Decoupled State-Estimation in Energy Control Centres

Abstract

Abstract STATE-ESTIMATION (SE) is the process of assigning a value to an unknown system state-variable based on measurements from that system according to some criteria. Usually, the process involves imperfect measurements inherent in the process and therefore estimating the system state is based on a statistical criteria that estimates the true value of the state-variable so as to minimize or maximize the selected criteria. A commonly used and familiar criteria is that of minimizing the sum of squares of the differences between the estimated and ‘true’ (i.e. measured) values. Power System Static State-Estimation (PSSE) is a proven technique for providing modern energy control centres with reliable real-time data bases for security monitoring and on-line control. The state-estimation processes real-time raw measurements to obtain optimal estimates of voltage magnitudes and angles at all buses, which determines the static state of the Power System (PS). The estimation problem of PSSE is usually formulated as a nonlinear least-square problem. Among state estimators based on the normal equations approach, the weighted least square (WLS) estimator provides reliable estimates but is slow, mainly due to its requirement for updating and factorization of the full-matrix in every iteration. The decoupled state-estimator requires less computation time per iteration and less storage requirement than WLS. The concept of p- δ, Q-V decoupling technique as applied in load flow studies is extended to state estimation technique also which reduces the storage requirement and also the time for convergence. The most common approach to the SE problem is to formulate it as a nonlinear problem usually solved by an iterative procedure based on successive linearization; in each iteration one has to solve a linear least-squares problem. Associated with WLS estimation is a set of redundant equations are to be solved to yield the solution. These equations are ‘Normal Equations’ and are solved using Cholesky factorization. The normal equations are very satisfactory with respect to preserving sparsity, but they may give rise to numerical ill-conditioning. Methods using orthogonal transformations, such as those of Householder have far better stability properties. The Method of Data Equations which uses the Householder orthogonal transformation is more efficient than the conventional method of normal equations. Also, it is less prone to computer round-off errors and is more numerically stable. The standard approach to the solution of the WLS state estimation in power system is the iterative normal equations method. Occassional ill-conditioning has been experienced with this method. Alternative approaches to state-estimation are based on ‘orthogonal transformation’. These methods have improved numerical behaviour, but generally their sparsity suffers when the measurement redundancy is high. In this paper the decoupled estimator based on transformation method is presented using different algorithms and the results agree with the method of normal equations. Measurements are transformed into new ‘measurements’ that are functions of the states and of the original measurements. In PSSE redundancy rate is an important aspect. Estimator obtained from various redundancy rates, by considering active and reactive redundancy seperately obtained by uniformly distributing the measurements over the system is presented. Line flows and bus injection measurements required for stateestimation studies, have been obtained from load-flow computations. Error (noise) terms (σ = 0.01 and 0.001) are added to these measurements. The error vector being simulated using a random number generator. Convergence tolerance of 0.001 PU and 0.001 are used for V and δ, respectively. Results obtained for various combinations of measurements; and with different order of processing these measurements have been presented. Measurements are classified as. Type 1, 2 : Power injections. Type 3, 4 : Power flows. Type 5 : Voltage magnitudes. Different cases analysed are. i) Case 1 : 1, 2, 3, 4 & 5 Type measurements. ii) Case 2 : 1, 3, 4 and 5 Type measurements. iii) Case 3 : 1, 2, 3 and 4 Type measurements. iv) Case 4 : 3 and 5 Type measurements. It is important that at least few voltage measurements (NBUS/ 10 to NBUS/5) must be included while estimating the states. When line-flows only are used as measurements, solution takes large number of iterations to converge. Comparative results obtained from ‘method of Normal equations’ and ‘Data equations’ have been presented. Illustrative examples considered are IEEE-14 bus system and 5-bus sytem.