Optimal Placement of Phasor Measurement Units for Harmonic State Estimation in Unbalanced Distribution System Using Genetic Algorithms

In this paper, a genetic-based algorithm is presented for optimal placement of phasor measurement units, which minimizes the number of the units and enhances the accuracy of the harmonic state estimation solutions. Also, weighted least square estimation is used for harmonic state estimation, which is based on singular value decomposition rather than the normal equations. The singular value decomposition approach eliminates the need of observability analysis prior to estimation. Optimal number and position of phasor measurement units among three different cases for harmonic state estimation in unbalanced distribution systems are compared. In first case, it is assumed that phasor measurement unit has enough channels to measure bus voltage phasor and all current phasors connected to this bus. In two other cases, phasor measurement unit has only single channel to measure a three-phase current. In one case, phasor measurement unit measured a current phasors along one branch that is connected to the bus, and in another case, phasor measurement unit measures three single phase current phasors along 1, 2 or 3 branches that are connected to the bus. The proposed algorithms for harmonic state estimation and optimal measurement placement are applied on a real 58-bus unbalanced distribution system and the results are presented.