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CEIC-06-06

"Power System Harmonic State Estimation and Observability Analysis via Sparsity Maximization"

Huaiwei Liao

Abstract:
Harmonic state estimation (HSE) is used to locate harmonic sources and estimate harmonic distributions in power transmission networks. When only a limited number of harmonic meters are available, existing HSE methods have limited effectiveness due to observability problems. This paper describes a new system-wide harmonic state estimator that can reliably identify harmonic sources using fewer meters than unknown state variables. Note there are only a small number of simultaneous harmonic sources among the suspicious buses.
We propose the concept of S-Observability by extending observability analysis to general underdetermined estimation when considering the sparsity of state variables. We show the underdetermined HSE can become observable with proper measurement arrangements by applying the sparsity of state variables. We formulate the harmonic state estimation as a constrained sparsity maximization problem based on L1-norm minimization. It can be solved efficiently by an equivalent linear programming. Numerical experiments are conducted in the IEEE 14-bus power system to test the proposed method. The underdetermined system contains nine meters and thirteen suspicious buses. The results show that the proposed sparsity maximization approach can reliably identify harmonic sources when presence of measurement noises, model parameter deviations and small non-zero injections.

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