Document Type : Article

**Authors**

Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran 15875/4416, Iran

**Abstract**

In this research, a bidding problem for a wind-power plant participating in a day-ahead power market with uncertain correlated market prices is studied. A new robust optimization approach considering correlation among uncertainty on the hourly prices in a day-ahead market is developed. This results in solutions with lower level of over-conservatism. For this purpose a new correlated polyhedral uncertainty set is introduced. To consider the uncertainty of market clearing prices and the value of power produced by wind power producer a bidding algorithm is developed. Results of the study using a robust modelling the bidding problem reveal that the appliance of the proposed model on the bidding problem for a price-taker wind power plant in a day-ahead market with uncertain correlated data leads to solutions with superior performance than that of the conventional polyhedral uncertainty sets.

**Keywords**

[1] Conejo, A.J., Nogales, F.J. and Arroyo, J.M. “Price-taker bidding strategy under price uncertainty”, IEEE Transactions on Power Systems, **17**(4), pp.1081-1088(2002).

[2] Baringo, A., Baringo, L. and Arroyo, J.M. “Self scheduling of a virtual power plant in energy and reserve electricity markets: A stochastic adaptive robust optimization approach”, In 2018 Power Systems Computation Conference (PSCC) (pp. 1-7). IEEE( June 2018).

[3] Darvishi, S., Sheisi, G. and Aghaei, J. “Bidding strategy of hybrid power plant in day-ahead market as price maker through robust optimization”, International Transactions on Electrical Energy Systems, **30**(7), p.e12426(2020).

[4] Baringo, A., Baringo, L. and Arroyo, J.M. “Day-ahead self-scheduling of a virtual power plant in energy and reserve electricity markets under uncertainty”, IEEE Transactions on Power Systems, **34**(3), pp.1881-1894(2018).

[5] Hasanzad, F. and Rastegar, H. “Robust Security Constrained Unit Commitment under Uncertain Wind Power Generation”, In 2020 10th Smart Grid Conference (SGC) (pp. 1-6). IEEE(December 2020).

[6] Khaloie, H. and Anvari-Moghaddam, A. “Robust optimization approach for generation scheduling of a hybrid thermal-energy storage system”, In 2020 IEEE 29th International Symposium on Industrial Electronics (ISIE) (pp. 971-976). IEEE(June 2020).

[7] Abdalla, O.H., Adma, M.A.A. and Ahmed, A.S. “Generation expansion planning under correlated uncertainty of mass penetration renewable energy sources”, IET Energy Systems Integration, **2**(3), pp.273-281(2020).

[8] Zhang, J., Gu, B., Meng, H., Fu, C. and Zhu, X. “Robust Optimal Dispatch of Power Systems with Wind Farm”, Journal of Power Technologies, **100**(2), pp.92-101(2020).
# [9] Gu, Z., Qi, H., Liu, Z. and Zhang, R. “Robust Optimization Model of Island Energy System Based on Uncertainty of Wind and Photovoltaic”, In International Conference on Application of Intelligent Systems in Multi-modal Information Analytics (pp. 171-179). Springer, Cham(March 2020).

[10] Dai, X., Li, Y., Zhang, K. and Feng, W. “A robust offering strategy for wind producers considering uncertainties of demand response and wind power”. Applied Energy, **279**, p.115742(2020).

[11] Han, X., Kardakos, E.G. and Hug, G. “A distributionally robust bidding strategy for a wind power plant”, Electric Power Systems Research, **177**, p.105986(2019).

[12] Jalilvand-Nejad, A., Shafaei, R. and Shahriari, H. “A Genco self-scheduling problem with correlated prices using a new robust optimization approach”, International Journal of Production Research, **55**(11), pp.3249-3265(2017).

[13] Daneshvari, H. and Shafaei, R. “A new correlated polyhedral uncertainty set for robust optimization”, Computers & Industrial Engineering, **157**, p.107346(2021).

[14] Jalilvand-Nejad, A., Shafaei, R. and Shahriari, H. “Robust optimization under correlated polyhedral uncertainty set”, Computers & Industrial Engineering, **92**, pp.82-94(2016).

[15] Soltani, R., Sadjadi, S.J. and Tavakkoli-Moghaddam, R. “Robust cold standby redundancy allocation for nonrepairable series–parallel systems through Min-Max regret formulation and Benders’ decomposition method”, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, **228**(3), pp.254-264(2014).

[16] Baringo, L. and Conejo, A.J. “Offering strategy via robust optimization”, IEEE Transactions on Power Systems, **26**(3), pp.1418-1425(2010).

[17] Lu, C.C., Ying, K.C. and Lin, S.W. “Robust single machine scheduling for minimizing total flow time in the presence of uncertain processing times”, Computers & Industrial Engineering, **74**, pp.102-110(2014).

[18] Mönch, L., Uzsoy, R. and Fowler, J.W. “A survey of semiconductor supply chain models part I: semiconductor supply chains, strategic network design, and supply chain simulation”. International Journal of Production Research, **56**(13), pp.4524-4545(2018).

[19] Yang, S.J.S. and Hsieh, K.Y. “Supply chain investment and de-escalation of capacity competition”, International Journal of Production Research, **59**(3), pp.942-958(2021).

[20] Yu, G., Li, F. and Yang, Y. “Robust supply chain networks design and ambiguous risk preferences”, International Journal of Production Research, **55**(4), pp.1168-1182(2017).

[21] Soyster, A.L. “Convex programming with set-inclusive constraints and applications to inexact linear programming”, Operations research, **21**(5), pp.1154-1157(1973).

[22] Ben-Tal, A. and Nemirovski, A. “Robust convex optimization”, Mathematics of operations research", **23**(4), pp.769-805(1998).

[23] Ben-Tal, A. and Nemirovski, A. “Robust solutions of linear programming problems contaminated with uncertain data”, Mathematical programming, **88**(3), pp.411-424(2000).

[24] El Ghaoui, L. and Lebret, H. “Robust solutions to least-squares problems with uncertain data”, SIAM Journal on matrix analysis and applications, **18**(4), pp.1035-1064(1997).

[25] El Ghaoui, L., Oustry, F. and Lebret, H. “Robust solutions to uncertain semidefinite programs”, SIAM Journal on Optimization, **9**(1), pp.33-52(1998).

[26] Bertsimas, D. and Sim, M. “The price of robustness”, Operations research, **52**(1), pp.35-53(2004).

[27] Jabr, R.A. “Worst-case robust profit in generation self-scheduling”, IEEE Transactions on Power Systems, **24**(1), pp.492-493(2009).

[28] Jabr, R.A. “Self-scheduling under ellipsoidal price uncertainty: conic-optimisation approach”, IET generation, transmission & distribution, **1**(1), pp.23-29(2007).

[29] Landry, J.C. “A Robust Optimization Approach to the Self-scheduling Problem Using Semidefinite Programming” (Master's thesis, University of Waterloo),2010.

[30] Bai, M. and Yang, Z.. “Distributionally robust self-scheduling optimization with CO2 emissions constraints under uncertainty of prices”, Journal of Applied Mathematics, (2014).

[31] Luo, X., Chung, C.Y., Yang, H. and Tong, X. “Robust optimization-based generation self-scheduling under uncertain price”, Mathematical Problems in Engineering, (2011).

[32] Thatte, A.A., Viassolo, D.E. and Xie, L. “Robust bidding strategy for wind power plants and energy storage in electricity markets”, In 2012 IEEE Power and Energy Society General Meeting (pp. 1-7). IEEE(2012, July).

[33] Thatte, A.A., Xie, L., Viassolo, D.E. and Singh, S. “Risk measure based robust bidding strategy for arbitrage using a wind farm and energy storage”, IEEE Transactions on Smart Grid, **4**(4), pp.2191-2199(2013).

[34] Soroudi, A. “Robust optimization based self scheduling of hydro-thermal Genco in smart grids”, Energy, **61**, pp.262-271(2013).

[35] Lima, R.M., Novais, A.Q. and Conejo, A.J. “Weekly self-scheduling, forward contracting, and pool involvement for an electricity producer”, An adaptive robust optimization approach. European Journal of Operational Research, **240**(2), pp.457-475(2015).

[36] Pachamanova, D.A. “A robust optimization approach to finance”, (Doctoral dissertation, Massachusetts Institute of Technology), (2002).

[37] Rashidizadeh-Kermani, H., Vahedipour-Dahraie, M., Shafie-khah, M. and Catalão, J.P. “A bi-level risk-constrained offering strategy of a wind power producer considering demand side resources”, International Journal of Electrical Power & Energy Systems, **104**, pp.562-574(2019).

Articles in Press, Accepted Manuscript

Available Online from 23 May 2022