Dynamic and Differential Games in Electric Power Markets

Open Access
Neto, Pedro Amaral
Graduate Program:
Industrial Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
December 17, 2013
Committee Members:
  • Terry Lee Friesz, Dissertation Advisor
  • Terry Lee Friesz, Committee Chair
  • Soundar Rajan Tirupatikumara, Committee Member
  • Tao Yao, Committee Member
  • Seth Adam Blumsack, Committee Member
  • Game Theory
  • Electric Power Markets
  • Dynamic Games
  • Differential Games
  • Optimal Feedback Control
  • Complementarity
Over the last two decades, the electricity industry has shifted from regulation of monopolistic and centralized utilities towards deregulation and promoted competition. With increased competition in electric power markets, system operators are recognizing their pivotal role in ensuring the efficient operation of the electric grid and the maximization of social welfare. In this research, we introduce a model of dynamic spatial network equilibrium among consumers, system operators and electricity generators as the solution of a dynamic Stackelberg game. In that game, generators form an oligopoly and act as Cournot-Nash competitors who non-cooperatively maximize their own profits. The market monitor attempts to increase social welfare by intelligently employing equilibrium congestion pricing anticipating the actions of generators. The market monitor influences the generators by charging network access fees that influence power flows towards a perfectly competitive scenario. Our approach anticipates un- competitive behavior and minimizes the impacts upon society. The resulting game is modeled as a Mathematical Program with Equilibrium Constraints (MPEC). We present an illustrative example as well as a stylized 15-node network of the Western European electric grid.
 We also introduce two unique differential oligopolistic games with excess demand and sticky price dynamics for feedback Nash equilibria applied to electric power markets. The resulting differential Nash games can be reformulated into a standard linear quadratic differential game framework. The linear quadratic differential games can then be solved using optimal feedback control by subse- quently solving a system of coupled algebraic feedback Nash Riccati equations. We introduce a computable algorithm to solve the feedback Nash equilibria of the differential games. The solution of a 28 market, 96 player differential game is presented using the proposed numerical algorithm.