Deep Multi-Fidelity Bayesian Data Fusion for Probabilistic Distribution System Voltage Estimation With High Penetration of PVs

The increasing penetration of PVs causes challenges in maintaining voltage security due to the lack of distribution system visibility. This article proposes a deep multi-fidelity Bayesian approach to fuse a limited number of SCADA/AMI data together with pseudo measurements in probabilistic distribution system voltage estimation. The relative high-fidelity SCADA/AMI data are fused with the low-fidelity pseudo measurements by the autoregressive algorithm embedded in the deep Gaussian process. This allows us to use multi-fidelity data to achieve entire distribution system voltage visibility. The proposed method does not require the observability of the system by real-time measurements and can achieve good robustness against measurement uncertainties and different system operating conditions. Numerical results carried out on the IEEE 123-node system and an actual 745-node utility system demonstrate that the proposed method can obtain high accuracy in estimating bus voltage and quantifying estimation uncertainties as compared to other machine learning approaches.