Harmonic State Estimation and Observability Analysis via Sparsity
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
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