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From system cost minimization to sustainability maximization – a new fuzzy program approach to energy systems analysis. (English) Zbl 1284.90113

Summary: The transformation of existing energy systems into sustainable energy systems is a task which is related to several of the most urgent global problems, e.g. security of energy supply, shortage of resources, and climate change. Energy system modeling has played an important role in the computation of optimal possible future energy systems. In particular, technology oriented bottom-up energy system models have given insight into the required evolution of the energy technology mix. In face of the discussion about climate change, energy systems analysis has focused on the calculation of cost minimal energy futures subject to greenhouse gas mitigation paths, especially CO2 mitigation paths. IKARUS-LP is a model of the German energy system which has been used for optimization tasks of this type. As CO2 mitigation covers only one facet of sustainability, IKARUS-LP has been enhanced to optimize the German energy system for various sustainability targets specified by energy indicators for sustainable development. The resulting model is a fuzzy linear program, IKARUS-FLP. It computes an optimal compromise between the partly contradictory sustainability targets and system cost minimization. In this paper we introduce this model. Emphasis is given to the derivation of the crisp equivalent of the fuzzy problem. We show that a context-based semantics of fuzzy constraints is not adequate and found our semantics on the fuzzy extension principle. In a real-world case study for a time horizon until 2030 the mitigation path approach of IKARUS-LP and the sustainability optimization approach of IKARUS-FLP are compared. The results prove the feasibility of our new approach and its usefulness.

MSC:

90C90 Applications of mathematical programming
90C05 Linear programming
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] Bellman, R.; Giertz, M., On the analytic formalism of the theory of fuzzy sets, Inf. Sci., 5, 149-156 (1973) · Zbl 0251.02059
[2] Bellman, R. E.; Zadeh, L. A., Decision-making in a fuzzy environment, Manage. Sci., 17, B-141-B-164 (1970)
[3] Coley, D., Energy and Climate Change—Creating a Sustainable Future (2008), Wiley
[4] Dubois, D.; Prade, H., Fuzzy Sets and SystemsTheory and Applications (1980), Elsevier
[5] Dubois, D.; Prade, H., Ranking fuzzy numbers in the setting of possibility theory, Inf. Sci., 30, 183-224 (1983) · Zbl 0569.94031
[6] Dubois, D., Linear programming with fuzzy data, (Bezdek, J. C., Analysis of Fuzzy InformationApplications in Engineering and Science, vol. III (1987), CRC Press: CRC Press Boca Raton, FL), 241-263
[8] Føyn, T. H.Y.; Karlsson, K.; Balyk, O.; Grohnheit, P. E., A global renewable energy system: a modelling exercise in ETSAP/TIAM, Applied Energy, 88, 2, 526-534 (2011)
[10] Haas, R.; Nakicenovic, N.; Ajanovic, A.; Faber, T.; Kranzl, L.; Müller, A.; Resch, G., Towards sustainability of energy systemsa primer on how to apply the concept of energy services to identify necessary trends and policies, Energy Policy, 36, 4012-4021 (2008)
[11] Hake, J.-F.; Markewitz, P.; Martinsen, D.; Vögele, S.; Walbeck, M., Mögliche Auswirkungen einer Laufzeitverlängerung deutscher Kernkraftwerke, Energiewirtschaftliche Tagesfragen, 55, 785-788 (2005)
[19] Inuiguchi, M.; Ramik, J., Possibilistic linear programminga brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets Syst., 111, 3-28 (2000) · Zbl 0938.90074
[20] Keppo, I., Short term decisions for long term problems—the effect of foresight on model based energy systems analysis, Energy, 35, 2033-2042 (2010)
[21] Klir, G. J.; Yuan, B., Fuzzy Sets and Fuzzy Logic—Theory and Applications (1995), Pearson · Zbl 0915.03001
[22] Lai, Y.-J.; Hwang, C.-L., Fuzzy Mathematical Programming (1992), Springer-Verlag
[23] Löschel, A.; Moslener, U.; Rübbelke, D. T.G., Energy security—concepts and indicators, Energy Policy, 38, 1607-1608 (2010)
[24] Löschel, A.; Moslener, U.; Rübbelke, D. T.G., Indicators of energy security in industrialised countries, Energy Policy, 38, 1665-1671 (2010)
[27] Ludwig, B., On the sustainability of future energy systems, Energy Convers. Manage., 38, 1765-1775 (1997)
[29] Martinsen, D.; Markewitz, P.; Müller, D.; Vögele, S.; Hake, J.-F., IKARUS - Energieszenarien bis 2030, (Markewitz, P.; Stein, G., Das IKARUS-ProjektEnergietechnische Perspektiven für Deutschland (2003), Forschungszentrum Jülich: Forschungszentrum Jülich Jülich)
[30] Martinsen, D.; Krey, V.; Markewitz, P.; Vögele, S., A time-step energy process model for Germany—model structure and results, Energy Stud. Rev., 14, 35-57 (2006)
[31] Martinsen, D.; Krey, V.; Markewitz, P., Implications of high energy prices for energy system and emissions—the response from an energy model for Germany, Energy Policy, 35, 4504-4515 (2007)
[32] Martinsen, D.; Linssen, J.; Markewitz, P.; Vögele, S., CCSA future \(\operatorname{CO}_2\) mitigation option for Germany? a bottom-up approach, Energy Policy, 35, 2110-2120 (2007)
[33] Martinsen, D.; Krey, V., Compromises in energy policy—using fuzzy optimization in an energy systems model, Energy Policy, 36, 2983-2994 (2008)
[35] Messner, S.; Golodnikov, A.; Gritsevskii, A., A stochastic version of the dynamic linear programming model MESSAGE III, Energy, 21, 775-784 (1996)
[36] Oder, C.; Haasis, H.-D.; Rentz, O., Analysis of the Lithuanian final energy consumption using fuzzy sets, Int. J. Energy Res., 17, 35-44 (1993)
[37] Ramik, J.; Vlach, M., Fuzzy mathematical programminga unified approach based on fuzzy relations, Fuzzy Optim. Decision Making, 1, 335-346 (2002) · Zbl 1079.90621
[38] Rommelfanger, H.; Keresztfalvi, T., Multicriteria fuzzy optimization based on Yager’s parametrized t-norm, Found. Comput. Decision Sci., 16, 99-110 (1991) · Zbl 0814.90130
[39] Rommelfanger, H., Fuzzy Decision Support-Systeme - Entscheiden bei Unschärfe (1994), Springer: Springer Berlin · Zbl 0795.90001
[40] Rommelfanger, H., Fuzzy linear programming and applications, Eur. J. Oper. Res., 92, 512-527 (1996) · Zbl 0914.90265
[41] Rommelfanger, H.; Slowinski, R., Fuzzy linear programming with single or multiple objective functions, (Slowinski, R., Fuzzy Sets in Decision Analysis, Operations Research and Statistics (1998), Kluwer Academic Publishers) · Zbl 0944.90048
[42] Rommelfanger, H., A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values, Fuzzy Sets Syst., 158, 1892-1904 (2007) · Zbl 1137.90766
[45] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning—Part 1, (Yager, R. R.; Ovchinnikov, S.; Tong, R. M.; Nguyen, H. T., Fuzzy Sets and ApplicationsSelected Papers by L.A. Zadeh (1975), John Wiley & Sons), 219-269
[46] Zadeh, L. A., Toward a generalized theory of uncertainty (GTU)—an outline, Inf. Sci., 172, 1-40 (2005) · Zbl 1074.94021
[47] Zadeh, L. A., Is there a need for fuzzy logic?, Inf. Sci., 178, 2751-2779 (2008) · Zbl 1148.68047
[48] Zhao, L.; Feng, L.; Hall, C. A.S., Is peakoilism coming?, Energy Policy, 37, 2136-2138 (2009)
[49] Zimmermann, H.-J., Fuzzy Sets Decision, Making and Expert Systems (1987), Kluwer Academic Publishers
[50] Zimmermann, H.-J., Fuzzy Set Theory and its Applications (1990), Kluwer Academic Publishers: Kluwer Academic Publishers Boston
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