Efficient Wind-PV Hybrid System Optimization with Storage

1. Analysis of Wind and Solar Photovoltaic Power Generation Characteristics

Analyzing the characteristics of wind and solar photovoltaic (PV) power generation is fundamental to designing a complementary hybrid system. Statistical analysis of annual wind speed and solar irradiance data for a specific region reveals that wind resources exhibit seasonal variation, with higher wind speeds in winter and spring and lower speeds in summer and autumn. Wind power generation is proportional to the cube of wind speed, resulting in significant output fluctuations.

Solar resources, on the other hand, show clear diurnal and seasonal patterns—longer daylight hours and stronger radiation in summer, and weaker conditions in winter. PV efficiency is negatively affected by rising temperatures. By comparing the temporal distribution of wind and solar energy, it is evident that they exhibit complementary behavior on both daily and annual cycles. This complementarity enables the design of efficient and stable power systems, where an optimal capacity ratio of the two energy sources can be configured to smooth overall power output.

2. Modeling of Wind-Solar Hybrid Power Generation Systems

2.1 Wind Power Subsystem Model

The wind power subsystem model is built upon wind speed data and turbine characteristics. The Weibull distribution is used to fit the wind speed probability distribution, accurately describing its statistical behavior. The relationship between turbine output power and wind speed is represented by a piecewise function incorporating key parameters such as cut-in wind speed, rated wind speed, and cut-out wind speed. 

The least squares method is applied to fit the turbine power curve, yielding a mathematical expression of power output versus wind speed. To account for wind speed randomness, the Monte Carlo simulation method is introduced to predict wind farm generation. The model accurately reflects the dynamic characteristics of wind power systems and provides a foundation for system optimization. It also incorporates the impact of wind direction changes on generation efficiency by introducing a wind direction correction factor, thereby improving prediction accuracy.

2.2 Photovoltaic Power Subsystem Model

The PV subsystem model comprehensively considers solar irradiance, ambient temperature, and PV module characteristics. A statistical model of solar irradiance is established to describe its temporal variations. The output characteristics of PV modules are represented by I-V curves. Temperature effects on efficiency are modeled using a single-diode equivalent circuit, with output power calculated by solving a system of nonlinear equations.

The model also includes factors such as shading and dust accumulation, introducing correction coefficients to enhance prediction accuracy. It accounts for PV module aging by incorporating an annual degradation rate to forecast long-term power output changes. This model accurately reflects PV system performance under varying environmental conditions.

2.3 Energy Storage System Model

The energy storage system model is primarily based on lithium-ion battery characteristics. A dynamic model of battery state of charge (SOC) is developed to describe charging and discharging processes. Self-discharge characteristics and charge/discharge efficiency are considered, with a temperature correction factor introduced to reflect environmental impacts. Battery lifespan is modeled using a combination of cycle count and depth of discharge (DOD) to predict capacity degradation.

The model accurately reflects battery performance under different operating conditions, supporting optimal sizing and dispatch strategies. It also considers internal resistance variation by establishing functional relationships between resistance, cycle count, and temperature, enabling more precise simulation of dynamic behavior. Key outputs include real-time SOC, available capacity, charge/discharge power, and expected lifespan—providing comprehensive data support for optimal operation and maintenance.

2.4 System Integration Model

The integrated system model combines wind, solar, and storage subsystems into a unified framework. The equivalent load method is used to handle load fluctuations, and a system power balance equation is established. Reliability indices such as Loss of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) are introduced to evaluate system performance. Sequential time-series simulation is used to compute system operating states across different time scales.

The model accounts for interactions between subsystems, such as wind turbine shadowing on PV panels. It also incorporates a grid interface, enabling analysis of grid-connected operation strategies, including economic dispatch under time-of-use tariffs and grid frequency regulation services. Outputs include total power generation, load satisfaction rate, and economic performance metrics, providing a comprehensive theoretical basis for system planning, design, and operational decision-making.

3. Optimization Methods and Experimental Analysis of Wind-Solar Hybrid Systems

3.1 Objective Function and Constraints

The optimization objective function integrates economic, reliability, and environmental considerations. The economic objective minimizes total system cost, including initial investment, operation and maintenance (O&M), and replacement costs. The reliability objective maximizes power supply reliability, quantified by minimizing LOLP. The environmental objective is measured by maximizing carbon emission reductions.

Constraints include power balance, energy storage capacity limits, and equipment operational limits. The power balance constraint ensures that load demand is met at all times. Storage capacity constraints limit depth of discharge (DOD) to extend battery life. Equipment constraints consider rated power and operational characteristics of components. A multi-objective weighting method integrates these goals into a single objective function, with weights determined based on decision-maker preferences and application scenarios.

3.2 Application of Particle Swarm Optimization (PSO)

Particle Swarm Optimization (PSO), an intelligent optimization algorithm, is applied to the design of wind-solar hybrid systems. Simulating bird flocking behavior, PSO searches for optimal solutions in the solution space. Each particle represents a potential system configuration, including decision variables such as wind turbine capacity, PV capacity, and storage capacity. Particle position and velocity are updated iteratively, converging toward the global optimum.

To enhance performance, a linearly decreasing inertia weight strategy is adopted—maintaining strong global exploration early and enhancing local exploitation later. Adaptive mutation is introduced to avoid local optima. Given problem complexity, a hierarchical encoding strategy separates continuous and discrete variables. The algorithm terminates upon reaching the maximum iteration count or when the optimal value changes by less than a threshold over consecutive iterations.

3.3 Experimental Design and Parameter Settings

The experiment is based on actual meteorological and load data from a specific region, using a typical year of hourly data. Meteorological inputs include hourly wind speed, solar irradiance, and ambient temperature. Load profiles follow a typical industrial park consumption pattern, reflecting seasonal and diurnal variations. Equipment parameters are selected from mainstream commercial wind turbines and PV modules, with performance data sourced from manufacturer test reports.

A lithium-ion battery is used for storage, with parameters including rated capacity, charge/discharge efficiency, and cycle life. PSO parameters are set as follows: population size = 50, maximum iterations = 1000, inertia weight linearly decreasing from 0.9 to 0.4, and learning factors c1 and c2 both set to 2. To ensure result reliability, each configuration is run 30 times, with the average taken as the final result.

3.4 System Performance Evaluation Metrics

Performance evaluation metrics cover technical, economic, and environmental aspects. Technical indicators include system reliability, energy utilization rate, and power smoothing. Reliability is measured by the Reliability of Supply Capability Index (RSCI) and Loss of Power Supply Probability (LPSP). Energy utilization reflects renewable energy efficiency, while power smoothing evaluates output stability. Economic indicators include Levelized Cost of Electricity (LCOE), Net Present Value (NPV), and payback period. LCOE considers lifecycle costs, NPV reflects project profitability, and payback period assesses capital recovery speed.

The environmental indicator is carbon emission reduction, calculated by comparison with conventional fossil-fuel-based generation. Additionally, a composite performance index—System Comprehensive Benefit Index (SCBI)—integrates technical, economic, and environmental factors through weighted summation. These metrics and their weights are determined based on expert judgment and practical needs, providing a comprehensive assessment of system performance and supporting informed decision-making.

3.5 Analysis of Optimization Results

The optimization results demonstrate that the wind-solar hybrid power generation system offers significant advantages over single-energy systems. Under the baseline scenario, the optimal configuration consists of 2 MW of wind power capacity, 1.5 MW of photovoltaic (PV) capacity, and 500 kWh of energy storage. This configuration reduces the Loss of Power Supply Probability (LPSP) to below 1% and lowers the Levelized Cost of Electricity (LCOE) by approximately 15% compared to standalone wind or PV systems. Sensitivity analysis reveals that equipment cost has the greatest impact on optimization outcomes— a 10% reduction in cost leads to an approximate 8% decrease in LCOE. 

Load profile variations significantly affect energy storage sizing; increased peak-to-valley load differences require larger storage capacity. Optimal configurations vary across regions: wind-rich areas favor higher wind power ratios, while sun-abundant regions increase the share of PV. Multi-objective optimization generates a Pareto front, enabling decision-makers to balance economic efficiency and reliability according to practical needs. Results also show that incorporating a carbon trading mechanism further improves economic performance, reducing LCOE by an additional 5%–10%. Long-term simulation confirms system stability, with performance degradation over a 20-year operational period remaining within the designed tolerance.

4 Conclusion

The integration and optimization of wind and solar photovoltaic hybrid power generation systems provide an effective solution to the intermittency issues of renewable energy. By establishing mathematical models and applying the Particle Swarm Optimization (PSO) algorithm, significant improvements in system performance have been achieved. Experimental results verify the feasibility and effectiveness of the proposed approach. However, large-scale deployment of wind-solar hybrid systems still faces numerous challenges, such as weather forecasting accuracy and energy storage technology limitations.

Future research should focus on enhancing system intelligence and improving adaptability to complex weather conditions, thereby further increasing the economic efficiency and reliability of these systems. This will make a significant contribution to building a clean, efficient, and secure modern energy system.