Mean-Conditional Value-at-Risk Optimal Energy Storage Operation in the Presence of Transaction Costs

This paper addresses the formulation and solution of an optimal energy storage management problem under risk consideration and transaction costs of trading energy with the power grid. The price evolves as a stochastic process, capable of correctly explaining the seasonality effects as well as the tail fatness and spikiness in its distribution. Transaction costs capture the price impact of the storage operation on the electricity spot price. A risk analysis of an optimal risk neutral deterministic policy as well as the simple myopic policy indicates that the realized operational cost may notably differ from the expected cost by a considerable probability. This difference suggests that we need to consider risk. Using the downside risk measure of conditional value-at-risk, an optimal risk averse conversion and transmission strategy, among the grid, the renewable power generation source, and an energy storage is proposed to fully satisfy the electricity demand and minimize the expected operational cost as well as the risk. Our numerical study using data from NYISO demonstrates the impacts of risk consideration and the transaction cost parameters on the optimal strategy structure, its expected cost, and its risk.

[1]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[2]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[3]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[4]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[5]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[6]  Ervin Bossanyi,et al.  Wind Energy Handbook , 2001 .

[7]  H. Föllmer,et al.  Stochastic Finance: An Introduction in Discrete Time , 2002 .

[8]  A. Eydeland,et al.  Energy and Power Risk Management: New Developments in Modeling, Pricing, and Hedging , 2002 .

[9]  Takashi Kanamura,et al.  A Structural Model for Electricity Prices with Spikes - Measurement of Jump Risk and Optimal Policies for Hydropower Plant Operation , 2004 .

[10]  H. Geman,et al.  Understanding the Fine Structure of Electricity Prices , 2004 .

[11]  J.P. Barton,et al.  Energy storage and its use with intermittent renewable energy , 2004, IEEE Transactions on Energy Conversion.

[12]  Thomas Ackermann,et al.  Wind Power in Power Systems , 2005 .

[13]  Á. Cartea,et al.  Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality , 2005 .

[14]  Thomas Ackermann,et al.  Wind Power in Power Systems: Ackermann/Wind Power in Power Systems , 2005 .

[15]  Alexander Shapiro,et al.  Convex Approximations of Chance Constrained Programs , 2006, SIAM J. Optim..

[16]  T. Coleman,et al.  Minimizing CVaR and VaR for a portfolio of derivatives , 2006 .

[17]  A. Conejo,et al.  A Stochastic Programming Approach to Electric Energy Procurement for Large Consumers , 2007, IEEE Transactions on Power Systems.

[18]  M. Medeiros,et al.  Modeling and forecasting short-term electricity load: A comparison of methods with an application to Brazilian data , 2008 .

[19]  M. Matos,et al.  Optimization of Pumped Storage Capacity in an Isolated Power System With Large Renewable Penetration , 2008, IEEE Transactions on Power Systems.

[20]  G. Pflug,et al.  Modeling, Measuring and Managing Risk , 2008 .

[21]  A.M. Gonzalez,et al.  Stochastic Joint Optimization of Wind Generation and Pumped-Storage Units in an Electricity Market , 2008, IEEE Transactions on Power Systems.

[22]  David J. C. MacKay.  Sustainable Energy - Without the Hot Air , 2008 .

[23]  Jean-Philippe Vial,et al.  Robust Optimization for Environmental and Energy Planning , 2009 .

[24]  Huifu Xu,et al.  Smooth sample average approximation of stationary points in nonsmooth stochastic optimization and applications , 2009, Math. Program..

[25]  Sandia Report,et al.  Energy Storage for the Electricity Grid: Benefits and Market Potential Assessment Guide A Study for the DOE Energy Storage Systems Program , 2010 .

[26]  R. Carmona,et al.  Valuation of energy storage: an optimal switching approach , 2010 .

[27]  S. Minner,et al.  Optimal day-ahead trading and storage of renewable energies—an approximate dynamic programming approach , 2010 .

[28]  A. Holder.  Parametric LP Analysis , 2011 .

[29]  B. Dunn,et al.  Electrical Energy Storage for the Grid: A Battery of Choices , 2011, Science.

[30]  C. A. Canizares,et al.  A Robust Optimization Approach for Planning the Transition to Plug-in Hybrid Electric Vehicles , 2011, IEEE Transactions on Power Systems.

[31]  Constantine Caramanis,et al.  Theory and Applications of Robust Optimization , 2010, SIAM Rev..

[32]  N. Jenkins,et al.  Wind Energy Handbook: Burton/Wind Energy Handbook , 2011 .

[33]  Han-I Su,et al.  Modeling and analysis of the role of fast-response energy storage in the smart grid , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[34]  J. Heggset,et al.  Challenges in the reliability and maintainability data collection for offshore wind turbines , 2011 .

[35]  Warren B. Powell,et al.  Optimal Energy Commitments with Storage and Intermittent Supply , 2011, Oper. Res..

[36]  Golbon Zakeri,et al.  Submitted to Operations Research manuscript ( Please , provide the mansucript number ! ) Electricity Contracting and Policy Choices under Risk-aversion , 2012 .

[37]  D. Infield,et al.  Application of Auto-Regressive Models to U.K. Wind Speed Data for Power System Impact Studies , 2012, IEEE Transactions on Sustainable Energy.

[38]  Igor Kuzle,et al.  Virtual power plant mid-term dispatch optimization , 2013 .

[39]  J. Cidrás,et al.  Review of power curve modelling for wind turbines , 2013 .

[40]  Laurent Massoulié,et al.  Optimal Control of End-User Energy Storage , 2012, IEEE Transactions on Smart Grid.

[41]  Antonio J. Conejo,et al.  Offering model for a virtual power plant based on stochastic programming , 2013 .

[42]  Jean-Philippe Vial,et al.  Robust Optimization , 2021, ICORES.

[43]  M. Dahleh,et al.  Optimal Management and Sizing of Energy Storage Under Dynamic Pricing for the Efficient Integration of Renewable Energy , 2015, IEEE Transactions on Power Systems.