Support Matrix Regression for Learning Power Flow in Distribution Grid With Unobservability

Increasing renewable penetration in distribution grids calls for improved monitoring and control, where power flow (PF) model is the basis many advanced functionalities. However, unobservability makes traditional way infeasible to construct PF analysis via admittance matrix grids. While data-driven approaches can approximate mapping, direct machine learning (ML) applications may suffer from several drawbacks. First, complex ML models like deep neural networks lack degradability explainability true system model, leading overfitting. There are also asynchronization issues among different meters without GPS chips. Last but not least, bad data quite common To resolve these problems all at once, we propose a variational support regression (SMR). It provides structural (1) embed kernels regularize physical form observable area while achieving good approximation unobservable area, (2) integrate temporal information into asynchronized imputation, (3) define margins be robust against data. We test performance mapping rule IEEE systems utility grid. Simulation results show high accuracy, robustness quality issues.