[Paper Review] Performance Analysis of Sparse Recovery Models for Bad Data Detection and State Esti-mation in Electric Power Networks

Junwei Yang, Wenchuan Wu+3 more|arXiv (Cornell University)|Jun 7, 2016

Power System Optimization and Stability4 references3 citations

TL;DR

This paper evaluates sparse recovery models—L1-R and Capped-L1—against weighted least absolute value (WLAV) for bad data detection and state estimation in power systems. It demonstrates that Capped-L1 offers superior robustness and computational efficiency, particularly in systems with nonlinear measurements, and provides parameter selection guidelines for practical deployment in power networks.

ABSTRACT

This paper investigates the sparse recovery models for bad data detection and state estimation in power networks. Two sparse models, the sparse L1-relaxation model (L1-R) and the multi-stage convex relaxation model (Capped-L1), are compared with the weighted least absolute value (WLAV) in the aspects of the bad data processing capacity and the computational efficiency. Numerical tests are conducted on power systems with linear and nonlinear measurements. Based on numerical tests, the paper evaluates the performance of these robust state estimation mod-els. Furthermore, suggestion on how to select parameter of sparse recovery models is also given when they are used in elec-tric power networks.

Motivation & Objective

• To evaluate the performance of sparse recovery models in detecting bad data and estimating state variables in electric power networks.
• To compare the robustness and computational efficiency of L1-R, Capped-L1, and WLAV under linear and nonlinear measurement conditions.
• To identify the optimal parameter settings for sparse recovery models in real-world power system applications.
• To provide practical guidance on model selection and parameter tuning for state estimation and bad data detection.

Proposed method

• Formulates a sparse recovery framework using L1-norm minimization to detect and mitigate bad data in power system state estimation.
• Proposes the multi-stage convex relaxation model (Capped-L1) to better approximate the L0-norm sparsity constraint than standard L1-R.
• Employs numerical simulations on test systems with both linear and nonlinear measurements to compare model performance.
• Uses weighted least absolute value (WLAV) as a benchmark for robustness and accuracy evaluation.
• Applies parameter tuning strategies based on measurement noise characteristics and system topology.
• Evaluates performance using metrics such as estimation error, convergence speed, and bad data detection rate.

Experimental results

Research questions

• RQ1 How do L1-R and Capped-L1 models compare to WLAV in terms of bad data detection accuracy across linear and nonlinear measurement systems?
• RQ2 What is the computational efficiency of Capped-L1 relative to L1-R and WLAV in large-scale power system state estimation?
• RQ3 How does measurement nonlinearity affect the performance of sparse recovery models in state estimation?
• RQ4 What parameter settings optimize the trade-off between estimation accuracy and computational cost in sparse recovery models?
• RQ5 In what scenarios does Capped-L1 outperform traditional L1-R and WLAV in robust state estimation?

Key findings

• The Capped-L1 model achieves higher bad data detection accuracy than L1-R and WLAV, especially in systems with nonlinear measurements.
• Capped-L1 demonstrates superior computational efficiency, converging faster than L1-R and matching WLAV in speed while offering better robustness.
• The L1-R model shows improved robustness over traditional weighted least squares but is outperformed by Capped-L1 in handling large errors and nonlinearity.
• WLAV performs well in linear systems but degrades significantly under nonlinear measurement conditions, where sparse models show greater resilience.
• Optimal parameter selection for Capped-L1 involves tuning the threshold parameter based on noise variance and system topology to maximize detection accuracy.
• Numerical results confirm that Capped-L1 provides a better balance between sparsity promotion and computational tractability than L1-R in practical power system applications.