[Paper Review] Robust Power System Dynamic State Estimator with Non-Gaussian Measurement Noise: Part II--Implementation and Results

Junbo Zhao, Lamine Mili|arXiv (Cornell University)|Mar 14, 2017

Power System Optimization and Stability8 references3 citations

TL;DR

This paper proposes a Generalized Maximum-Likelihood-type robust Unscented Kalman Filter (GM-UKF) for power system dynamic state estimation under non-Gaussian noise and system stress. It systematically tunes filter parameters and demonstrates through IEEE 39-bus simulations that the GM-UKF outperforms UKF and GM-IEKF in convergence, statistical efficiency, and robustness under Laplace/Cauchy noise, outliers, communication losses, cyber attacks, and strong nonlinearities.

ABSTRACT

This paper is the second of a two-part series that discusses the implementation issues and test results of a robust Unscented Kalman Filter (UKF) for power system dynamic state estimation with non-Gaussian synchrophasor measurement noise. The tuning of the parameters of our Generalized Maximum-Likelihood-type robust UKF (GM-UKF) is presented and discussed in a systematic way. Using simulations carried out on the IEEE 39-bus system, its performance is evaluated under different scenarios, including i) the occurrence of two different types of noises following thick-tailed distributions, namely the Laplace or Cauchy probability distributions for real and reactive power measurements; ii) the occurrence of observation and innovation outliers; iii) the occurrence of PMU measurement losses due to communication failures; iv) cyber attacks; and v) strong system nonlinearities. It is also compared to the UKF and the Generalized Maximum-Likelihood-type robust iterated EKF (GM-IEKF). Simulation results reveal that the GM-UKF outperforms the GM-IEKF and the UKF in all scenarios considered. In particular, when the system is operating under stressed conditions, inducing system nonlinearities, the GM-IEKF and the UKF diverge while our GM-UKF does converge. In addition, when the power measurement noises obey a Cauchy distribution, our GM-UKF converges to a state estimate vector that exhibits a much higher statistical efficiency than that of the GM-IEKF; by contrast, the UKF fails to converge. Finally, potential applications and future work of the proposed GM-UKF are discussed in concluding remarks section.

Motivation & Objective

• Address the limitations of conventional Kalman filters in power system dynamic state estimation when process and measurement noises are non-Gaussian.
• Overcome the poor convergence and statistical inefficiency of existing robust filters like GM-IEKF under thick-tailed noise and system nonlinearities.
• Develop a robust, high-efficiency dynamic state estimator that maintains stability and accuracy under realistic system disturbances including outliers, communication losses, and cyber attacks.
• Provide a systematic parameter tuning framework for the proposed robust UKF to ensure practical implementation in real-time power system monitoring.
• Validate the proposed GM-UKF’s robustness and efficiency across diverse operational scenarios on the IEEE 39-bus system.

Proposed method

• Adopt a Generalized Maximum-Likelihood-type robust framework to handle non-Gaussian measurement noise, particularly Laplace and Cauchy distributions.
• Implement an Unscented Kalman Filter (UKF) with Huber-type M-estimator functions to reduce sensitivity to outliers and improve statistical efficiency.
• Integrate projection statistics for robust initialization and outlier detection in the state estimation process.
• Use standardized residuals and influence functions to assess bias- and variance-robustness under contamination and model uncertainty.
• Apply a systematic parameter tuning procedure for the GM-UKF, including selection of tuning constants based on asymptotic efficiency and breakdown point analysis.
• Utilize the unscented transform to capture nonlinear state transitions more accurately than EKF-based methods, especially under strong system nonlinearities.

Experimental results

Research questions

• RQ1 How does the proposed GM-UKF perform under thick-tailed measurement noise (Laplace and Cauchy distributions) compared to standard UKF and GM-IEKF?
• RQ2 Can the GM-UKF maintain convergence and accuracy when subjected to observation and innovation outliers, including those induced by model errors?
• RQ3 How does the GM-UKF handle intermittent PMU measurement losses due to communication failures in dynamic state estimation?
• RQ4 What is the resilience of the GM-UKF against cyber attacks that corrupt or inject false measurements?
• RQ5 Does the GM-UKF maintain high statistical efficiency and convergence under strong system nonlinearities where UKF and GM-IEKF diverge?

Key findings

• The GM-UKF converges under strong system nonlinearities where both the UKF and GM-IEKF diverge, demonstrating superior stability.
• Under Cauchy-distributed measurement noise, the GM-UKF achieves significantly higher statistical efficiency than the GM-IEKF, while the UKF fails to converge.
• The GM-UKF exhibits finite bias and variance robustness, with a breakdown point that ensures stability under contamination up to a certain threshold.
• The filter maintains high accuracy and convergence even when PMU measurements are lost intermittently due to communication failures.
• The GM-UKF outperforms both the UKF and GM-IEKF in all tested scenarios, including cyber attacks and thick-tailed noise, due to its robust parameter tuning and statistical efficiency.
• The standardized residual analysis confirms that the GM-UKF’s asymptotic variance remains bounded under contamination, validating its robustness properties.