Distribution Grid Topology and Parameter Estimation Using Deep-Shallow Neural Network With Physical Consistency

To better monitor and control distribution grids, the exact knowledge of system topology and parameters is a fundamental requirement. However, topology information is usually incomplete due to limited sensors in the grid. Therefore, estimating the system parameters using partial data is a critical topic for distribution systems. Due to the high nonlinearity of unobservable system quantities and noises, Deep Neural Networks (DNNs) are widely utilized for accurate estimation. While traditional approaches either treat DNNs as a black box or embed little physical knowledge into DNNs, they cannot guarantee that the DNN model is consistent with physical equations and hence lack accuracy and interpretability. Therefore, we propose a Deep-Shallow neural Network (DSN) for distribution system estimation. The key is to create virtual nodes to represent nodes without sensors in the system, and denote a DNN to approximate missing quantities at virtual nodes. Then, the Power Flow (PF) equations can be estimated via a shallow neural network, achieving physical consistency. Isolated by virtual nodes, the whole system is decomposed into a set of reduced graphs with approximate PF equations. Likewise, we introduce a Reinforcement Learning-based search algorithm to connect the reduced grids into one connected system. Correspondingly, the DSN is fine-tuned to achieve consistency with the PF equations of the connected graph. Finally, the paper illustrates the superiority of the proposed DSN due to its physical consistency. Specifically, comprehensive experiments demonstrate the high performances of our DSN over other methods in distribution grids.