Physics-Informed Learning of Flow Distribution and Receiver Heat Losses in Parabolic Trough Solar Fields

Parabolic trough Concentrating Solar Power (CSP) plants operate large hydraulic networks of collector loops that must deliver a uniform outlet temperature despite spatially heterogeneous optical performance, heat losses, and pressure drops. While loop temperatures are measured, loop-level mass flows and receiver heat-loss parameters are unobserved, making it impossible to diagnose hydraulic imbalances or receiver degradation using standard monitoring tools. We present a physics-informed learning framework that infers (i) loop-level mass-flow ratios and (ii) time-varying receiver heat-transfer coefficients directly from routine operational data. The method exploits nocturnal homogenization periods -- when hot oil is circulated through a non-irradiated field -- to isolate hydraulic and thermal-loss effects. A differentiable conjugate heat-transfer model is discretized and embedded into an end-to-end learning pipeline optimized using historical plant data from the 50 MW Andasol 3 solar field. The model accurately reconstructs loop temperatures (RMSE $<2^\circ$C) and produces physically meaningful estimates of loop imbalances and receiver heat losses. Comparison against drone-based infrared thermography (QScan) shows strong correspondence, correctly identifying all areas with high-loss receivers. This demonstrates that noisy real-world CSP operational data contain enough information to recover latent physical parameters when combined with appropriate modeling and differentiable optimization.