Voltage sag state estimator based on compressive sensing in distribution systems

•A deterministic optimization problem to solve the voltage sag estimation problem.•Utilization of the smart metering capabilities to solve power quality problems.•Estimation of residual voltages by faults, even at points along a power line.•Use of sparse nature of voltage sag measurements to improve the estimation. This paper presents a new formulation for voltage sag state estimation based on compressive sensing (CS) theory. In a modern context, voltage sags can deteriorate the reliability, stability, and security of current networks and future smart grids. Several studies have focused on voltage sag estimation (VSE), but prefault currents, nonzero fault impedances, and unbalances are issues that can lead to inaccurate results. To overcome these limitations, we proposed a novel ℓ1-based voltage sag state estimator (ℓ1-VSSE). Only voltage measurements and a limited number of power quality meters with synchronization capabilities are considered. Sensing matrices of residual voltages per unit and a solution of a ℓ1-regularized least square problem using convex optimization are the innovative characteristics of the proposed estimator. ℓ1-VSSE efficiency has been validated by using three unbalanced distribution test systems: IEEE 34-bus, IEEE 123-bus, and EPRI-Ckt7. The results confirm the estimator’s robustness to the different faults, voltage regulation, and loading profiles.