Learning-Based Power Flow Estimation with Sparse PMU Deployment in Power Systems

Accurate monitoring of power flow is fundamental to the secure and reliable operation of modern power systems. Existing data-driven power flow estimation methods typically assume that synchronized measurements are available at every bus, requiring extensive deployment of phasor measurement units (PMUs). Such dense sensing infrastructures substantially increase installation, communication, and maintenance costs. This paper proposes a learning-based framework that minimizes the number of installed PMUs while maintaining high-accuracy systemwide power flow estimation. Instead of relying on measurements from all buses, the proposed method identifies an informative subset of buses whose synchronized measurements are sufficient to accurately reconstruct branch power flow across the network. To this end, a neural network is developed to learn the nonlinear relationship between PMU measurements and system-wide power flows, and multiple PMU deployment scenarios are evaluated to quantify the trade-off between measurement availability and estimation accuracy. The results enable utilities to identify cost-effective PMU placement strategies that balance deployment cost and prediction performance. Case studies on the IEEE 30-bus test system demonstrate that the proposed framework significantly reduces the number of required PMUs while maintaining accurate power flow estimation.