Data-driven joint topology and line parameter estimation for renewable integration

The increasing integration of distributed energy resources (DERs) calls for new planning and operational tools in the distribution grids to ensure stability and sustainability. The current system planning and operation usually depend on the knowledge of the system model, in particular, the topology and line parameters. However, such system information may be missing or inaccurate in distribution grids, leading to difficulties in calculating DER's locational benefits and planning DER's growth. While the data-driven joint estimation of the topology and the line parameters under noiseless scenario can be achieved by solving a linear system of equations, the problem under noisy scenario is hard. This is because noises appear in both the input measurements (e.g., voltage magnitude and phase angle) and output measurements (e.g., active and reactive power). To solve this problem with accurate modeling, we propose the error-in-variables (EIV) model in a maximum likelihood estimation (MLE) problem. While directly solving the problem is NP-hard, we adapt the problem into a generalized low-rank approximation problem via variable transformation and noise decorrelation. Interestingly, the new problem has a closed form solution while being non-convex. We demonstrate the superior performance in accuracy for our method on IEEE test cases with actual feeder data from South California Edison. Notably, our parameter estimation is highly accurate even without topology information.