Research on the Optimal Power Flow Problem—The Fusion of Particle Swarm Optimization Algorithm and Regularized Dual Method

针对电力系统最优潮流问题中约束条件复杂、易陷入局部最优等难点，本研究创新性地构建了粒子群优化算法与正则对偶理论的三阶段求解框架。首先设计混沌映射初始化与自适应惩罚机制的粗粒度搜索算法，让初始解在解空间广泛分布，扩大搜索范围；继而通过正则化对偶映射实现约束边界的梯度修复，生成严格可行解集；最终建立多策略协同的精细搜索机制，采用拓扑迁移和柯西变异操作，延缓种群退化现象。并将IEEE-30节点的数据代入本方法求解，与传统粒子群算法相比，本方法显著增强了约束处理能力和解的质量稳定性。此方法在约束处理能力、解的稳定性方面都有明显增强。这一成果为解决电力系统最优潮流问题提供了新的有效途径。To address the challenges of complex constraints and the tendency to get trapped in local optima in optimal power flow (OPF) problems of power systems, a three-stage solution framework that integrates particle swarm optimization (PSO) with regularized dual theory is innovatively constructed. Firstly, a coarse-grained search algorithm featuring chaotic mapping initialization and an adaptive penalty mechanism is designed. This algorithm enables the initial solutions to be widely distributed within the solution space, thus expanding the search scope. Subsequently, the gradient repair of the constraint boundaries is achieved through regularized dual mapping, which generates a set of strictly feasible solutions. Finally, a refined search mechanism with multi-strategy collaboration is established. Topology migration and Cauchy mutation operations are adopted to slow down the phenomenon of population degeneration. When the data of the IEEE-30 bus system is applied to solve the problem using this proposed method, compared with the traditional particle swarm algorithm, this method significantly enhances the constraint handling ability and the stability of solution quality. Specifically, obvious improvements are observed in terms of constraint handling ability and solution stability. This achievement provides a new and effective approach to solving the optimal power flow problem in power systems.