ARTICLE IN PRESS

Energy Policy 36 (2008) 2983– 2994

Contents lists available at ScienceDirect

Energy Policy

0301-42

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/enpol

Compromises in energy policy—Using fuzzy optimization in an energysystems model

Dag Martinsen a,�, Volker Krey b

a Forschungszentrum Julich, Institute of Energy Research, Systems Analysis and Technology Evaluation (IEF-STE), 52425 Julich, Germanyb International Institute for Applied Systems Analysis (IIASA), Energy Program (ENE), Schlossplatz 1, A-2361 Laxenburg, Austria

a r t i c l e i n f o

Article history:

Received 12 February 2008

Accepted 9 April 2008Available online 2 June 2008

Keywords:

Energy model

Fuzzy optimization

Energy policy compromise

15/$ - see front matter & 2008 Elsevier Ltd. A

016/j.enpol.2008.04.005

esponding author. Tel.: +49 2461613587; fax

ail address: d.martinsen@fz-juelich.de (D. Ma

a b s t r a c t

Over the last year in Germany a great many political discussions have centered around the future

direction of energy and climate policy. Due to a number of events related to energy prices, security of

supply and climate change, it has been necessary to develop cornerstones for a new integrated energy

and climate policy. To supplement this decision process, model-based scenarios were used. In this paper

we introduce fuzzy constraints to obtain a better representation of political decision processes, in

particular, to find compromises between often contradictory targets (e.g. economic, environmentally

friendly and secure energy supply). A number of policy aims derived from a review of the ongoing

political discussions were formulated as fuzzy constraints to explicitly include trade-offs between

various targets. The result is an overall satisfaction level of about 60% contingent upon the following

restrictions: share of energy imports, share of biofuels, share of CHP electricity, CO2 reduction target and

use of domestic hard coal. The restrictions for the share of renewable electricity, share of renewable

heat, energy efficiency and postponement of nuclear phase out have higher membership function

values, i.e. they are not binding and therefore get done on the side.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Over the last year in Germany a lot of political discussions havecentered on the future direction of energy and climate policy.Several events, such as the currently exceedingly high oil prices,recent disruptions of the short-term gas and oil supply fromRussia and the release of the IPCC’s 4th assessment report, havedrawn attention to both issues. As a result, at its meeting in March2007 the European Council laid the foundations for an integratedEuropean climate and energy policy (European Council, 2007).Also, despite opposition from some countries, the G8 Summitat Heiligendamm in June 2007 made reference to the globalchallenge of climate change and the related topics of energyefficiency and security (G8, 2007). On the national level, the 3rdenergy summit (Energiegipfel) in July 2007 produced the basis foran integrated energy and climate policy framework (Bundesre-gierung, 2007c). Finally, the federal government’s closed sessionmeeting in Meseberg in late August 2007 resulted in thepublication of cornerstones for a new integrated energy andclimate program, defining ambitious goals in this area (Bundesre-gierung, 2007a, b).

ll rights reserved.

: +49 2461612540.

rtinsen).

Energy systems models are frequently used to aid scenarioanalysis and to provide quantitative information about possiblefuture development pathways in the energy sector (see forexample the scenario for the German energy summit (EWI/Prognos, 2007)). Although it has a number of drawbacks, linearprogramming (LP) is still the standard methodology used in large-scale energy systems models (e.g. MARKAL (Fishbone et al., 1983;Loulou et al., 2004), TIMES (Loulou et al., 2005), MESSAGE(Messner et al., 1996; Messner and Strubegger, 1995)). Amongthe frequently criticized characteristics of LP models is the factthat the optimal solution strongly depends on a limited number ofbinding constraints, whose numerical specification often lacks theprecision needed to justify this strong influence. The so-called softconstraints, based on fuzzy sets, can remedy this drawback andincrease the applicability of LP to real-world problems (cf. e.g.(Rommelfanger, 1996)). Examples of applications of fuzzy LP toenergy systems models can be found for example in Canz (1998),Oder et al. (1993).

We introduce fuzzy constraints to obtain a better representa-tion of political decision processes, in particular, to find compro-mises between often contradictory targets (e.g. economic,environmentally friendly and secure energy supply). In addition,some of the targets formulated by policy makers apparently pushin the same direction; as for instance, a minimum share of rene-wables and GHG emission reduction. Fuzzy linear optimization

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D. Martinsen, V. Krey / Energy Policy 36 (2008) 2983–29942984

means that fuzzy aspiration levels are assumed for each of thetargets. The main idea then is to maximize ‘‘total satisfaction’’, i.e.maximize a minimum operator for the set of targets. Thisapproach results in a solution being some kind of compromise.

The paper is organized as follows: Section 2 gives a briefintroduction to the IKARUS energy systems model and themethodological extension that we use in this paper, i.e. theimplementation of fuzzy constraints. In Section 3 we outlinethe general scenario setup, concentrating on key drivers, such asdevelopment of GDP, population, employment and transportdemand. In addition, the soft constraints are parametrized onthe basis of political targets recently discussed among decisionmakers. Section 4 contains the results of the fuzzy optimizationprocedure. We focus on the differences from and advantages overLP with crisp restrictions. Finally, we summarize our main resultsand provide concluding remarks in Section 5.

2. The IKARUS energy systems model

2.1. Model structure

In order to examine the interaction of numerous politicaltargets, we employ the bottom-up IKARUS model (Martinsen etal., 2003, 2006). The IKARUS model is a time-step dynamicallinear optimization model mapping the energy system of theFederal Republic of Germany in the form of cross-linked processesfrom primary energy supply to energy services (Fig. 1). All relevantsectors with a detailed representation of the technological optionsare included, characterized by their corresponding specific

Oil productimports

Primary energy

Coalimports

Nuclear fuel import

Energy conversion and transport

Crude Oilimports

Renewablesources

Coal extraction

Natural gasimports

Decentralisedco-

generation

Centralised co-

generation

Natural gasextraction

Power plants

Transport/Distrtibution

Renewable

Nuclea

Gas

Electricity

Distric

Coal

Crude oil

Light fuel oil

GasolineDiesel and kerosine

TraDis

TraDist

Import of electricity

Refinery

CoalConversion

Fig. 1. Structure of the IKARU

emissions and costs as well as possible networks of energy fluxes.Demands for energy services are the driving forces of the model,and equilibria are formed on various intermediate conversionlevels (partial equilibrium model). In addition, general politicalset-ups are considered (e.g. phase-out of nuclear power inGermany, coal subsidies).

The model’s time horizon extends to 2030 and is divided into5-year intervals. Each time interval is optimized by itself, takinginto account past events by the heritage due to results from allprevious periods in a separate dynamic program module. Incontrast to the more common class of perfect-foresight energysystems models, such as MARKAL (Fishbone et al., 1983; Loulouet al., 2004), TIMES (Loulou et al., 2005) or MESSAGE (Messneret al., 1996; Messner and Strubegger, 1995), the time-step model ismyopic and does not take into account future changes in eachoptimization step. It is therefore a model with a more realisticcharacter of prognosis and projection.

Recent model applications include lifetime extensions fornuclear power plants (Hake et al., 2005), the analysis of carboncapture and storage (CCS) as a mitigation option for Germany(Martinsen et al., 2007b) and the impacts of high oil prices onenergy-economy strategies (Martinsen et al., 2007a).

2.2. Implementation of fuzzy sets

In the following section we provide a very brief descriptionof the implementation of the fuzzy constraints that we used inthe present analysis. For technical details, the interested readeris referred to the extensive literature on fuzzy optimization.

End use sectors

ProductionIndustry

Non-energy consumpt.

Households

Transportand traffic

Smallconsumers

t heating

nsport/trtibution

nsport/rtibution

Housing space

Number of Employees

Passenger and freight

transport capacities

Demand

Demand for raw materials

S energy systems model.

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Table 1Comparison of generic crisp and fuzzy LP

Conventional (crisp) LP Fuzzy LP

MIN z ¼ Cx Cx ~p~z

s:t: Axpb Ax ~p ~b ðincluding some crisppÞ

xX0 xX0

1

0bi

µi

(Ax)ibi +di

Fig. 2. Example of a membership function mi.

D. Martinsen, V. Krey / Energy Policy 36 (2008) 2983–2994 2985

A comprehensive review of fuzzy LP and its applications is e.g.provided by Rommelfanger (1996).

Table 1 contains a comparison of a generic LP and its fuzzyversion as we applied it. We restrict ourselves to fuzzy right-handsides and therefore obtain the simplest form of a fuzzy linearprogram as first discussed by Zimmermann (1975). The crisp LP inTable 1 includes the total sytems costs z, C is the vector ofcost coefficients, x represents the decision variables, A is thetechnology matrix and b the vector of right hand sides. In thefuzzy version, the crisp right-hand sides are (partly) replaced byfuzzy right-hand sides ~b and ~z.

Our main objective is to obtain a better representation of thepolitical decision processes; in particular, to find compromisesbetween often contradictory, but sometimes also collinear targets.In our application, fuzzy linear optimization means assumingfuzzy aspiration levels for each of the aims. As illustrated in Fig. 2,the membership function has a value of 1 if the fuzzy constrainedlinear combination of variables (Ax)i is below the boundary bi andvalue 0 if (Ax)i is larger than a threshold bi+di. For simplicity, welinearly interpolate between these two levels, although in generalpiece-wise linear interpolation can be used to obtain a differentshape of membership function (cf. e.g Rommelfanger (1996)).Total system costs z, which are typically used as the objectivefunction in energy systems models, should also be included in theset of membership functions to obtain a fuzzy constraint ~z.Otherwise, solutions of the original crisp LP and the fuzzy versionare not comparable, because system costs would not matter forthe fuzzy solution.

Subsequently, the problem is transformed into a crisp‘‘satisfaction model’’ by using membership functions mi(x) forthe fuzzy constraints. The main idea is to maximize ‘‘totalsatisfaction’’, i.e. maximizing a minimum operator for the set ofmembership functions mi(x). The equivalent crisp LP can bewritten as

MAX l

s:t: lpmi

mi ¼1di

bi þ di � ðAxÞi� �

(Rommelfanger, 1996), where l is the total satisfaction andtherefore the new objective function, and the index i includes allmembership functions. The total satisfaction variable l has to berestricted to the interval [0,1], i.e. constraints 0plp1 have to beincluded. In addition, the crisp part of the original LP remainsunchanged. This approach results in a solution which is some kindof compromise, if total satisfaction l is larger than 0, but smallerthan 1. It can also be interpreted as a multi-objective optimizationsystem (Rommelfanger, 1996).

3. Scenario definition

In the political decision process, many aims are formulatedthat are partly complementary, but which partly also contracteach other. In the scenarios, we therefore adopt the followingprocedure: the general scenario setup, including energy prices,economic growth, behavioral patterns and, correspondingly, theevolution of demands for energy services, will be treated in thetraditional way, i.e. they will be implemented as crisp restrictions.On the other hand, policy aims are formulated as fuzzy constraintsto explicitly include trade-offs between various targets. Thisapproach allows us to find compromises between these aims.

3.1. General scenario setup

The consistent socio-economic data on which the scenarios arebased were compiled as part of the IKARUS project (Markewitzand Stein, 2003). In contrast to the former model applications, weconcentrate on development up to 2020, because most targets inthe political discussion are formulated for this time horizon. As faras economic development is concerned, a GDP growth of 1.9%/a(2000/2010) to 1.7%/a (2010/2020) is assumed. Accordingly, theevolution of the industrial gross value added shows a real increasein all industrial sectors, however, to a different extent in differentindustries. The demographic trend is assumed to be in agreementwith the 2nd variant of the population development of the FederalStatistical Office (destatis, 2000). Population decreases from about82 million today to approx. 80 million over the next 15 years.Whereas the number of employees and residential floor space willnot change a lot, the demand for transportation increasessignificantly. The demand for passenger transport increases fromabout 1054 billion passenger kilometers (pkm) in 2000 to 1160billion pkm in the year 2020. Far more drastic is the increase infreight transport from about 491 billion ton kilometers (tkm) inthe base year 2000 to about 728 billion tkm in 2020, correspond-ing to a rise of almost 50% (IFEU, 2005). A more detaileddescription of all the assumed demands and general data can befound in Martinsen et al. (2006).

Besides limitations on quantities of domestic and importedenergy carriers like coal, lignite and natural gas, other restrictionsbased on domestic potentials for fossil and renewable energycarriers and the political framework set by the Federal Govern-ment are present in the model. In recent applications of theIKARUS model (Hake et al., 2005; Martinsen et al., 2007a, b) thesehave been modeled as crisp bounds, but will be treated as fuzzyconstraints in the scenarios presented in the present paper.

3.2. Fuzzy constraints

Among the energy-related policy targets currently beingdiscussed in Germany are emission reduction targets, security ofsupply, employment of renewables in electricity and heat gene-ration, application of biofuels, subsidies for domestic hard coaland decommissioning of existing nuclear power plants. Table 2

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Table 2Important targets in energy and climate policy (BMU, 2007; Bundesregierung, 2000, 2005, 2007a, b; Bundestag, 2002, 2006; EWI/Prognos, 2007; Wodopia, 2007)

Indicator Type State (2005) Target Acceptable

Energy imports Share of TPES 73.7% 60% 73.7%

Renewable electricity Share of tot. electricity 10.4% 30% 20%

Renewable heat Share of heat production 5.4% 14% 10%

Biofuels Share of transport fuels 3.7% 17% 8%

CHP electricity Share of tot. electricity 12.5% 25% 13%

Energy efficiency (GDP/TPES) Rel. 1990 level 124% 200% 171%

CO2 emissions Rel. 1990 level �17% �40% �30%

Domestic hard coal Absolute (PJ) 740 352 0

Nuclear energy Lifetime (a) 32 32 40

D. Martinsen, V. Krey / Energy Policy 36 (2008) 2983–29942986

lists these indicators derived from recent political discussionsalong with the type of target (share, relative change with respectto some base year, absolute target), the current state for the year2005 as well as the targeted value and a minimally acceptablevalue for 2020. On the other hand, economic implications ofmeasures/targets are often criticized by the energy industry, aswell as the ministry of economics. Hence, the total system costshave also been included in the set of fuzzy restrictions.

Relatively easy to determine are the targets related to renew-able energy carriers. By 2020 it is aimed to supply 30% ofelectricity generation, 14% of heat generation and 17% of transportfuels from renewable sources (Bundesregierung, 2007a). Electri-city production from CHP (target: 25% by 2020) also falls into thiscategory (Bundesregierung, 2007a). In general, much harder toderive are acceptable levels as these are typically not published.Therefore, we either determine the acceptable level by lawsalready in force (e.g. share of biofuels: 8% by 2015 (Bundestag,2006)) or by the current deployment level (e.g. CHP electricity). Incase of renewable electricity generation we fix the acceptablelevel at the earlier target of 20% as defined in the coalitionagreement of 2005 (Bundesregierung, 2005).

A lot of discussion has centered around the emission target for2020, ranging from a reduction of 30% to 40% with respect to 1990levels (BMU, 2007), partly depending on the commitments of theEuropean Union as a whole and on the outcome of a post-Kyotoprocess (e.g. (Gabriel, 2007)). The more ambitious 40% reductiontarget is used as the target level throughout this paper, whereasthe 30% reduction, being the fallback solution in case othercountries do not make a similar commitment, has been adopted asthe acceptable level.

The aim is to significantly improve energy efficiency by 2020.With respect to 1990, energy efficiency, defined as gross domesticproduct per unit of total primary energy consumption (GDP/TPES),is supposed to double by 2020. The lower acceptable improve-ment of 171% is derived by keeping TPES constant at the 2005level, whereas GDP develops as described in Section 3.1. Althoughthis target is well defined, there are ambiguities due to differentaccounting frameworks for total primary energy supply. Ascommonly done in German energy statistics, we use the physicalenergy content method (OECD/IEA/Eurostat, 2005). However, inparticular, the German situation with its targeted transition awayfrom nuclear energy towards a higher share of renewables cancreate distortions which should be kept in mind when interpret-ing the results (Lightfoot, 2007).

In the case of domestic hard coal, the situation is settled until2012, when a review of policy objectives is scheduled. It then willbe decided whether to completely phase out domestic hardcoal extraction by 2018 or whether to keep a minimum level(‘‘Sockelbergbau’’) of around 12 Mtce (�350 PJ) per annum in thelong run (Wodopia, 2007). Therefore, we adopt the 350 PJ per yearas the target value and take the phase out (0 PJ) as still acceptable.

In some cases, it is difficult to actually derive numerical valuesfrom the political debates, which stresses once again the need toapply fuzzy techniques to deal with these issues. For the importshare of TPES, we chose the current level as a lower acceptablelimit and ideally would reduce it to 60% of TPES in 2020. The lattercorresponds to the lowest value achieved in the set of scenariosanalyzed by EWI/Prognos in preparation for the energy summit inJuly 2007 and is therefore adopted as the target level (EWI/Prognos, 2007).

The phase-out of nuclear power is determined by theremaining amount of electricity produced in nuclear powerstations (Bundesregierung, 2000). However, this translates fairlywell into a shut-down of nuclear power stations after 32 years ofoperation, whereas the design lifetime is usually estimated tobe 40 years. Therefore, we define the target to be compliant withthe phase-out agreement and an acceptable relaxation to extendthe average lifetime by 8 years, i.e. from 32 to 40 years, thusincreasing the permissible electricity generation from nuclearpower.

To estimate the acceptable range of costs, we adopt thefollowing method. Two scenarios with crisp bounds are analyzed,one adopting the more stringent values from Table 2, i.e. the targetvalues. This scenario is referred to as the ‘‘UP’’ scenario. Thesecond scenario, called the ‘‘LO’’ scenario, uses the relaxed boundvalues from the table, specifying the still acceptable level of theindicators. The first scenario is, of course, more expensive andtherefore determines the maximum acceptable cost level,whereas the relaxed scenario reflects the costs that one ideallyis willing to pay. The compromise between those two scenariosis the scenario formulated with fuzzy constraints, named‘‘FUZZY’’.

Due to methodical and structural reasons, some of the targets(shares) in Table 2 are split into subtargets and specified asabsolute values in the model. This is mainly done to avoiditerations.

4. Scenario results

With the dynamic IKARUS bottom-up model, we performedcalculations for the period 2000–2020 for the crisp scenarios LOand UP as well as for the FUZZY scenario where targets andminimum values were defined in a manner similar to Table 2.

Fig. 3 shows the development of total primary energy supply(TPES), final energy consumption and CO2 emissions for the threescenarios as compared to the reference year 2000, i.e. the modelcalibration year. The decline of all indicators up to 2020 isnoticeable, especially for the UP scenario. Whereas the drop ofTPES, final energy and CO2 in this scenario are 20%, 13% and 30%(40% as compared to 1990), respectively; the corresponding valuesfor the LO scenario are 9%, 5% and about 18% (30% as compared to

ARTICLE IN PRESS

TPES

10000

10500

11000

11500

12000

12500

13000

13500

14000

14500

15000

2000 2005 2010 2015 2020

PJ

Final Energy

8000

8200

8400

8600

8800

9000

9200

9400

9600

9800

10000

2000 2005 2010 2015 2020

PJ

LO

UP

FUZZY

CO2 Emissions

600

650

700

750

800

850

900

2000 2005 2010 2015 2020

Mt

Fig. 3. Dynamics of TPES, final energy and CO2 emissions in LO, UP and FUZZY scenarios.

D. Martinsen, V. Krey / Energy Policy 36 (2008) 2983–2994 2987

1990). The results for the FUZZY scenario stay—as expected—

between the lines for the crisp scenarios giving a decay of about15%, 8% and 25% for TPES, final energy and CO2 emissions between2000 and 2020. However, the results for the FUZZY scenario arenot to be confused with trivial interpolations between the LO andUP scenarios (as can also be seen in Fig. 3). This type ofinterpolation would not normally give a consistent scenario dueto the interweaving dependencies in the model and it wouldcertainly not represent a maximum satisfaction in the sense offuzzy membership functions.

As stressed above, system costs are the main limiting factorwhen searching for a compromise scenario because if very highcosts were tolerated any optimal scenario could be accepted. Fig. 4illustrates the additional annual costs as compared to the LOscenario which is the scenario with preferential or minimumcosts. On the left side of the figure, annual costs for the period2005–2020 are shown as well as the cumulated costs. In the UPscenario, additional cumulated costs from 2005 to 2020 add up toabout 116 billion h, whereas additional costs for the FUZZYscenario are considerably less, amounting to 51 billion h, i.e. thecost saving as compared to the expensive UP scenario is 65 billionh. The right-hand side of Fig. 4 shows the structure of costs forthe year 2020. In the FUZZY scenario there are additional costs(7.8 billion h/a) in most of the sectors as compared to the LOscenario, especially in the sectors of conversion (power plants,CHP) and transport. When compared to the UP scenario, theFUZZY results for 2020 show considerable cost savings (11.3billion h/a) particularly in the residential, transport and conver-sion (CHP) sectors.

The extra costs for primary energy supply shown in Fig. 4(about 2 billion h/a in 2020 for FUZZY—LO and close to zero forFUZZY-UP) are total net additional costs. Of special interest are,however, the structural changes of costs for primary energysupply, which have positive and negative terms for domestic aswell as for imported energy carriers.

Table 3 illustrates the manifold changes in costs for primaryenergy for the FUZZY scenario in 2020. In comparison with the LOscenario there are higher expenses for domestic carriers (1.8billion h mainly for hard coal and biomass) and for importedbioethanol, oil products and natural gas. These additional importcosts are practically compensated by cost savings for importedhard coal, crude oil and to a minor extent nuclear fuels, givingtotal additional costs of about 2 billion h/a. As compared to the UPscenario, there is virtually no net cost difference. This might atfirst be surprising, however, Table 3 shows large differences fordifferent energy carriers. First of all, there is a net saving fordomestic primary energy (coal and renewables) in the order of 2.8billion h. At the same time, there are net additional costs in thesame order for imported energy carriers. Higher costs forimported coal, crude oil and natural gas therefore arise, whereasthere is a cost reduction for the import of oil products, bioethanoland electricity.

In the following, we will discuss the most important results forCO2 emissions, primary energy, the electricity sector and finalenergy. On doing so we will concentrate on the year 2020, whichis the year of the main policy targets for the energy economy inGermany. Attention will be focused on the FUZZY scenario ascompared to the LO and UP scenarios.

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Annual costs 2005 - 2020

0

2

4

6

8

10

12

14

16

18

20

2005

Bill

ion

€/a

Cost Saving:

Cumulated

65 Billion €

Additional Costs:

Cumulated

51 Billion €

FUZZY - UP

FUZZY - LO

Structure of costs 2020

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

Bill

ion

€/a

TransportResidence

SmallconsumersIndustry

Processing

Gas distribution

Refinery

CHP

Power plants

Primary energy

NetFUZZY - LO(Additional

Costs)

FUZZY - UP(Cost

Saving)2010 2015 2020

Fig. 4. Evolution of annual additional costs (left) and structure of annual additional costs in 2020 (right).

Table 3Changes of costs for primary energy in 2020

Million h/a FUZZY-LO FUZZY-UP

Domestic Import Domestic Import

Lignite +65 0 �224 0

Hard coal +946 �1995 �650 +718

Crude oil 0 �740 0 +3789

Oil products 0 +527 0 �2202

Gas 0 +489 0 +2259

Electricity 0 �813

Nuclear 0 �251 0 +65

Biomass +493 0 �614 0

Rapeseed oil +263 0 0 0

Bioethanol 0 +2256 �974 �951

Biogas 0 0 �376 0

Net +1767 +286 �2839 +2866

Total +2053 +27

D. Martinsen, V. Krey / Energy Policy 36 (2008) 2983–29942988

Fig. 5 shows the membership function values (MFVs) in 2020for the fuzzy constraints in Table 2, i.e. the degree of satisfactionfor the different scenario indicators. Among the 10 indicators, 6 ofthem—primary energy import share, biofuels, CHP electricity, CO2

emissions, use of domestic hard coal and system costs—aresettled at the value corresponding to the objective function value,i.e. the maximization of the smallest MFV, of about 0.6 (satisfac-tion level of 60%). These indicators therefore represent thestrongest restrictions limiting the total satisfaction, whereas theindicators of renewable electricity, renewable heat, the ratio ofGDP to TPES and the use of nuclear power have values between0.8 and 1. The higher satisfaction level of the latter indicators cantherefore be interpreted as a ‘‘spin-off’’ from the 6 bindingconstraints.

The compromise values of the fuzzy indicators correspondingto Table 2 can easily be calculated by interpolation betweentarget—and acceptable values using the MFV in Fig. 5. Anexception is the value for renewable heat where the target ismore than fulfilled. In this case the model shows a share of about15% of renewables to heat production (target 14%).

A central aspect of future energy supply and an important topicin energy policy is the emissions of greenhouse gases, in particularCO2. In these calculations we did not consider CCS technologiessince they are not likely to play any substantial role withinthe time frame of our calculations, i.e. up to 2020. Fig. 6 shows theshare of sectors for CO2 emissions in 2020 (left side) and thecorresponding differences between the FUZZY scenario and the LOrespectively UP scenario (right-hand side with a magnificationfactor of 10). In the FUZZY scenario the emissions of CO2 in2020 are about 60 million tons lower than in the LO scenario.More than half of the reduction is reached in the conversion sector(nearly 35 Mt) where power plants contribute the most (about24 Mt), but end-use sectors (about 26 Mt) also add a substantialamount to the cutback of CO2 in particular in the residential(8.5 Mt) and transport sector (9.6 Mt). In comparison to theUP scenario, the FUZZY optimization shows a surplus ofabout 40 Mt CO2. This is of course part of the compromise in theFUZZY scenario. The additional CO2 is mainly emitted in the end-use sectors (35 Mt or 86%), whereas the differences in theconversion sector are relatively small, i.e. the compromise forCO2 is mainly accepted in the end-use sectors where measures forCO2 reduction are generally more expensive than in the conver-sion sector.

The corresponding changes in the share of energy carriers inTPES are demonstrated in Fig. 7. TPES in the FUZZY scenario isabout 950 PJ or 7% lower than in the LO scenario and about 650 PJor 5.5% higher than in the UP scenario. The use of hard coal isconsiderably less (�920 PJ of imported hard coal) than in the LO

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00.10.20.30.40.50.60.70.80.9

1Primary energy import

Renewables electricity

Renewables heat

Biofuels

CHP electricity

GDP/TPES

CO2

Domestic hard coal

Costs

Nuclear

Objective function:

Max (Min MFVi) = 0.595

Fig. 5. Membership function values (MFV) for the fuzzy indicators in 2020.

0

200

400

600

800

Mt

-80

-60

-40

-20

0

20

40

60

80

Mt

Primary energy Power plants

CHP Refinery

Gas distribution Processing

Industry Small consumers

Residence Transport

Net

LO FUZZY UP

FUZZY-LO

FUZZY-UP

Fig. 6. CO2 emissions in 2020.

D. Martinsen, V. Krey / Energy Policy 36 (2008) 2983–2994 2989

scenario and somewhat greater (+260 PJ) than in the UP scenario.Due to less enhanced energy savings in the end-use sectors in theFUZZY scenario as compared to the UP scenario, the use of naturalgas is higher in the FUZZY calculation (+540 PJ). The use ofrenewables is about 530 PJ higher than in the LO scenario with anincrease of biomass (+320 PJ) followed by bioethanol (+110 PJ) andwind (+80 PJ) and somewhat less than in the UP scenario(�280 PJ). The extraction of domestic lignite (for example toreduce the share of imports in TPES) is considerably lower (270 PJ

or about 18%) than in the UP scenario where the mining of ligniteis at the upper bound. In the LO scenario, we assumed aprolongation of 8 years for the lifetime of nuclear power plantsto be the maximum value tolerated. The actual extension oflifetime in the FUZZY scenario is on the average only 1.6 years, i.e.the use of nuclear fuels is much lower in this scenario ascompared to the LO scenario.

This is also illustrated in Fig. 8, showing the structure ofelectricity production.

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0

5000

10000

15000

PJ

-3000

-2000

-1000

0

1000

2000

3000

PJ

Hard coal Lignite

Others Oil

Gas Electricity

Renewables Nuclear

Net

LO FUZZY UP

FUZZY-LO

FUZZY-UP

Fig. 7. Total primary energy supply in 2020.

-100

0

100

200

300

400

500

600

TWh

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

TWh

Imports Nuclear Lignite

Hard coal Oil Gas

Hydro Wind PV

Auxilliary CHP Net

LO FUZZY UP

FUZZY-LO

FUZZY-UP

Fig. 8. Electricity production in 2020.

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Whereas total electricity production (TEP) does not differ verymuch among the scenarios (less than 20 TWh or 4%), there aresome important changes in the share of different power plants inoverall electricity production. As already seen for the TPES, theuse of nuclear power plants drops from LO via FUZZY to UP,having a share of 22%, 11% and 8%, respectively, in 2020 in TEP.These changes are even more pronounced for hard coal powerplants whose share decreases from 19% in the LO scenario to

6% in the FUZZY scenario. In the UP scenario, hard coal powerplants will not be used at all, i.e. the annual load will drop tozero. To compensate for the reduction of electricity from nuclearand hard coal power plants, the use of lignite, wind and CHP(mainly based on biomass) increases from LO to UP. Electricityproduction from natural gas power plants is higher in theFUZZY scenario than in both LO and UP scenarios. This is anexample of the fact that a simple interpolation between LO and UP

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would lead to a non-optimal compromise and even inconsistentresults.

Contrary to TEP, there is an increase of total installed capacityfrom LO to FUZZY and UP (Fig. 9). This is due to a decline of theaverage annual load of public utilities because of the extension ofwind converters and a decrease of load for hard coal power plants(from 4900 h/a in the LO scenario, 1500 h/a in the FUZZY scenarioand to 0 h/a in the UP scenario). Installed capacity needed in theFUZZY scenario is nearly 16 GW higher than in the LO scenario;however, it is about 9 GW lower than in the UP scenario. Thechanges of the structure of net installed capacity are shown in theright-hand part of Fig. 9.

Besides the noticeable changes in the conversion sector, thereare also important differences in the end-use sectors whencomparing LO, FUZZY and UP scenarios (Fig. 10). First of all, thereare increased savings of final energy in the FUZZY and UPscenarios as compared to the LO scenario. Whereas savings inthe FUZZY scenario are rather modest (300 PJ or about 3%), thereduction of final energy in the UP scenario is close to 800 PJ ornearly 9%. Fig. 10 shows that there are energy savings in allsectors, especially in the residential sector. Contrary to the UPscenario, in the FUZZY scenario the changes in the transport sectorare very small as compared to the LO scenario. The relativechanges in the FUZZY scenario as compared to the LO or UPscenario can be seen in each sector: industry �4.7% and +4.8%,small consumer �3.8% and +8.2%, residential �4.5% and +9.8% andtransport �0.9% and. +3.0%, respectively.

In the following discussion we will show as an example thedifferent results in the residential and transport sector.

For the residential sector (Fig. 11), there are mainly additionalmeasures for thermal insulation of buildings in the FUZZY andespecially in the UP scenario. In the FUZZY scenario thesemeasures are taken for old buildings within the renovation cycle,which are less expensive than measures outside the renovationcycle. In the UP scenario, more expensive measures for thermalinsulation are also chosen by the model outside of the renovationcycle in addition to better isolation of new buildings. This results

in a smaller demand for natural gas in the FUZZY scenario ascompared to the LO scenario, but a higher demand as compared tothe UP scenario. The share of fuel oil for heating purposes showsminor changes because the use of heating oil drops considerablyeven in the LO scenario in the period 2005–2020 and is part of alower limit describing rural areas where a distribution of gas (ordistrict heat) is not profitable. There is a relatively small (about50 PJ or 20%) increase of district heat in the FUZZY scenario,mainly replacing natural gas in apartment buildings.

Fig. 12 illustrates the share of energy carriers in the finalenergy consumption of the transport sector. To sum up, one maysay that the total final energy consumption is nearly scenario-independent (showing a variation of maximum 3–4%). However,there is a shift of energy carriers towards alternative fuels (likebioethanol for cars) replacing gasoline (�130 PJ or �12% and�250 PJ or �23%) in the FUZZY and UP scenario, respectively,together with improvements in car engines. In addition, truckswith higher efficiency engines replace conventional trucks in theUP scenario (but not in the FUZZY scenario), giving rise to amoderate saving of diesel (�4%) in relation to the LO scenario.

5. Summary and conclusions

The introduction of fuzzy constraints in a bottom-up energysystem model gives a better representation of political decisionprocesses in the energy economy and energy policy than aqualitative examination. It can help policy makers find compro-mises between often contradictory targets and to focus theirefforts on the most relevant indicators, thus avoiding to overloadthe debate with too many issues. In addition, some of the targetsformulated by policy makers apparently push in the samedirection, as for instance a minimum share of renewables andGHG emission reduction.

Fuzzy linear optimization was carried out assuming fuzzyaspiration levels for each of the targets. The main idea was tomaximize ‘‘total satisfaction’’, i.e. to maximize a minimum

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Fig. 11. Final energy demand in the residential sector in 2020.

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operator for the set of targets in order to find a solution which issome kind of compromise. In the scenarios we adopted thefollowing procedure:

The general scenario setup, including energy prices, economicgrowth, behavioral patterns and, correspondingly, the evolution ofdemands for energy services and demands (although highlyuncertain) was treated in the traditional way, i.e. they wereimplemented as crisp restrictions. On the other hand, policyaims were formulated as fuzzy constraints to explicitly include

trade-offs between various targets. This approach allowed us tofind compromises between political aims.

Another advantage of such a quantitative method is the abilityto reproduce results and calculate different scenarios withdifferent boundary conditions. It further separates targets whichhave opponent effects from targets pushing in the same directionand makes the dependencies of targets more transparent. Besidesdetermining the set of values for the fuzzy targets, i.e. the degreeof satisfaction within the compromise, the conciliated solution

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Fig. 12. Final energy demand in the transport sector in 2020.

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(FUZZY scenario) also shows the impact on emissions, costs andstructure of energy supply and demand in different sectors whencompared to crisp scenarios with exact target values (UP scenario)and crisp scenarios where the minimally acceptable values arefixed (LO scenario).

The results shown above do not claim to represent an in-depthanalysis of energy-related decision processes. However, they arean example using targets of current interest with up-to-datevalues for Germany. We thus demonstrate the utilization of fuzzyoptimization for a typical problem using fuzzy restrictions for 10quantities that have been intensively discussed over the past fewyears, with increasing intensity in the last year.

The result is an overall satisfaction level of about 60%contingent upon the following restrictions: share of energyimports, share of biofuels, share of CHP electricity, CO2 reductiontarget and use of domestic hard coal in addition to extra costs. Therestrictions for the share of renewable electricity, share ofrenewable heat, energy efficiency (relation GDP/TPES) and post-ponement of nuclear phase-out have higher MFVs, i.e. they getdone on the side. This raises the question whether it is necessaryto define so many targets which do not provide any added value,but might lead to the implementation of suboptimal solutions. Onthe other hand, market inefficiencies, which are not covered bythe model, could require additional guidance to assure that themost central targets are reached.

For the important indicators TPES and CO2 emissions, theFUZZY scenario shows values in 2020 closer to the UP scenariothan to the LO scenario, whereas final energy is closer to the LOscenario—showing a certain preference for measures in theconversion sector as compared to end-use sectors. As a result,costs of primary energy supply turn out to be almost identical inthe FUZZY and UP scenarios, since more expensive supply optionsin the UP scenario are compensated by reduced total primaryenergy supply. There is also a considerable saving of costs(65 billion h in the period from 2005 to 2020) in the FUZZYscenario as compared to the target scenario UP (with additionalcosts of 116 billion h compared to the LO scenario).

A typical compromise solution features lower shares ofdomestic lignite and renewables within TPES, but higher sharesof imported natural gas, hard coal and nuclear fuels as comparedto the UP scenario. Despite the lower share of renewables thiswould imply a reduction of CO2 emissions relative to the UPscenario. However, as energy saving is less dominant in the FUZZYscenario there is a net increase of CO2 emissions compared to theUP scenario. On the other hand, there is also a net decrease ofsystem costs due to a renouncement of rather expensive measuresfor energy saving in the end-use sectors. The trade-off betweenimport share, renewables, CO2 emissions and costs is an interest-ing example for the ability to find compromises in fuzzycalculations.

Similar trade-offs can also be found within the electricitysector. As the model (partly) refrains from extending the lifetimeof nuclear power plants, additional capacities for lignite- and gas-fired power plants are built to replace nuclear power. In order tocompensate for the increase of CO2 emissions caused by thissubstitution, the annual load of existing hard coal power plants isreduced considerably and new wind turbines and CHP plants arebuilt leading to an increase of installed capacity for the FUZZY andUP scenarios as compared to the LO scenario, whereas TEP staysnearly constant. The result is an increase of costs for power plantsand CHP of approximately 2.7 billion h/a in the FUZZY scenarioand 5.1 billion h/a in the UP scenario in 2020 as compared to theLO scenario. This balance between postponement of nuclear phaseout, surplus capacity, CO2 emissions and costs in electricitygeneration is another aspect of compromise solutions extractedfrom our calculations.

The process of determining the fuzzy constraints from politicaldiscussion processes has shown that it is not easy and sometimesanything but unambiguous to fix parameters and therefore hasunderlined the need to apply soft or fuzzy instead of crispconstraints that might have an unjustifiably strong impact on theoptimal solution.

In our further work we intend to include more fuzzy quantitiesand extend the fuzzy method to also include uncertainties in

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demand for energy services, future prices of energy carriers andtechnology attributes like costs and efficiencies. Also sensitivity ofresults with respect to the impact of threshold values and shape ofmembership functions need to be investigated.

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