Assessing the statistical consistency of the AMB State Estimator in distribution systems

Abstract

-In this paper the statistical consistency of the singlephase Admittance Matrix-Based State Estimator (AMB SE) originally proposed for distribution systems is for the first time assessed and compared to that of the widely used Traditional SE (TSE). The AMB SE is an interesting alternative for distribution systems given the use of a constant Gain matrix, thus simplifying its implementation and significantly reducing the computational time. However, it is crucial to statistically assess its consistency so as to ensure estimated values and variances (outputs) are in agreement with the specified measurements and variances (inputs). This is carried out using a Monte Carlo analysis and a generic 16-bus UK distribution system. Despite the conversion from actual to equivalent measurements required by the AMB SE, as well as the approximations regarding the variances of the equivalent measurements, the results demonstrate that the single-phase AMB SE is as consistent and precise as the TSE.

An Improved Three-Phase AMB Distribution System State Estimator

“…However, given that a magnitude measurement is converted into a pair of equivalent measurements (real and imaginary parts of the equivalent complex voltage), the observability of the system and the redundancy of the measurements set are artificially improved. This, in turn, can have negative effects on the convergence of the AMB SE, as demonstrated in [17] for a single-phase distribution power system. In this case, a simple but effective solution is to discard the imaginary part of the equivalent complex voltages.…”

“…To allocate adequate variances to the equivalent voltage measurements prior to the SE, knowledge of complex voltages is required. Then, considering the error propagation theory and given the variance of a voltage measurement, the variance for the equivalent voltage measurement , for any phase, is (17), where + is the complex voltage (for a given phase) regarding the bus k calculated from a power flow [13]. The complex voltages + can also be obtained from the previous estimation.…”

“…The diagonal element , contains the weight associated to the i-th equivalent measurement while the offdiagonal element , contains the weight relating the i-th and the j-th equivalent measurements. The weights for the equivalent voltage measurements are the inverse of the variances (17). Given that the real and imaginary parts of the equivalent current measurements are correlated for a given phase, i.e., the corresponding covariances cannot be neglected, the inverse of the covariance matrix (18) produces two diagonal and two off-diagonal elements in the weighting matrix.…”

“…It was concluded that the single-phase traditional WLS NE state estimator is consistent and suitable for estimating the state of balanced medium voltage power systems. For the single-phase WLS AMB NE state estimator, however, it was shown in [17] that some improvements are required to make it consistent.…”

“…According to (17) and (18), the variances and covariances and, therefore, the weights of the equivalent measurements depend on the voltages and . Since, in practice, these voltages are likely to be obtained from a previously estimated state with a relatively similar load level (e.g., 15 min before), it is crucial to investigate the impact of these voltages.…”