Aggregation and Coordination Method for Flexible Resources Based on GNMTL-LSTM-Zonotope

Demand-side flexible resources in building energy systems hold significant potential for enhancing grid reliability and operational efficiency. However, their effective coordination remains challenging due to the complexity of modeling and aggregating heterogeneous loads. To address this, this paper proposes a feasible region aggregation and coordination method for load aggregators based on a GNMTL-LSTM-Zonotope framework. A Gradient Normalized Multi-Task Learning Long Short-Term Memory (GNMTL-LSTM) model is developed to forecast the power trajectories of diverse flexible resources, including air-conditioning systems, energy storage units, and diesel generators. Using these predictions and associated uncertainty bounds, dynamic feasible regions for individual resources are constructed with Zonotope structures. To enable scalable aggregation, a Minkowski sum-based method is applied to merge the feasible regions of multiple resources efficiently. Additionally, a directionally weighted Zonotope refinement strategy is introduced, leveraging time-varying flexibility revenues from energy and reserve markets to enhance approximation accuracy during high-value periods. Case studies based on real-world office building data from Shandong Province validate the effectiveness, modeling precision, and economic responsiveness of the proposed method. The results demonstrate that the framework enables fine-grained coordination of flexible loads and enhances their adaptability to market signals. This study is the first to integrate GNMTL-LSTM forecasting with market-oriented Zonotope modeling for heterogeneous demand-side resources, enabling simultaneous improvements in dynamic accuracy, computational scalability, and economic responsiveness.