Physics-Informed Machine Learning Framework for Robust Renewable Energy Forecasting in High-Altitude Isolated Power Systems

High-altitude isolated power systems characterized by hybrid run-of-river hydropower and distributed solar photovoltaic installations face severe operational instability due to localized microclimatic volatility. Managing this instability is fundamentally hindered because standard data-driven forecasting methods optimize purely statistical objectives, frequently generating predictions that violate fundamental physical laws such as hydraulic mass balances and grid admittance constraints. This paper presents a novel Physics-Informed Machine Learning (PIML) framework that embeds deterministic physical principles directly into the loss regularization layer of a temporal deep recurrent network. The proposed architecture integrates the one-dimensional Saint-Venant equations for open-channel flows, digital elevation horizon tracking for orographic shading, and node-level active power balance formulations. Validated against empirical hydrological and meteorological datasets from a high-altitude cascade system, the framework achieves a 14.2% reduction in unconstrained gradient errors and completely eliminates physically anomalous prediction regimes (Φhydro=0.00%). Crucially, because the mathematical constraints rely on universal fluid mechanics, solar geometry, and grid topologies rather than site-specific statistical profiles, the framework demonstrates direct structural generalizability to alternative mountainous regions globally.