Time-Synchronized Distribution System State Estimation for Incompletely Observed Networks

Real-time monitoring of active distribution systems can be done by using micro-phasor measurement units (µPMUs). In the first part of this report, an innovative μPMU placement algorithm is presented to completely observe the system and facilitate state estimation for unbalanced distribution systems. The proposed algorithm considers practical constraints such as single-phase laterals, distributed loads and variable tap-ratios and ensures complete phase observability while minimizing the number of μPMUs needed. However, complete observability of distribution systems may not be economically and practically viable. Hence, in the second part of this report the challenge of limited availability of μPMUs in distribution systems is addressed using deep learning (DL). The proposed DL-based method offers superior accuracy with fewer μPMUs compared to conventional least squares method, even during topology changes. The robustness of the deep neural network (DNN) used in DL is further evaluated by considering realistic measurement errors in the μPMUs, ensuring the practicality of the approach.In the third part of this report, the research delves into the verification of the DNN for distribution system state estimation (DSSE) by analyzing its performance under input perturbations. A mixed-integer linear programming (MILP) approach is proposed to analytically verify the DNN's robustness. This ensures that the DNN output remains bounded given a bounded perturbation in the input. This essentially builds trust in using DNN-based solutions for critical tasks such as power grid monitoring. Finally, due to the scalability challenges of MILP problems, a linear bound propagation method is proposed for DNN verification. The proposed method significantly increases the speed (of verification) and makes the verification problem scalable for wider and deeper DNNs. In conclusion, this research provides a comprehensive monitoring framework for distribution system operators, empowering them to effectively manage the addition of distributed energy resources. It combines optimal μPMU placement, a robust DNN-based DSSE, and a rigorous DNN verification analyses. By ensuring reliable and trustworthy system monitoring, the approaches developed in this report can contribute to a more stable, resilient, and renewable-rich power distribution grid.