Summary
Phasor measurement units (PMUs) can obtain synchronized voltage and current phasors to increase the accuracy of state estimation results. Optimal PMU placement (OPP) reduces the required number of PMUs to make the system fully observable. In this paper, two mathematical programming formulations, which are mixed integer linear programming (MILP) and nonlinear programming (NLP), for power grid observability modeling to solve the OPP problem are presented. Power flow and zero injection measurement modeling along with restricted communication facilities, PMU failure, and limited channel capacity contingencies are investigated. MILP zero injection formulation is improved to overcome the observability redundancy and optimality drawbacks. A new formulation for nonlinear programming‐based PMU placement for zero injection measurement is proposed. MILP and NLP methods are compared to illustrate the advantages and disadvantages of each method. The comparison and proposed formulations are examined on IEEE 14‐, 57‐, 118‐, 300‐bus test systems and a large 2383‐bus Polish system to demonstrate their effectiveness.
Summary
To identify power system eigenvalues from measurement data, Prony analysis, matrix pencil (MP), and eigensystem realization algorithm (ERA) are three major methods. This paper reviews the three methods and sheds insight on the principles of the three methods: eigenvalue identification through various Hankel matrix formulations. In addition, multiple channel data handling and noise‐resilience techniques are investigated. In the literature, singular value decomposition (SVD)‐based rank reduction technique has been applied to MP and resulted in a reduced‐order system eigenvalue estimation and an excellent noise resilient feature. In this paper, ERA is refined using the SVD‐based rank reduction to achieve superior performance. Further, a reduced‐order Prony analysis method is proposed. With this technique, Prony analysis can not only give reduced‐order system eigenvalues, but also become noise resilient. Four case studies are conducted to demonstrate the effectiveness of the eigenvalue identification methods, including a tutorial example of an RLC circuit resonance, a power grid oscillation case study for a 16‐machine 68‐bus system, an example of subsynchronous resonance (SSR) of a type‐3 wind grid integration system, and real‐world oscillation events captured by Independent System Operator‐New England (ISO‐NE).
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