Condition indicator analysis for the enhancement of power system state estimators

Most utilities have state estimators in the package of energy management systems. The main functions of state estimators are to represent steady state system voltage, currents, and power flows---utilizing mathematics to enhance the accuracy of measurements. In this dissertation, the author examines how the new technology of phasor measurement units (PMUs) can be used to enhance state estimation in electric power systems. A study and review of condition analysis for state estimation is presented in this report. Condition analysis is a linear algebra analysis of the sensitivity of the estimations error due to measurement error. The basis of the analysis in the evaluation of the error ellipsoid in the linear least squares formulation of the state estimator problem. The study reveals that decreasing the condition number of the gain matrix increases the accuracy of state estimates. Some other innovative concepts presented in this report include: singular distance---calculating the distance between matrix G and the closest singular matrix; scaling factor---viewing the largest singular value of matrix G as a condition indicator; measurement placement using eigenvectors---the use of eigenvector of smallest eigenvalue to find placement of measurements. Linearized equations are developed estimate the change in the condition indicators for the addition of a state measurement. The analysis of condition indicators for PMU placement led to significant improvement of condition number of the gain matrix. Two test bed systems are used in this report: the IEEE 57 test bed and a representation of a power system in the southwest US. The test bed system representing the southwest US power system is 180 buses, 245 transmission lines, and 748 measurements. An algorithm is developed to use condition indicators as an additive tool to other sensory placement strategies.