Robust H∞ State Estimation for Distribution System Considering Randomly Missing Measurements

The randomly missing measurements may introduce outliers that deteriorate the accuracy of distribution system state estimation (DSSE). This article proposes a robust H-infinity DSSE method considering randomly missing measurements. First, a stochastic DSSE model is developed, in which Bernoulli process-based random binary variables are introduced to represent whether measurements are lost. The probability distributions of these binary variables are calculated with cyber topology analysis and Boolean operation. Then, a novel robust H-infinity state estimator is designed for the proposed stochastic DSSE model, in which a nonlinear matrix inequality condition is analytically derived to maintain the estimation error bounded. This nonlinear matrix inequality is further linearized via the intermediate variable substitution and matrix transformation to reduce the computational complexity. Finally, an optimization problem constrained by this linear matrix inequality (LMI) is formulated to determine the parameter matrices of the optimal H-infinity state estimator by finding the smallest estimation error bound. The robustness of the proposed method against randomly missing measurements caused by cyber unit worn out and denial of service (DoS) attack is demonstrated via simulations performed on the IEEE 33-bus and 123-bus feeders.