Integrated Primary-Secondary Distribution System State Estimation With Bimodal Error Distribution

Traditionally, measurement errors are assumed to follow Gaussian distribution in the state estimation process. However, statistical analysis of field measurements has shown that measurement errors can have multimodal and skewed distribution. This work aims to develop a static power distribution system state estimator that can capture skewed bimodal measurement error distribution and enable a joint medium-voltage (MV) primary feeders and low-voltage (LV) secondary feeders state estimation. A distributed primary-secondary (MV-LV) state estimation algorithm is proposed and iteratively executed until convergence at the MV-LV boundary. The primary state estimator is formulated as an equality-constrained maximum likelihood estimation problem and the secondary state estimator is formulated as a forward-backward sweep power flow problem. The proposed algorithm is demonstrated using the IEEE 123 bus distribution test feeder modified to include secondary network extensions at 47 different nodes. The simulation results show that the state estimation results are improved by considering skewed bimodal distribution for measurement errors, the performance of the state estimator with the approximate secondary model is highly sensitive to unbalanced loadings of the split-phase customer and the convergence speed of the joint MV-LV state estimation process is improved by collecting all the legs active and reactive power demands of the split-phase customer in LV feeders.