A Convex Method of Generalized State Estimation using Circuit-theoretic Node-breaker Model

TL;DR

This work tackles topology errors in power-grid state estimation by introducing a circuit-theoretic generalized state estimation framework on a Node-Breaker model (ckt-GSE). It builds an aggregated linear circuit from RTU/PMU measurements and switch models, and solves a convex WLAV LP with slack variables to jointly estimate AC states and topology while identifying data errors. Key contributions include a fully linearized NB representation, a robust WLAV objective with node- and switch-level error indicators, and a circuit-based solver that scales to large networks. The method demonstrates superior robustness over traditional WLS, identifies topology errors and bad data, and remains computationally scalable for networks with thousands of nodes. This approach enables reliable, topology-aware situational awareness in real-world grids facing cyber-physical threats and measurement errors.

Abstract

An accurate and up-to-date topology is critical for situational awareness of a power grid; however, wrong switch statuses due to physical damage, communication error, or cyber-attack, can often result in topology errors. To maintain situation awareness under the possible topology errors and bad data, this paper develops ckt-GSE, a circuit-theoretic generalized state estimation method using node-breaker (NB) model. Ckt- GSE is a convex and scalable model that jointly estimates AC state variables and network topology, with robustness against different data errors. The method first constructs an equivalent circuit representation of the AC power grid by developing and aggregating linear circuit models of SCADA meters, phasor measurement units(PMUs), and switching devices. Then based on this circuit, ckt-GSE defines a constrained optimization problem using weighted least absolute value (WLAV) objective to form a robust estimator. The problem is a Linear Programming (LP) problem whose solution includes accurate AC states and a sparse vector of noise terms to identify topology errors and bad data.This paper is the first to explore a circuit-theoretic approach for an AC-network constrained GSE algorithm that is: 1) applicable to the real-world data setting, 2) convex without relaxation, scalable with our circuit-based solver; and 3) robust with the ability to identify and reject different data errors

Figures (11)

• Figure 1: Toy example: the node breaker (NB) model of a grid sub-network around a substation.
• Figure 2: RTU and PMU injection models.
• Figure 3: Open switch model: $n_{sw}$ close to zero if the status is correct; $n_{sw}$ compensates the current flow on the branch if the status is wrong.
• Figure 4: Closed switch model: $n_{sw}$ close to zero if the status is correct; $n_{sw}$ will offset the current flow on the branch if the status is wrong. $x_{sw}$ is in p.u.
• Figure 5: The NB example in Fig \ref{['fig:NB model']} is converted to a linear circuit after replacing grid components with their circuit models. To save space, this figure shows the complex models. It can be further split into real and imaginary parts by using the split circuit models in Section \ref{['sec: models']} and \ref{['sec: physical_models']}

Theorems & Definitions (1)

• Definition 1.1: ckt-GSE task