A Methodology for Explicit Representation of the Stochastic Demand due to Electric Vehicles in Generation Expansion Planning Problems

Generation expansion planning (GEP) problems are solved to find the optimum investment decisions to satisfy the increasing electricity demand. Integration of electric vehicles (EVs) with the capability of charging from the grid will also increase the electricity demand of the grid. Depending on the charging/driving characteristics of users, demand curves for EVs will be shaped and it will be different on each day. Therefore, it is very crucial to represent this stochastic nature of EVs demand in the associated GEP problems. This paper is proposing a methodology to represent EVs demand realistically on GEP models. The proposed methodology starts with generating random demand patterns to demonstrate possibilities for the EVs demand patterns via Monte Carlo Simulation, then using an optimization-based model to select a representative set. Two stage stochastic programming model is proposed for GEP problems and solved to minimize the expected cost over the entire set, the representative set and the average EVs demand. The results show that GEP models with selected demand curves produce more realistic decisions (closer to the solutions obtained by using the entire demand patterns) than the decisions obtained by the models with average EVs demand. In most cases, the models using average EVs demand fail to capture the new peaks generated by EVs, therefore, they suggest less capacity expansion then the required amount. This results in more unmet demand in the system.

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[1] T. Saraç and S. Kaya, “Plasti̇ k enjeksi̇ yon maki̇ neleri̇ ni̇ n vardi̇ ya bazinda çi̇ zelgelenmesi̇ problemi̇ i̇ çi̇ n bi̇ r hedef programlama modeli̇ ,” Journal of Industrial Engineering, vol. 24, pp. 12–26.
[2] T. Eren and E. Güner, “Sira-Bağimli Hazirlik Zamanli İki Ölçütlü Çizelgeleme Problemi: Toplam Tamamlanma Zamani Ve Maksimum Erken Bitirme,” Erciyes University Journal of Science and Technology, vol. 23, no. 1-2, pp. 95–105, 2007.
[3] T. Eren, “Learning and Deteriorating Effects on the Single Machine Scheduling Problems,” International Journal of Engineering Research and Development, vol. 6, no. 1, pp. 15–20, Jan. 2014.
[4] "Digital Conversion on the Way to Industry 4.0", Springer Science and Business Media LLC, 2021
[5] V.F. Viagas, A. Costa, Two novel population based algorithms for the single machine scheduling problem with sequence dependent setup times and release times, Swarm and Evolutionary Computation, Volume 63, 2021, 100869, ISSN 2210-6502, https://doi.org/10.1016/j.swevo.2021.10086.
[6] Y. Zhao and G. Wang, “A dynamic differential evolution algorithm for the dynamic single-machine scheduling problem with sequence-dependent setup times Yue,” Journal of the Operational Research Society, vol. 71, no. 2, pp. 225–236, 2020.
[7] S. Muştu and T. Eren, “The Single Machine Scheduling Problem with Sequence-Dependent Setup Times and a Learning Effect on Processing Times.,” Applied Soft Computing, vol. 71, pp. 291–306, 2018.
[8] P. Perez-Gonzalez and J. M. Framinan, “Single machine scheduling with periodic machine availability,” Computers & Industrial Engineering, vol. 123, pp. 180–188, 2018.
[9] R. M. Souza, S. Ricardo, and M. Felizardo, “Algorithms for job scheduling problems with distinct time windows and general earliness/tardiness penalties,” Computers and Operations Research, vol. 81, pp. 203–215, 2017.
[10] Z. Ceylan, E. Karan, Ç. Bakirci, and S. Sabuncu “Single Machine Scheduling Problem with Sequence Dependent Setup Times : An Application in White Goods I,” International Journal of Multidisciplinary Studies and Innovative Technologies, vol. 3, no. 1, pp. 14–21, 2019.
[11] O. Herr and A. Goel, “Minimising total tardiness for a single machine scheduling problem with family setups and resource constraints,” European Journal of Operational Research, vol. 248, no. 1, pp. 123–135, 2016.
[12] T. Prabhakar, “A Production Scheduling Problem with Sequencing,” Management Science , vol. 21, no. 1, pp. 34–42, 2014.
[13] T. C. E. Cheng, W. C. Lee, and C. C. Wu. “SingleMachine Scheduling with Deteriorating Jobs and PastSequence-Dependent Setup Times.” Applied Mathematical Modelling 35 (4):1861–67,2011. https://doi.org/10.1016/j.apm.2010.10.015.
[14] J.B. Wang and J. X. Li., Single Machine PastSequence-Dependent Setup Times Scheduling with General Position-Dependent and Time-Dependent Learning Effects. Applied Mathematical Modelling 35 (3): 1388–95,2011. https://doi.org/10.1016/j.apm.2010.09.017.
[15] K. Türker and Ç. Sel, “Sira Bağimli Hazirlik Operasyonlari İçin Tek Ekipli Paralel Makinalarda Çizelgeleme Problemine Karma Yaklaşim,” J. Fac. Eng. Arch. Gazi Univ., vol. 26, no. 4, pp. 731–740, 2011.
[16] C. Zhao and H. Tang, “Single machine scheduling with past-sequence-dependent setup times and deteriorating jobs,” Computers & Industrial Engineering, vol. 59, no. 4, pp. 663–666, 2010.
[17] J.-B. Wang, D. Wang, L.-Y. Wang, L. Lin, N. Yin, and W.-W. Wang, “Single machine scheduling with exponential time-dependent learning effect and pastsequence-dependent setup times,” Computers & Mathematics with Applications, vol. 57, no. 1, pp. 9–16, 2009.
[18] D. Biskup and J. Herrmann. “Single-Machine Scheduling against Due Dates with Past-SequenceDependent Setup Times”, European Journal of Operational Research 191 (2): 587–92,2008. https://doi.org/10.1016/j.ejor.2007.08.028.
[19] S. Karabati and C. Akkan., “Minimizing Sum of Completion Times on a Single Machine with SequenceDependent Family Setup Times.” Journal of the Operational Research Society 57 (3): 271–80,2006. https://doi.org/10.1057/palgrave.jors.2601989.
[20] G. Rabadi, M. Mollaghasemi, G.C. Anagnostopoulos, “A Branch-And-Bound Algorithm For The Early/Tardy Machine Scheduling Problem With A Common Due-Date And Sequence Dependent Setup Time,” Computers and Operations Research, 31, 1727–1751, 2004.
[21] S.R. Gupta and J. S. Smith. “Algorithms for Single Machine Total Tardiness Scheduling with Sequence Dependent Setups.” European Journal of Operational Research 175 (2): 722–39,2006. https://doi.org/10.1016/j.ejor.2005.05.018.
[22] V. A. Armentano and R. Mazzini. “A Genetic Algorithm for Scheduling on a Single Machine with Set-up Times and Due Dates.” Production Planning and Control 11 (7): 713–20, 2000. https://doi.org/10.1080/095372800432188.
[23] Y.H. Lee, K. Bhaskaran and M. Pinedo. “A Heuristic to Minimize the Total Weighted Tardiness with Sequence-Dependent Setups.” IIE Transactions (Institute of Industrial Engineers) 29 (1): 45–52,1997. https://doi.org/10.1080/07408179708966311.
[24] K.C. Tan and R. Narasimhan. “Minimizing Tardiness on a Single Processor with Sequence-Dependent Setup Times: A Simulated Annealing Approach.” Omega 25 (6): 619–34, 1997.https://doi.org/10.1016/S0305- 0483(97)00024-8.
[25] H. J. Shin, C.-O. Kim, and S. S. Kim, “A Tabu Search Algorithm for Single Machine Scheduling with Release Times, Due Dates, and Sequence-Dependent Set-up Times,” The International Journal of Advanced Manufacturing Technology, vol. 19, no. 11, pp. 859–866, 2002.
[26] P.A. Rubinand and G. L. Ragatz. “Scheduling in a Sequence Dependent Setup Environment with Genetic Search.” Computers and Operations Research 22 (1): 85– 99,1995. https://doi.org/10.1016/0305-0548(93)E0021-K.
[27] F. Glover, “Tabu Search-Part I”, ORSA Journal on Computing, Cilt 1, No 3, 190-206, 1989.
[28] F. Glover, “Tabu Search-Part II”, ORSA Journal on Computing, Cilt 2, No 1, 4-32 1990
[29] S. Özyön , C. Yaşar ve H. Temurtaş , "Ham Enerji Kaynaği Kisitli Termik Birim İçeren Sistemlerde Çevresel Ekonomik Güç Dağitimi Probleminin Çözümü", Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlik Fakültesi Dergisi, c. 24, sayi. 1, ss. 47-72, Haz. 2011
[30] F. Glover and M. Laguna, “Tabu Search,” Tabu Search, no. July, 1997, doi: 10.1007/978-1-4615-6089-0.
[31] J. Xu, M. Sohoni, M. McCleery, and T. G. Bailey, “A dynamic neighborhood based tabu search algorithm for real-world flight instructor scheduling problems,” Eur. J. Oper. Res., vol. 169, no. 3, pp. 978–993, 2006, doi: 10.1016/j.ejor.2004.08.023.
[32] A. M. Mohammed and S. O. Duffuaa, “A tabu search based algorithm for the optimal design of multiobjective multi-product supply chain networks,” Expert Syst. Appl., vol. 140, p. 112808, 2020, doi: 10.1016/j.eswa.2019.07.025.
[33] A. Y. Abdelaziz, F. M. Mohamed, S. F. Mekhamer, and M. A. L. Badr, “Distribution system reconfiguration using a modified Tabu Search algorithm,” Electr. Power Syst. Res., vol. 80, no. 8, pp. 943–953, 2010, doi: 10.1016/j.epsr.2010.01.001.
[34] Wan, Guohua, and Benjamin P.-C. Yen, “Tabu Search for Single Machine Scheduling with Distinct Due Windows and Weighted Earliness/Tardiness Penalties.,” European Journal ofOperational Research, vol. 142, no. 2, pp. 271–281, 2002.