M.Sc Student M.Sc Thesis Barel Yehuda Shabtay An Analytic Solution for State Estimation and Observability Analysis in Power Systems Department of Electrical and Computer Engineering ASSOCIATE PROF. Yoash Levron Abstract

In this research thesis we present a new approach for observability analysis and state estimation in power systems. State estimation is one of the most important tasks, taking place in the network control center. Its purpose is to analyze a given measurement set, and evaluate the voltage magnitude and phase of every bus on the system. This evaluation is performed, by solving a weighted least squares optimization problem using a variation of the Gauss Newton method. However, this method is known to suffer from sensitivity to a good starting point, and might not always converge to the optimal solution.

We propose finding the state estimator, by solving a low dimensional, weighted least squares problem. This is done by approximating the state estimator, as a linear transformation, operating on a low dimensional vector of coefficients. In order to understand how this transformation is obtained, we introduce the Characteristic Matrix, comprised of network measurements and admittance data. A main theoretical result regarding this matrix, is that the true state of the network is a member of its null space, when there is no noise. By calculating a null space base for this matrix, the state estimator can be approximated as a linear combination of this base with unknown coefficients. This approximation is casted back to the traditional weighted least squares problem, in order to minimize the objective function with respect to these coefficients. We then solve a relaxation of this problem and produce a solution which can formulated analytically. This solution enables the calculation of the final state estimator, with high accuracy.

Observability analysis is the process of determining whether or not the measurement set is sufficient for a unique state estimation. It is usually conducted under strict assumptions on the network state and admittance values, and might not always produce a reliable result, when the network operates far from these assumptions. We propose treating observability analysis as a state estimation problem, where the state vector is known in advance and the measurements are without noise. We then demonstrate how to find different possible solutions to the problem and compare them to the original state vector, in order to recover the networks observable islands. The advantage in this approach is the ability to perform the analysis on the real network admittance values and for every state.

Numerical simulations were conducted on 9,14,30,57,118,300 bus test cased. Regarding Observability analysis, results show successful detection of the observable islands in all cases, and with low computation times. Regarding state estimations, results show improved performance compared to the traditional Weighted Least Squares approach, solved using the Gauss-Newton method.