Robust mapping rule estimation for power flow analysis in distribution grids

The increasing integration of distributed energy resources (DERs) calls for new monitoring and operational planning tools to ensure stability and sustainability in distribution grids. One idea is to use existing monitoring tools in transmission grids and some primary distribution grids. However, they usually depend on the knowledge of the system model, e.g., the topology and line parameters, which may be unavailable in primary and secondary distribution grids. Furthermore, a utility usually has limited modeling ability of active controllers as they may belong to a third party like residential customers. To solve the modeling problem in traditional power flow analysis, we propose a support vector regression (SVR) approach to reveal the mapping rules between different variables and recover useful variables based on historical data. We illustrate the advantages of using the SVR model over traditional regression method that finds line parameters in distribution grids. Specifically, the SVR model is robust enough to recover the mapping rules when the regression method fails. This happens when 1) there are measurement outliers, 2) there are active controllers, or 3) measurements are only available at some part of a distribution grid. We demonstrate the superior performance of our method through extensive numerical validation on different scales of distribution grids and IEEE test buses. Robustness of our method is observed.