Constrained State Estimation with Probabilistic Error Model for Underdetermined Systems Such as Distribution Network

Constrained state estimation (CSE) clarifies the interval of the feeder voltage profile of an unobservable distribution network containing fewer telemetric sensors than state variables to be estimated. By using the given information about the power flow equations and network operating ranges such as maximum load and photovoltaic generator ratings, CSE provides the estimation interval that minimizes the square error against the partial telemetric measurements while satisfying the network operating ranges. We also developed a probabilistic model of the estimation error outside the estimation interval characteristic of the CSE algorithm. The probabilistic error model is derived by superposition of the error distribution around the arbitrary estimation within the estimation interval. The validity of the probabilistic error model was confirmed by a case study simulation on a benchmark network, in which the model-based probabilistic error distribution well explained the simulation-based estimation errors. This result is necessary to understand the estimation accuracy of CSE for the voltage control application of the distribution network. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.