A Novel Data-Driven Approach Integrating DGCN and TILDE-Q for Ultra-Short-Term Photovoltaic Power Forecasting

Accurate ultra-short-term photovoltaic (PV) power forecasting is essential for the reliable operation and energy management of PV systems. However, rapid irradiance variations and complex meteorological conditions result in highly intermittent, nonlinear, and nonstationary PV power generation. Existing forecasting methods generally focus on temporal dependencies but provide limited representation of the dynamic relationships among meteorological variables and PV power. Moreover, conventional point-wise loss functions do not explicitly preserve the temporal shape of multi-step forecasts. To address these limitations, this study proposes a forecasting framework integrating a dynamic graph convolutional network (DGCN), long short-term memory (LSTM), and the transformation-invariant loss function with distance equilibrium (TILDE-Q). Meteorological variables and historical PV power are represented as graph nodes, and DGCN dynamically learns their sample-specific dependencies. LSTM captures temporal evolution patterns, while TILDE-Q constrains amplitude, phase, and scaling variations to improve trajectory consistency. The proposed method was evaluated on two independent operational PV datasets under 1-, 4-, 8-, and 16-step forecasting horizons, corresponding to 15 min, 1 h, 2 h, and 4 h ahead, respectively. DGCN-LSTM achieved the lowest RMSE and highest $R^2$ across all forecasting horizons on both datasets. Compared with the MAE training objective, TILDE-Q reduced RMSE and MAE by up to 15.35% and 25.90%, respectively, and consistently outperformed DILATE. These results demonstrate that combining dynamic variable-dependency modeling with shape-aware optimization can effectively improve the accuracy and trajectory consistency of multi-step PV power forecasts.