Distributed optimization approaches for the energy management of aggregated energy systems

The increasing presence of distributed energy resources can bring both local benefits, such as cost savings and reduced grid dependence, and global benefits, such as emissions reduction. However, if not properly managed, they can also impose significant strain on the electricity network. For this reason, aggregated energy systems have emerged with the aim of providing cost-efficient and grid-friendly coordination of heterogeneous entities. The state-of-the-art approach for their operational planning relies on mathematical optimization solvers used in a centralized manner, where a single entity, such as an aggregator or system owner, has complete knowledge of the system and makes all operational decisions. Yet, this is poorly suited to the context of aggregated assets and energy communities, where multiple actors are involved and data-sharing may raise privacy concerns and limit participation. To overcome these limitations, this thesis advances aggregated energy system operational planning through three complementary approaches tailored to different system characteristics. The first contribution is a distributed single–decision-maker framework based on the derivative-free Augmented Lagrangian-based Alternating Direction Inexact Newton (ALADIN) algorithm. It is designed for aggregated energy systems with system-level objectives, such as peak shaving, that involve complex local-level optimization problems. Its performance is evaluated on two test cases. The first considers an energy community in which prosumers’ thermal equipment is modeled using an \emph{energy-flow} formulation, allowing the analysis of algorithm convergence as a function of its key parameters. The second test case adopts a \emph{water-flow-based} formulation, explicitly optimizing water mass flow rates and temperatures, yielding a computationally challenging nonconvex Mixed-Integer Quadratically Constrained Quadratic Programming (MIQCQP) problem. The results show that ALADIN is highly effective, achieving solutions comparable to a centralized benchmark while offering superior scalability. The second contribution introduces a multiple–decision-maker framework for internal price optimization within energy communities. It is designed to address key limitations of centralized approaches, including privacy concerns, limited prosumer autonomy, and unfair cost–benefit allocation. The problem is formulated as a bi-level Stackelberg game in which the aggregator, acting as the leader, optimizes internal trading prices using a metaheuristic algorithm, while the prosumers, acting as followers, respond to these price signals by independently optimizing their electricity exchange with the grid. The methodology is applied to four energy community configurations featuring different combinations of residential and commercial prosumers. The results show that the proposed approach substantially increases community self-consumption relative to independent operation, with particularly pronounced benefits in heterogeneous communities. The third contribution proposes an asynchronous convex hull-based approach tailored to virtual power plants and aggregated assets participating in multiple electricity markets. Each entity locally approximates its feasible operating region through a reduced set of extreme operating points (vertices) describing admissible net grid exchanges, which are shared with the aggregator without disclosing internal models or constraints. The aggregator reconstructs the aggregated feasible region via convex combinations of these vertices and solves a scenario-based two-stage stochastic program to determine optimal bids for the day-ahead and automatic frequency restoration reserve markets. The temporal decoupling between vertex generation and aggregator-level optimization eliminates iterative coordination during market clearing and real-time activation, enabling fast responsiveness compatible with balancing requirements. The methodology is evaluated on three virtual power plant configurations using key performance indicators covering computational tractability, bid feasibility, and operational optimality. For the first configuration, a suitable vertex–scenario combination achieves near-centralized economic performance while satisfying strict computational and feasibility requirements. For the other two configurations, the approach maintains computational efficiency and high reserve satisfaction but yields more conservative bidding strategies and higher expected costs, reflecting the sensitivity of the convex hull approximation to the distribution of flexibility across entities. In summary, this thesis advances the state-of-the-art in aggregated energy system operational planning by proposing three complementary approaches that collectively address the main technical and organizational challenges of virtual power plants and energy communities. The methods target different sources of complexity, nonconvex prosumer-level behavior, coordination among multiple autonomous decision-makers, and participation in multi-market environments, while sharing the common objective of enabling scalable and privacy-preserving operation. Across all case studies, the results demonstrate that performance comparable to centralized optimization can be achieved without requiring access to detailed prosumer data, while highlighting key design tradeoffs related to parameter tuning, fairness, and approximation accuracy.

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