Research on Capacity Configuration of Hydro-Wind-Solar Complementary System Based on Bi-level Optimization

To address the problems of low optimization efficiency and late-stage stagnation in the outer module, and insufficient solution diversity in the inner module, during bi-level capacity configuration of hydro–wind–solar hybrid systems, this paper proposes an improved bi-level optimization model. The outer module aims to maximize a comprehensive score obtained by the entropy-weighted sum of three indicators: system output stability, uniformity of release flow, and theoretical wind–solar generation potential. Its optimization process is built on a Gaussian process surrogate and employs a two-stage Bayesian strategy designed to balance global exploration and local convergence. In the early stage, the algorithm conducts global exploration via the Expected Improvement criterion; when the improvement stagnates or the maximum number of generations is reached, it switches to local refinement guided by the gradient of the posterior mean. The inner module pursues two objectives—maximizing annual total power generation and maximizing the minimum system output. A multi-island parallel NSGA-II algorithm is introduced to simulate the joint operation for each capacity scheme, and an adaptive migration mechanism based on the Pareto contribution rate is designed to maintain population diversity. A compromise solution is then selected from the resulting Pareto front, and the three operational indicators are extracted and fed back to the outer module, forming a closed-loop optimization. The model is validated using the Longyangxia–Liujiaxia cascade hydropower stations on the upper Yellow River as a case study. Results show that the two-stage Bayesian optimization in the outer module overcomes the local stagnation problem, reducing the number of inner-module calls by 85% while achieving the same optimal solution as a grid search with identical step size. The improved multi-island parallel NSGA-II produces a Pareto front with superior solution coverage and distribution compared with conventional algorithms. The recommended capacity configuration—3000 MW wind power and 7000 MW solar photovoltaic—maintains favorable generation and flow stability under typical scenarios corresponding to 25%, 50%, and 75% joint probability of hydro–wind–solar resources, achieving an overall average score of 0.6752, which outperforms the alternatives. An economic analysis indicates that its levelized cost of electricity ranges from 0.16 to 0.18 CNY/kWh, lower than the marginal cost of thermal power and prevailing market prices, demonstrating notable cost competitiveness. The proposed model offers effective methodological support for capacity planning of hydro–wind–solar hybrid systems.