Document Type : Article

**Authors**

Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran

**Abstract**

In this paper, we focus on solving the integrated energy and flexiramp procurement problem in the day-ahead market. The problem of energy and ramp procurement could be perfectly analyzed through Stackelberg concept, because of its hierarchical nature of the decision-making process. Such a circumstance is modeled via a bi-level programming, in which suppliers act as leaders and the ISO appear as the follower. The ISO intends to minimize the energy and spinning reserve procurement cost, and the suppliers aim to maximize their profit. To solve the proposed model, a fuzzy max-min approach is applied to maximize the players’ utilities. The objectives and suppliers’ dynamic offers, determined regarding the market clearing prices, are reformulated through fuzzy utility functions. The proposed approach is an effective and simple alternative to the KKT method, especially for problems with non-convex lower-level.

**Keywords**

**Main Subjects**

References:

1. Milligan, M., Holttinen, H., Kiviluoma, J., Orths, A., Lynch, M.A., and Soder, L. "Market designs for high levels of variable generation", In 2014 IEEE PES General Meeting Conference & Exposition, pp. 1-5 (July 2014).

2. Wang, B. and Hobbs, B.F. "A flexible ramping product: Can it help real-time dispatch markets approach the stochastic dispatch ideal?", Electric Power Systems Research, 109, pp. 128-140 (2014).

3. Wang, B. and Hobbs, B.F. "Flexiramp market design for real-time operations: Can it approach the stochastic optimization ideal?", In Power and Energy Society General Meeting (PES), 2013 IEEE, pp. 1-5 (July 2013).

4. Wang, B. and Hobbs, B.F., Real-Time Markets for Flexiramp: A Stochastic Unit Commitment-Based Analysis, IEEE Transactions on Power Systems, 31(2), pp. 846-860 (2015).

5. Wang, B. and Hobbs, B.F. "Real-time markets for flexiramp: A stochastic unit commitment-based analysis", IEEE Transactions on Power Systems, 31(2), pp. 846-860 (2016).

6. California ISO. Folsom, CA, USA, "Addition of a new flexible ramping constraint in the real time pre-dispatch and real time dispatch process", Tech. Bulletin (Feb. 2011) [Online], Available at: http://www.caiso.com/2b30/2b307b2a64380.pdf.

7. Navid, N., Rosenwald, G., and Chatterjee, D., Ramp Capability for Load Following in the MISO Markets, Midwest Independent System Operator (2011).

8. Moiseeva, E., Hesamzadeh, M.R., and Biggar, D.R. "Exercise of market power on ramp rate in windintegrated power systems", Power Systems, IEEE Transactions on, 30(3), pp. 1614-1623 (2015).

9. Milligan, M., Frew, B., Zhou, E., and Arent, D.J. "Advancing system flexibility for high penetration renewable integration (No. NREL/TP-6A20-64864)", NREL (National Renewable Energy Laboratory) (2015).

10. Soares, T., Pinson, P., Jensen, T.V., and Morais, H. "Optimal offering strategies for wind power in energy and primary reserve markets", IEEE Transactions on Sustainable Energy, 7(3), pp. 1036-1045 (2016).

11. Riaz, S., Chapman, A.C., and Verbic, G. "Evaluation of concentrated solar-thermal generation for provision of power system flexibility", In Power Systems Computation Conference (PSCC), 2016, pp. 1-7 (June 2016).

12. Wu, H., Shahidehpour, M., and Khodayar, M.E. "Hourly demand response in day-ahead scheduling considering generating unit ramping cost", IEEE Transactions on Power Systems, 28(3), pp. 2446-2454 (2013).

13. Carrion, M., Arroyo, J.M., and Conejo, A.J. "A bilevel stochastic programming approach for retailer futures market trading", Power Systems, IEEE Transactions on, 24(3), pp. 1446-1456 (2009).

14. Haghighat, H. and Kennedy, S.W. "A bilevel approach to operational decision making of a distribution company in competitive environments", Power Systems, IEEE Transactions on, 27(4), pp. 1797-1807 (2012).

15. Shi, L., Luo, Y., and Tu, G.Y. "Bidding strategy of microgrid with consideration of uncertainty for participating in power market", International Journal of Electrical Power & Energy Systems, 59, pp. 1-13 (2014).

16. Khojasteh, M. and Jadid, S. "Decision-making framework for supplying electricity from distributed generation-owning retailers to price-sensitive customers", Utilities Policy, 37, pp. 1-12 (2015).

17. Tohidi, Y., Hesamzadeh, M.R., Baldick, R., and Biggar, D.R. "Transmission network switching for reducing market power cost in generation sector: A Nash-equilibrium approach", Electric Power Systems Research, 146, pp. 71-79 (2017).

18. Carrion, M., Arroyo, J.M., and Conejo, A.J. "A bilevel stochastic programming approach for retailer futures market trading", IEEE Transactions on Power Systems, 24, pp. 1446-1456 (2009).

19. Cheng, C.-B. "Reverse auction with buyer-supplier negotiation using bi-level distributed programming", European Journal of Operational Research, 211(3), pp. 601-611 (2011).

20. Chen, Y., He, L., Li, J., Cheng, X., and Lu, H. "An inexact bi-level simulation-optimization model for conjunctive regional renewable energy planning and air pollution control for electric power generation systems", Applied Energy, 183, pp. 969-983 (2016).

21. European Wind Energy Association, Support Schemes for Renewable Energy. A Comparative Analysis of Payment Mechanisms in the EU. Directorate-General Energy and Transport (2002).

22. Cheng, C.-B. "Reverse auction with buyer-supplier negotiation using bi-level distributed programming", European Journal of Operational Research, 211(3), pp. 601-611 (2011).

23. Pozo, D., Sauma, E., and Contreras, J. "Basic theoretical foundations and insights on bilevel models and their applications to power systems", Annals of Operations Research, 254(1-2), pp. 303-334 (2017).

24. Shih, H.S., Lai, Y.J., and Lee, E.S. "Fuzzy approach for multi-level programming problems", Computers & Operations Research, 23(1), pp. 73-91 (1996).

25. Ungureanu, V. "Taxonomy of strategic games with information leaks and corruption of simultaneity", In Pareto-Nash-Stackelberg Game and Control Theory, pp. 255-273. Springer, Cham (2018).

26. Nie, P.Y., Chen, L.H., and Fukushima, M. "Dynamic programming approach to discrete time dynamic feedback Stackelberg games with independent and dependent followers", European Journal of Operational Research, 169(1), pp. 310-328 (2006).

27. Simaan, M. and Cruz Jr, J.B. "On the Stackelberg strategy in nonzero-sum games", Journal of Optimization Theory and Applications, 11(5), pp. 533-555 (1973).

28. Ben-Ayed, O. and Blair, C.E. "Computational difficulties of bi level linear programming", Operations Research, 38, pp. 556-560 (1990).

29. Gongxian, X. and Yang, L. "Steady-state optimization of biochemical systems by bi-level programming", Computers & Chemical Engineering, 106, pp. 286-296 (2017).

30. Roghanian, E., Aryanezhad, M.B., and Sadjadi, S.J. "Integrating goal programming, Kuhn-Tucker conditions, and penalty function approaches to solve linear bi-level programming problems", Applied Mathematics and Computation, 195(2), pp. 585-590 (2008).

31. Sakawa, M. and Matsui, T. "Interactive random fuzzy two-level programming through possibility-based probability model", Information Sciences, 239, pp. 191- 200 (2013).

32. Hejazi, S.R., Memariani, A., Jahanshahloo, G., and Sepehri, M.M. "Linear bilevel programming solution by genetic algorithm", Computers & Operations Research, 29(13), pp. 1913-1925 (2002).

33. Kuo, R.J. and Huang, C.C. "Application of particle swarm optimization algorithm for solving bi-level linear programming problem", Computers & Mathematics with Applications, 58(4), pp. 678-685 (2009).

34. Kuo, R.J. and Han, Y.S. "A hybrid of genetic algorithm and particle swarm optimization for solving bilevel linear programming problem - A case study on supply chain model", Applied Mathematical Modelling, 35(8), pp. 3905-3917 (2011).

35. Kato, K., Sakawa, M., Matsui, T., and Ohtsuka, H. "A computational method for obtaining Stackelberg solutions to noncooperative two-level programming problems through evolutionary multi-agent systems", In Agent and Multi-Agent Systems: Technologies and Applications, pp. 639-648, Springer Berlin Heidelberg (2009).

36. Lai, Y.-J. "Hierarchical optimization: A satisfactory solution", Fuzzy Set and Systems, 77, pp. 321-335 (1996).

37. Soares, T., Pinson, P., Jensen, T.V., and Morais, H., Optimal Offering Strategies For Wind Power in Energy and Primary Reserve Markets, IEEE Transactions on Sustainable Energy, 7(3), pp. 1036-1045 (2016).

38. Bellman, R.E. and Zadeh, L.A. "Decision-making in a fuzzy environment", Management Science, 17(4), B-141 (1970).

39. Saranwong, S. and Likasiri, C. "Bi-level programming model for solving distribution center problem: A case study in Northern Thailand's sugarcane management", Computers & Industrial Engineering, 103, pp. 26-39 (2017).

40. Shih, H.S., Lai, Y.J., and Lee, E.S. "Fuzzy approach for multi-level programming problems", Computers & Operations Research, 23(1), pp. 73-91 (1996).

2. Wang, B. and Hobbs, B.F. "A flexible ramping product: Can it help real-time dispatch markets approach the stochastic dispatch ideal?", Electric Power Systems Research, 109, pp. 128-140 (2014).

3. Wang, B. and Hobbs, B.F. "Flexiramp market design for real-time operations: Can it approach the stochastic optimization ideal?", In Power and Energy Society General Meeting (PES), 2013 IEEE, pp. 1-5 (July 2013).

4. Wang, B. and Hobbs, B.F., Real-Time Markets for Flexiramp: A Stochastic Unit Commitment-Based Analysis, IEEE Transactions on Power Systems, 31(2), pp. 846-860 (2015).

5. Wang, B. and Hobbs, B.F. "Real-time markets for flexiramp: A stochastic unit commitment-based analysis", IEEE Transactions on Power Systems, 31(2), pp. 846-860 (2016).

6. California ISO. Folsom, CA, USA, "Addition of a new flexible ramping constraint in the real time pre-dispatch and real time dispatch process", Tech. Bulletin (Feb. 2011) [Online], Available at: http://www.caiso.com/2b30/2b307b2a64380.pdf.

7. Navid, N., Rosenwald, G., and Chatterjee, D., Ramp Capability for Load Following in the MISO Markets, Midwest Independent System Operator (2011).

8. Moiseeva, E., Hesamzadeh, M.R., and Biggar, D.R. "Exercise of market power on ramp rate in windintegrated power systems", Power Systems, IEEE Transactions on, 30(3), pp. 1614-1623 (2015).

9. Milligan, M., Frew, B., Zhou, E., and Arent, D.J. "Advancing system flexibility for high penetration renewable integration (No. NREL/TP-6A20-64864)", NREL (National Renewable Energy Laboratory) (2015).

10. Soares, T., Pinson, P., Jensen, T.V., and Morais, H. "Optimal offering strategies for wind power in energy and primary reserve markets", IEEE Transactions on Sustainable Energy, 7(3), pp. 1036-1045 (2016).

11. Riaz, S., Chapman, A.C., and Verbic, G. "Evaluation of concentrated solar-thermal generation for provision of power system flexibility", In Power Systems Computation Conference (PSCC), 2016, pp. 1-7 (June 2016).

12. Wu, H., Shahidehpour, M., and Khodayar, M.E. "Hourly demand response in day-ahead scheduling considering generating unit ramping cost", IEEE Transactions on Power Systems, 28(3), pp. 2446-2454 (2013).

13. Carrion, M., Arroyo, J.M., and Conejo, A.J. "A bilevel stochastic programming approach for retailer futures market trading", Power Systems, IEEE Transactions on, 24(3), pp. 1446-1456 (2009).

14. Haghighat, H. and Kennedy, S.W. "A bilevel approach to operational decision making of a distribution company in competitive environments", Power Systems, IEEE Transactions on, 27(4), pp. 1797-1807 (2012).

15. Shi, L., Luo, Y., and Tu, G.Y. "Bidding strategy of microgrid with consideration of uncertainty for participating in power market", International Journal of Electrical Power & Energy Systems, 59, pp. 1-13 (2014).

16. Khojasteh, M. and Jadid, S. "Decision-making framework for supplying electricity from distributed generation-owning retailers to price-sensitive customers", Utilities Policy, 37, pp. 1-12 (2015).

17. Tohidi, Y., Hesamzadeh, M.R., Baldick, R., and Biggar, D.R. "Transmission network switching for reducing market power cost in generation sector: A Nash-equilibrium approach", Electric Power Systems Research, 146, pp. 71-79 (2017).

18. Carrion, M., Arroyo, J.M., and Conejo, A.J. "A bilevel stochastic programming approach for retailer futures market trading", IEEE Transactions on Power Systems, 24, pp. 1446-1456 (2009).

19. Cheng, C.-B. "Reverse auction with buyer-supplier negotiation using bi-level distributed programming", European Journal of Operational Research, 211(3), pp. 601-611 (2011).

20. Chen, Y., He, L., Li, J., Cheng, X., and Lu, H. "An inexact bi-level simulation-optimization model for conjunctive regional renewable energy planning and air pollution control for electric power generation systems", Applied Energy, 183, pp. 969-983 (2016).

21. European Wind Energy Association, Support Schemes for Renewable Energy. A Comparative Analysis of Payment Mechanisms in the EU. Directorate-General Energy and Transport (2002).

22. Cheng, C.-B. "Reverse auction with buyer-supplier negotiation using bi-level distributed programming", European Journal of Operational Research, 211(3), pp. 601-611 (2011).

23. Pozo, D., Sauma, E., and Contreras, J. "Basic theoretical foundations and insights on bilevel models and their applications to power systems", Annals of Operations Research, 254(1-2), pp. 303-334 (2017).

24. Shih, H.S., Lai, Y.J., and Lee, E.S. "Fuzzy approach for multi-level programming problems", Computers & Operations Research, 23(1), pp. 73-91 (1996).

25. Ungureanu, V. "Taxonomy of strategic games with information leaks and corruption of simultaneity", In Pareto-Nash-Stackelberg Game and Control Theory, pp. 255-273. Springer, Cham (2018).

26. Nie, P.Y., Chen, L.H., and Fukushima, M. "Dynamic programming approach to discrete time dynamic feedback Stackelberg games with independent and dependent followers", European Journal of Operational Research, 169(1), pp. 310-328 (2006).

27. Simaan, M. and Cruz Jr, J.B. "On the Stackelberg strategy in nonzero-sum games", Journal of Optimization Theory and Applications, 11(5), pp. 533-555 (1973).

28. Ben-Ayed, O. and Blair, C.E. "Computational difficulties of bi level linear programming", Operations Research, 38, pp. 556-560 (1990).

29. Gongxian, X. and Yang, L. "Steady-state optimization of biochemical systems by bi-level programming", Computers & Chemical Engineering, 106, pp. 286-296 (2017).

30. Roghanian, E., Aryanezhad, M.B., and Sadjadi, S.J. "Integrating goal programming, Kuhn-Tucker conditions, and penalty function approaches to solve linear bi-level programming problems", Applied Mathematics and Computation, 195(2), pp. 585-590 (2008).

31. Sakawa, M. and Matsui, T. "Interactive random fuzzy two-level programming through possibility-based probability model", Information Sciences, 239, pp. 191- 200 (2013).

32. Hejazi, S.R., Memariani, A., Jahanshahloo, G., and Sepehri, M.M. "Linear bilevel programming solution by genetic algorithm", Computers & Operations Research, 29(13), pp. 1913-1925 (2002).

33. Kuo, R.J. and Huang, C.C. "Application of particle swarm optimization algorithm for solving bi-level linear programming problem", Computers & Mathematics with Applications, 58(4), pp. 678-685 (2009).

34. Kuo, R.J. and Han, Y.S. "A hybrid of genetic algorithm and particle swarm optimization for solving bilevel linear programming problem - A case study on supply chain model", Applied Mathematical Modelling, 35(8), pp. 3905-3917 (2011).

35. Kato, K., Sakawa, M., Matsui, T., and Ohtsuka, H. "A computational method for obtaining Stackelberg solutions to noncooperative two-level programming problems through evolutionary multi-agent systems", In Agent and Multi-Agent Systems: Technologies and Applications, pp. 639-648, Springer Berlin Heidelberg (2009).

36. Lai, Y.-J. "Hierarchical optimization: A satisfactory solution", Fuzzy Set and Systems, 77, pp. 321-335 (1996).

37. Soares, T., Pinson, P., Jensen, T.V., and Morais, H., Optimal Offering Strategies For Wind Power in Energy and Primary Reserve Markets, IEEE Transactions on Sustainable Energy, 7(3), pp. 1036-1045 (2016).

38. Bellman, R.E. and Zadeh, L.A. "Decision-making in a fuzzy environment", Management Science, 17(4), B-141 (1970).

39. Saranwong, S. and Likasiri, C. "Bi-level programming model for solving distribution center problem: A case study in Northern Thailand's sugarcane management", Computers & Industrial Engineering, 103, pp. 26-39 (2017).

40. Shih, H.S., Lai, Y.J., and Lee, E.S. "Fuzzy approach for multi-level programming problems", Computers & Operations Research, 23(1), pp. 73-91 (1996).

Transactions on Industrial Engineering (E)

March and April 2020Pages 846-861