Renewable energy sources play a pivotal role in the global energy transition, yet wind and solar power generation are inherently intermittent and unpredictable due to their dependence on natural conditions. This unpredictability poses significant challenges to grid stability and reliability. To address these issues, this paper focuses on the design of an energy storage unit within a wind-solar-storage combined grid-connected power generation system and employs optimization techniques to enhance collaborative scheduling. The integration of energy storage helps mitigate power fluctuations, improve scheduling flexibility, and reduce operational costs. Through detailed modeling and simulation, we demonstrate the effectiveness of our approach in smoothing current variations and facilitating better interaction with grid dispatch centers. The solar power system, as a key component, is emphasized throughout this study for its critical role in hybrid energy systems.
In recent years, the adoption of renewable energy has accelerated, driven by environmental concerns and technological advancements. However, the variable nature of wind and solar resources necessitates the incorporation of energy storage solutions to ensure a stable power supply. Previous research has explored various scheduling strategies, but many suffer from limitations such as high computational demands, inflexibility in real-time adjustments, or inadequate handling of uncertainties. For instance, some methods require extensive data processing, making them unsuitable for rapid dispatch decisions, while others rely on multi-timeframe approaches that may lack agility. In contrast, our work proposes a comprehensive framework that combines energy storage design with intelligent scheduling algorithms, specifically leveraging the Particle Swarm Optimization (PSO) algorithm to dynamically adjust charging and discharging plans. This not only enhances the synergy between wind, solar, and storage components but also optimizes economic performance. The solar power system, in particular, benefits from this integrated approach, as it allows for more efficient energy management and grid compatibility.
The core of our methodology involves three main aspects: predicting the combined output of wind and solar generation, designing the energy storage unit using equivalent circuit models, and developing a collaborative scheduling model. Each of these elements is detailed in the following sections, supported by mathematical formulations, tables, and simulation results. By addressing the gaps in existing literature, our approach offers a practical solution for large-scale renewable integration, with a focus on scalability and real-world applicability. The repeated emphasis on the solar power system underscores its importance in achieving a balanced and resilient energy infrastructure.
Prediction of Combined Wind-Solar-Storage Power Output
Accurate prediction of power output is essential for effective grid management. Wind turbines convert kinetic energy from wind into mechanical energy, which is then transformed into electrical power. The output of a wind turbine is highly dependent on wind speed, and its predictive power can be modeled using the following equation:
$$P_{wt} = \frac{1}{2} \rho \pi R^2 C_p(\gamma, \beta) v^3$$
where \(P_{wt}\) represents the predicted output of the wind turbine, \(\rho\) is the air density, \(R\) is the rotor blade diameter, \(C_p\) is the power coefficient as a function of tip speed ratio \(\gamma\) and blade pitch angle \(\beta\), and \(v\) denotes the wind speed. This equation highlights the nonlinear relationship between wind speed and power generation, which contributes to the volatility of wind energy.
Similarly, solar power generation is influenced by factors such as solar irradiance and ambient temperature. The output of a photovoltaic (PV) system can be expressed as:
$$P_{PV} = P_{STC} \cdot \frac{G_{AC}}{G_{STC}} \cdot \left[1 + k \cdot (T_c – T_r)\right]$$
where \(P_{PV}\) is the PV output power, \(P_{STC}\) is the rated power under standard test conditions, \(G_{AC}\) is the actual solar irradiance, \(G_{STC}\) is the reference irradiance (typically 1000 W/m²), \(k\) is the temperature coefficient, \(T_c\) is the cell temperature, and \(T_r\) is the reference temperature. This formulation accounts for the efficiency losses due to temperature variations, which are common in solar power systems.
To derive the combined predicted output for the wind-solar-storage system, we integrate the individual contributions with the storage component. The net power output \(\Delta P\) at time \(t\) is given by:
$$\Delta P(t) = \lambda \cdot \left[ P_{wt}(t) + P_{PV}(t) + P_1(t) \right]$$
Here, \(P_1(t)\) denotes the power from the storage unit, and \(\lambda\) is the grid connection coefficient that accounts for transmission losses and other inefficiencies. This equation forms the basis for our scheduling model, as it encapsulates the dynamic interplay between generation sources and storage.
| Parameter | Symbol | Typical Value |
|---|---|---|
| Air Density | \(\rho\) | 1.225 kg/m³ |
| Rotor Diameter | \(R\) | 50 m |
| Power Coefficient | \(C_p\) | 0.4 |
| Tip Speed Ratio | \(\gamma\) | 7 |
| Blade Pitch Angle | \(\beta\) | 0° |
| Reference Irradiance | \(G_{STC}\) | 1000 W/m² |
| Temperature Coefficient | \(k\) | -0.0045 /°C |
| Reference Temperature | \(T_r\) | 25°C |
Design of the Energy Storage Unit
The energy storage unit is a critical element in stabilizing the wind-solar-storage system. We adopt the Thevenin equivalent circuit model to represent the storage unit, which provides a balance between accuracy and computational efficiency. The model equations are as follows:
$$U_L = U_{OCV} – U_m – I_L \cdot \Omega$$
where \(U_L\) is the terminal voltage, \(U_{OCV}\) is the open-circuit voltage, \(U_m\) is the polarization voltage, \(I_L\) is the output current, and \(\Omega\) is the internal resistance. The power throughput \(P_L\) of the battery is related to the current and voltage by \(P_L = U_L \cdot I_L\). The state of charge (SOC) \(S\) is a key parameter defined as:
$$S(t) = S(0) – \frac{1}{Q} \int_0^t I_L(\tau) \, d\tau$$
where \(Q\) is the battery capacity, and \(S(0)\) is the initial SOC. This differential equation captures the energy dynamics over time, essential for scheduling decisions.
To ensure the storage unit can handle the demands of the solar power system and wind generation, the battery bank must be appropriately sized. The capacity of the battery bank \(C_B\) is calculated as:
$$C_B = \frac{A \cdot Q_L}{U_B \cdot (1 – C_B) \cdot \eta}$$
where \(A\) is a safety factor (typically 1.1 to 1.2), \(Q_L\) is the average energy consumption, \(U_B\) is the rated voltage, \(C_B\) is the depth of discharge, and \(\eta\) is the round-trip efficiency. This formulation ensures that the storage system can buffer the variability inherent in renewable sources, particularly the solar power system, which experiences diurnal and weather-related fluctuations.
| Parameter | Value | Unit |
|---|---|---|
| Rated Capacity | 400 | kWh |
| Rated Power | 100 | kW |
| Charge/Discharge Efficiency | 0.91 | – |
| SOC Range | 0.2 – 0.9 | – |
| Internal Resistance | 0.05 | Ω |
Calculation of Storage Unit Adjustment Commands
Given the stochastic nature of wind and solar resources, real-time adjustments are necessary to maintain power balance. The storage unit serves as a buffer to compensate for deviations between planned and actual power outputs. The adjustment command \(P_Z\) for the storage unit is derived as:
$$P_Z = P_{plan}^L + \left( P_{plan}^{wt} – P_{act}^{wt} \right) + \left( P_{plan}^{PV} – P_{act}^{PV} \right)$$
where \(P_{plan}^L\) is the planned output of the storage unit, \(P_{plan}^{wt}\) and \(P_{plan}^{PV}\) are the planned outputs for wind and solar, respectively, and \(P_{act}^{wt}\) and \(P_{act}^{PV}\) are the actual measured outputs. This command is fed into the power control strategy to generate final dispatch instructions, ensuring that the solar power system and wind farms operate in harmony with the grid.
The adjustment process involves continuous monitoring and feedback. For instance, if the actual solar power output from the solar power system falls short of the plan due to cloud cover, the storage unit discharges to fill the gap. Conversely, during periods of excess generation, the storage unit charges to store surplus energy. This dynamic response enhances the system’s resilience and reliability.
Collaborative Scheduling Model for Wind-Solar-Storage Systems
We formulate the collaborative scheduling as an optimization problem with the objective of minimizing total costs, which include penalties for curtailment of wind and solar power, operational costs of wind farms, solar power systems, and storage units. The overall objective function is:
$$\min \sum_{t=1}^{T} \left[ C_{curt}(t) + C_{wt}(t) + C_{PV}(t) + C_{storage}(t) \right]$$
where \(C_{curt}(t)\) is the cost associated with wasted wind or solar energy, \(C_{wt}(t)\) and \(C_{PV}(t)\) are the operating costs of wind and solar systems, respectively, and \(C_{storage}(t)\) is the storage operational cost. These costs are subject to various constraints to ensure feasible operation.
The power balance constraint ensures that the total planned output matches the grid schedule:
$$P_{wt}(t) + P_{PV}(t) + P_1(t) = P_{grid}(t)$$
where \(P_{grid}(t)\) is the grid demand. Additionally, ramp rate constraints for wind and solar power are imposed to reflect their physical limitations:
$$-V_{d}^{max, wt} \leq V_{wt}(k) \leq V_{u}^{max, wt}$$
$$-V_{d}^{max, PV} \leq V_{PV}(k) \leq V_{u}^{max, PV}$$
Here, \(V_{wt}(k)\) and \(V_{PV}(k)\) represent the rate of change of wind and solar power outputs at interval \(k\), while \(V_{d}^{max, wt}\) and \(V_{u}^{max, wt}\) are the maximum downward and upward ramp rates for wind, and similarly for solar. These constraints prevent abrupt changes that could destabilize the grid.
For the storage unit, the SOC must remain within safe bounds to prolong battery life and prevent damage:
$$S_{min} \leq S(t) \leq S_{max}$$
where \(S_{min}\) and \(S_{max}\) are the minimum and allowable SOC levels, typically set to 0.2 and 0.9, respectively. This constraint is critical for maintaining the longevity of the solar power system’s storage component.
To solve this optimization problem, we employ the Particle Swarm Optimization (PSO) algorithm. PSO is a population-based metaheuristic that iteratively adjusts candidate solutions to find the global optimum. The algorithm parameters include swarm size, inertia weight, and acceleration coefficients. The process begins by initializing a population of particles representing potential scheduling solutions. Each particle’s position corresponds to a set of decision variables, such as charging/discharging schedules for the storage unit. The fitness of each particle is evaluated based on the objective function, and particles update their positions and velocities based on personal and global best solutions. The iteration continues until convergence criteria are met, such as a maximum number of iterations or a tolerance in cost reduction.
The PSO-based scheduling outputs a detailed plan that specifies the power allocations for wind, solar, and storage units over the scheduling horizon. This plan enhances the economic efficiency and reliability of the solar power system by dynamically adapting to real-time conditions.
| Cost Component | Value (USD/MW) |
|---|---|
| Wind Curtailment Penalty | 500.0 |
| Wind Farm Operating Cost | 89.6 |
| Solar Power System Operating Cost | 110.3 |
| Storage Unit Operating Cost | 185.6 |
Simulation and Validation
To validate our approach, we conducted simulations based on a large-scale wind-solar-storage power generation base. The wind farm has an installed capacity of 375 MW, the solar power system has a capacity of 1000 MW, and the storage station is rated at 140 MW with an energy capacity of 280 MWh. The simulation parameters are summarized in the tables above, and the models were implemented in a MATLAB/Simulink environment to replicate real-world conditions.
The SOC profiles of multiple storage units were analyzed to assess performance. As shown in the figure below, the SOC values for three storage units exhibit consistent behavior: discharging until approximately 189 seconds, followed by a charging phase. This synchronization indicates balanced energy distribution among units, which simplifies grid调度 and enhances response times. The solar power system benefits from this uniformity, as it allows for predictable storage operations during peak generation periods.
In terms of collaborative scheduling, the system successfully tracks the planned power curve by leveraging storage flexibility. For example, during hours 10 to 14, when wind and solar generation exceed demand, the storage units absorb excess energy. Conversely, from hours 22 to 24, when generation is insufficient, the storage units discharge to meet grid requirements. This “peak shaving and valley filling” strategy reduces the need for conventional backup power and minimizes curtailment losses. The solar power system, in particular, demonstrates improved utilization rates due to this adaptive scheduling.
Economic analysis reveals that our method lowers operational costs by optimizing the dispatch of resources. The PSO algorithm effectively minimizes the total cost function, resulting in savings compared to traditional scheduling methods. Additionally, the enhanced interaction with the grid dispatch center facilitates better real-time coordination, contributing to overall system stability.
Conclusion
In this paper, we have presented a comprehensive framework for designing and scheduling energy storage units in wind-solar-storage combined power systems. The use of the Thevenin equivalent model ensures robust storage performance, while the PSO-based collaborative scheduling optimizes economic and operational objectives. Our simulations confirm that the proposed approach smooths power fluctuations, increases scheduling flexibility, and reduces costs, thereby supporting the integration of renewable sources like solar power systems into the grid. Future work will explore advanced machine learning techniques for prediction and scheduling, as well as the integration of emerging storage technologies to further enhance system resilience. By continuing to refine these methods, we aim to contribute to the global transition toward sustainable and reliable energy systems.