[Paper Review] Robust Power System State Estimation for the Nonlinear AC Flow Model

Hao Zhu, Georgios B. Giannakis|arXiv (Cornell University)|Jun 21, 2012

Power System Optimization and Stability20 references3 citations

TL;DR

This paper proposes a robust power system state estimation (R-SE) method for the nonlinear AC power flow model using a sparse overcomplete outlier model and semidefinite relaxation (SDR) to achieve globally optimal solutions. By leveraging sparsity and convex relaxation, the method outperforms iterative Gauss-Newton solvers in handling bad data and cyber-attacks, demonstrating superior accuracy in voltage angle estimation on the IEEE 30-bus system.

ABSTRACT

An important monitoring task for power systems is accurate estimation of the system operation state. Under the nonlinear AC power flow model, the state estimation (SE) problem is inherently nonconvex giving rise to many local optima. In addition to nonconvexity, SE is challenged by data integrity and cyber-security issues. Unfortunately, existing robust (R-) SE schemes employed routinely in practice rely on iterative solvers, which are sensitive to initialization and cannot ensure global optimality. A novel R-SE approach is formulated here by capitalizing on the sparsity of an overcomplete outlier vector model. Observability and identifiability issues of this model are investigated, and neat links are established between R-SE and error control coding. The \emph{convex} semidefinite relaxation (SDR) technique is further pursued to render the nonconvex R-SE problem efficiently solvable. The resultant algorithm markedly outperforms existing iterative alternatives, as corroborated through numerical tests on the standard IEEE 30-bus system.

Motivation & Objective

• To address the nonconvexity and local optima challenges in traditional power system state estimation under the nonlinear AC flow model.
• To improve resilience against bad data and cyber-attacks by modeling measurement outliers as sparse, overcomplete disturbances.
• To develop a globally optimal R-SE solver with polynomial-time complexity, overcoming the initialization sensitivity and convergence issues of iterative methods.
• To establish theoretical links between R-SE and error control coding via the concept of measurement distance.
• To demonstrate the performance advantage of the proposed SDR-based R-SE framework through numerical validation on the IEEE 30-bus system.

Proposed method

• Formulates a sparse overcomplete outlier model where corrupted measurements are represented as a sparse vector of anomalies.
• Introduces the notion of measurement distance to quantify resilience to outliers, drawing parallels with channel coding theory.
• Applies semidefinite relaxation (SDR) to transform the nonconvex R-SE problem into a convex semidefinite program (SDP), enabling global optimization.
• Uses randomization techniques on the relaxed solution to extract a feasible R-SE estimate with quantifiable approximation accuracy.
• Employs a convex optimization framework via CVX and SeDuMi to solve the SDR problem efficiently using interior-point methods.
• Incorporates weighted least-squares and weighted least-absolute deviation criteria within the SDR framework to enhance robustness.

Experimental results

Research questions

• RQ1 Can a robust state estimation framework be developed for the nonlinear AC power flow model that ensures global optimality despite nonconvexity?
• RQ2 How can sparsity in measurement outliers be exploited to improve observability and identifiability in state estimation?
• RQ3 What is the role of measurement distance in characterizing the resilience of the nonlinear regression model to corrupted data?
• RQ4 To what extent does semidefinite relaxation preserve the global optimum in nonconvex R-SE problems?
• RQ5 How does the proposed SDR-based R-SE method compare to conventional iterative Gauss-Newton solvers in terms of accuracy and robustness?

Key findings

• The proposed SDR-based R-SE method significantly reduces voltage angle estimation errors compared to conventional WLS Gauss-Newton solvers, especially under bad data conditions.
• On the IEEE 30-bus system, the method achieved markedly lower average voltage angle errors across all buses, with improvements most pronounced in the presence of corrupted power flow measurements.
• The algorithm demonstrated robustness to a single corrupted power flow meter (multiplied by 1.2), maintaining low estimation error even when standard WLS methods diverged.
• The measurement distance concept was shown to be instrumental in characterizing the error-control capability of the R-SE model, linking it to coding theory.
• The SDR relaxation yielded a solution that closely approximates the global optimum, with numerical results indicating high feasibility and accuracy.
• The framework enables theoretical guarantees on outlier observability and identifiability, extending prior work limited to linear approximations.