Active Distribution Network Bi-Level Programming Model Based on Hybrid Whale Optimization Algorithm

In recent years, the integration of flexible resources into active distribution networks (ADNs) has been significantly enhanced. By coordinating a variety of such resources, the economic efficiency, operational security, and overall stability of ADNs can be improved. In this study, a bi-level planning model is proposed for active distribution networks. The upper-level model aims to minimize the annual comprehensive cost, while the lower-level model focuses on reducing network losses. To solve the upper-level problem, a hybrid whale optimization algorithm (HWOA) is developed. The algorithm integrates adaptive mutation based on Gaussian–Cauchy distributions, a nonlinear cosine-based control strategy, and a dual-population co-evolution mechanism. These enhancements allow HWOA to achieve faster convergence, higher accuracy, and stronger global search capabilities, thereby reducing the risk of falling into local optima. The lower-level problem is addressed using the interior point method due to its nonlinear and continuous nature. The proposed model and algorithm are validated through simulations on the IEEE 33-bus system. The results show that DG consumption increases by 88.77 MWh, network losses decrease by 6.8 MWh, and the total system cost is reduced by CNY 3.62 million over the entire project lifecycle. These improvements contribute to both the economic and operational performance of the ADN. Compared with the polar fox optimization algorithm (PFA), HWOA improves algorithmic efficiency by 18.92%, lowers network loss costs by 6.22%, and reduces the total system costs by 0.71%, demonstrating its superior effectiveness in solving complex bi-level optimization problems in active distribution networks. These findings not only demonstrate the technical efficiency of the proposed method but also contribute to the long-term goals of sustainable energy systems by improving renewable energy utilization, reducing operational losses, and supporting carbon reduction targets in active distribution networks.