Alternative Auto-Encoder for State Estimation in Distribution Systems With Unobservability

The landscape of energy systems is ever changing due to the introduction of distributed energy resources (DERs) on the generation side and new demand-response technologies on the demand side. This ever-changing landscape calls for accurate real-time monitoring of distribution networks. However, the low observability in the secondary distribution grids makes monitoring hard, due to limited investment in the past and the vast coverage of distribution grids. To recover measurements for robustness, past methods proposed machine learning models by approximating mapping rules. However, mapping rule learning using traditional machine learning tools is one way only, from measurement variables to the state vector variables. Usually, it is hard to be reverted, thereby losing information consistency. This loses the physical relationship on invertibility for applications, such as state estimation. Hence, we propose a structural deep neural network to provide a robust two-way functional approximation. The proposed alternative auto-encoder includes constraints in the latent layer according to available voltage measurements for ensuring two-way information flow and utilizes symbolic regression using the latent variables for explainability. For using physics to regulate the mapping rule, we embed non-linear power flow kernels into the decoder of a variational auto-encoder to regulate both forward and inverse mapping simultaneously. The proposed method of system physics recovery is validated extensively using the IEEE standard distribution test systems. Simulation results show highly accurate two-way information flow.