Tensor Completion based State Estimation in Distribution Systems

State estimation in distribution systems is difficult due to the lack of observability and inability to aggregate measurements from all metering/sensing equipment in a timely manner. However, both these issues can be addressed by exploiting the underlying smoothness in the measurement/state variables leading to compressed sensing/matrix completion based state estimation strategies. Existing matrix completion methods for state estimation do not exploit the temporal correlation of the system states and measurements. This paper proposes tensor completion based approaches to estimate bus voltages under very-low, low and full observablilty conditions. The proposed methods utilize tensor trace norm minimization formulations with power flow equations as constraints. The proposed methods are compared with existing robust matrix completion methods and evaluated on the IEEE 33-node radial distribution system to demonstrate their superior performance and robustness to bad data. The tensor completion methods are able to estimate voltage magnitude with Mean Absolute Percentage Error (MAPE) less than 0.25% even in the case of low observability systems with only 50% of the total measurements.