Analysis of Moving Target Defense in Unbalanced and Multiphase Distribution Systems Considering Voltage Stability

Moving Target Defense (MTD) is a new technology to defend against the false data injection attack (FDIA) on distribution system state estimation (DSSE). It works by proactively perturbing the branch reactance. However, due to the challenges induced by the nonlinear dynamics and the coupling phases in the three-phase AC DSSE model, the analysis on the effectiveness and hiddenness of MTD, which are two essential performance metrics, has not yet been conducted. In this paper, we attempt to optimize the effectiveness and hiddenness of MTD while considering voltage stability. Firstly, we quantify the two metrics with approximated measurement residuals. Based on the quantified metrics, we formulate an optimization problem to maximize the effectiveness with guaranteed hiddenness and ensure voltage stability by minimizing the voltage variation induced by MTD. The original problem is transformed to a polynomial optimization problem based on the observation that the alteration of the projection matrix caused by reactance perturbation is neglectable, such that the near-optimal result can be obtained. Finally, extensive simulations are conducted on the IEEE 13-bus test feeder to evaluate the performance of the proposed MTD.