Stability Analysis for the Implementation of Game Theory-based On-Line Pricing Schemes in Micro-Grids

An existing challenge in power systems is the implementation of optimal demand management through dynamic pricing. This research project deals with on-line pricing schemes for electricity in micro-grid network systems and the ways in which their implementation affects the physical system's response. Two approaches were devised in this study: First, the ways in which micro-grid networks can be modelled as less prescriptive multi-agent consensus systems; examining their response under uncertainties and gaining insights on the relation between the network topology, the heterogeneous parameters of its components, and the system's response. Secondly, deriving game-theoretic novel pricing schemes and integrating them with the physical system model to perform a stability analysis. The proposed schemes consider the rational behaviour of the end-users and the entailing tension with the energy supplier(s); demonstrating the ways in which the decisions of the players involved influence the physical system. The study aims to clarify the interconnection between the market and physical layers of the problem, leading to a better future implementation of such schemes. The first part of this thesis studies networks of heterogeneous micro-grids, treating them as agents and modelling their dynamics as an averaging process that is subject to uncertain non-linear parameters. The second part introduces a pricing scheme based on the Stackelberg game with incentive strategies in a micro-grid, where the leader is the energy supplier, and the follower the consumer. The scheme is then improved and carried out in a droop-controlled low-voltage resistive AC micro-grid. The final part of this research is about the design of a scheme based on coalitional game theory, where there are multiple competing energy retailers attracting consumers. For all the propositions above, analysis and simulations that illustrate system stability, agent rationality, profit improvement, and the convergence to different equilibria in the physical and market responses are implemented.