Sensor-Limited Critical-Bus Voltage Forecasting for Virtual Metering in DER-Rich Distribution Networks

초록

Distribution networks with high photovoltaic generation, electric-vehicle charging, and customer-side secondary circuits require better voltage awareness, but dense voltage sensing at every critical location is rarely practical. This paper formulates sensor-limited critical-bus voltage forecasting as a virtual metering task: historical voltage measurements from a small set of observed feeder locations are used to forecast future voltage trajectories at unmetered critical buses. The study uses a DER-rich modified IEEE 123-bus distribution-system dataset with secondary-circuit effects and constructs a reproducible benchmark pipeline with fixed chronological train/validation/test splits, metadata-based signal resolution, direct multi-output forecasting, and target-wise and horizon-wise evaluation. Four representative temporal baselines are evaluated: persistence, multilayer perceptron (MLP), one-dimensional convolutional neural network (CNN1D), and long short-term memory (LSTM). Sparse observation cases use only one to six voltage sensors, while a dense non-target observation case is included as a near full-observation reference rather than as a practical deployment scenario. The results show that accurate 24-hour multi-step voltage forecasting is feasible under low observability. In the primary sparse cases, CNN1D and LSTM achieve test mean absolute error near 0.0048 p.u. across three unmetered target buses, with stable multi-seed behavior. The dense non-target reference provides no large accuracy gain over the strongest sparse learned models, indicating that the evaluated sparse measurements already contain substantial predictive information for the selected critical buses. Target-wise and horizon-wise analyses further show that forecasting difficulty varies across buses and lead times. The paper therefore provides a defensible benchmark and feasibility evidence for sensor-limited virtual metering in DER-rich distribution networks, while explicitly limiting claims beyond the evaluated dataset, sensor sets, and baseline models. © 2026 The Authors.

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