Derivation of a mathematical structure for market-based transmission augmentation in oligopoly electricity markets using multilevel programming

In this paper, we derive and evaluate a new mathematical structure for market-based augmentation of the transmission system. The closed-form mathematical structure can capture both the efficiency benefit and competition benefit of the transmission capacity. The Nash solution concept is employed to model the price-quantity game among GenCos. The multiple Nash equilibria of the game are located through a characterisation of the problem in terms of minima of the R function. The worst Nash equilibrium is used in the mechanism of transmission augmentation. The worst Nash equilibrium is defined as the one which maximises the social cost, total generation cost + total value of lost load. Thorough analysis of a simple three-node network is presented to clearly highlight the mechanism of the derived mathematical structure from different perspectives.