A Distributed Cooperative Co-Evolutionary Algorithm for Multi-Area Power Flow Optimization

Multi-area optimal power flow (OPF) considering valve-point loading effects (VPL) is a large-scale constrained optimization problem with non-convexity and non-differentiability. Existing methods struggle to solve this non-differentiable problem effectively due to the vast search space. To address this problem, this paper combines the cooperative co-evolution (CC) framework with the level-based learning swarm optimizer (LLSO) to propose a distributed cooperative co-evolutionary algorithm. The CC framework decomposes the multi-area OPF problem into several sub-area problems to reduce the problem size, while LLSO is employed to tackle the challenges of non-convexity and non-differentiability. In this algorithm, each area independently optimizes local variables using LLSO and collaborates with others to jointly optimize the global objective function based on the CC framework. To adapt to the distributed computing framework, a distributed power flow calculation method is embedded to address the alternating current power flow constraints. Case studies on two multi-area power systems modified from standard IEEE test systems demonstrate the effectiveness of the proposed algorithm.