An analytic method for optimizing hydropower installed capacity expansion size in hydro-solar-wind hybrid system

The worldwide renewable energy installed capacities have increased rapidly, aiming to secure power supply and replace fossil fuels. However, challenges persist in optimizing the size of hydropower installed capacity expansion (HICE) in hydro- solar-wind hybrid system. In this study, an analytic method is proposed to determine the optimal hydropower installed capacity expansion size based on the relationship between HICE and generation, as well as the relationship between HICE and energy-loss. Firstly, an optimization function for HICE is proposed using the net present value method. Then, function assumptions are made and validated for the relationship between HICE and generation (HICE-generation function) and the relationship between HICE and energy loss (HICE-energy-loss function). Finally, the optimal sizes of HICE derived from the numerical and analytical methods are compared. A case study in the Yalong River basin in China reveals that: (1) the proposed HICE-generation and HICE-energy-loss functions can quantitatively characterize the relationship between HICE and generation and energy loss; (2) the proposed analytical method could yield the optimal HICE size without the need for a simulation process and heavy computational burden; and (3) it provides an optimal HICE size of 1210 MW with a relative error of only 5.5% compared to the numerical solution. Therefore, the proposed analytical method can be an effective tool for the planning and management of large hybrid energy systems.