Mathematical modeling of competitive equilibrium in electricity markets
According to the materials of scientific report at the meeting of the Presidium of NAS of Ukraine, February 28, 2018
DOI:
https://doi.org/10.15407/visn2018.04.053Keywords:
energy market, equilibrium state, modeling methodology, complementary problem, solver of large-scale complementary problems, computational experimentAbstract
The report analyzes world tendencies in the development of energy complexes modeling systems and the possibility of using existing systems in modern conditions of decentralized management of energy complexes. The requirements for ensuring the adequacy of energy complexes modeling systems in market conditions are formulated. A generalized mathematical model of the competitive equilibrium on the electricity market in the form of a system of nonlinear programming problems and its equivalent form — a complementary problem — is presented. On the base of computational experiments power markets modeling, significant limitations on using well-known solvers of complementary problems are identified. Original methods of solving large-scale complementary problems are presented and the advantages of the solver created on the base of such methods are shown. The particulars in the application of the modeling methodology for the construction of adequate mathematical models of energy markets and the advantages of the proposed methods for solving complementary problems are demonstrated through the test problems of modeling the equilibrium states of the electricity market of Ukraine as well as united electricity market of Benelux countries, France and Germany.
References
Jebaraja S., Iniyan S. A review of energy models. Renewable and Sustainable Energy Reviews. 2006. 10(4): 281. https://doi.org/10.1016/j.rser.2004.09.004
Connolly D., Lund H., Mathiesen B.V., Leahy M. A review of computer tools for analysing the integration of renewable energy into various energy systems. Applied Energy. 2010. 87(4): 1059. https://doi.org/10.1016/j.apenergy.2009.09.026
Amerighi O., Ciorba U., Tommasino M.C. Inventory and characterization of existing tools. D2.1 ATEsT Models Characterization Report. (Italian National Agency for New Technologies, 2010). http://www.cres.gr/atest/pdf/D_2_1_Models_Characterisation_Report.pdf
Pina A.A. Supply and Demand Dynamics in Energy Systems Modeling. PhD Thesis. (Universidade Técnica de Lisboa, 2012). https://www.mitportugal.org/about/documents/curriculum-vitae/sustainable-energy-systems/968-thesis-andrepina/file
Beeck N. Classification of Energy Models. Tech. report FEW 777. (Tilburg University & Eindhoven University of Technology, 1999). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.43.8055&rep=rep1&type=pdf
Daniels D. Overview of the National Energy Modeling System (NEMS). U.S. Energy Information Administration, 2017. https://cepl.gatech.edu/sites/default/files/attachments/NEMS%20Overview_8-31-17FINAL_0.pdf
PLEXOS® Integrated Energy Model. http://utilitiesnetwork.energy-business-review.com/suppliers/energy-exemplar/products/plexos-integrated-energy-model-ebr
PRIMES MODEL 2013–2014. Detailed model description. (E3MLab/ICCS at National Technical University of Athens). https://ec.europa.eu/clima/sites/clima/files/strategies/analysis/models/docs/primes_model_2013-2014_en.pdf
Parkkonen O. Customer benefits of Demand-Side Management in the Nordic electricity market. PhD Thesis: (Jyväskylä University School of Business and Economics, 2016). https://jyx.jyu.fi/dspace/handle/123456789/52033
NEMSIM: the National Electricity Market simulator.
http://press-files.anu.edu.au/downloads/press/p96431/mobile/ch11s08.html
Hogan W.W. Energy Policy Models for Project Independence. Computers & Operations Research. 1975. 2(3): 251. https://doi.org/10.1016/0305-0548(75)90008-8
Gabriel S.A., Kydes A.S., Whitman P. The National Energy Modeling System: A Large-Scale Energy-Economic Equilibrium Model. Operations Research. 2001. 49(1): 14. https://doi.org/10.1287/opre.49.1.14.11195
Murphy F.H., Susan J.C., Shaw S.H., Sanders R. Modeling and forecasting energy markets with the intermediate future forecasting system. Operations Research. 1988. 36(3): 406. http://www.jstor.org/stable/170984
Integrating Module of the National Energy Modeling System: Model Documentation. U.S. Energy Information Administration. 2014. https://www.eia.gov/outlooks/aeo/nems/documentation/integrating/pdf/m057(2014).pdf
Overview of the Energy and Power Evaluation Program (ENPEP-BALANCE). Center for Energy, Environmental, and Economic Systems Analysis (CEEESA). Argonne National Laboratory. https://ceeesa.es.anl.gov/pubs/61124.pdf
Nesbitt D., Calvez А. Network Agent Based modeling for EIA. 2014. https://www.eia.gov/outlooks/documentation/workshops/pdf/day_2__2_dale_nesbitt_arrowheadeianetworkmodelingapproachassent.pdf
Bernarda F., Viellec M. GEMINI-E3, a general equilibrium model of international-national interactions between economy, energy and the environment. Computational Management Science. 2008. 5(3): 173. https://doi.org/10.1007/s10287-007-0047-y
PRIMES MODEL. Version 2 Energy System Model: Design and features. E3Mlab – ICCS / National Technical University of Athens. http://www.e3mlab.ntua.gr/manuals/PRIMREFM.pdf
Qi T., Winchester N., Zhang D., Zhang X., Karplus V.J. The China-in-Global Energy Model. Massachusetts Institute of Technology. MA, USA. Tsinghua University. Beijing, China, 2014. https://dspace.mit.edu/bitstream/handle/1721.1/88606/MITJPSPGC_Rpt262.pdf?sequence=1
Dirkse S., Ferris M.C., Munson T. The PATH Solver. University of Wisconsin. http://pages.cs.wisc.edu/~ferris/path.html
Dirkse S.P., Ferris M.C. The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software. 1995. 5(2):123. https://doi.org/10.1080/10556789508805606
Dirkse S.P., Ferri M.C. A pathsearch damped Newton method for computing general equilibria. University of Wisconsin. Madison, Wisconsin, 1994. http://pages.cs.wisc.edu/~ferris/techreports/94-03.pdf
Billups S.C., Dirkse S.P., Ferris M.C. A comparison of large scale mixed complementarity problem solvers. Computational Optimization and Applications. 1997. 7(1): 3. https://doi.org/10.1023/A:1008632215341
Hobbs B.F. Linear Complementarity Models of Nash–Cournot Competition in Bilateral and POOLCO Power Markets. IEEE Transactions on Power Systems. 2001. 16(2). https://doi.org/194. 10.1109/59.918286
Murphy F., Smeers Y. On the Impact of Forward Markets on Investments in Oligopolistic Markets with Reference to Electricity. Harvard Electricity Policy Group Research Paper, 2007. Operations Research. 2010. 58(3): 515. https://doi.org/10.1287/opre.1090.0753 Part 2. Uncertain Demand. http://www.hks.harvard.edu/hepg/Papers/Murphy_and_Smeers_June_18_07.pdf
Pineau P.-O. Electricity market reforms: Industrial developments, investment dynamics and game modeling. Ph.D. Thesis. (Montreal). 2000. http://www.irec.net/upload/File/memoires_et_theses/260.pdf
Murphy F., Smeers Y. Generation capacity expansion in imperfectly competitive restructured electricity markets. Operations Research. 2005. 53(4): 646. https://doi.org/10.1287/opre.1050.0211
Hobbs B., Helman U. Complementarity-Based Equilibrium Modeling for Electric Power Markets. In: Modeling Prices in Competitive Electricity Markets. Series in Financial Economics. (Chichester, Wiley, 2004).
Borisenko A.V., Saukh S.Ye., Modeling of equilibrium state of electric power systems in market conditions. In: Simulation-2008: Proc. Int. Conf. (14-16 May, 2008, Kiev, Ukraine).
Borisenko A.V., Saukh S.Ye., Model of market equilibrium in the electric power sector of Ukraine. News of the energy complex. 2009. (5): 29.
Borisenko A.V., Saukh S.Ye. Equilibrium model for the introduction of generating capacities in conditions of imperfect competition. News of the energy complex. 2009. (11): 36. (12): 23.
Borisenko A.V., Saukh S.Ye., Model of functioning and development of generating capacities in market conditions. Works of the Institute of Electrodynamics of the National Academy of Sciences of Ukraine. 2010. 25: 21.
Saukh S.Ye., Borysenko A.V. Equilibrium model of Ukrainian generating capacities operation and development under market conditions. In: Energy of Russia in XXI century: development strategy: Proc. conf. (Irkutsk: Melentiev Energy Systems Institute, SB RAS, 2010). http://isem.irk.ru/symp2010/en/papers/ENG/S3-12e.pdf
Saukh S.Ye. Methods of computer simulation of competitive equilibrium in electricity markets. Electronic modeling. 2013. 35(5): 11.
Energy Research Centre of the Netherlands. COMPETES input data. http://www.ecn.nl/fileadmin/ecn/units/bs/COMPETES/cost-functions.xls
Saukh S.Ye. 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. Electronic modeling. 2015. 37(4): 3.
Saukh S.Ye. Application of incomplete column-row factorization of matrices in quasi-Newton methods for solving large-scale variational inequalities problems. Electronic modeling. 2015. 37(5): 3.
Fischer A. A special Newton-type optimization method. Optimization. 1992. 24(3-4): 269. https://doi.org/10.1080/02331939208843795
Facchinei F., Pang J.-S. Finite-dimensional Variational Inequalities and Complementarity Problems. Vol. 1. (Springer, 2003). https://doi.org/10.1007/b97543
Facchinei F., Pang J.-S. Finite-dimensional Variational Inequalities and Complementarity Problems. Vol. 2. (Springer, 2003). https://doi.org/10.1007/b97544
Saukh S.Ye. CR-factorization method for large dimensional matrices. Electronic modeling. 2007. 29(6): 3.
Saukh S.Ye. Incomplete column-row factorization of matrices for solving of large-scale system of equations. Electronic modeling. 2010. 32(6): 3.
Anderson S.C. Analyzing strategic interaction in multi-settlement electricity markets: A closed-loop supply function equilibrium model. (Harvard University, 2004). https://www.hks.harvard.edu/crump/papers/Anderson_thesis.pdf
Saukh S.Ye., Borisenko A.V., Jigun E.N. Model of the network of high-voltage transmission lines in the tasks of planning of the development of power systems. Electronic modeling. 2014. 36(4): 3.
Wei J.-Y., Smeers Y. Spatial Oligopolistic Electricity Models with Cournot Generators and Regulated Transmission Prices. Operations Research. 1999. 47(1): 102. http://dx.doi.org/10.1287/opre.47.1.102
Saukh S.Ye., Borisenko A.V. Modeling of competitive equilibrium at the electricity market with regard for energy losses in electric networks. The Problems of General Energy. 2016. 46(3): 5.
