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In recent years, the ever-increasing research interest in various aspects of the electricity pool-based markets has generated a plethora of complementarity-based approaches to determine participating agents’ optimal offering/bidding strategies and model players’ interactions. In particular, the integration of multiple and diversified market agents, such as conventional generation companies, renewable energy sources, electricity storage facilities and agents with a mixed generation portfolio has instigated significant competition, as each player attempts to establish their market dominance and realize substantial financial benefits. The employment of complementarity modelling approaches can also prove beneficial for the optimal coordination of the electricity and natural gas market coupling. Linear and nonlinear programming as well as complementarity modelling, mainly in the form of mathematical programs with equilibrium constraints (MPECs), equilibrium programs with equilibrium constraints (EPECs) and conjectural variations models (CV) have been widely employed to provide effective market clearing mechanisms, enhance agents’ decision-making process and allow them to exert market power, under perfect and imperfect competition and various market settlements. This work first introduces the theoretical concepts that regulate the majority of contemporary competitive electricity markets. It then presents a comprehensive review of recent advances related to complementarity-based modelling methodologies and their implementation in current competitive electricity pool-based markets applications.

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