S.Ye. Saukh, Dr Sc. (Eng.),
Pukhov Institute for Problems of Modeling in Energy Engineering, NAS of Ukraine (15 General Naumov St, Kyiv, 03164, Ukraine, e-mail:
Èlektron. model. 2018, 40(3):03-32
Peculiarities of development of energy engineering modeling systems under conditions of market mechanisms of energy complex management have been analyzed. The requirements on ensuring the adequacy of energy modeling systems in market conditions have been formulated. The generalized mathematical model of the competitive equilibrium on the electricity market has been presented in the form of a system of problems of mathematical programming with complementarity constraints. The search for the solution of such a system of problems we reduce to finding a solu tion of large scale mixed nonlinear complementary problem in the form of a Karush-Kuhn-Tucker system. A collection of original methods is presented for solving individual subtasks arising from the application of the quasi-Newtonian method for solving complementary problems of large dimension. The benefits of our solver (ICRS) created on the original methodology in comparison with the worldwide PATH solver are shown. A model of equilibrium states of the electricity market of Ukraine is presented in the form of a detailed description of the system of tasks of mathematical programming with complementarity constraints. The computational experiments show the application of the methodology for constructing adequate mathematical models of energy markets and propose methods for solving a system of problems of mathematical programming with complementarity constraints.
energy market, equilibrium state, modeling methodology, mathematical programming, complementary problem, solver of large-scale complementary problems, computational experiment.
1. Jebaraja, S. and Iniyan, S. (2006), A review of energy models. Renewable and Sustainable Energy Reviews, Vol. 10, no. 4, pp. 281-311.
2. Connolly, D., Lund, H., Mathiesen, B.V. and Leahy, M. (2010), A review of computer tools for analyzing the integration of renewable into various energy systems, Applied Energy, Vol. 87, no. 4, pp. 1059-1082.
3. Amerighi, O., Ciorba, U. and Tommasino, M.C. (2010), Inventory and characterization of existing tools, D2.1 ATEsT Models Characterization Report, Italian National Agency for New Technologies, available at: http://www.cres.gr/atest/pdf/D_2_1_Models_Characterisation_Report.pdf.
4. Pina, A.A. (2012), Supply and demand dynamics in energy systems modeling. PhD Thesis. Universidade Tåcnica de Lisboa, available at: https://www.mitportugal.org/about/documents/curriculum-vitae/sustainable-energy-systems/968-thesis-andrepina/file.
5. Beeck, N. (1999), Classification of energy models. Tech. report FEW 777. Tilburg University & Eindhoven University of Technology, available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.43.8055&rep=rep1&type=pdf.
6. Daniels, D. (2017), Overview of the national energy modeling system (NEMS). U.S. Energy Information Administration, 2017, available at: https://cepl.gatech.edu/sites/default/files/attachments/NEMS%20Overview_8-31-17FINAL_0.pdf.
7. PLEXOS® Integrated Energy Model, available at: http://utilitiesnetwork.energy-businessreview.com/suppliers/energy-exemplar/products/plexos-integrated-energy-model-ebr.
8. PRIMES MODEL 2013-2014. Detailed model description. E3MLab/ICCS at National Technical University of Athens, available at: https://ec.europa.eu/clima/sites/clima/files/strategies/analysis/models/docs/primes_model_2013-2014_en.pdf.
9. Parkkonen, O. (2016), Customer benefits of demand-side management in the Nordic electricity
market. PhD Thesis: Jyväskylä University School of Business and Economics, 2016,
available at: https://jyx.jyu.fi/dspace/handle/123456789/52033.
10. NEMSIM: the National Electricity Market simulator, available at: http://press-files.anu.edu.au/downloads/press/p96431/mobile/ch11s08.html.
11. Hogan, W.W. (1975), Energy policy models for project independence, Computers&Operations Research, no. 2, pp. 251-271.
12. Gabriel, S.A., Kydes, A.S. and Whitman, P. (2001), The National Energy Modeling System:
A large-scale energy-economic equilibrium model, Operations Research, Vol. 49, no. 1, pp. 14-25.
13. Murphy, F.H., Susan, J.C., Shaw, S.H. and Sanders, R. (1988), Modeling and forecasting energymarketswith the intermediate future forecasting system, Operations Research, Vol. 36, no. 3, pp. 406-420.
14. Integrating module of the National Energy Modeling System: Model documentation. U.S. Energy Information Administration. 2014, available at: https://www.eia.gov/outlooks/aeo/nems/documentation/integrating/pdf/m057(2014).pdf.
15. Overview of the Energy and Power Evaluation Program (ENPEP-BALANCE). Center for Energy, Environmental, and Economic Systems Analysis (CEEESA). Argonne National Laboratory, available at: https://ceeesa.es.anl.gov/pubs/61124.pdf.
16. Nesbitt, D. and Calvez, À. (2014), Network agent based modeling for EIA, available at: https://www.eia.gov/outlooks/documentation/workshops/pdf/day_2__2_dale_nesbitt_arrowheadeianetworkmodelingapproachassent.pdf .
17. Bernarda F. and Viellec, M. (2008), GEMINI-E3, a general equilibrium model of international-national interactions between economy, energy and the environment, Computational Management Science, Vol. 5, no. 3, pp. 173-206.
18. PRIMES MODEL. Version 2 Energy System Model: Design and features. E3Mlab – ICCS. National Technical University of Athens, available at: http://www.e3mlab.ntua.gr/manuals/PRIMREFM.pdf.
19. Qi, T., Winchester, N., Zhang, D., Zhang, X. and Karplus, V.J. (2014), The China-in-Global Energy Model. Massachusetts Institute of Technology. MA, USA. Tsinghua University. Beijing, China 2014, available at: https://dspace.mit.edu/bitstream/handle/1721.1/88606/MITJPSPGC_Rpt262.pdf?sequence=1.
20. Dirkse, S., Ferris, M.C. and Munson, T. The PATH solver. University of Wisconsin, USA, available at: http://pages.cs.wisc.edu/~ferris/path.html.
21. Dirkse, S.P. and Ferris, M.C. (1995), The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems, Optimization Methods and Software, no. 5, pp. 123-156.
22. Dirkse, S.P. and Ferri, M.C. (1994), A pathsearch damped Newton method for computing general equilibria, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, USA, available at: http://pages.cs.wisc.edu/~ferris/techreports/94-03.pdf.
23. Billups, S.C., Dirkse, S.P. and Ferris, M.C. (1997), A comparison of large scale mixed complementarity problem solvers, Computational Optimization and Applications, Vol. 7, pp. 3-25.
24. Hobbs, B.F. (2001), Linear complementarity models of Nash-Cournot competition in bilateral and POOLCO power markets, IEEE Transactions on Power Systems, Vol. 16, no. 2, pp. 194-202.
25. Murphy, F. and Smeers, Y. (2007), On the impact of forward markets on investments in oligopolistic markets with reference to electricity. Part 2, Uncertain demand. Harvard Electricity Policy Group Research Paper, available at: http://www.hks.harvard.edu/ hepg/Papers/Murphy_and_Smeers_June_18_07.pdf.
26. Pineau, P.-O. (2000), Electricity market reforms: Industrial developments, investment dynamics and game modeling. Ph.D Thesis. Montreal, 2000, available at: http://www.irec.net/upload/File/memoires_et_theses/260.pdf.
27. Murphy, F. and Smeers, Y. (2005), Generation capacity expansion in imperfectly competitive restructured electricity markets, Operations Research, Vol. 53, no. 4, pp. 646-661.
28. Hobbs, B. and Helman, U. (2004), Complementarity-based equilibrium modeling for electric power markets. Modeling prices in competitive electricity markets, Series in Financial Economics, Wiley, Chichester, UK.
29. Borisenko, A.V. and Saukh, S.Ye. (2008), “Modeling of equilibrium state of electric power systems in market conditions”, Modelirovanie – 2008, Materialy mezhdunarodnoi konferentsii [Simulation-2008, Proceedings of International Conference], Kyiv, May 14-16, 2008, pp. 172-177.
30. Borisenko, A.V. and Saukh, S.Ye. (2009), “Model of market equilibrium in the electric power sector of Ukraine”, Novyny energetyky, no. 5, pp.29-44.
31. Borisenko, A.V. and Saukh, S.Ye. (2009), “Equilibrium model for the introduction of generating capacities in conditions of imperfect competition”, Novyny energetyky, no. 11, pp. 36-39; no. 12, pp. 23-39.
32. Borisenko, A.V. and Saukh, S.Ye. (2010), “Model of functioning and development of generating capacities in market conditions”, Pratsi Institutu Electrodynamiky NAN Ukrainy, Iss. 25, pp. 21-32.
33. Saukh, S.Ye. and Borysenko, A.V. (2010), Equilibrium model of Ukrainian generating capacities operation and development under market conditions, Joint Symposium Proceedings of the conferences “Energy of Russia in XXI century: development strategy” and “Eastern vector and Asian energy cooperation: what is after the crisis?”, Irkutsk: Melentiev Energy Systems Institute, SB RAS, 2010. http://isem.irk.ru/symp2010/en/papers/ENG/S3-12e.pdf.
34. Saukh, S.Ye. (2013), “Methods of computer simulation of competitive equilibrium in electricity markets”, Elektronnoe modelirovanie, Vol. 35, no. 5, pp. 11-26.
35. Energy Research Centre of the Netherlands. COMPETES input data, available at: http://www.ecn.nl/fileadmin/ecn/units/bs/COMPETES/cost-functions.xls http://www.ecn.nl/fileadmin/ecn/units/bs/COMPETES/flowgate-information.xls.
36. Saukh, S.Ye. (2015), “Method of correction of special elements in Clarke’s generalized Jacobian to ensure numerical stability of the quasi-Newton methods for solution of variational inequalities problems” Elektronnoe modelirovanie, Vol. 37, no. 4, pp. 3-18.
37. Saukh, S.Ye. (2015), “Application of incomplete column-row factorization of matrices in quasi-Newton methods for solving large-scale variational inequalities problems”, Elektronnoe modelirovanie, Vol. 37, no. 5, pp. 3-15.
38. Fischer, A. (1992), A special Newton-type optimization method, Optimization. Vol. 24, no. 3-4, pp. 269-284.
39. Facchinei, F. and Pang, J.-S. (2003), Finite-dimensional variational inequalities and complementarity problems. Vol. I, Springer Int.
40. Facchinei, F. and Pang, J.-S. (2003), Finite-dimensional variational inequalities and complementarity problems. Vol. II. Springer Int.
41. Saukh, S.Ye. (2007), “CR-factorization method for large dimensional matrices”, Elektronnoe modelirovanie, Vol. 29, no. 6, pp. 3-22.
42. Saukh, S.Ye. (2010), “Incomplete column-row factorization of matrices for solving of largescale system of equations”, Elektronnoe modelirovanie, Vol. 32, no. 6, pp. 3-14.
43. Anderson, S.C. (2004), Analyzing strategic interaction in multi-settlement electricity markets: A closed-loop supply function equilibrium model, available at: https://www.hks.harvard.edu/crump/papers/Anderson_thesis.pdf.
44. Saukh, S.Ye., Borisenko, A.V. and Dzhyigun, E.N. (2014), “Model of the network of high-voltage transmission lines in the tasks of planning of the development of power systems”, Elektronnoe modelirovanie, Vol. 36, no. 4, pp. 3-14.
45. Wei, J.-Y. and Smeers, Y. (1999), Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices, Operations Research, Vol. 47, no. 1, pp. 102-112.
46. Saukh, S.Ye. and Borisenko, A.V. (2016), “Modeling of competitive equilibrium at the electricity market with regard for energy losses in electric networks”, Problemy zagalnoi energetyky, Vol. 46, no. 3, pp. 5-11, available at: https://doi.org/10.15407/pge2016.03.005.
47. Saukh, S.Ye. (2017), “Mathematical model of the equilibrium state of the new competitive electricity market of Ukraine”, Elektronnoe modelirovanie, Vol. 39, no. 6, pp. 3-14.
48. Saukh, S.Ye. (2018), “Mathematical modeling of competitive equilibrium in electricity markets”, Visnyk NAN Ukrainy, no. 4, pp. 53-67, available at:https://doi.org/10.15407/visn2018.04.053.