A Multistage Game in an Off-Grid Microgrid Market: A Non-Cooperative Game Theoretic Approach

Abstract

Although national grids are commonly responsible for ensuring reliable electricity, decentralized solutions became crucial alternatives, especially in isolated locations or when grid availability is uncertain. Furthermore, critical facilities that can not withstand interruptions in electricity supply often rely on off-grid microgrids. The existing literature has extensively addressed off-grid microgrids, particularly in centralized decision-making frameworks while allowing multi-stage investments, but as the complexity of electricity systems has increased and with the rise of prosumers (agents who produce and consume electricity), the suggested centralized solution approaches have become questionable. This thesis develops and analytically solves a game-theoretical model for an off-grid microgrid consisting of multiple heterogeneous agents while tackling multi-stage investment planning. The model studies the interactions and behavior of four major participants: a dispatchable source of supply, household prosumers, household consumers, and a neutral microgrid operator. The thesis investigates the existence and uniqueness of a Nash Equilibrium while proving its equivalence to a welfare maximization problem. The model is utilized to implement different pricing mechanisms that can be exercised by the neutral microgrid operator and then applied to a Lebanese case study. The results show that achieving cost-reflective and efficient prices requires the presence of a neutral operator that controls the rates of return of the dispatchable source of supply and household prosumers. Both household consumers and prosumers prefer to satisfy their demand through the grid and have no shortage. The results further reveal a complementarity pattern in which the dispatchable source of supply dominates the night-time supply and price formation, while household prosumers determine their optimal size of photovoltaic systems to meet the total day-time demand in the grid.