Enhanced Tensor Completion Based Approaches for State Estimation in Distribution Systems

Grid state estimation is essential for effective control and management of distribution systems. While weighted least squares has been the conventional method for state estimation, sparsity-aware methods have become popular due to their superior performance with limited data. Matrix completion and compressed sensing-based state estimation approaches exploit the underlying smoothness in the state variables. However, classic matrix completion methods do not take into account the temporal correlation of system states. Compressed sensing methods, on the other hand, require an appropriate choice of sparsifying basis that may not be easy to identify. This article proposes a block tensor completion based framework which uses an alternative approach to estimate voltage phasor, power injections, and branch currents. This approach utilizes the temporal correlation of the system states in a tensor trace-norm minimization formulation with power flow equations as constraints. Feature scaling is introduced in the problem formulation to benefit from the improved sensitivity of the tensor trace norm to the matrix columns in the scaled unfoldings of the tensor. Weighted tensor norm is utilized to exploit the structures of the different unfoldings of the state measurement tensor to improve the voltage estimation. The estimation accuracy is further improved by alternatively estimating the tensor columns and increasing the available data at each stage in the tensor completion process. The proposed methods are evaluated on the IEEE-33, 37 test systems, and a 100-node test system. The proposed methods are shown to provide significant performance gains relative to the classic matrix and tensor completion based approaches.