Substation-Constrained Bi-Level Capacity Planning of Multi-Energy Power Systems Using an Improved Whale Optimization Algorithm

Under high renewable-energy penetration, regional power systems face increasing operational variability caused by wind and photovoltaic generation. Capacity planning for multi-energy complementary systems must therefore consider both investment economy and operation-related reliability costs under practical grid-access constraints. This study proposes a substation-constrained bi-level capacity-planning framework for a regional multi-energy power system in Ningxia. In the upper level, the installed capacities of wind, photovoltaic, thermal, and energy-storage resources are optimized by minimizing the annualized comprehensive cost subject to regional substation capacity limits. In the lower level, a mixed-integer linear programming dispatch model evaluates the operating cost of each candidate capacity scheme under representative seasonal scenarios, including thermal fuel cost, net grid-exchange cost, and reliability-related penalty costs associated with load curtailment, reserve shortage, and power imbalance. An Improved Whale Optimization Algorithm is used as the outer planning optimizer and is coupled with the lower-level MILP dispatch model. The case study uses normalized hourly load, wind power, and photovoltaic power data from Ningxia to construct an equivalent three-region planning system. The results show that the proposed bi-level framework reduces the annualized comprehensive cost by 28.3% compared with the single-level model, with the minimum total system cost reaching 2.71 × 108 CNY. Compared with the standard WOA, PSO, and GA under the same case setting, the proposed IWOA obtains a lower objective value and smaller variation across repeated runs. The reliability-related terms in the model are interpreted as economic operational proxies rather than direct probabilistic reliability indices. The proposed framework provides a planning-oriented method for evaluating multi-energy capacity allocation under substation capacity constraints and representative operational scenarios.