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July  2008, 4(3): 425-452. doi: 10.3934/jimo.2008.4.425

Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints

Reetabrata Mookherjee 1, , Benjamin F. Hobbs 2, , Terry L. Friesz 3, and  Matthew A. Rigdon 4,

1. 

Senior Scientist, Zilliant Inc, 3815 S Capital of Texas Highway, Suite 300, Austin, TX 78704, United States
2. 

Professor, Depts of Geography & Environmental Engineering & Applied Math. & Stat., The Johns Hopkins University, Baltimore, MD 21218, United States
3. 

Marcus Chaired Professor of Industrial Engineering, The Pennsylvania State University, University Park, PA 16802, United States
4. 

Doctoral Candidate, Dept of Industrial & Manufacturing Engineering, The Pennsylvania State University, University Park, PA 16802, United States

Received  July 2007 Revised  June 2008 Published  July 2008

Most previous Cournot-Nash models of competition among electricity generators have assumed a static perspective, resulting in finite dimensional variational and quasi-variational inequality formulations. However, these models' system costs and constraints fail to capture the dynamic nature of power networks. In this paper we propose a more general and complete model of Cournot-Nash competition on power networks that accounts for these features by including ($i$) explicit intra-day dynamics that describe the market's evolution from one Generalized Cournot-Nash Equilibrium to another for a 24 hour planning horizon, ($ii$) ramping constraints and costs for changing the power output of generators, and ($ iii $) joint constraints that include variables from other generating companies within the profit maximization problems for individual generators. These joint constraints yield a generalized Nash equilibrium problem which can be represented as a differential quasi-variational inequality (DQVI); such generalized Nash equlibrium problems can have multiple solutions. The resulting formulation poses computational challenges that can cause traditional algorithms for DVIs to fail. A restricted formulation is proposed that can be solved by an implicit fixed point algorithm. A numerical example is provided.
Keywords: differential quasi-variational inequalities, ramping costs., generalized Nash equilibrium.
Mathematics Subject Classification: Primary: 49N70, 58E35; Secondary: 49J1.
Citation: Reetabrata Mookherjee, Benjamin F. Hobbs, Terry L. Friesz, Matthew A. Rigdon. Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints. Journal of Industrial & Management Optimization, 2008, 4 (3) : 425-452. doi: 10.3934/jimo.2008.4.425
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