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Convexification of Power Flow Equations in the Presence of Noisy Measurements

机译：存在噪声测量时潮流方程的凸化

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This paper is concerned with the power system state estimation (PSSE) problem that aims to find the unknown operating point of a power network based on a given set of measurements. We first study the power flow (PF) problem as an important special case of PSSE. PF is known to be nonconvex and NP-hard in the worst case. To this end, we propose a set of semidefinite programs (SDPs) with the property that they all solve the PF problem as long as the voltage angles are relatively small. Associated with each SDP, we explicitly characterize the set of all the complex voltages that can be recovered via that convex problem. As a generalization, the design of an SDP problem that recovers multiple nominal points and a neighborhood around each point is also cast as a convex program. The results are, then, extended to the PSSE problem, where the measurements used in the PF problem are subject to noise. A two-term objective function is employed for each convex program developed for the PSSE problem: 1) the first term accounting for the nonconvexity of the PF equations and 2) other one for estimating the noise levels. An upper bound on the estimation error is derived with respect to the noise level, and the proposed techniques are demonstrated on multiple test systems, including a 9241-bus European network. Although the focus of this paper is on power networks, yet the developed results apply to every arbitrary state estimation problem with quadratic measurement equations.
机译：本文涉及电力系统状态估计（PSSE）问题，该问题旨在基于给定的一组测量值来找到电力网络的未知工作点。我们首先研究功率流（PF）问题，将其作为PSSE的重要特例。已知PF在最坏的情况下是非凸的并且是NP硬的。为此，我们提出了一组半定程序（SDP），其性质是只要电压角相对较小，它们都可以解决PF问题。与每个SDP关联，我们明确地描述了可以通过凸问题恢复的所有复电压的集合。概括地说，将恢复多个标称点和每个点附近的SDP问题的设计也强制转换为凸程序。然后，将结果扩展到PSSE问题，其中PF问题中使用的测量会受到噪声的影响。对于为PSSE问题开发的每个凸程序，均采用了两项目标函数：1）第一项考虑PF方程的非凸性； 2）另一项用于估计噪声水平。推导了相对于噪声水平的估计误差的上限，并且所提出的技术在包括9241总线的欧洲网络在内的多个测试系统上得到了证明。尽管本文的重点是电力网络，但是开发的结果适用于具有二次测量方程的每个状态估计问题。

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