交替最小化在电力系统坏数据检测中的应用

Application of Alternating Minimization in Bad Data Detection of Power Systems

摘要: 本文系统研究了交替最小化方法的基本原理与算法框架，并创新性地提出一种融合梯度正则化牛顿算法与稀疏优化技术的交替优化模型，应用于电力系统状态估计与坏数据检测问题。针对多变量非凸优化难题，所提方法通过交替优化状态变量和稀疏坏数据向量，有效实现了快速收敛速率下状态估计与坏数据识别的联合处理。在IEEE 14、30和57节点系统上的实验结果表明，与传统半定规划和二阶锥规划松弛方法相比，该算法在计算效率上展现出显著的优越性，同时保持了良好的精度水平与坏数据识别准确率。本研究为优化算法理论研究提供了典型应用案例，也为电力系统安全运行提供了有效的技术支撑。

Abstract: This paper systematically investigates the fundamental principles and algorithmic framework of the alternating minimization method, and innovatively proposes an alternating optimization model that integrates a gradient-regularized Newton algorithm with sparse optimization techniques, applied to power system state estimation and bad data detection problems. For the multivariate non-convex optimization challenge, the proposed method alternately optimizes state variables and sparse bad data vectors, effectively achieving joint processing of state estimation and bad data identification with a fast convergence rate. Experimental results on the IEEE 14-, 30-, and 57-bus test systems demonstrate that, compared to traditional semidefinite programming and second-order cone programming relaxation methods, the proposed algorithm exhibits significant superiority in computational efficiency while maintaining good accuracy levels and bad data identification performance. This study provides a typical application case for theoretical research on optimization algorithms and offers effective technical support for the secure operation of power systems.