Motivated by the development of novel and practically implementable coordination algorithms for multi-agent systems, here we investigate the adaptation of classical best-response dynamics by means of self-triggered communications. First, we show that, if the best response dynamics is defined for a continuous-action-space potential game, convergence towards the Nash Equilibria set is guaranteed under continuity on utilities and component-wise pseudo-concavity of the potential function. Then, we modify the best-response dynamics to account for more economic self-triggered communication strategies while ensuring convergence to the equilibrium set. The proposed algorithm is then analyzed in the framework of hybrid systems theory.

The European Union’s vision for energy transition not only foresees decarbonization of the electricity sector, but also requires commitment across different sectors such as gas, heating, and cooling through an integrated approach. It also sets local energy communities at the center of the energy transition as a bottom-up approach to achieve these ambitious decarbonization goals. The energy hub is seen as a promising conceptual model to foster the optimization of multi-carrier energy systems and cross-sectoral interaction. Especially in the context of local energy communities, the energy hub concept can enable the optimal design, management, and control of future integrated and digitalized networks where multiple energy carriers operate seamlessly and in complementarity with each other. In that sense, the optimal design and operation of energy hubs are of critical importance, especially under the effect of multiple objectives taking on board not only technical, but also other aspects that would enable the sustainability of local energy communities, such as economic and environmental. This paper aims to provide an in-depth review of the literature surrounding the existing state-of-the-art approaches that are related to the design and operation optimization of energy hubs by also exploring their interaction with the external network and multiple markets. As the planning and operation of an energy hub is a multifaceted research topic, this paper covers issues such as the different optimization methods, optimization problems formulation including objective functions and constraints, and the hubs’ optimal market participation, including flexibility mechanisms. By systematizing the existing literature, this paper highlights any limitations of the approaches so far and identifies the need for further research and enhancement of the existing approaches.