Graduation Year


Document Type




Degree Granting Department

Industrial Engineering

Major Professor

Tapas K. Das, Ph.D.


Deregulated electricity markets, Financial transmission rights, Nash equilibrium, FTR and energy settlement, Matrix game, Reinforcement learning


Participants in deregulated electric power markets compete for financial transmission rights (FTRs) to hedge against losses due to transmission congestion by submitting bids to the independent system operator (ISO). The ISO obtains an FTR allocation, that maximizes sales revenue while satisfying simultaneous feasibility. This FTR allocation remains in place for a length of time during which the participants compete in the energy market to maximize their total payoff from both FTR and energy markets. Energy markets (bi-lateral, day ahead, real time) continue until the the end of the current FTR period, at which time the participants can choose to modify their FTR holdings for the next FTR period. As in any noncooperative game, finding Nash equilibrium bidding strategies is of critical importance to the participants in both FTR and energy markets.

In this research, a two-tier matrix game theoretic modeling approach is developed that can be used to obtain equilibrium bidding behavior of the participants in both FTR and energy markets considering the total payoff from FTR and energy. The matrix game model presents a significant deviation from the bilevel optimization approach commonly used to model FTR and energy allocation problems. A reinforcement learning (RL) algorithm is also developed which uses a simulation model and a value maximization approach to obtain the equilibrium bidding strategies in each market. The model and the RL based solution approach allow consideration of multi-dimensional bids (for both FTR and energy markets), network contingencies, varying demands, and many participants. The value iteration based RL algorithm obtains pure strategy Nash equilibrium for FTR and energy allocation.

A sample network with three buses and four participants is considered for demonstrating the viability of the game theoretic model for FTR market. A PJM network example with five buses, five generators and three loads is also considered to analyze equilibrium bidding behavior in joint FTR and energy markets. Several numerical experiments on the sample networks are conducted using the approach of statistical design of experiments (DOE) to assess impacts of variations of bid and network parameters on the market outcomes like participant payoffs and equilibrium strategies.