A physics-informed method for joint forecasting of heat load and battery surface temperature in heating stations integrating photovoltaic generation, battery energy storage, and heat pumps

Accurate joint forecasting of heat load and battery surface temperature is critical for reliable operation of heating stations that integrate photovoltaic generation, battery energy storage, and heat pumps in mountainous townships. These two targets are dynamically coupled because heat demand affects heat pump operation, while heat pump power consumption influences battery charging/discharging behavior and heat generation. However, existing methods either predict them independently or rely on data-driven multi-task learning, which ignores cross-system coupling and thermodynamic consistency. To address this issue, this paper proposes PMamba, a physics-informed Mamba framework for cross-system joint forecasting. Two physics-derived indicators are first constructed: the logarithmic mean temperature difference (LMTD), reflecting the heat-transfer driving potential, and the Joule heating rate ( Q gen ), characterizing the battery electro-thermal state. Guided by these indicators, a dual-branch thermal state-guided channel attention mechanism adaptively recalibrates input features for the thermal and electrical subsystems. A shared Mamba predictor then encodes the reweighted features to jointly forecast both targets. In addition, task-specific physics-constrained losses with learnable parameters are introduced to improve heat-transfer and thermal-balance consistency. Experiments on two heating seasons of operational data from a real station show that PMamba outperforms eight baselines. Compared with the strongest baseline for each target, PMamba reduces RMSE by 13.2% for heat load and 15.8% for battery surface temperature. The heat-transfer and thermal-balance residuals are also reduced by 34.3% and 41.7%, respectively. These results demonstrate that PMamba enables coherent and physically consistent forecasting for reliable energy management of such heating stations.