Hierarchical distributed optimization based bidding algorithm for electric water heater flexibility aggregators in nordic energy activation markets

Coordinated flexibility from electric water heaters (EWHs) holds significant potential to provide frequency regulation services through reserve markets, particularly manual frequency restoration reserve (mFRR) in near real-time Energy Activation Markets (EAM). To fully exploit this potential, EWH aggregators require bidding algorithms that are not only high-performing but also scalable and computationally efficient. This work introduces a model predictive control (MPC)-based optimization model and proposes a novel Hierarchical Distributed Optimization (HDO) algorithm specifically designed to meet these demands. The proposed HDO algorithm adopts a two-level hierarchical structure: the upper-level focuses on binary bidding decisions (i.e., to bid or not), while the lower-level manages control decisions for individual EWHs. An iterative coordination approach is developed in which both levels are solved sequentially and iteratively until convergence is reached. A problem-specific heuristic is developed for the upper-level, integrating local search techniques with shadow price (dual variable) information to enhance tractability and improve computational efficiency. At the lower-level, Lagrangian dual decomposition is employed to decompose the centralized problem into smaller, independent sub-problems, each corresponding to an individual EWH, which can be solved in parallel during dual ascent, thereby significantly improving scalability. To further accelerate convergence during dual ascent, a Newton-based dual update strategy is incorporated, improving performance over standard gradient-based methods. Performance evaluation under deterministic setting for providing up-regulation service, using real-world market price data and synthetic hot water demand profiles, demonstrates that the proposed method achieves significant computational gains and scalability while delivering solutions with optimality levels comparable to a centralized commercial solver.