求解PMU多目标优化配置问题的非劣排序微分进化算法

Non-dominated sorting differential evolution algorithm for multi-objective optimal PMU placement

为实现电网完全可观测,同时保证PMU(同步相量测量单元)的安装数目尽量少,且系统的N-1量测可靠性尽量高,笔者提出了一种混合算法,对电网中PMU进行多目标优化配置.在此算法中,通过将Pareto非劣排序操作与微分进化算法有机融合,并对个体的排挤机制和变异策略进行改进以克服进化早熟和搜索不均匀的问题,设计出了一种新的非劣排序微分进化算法对模型进行求解,并采用模糊集理论提取出最优折中解.最后以IEEE39母线系统为例进行了PMU多目标优化配置,结果表明该方法可简单快速地实现全局多目标寻优,找到更多更合理的PMU优化配置方案,能得到准确而完整的Pareto最优前沿.

For a power grid to be completely observable when employing a minimal number of placed phasor measurement units（PMU） to achieve the highest reliability of the N - 1 measurements, we propose a new hybrid algorithm to optimize this PMU multi-objective placement problem. In this algorithm, the Pareto non-dominated sorting mechanism is integrated with the differential evolution algorithm; meanwhile the individual crowding mechanism and the mutation strategy are improved to cope with the premature convergence and the search bias. Moreover, fuzzy set theory is employed to extract the best compromise non-dominated solution. Both the Pareto-optimal solution and the desired Pareto front can be rapidly found by the proposed algorithm. This is demonstrated by the results in the application to the IEEE 39-bus systems.