ST-MRC: A Service-Oriented Probabilistic Forecasting Method for Virtual Power Plant Aggregated Coupled Loads Based on Set Attention Encoding and Multi-Scale Residual Correction

Abstract Virtual power plants (VPPs) represent a novel energy service paradigm that aggregates distributed resources. With the rapid development of these services, individual resources within aggregations have been increasingly integrated as flexible loads for participation in electricity market trading and demand response. However, accurate forecasting of coupled loads remains challenging due to the stochastic nature of individual loads, coupling effects among multiple entities, and dynamic membership changes within aggregations. To address these issues, this paper proposes a Set Transformer-based Multi-scale Residual Correction method ST-MRC for probabilistic load forecasting. The framework adopts a three-stage progressive architecture: individual forecasting, interaction encoding, and residual correction. Load forecasts are first generated for each entity, after which a Set Transformer encodes multi-entity interaction features via attention to capture nonlinear couplings such as coincident and complementary peak demands; subsequently, a multi-scale temporal convolutional network (TCN) with varying dilation rates extracts residual evolution patterns for adaptive error correction, and finally quantile regression produces both point forecasts and probabilistic prediction intervals to support deterministic decisions and uncertainty quantification. Experiments show that the proposed method significantly improves point forecasting accuracy. In probabilistic forecasting, it achieves high empirical coverage while producing narrower prediction intervals, effectively supporting uncertainty-aware decisions in VPP electricity market trading and demand response.