Game-Theoretic Modeling of Merchant Transmission Investments

Abstract

Merchant transmission investment planning has recently emerged as a promising alternative or complement to the traditional centralized planning paradigm and it is considered as a further step toward the deregulation and liberalization of the electricity industry. However, its widespread application requires addressing two fundamental research questions: which entities are likely to undertake merchant transmission investments and whether this planning paradigm can maximize social welfare as the traditional centralized paradigm. Unfortunately, previously proposed approaches to quantitatively model this new planning paradigm do not comprehensively capture the strategic behavior and decision-making interactions between multiple merchant investors. This Chapter proposes a novel non-cooperative game-theoretic modeling framework to capture these realistic aspects of merchant transmission investments and provide insightful answers to the above research questions. More specifically, two different models, both based on non-cooperative game theory, have been developed. The first model addresses the first research question by adopting an equilibrium programming approach. The decision-making problem of each merchant investing player is formulated as a bi-level optimization problem, accounting for the impacts of its own actions on locational marginal prices (LMP) as well as the actions of all competing players. This problem is solved after converting it to a mathematical program with equilibrium constraints (MPEC). An iterative diagonalization method is employed to search for the likely outcome of the strategic interactions between multiple players, i.e., Nash equilibria (NE) of the game. Case studies on a simple 2-node system demonstrate that merchant networks investments will be mostly undertaken by generation companies in areas with low LMP and demand companies in areas with high LMP, as apart from collecting congestion revenue they also increase their energy surpluses. These case studies also demonstrate that the merchant planning solution approaches the centralized one as the number of competing players increases. However, because of its iterative nature, this first model cannot guarantee convergence to existing NE, especially as the number of players and the size of the network increase. Therefore, it cannot establish whether the merchant planning solution yields the same solution as centralized planning under the participation of a “sufficiently large” number of competing investors, as it cannot deal with a large number of players, especially in large networks. In order to address this challenge and provide insightful answers to this second research question, a second model is developed, where the set of merchant investors is approximated as a continuum. The proposed approximation makes the impact of each infinitesimal player’s decisions on system quantities negligible, allowing us to derive mathematical conditions for the existence of a NE solution in an analytical fashion. Based on this model, we perform an analytical comparison of the merchant planning solution under the participation of a “sufficiently large” number of competing investors against the one obtained through the traditional centralized paradigm, as well as a numerical comparison through case studies on a 2-node, a 3-node, and a 24-node system. These comparisons demonstrate that merchant planning can achieve the same (maximum) social welfare as the centralized planning approach only when the following conditions are satisfied: (a) fixed investment costs are neglected, and (b) the network is radial and does not include any loops. As these conditions do not generally hold in reality, our findings suggest that even a fully competitive merchant transmission planning framework, involving the participation of a very large number of competing merchant investors, is not generally capable of maximizing social welfare, as implied by previous work.