Robust bi-level risk-based optimal scheduling of microgrid operation against uncertainty
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 4, pp. 993-1012.

The model introduced in this paper is the first to propose a decentralized robust optimal scheduling of MG operation under uncertainty and risk. The power trading of the MG with the main grid is the first stage variable and power generation of DGs and power charging/discharging of the battery are the second stage variables. The uncertain term of the initial objective function is transformed into a constraint using robust optimization approach. Addressing the Decision Maker’s (DMs) risk aversion level through Conditional Value at Risk (CVaR) leads to a bi-level programming problem using a data-driven approach. The model is then transformed into a robust single-level using Karush–Kahn–Tucker (KKT) conditions. To investigate the effectiveness of the model and its solution methodology, it is applied on a MG. The results clearly demonstrate the robustness of the model and indicate a strong almost linear relationship between cost and the DMs various levels of risk aversion. The analysis also outlines original characterization of the cost and the MGs behavior using three well-known goodness-of-fit tests on various Probability Distribution Functions (PDFs), Beta, Gumbel Max, Normal, Weibull, and Cauchy. The Gumbel Max and Normal PDFs, respectively, exhibit the most promising goodness-of-fit for the cost, while the power purchased from the grid are well fitted by Weibull, Beta, and Normal PDFs, respectively. At the same time, the power sold to the grid is well fitted by the Cauchy PDF.

DOI : 10.1051/ro/2019046
Classification : 93B35
Mots-clés : Microgrid, mixed integer linear programming, robust optimization, conditional value at risk, goodness of fit test
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     author = {Golp{\^\i}ra, H\^eriș and Bahramara, Salah and Khan, Syed Abdul Rehman and Zhang, Yu},
     title = {Robust bi-level risk-based optimal scheduling of microgrid operation against uncertainty},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {993--1012},
     publisher = {EDP-Sciences},
     volume = {54},
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     mrnumber = {4091857},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2019046/}
}
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Golpîra, Hêriș; Bahramara, Salah; Khan, Syed Abdul Rehman; Zhang, Yu. Robust bi-level risk-based optimal scheduling of microgrid operation against uncertainty. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 4, pp. 993-1012. doi : 10.1051/ro/2019046. http://www.numdam.org/articles/10.1051/ro/2019046/

[1] A. Abdulkarim, S.M. Abdelkader and D.J. Morrow, Statistical analyses of wind and solar energy resources for the development of hybrid microgrid. Springer (2015) 9–14.

[2] M. Aman, G. Jasmon, H. Mokhlis and A. Bakar, Optimal placement and sizing of a DG based on a new power stability index and line losses. Int. J. Electr. Power Energy Syst. 43 (2012) 1296–1304. | DOI

[3] G.E. Asimakopoulou, A.L. Dimeas and N.D. Hatziargyriou, Leader-follower strategies for energy management of multi-microgrids. IEEE Trans. Smart Grid 4 (2013) 1909–1916. | DOI

[4] S. Bahramara and H. Golpîra, Robust optimization of micro-grids operation problem in the presence of electric vehicles. Sustainable Cities Soc. 37 (2017) 388–395. | DOI

[5] A. Ben-Tal and A. Nemirovski, Robust solutions of uncertain linear programs. Oper. Res. Lett. 25 (1999) 1–13. | DOI | MR | Zbl

[6] D. Bertsimas and M. Sim, The price of robustness. Oper. Res. 52 (2004) 35–53. | DOI | MR | Zbl

[7] D. Bertsimas and D.B. Brown, Constructing uncertainty sets for robust linear optimization. Oper. Res. 57 (2009) 1483–1495. | DOI | MR | Zbl

[8] E. Carpaneto and G. Chicco, Probability distributions of the aggregated residential load. In: 2006 International Conference on Probabilistic Methods Applied to Power Systems. IEEE (2006) 1–6.

[9] E. Carpaneto and G.J.I.G. Chicco, Probabilistic characterisation of the aggregated residential load patterns. IET Gener. Transm. Distrib. 2 (2008) 373–382. | DOI

[10] Z. Chen, L. Wu and Y. Fu, Real-time price-based demand response management for residential appliances via stochastic optimization and robust optimization. IEEE Trans. Smart Grid 3 (2012) 1822–1831. | DOI

[11] S. Dempe, Foundations of Bilevel Programming. Springer Science & Business Media, Berlin (2002). | MR | Zbl

[12] X. Fang, F. Li, Y. Wei and H. Cui, Strategic scheduling of energy storage for load serving entities in locational marginal pricing market. IET Gener. Transm. Distrib. 10 (2016) 1258–1267. | DOI

[13] F.S. Gazijahani and J. Salehi, Robust design of microgrids with reconfigurable topology under severe uncertainty. IEEE Trans. Sustainable Energy 9 (2018) 559–569. | DOI

[14] F.S. Gazijahani and J. Salehi, Reliability constrained two-stage optimization of multiple renewable-based microgrids incorporating critical energy peak pricing demand response program using robust optimization approach. Energy 161 (2018) 999–1015. | DOI

[15] F.S. Gazijahani and J. Salehi, Game theory based profit maximization model for microgrid aggregators with presence of EDRP using information gap decision theory. IEEE Syst. J. 1–9 (2018).

[16] F.S. Gazijahani, S.N. Ravadanegh and J. Salehi, Stochastic multi-objective model for optimal energy exchange optimization of networked microgrids with presence of renewable generation under risk-based strategies. ISA Trans. 73 (2018) 100–111. | DOI

[17] H. Golpîra, Supply chain network design optimization with risk-averse retailer. Int. J. Inf. Syst. Supply Chain Manage. 10 (2017) 16–28. | DOI

[18] H. Golpîra, Robust bi-level optimization for an opportunistic supply chain network design problem in an uncertain and risky environment. Oper. Res. Decis. 27 (2017). | MR

[19] H. Golpîra, A novel multiple attribute decision making approach based on interval data using U2P-Miner algorithm. Data Knowl. Eng. 115 (2018) 116–128. | DOI

[20] H. Golpîra and S.A.R. Khan, A multi-objective risk-based robust optimization approach to energy management in smart residential buildings under combined demand and supply uncertainty. Energy 170 (2019) 1113–1129. | DOI

[21] H. Golpîra, E. Najafi, M. Zandieh and S. Sadi-Nezhad, Robust bi-level optimization for green opportunistic supply chain network design problem against uncertainty and environmental risk. Comput. Ind. Eng. 107 (2017) 301–312. | DOI

[22] H. Golpîra, S.A.R. Khan and Y. Zhang, Robust smart energy efficient production planning for a general job-shop manufacturing system under combined demand and supply uncertainty in the presence of grid-connected microgrid. J. Cleaner Prod. 202 (2018) 649–665. | DOI

[23] J. Lee, J. Guo, J.K. Choi and M. Zukerman, Distributed energy trading in microgrids: A game-theoretic model and its equilibrium analysis. IEEE Trans. Ind. Electron. 62 (2015) 3524–3533. | DOI

[24] X. Lu, K. Zhou and S. Yang, Multi-objective optimal dispatch of microgrid containing electric vehicles. J. Cleaner Prod. 165 (2017) 1572–1581. | DOI

[25] L. Ma, N. Liu, J. Zhang, W. Tushar and C. Yuen, Energy management for joint operation of CHP and PV prosumers inside a grid-connected microgrid: a game theoretic approach. IEEE Trans. Ind. Inf. 12 (2016) 1930–1942. | DOI

[26] A. Mehdizadeh, N. Taghizadegan and J. Salehi, Risk-based energy management of renewable-based microgrid using information gap decision theory in the presence of peak load management. Appl. Energy 211 (2018) 617–630. | DOI

[27] A. Mondal, S. Misra and M.S. Obaidat, Distributed home energy management system with storage in smart grid using game theory. IEEE Syst. J. 11 (2017) 1857–1866. | DOI

[28] J.M. Morales, P. Pinson and H. Madsen, A transmission-cost-based model to estimate the amount of market-integrable wind resources. IEEE Trans. Power Syst. 27 (2012) 1060–1069. | DOI

[29] N. Nikmehr, S. Najafi-Ravadanegh and A. Khodaei, Probabilistic optimal scheduling of networked microgrids considering time-based demand response programs under uncertainty. Appl. Energy 198 (2017) 267–279. | DOI

[30] S.M. Nosratabadi, R.-A. Hooshmand and E. Gholipour, A comprehensive review on microgrid and virtual power plant concepts employed for distributed energy resources scheduling in power systems. Renew. Sustainable Energy Rev. 67 (2017) 341–363. | DOI

[31] M. Patriksson and L. Wynter, Stochastic mathematical programs with equilibrium constraints. Oper. Res. Lett. 25 (1999) 159–167. | DOI | MR | Zbl

[32] N. Rezaei, A. Ahmadi, A. Khazali and J.M. Guerrero, Energy and frequency hierarchical management system using information gap decision theory for islanded microgrids. IEEE Trans. Ind. Electron. 65 (2018) 7921–7932. | DOI

[33] A. Thiele, A robust optimization approach to supply chains and revenue management. Ph.D dissertion Massachusetts Institute of Technology (2004).

[34] E.C. Umeozor and M. Trifkovic, Operational scheduling of microgrids via parametric programming. Appl. Energy 180 (2016) 672–681. | DOI

[35] Z. Wang, B. Chen, J. Wang, M.M. Begovic and C. Chen, Coordinated energy management of networked microgrids in distribution systems. IEEE Trans. Smart Grid 6 (2015) 45–53. | DOI

[36] L. Wang, Q. Li, R. Ding, M. Sun and G. Wang, Integrated scheduling of energy supply and demand in microgrids under uncertainty: a robust multi-objective optimization approach. Energy 130 (2017) 1–14. | DOI

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