Abstract
The paper concerns the estimation of the state of a power system in which there is a phase shifter called a quadrature booster. The aim of the paper is a comparative analysis of two different cases including the quadrature booster in the state estimation. In the first case, the quadrature booster is represented by a model consisting of two real voltage sources, one in series with a power line and the other in a shunt branch. In the second case, in the power system model, the real branch with the quadrature booster is represented as off at the end where the considered quadrature booster is actually installed. The state estimation is assumed to be carried out in the polar coordinate system. The properties of the state estimation are characterized by: the number of iterations in the calculation process, the index of conditioning of the matrix of coefficients in the equations to be solved (cond(G)), and ratio Je/Jm, which is a measure of the accuracy of the estimation. Using IEEE 14-bus test system, investigations are carried out in such a way as to cover the entire state space of the power system as possible. In the investigations, Monte Carlo experiments are carried out for each of the considered cases of the state estimation. Each of these cases is also analyzed from the point of view of the assumed definition of the state estimation. Investigations show that in the first of the previously described cases, the state estimation is more accurate, but there are more iterations in the calculations and worse conditioning of the estimation process. The comparative analysis also shows that, the accuracy of the results obtained in each of the considered cases is practically independent of the coordinate system in which the estimation calculations are performed. Taking into account the number of iterations in the estimation process and index cond(G), it can be concluded that the implementation of each of the above-mentioned estimation cases in the rectangular coordinate system is more reasonable.
Highlights
IntroductionKnowing the state of the power system is essential to be able to influence effectively the system
One of the important factors influencing that accuracy is the system model, which is used in state estimation
Comparison of Method 1 in the rectangular coordinate system and Method 1 in the polar coordinate system shows that accuracy of results of the state estimation in each of these cases is practically the same
Summary
Knowing the state of the power system is essential to be able to influence effectively the system. One of the important factors influencing that accuracy is the system model, which is used in state estimation. The paper considers the estimation of the state of the power system in which there is a phase shifter, being one of the FACTS controllers [2]. One of the types of phase shifters [3] is considered, namely the quadrature boosting transformer, known as quadrature booster [4]. The term of “the classical state estimation” is understood as a state estimation for a power system without a quadrature booster. The weighted-least-squares power-system state-estimation method is considered [17]. Where: x is a power-system state vector; z is a vector of measurements; h(x) is a vector of functions of vector x, representing dependence of measured quantities on the state vector; and R is a diagonal matrix of measurement-data covariances.
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