Optimal PMU Placement for Kalman Filtering of DAE Power System Models

TL;DR

The paper tackles optimal PMU placement for dynamic state estimation in power systems modeled by differential-algebraic equations (DAEs). It introduces a principled MISDP formulation that minimizes the steady-state Kalman covariance $P_ ext{infty}(\gamma)$ by selecting PMU locations under a budget, with a rigorous change-of-variables $X = P^{-1}$ and SDP-based constraints; a continuous relaxation enables branch-and-bound to obtain optimality guarantees. The methodology is validated on 3-bus and 11-bus test cases, showing that the proposed MISDP approach outperforms greedy baselines and that using injected currents as algebraic states substantially improves numerical conditioning of the Kalman filter. The work demonstrates provable optimal sensor configurations for joint dynamic-algebraic state estimation in partially known networks and highlights practical implications for offline PMU deployment and online estimation.

Abstract

Optimal sensor placement is essential for minimizing costs and ensuring accurate state estimation in power systems. This paper introduces a novel method for optimal sensor placement for dynamic state estimation of power systems modeled by differential-algebraic equations. The method identifies optimal sensor locations by minimizing the steady-state covariance matrix of the Kalman filter, thus minimizing the error of joint differential and algebraic state estimation. The problem is reformulated as a mixed-integer semidefinite program and effectively solved using off-the-shelf numerical solvers. Numerical results demonstrate the merits of the proposed approach by benchmarking its performance in phasor measurement unit placement in comparison to greedy algorithms.

Figures (4)

• Figure 1: Single line diagram of the 3-bus system.
• Figure 2: Steady state covariance matrix of the Kalman filtering for measurements selected by different algorithms evaluated under varying process noise at node 2.
• Figure 3: Single-line diagram of an 11-bus subsystem obtained by isolating a portion of the IEEE 39-bus test system.
• Figure 4: Average Kalman filter steady state covariance matrix for 20 random PMU measurement configurations with injected currents and injected voltages being the algebraic states.