Control of phase shifting transformers by multiple transmission system operators

A general framework is proposed for the control of phase shifting transformers owned by several TSOs, taking into account their interactions. The proposed solution is the Nash equilibrium of a sequence of optimizations performed by the various TSOs, each of them taking into account the other TSOs' control settings as well as operating constraints relative to the whole system. The method is applied to a linearized network model and illustrated on the IEEE 118-bus system.