Estimation of aggregate flexibility regions for distributed flexible resources using limited information

Distributed flexible resources (DFRs) can support power-system operation only if aggregators can report their flexibility regions as operating conditions change. Existing aggregation methods generally require detailed device-level states, which may be unavailable, as well as repeated online optimization. This paper proposes a limited-information physics-informed neural network (PINN) for estimating aggregate flexibility regions of DFRs. Its inputs are low-dimensional operating-condition descriptors, and its output is a feasibility-oriented representative polyhedral region conditioned on those descriptors. Physical feasibility and boundary tightness are embedded through support- and projection-based errors and differentiable active-hyperplane residuals, enabling training without precomputed ground-truth flexibility-region labels. The proposed pretraining, full-network training, and loss-weight scheduling scheme prioritizes physical feasibility while retaining boundary tightness. Case studies show that the estimated regions vary predictably with operating conditions and achieve a favorable balance between physical implementability and economic performance relative to alternative aggregation models. Across the operational tests, 96.25% of PINN dispatch trajectories had zero relative disaggregation error, and the maximum error was 4.72%. Dispatch costs remained comparable to those of the full-information inner approximation. Once trained, the estimator requires neither complete device-level information nor an online optimization solver. The proposed framework therefore lowers the deployment barrier for condition-dependent flexibility estimation in practical distributed-resource aggregation.