A Dynamic Mechanism for Wholesale Energy Market: Stability and Robustness

In this paper, a dynamic model of the wholesale energy market that captures the effect of uncertainties of renewable energy sources and real-time pricing with demand response is derived. Beginning with a framework that includes real-time pricing as an underlying state, an attempt is made in this model to capture the dynamic interactions between generation, demand, locational marginal price (LMP), and congestion price near the equilibrium of the optimal dispatch. Conditions under which stability of the market can be guaranteed are derived. Modeling the effect of renewable energy resources (RERs) and demand response as perturbations, robust stability of the energy market model in the presence of such perturbations is discussed. Numerical studies of an IEEE 30-bus are reported to illustrate the effect of transmission lines constraints on the wholesale market stability in the presence of wind power.

[1]  P. Varaiya,et al.  Bringing Wind Energy to Market , 2012, IEEE Transactions on Power Systems.

[2]  Anuradha M. Annaswamy,et al.  Perturbation Analysis of the Wholesale Energy Market Equilibrium in the Presence of Renewables , 2012, ArXiv.

[3]  W. Short,et al.  Evaluating the Impacts of Real-Time Pricing on the Usage of Wind Generation , 2009, IEEE Transactions on Power Systems.

[4]  Sjur Didrik Flåm,et al.  Equilibrium, Evolutionary stability and Gradient Dynamics , 2002, IGTR.

[5]  A. Conejo,et al.  Economic Valuation of Reserves in Power Systems With High Penetration of Wind Power , 2009 .

[6]  Masood Parvania,et al.  Demand Response Scheduling by Stochastic SCUC , 2010, IEEE Transactions on Smart Grid.

[7]  W. Marsden I and J , 2012 .

[8]  B. Hobbs,et al.  Linear Complementarity Models of Nash-Cournot Competition in Bilateral and POOLCO Power Markets , 2001, IEEE Power Engineering Review.

[9]  L. Hurwicz,et al.  ON THE STABILITY OF THE COMPETITIVE EQUILIBRIUM, I1 , 1958 .

[10]  R. Baldick,et al.  Stability of supply function equilibria implications for daily versus hourly bids in a poolco market , 2006 .

[11]  Anuradha M. Annaswamy,et al.  Wholesale energy market in a smart grid: Dynamic modeling and stability , 2011, IEEE Conference on Decision and Control and European Control Conference.

[12]  M. Ilić,et al.  Potential benefits of implementing load control , 2002, 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309).

[13]  David C. Yu,et al.  An Economic Dispatch Model Incorporating Wind Power , 2008, IEEE Transactions on Energy Conversion.

[14]  Jason R. Marden,et al.  Designing games for distributed optimization , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  Antonio J. Conejo,et al.  Electricity market near-equilibrium under locational marginal pricing and minimum profit conditions , 2006, Eur. J. Oper. Res..

[16]  Jian Yao,et al.  Modeling and Computing Two-Settlement Oligopolistic Equilibrium in a Congested Electricity Network , 2006, Oper. Res..

[17]  Antonio J. Conejo,et al.  Economic Valuation of Reserves in Power Systems With High Penetration of Wind Power , 2009, IEEE Transactions on Power Systems.

[18]  Arman,et al.  Wholesale Energy Market in a Smart Grid: Dynamic modeling, stability, and robustness , 2013 .

[19]  S. Borenstein,et al.  An Empirical Analysis of the Potential for Market Power in California&Apos;S Electricity Industry , 1998 .

[20]  Edward J. Anderson,et al.  Finding Supply Function Equilibria with Asymmetric Firms , 2008, Oper. Res..

[21]  J. Valenzuela,et al.  Cournot Equilibrium Considering Unit Outages and Fuel Cost Uncertainty , 2011, IEEE Transactions on Power Systems.

[22]  Anuradha M. Annaswamy,et al.  Equilibrium in Wholesale Energy Markets: Perturbation Analysis in the Presence of Renewables , 2014, IEEE Transactions on Smart Grid.

[23]  Y. Smeers,et al.  A stochastic version of a Stackelberg-Nash-Cournot equilibrium model , 1997 .

[24]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[25]  Peter W. Glynn,et al.  A Complementarity Framework for Forward Contracting Under Uncertainty , 2011, Oper. Res..

[26]  Masood Parvania,et al.  Integrating Load Reduction Into Wholesale Energy Market With Application to Wind Power Integration , 2012, IEEE Systems Journal.

[27]  P. Klemperer,et al.  Supply Function Equilibria in Oligopoly under Uncertainty , 1989 .

[28]  Benjamin F. Hobbs,et al.  Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints , 2007, Oper. Res..

[29]  Sean P. Meyn,et al.  Dynamic Competitive Equilibria in Electricity Markets , 2012 .

[30]  Huifu Xu,et al.  A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application , 2009, Oper. Res..

[31]  A. Conejo,et al.  Pool Strategy of a Producer With Endogenous Formation of Locational Marginal Prices , 2009, IEEE Transactions on Power Systems.

[32]  E. Centeno,et al.  Strategic Analysis of Electricity Markets Under Uncertainty: A Conjectured-Price-Response Approach , 2007, IEEE Transactions on Power Systems.

[33]  Angelia Nedic,et al.  Subgradient Methods for Saddle-Point Problems , 2009, J. Optimization Theory and Applications.

[34]  E. Bompard,et al.  The Demand Elasticity Impacts on the Strategic Bidding Behavior of the Electricity Producers , 2007, IEEE Transactions on Power Systems.

[35]  Munther A. Dahleh,et al.  Volatility of Power Grids Under Real-Time Pricing , 2011, IEEE Transactions on Power Systems.

[36]  A. Smithies The Stability of Competitive Equilibrium , 1942 .

[37]  Anuradha M. Annaswamy,et al.  Perturbation analysis of market equilibrium in the presence of renewable energy resources and demand response , 2010, 2010 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT Europe).

[38]  A. J. Conejo,et al.  Equilibria in an Oligopolistic Electricity Pool With Stepwise Offer Curves , 2012, IEEE Transactions on Power Systems.

[39]  Jeff S. Shamma,et al.  Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria , 2005, IEEE Transactions on Automatic Control.

[40]  Bohn Stafleu van Loghum,et al.  Online … , 2002, LOG IN.

[41]  M. Mazumdar,et al.  Cournot Prices Considering Generator Availability and Demand Uncertainty , 2007, IEEE Transactions on Power Systems.