Applied Energy 91 (2012) 245–254

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Applied Energy

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Multicriteria synthesis of trigeneration systems considering economicand environmental aspects

Monica Carvalho ⇑, Miguel A. Lozano, Luis M. SerraGroup of Thermal Engineering and Energy Systems (GITSE), Aragon Institute of Engineering Research (I3A), Department of Mechanical Engineering,Universidad de Zaragoza, Zaragoza, Spain

a r t i c l e i n f o a b s t r a c t

Article history:Received 4 May 2011Received in revised form 23 August 2011Accepted 20 September 2011Available online 19 October 2011

Keywords:Multicriteria optimizationTrigenerationCO2-emissionsEco-indicator 99Life Cycle Assessment

0306-2619/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.apenergy.2011.09.029

⇑ Corresponding author.E-mail address: carvalho@unizar.es (M. Carvalho).

The necessity of considering the environment as an additional design factor arises due to increasing envi-ronmental conscience worldwide and stricter requirements to reduce the environmental impact ofenergy systems. Designing such systems very often involves conflicting objectives as eco-friendly tech-nologies are usually more expensive. This paper considers simultaneously economic and environmentalcriteria in the synthesis of a trigeneration system to be installed in a hospital. Synthesis includes optimalconfiguration (commercially available equipment) and optimal operation throughout the year. The mul-tiobjective optimization accounts for minimization of total annual cost and CO2 emissions released in theatmosphere, as well as the Eco-indicator 99 (EI-99) in order to broaden environmental considerations inthe impact assessment. A Pareto frontier, set of solutions representing optimal trade-offs between theeconomic and environmental objectives, is obtained from the solution of a Mixed Integer Linear Program-ming (MILP) model. Two bicriteria problems were solved using the MILP model: (1) annual cost (€/yr)versus CO2 emissions (kg CO2/yr) and (2) annual cost (€/yr) versus EI-99 Single Score (points/yr). The Par-eto solutions consist of optimal configurations that adapt their operational strategy during a specificrange in the Pareto frontier. Solutions are compared and it is observed that some configurations are morestable along the Pareto frontier, and that significant reductions in economic cost can be attained if theenvironmental impact is partially compromised. After the judgment of the solutions obtained and thetrade-offs involved, one ultimate configuration is selected, which presents a flexible range of adaptabilityin the economic/CO2 and economic/EI-99 optimizations.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

A transition to alternative energy systems is presently in thespotlight, propelled by concerns on global warming caused bygreenhouse gas emissions and dependence on depleting fossil fuelreserves. This transition will certainly involve meeting the futureenergy demand considering, among others, environmental impactsand greater efficiency of energy production and usage. Polygener-ation systems have important socio-economical and environmen-tal benefits related to its efficient use of energy resources andthe enhanced economic competitiveness of the products obtained[1,2].

Polygeneration is defined as the concurrent production of twoor more energy services and/or manufactured products that, bene-fiting from the energy integration of the processes in its equip-ment, extracts the maximum thermodynamic potential of theresources consumed. The residential-commercial sector is an en-ergy-intensive consumption sector requiring different energy ser-

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vices, in which polygeneration systems are very suitable to beimplemented. The residential-commercial sector includes residen-tial buildings, office buildings, hotels, restaurants, shopping cen-ters, schools, universities and hospitals, among others. Hospitalsare good candidates for trigeneration systems because of their highenergy requirements (heat for sanitary hot water and space heat-ing, cooling and electricity) compared to other commercial build-ings as well as their need for high power quality and reliability.Moreover, in many temperate climate zones of the world, as it isthe case of Mediterranean countries, the need for heating in build-ings is restricted to a few winter months, limiting the applicationof cogeneration systems thus far. However, there is a significantneed for cooling during the summer period, as well as some otherperiods of the year requiring heating and cooling simultaneously.By combining cogeneration and heat-driven absorption chillers,the energy demand covered by cogeneration could be throughoutthe year, covering electricity, heating and cooling loads via trigen-eration [3,4].

Energy demands in buildings depend on climatic conditions,architectonic features, and occupancy. The optimal configurationfor a polygeneration system remains a complex problem throughout

Nomenclature

AA ambient airC costCfix fixed cost (equipment) (€/yr)Cope variable cost (operation) (€/yr)Ctot total annual cost (€/yr)CG natural gasCGWH hot water boilerCGVA steam boilerCI capital cost of a piece of equipmentCO2 (followed by subscript) CO2 emissions associated with the

subscriptCO2e emissions associated with electricity (kg CO2/kW h)CO2fix fixed emissions (equipment) (kg CO2/yr)CO2g emissions associated with natural gas (kg CO2/kW h)CO2ope variable emissions (operation) (kg CO2/yr)CO2tot total annual emissions (kg CO2/yr)CO2I CO2 emissions associated with the construction of a unit

of equipmentD demand of a utilityEd electricity demand of the hospitalEp electricity purchased from the grid (MW)Es electricity sold to the grid (MW)EE electricityEI-99 Eco-indicator 99Fg consumption of natural gas (MW)fam amortization and maintenance factor (yr�1)fame environmental amortization factor (yr�1)FAVA double effect absorption chillerFAWH single effect absorption chillerFMWR mechanical chilleri utilityICWH hot water–cooling water heat exchangerICWR cooling towerICVA steam–cooling water heat exchanger

ISO International Organization for Standardizationj technologyL loss of a utilityLCA Life Cycle AssessmentLCI Life Cycle InventoryLCIA Life Cycle Impact AnalysisMGWH gas engineMILP Mixed Integer Linear ProgrammingNIN number of pieces of equipment installedP purchase of an utilitypep purchase price of electricity (€/kW h)pes sale price of electricity (€/kW h)pg purchase price of natural gas (€/kW h)Pnom nominal power (MW)Qd heat demand (SHW + heating) of the hospitalRd cooling demand of the hospitalS sale of a utilitySHW sanitary hot waterSS (followed by subscript) Eco-indicator 99 Single Score associ-

ated with the subscriptSSe environmental loads associated with electricity

(points/kW h)SSfix fixed environmental loads (equipment) (points/yr)SSg environmental loads associated with natural gas

(points/kW h)SSope variable environmental loads (operation) (points/yr)SStot total annual environmental loads (points/yr)SSI Eco-indicator 99 Single Score associated with the

equipmentTGVA gas turbineVA high temperature steamWC chilled waterWH hot waterWR cooling water

246 M. Carvalho et al. / Applied Energy 91 (2012) 245–254

the years in the residential-commercial sector, because of the widevariety of technology options for the provision of energy services,great diurnal and annual fluctuations in energy consumption, andtemporal variations in energy prices. In recent years, the analysisand design tools for energy systems have undergone importantdevelopments.

Particularly, the synthesis and design of cogeneration and tri-generation systems in the residential-commercial sector has be-come increasingly elaborate, with numerous possibilities forenergy sources and technological options. The synthesis of trigen-eration systems implies searching for a design that minimizes ormaximizes an objective function, such as economic cost, environ-mental load, or thermodynamic efficiency. Ortiga et al. [5] pre-sented a review on the optimization techniques that have beenused so far for building applications. The search process is boundby the system’s model, which is expressed by equality and inequal-ity mathematical restrictions. The design methodology must pro-vide systems that produce energy services efficiently, are capableof adapting to different economic markets and demand conditions,and operate optimally [6].

Although there are many technical options to develop sustain-able and eco-friendly energy supply systems, the question is thatthe minimization of costs and environmental burdens are usuallycontradictory objectives, as it is often expensive to utilize environ-mentally friendly technologies. Multiobjective optimizations tacklethe issue of conflicting objective functions (such as environmentand economy), finding a ‘balanced’ optimal solution. Environmen-tal constraints are expected to play a more and more important

role in the energy supply systems, besides the economic objective[7].

Focusing on the criteria adopted to the design of trigenerationsystems in the residential–commercial sector, a purely economicstandpoint has been taken by the majority of optimization studies[8–13]. Environmental concerns have been a growing issue whenplanning energy supply systems. The need to consider the environ-ment as an additional design factor arises due to an ever-increasingenvironmental conscience worldwide and stricter requirements toreduce the environmental impact of modern society. A purely envi-ronmental viewpoint has also been the focus of optimization stud-ies specifically targeting polygeneration in buildings [14–19].

Nowadays, environmental issues are becoming increasinglyimportant and the operation problem becomes more challengingwhen the environmental burdens should be minimized at the sametime when costs, too, are to be minimized [7]. In general, the con-figuration and operating conditions of a system yielding the besteconomy are pushed into a range where environmental loads arehigher than the least otherwise possible. Reviews and consider-ations on methods for multicriteria decision-making for energysupply systems can be found in [20–22], with specific applicationsto cogeneration systems in [23,24]. Regarding trigeneration sys-tems, Wang et al. [17] presented a multicriteria operational opti-mization for a residential building in China, consideringtechnological and economical aspects. Kavvadias and Maroulis[25] carried out an optimization of the operation of a trigenerationsystem in a hospital in Greece, considering economical and envi-ronmental aspects. Liu et al. [26] applied a multiobjective mixed

M. Carvalho et al. / Applied Energy 91 (2012) 245–254 247

integer nonlinear programming approach to the optimal design ofpolygeneration energy systems in a supermarket. Costs and CO2

emissions were utilized in the operational optimization of the tri-generation system accomplished by Ren et al. [7] at a universitycampus in Japan. Although the situation of trigeneration systemsproviding energy services to the residential-commercial sector iscommon, there is a lack of detailed studies on multicriteria consid-erations and most existing studies concentrate on operationaloptimization.

Research on the optimal synthesis of energy supply systemswhile considering conflicting objectives has not been fully con-fronted. In addition, the resiliency of some configurations with re-spect to the trade-off relationship between economic andenvironmental performances is uncertain and must be investigatedto a greater extent.

This paper proposes an integrated energy-planning frameworkbased on Mixed Integer Linear Programming (MILP) to determinethe optimal configuration and operation of a trigeneration systemto be installed in a hospital located in Zaragoza, Spain. A multiob-jective optimization procedure will be presented, consideringsimultaneously the total annual cost and total annual environmen-tal loads (CO2 emissions or Eco-indicator 99 points) involved in thedesign and operation of trigeneration systems. Besides the impor-tance of optimal system sizing and dispatch strategy determina-tion, it is essential to provide useful insights on the synthesis of asystem based on commercially available equipment. All equipmentconsidered herein is commercially readily-available, which furtherenriches the applicability of results.

2. Trigeneration system

2.1. Demand

This paper considers a medium size hospital with 500 beds, lo-cated in Zaragoza (Spain). The energy demands considered wereheat, cooling, and electricity. The heat load included heat forsanitary hot water (SHW) and for heating. Steam demand couldalso have been considered, to attend laundry and sterilizationnecessities. However, the current trend is to eliminate such a ser-

Fig. 1. Superstructure of the

vice, subcontracting an external company, and for this reasonsteam demand was not considered in this investigation.

In order to establish the energy demands for the hospital, astudy period of 1 year was considered, distributed in 24 represen-tative days (one working day and one holiday/weekend day foreach month), each day being divided into 24 hourly periods. En-ergy demand patterns for each representative day were calculatedaccording to the procedure described by Sánchez [27], which esti-mated demand profiles for the representative days based on thesize of the hospital and its geographical location in Spain. Theannual electricity consumption of the hospital was 3250 MW h,the cooling demand was 1265 MW h, and the heat requirements(SHW + heating) were 8059 MW h.

2.2. Superstructure

The synthesis of an energy supply system’s configuration beginswith the creation of a superstructure, which must include all feasi-ble process options and connections, based on appropriate processintegration. Heat integration methodologies are particularly pow-erful tools that should be included in the synthesis of trigenerationsystems. Ryan [28] presents considerations on heat recovery, selec-tion of the best absorption chiller type and configurations foroptimal integration. Simulation of the main components of a trigen-eration system and a fast and interactive way to design optimalheat integrated schemes using commercial equipment data is pre-sented in Teopa et al. [29].

The superstructure must include all features that are potentiallypart of an optimal solution, even if presented in a redundant man-ner. After the optimization process, the superstructure is reducedto an optimal configuration. The superstructure shown in Fig. 1 isproposed considering potential technologies for installation, avail-able utilities and interactions between utilities and technologies.Potential technologies have been selected based on a previous de-tailed analysis of energy generation technologies commerciallyavailable today, considering its suitability for the considered appli-cation: common technologies used in the residential–commercialsector, the energy loads of the different energy demands as wellas their features, i.e. quantity, temperature levels, demand profiles.

energy supply system.

Table 1Selected equipment and matrix of production coefficients.

Technology i Selected equipment Utility j

Cost CI (103 €) Nominal power Pnom (MW) CG VA WH WR AA WC EE

TGVA 1 530 1.21 �4.06 +1.83 +0.53 +1MGWH 435 0.58 �2.45 +0.96 +0.20 +1CGVA 182 0.78 �1.20 +1CGWH 30 0.57 �1.08 +1ICVA 2.5 0.40 �1.00 +1ICWH 6.5 0.40 �1.00 +1FAVA 370 1.26 �0.83 +1.83 +1 �0.01FAWH 200 0.49 �1.50 +2.50 +1 �0.01FMWR 175 0.49 +1.23 +1 �0.23ICWR 25 1.00 �1.00 +1 �0.02

248 M. Carvalho et al. / Applied Energy 91 (2012) 245–254

Technical production coefficients of equipment were evaluatedprior to the inclusion in the superstructure.

The available utilities were: CG (natural gas), VA (saturatedsteam, 180 �C), WH (hot water, 90 �C), WR (cooling water,t0 + 5 �C), AA (ambient air, t0), WC (chilled water, 5 �C), and EE (elec-tricity). D, S, P and L refer to, respectively, demand, sale, purchaseand waste/loss of a utility. The designer must include some or allof the following technologies: TGVA (gas turbine + heat recoveryboiler, producing steam and hot water), MGWH (gas engine + hotwater heat recovery system), CGVA (steam boiler), CGWH (hotwater boiler), ICVA (steam–hot water heat exchanger), ICWH (hotwater–cooling water heat exchanger), FAVA (double effect absorp-tion chiller, driven by steam), FAWH (single effect absorption chil-ler, driven by hot water), FMWR (mechanical chiller, driven byelectricity and cooled by water), and ICWR (cooling tower, to evac-uate the heat from the cooling water to the ambient air).

2.3. Technical and economic data

Table 1 depicts the selected equipment and technical produc-tion coefficients for the superstructure.

The rows contain potential technologies for installation and thecolumns contain the utilities. The production coefficient with a va-lue in bold shows the flow that defines the equipment’s capacity.Positive coefficients indicate that the utility is produced, whilenegative coefficients indicate the consumption of such utility. Tak-ing MGWH technology in Table 1 as an example, electricity is themain product as its coefficient is 1. To produce 1 MW of electricity(EE), 2.45 MW of natural gas (CG) will be consumed, recuperating0.96 MW of hot water (WH), and evacuating 0.20 MW of heat tocooling water (WR). Consequently, the electrical efficiency ofMGWH is 1/2.45 (�41%). As all technology and equipment consid-ered in the optimization were commercially available, the size/configuration of the system was determined in terms of pieces ofequipment. This criterion has been applied because the installationof several pieces of equipment of the same technology presentsadvantages in the case of the residential-commercial sector, e.g.(i) it facilitates the coverage of the highly variable – both dailyand seasonally – energy demands with high efficiency, (ii) the en-ergy supply availability is higher in case of a failure of a piece ofequipment and (iii) there are advantages in terms of maintenance,which can be programmed for periods when energy demands arelower and some pieces of equipment are not in operation. The datashown in Table 1 was obtained from equipment catalogs andconsultations with manufacturers. For each piece of equipment,Pnom(i) is the nominal power of the equipment selected of technol-ogy i, and CI(i) was its investment cost the obtained from catalogprices and multiplied by a simple module factor that took intoaccount aspects such as transportation and installation.

In the case of natural gas in Spain, the consumer chooses themost adequate rate for the consumption volume and supply pres-

sure. This investigation considered a constant purchase cost ofpg = 0.025 €/kW h for natural gas [30], which includes taxes andthe distribution of fixed costs throughout the estimated annualconsumption.

Considering other costs such as taxes, and approximating thedistribution of fixed costs, an electricity purchase price of pep =0.095 €/kW h for off-peak hours, and pep = 0.130 €/kW h for on-peak hours was considered [31]. For the sale of surplus cogenerat-ed electricity, the tariff and premium depend on the power outputand fuel utilized by the plant. Considering the energy demand ofthe hospital and the nominal power of the cogeneration modules(cogeneration installations using natural gas, 1000–10,000 kWcapacity), the price for sold electricity was pes = 0.077 €/kW h [32].

2.4. Environmental data

Life Cycle Assessment (LCA) provides a comprehensive view ofthe environmental aspects of a product or process and a pictureof the true environmental trade-offs in product and process selec-tion [33]. LCA analyzes the environmental impacts associated witha process or product from the cradle to the grave, which begins withthe gathering of raw materials from the earth to create the prod-uct/service and ends at the point when all materials are returnedto the earth [34]. A framework for LCA has been standardized bythe International Organization for Standardization (ISO) in theISO 14040 series. This LCA framework consists of the following ele-ments: (1) Goal and Scope definition, which specifies the goal andintended use of the LCA and delineates the assessment (systemboundaries, function and flow, required data quality, technologyand assessment parameters); (2) Life Cycle Inventory analysis(LCI), which includes the collection of data on inputs and outputsfor all processes in the product system; (3) Life Cycle ImpactAssessment (LCIA), which translates inventory data on inputs andoutputs into indicators about the product system’s potentialimpacts on the environment, human health, and availability ofnatural resources; and (4) Interpretation, the phase where theresults of the LCI and LCIA are interpreted according to the goalof the study and where sensitivity and uncertainty analysis areperformed to qualify the results and conclusions. SIMAPRO [35]is a specialized LCA tool and was utilized to calculate the impactassociated with the configuration (equipment) and operation ofthe system.

CO2 emissions were selected to quantify the environmentalloads because global heating and the associated climate changeare one of the main medium- and long-term identified threats,with great consequences on a global scale [36].

The Eco-indicator 99 method was included to broaden environ-mental considerations in the impact assessment, being selectedbecause it is widely used in LCA, incorporating relevant environ-mental burdens into different impact categories that allow theevaluation of damages to human health, ecosystem quality, and

Table 2Technologies, main material composition, CO2 emissions, and EI-99 Single Score.

Technology Main material composition(kg)

CO2I(kg CO2)

SSI(points)

TGVA 9080 kg steel, 500 kg aluminum 80,500 8700MGWH 5700 kg steel 37,350 4030CGVA 1000 kg cast iron, 1850 kg steel, 50 kg

aluminum15,810 1420

CGWH 850 kg steel, 25 kg aluminum 3050 205ICVA 360 kg stainless steel 2350 251ICWH 760 kg stainless steel 5010 532FAVA 3700 kg iron alloy, 10,044 kg steel 98,600 11,100FAWH 9000 kg steel 58,900 5890FMWR 20 kg aluminum, 2000 kg steel, 500 kg

copper, 1000 kg PVC85,420 3130

ICWR 3500 kg steel, 1605 kg PVC 23,530 2990

M. Carvalho et al. / Applied Energy 91 (2012) 245–254 249

resources. The EI-99 method considers the values of eleven impactcategories, which are added into three damage categories,weighted, and then aggregated into an index (the Single Score) thatrepresents the overall environmental load in points [37]. The high-er the EI-99 Single Score, the higher the environmental impact ofthis component/process along its operational life. The Hierarchistperspective (H/H) of the EI-99 was selected for the damage modelherein because of its balanced time perspective, as a consensusamong scientists determined inclusion of environmental effects[37].

Table 2 summarizes the technologies and their associated mainmaterial composition, CO2 emissions, CO2I, and the Single Scoreobtained by applying EI-99, SSI.

The CO2 emissions associated with the consumption of naturalgas in Spain were calculated as CO2g = 0.272 kg CO2 per kWh ofconsumed natural gas (related emissions of burning natural gasand total aggregated system inventory for a user in Spain). TheEI-99 Single Score obtained was SSg = 0.0378 points per kW h con-sumed for natural gas.

The Spanish electricity mix in Spain in 2007 considered the pro-portions [38]: 25.8% Coal, 24.4% Natural gas in combined cycle,19.7% Nuclear, 9.4% Eolic, 9.4% Hydraulic, 11.3% Others (biomass,cogeneration, minihydraulic, etc.). The average CO2 emissions asso-ciated with the electricity mix were calculated as CO2e = 0.385 kgCO2 per kWh consumed. The EI-99 Single Score obtained wasSSe = 0.0226 points per kW h consumed for the Spanish electricitymix.

The reader is referred to Carvalho [39] for more details on envi-ronmental data.

3. Optimization model and single optimization solutions

The issue to be solved consists of selecting the optimal combi-nation of technologies. Specifically, selecting the type of technol-ogy and installed power that meets the energy demands set bythe building and establishing the operational mode for the in-stalled technologies for each defined time period of the year.

An optimization model was built based on mixed integer linearprogramming and its solution provides the means for selecting themost convenient configuration and operation modes. The modelrepresented the superstructure, considering all possible configura-tion and operation options as well as particular circumstances(such as demand and tariffs).

The functional unit (reference to all inputs and outputs of thesystem) was the production of energy services during 1 year (yr)of operation (8760 h) of the trigeneration plant.

A first objective function was introduced into the model to con-sider the economic aspect of the energy supply system installed interms of the total annual cost Ctot (in €/yr), which minimized

equipment and fuel costs as well as purchase/sale of energyservices.

MinCtot ¼ Cfix þ Cope ð1aÞ

The annual capital cost of the equipment Cfix was expressed by

Cfix ¼ famX

i

NINðiÞCIðiÞ ð2aÞ

where NIN(i) and CI(i) were, respectively, the number of pieces ofequipment installed and the capital cost of each piece of equipmentinstalled for technology i. According to current conditions in Spain,an amortization and maintenance factor fam = 0.23 yr�1 wasconsidered.

Considering that the year was divided into days, which were inturn subdivided into hours, (d,h) represented the hth hour of thedth day. The annual operation cost Cope associated with the opera-tion of the system was expressed by

Cope ¼X

d

X

d

pgFgðd; hÞ þ pepðd;hÞEpðd;hÞ � pesEsðd;hÞ� �

ð3aÞ

Fg was the consumption of natural gas, and Ep and Es were theamount of electricity purchased and sold, respectively.

The first environmental objective function considered was tominimize the total annual carbon dioxide emissions (CO2tot), whichincluded the annual fixed emissions of the equipment (CO2fix) andthe annual operation emissions (CO2ope) associated with operationof the system.

MinCO2tot ¼ CO2fix þ CO2ope ð1bÞ

The annual fixed emissions of the equipment was expressed by

CO2fix ¼ fame

X

i

NINðiÞCO2IðiÞ ð2bÞ

where CO2I(i) is the environmental emissions of CO2 required toproduce each piece of equipment installed for technology i. Theenvironmental amortization factor fame represents the share of glo-bal environmental impact throughout the system’s lifetime and wasconsidered equal to 0.10 yr�1.

The annual emissions of CO2 due to the operation of the systemwas expressed by

CO2ope ¼X

d

X

h

½CO2gFgðd;hÞ þ CO2eEpðd;hÞ � CO2e Esðd;hÞ� ð3bÞ

The second environmental objective function was to minimizethe EI-99 Single Score, which evaluated global environmental im-pact (considering human health, ecosystem quality, and consump-tion of resources). This score considered the total annual impact(SStot), including the annual fixed impact of the equipment (SSfix)and the annual operation impact (SSope) associated with the oper-ation of the system. Eqs. (1)–(3) were changed to

MinSStot ¼ SSfix þ SSope ð1cÞ

The annual fixed impact of the equipment (CO2fix) was ex-pressed by

SSfix ¼ fame

X

i

NINðiÞSSIðiÞ ð2cÞ

And the annual impact due to the operation of the system wasexpressed by

SSope ¼X

d

X

h

½SSg Fgðd;hÞ þ SSe Epðd;hÞ � SSe Esðd;hÞ� ð3cÞ

Operation was subject to capacity limits, production restric-tions, and balance equations, which were presented in Lozanoet al. [40]. The economic objective function considered the eco-nomic aspect of the energy supply system installed in terms of

Table 3Results for the economic optimal, CO2 optimal, and Eco-indicator 99 optimal.

System composition Economic optimal CO2 optimal EI-99 optimal

Installed power Number Installed power Number Installed power Number

MGWH gas engines 1739 kW 3 0 0CGWH hot water boilers 1710 kW 3 3420 kW 6 3420 kW 6ICWH heat exchangers WH ? WR 1600 kW 4 0 0FAWH Single effect absorption chillers 490 kW 1 0 0FMWR mechanical chillers 1470 kW 3 1960 kW 4 1960 kW 4ICWR cooling towers 3000 kW 3 3000 kW 3 3000 kW 3

Natural gas (total) (MW h/yr) 37,324 8703 8703Purchased electricity (MW h/yr) 29 3572 3572Sold electricity (MW h/yr) 11,389 – –Natural gas (cogeneration) (MW h/yr) 36,638 – –Cogenerated work (MW h/yr) 14,954 – –Cogenerated useful heat (MW h/yr) 8602 – –Primary energy savings (%) 10.01 – –Equivalent electrical efficiency (%) 55.22 – –Cost of equipment (€/yr) 510,830 219,650 219,650Cost of natural gas (€/yr) 933,092 217,582 217,582Cost of electricity (€/yr) 3207 366,951 366,951Profit with the sale of electricity (€/yr) �876,960 – –Total annual cost (€/yr) 570,169 804,184 804,184Emissions of equipment (kg CO2/yr) 52,699 43,057 43,057Emissions of natural gas (kg CO2/yr) 10,152,037 2367,296 2367,296Emissions of electricity (kg CO2/yr) 11,168 1375,264 1375,264Avoided emissions/sale electricity (kg CO2/yr) �4384,799 – –Total annual emissions (kg CO2/yr) 5831,105 3785,617 3785,617Single Score of equipment (points/yr) 3908 2272 2272Single Score of natural gas (points/yr) 1410,835 328,984 328,984Single Score of electricity (points/yr) 656 80,730 80,730Avoided Single Score/sale electricity (points/yr) �257,393 – –Total annual Single Score (points/yr) 1158,005 411,986 411,986

250 M. Carvalho et al. / Applied Energy 91 (2012) 245–254

the total annual cost (in €/yr), which minimized equipment andfuel costs as well as purchase/sale of energy services. The environ-mental objective functions minimized the total annual environ-mental load, which included the annual fixed load of theequipment and the annual operation load associated with opera-tion of the system. The complete optimization model can be foundin Carvalho [39].

Once the scenario was completely defined by the optimizationmodel and conditions previously specified (energy demands, eco-nomic and environmental data), the following results were ob-tained. The model was solved by LINGO v13.0 [41], with freeselection of technologies and minimizing the different objectivefunctions considered. Each single-objective MILP problem involves78,536 total variables, 1172 integer variables and 62,985 con-straints, with a CPU solution time of 33 s on an Intel� Core™ i7of 2801 MHz processor with a 8 GB memory size. Table 3 showsthe results for the optimization of annual CO2 emissions, EI-99 Sin-gle Score, and the total annual cost.

Surprisingly, the configuration obtained for the optimal CO2 andEI-99 Single Score was the same and suggested the installation of‘‘conventional’’ equipment, including hot water boilers, mechanicalchillers, and cooling towers.

Economic optimization suggested the installation of ‘‘non-con-ventional’’ equipment: cogeneration modules and one absorptionchiller. The system took advantage of the lower purchase cost ofnatural gas and achieved profit by selling cogenerated electricityto the electric grid.

4. Multiobjective optimization

In the case of multiple objectives, a unique solution to the prob-lem in general does not exist, because most often the best solutionfor one objective is not the best for others. Therefore, there usually

exists a set of solutions for the multiple-objective case, which can-not simply be compared with each other. For such solutions, calledPareto optimal solutions or non-dominated solutions, no improve-ment is possible in any objective function without sacrificing atleast one of the other objective functions. Additional informationon the fundamentals on Pareto optimization can be found in[42–46].

Pareto optimization has been extensively applied in the litera-ture concerned with multi-criteria problems, and many methodsare available for solving multiobjective optimization problems[47]. Some methods involve converting the multiobjective probleminto a series of single objective optimization problems. An impor-tant question is the role of the decision maker in solving the mul-tiobjective problem. Generating methods with a posteriori analysisof Pareto fronts are preferred [48]. Among them, the 2-constrainthas been applied by various authors to the optimization of energysupply systems [49–51].

The design task is posed as a bicriteria (economic and environ-mental) programming problem, which can be expressed as

Min fðxÞ ¼ ff1ðxÞ; f2ðxÞg ð4Þ

The solution to this problem is given by a set of efficient or Par-eto optimal points representing alternative process designs, eachachieving a unique combination of environmental and economicperformances. The 2-constraint method is based on formulatingan auxiliary model for the calculation of the Pareto points, whichis obtained by transferring one of the objectives of the originalproblem to an additional constraint. This constraint imposes anupper limit on the value of the secondary objective. The problemis repeatedly solved for different values of 2 to generate the entirePareto set; it is a relatively simple technique, yet it is computation-ally intensive [42]. The 2-constraint version of the bi-criteria prob-lem can be mathematically expressed as

500000

550000

600000

650000

700000

750000

800000

850000

3500000 4000000 4500000 5000000 5500000 6000000

/yea

r

Fig. 2. Pareto frontier considering the annual cost and annual CO2 emissions.

M. Carvalho et al. / Applied Energy 91 (2012) 245–254 251

Min f 2ðxÞ; subject to f 1ðxÞ6 2j with 2j ¼ 21;22; . . . and Liminf 6 2j 6 Limsup ð5Þ

where f2(x) is the economic objective function and f1(x) is the envi-ronmental objective function.

If the model is solved for all possible values of 2 and the result-ing solutions are unique, then these solutions represent the entirePareto set of solutions of the original multiobjective problem. Theextreme points of the interval [liminf, limsup] within which 2 shouldfall, can be determined by solving each single objective problemseparately.

Each point in the Pareto frontier represents a different optimalsystem (optimal configuration and operation, as both configurationand operational conditions may vary) which operates under a setof specific conditions. Furthermore, each trade-off solution in-volves a different compromise between both criteria.

4.1. Economic and CO2 emissions multiobjective optimization

The solution of each single optimization problem provided theextreme limits, obtaining liminf = 3785.617 kg CO2/yr (environ-mental optimal) and limsup = 5831.105 kg CO2/yr (economicoptimal). The interval [liminf, limsup] was partitioned into sub-intervals, and the model was solved for each of the limits of thesesub-intervals. Points A and B are the optimal solutions with respe-tively, minimum total annual CO2 emissions and minimum totalannual cost. Table 4 shows some of the limits for 2, with the result-ing configuration and primary and secondary objective values. Foreach configuration, E = gas engine, B = hot water boiler, A = singleeffect absorption chiller, and M = mechanical chiller. The numberaccompanying the equipment indicates how many pieces of equip-ment are installed.

It is interesting to point out the fact that the optimization car-ried out encompasses not only the operational strategy of the sys-tem, but also the configuration. The set of optimal solutions wascomposed of configurations that were able to adapt their strategyonly within a specific range of the Pareto frontier. Fig. 2 shows thedifferent configurations obtained and their behavior.

Point C (configuration 2E 4B 1A 3M: two gas engines, four hotwater boilers, one single effect absorption chiller, and three

Table 42-Constraint method for the multiobjective consideration of CO2 and cost.

Limsup (2)(kg CO2/yr)

CO2 emissions(kg CO2/yr)

Minimumcost (€/yr)

Configuration

A Optimal CO2 3785,617 804,184 6B 4 M3900,000 3899,989 669,116 1E 5B 1A 3 M4000,000 3999,964 645,177 1E 5B 1A 3 M

C 4100,000 4099,743 629,329 2E 4B 1A 3M4200,000 4199,954 614,377 2E 4B 1A 3 M4300,000 4299,959 605,757 2E 4B 1A 3 M4400,000 4399,418 600,033 2E 4B 1A 3 M4500,000 4499,995 594,508 2E 4B 1A 3 M4600,000 4599,585 589,613 2E 4B 1A 3 M4700,000 4697,918 585,008 2E 4B 1A 3 M4800,000 4799,968 581,495 2E 4B 1A 3 M4900,000 4813,608 580,839 2E 4B 1A 3 M5000,000 4813,608 580,839 2E 4B 1A 3 M5100,000 4813,608 580,839 2E 4B 1A 3 M5200,000 4813,608 580,839 2E 4B 1A 3 M5300,000 4813,608 580,839 2E 4B 1A 3 M5400,000 4813,608 580,839 2E 4B 1A 3 M5500,000 4813,608 580,839 2E 4B 1A 3 M5600,000 5584,245 580,523 3E 3B 1A 3 M5700,000 5699,085 576,519 3E 3B 1A 3 M5800,000 5799,952 571,667 3E 3B 1A 3 M

B Optimal economic 5831,105 570,169 3E 3B 1A 3 M

mechanical chillers) represents our preferred intermediate Paretooptimal solution in the Pareto frontier. Point C was chosen becauseit was considered to be a good trade-off between CO2 emissionsand cost, after systematic calculations of decrease in emissions ver-sus increase in cost for each point of the Pareto frontier. Point Crepresents a pronounced decrease in cost (�22%) compared topoint A and a small sacrifice in CO2 emissions (+9%). Configuration2E 4B 1A 3M presents a wide range of possible operation modesand is an adequate option, adaptable to different operational cir-cumstances. Table 6 shows the main features of solutions A–C.

Significant reductions in costs could be attained if the decision-maker was willing to compromise the environmental performanceof the system. The considerable drop in annual cost between pointsA and C is due to installation of cogeneration modules and conse-quent sale of electricity to realize profit. From point A on, the con-sumption of natural gas and sale of cogenerated electricity isincreasing, and the purchase of electricity from the grid isdecreasing.

4.2. Economic and EI-99 Single Score multiobjective optimization

The two extreme points of the Pareto frontier were obtainedby optimizing each objective function separately, providing thesuperior and inferior limits for 2: liminf = 411.986 points/yr (envi-ronmental optimal) and limsup = 1158.005 points/yr (economicoptimal). Points A and B are the optimal design solutions withminimum EI-99 points and total annualized cost values. Some

Table 52-Constraint method for the multiobjective consideration of EI-99 and cost.

Limsup (2)(EI-99/yr)

Env. loads(EI-99/yr)

Minimumcost (€/yr)

Configuration

A Optimal EI-99 411,986 804,184 6B 4M449,287 411,986 804,184 6B 4M486,588 486,517 751,970 1E 5B 4M523,889 523,888 695,577 1E 5B 4M561,190 561,164 663,464 1E 5B 4M

D 598,491 598,488 638,148 1E 5B 1A 3M635,792 614,418 629,589 1E 5B 1A 3M673,093 614,418 629,589 1E 5B 1A 3M710,394 710,347 616,475 2M 4B 1A 3M747,695 747,663 604,361 2M 4B 1A 3M784,996 784,956 597,739 2M 4B 1A 3M822,296 822,263 588,649 2M 4B 1A 3M859,597 859,299 582,823 2M 4B 1A 3M896,898 869,322 580,839 2M 4B 1A 3M934,199 869,322 580,839 2M 4B 1A 3M971,500 869,322 580,839 2M 4B 1A 3M1008,801 869,322 580,839 2M 4B 1A 3M1046,102 869,322 580,839 2M 4B 1A 3M1083,403 869,322 580,839 2M 4B 1A 3M1120,704 1120,491 577,596 3M 3B 1A 3M

B Optimal economic 1158,005 570,169 3M 3B 1A 3M

Table 6Optimal solutions A–D.

System composition A number C number D number B number

MGWH gas engines 0 2 1 3CGWH hot water boilers 6 4 5 3ICWH heat exchangers WH ? WR 0 1 1 4FAWH single effect absorption chillers 0 1 1 1FMWR mechanical chillers 4 3 3 3ICWR cooling towers 3 3 3 3Natural gas (total) (MW h/yr) 8703 20,370 16,538 37,324Purchased electricity (MW h/yr) 3572 203 226 29Sold electricity (MW h/yr) – 4070 1537 11,389Natural gas (cogeneration) (MW h/yr) – 18,068 11,782 36,638Cogenerated work (MW h/yr) – 7375 4809 14,954Cogenerated useful heat (MW h/yr) – 6706 4412 8602Primary energy savings (%) – 20.80 21.04 10.01Equivalent electrical efficienc (yr%) – 69.50 69.91 55.22Cost of equipment (€/yr) 219,650 413,195 320,045 510,830Cost of natural gas (€/yr) 217,582 509,252 413,452 933,092Cost of electricity (€/yr) 366,951 20,278 23,003 3207Profit with the sale of electricity (€/yr) – �313,396 �118,353 �876,960Total annual cost (€/yr) 804,184 629,329 638,148 570,169Emissions of equipment (kg CO2/yr) 43,057 47,775 44,336 52,699Emissions of natural gas (kg CO2/yr) 2367,296 5540,660 4498,336 10,152,037Emissions of electricity (kg CO2/yr) 1375,264 78,297 87,010 11,168Avoided emissions/sale electricity (kg CO2/yr) – �1566,980 �591,745 �4384,799Total annual emissions (kg CO2/yeat) 3785,617 4099,743 4037,937 5831,105Single Score of equipment (points/y) 2272 3366 2984 3908Single Score of natural gas (points/y) 328,984 769,986 625,140 1410,835Single Score of electricity (points/yr) 80,730 4588 5102 656Avoided Single Score/sale electricity (points/yr) – �91,982 �34,737 �257,393Total annual Single Score (points/yr) 411,986 685,958 598,488 1158,005

252 M. Carvalho et al. / Applied Energy 91 (2012) 245–254

sub-intervals of [liminf, limsup] are shown in Table 5, along with theresulting configuration and primary and secondary objective val-ues. The number accompanying the equipment indicates howmany pieces of equipment are installed.

Similarly to the trend in the economic and CO2 multiobjectivesolutions, the consumption of natural gas and sale of cogeneratedelectricity increased with the increase of EI-99 Single Scores, whilepurchase of electricity from the grid decreased. The system slowlyinstalled cogeneration modules and removed hot water boilers,while the production of cooling remained almost fixed by oneabsorption chiller and three mechanical chillers. The number ofhot water – refrigeration water heat exchangers oscillated toaccommodate the restriction on EI-99 points ([liminf, limsup]), andexchangers were added when more heat was wasted.

Fig. 3 shows the Pareto frontier obtained.Point D (configuration 1E 5B 1A 3M: one gas engine, five hot

water boilers, one absorption chiller and three mechanical chillers)represents the preferred intermediate Pareto optimal solution inthe interval [liminf, limsup], being a good trade-off between EI-99and cost, after systematic calculations of decrease in points versusincrease in cost for each point of the interval [liminf, limsup]. Point Drepresents a pronounced decrease in cost (�21%) compared topoint A but a considerable increase in EI-99 points (+45%).

500000

600000

700000

800000

900000

400000 600000 800000 1000000 1200000

EI-99 points/year

/yea

r

Fig. 3. Pareto frontier considering the annual cost and annual EI-99 points.

Table 6 shows the main features of solutions A, B, C and D.From the optimal solutions selected, it is necessary to further

select the ultimate global solution, which is carried out after aresilience analysis, presented in the next section.

4.3. Resilience and optimal solution

The concept of resilience is borrowed from the field of ecology,and enables sustainability to be viewed as an inherent systemproperty rather than an abstract goal [52]. Resilience is the capac-ity of a system to absorb disturbance and reorganize while under-going change, so as to retain essentially the same function,structure, identity and feedbacks [53]. In our case, resilience isthe capacity of the system to undergo changes in operation (dueto different 2 limits) while retaining the same configuration. Ittakes progressively larger disturbances to push the system into adifferent configuration as resilience increases.

Figs. 4 and 5 show a resilience analysis for some of the differentconfigurations that compose the Pareto frontiers of Figs. 2 and 3.Figs. 4 and 5 were generated by maintaining a fixed configurationand varying only the 2 intervals, establishing a range of operationalfeasibility for each configuration in the Pareto frontier.

550000

600000

650000

700000

750000

800000

850000

900000

950000

3500000 4000000 4500000 5000000 5500000 6000000

kg CO2 /year

/yea

r

Fig. 4. Economic and CO2 emissions multiobjective optimization solutions.

550000

600000

650000

700000

750000

800000

850000

400000 600000 800000 1000000 1200000

EI-99 points /year

/yea

r

Fig. 5. Economic and EI-99 Single Score multiobjective optimization solutions.

M. Carvalho et al. / Applied Energy 91 (2012) 245–254 253

Within a framework of understanding and mutual compromise,the choice of an ultimate global configuration considering eco-nomic and environmental viewpoints led to the choice of configu-ration 2E 4B 1A 3M, which performs in a wider range ofadaptability. Adaptability is a part of resilience and is the capacityof the solution to adjust its responses to changing external drivers(2 limits) along the current trajectory.

Note that configuration 2E 4B 1A 3M does not perform signifi-cantly worse in the economic/EI-99 optimization and presentsoperation modes close to the optimal point D. The designer may ac-cept small increases in costs over the economic minimum and stillguarantee optimal conditions under relatively small increases inthe annual EI-99 Single Score. The solution is highly dependent onthe preferences of the decision-maker and must be a compromise.

The validity of the obtained results has been justified with de-tailed sensitivity analyses with respect to variation of exogenousfactors. Ref. [40] analyzed the effect of varying financial factorsin equipment and energy prices. Furthermore sensitive analyseswith respect to the energy services demands, legal factors relatedto the electricity sale, as well as environmental aspects associatedto the energy sources and sale of electricity and geographical andenvironmental constraints have also been studied [39].

5. Conclusions

The issue of multiobjective optimization was addressed in thispaper, where two bicriteria optimizations were carried out. Thesolution of the MILP model provided sets of Pareto optimal designalternatives, which were analyzed and evaluated based on trade-offs. This detailed analysis highlighted the important role of thedecision maker in solving and using their specialized judgmentin the multiobjective problem.

The energy supply system was optimized considering specificdemands of a medium size hospital (500 beds) located in Zaragoza,Spain.

Comparison of economic and environmental optimals showedclearly different structures. Optimal configurations based on con-ventional equipment (hot water boilers, mechanical chillers andcooling towers) were obtained by separately minimizing CO2 emis-sions and then EI-99 Single Score for current conditions in Spain.Regarding the economic objective function, the optimal solutionsuggested the installation of energy-efficient technologies (cogen-eration modules and absorption chillers) was beneficial to achievethe minimum annual cost.

Multiobjective optimization techniques allow the enlargementof the perspective of single-objective energy system analyses andthe determination of the complete spectrum of solutions that opti-mize the design according to more than one objective at a time. Asin most practical problems, multiple objectives compete with oneanother and a unique optimal solution with respect to all of themcannot be identified. The issue of multiobjective optimization was

tackled, in the form of a bicriteria programming problem. The MILPmodel of single-objective optimization was adapted for applicationof the 2-constraint method, and the solution of the model provideda set of Pareto optimal design alternatives.

Two multiobjective optimizations were carried out, consideringeconomic (annual cost) and environmental viewpoints (repre-sented separately by annual CO2 emissions and EI-99 points). Solu-tions close to the environmental minimum were associated with asteep increase in the economic objective. Problems were comparedand it was observed that some configurations were more stablealong the Pareto frontier. The judgment of the solutions and thetrade-offs involved led to the choice of configuration 2E 4B 1A3M, where significant reductions in economic cost could beattained if the environmental impact was compromised.

Acknowledgments

This work was developed within the framework of researchProjects ENE2007-67122 and ENE2010-19346, funded in part bythe Spanish Government (Energy program) and the EuropeanUnion (FEDER program).

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