Optimization of Transmission Capacities for Multinodal Markets

This paper considers a homogeneous good competitive market consisting of n local markets with given supply and demand functions. The markets are connected by several transmission lines. For every line, the cost functions of transmission capacity increment include fixed and variable components. We set a problem of the total social welfare optimization and discuss its generalization for markets with exporting and importing nodes. We distinguish several cases where the structure of connections corresponds to a tree-type graph and the social welfare function is submodular or supermodular with respect to the set of expanded transmission lines. These properties permit to employ known efficient algorithms that determine the optimal transmission capacities.