Equilibrium models with network constraints for medium term planning of power generation

This paper introduces a model to simulate zonal pricing under oligopolistic markets. The model extends a previous work where a single-node conjectural variation equilibrium was established for any differentiable convex cost function, and solved via optimisation. Several zones are included with a limited transmission capacity among them. In this new situation, the value of conjectures depends on network constraints and a set of values for these parameters has to be defined for each network status. Market equilibrium is defined in this framework and a new optimisation problem has to be stated requiring only convexity of cost functions. The existence of equilibrium is not guaranteed in this multi-area situation, and iterative search is required to seek it if it does exist. A two areas multi-period case study is built and analysed. The model reaches equilibrium for some cases, mainly depending on the number of periods considered and on the value of conjectures. Some interesting oscillating patterns are observed that can be interpreted as quasi-equilibriums. This methodology can be immediately applied to the study of the future Iberian electricity market.