An equilibrium analysis of investment opportunities in a regional electrical grid

Abstract

A tool for quantitatively analyzing perspectives of investing in a regional electrical grid that allows regional authorities to estimate (a) the level of potential investments in developing this system, and (b) the volumes and the prices of electricity to be provided for the population and for the industry in the region (in the framework of this system) in a certain period of time in the future (as a result of these investments) is presented. The problem of estimating such perspectives is modeled as a static, two-person, non-cooperative game on disjoint polyhedra with the payoff functions being a sum of a bilinear and a linear function of vector arguments (for the first player), and a bilinear function of the same vector arguments (for the second player). It is proved that equilibria in this game, which determine (a) optimal investment strategies proceeding from financial capabilities of the electricity producers in the region and their ability to borrow money from external investors, and (b) electricity prices expected to be mutually acceptable to both the consumers and the producers of electricity in the developed electrical grid, can be found by solving linear programming problems forming a dual pair. An illustrative numerical example of developing the proposed game model and calculating both optimal investment strategies and equilibrium electricity prices is considered.