1 Abstract - This paper presents a new observability analysis method of a power system for a combined parameter and state estimation based on the weighted least-squares (WLS) state estimator. In this approach, the state vector is expanded to include both the V-θ sate variables and a given set of branch parameters. This augmented state vector is estimated by processing a large collection of measurements recorded over several snapshots of the power system during which the actual system state is quasi static, that is, varies over a small range. This situation typically occurs during the night off-peak periods. The performance of the proposed observability algorithm is evaluated on a small-scale test system. Keywords – Parameter Estimation, Augmented State Estimation, Observability Analysis, Power Systems. I. INTRODUCTION HE state estimator is an essential tool for security monitoring and security analysis of a power system. It aims at estimating in a reliable manner the nodal voltage magnitudes and phase angles of the system by processing a redundant collection of analog measurements. This processing is based on a given mathematical model of the lines and transformers and other transmission devices (i.e. FACTS devices) and on a given topology of the network, which is typically determined from the telemetered signals about the status of switching devices. Consequently, the state estimator is subject to three types of errors, which are (i) errors on analogical measurements (bad data); (ii) incorrect topology information (topology errors) and (iii) errors on the model of the system equipment (parameter errors). The latter can have adverse impact on the state estimator and are less evident to detect than gross measurements and topology errors. Despite the importance of the problem, the number of papers devoted to parameter errors is modest as compared to those dealing with gross measurements and topological errors [1]. In the literature, parameter error identification is carried L. Mili is with the Electrical and Computer Engineering Department, Virginia Tech, Alexandria Research Institute (e-mail: lmili@vt.edu ). J.B.A. London Jr. and N.G. Bretas are with the Department of Electrical Engineering of the E.E.S.C. – University of São Paulo, Brazil (e-mails: jbalj@sel.eesc.usp.br , ngbretas@sel.eesc.usp.br ). out either through residual sensitivity analysis [2, 3] or through an augmented state vector. The latter method is of interest to us. Depending on the way that the augmented state is being estimated, we may distinguish two groups of methods: (i) those based on the WLS normal equations [4, 5] and (ii) those that make use of the Kalman filter [6, 7]. The first group of methods suffers from system observability problems since there are rarely enough measurements to enable the estimation of the augmented state vector. To overcome this difficulty, the methods of the second group rely on a transition matrix to predict the state at consecutive scan times through the so-called dynamic equation. However, this transition matrix is usually unknown and hence, has to be identified from real-time measurements, a task rarely considered in the literature. In most of the papers, this matrix is just set equal to the identity matrix, which amounts to assuming that the system state is quasi static. Taking advantage of the fact that a certain fraction of the measurements remains nearly unchanged during a long period of time, typically during night off-peak hours, we propose to include all these measurements in a single vector and to estimate in a unified manner some branch parameters together with the V-θ state variables. By doing so, the measurement redundancy is significantly increased. Note that during that time period, it is reasonable to assume that the associated state variables are quasi static. In this paper, the observability method developed in [8] is expanded to the augmented state estimation problem. This paper is organized as follows: Section II revisits the WLS normal equations for the augmented state estimation. Section III outlines the observability method proposed in [8]. Section IV modifies this method to the augmented state while Section V describes some simulation results on a small test system. II. STATE ESTIMATION BASED ON THE NORMAL EQUATIONS Power system state estimation is closely related to the statistics regression methods. The non-linear equations relating the (mx1) measurement vector “z” and the (nx1) state vector “x” are: w x h z + = ) ( (1) where “w” is an (mx1) random noise vector with zero mean jointly Gaussian distribution and h(.) is a vector-valued non- An Observability Analysis Method for a Combined Parameter and Sate Estimation of a Power System J.B.A London Jr., L. Mili, and N.G. Bretas T Proceedings of the 8 th International Conference on Probabilistic Method Applied to Power Systems Iowa State University, Ames, Iowa, Sept. 12-16, 2004