Abstract:

Research on renewable energy， including wind power， is currently centered on the reduction of costs associated with large-scale deployment， the integration of intermittent resources into the power grid， and the formulation of supportive policy frameworks. In the realm of practical development， wind power， akin to non-renewable resources such as oil， is constrained by geographical limitations for exploitable locations， implying that there is an upper limit to the total potential installed capacity. The optimal control theory of exhaustible resources is applied to the context of wind energy， considering the regional wind energy reserves（remained capacity potential） as exhaustible resources. The model in this paper takes into account a multitude of factors， including the reserves of wind energy， the benchmark on-grid electricity prices for wind power， investment costs， construction and grid consumption costs， as well as the depreciation and eventual retirement of wind turbines. The primary aim of this study is the maximization of the long-term net benefits from wind power development. Consequently， a dynamic optimization model has been constructed to achieve this goal. In the analysis and resolution of the model， the Hamiltonian function and Pontryagin's Maximum Principle are utilized to find the optimal development path for the incremental installed capacity. Furthermore， under specific conditions， the existence and uniqueness of the optimal solution are established using Picard's existence and uniqueness theorem， as well as the theorem on the extensibility of solutions. An algorithm for finding an approximate optimal solution under general conditions is also presented. A case study analysis of the Jiuquan Wind Power Base in Gansu Province is also provided， assessing the congruence between the projected development outcomes and the model's predictions.

Key words: renewable energy, wind energy, dynamic optimization model, optimal control theory, Jiuquan wind power base