typically assume simplified component models (constant power or linearized representations) to maintain computational tractability. A detailed treatment of uncertainty propagation, specifically how prediction errors in irradiance and wind speed transmit through component models to EMS decisions, is beyond the scope of this review, which focuses on deterministic model-EMS matching. Nonetheless, we note that high-fidelity models (single-diode PV, BEM wind) amplify input errors due to their nonlinearities, while simplified models are less sensitive but cannot capture voltage or reactive power uncertainty.

Regarding scalability, specific trade-offs emerge between model fidelity and computational tractability. A single-diode PV model requires iterative numerical solution of a transcendental equation per module, becoming impractical for real-time EMS when scaled to hundreds of arrays. In contrast, constant power or lookup table models (Section 3.2.2) evaluate very fast, enabling farm-level optimization, but do not support voltage-based curtailment and reactive power capabilities. Similarly, simulating each wind turbine with blade element momentum theory is computationally prohibitive for large farms. The scalability trade-off, therefore, centers on whether the EMS requires per-unit dispatch granularity or can operate on aggregated power setpoints.

In summary, the discussion synthesizes three key trade-offs that must be navigated in designing hybrid PV-wind systems:

• Model accuracy versus computational cost: High-fidelity models (single-diode PV, BEM wind) require iterative numerical solutions, making them mismatched with real-time EMS deadlines; simplified models (constant power, lookup tables) enable fast computation but lack voltage-based curtailment, reactive power support, and wake-aware dispatch;
• EMS complexity versus interpretability: Learning-based EMS (reinforcement learning) can outperform rule-based systems but produces black-box policies that lack certification guarantees for safety-critical operation; rule-based systems are verifiable but cannot adapt to changing conditions or optimize multiple objectives.
• Component-level detail versus system-level scalability: Per-turbine BEM and per-module single-diode models are computationally intractable for large farms, but aggregated models fail to capture inter-turbine dynamics and individual degradation. Static simplified models also do not account for aging or soiling over time.

These mismatches can be mitigated through existing approaches. Reduced-order and explicit Lambert W-based approximations address iterative model incompatibility with real-time EMS. Piecewise linear reformulations enable convex optimization. Fallback safety layers and probabilistic constraints offer pathways for learning-based and uncertainty-aware EMS, respectively.

Actionable guidelines derived from this review for small off-grid systems, rule-based EMS with constant power models, are sufficient. In the case of grid-connected microgrids, optimization-based EMS with piecewise linear PV and lookup table wind models is recommended. For complex or uncertain environments with multiple objectives, learning-based EMS warrants consideration, provided adequate training data and validation protocols are in place. The path forward lies not in pursuing maximum fidelity in every component but in achieving conscious, intentional alignment between model capabilities and EMS requirements.

6. Conclusions

This review has provided a comprehensive analysis of photovoltaic and wind turbine models and their integration within energy management systems for hybrid renewable energy applications, synthesizing the technological, modeling, and coordination challenges inherent to this critical nexus of component-level fidelity and system-level control. Drawing from 120 references from 1994 to 2026 and spanning the fields of PV equivalent circuits, aerodynamic wind turbine theory, simplified reduced-order representations, and EMS architectures, this work maps the pathway towards more efficient, reliable, and scalable hybrid renewable energy systems.

The paper underscores that while individual modeling approaches for PV and wind technologies have reached a significant level of maturity, from single-diode equivalent circuits to blade element momentum theory and from constant power approximations to physics-informed neural networks, their true potential is unlocked only through intelligent integration with appropriate EMS architectures. The inherent intermittency of solar and wind resources necessitates a sophisticated, multi-fidelity modeling strategy. Effective hybrid systems must seamlessly combine source-level models with supervisory EMS that can exploit the information content of these models without exceeding computational constraints. The review particularly highlights the role of hybrid models and the transformative potential of predictive optimization-based and reinforcement learning-based EMS in transforming renewable generation from an uncontrollable stochastic input into a partially dispatchable, coordinated asset.

Ultimately, the transition to hybrid PV-wind systems is not merely a matter of adding more generation sources but a fundamental re-engineering of modeling philosophy and control architecture. Future progress depends on bridging the identified gap between component-focused model development and system-level EMS validation. By prioritizing the development and field validation of robust, computationally efficient, and intelligent control frameworks that can harmonize the dynamics of meteorology, power electronics, and multi-source generation, the vision of resilient, cost-effective, and high-renewable-penetration energy systems can be realized, securing a sustainable energy future.