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Energy 64 (2014) 719e733

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Optimal structural design of residential cogeneration systems inconsideration of their operating restrictions

Tetsuya Wakui*, Ryohei YokoyamaDepartment of Mechanical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan

a r t i c l e i n f o

Article history:Received 29 May 2013Received in revised form22 August 2013Accepted 2 October 2013Available online 22 November 2013

Keywords:CogenerationOptimizationStructural designOperation planningEnergy savingsResidential use

* Corresponding author. Tel.: þ81 72 254 9232; faxE-mail address: wakui@ese.me.osakafu-u.ac.jp (T.

0360-5442/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2013.10.002

a b s t r a c t

An optimal structural design model of a residential cogeneration system, known as combined heat andpower, considering various kinds of operating restrictions is developed from the energy-saving view-point. As principal operating restrictions of cogeneration units, a constant power output operation, adaily startestop operation, and a continuous operation are focused on. The developed model results in amixed-integer linear programming problem and the selection and multi-period operation are simulta-neously optimized. Moreover, the model is applied to the structural design of a residential cogenerationsystem, consisting of a cogeneration unit and its peripheral devices, for simulated energy demands in aJapanese residence. The candidates for a cogeneration unit are a gas engine employing a constant poweroutput operation, a polymer electrolyte fuel cell employing a daily startestop operation, and a solid oxidefuel cell employing a continuous operation, and the candidates for peripheral devices are an electricwater heater and an air-cooled heat exchanger. The optimization results reveal that the selection of thecogeneration unit is influenced more by their operating restrictions than by the consistency in the heat-to-power ratios of the cogeneration unit and energy demands. In addition, it is found that the selection ofthe peripheral devices varies with the selected cogeneration unit and energy demands.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Background of the study

Energy savings is strongly required not only in industrial andcommercial sectors but also in residential sector for global envi-ronment and resources. Cogeneration, which is known as com-bined heat and power, is an effective energy supply method toachieve energy savings and cost reduction. Recently, small-scale,high performance cogeneration units have been developed forresidential use [1]. In Japan, following a 1-kWe gas GE-CGU (en-gine-based cogeneration unit) [2] and a 0.75-kWe PEFC-CGU(polymer electrolyte fuel cell-based cogeneration unit) [3], a 0.7-kWe SOFC-CGU (solid oxide fuel cell-based cogeneration unit)was released [4]. A 1-kWe Stirling engine-based cogeneration unitand a 1-kWe Rankine cycle-based cogeneration unit are alsoavailable in other countries [5]; however, these two types ofcogeneration units have heat-to-power supply ratios higher thansix and are not appropriate for residential use in Japan where theheat-to-power demand ratio is generally low.

: þ81 72 254 9904.Wakui).

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The three types of residential cogeneration units released inJapan have different heat-to-power supply ratios and operatingrestrictions. The GE-CGU has the highest heat-to-power supplyratio among them and must be always operated under the ratedpower output in order to maintain a high generation efficiency. ThePEFC-CGU has a higher generation efficiency than the GE-CGU andadopts a daily startestop operation, in which they can be startedand stopped up to once a day. The latter is due to thermal degra-dation of the stacks [6] and the input energies for start-up. TheSOFC-CGU has the highest generation efficiency among them;however, it must be operated continuously because its high oper-ating temperature requires a long warm-up time and a largeamount of input energies. Moreover, the electric power export fromresidential cogeneration units to commercial electric power sys-tems is not permitted in Japan. Thus, to obtain benefits includingenergy savings, CO2 emission reduction, and cost reduction, resi-dential cogeneration units must be appropriately operated inresponse to variations in residential energy demands. However, thePEFC-CGU and SOFC-CGU may have minimum electric power out-puts because of the decrease in their generation efficiencies.Furthermore, a storage tank must be installed along with the res-idential cogeneration units to meet the mismatch between pro-duction and demand [7]. If the electric power export fromresidential cogeneration units can be conducted, residential

Nomenclature

Indices/setsi˛I candidates of cogeneration unitk˛K sampling timesl˛L candidates of peripheral devicesm˛M representative daysn˛N divided parts for inputeoutput relationship

Binary variablesg selection of candidates of system componentsd operating status of candidates of system componentsdL stored status lower than upper limitdSTA migration from standby state to operating statedSTO migration from operating state to standby statedU stored status equal to upper limit

Continuous variablesE electric power [kWh/h]ED electric power demand [kWh/h]EP purchased electric power [kWh/h]Ea electric power consumed in auxiliary machines

[kWh/h]F natural gas consumption [m3/h]Q heat flow rate of hot water [kWh/h]QDH hot water heating demand [kWh/h]QDS hot water supply demand [kWh/h]Q inST heat flow rate of hot water stored into storage tank

[kWh/h]QoutST heat flow rate of hot water supplied from storage tank

[kWh/h]S stored energy [kWh]SL stored energy lower than upper limit [kWh]SU stored energy equal to upper limit [kWh]X flow rate of input energy [kWh/h]Y flow rate of output energy [kWh/h]x continuous variable to linearize nonlinear term

Objective functionJCGS annual primary energy consumption of residential

cogeneration system [MJ]

Performance variablesJCO annual primary energy consumption of conventional

energy supply system [MJ]a reduction rate of annual primary energy consumption

by utilizing residential cogeneration system [%]

Parametersa; b performance characteristic values [e, kWh/h]c specific heat of water [kWh/(kg �C)]EaSB standby electric power consumed in auxiliary

machines [kWh/h]ESTA electric power to start up [kWh/h]FSTA natural gas consumption to start up [m3/h]p; q; s;u performance characteristic values [(kWh/h)/(m3/h),

kWh/h, (kWh/h)/(m3/h), kWh/h]rE ratio of varied annual demand to original annual

demand for electric powerrQ ratio of varied annual demand to original annual

demand for heatDt sampling time [h]V storage tank volume [L]W number of representative days in typical yearq temperature [�C]k installation energy [MJ]L energy loss rate [1/h]r water density [kg/m3]fE conversion factor for primary energy of purchased

electric power [MJ/kWh]fG conversion factor for primary energy of natural gas

[MJ/(m3)]ðÞ; ðÞ upper and lower limits

SubscriptsCGU cogeneration unitF feed waterPD peripheral deviceST storage tank

SuperscriptsO original value

AbbreviationGE-CGU gas engine-based cogeneration unitPEFC-CGU polymer electrolyte fuel cell-based cogeneration unitSOFC-CGU solid oxide fuel cell-based cogeneration unit

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733720

cogeneration units can operate in response to variations in heatdemand; it is called heat demand following operation [8,9]. How-ever, in a residential cogeneration unit without electric powerexport, its heat output varies in response to its electric poweroutput that follows the electric power demand [10]. Because heatdemand in a residence is not always synchronized with electricpower demand and intermittently arise as shown in Ref. [11], thesurplus heat output generated by the residential cogeneration unitmust be stored in the storage tank. On the other hand, if instan-taneous heat demand exceeds the heat output of a residentialcogeneration unit, the shortage in the heat must be supplementedfrom a storage tank [5]. In light of these features of residentialcogeneration units without electric power export, peripheral de-vices may also be required, including an air-cooled heat exchangertowaste surplus hotwater [10], an electric water heater to consumesurplus electric power [11], and a gas-fired boiler to compensate forthe shortage in hot water supply from a storage tank [10,11].

Combining these peripheral devices with the above-mentionedresidential cogeneration units increases the flexibility of the sys-tem structure; thus, an optimal design of the residential cogene-ration systems, consisting of cogeneration units and theirperipheral devices, for various energy demands is strictly requiredto archive their potential benefits.

1.2. Review of previous works

The previous works for the optimal design of energy supply sys-tems including the residential cogeneration systems were broadlyclassified into the optimal sizing and the optimal structural design.

1.2.1. Optimal sizing of energy supply systemsIn the optimal sizing, the system structure was previously

defined and the sizes of system components including the cogen-eration units are determined so as to maximize the above-

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733 721

mentioned benefits. Generally, there are two types of approachesfor the optimal sizing: a parametric analysis approach and opti-mization approach.

In a parametric analysis approach, the benefit of various sizes ofsystem components is parametrically analyzed by conducting asimulation or optimal operation planning, and then the optimalsize is determined from the result. Hourly simulation wasemployed for performance analyses of 1e5-kWe PEFC-CGUs [12],1e5-kWe SOFC-CGUs with a storage tank [13], 2e6-kWe GE-CGUs[14], 1e5-kWe GE-CGUs [5], MWe-class GE-CGUs [15], and 1e4-MWe GE-CGUs with a storage tank [16]. Moreover, optimal oper-ation planning based on mixed-integer linear programming wasconducted for the economically optimal sizing of a PEFC-CGU [17]and a MWe-class GE-CGUs with an absorption chiller for a hospi-tal [18]; in Ref. [17], a daily start constraint of a PEFC-CGU, which isonly part of the daily startestop operation, was modeled. Further-more, a sparse sequential quadratic programming [19] and mixed-integer nonlinear programming [20] were employed to optimizethe operation planning of the residential cogeneration units withnonlinear performance characteristics. In these previous works[12e20], the cogeneration units could be operated flexibly to obtainthe reported benefits because electric power export could be con-ducted. On the other hand, Wakui et al. conducted optimal opera-tion planning of GE-CGUs [21] and SOFC-CGUs [22] by usingmixed-integer linear programming; they were assumed to be installed in aJapanese housing complex and a microgrid using them was con-structed without the electric power export.

In an optimization approach, not only the multi-period opera-tion but also the sizes of system components are considered asdecision variables. In some previous works, the optimal sizingmodels were developed as linear programming for district energysupply systems [23,24] and residential cogeneration units includinga GE-CGU, a PEFC-CGU, and an SOFC-CGU [25]. Beihong et al. [26]employed binary variables expressing the oneoff status of thesystem components and developed an optimal sizing model byusing mixed-integer nonlinear programming, which is often hardto solve. To avoid the difficulty in the optimization calculation, asimple calculation approach to estimate the optimal sizing ofcogeneration units was also developed [27].

1.2.2. Optimal structural design of energy supply systemsIn the optimal structural design, the optimal system compo-

nents are selected from candidates in a previously defined super-structure so as to maximize the above-mentioned benefits inconsideration of multi-period operation of the selected candidates;thus, the selection and operation planning of the system compo-nents are simultaneously optimized. Generally, the selection fromthe candidates, whose sizes are previously fixed, and their instal-lation number are expressed by binary variables and integer vari-ables, respectively. Yokoyama et al. developed an optimal structuraldesign model of energy supply systems by using mixed-integerlinear programming [28]. Furthermore, they developed anoptimal structural designmodel that considers discreteness of sizesof system components [29]. Other previous works [30e38] werealso based on mixed-integer linear programming. Buoro et al. [30]developed an optimization model of a residential energy supplysystem, in which 1 and 3-kWe GE-CGUs and 1 and 3-kWe Stirlingengine-based cogeneration units were candidates. Lozano et al. [31]developed an optimization model of a trigeneration system, whichconsists of a GE-CGU and an absorption chiller, by considering someSpanish legal constraints for grid-connected cogeneration. Car-valho et al. [32] developed an optimizationmodel of a trigenerationsystem from the environmental viewpoint; the CO2 emission in theproduction process of system components is considered. Casisiet al. [33], Mehleri et al. [34], and Weber et al. [35] developed

optimal layout models of distributed energy supply systems; inthese works, the installation location of system components andthe piping network deployment were optimized by consideringtheir multi-period operation. Recently, multi-objective optimiza-tion models from the economical and environmental viewpointswere developed by Bracco et al. [36] and Buoro et al. [37]. Anautomated superstructure-based optimization model was alsodeveloped by Voll et al. [38].

1.3. Objective of the study

With such a background and review of previous works, thepresent study develops an optimal structural design model of res-idential cogeneration systems, considering various kinds of oper-ating restrictions, from the energy-saving viewpoint; this model isbased on mixed-integer linear programming. The reason why theoptimal structural design is focused on is because the sizes of theresidential cogeneration units released in Japan have been alreadyfixed as shown in Refs. [2e4] and the current sizes of GE-CGU andSOFC-CGU are suitable for the residential use in Japan according tothe optimal sizing analyses by Wakui et al. [21,22].

In some previous works on the optimal structural design[31,32,34,35], the electric power output of the cogeneration units ismodulated from 0 to 100%; this is not realistic operating restriction.The other previous works on the optimal structural design [28e30,33,36e38] considered the oneoff status of the cogenerationunits; however, residential cogeneration units have various kinds ofthe operating restrictions other than the oneoff status, as stated inSubSection 1.1. Moreover, the performance characteristics ofvarious kinds of the cogeneration units were distinguished only bythe difference in the energy conversion efficiencies in these pre-vious works [28e38]. Hence, the present study uniquely focuses onvarious kinds of the operating restrictions of residential cogene-ration units, including the constant power output operation, thedaily startestop operation, and the continuous operation with aminimum power output. As a result, residential cogeneration unitscan be distinguished by not only the difference in the energyconversion efficiencies but also their inherent operating re-strictions. Furthermore, although the previous works employed asparse sequential quadratic programming [19] and mixed-integernonlinear programming [20] to model the nonlinear performancecharacteristics of cogeneration units under partial-load conditions,the developed model employs piecewise linear equations [39] andresults in mixed-integer linear programming.

This paper consists of four sections. Following this section tostate the introduction, the optimal structural design model of res-idential cogeneration systems in consideration of their operatingrestrictions is uniquely developed in Section 2. In Section 3, thedeveloped model is applied to the structural design of a residentialcogeneration system without the electric power export for simu-lated energy demands in a Japanese residence. Finally, the derivedresults and future studies are summarized in Section 4.

2. Optimal structural design model of residentialcogeneration systems

2.1. Framework of optimal structural design model

The framework of the optimal structural design model of resi-dential cogeneration systems from the energy-saving viewpoint,developed in this study, is shown in Fig. 1. The developed optimalstructural design model is basically an extension of the super-structure approach developed by Yokoyama et al. [29]. A super-structure for a residential cogeneration system, which expressesthe inputeoutput relationships of all the system components

Fig. 1. Framework of developed optimal structural design model of residential cogeneration systems.

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733722

considered as candidates for selection and their feasible connectingrelationships, is previously created. Operating restrictions of sys-tem components are also previously considered in their inputeoutput relationships. In the optimization calculation, a real struc-ture is created by selecting the system components from the can-didates, and multi-period operation of the selected systemcomponents are determined in accordance with their operatingrestrictions; the multi-period operation is separately determinedon each representative day in order to consider seasonal and hourlychanges in residential energy demands. The input data for thiscalculation are the performance characteristic values of the can-didates, residential energy demands, and conversion factors forprimary energy. Consequently, the structure and multi-periodoperation of the residential cogeneration system are

Fig. 2. Superstructure for selection of cogeneration unit.

simultaneously optimized so as to minimize the annual primaryenergy consumption. Moreover, the energy-saving effect of theoptimal system structure can be evaluated from the minimizedobjective function.

For the multi-period operation, a typical year is divided into Mrepresentative days; the index for the representative days isdesignated bym. Each representative day is divided into K samplingtimes, with an interval of Dt (i.e., Dt ¼ 24/K), and the index for thesampling times is designated by k. The operation of a residentialcogeneration system with a storage tank cannot be determinedindependently at each sampling time; thus, a daily cyclic operationis considered, assuming that the energy demands change cyclicallywith a period of 24 h on each representative day.

2.2. Decision variables

The decision variables in this optimal structural design modelare classified into two types: design variables and operation vari-ables. The selection of the system components is expressed by bi-nary variables, classified as the design variables; the designvariables do not depend on representative days and samplingtimes. For the operation variables, continuous variables are used toexpress energy flow rates of inputs and outputs of energy conver-sion devices and stored energies of energy storage devices at thekth sampling time on themth representative day, and the operationstatus of the system components at the kth sampling time on themth representative day is expressed by binary variables.

2.3. Constraints

The constraints consist of the selection and the inputeoutputrelationship of each system component, and the energy balancerelationships.

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733 723

2.3.1. Selection of system componentsThe selection of the system components is formulated using

the design variables. As an example, a simple superstructurefor the cogeneration unit, which has I candidates for the se-lection, is shown in Fig. 2; the index for the candidates isdesignated by i. For any candidate, the input is the natural gasbecause fuel cell-based cogeneration units are driven byhydrogen reformed from natural gas in built-in fuel reformers;and the outputs are the electric power and hot water. Gener-ally, one cogeneration unit is installed per single-family resi-dence; thus, the constraint for the selection is formulated asfollows:

PIi¼1

gCGUi � 1

gCGUi˛f0; 1g ði ¼ 1; 2; /; IÞ

9=; (1)

where gCGUi denotes the binary variable (design variable)expressing the selection of the ith candidate for the cogenerationunit. Equation (1) indicates the possibility that no cogeneration unitis selected in the optimal system structure. This constraint can alsobe applied to other system components, which are selected frommultiple candidates.

2.3.2. Inputeoutput relationships of system componentsconsidering their operating restrictions2.3.2.1. Cogeneration unit. Some cogeneration units can beoperated under partial-load conditions; however, the genera-tion and heat recovery efficiencies depend on their loadfactors. Because the inputeoutput relationship of the cogene-ration units may have nonlinear characteristics, it is modeledusing piecewise linear equations [39]. The inputeoutputrelationship of cogeneration units between their minimum andrated outputs is divided into N parts; the index for thedivided parts is designated by n. The inputeoutputrelationship in the nth part of the ith candidate at the kthsampling time on the mth representative day is formulated asfollows:

EnCGUiðk; mÞ ¼ pnCGUiFnCGUiðk; mÞ þ qnCGUid

nCGUiðk; mÞ

QnCGUiðk; mÞ ¼ snCGUiF

nCGUiðk; mÞ þ unCGUid

nCGUiðk; mÞ

EanCGUiðk; mÞ ¼ panCGUiFnCGUiðk; mÞ þ qanCGUid

nCGUiðk; mÞ

FnCGUidnCGUiðk; mÞ � FnCGUiðk; mÞ � F

nCGUid

nCGUiðk; mÞ

dnCGUiðk; mÞ˛f0; 1g

9>>>>=>>>>;

ðn ¼ 1; 2; /; N; i ¼ 1; 2; /; I;

k ¼ 1; 2; /; K;m ¼ 1; 2; /; MÞ (2)

where EnCGU, QnCGU, EanCGU, and FnCGU denote the electric power

output, heat flow rate of the hot water output, electric powerconsumed in auxiliary machines including a water pump andblower, and natural gas consumption in the nth part, respectively;

FnCGU and FnCGU denote the lower and upper limits of natural gas

consumption in the nth part, respectively; dnCGU denotes the binaryvariable expressing whether the current output is included in thenth part; and the coefficients pnCGU, q

nCGU, s

nCGU, u

nCGU, p

anCGU, and qanCGU

express the performance characteristic in the nth part of the linearequations. The actual electric power output, ECGUi, heat flow rateof hot water output, QCGUi, electric power consumed in theauxiliary machines, EaCGUi, and natural gas consumption, FCGUi, ofthe ith candidate at the kth sampling time on the mth represen-tative day are expressed by summing up those at N parts asfollows:

ECGUiðk;mÞ ¼ PNEnCGUiðk;mÞ >>>>>

n¼1

QCGUiðk;mÞ ¼ PNn¼1

QnCGUiðk;mÞ

EaCGUiðk;mÞ ¼ PNn¼1

EanCGUiðk;mÞþEaSBCGUifgCGUi�dCGUiðk;mÞg

FCGUiðk;mÞ ¼ PNn¼1

FnCGUiðk;mÞ

dCGUiðk;mÞ ¼ PNn¼1

dnCGUiðk;mÞ

dCGUiðk;mÞ˛f0; 1g

9>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>>>>>>;

ði¼ 1; 2;/; I;k¼ 1; 2;/; K;m¼ 1; 2;/;MÞ(3)

where dCGUi denotes the binary variable expressing the oneoffstatus of the ith candidate; and EaSBCGU denotes the standby electricpower consumed in the auxiliary machines.

The optimal structural design model developed in this study isfeatured by considering the following operating restrictions: aconstant power output operation, a daily startestop operation, anda continuous operation with a minimum power output. For acogeneration unit employing the constant power output operation,N is set to be 1 and the following condition is additionallyconsidered.

F1CGUi ¼ F1CGUi ði ¼ 1; 2; /; IÞ (4)

To model the daily startestop operation, the binary variablesexpressing the migration from standby state to operating state and

that from operating state to standby state, dSTACGU and dSTOCGU, areemployed. The relationship between the binary variables express-ing the state migration and the binary variable expressing the oneoff status is formulated as follows:

dCGUiðk;mÞ�dCGUiðk�1;mÞ ¼ dSTACGUiðk;mÞ�dSTOCGUiðk;mÞ

dSTACGUiðk;mÞþdSTOCGUiðk;mÞ�gCGUi

dSTACGUiðk;mÞ˛f0; 1g

dSTOCGUiðk;mÞ˛f0; 1g

9>>>>>>>=>>>>>>>;

ði¼ 1; 2;/; I;k¼ 1; 2;/; K;m¼ 1; 2;/;MÞ

(5)

In Eq. (5), if the cogeneration unit is started at the kth sampling

time, dCGUiðk;mÞ ¼ 1 and dCGUiðk�1;mÞ ¼ 0; thus, dSTACGUiðk;mÞ ¼ 1

and dSTOCGUiðk;mÞ ¼ 0. On the other hand, if the cogeneration unit isstopped at the kth sampling time, dCGUiðk;mÞ ¼ 0 and

dCGUiðk�1;mÞ ¼ 1; thus, dSTACGUiðk;mÞ ¼ 0 and dSTOCGUiðk;mÞ ¼ 1. Inaddition, assuming the daily cyclic operation, the oneoff status inthe initial state is considered to be equal to that in the terminalstate on each representative day. The constraint for the daily startestop operation is formulated by providing the upper limit to thenumber of times for the state migration on each representative dayas follows:

PKk¼1

ndSTACGUiðk;mÞþdSTOCGUiðk;mÞ

o�2gCGUi

ði¼ 1; 2;/; I;m¼ 1; 2;/;MÞ(6)

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733724

Furthermore, the constraint to create an association between thedesign variable and the operation variables is considered to preventthe operation of the cogeneration units that are not selected. Thisconstraint is separately formulated for the cogeneration units withand without the continuous operation as follows:

dCGUiðk;mÞ�gCGUi ðwithout continuous operationÞdCGUiðk;mÞ ¼ gCGUi ðwith continuous operationÞ

)

ði¼ 1; 2;/; I;k¼ 1; 2;/; K;m¼ 1; 2;/;MÞ(7)

By formulating Eq. (7), the constraint for the continuous operationis also modeled.

The electric power output, ECGU, heat flow rate of hot wateroutput, QCGU, electric power consumed in the auxiliary machines,EaCGU, and natural gas consumption, FCGU, of the selected cogenera-tion unit at the kth sampling time on themth representative day areexpressed by summing up those for all the candidates as follows:

ECGUðk;mÞ ¼ PIi¼1

ECGUiðk;mÞ

QCGUðk;mÞ ¼ PIi¼1

QCGUiðk;mÞ

EaCGUðk;mÞ ¼ PIi¼1

nEaCGUiðk;mÞþESTACGUid

STACGUiðkþ1;mÞ

o

FCGUðk;mÞ ¼ PIi¼1

nFCGUiðk;mÞþFSTACGUid

STACGUiðkþ1;mÞ

o

9>>>>>>>>>>>>>>=>>>>>>>>>>>>>>;

ðk¼ 1; 2;/; K;m¼ 1; 2;/;MÞ

(8)

In Eq. (8), the additional electric power and natural gas consump-tion to start up the ith cogeneration unit, ESTACGUi and FSTACGUi, areconsidered. They are consumed at one sampling time before the

start-up; thus, the daily cyclic operation is applied to dSTACGUi.

2.3.2.2. Storage tank. The storage tank is selected along with thecogeneration unit, and its capacity depends on the selected cogene-ration unit; the optimal sizing of the storage tank is an issue for futurestudies. Although storage tanks generally have temperature stratifi-cations in the vertical direction [40], an energy balance relationshipbased on heat flow rates is applied to express the inputeoutputrelationship in the storage tank; this model is defined as an idealstratificationmodel by Celador et al. [7].Moreover, in order to expressthe full storage state that is used to express the operating condition ofan air-cooled heat exchanger, the stored energy is divided into twoparts: stored energy smaller than its upper limit and stored energyequal to its upper limit. By introducing thebinaryvariablesexpressingthe two parts of the stored energy, dLST and dUST, the inputeoutputrelationship of the ith storage tank at the kth sampling time on themth representative day is formulated as follows:

SSTiðk; mÞ � SSTiðk� 1; mÞDt

¼ Q inSTiðk; mÞ � Qout

STi ðk; mÞ � LiSSTiðk� 1

SSTiðk; mÞ ¼ SLSTiðk; mÞ þ SUSTiðk; mÞSSTiðmÞdLSTiðk; mÞ � SLSTiðk; mÞ � SSTiðmÞdLSTiðk; mÞSUSTiðk; mÞ ¼ SSTiðmÞdUSTiðk; mÞdLSTiðk; mÞ˛f0; 1gdUSTiðk; mÞ˛f0; 1gdLSTiðk; mÞ þ dUSTiðk; mÞ ¼ gCGUi

ði ¼ 1; 2; /; I; k ¼ 1; 2; /; K;m ¼ 1

where SST denotes the energy stored in the storage tank;Q inST andQout

STdenote the heat flow rates of hot water stored into and supplied fromthe storage tank, respectively; L denotes the energy loss rate of thestorage tank; SLST and SUST denote the stored energy lower than andequal to the upper limit; and SST and SST denote the lower and upperlimits of the stored energy, respectively. The upper limit of the storedenergy in the storage tank varies according to the selected cogene-rationunit and the representative day. It is calculatedby the followingequation:

SSTiðmÞ ¼ rcVSTifqSTi�qFðmÞgði¼ 1; 2;/; I;k¼ 1; 2;/; K;m¼ 1; 2;/;MÞ

(10)

where r and c denote the density and specific heat of water,respectively; VST and qST denote the volume of the storage tank andhot water temperature in the storage tank, respectively; and qFdenotes the feed water temperature and depends on the represen-tative day. Furthermore, based on the assumption of the daily cyclicoperation, the energy stored in the initial state is considered to beequal to that stored in the terminal state on each representative day.

2.3.2.3. Peripheral devices. Peripheral devices are operated onlywhen they are selected and their operating conditions are satisfied.They consist of L types and their index is designated by l. Theinputeoutput relationship of the lth peripheral device at the kthsampling time on the mth representative day is formulated by thelinear equation using the flow rates of the input and output en-ergies, XPDI and YPDI , as follows:

YPDIðk;mÞ ¼ aPDIXPDIðk;mÞþbPDIdPDIðk;mÞXPDIdPDIðk;mÞgPDI�XPDIðk;mÞ�XPDIdPDIðk;mÞgPDI

9=;

ðl¼ 1; 2;/; L;k¼ 1; 2;/; K;m¼ 1; 2;/;MÞ(11)

where gPDI denotes the binary variable (design variable) expressingthe selection; dPDI denotes the binary variable (operation variable)expressing the oneoff status that is associated with its operatingcondition; XPDI and XPDI denote the lower and upper limits of theflow rate of the input energy; and the coefficient aPDI and bPDIexpress the performance characteristic in the linear equation. Forthe peripheral devices, the association between the design variablegPDI and the operation variable dPDI is not considered unlike Eq. (7)for the cogeneration unit. This is because the operating condition ofthe peripheral devices is associated with the operation of othersystem components. The inputeoutput relationship of the

; mÞ

; 2; /; MÞ

9>>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>>;

(9)

Fig. 3. Superstructure of residential cogeneration system.

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733 725

peripheral devices can also be formulated using piecewise linearequations as in the case of the cogeneration units.

2.3.3. Energy balance relationshipsThe energy balances are considered at the connecting points

between the system components and at the boundaries of theresidential cogeneration system, meaning the supply points to theenergy demands.

2.4. Objective function

Many evaluation criteria, including energy savings, CO2 emissionreduction, and cost reduction, are required to quantify the benefits ofusing a cogeneration system. First, a cost reduction should be dis-cussed on the basis of the total cost consisting of initial and opera-tional costs of selected system components. The operational costs canbe calculated from purchased electric power and natural gas con-sumption. However, a cost reduction by utilizing fuel cell-basedcogeneration units is not currently expected because of their highinitial costs. Second, CO2 emission reduction can be calculated formpurchased electric power and natural gas consumption; however, theCO2 emission factor for electric power purchased from an electricpower company must be estimated appropriately. In Japan, twomethods for estimating theCO2 emission factor for purchased electricpower have been discussed for several years. Onemethod is based onthe average CO2 emission of only thermal power plants in the electricpower system, and the other method is based on the average CO2emission of all power plants. Because this discussion remainsinconclusive, the feasibility study from the perspective of reducingCO2 emission is regarded as a future study. However, the Act on theRational Use of Energy of Japan [41] officially states that the conver-sion factor for the primary energy of purchased electric power shallbe calculated on the basis of the average consumption of only thermalpower plants. Therefore, this study focuses on the energy savings byutilizing a residential cogeneration system as the first phase.

The objective function to be minimized is the annual primaryenergy consumption, which is calculated from purchased electricpower and natural gas consumption in the cogeneration unit andperipheral devices on each representative day. The objectivefunction, JCGS, is expressed by the following linear equation:

JCGS ¼PMm¼1

WðmÞ( PK

k¼1fEðkÞEPðk;mÞDt

þfGPKk¼1

"FCGUðk;mÞþPL

l¼1FPDIðk;mÞ

#Dt

)

þk

PIi¼1

gCGSiþPLl¼1

gPDI

!

(12)

whereW denotes the number of the representative days in a typicalyear; EP denotes the purchased electric power; FPDI denotes thenatural gas consumption in the lth peripheral device; and fE and fGdenote the conversion factors for the primary energy of purchasedelectric power and natural gas, respectively. fE may vary hourlybecause of variations in the thermal power plant configuration. Toavoid installing the system components when they are not oper-ated on any representative day, a negligible energy for theirinstallation, k, is added in the objective function.

2.5. Solution method

The formulated model has the nonlinear term, which is theproduct of dPDI and gPDI in Eq. (10). To reformulate this model as a

mixed-integer linear programming problem, this nonlinear term isreplaced by the continuous variable xPDI as follows:

xPDIðk;mÞ¼dPDIðk;mÞgPDI ðl¼1;2;/;L;k¼1;2;/;K;m¼1;2;/;MÞ(13)

Moreover, the following constraint for xPDI is introduced:

dPDIgPDI � xPDIðk;mÞ�dPDIgPDI

dPDIðk;mÞþdPDIðgPDl�1Þ� xPDIðk;mÞ�dPDIðk;mÞ

9=;

ði¼ 1; 2;/; I;k¼ 1; 2;/; K;m¼ 1; 2;/;MÞ(14)

where dPDI and dPDI denote the lower and upper limits of dPDI ,respectively, and they are set as 0 and 1, respectively. In Eq. (14), ifgPDI ¼ 0, xPDI ¼ 0, or else if gPDI ¼ 1, xPDI ¼ dPDI . Thus, this pro-cedure can linearize Eq. (13) without any approximation [29].

The reformulated problem is coded using the algebraicmodeling language, GAMS distribution 23.1 [42], and is solved us-ing the optimization solver for large-scale problems, CPLEX version12.2 [43]. The solver can evaluate the lower bound of the objectivefunction by using linear relaxation during computation. All of thesolutions in this study are derived under the condition that thevalue of the objective function completely coincides with its lowerbound. Hence, it is guaranteed that the results obtained by usingthis solver are optimal.

3. Case study

As a case study, the developed optimal structural design modelis applied to the structural design of a residential cogenerationsystem without electric power export for simulated energy de-mands in a Japanese residence. First, the superstructure of theresidential cogeneration system targeted in this study is shown,then the input data for the optimal structural design are stated.Finally, the derived results are discussed.

3.1. Superstructure of residential cogeneration system

The superstructure of the residential cogeneration systeminvestigated as a case study is shown in Fig. 3. It consists of acogeneration unit, a storage tank, an electric water heater, an air-cooled heat exchanger, and a gas-fired boiler. There is no electricpower export from the cogeneration unit to the commercial electric

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733726

power system. The surplus electric power generated by the cogen-eration unit is used in the electric water heater, while the shortage inthe electric power is supplemented by purchasing from an electricpower company. These constraints are considered in the energybalance relationship. The hot water produced by the cogenerationunit and electric water heater is stored in the storage tank. Thesurplus energy of hot water produced by the cogeneration unit iswasted in the air-cooled heat exchanger. The hot water supply de-mand is met by supplying from the storage tank and gas-fired boiler.For the winter days, the two methods of heating are separatelyemployed: heating by electric air conditioners and that by hot water.

Candidates for the cogeneration unit comprise a GE-CGUemploying the constant power output operation, a PEFC-CGUemploying the daily startestop operation, and an SOFC-CGUemploying the continuous operation with a minimum poweroutput; i.e., I ¼ 3. Only the GE-CGU can directly supply hot water tothe heating demand. The storage tank is selected along with thecogeneration unit and its volume depends on the cogenerationunit. As candidates for peripheral devices, the electric water heater,air-cooled heat exchanger, and gas-fired boiler are considered; i.e.,L ¼ 3. The electric water heater is operated only when the surpluselectric power is generated under the minimum power outputoperation of the cogeneration unit. The air-cooled heat exchanger isoperated only when the energy stored in the storage tank reachesits upper limit. Thus, the binary variables, d1CGU and dUST, areemployed to express the oneoff status of the electric water heaterand the air-cooled heat exchanger, respectively. The gas-fired boileris preselected by preliminarily setting the binary variable to selectthe gas-fired boiler to 1; thus, the negligible energy for the instal-lation of the gas-fired boiler is not considered in Eq. (12). As aconsequence, the selection of the cogeneration unit with the stor-age tank, electric water heater, and air-cooled heat exchanger is

Table 1Performance characteristics of system components.

System component Item

Gas engine-basedcogeneration unit (GE-CGU)

Rated electric powerRated hot water outpRated natural gas conPower consumptionPower consumptionTemperature of gene

Polymer electrolyte fuel cell-basedcogeneration unit (PEFC-CGU)

Rated/minimum elecRated/minimum hotRated/minimum natuPower consumptionPower consumptionElectric power for staNatural gas consumpTemperature of gene

Solid oxide fuel cell-basedcogeneration unit (SOFC-CGU)

Rated/minimum elecRated/minimum hotRated/minimum natuPower consumptionTemperature of gene

Storage tank Volume (GE-CGU)Volume (PEFC-CGU)Volume (SOFC-CGU)Heat loss rate (GE-CGHeat loss rate (PEFC-Heat loss rate (SOFC-

Latent heat recovery type gas-fired boiler Rated hot water outpHot water supply effiHot water heating efRated power consum

Electric water heater (EH) Maximum electric poHeating efficiency

Air-cooled heat exchanger (AC) Maximum heat dischPower consumption

determined in this case study. If no cogeneration unit is selectedbased on Eq. (1), the electric power demand is met only by pur-chasing electric power, and the hot water supply and heating de-mands are met by supplying only from the gas-fired boiler.

3.2. Input data

3.2.1. Performance characteristics of system componentsThe performance characteristics of the system components are

listed in Table 1, and the generation and heat recovery efficienciesof the three types of cogeneration units as a function of the electricpower output, calculated using the higher heating value of naturalgas, are shown in Fig. 4. These are estimated on the basis of Ref. [2]for the GE-CGU, Ref. [3] for the PEFC-CGU, and Ref. [4] for the SOFC-CGU. The rated electric power outputs of the GE-CGU, PEFC-CGU,and SOFC-CGU are 1.0, 0.75, and 0.7 kW, respectively. The inputeoutput relationship of the PEFC-CGU and SOFC-CGU is divided intothree (N ¼ 3) and five (N ¼ 5) parts, respectively; the divided partsinclude the part of the minimum power output operation (n ¼ 1).The performance characteristics of the cogeneration units aresummarized as follows: the GE-CGU has the highest heat-to-powersupply ratio at the rated electric power output; the PEFC-CGU hashigh generation efficiency under partial-load conditions; and theSOFC-CGU has the smallest minimum and rated electric poweroutputs and the highest generation efficiency at the rated electricpower output. For the PEFC-CGU, the electric power and natural gasconsumed for the start-up are considered [3]. The load-followingcharacteristic [6] of the PEFC-CGU and SOFC-CGU is not consid-ered. This is because the sampling time of the residential energydemand is 1 h as described later, and the electric power output of aprototype SOFC-CGU follow the variations in the electric powerdemand of an actual residence very well according to the

Value

output 1.0 kWut 2.50 kWsumption 0.337 m3/hof auxiliary machines during operation 0.050 kWof auxiliary machines during standby 0.005 kWrated hot water 75 �Ctric power output 0.750/0.250 kWwater output 0.940/0.200 kWral gas consumption 0.167/0.0617 m3/hof auxiliary machines during operation 0.03 kWof auxiliary machines during standby 0.005 kWrt-up 0.400 kWtion for start-up 0.0600 m3/hrated hot water 60 �Ctric power output 0.700/0.150 kWwater output 0.640/0.240 kWral gas consumption 0.135/0.0533 m3/hof auxiliary machines 0.020 kWrated hot water 70 �C

90 L200 L90 L

U) 1.20%/hCGU) 0.090%/hCGU) 1.20%/hut 41.9 kWciency (HHV) 90.0%ficiency (HHV) 84.0%ption of auxiliary machines 0.205 kWwer input 0.950 kW

90.0%arge rate 1.00 kWof auxiliary machines 0.005 kW

Fig. 4. Generation and heat recovery efficiencies of three types of cogeneration units.

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733 727

demonstration [44]. The lower limit of the stored energy, SST, is setto be 10% of SST to consider unusable hot water because of actualtemperature stratification. For the gas-fired boiler, a latent heatrecovery type, which is more efficient than a conventional type, isemployed. The power consumption of pumps to send hot waterfrom the gas-fired boiler to demands is set to be proportional to theheat flow rate of the hot water output.

3.2.2. Residential energy demandsThis study focuses on the simulated energy demands of a typical

single-family residence in Japan, as defined by the Institute forBuilding Environment and Energy Conservation in Japan [45]. The

Fig. 5. Time evolution of sim

calculation condition to simulate the energy demands of the single-family residence was particularly described in Ref. [39]. In thecurrent study, these energy demands are rearranged for thefollowing five representative days, i.e., M ¼ 5: a summer day, asummer day with peak demand, a mid-season day, a winter day,and awinter daywith peak demand. The numbers of a summer day,a summer day with peak demand, a mid-season day, a winter day,and a winter day with peak demand in a typical year are 105, 17,122, 104, and 17, respectively. The energy demands on eachrepresentative day are estimated at 24 sampling times; i.e., K ¼ 24andDt ¼ 1 h. The time evolution of the energy demands is shown inFig. 5; the electric power demand depends on the winter heating

ulated energy demands.

Fig. 6. Optimal structures of residential cogeneration system.

Table 3Detail of optimal structures of residential cogeneration system.

Selected (S)/not selected (NS)

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methods, while the hot water supply demand is the same for theboth winter heating methods. From Fig. 5, the features of the en-ergy demands are summarized as follows: (1) the electric powerdemand increases in the morning and at night; (2) the hot watersupply demand is mostly concentrated at night; (3) there is the hotwater heating demand in the morning and after the evening; and(4) the variations in the hot water supplying and heating demandsare not always synchronized with that in the electric power de-mand. The annual electric power demand and the annual heatdemand that is the sum of the annual hot water supply and heatingdemands in the case of the winter heating by electric air condi-tioners are 21.5 and 15.7 GJ/y, respectively, and those in the case ofthe winter heating by hot water are 17.9 and 26.0 GJ/y, respectively;they are calculated by considering the number of the representativedays in a typical year. FromRef. [45], the feedwater temperatures insummer, mid-season, and winter are set to be 24, 16, and 8 �C,respectively.

In order to analyze the optimal structure of the residentialcogeneration system for a wide range of the energy demands, theenergy demands at each sampling time are varied from the originaldemands, shown in Fig. 5, in proportion to the annual energy de-mands parametrically varied as follows:

EDðk; mÞ ¼ rEEODðk; mÞQDSðk; mÞ ¼ rQQO

DSðk; mÞQDHðk; mÞ ¼ rQQO

DHðk; mÞ

9>>>=>>>;

ðk ¼ 1; 2; /; K;m ¼ 1; 2; /; MÞ (15)

where ED, QDS, and QDH denote the electric power demand, the hotwater supply demand, and the hot water heating demand,respectively; rE and rQ denote the ratio of the varied demand to theoriginal demand for electric power and heat, respectively; and EOD,QODS, and QO

DH denote the electric power demand, the hot watersupply demand, and the hot water heating demand, respectively,which are originally simulated. For the residence employing thewinter heating by electric air conditioners, rE is varied in the rangeof 0.23e1.40 and rQ , in the range of 0.16e1.91. For the residenceemploying the winter heating by hot water, rE is varied in the rangeof 0.28e1.40 and rQ , in the range of 0.15e1.92.

3.2.3. Conversion factors for primary energyThe conversion factors for the primary energy of purchased

electric power and natural gas are listed in Table 2. For the pur-chased electric power, the thermal power average conversion factordescribed previously is introduced; this has two values, dependingon the time period, because the configuration of the thermal powerplant in the electric power system varies [41]. For natural gas, thevalue of the conversion factor is reported as the statistics by Japa-nese gas companies [46].

3.3. Results and discussion

In this optimal structural design problem, the numbers are as fol-lows: equation, 18,900; continuous variables, 13,120; and binary vari-ables, 3847. As numerical results, the optimal structure of the

Table 2Conversion factors for primary energy.

Energy source Value

Purchased electric power (8:00 to 22:00) 9.97 MJ/kWhPurchased electric power (22:00 to 8:00) 9.28 MJ/kWhNatural gas 45.0 MJ/m3

residential cogeneration system and the correlation between itsoptimal structure and operation planning are first analyzed. Then, theenergy-saving effect of its optimal and suboptimal structures isanalyzed.

3.3.1. Optimal structure analysisThe optimal structures of the residential cogeneration system

are plotted in Fig. 6, showing the relationship between the annualelectric power and heat demands, and the heat-to-power supplyratio of the three types of cogeneration units at the rated electricpower output. The detail of the optimal structures of the residentialcogeneration system, which have five types, is listed in Table 3.

The distribution of the optimal structures in the relationship be-tween the annual electric power and heat demands is almost thesame for both the winter heating methods. Moreover, there is weakcorrelation between the selected cogeneration units and the heat-to-power supply ratio of the three types of cogeneration units, althoughthe consistency of the heat-to-power ratios of the cogeneration unit

Optimal structure GE-CGU PEFC-CGU SOFC-CGU EH AC

No CGU NS NS NS NS NSGE S NS NS S NSPEFC-A NS S NS S NSPEFC-B NS S NS NS NSSOFC-A NS NS S S SSOFC-B NS NS S NS S

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733 729

and energy demands is generally regarded as important for thedesign of cogeneration systems. In the case of considerably lowannual demands for both electric power and heat, no cogeneration isselected; the corresponding demands are indicated by No CGU inFig. 6. In the case where the annual electric power demand is quitelow, but the annual heat demand is relatively high, theGE-CGUwith ahigh heat-to-power supply ratio is selected; the corresponding de-mands are indicated by GE in Fig. 6. The electric water heater isselected along with the GE-CGU, as shown in Table 3. In the casewhere the annual heat demand is quite low, but the annual electricpower demand is relatively high, the PEFC-CGU, which has highgeneration efficiencies under partial-load conditions, is selectedalongwith the electric water heater; the corresponding demands areindicated by PEFC-A in Fig. 6. The electric water heater is required tooperate the PEFC-CGU under the electric power demand lower thanits minimum electric power output (0.25 kW). For higher annualdemands for electric power and heat than the demands indicated byPEFC-A, the SOFC-CGU that has the smallest rated electric poweroutput but the highest generation efficiency at the rated electric po-wer output is selected; the corresponding demands are indicated bySOFC-A and SOFC-B in Fig. 6. The air-cooled heat exchanger iscertainly selected along with the SOFC-CGU employing the contin-uous operation. The electric water heater is selected along with theSOFC-CGU only in low annual electric power demands, which areindicated by SOFC-A in Fig. 6, because the minimum electric powerdemand on the representative days is lower than the minimumelectric poweroutput of the SOFC-CGU (0.15 kW). Furthermore, in the

Fig. 7. Optimal operation planning of PEFC-CGU on representative summer day(Winter heating by electric air conditioners: rE ¼ 0.5, rQ ¼ 0.4).

case of considerably high annual demands for both the electric powerand heat, the PEFC-CGU whose heat-to-power supply ratio is higherthan that of the SOFC-CGU is selected; the corresponding demandsare indicated by PEFC-A and PEFC-B in Fig. 6. The electricwater heateris not selected for considerably high annual electric power demands,which are indicated by PEFC-B in Fig. 6. Moreover, Table 3 shows thatthe air-cooled heat exchanger is not selected along with the GE-CGUand PEFC-CGU. This result indicates that the GE-CGU and PEFC-CGUwith high heat-to-power supply ratios need to effectively utilize thegenerated hot water to achieve energy savings.

3.3.2. Correlation analysis between optimal structure and operationplanning

Fig. 6 shows the following distinctive result: for the same annualelectric power demand, the SOFC-CGU with a low heat-to-powersupply ratio is selected in a high annual heat demand, indicatedby demand (B) in Fig. 6(a), while the PEFC-CGUwith a high heat-to-power supply ratio is selected in a low annual heat demand, indi-cated by demand (A) in Fig. 6(a). To analyze this result, for demand(A) where rE ¼ 0.5 and rQ ¼ 0.4, the optimal operation planning ofthe PEFC-CGU and the SOFC-CGU on the representative summerday are shown in Figs. 7 and 8, respectively. The result for the SOFC-CGU is derived by preliminarily setting the binary variable to selectthe SOFC-CGU to 1. First, the operation of the PEFC-CGU isconcentrated in the nighttime with a high heat demand due toemploying the daily startestop operation. Although the result isnot shown here, all the heat demand is met by the supply from the

Fig. 8. Optimal operation planning of SOFC-CGU on representative summer day(Winter heating by electric air conditioners: rE ¼ 0.5, rQ ¼ 0.4).

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733730

storage tank. On the other hand, the electric power output of theSOFC-CGU employing the continuous operation is always varied inresponse to the electric power demand indicated by the solid line.The surplus electric power is used in the electric water heater, andthe surplus energy of hot water output is wasted at the air-cooledheat exchanger. However, due to wastage of surplus energy of hotwater, the annual primary energy consumption for the SOFC-CGU(35.1 GJ/y) is larger than that for the PEFC-CGU (34.3 GJ/y); thus,the PEFC-CGU is selected as the optimal cogeneration unit. Fordemand (B) where rE ¼ 0.5 and rQ ¼ 0.85, the operation time of thePEFC-CGU is increased with the amount of the heat demand, whilethe wastage of surplus energy of hot water generated by the SOFC-CGU is decreased. Since the latter provides a greater contribution toenergy savings, the annual primary energy consumption for theSOFC-CGU (38.8 GJ/y) is smaller than that for the PEFC-CGU

Fig. 9. Optimal energy supply planning in the case of PEFC-CGU on representativewinter day (Winter heating by hot water: rE ¼ 1.0, rQ ¼ 1.55).

(39.8 GJ/y); thus, the SOFC-CGU is selected as the optimal cogen-eration unit.

As shown in Fig. 6, the GE-CGU with the highest heat-to-powersupply ratio is selected only in considerably low annual electricpower and heat demands and not selected in high annual heatdemands with high heat-to-power demand ratios. To analyze thisresult, for demand (C) where rE ¼ 1.0 and rQ ¼ 1.55, the optimalenergy supply planning for the PEFC-CGU and the GE-CGU on therepresentative winter day are shown in Figs. 9 and 10, respectively.Although the heat-to-power ratios of the GE-CGU and the demand(C) are identical, the PEFC-CGU is identified as the optimal cogen-eration unit. The PEFC-CGU operates continuously because of thehigh heat demand; however, its electric power output is modulatedin response to the electric power demand. On the other hand, the

Fig. 10. Optimal energy supply planning in the case of GE-CGU on representativewinter day (Winter heating by hot water: rE ¼ 1.0, rQ ¼ 1.55).

Fig. 11. Reduction rate of annual primary energy consumption for a wide range ofenergy demands.

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733 731

electric power supply from the GE-CGU employing the constantpower output operation is modulated by utilizing the electric waterheater. The GE-CGU operates in the morning and nighttime withhigh heat demand. However, its operation time is insufficient tomeet the daily heat demand because further operation under a lowelectric power demand is unfavorable from the perspective ofsaving energy. Since the reduction in the amount of the purchasedelectric power greatly surpasses the increase in the hot watersupply from the gas-fired boiler, the primary energyconsumption for PEFC-CGU (83.2 GJ/y) is smaller than that for GE-CGU (86.8 GJ/y).

These analyses reveal that the selection of the cogeneration unitis influenced more by their operating restrictions than by theconsistency in the heat-to-power ratios of the cogeneration unitand energy demands. Moreover, the GE-CGU and PEFC-CGU withhigh heat-to-power supply ratios aim to operate so as to meet thedaily heat demand by their hot water output but their operation islimited by low electric power demands. The SOFC-CGU with thehigh generation efficiency and continuous operation constraint isoperated in the electric demand following mode.

3.3.3. Energy-saving analysis of optimal structuresThe energy-saving effect of the residential cogeneration system

with the optimal structure is analyzed. The reduction rate of theannual primary energy consumption by utilizing the residentialcogeneration system, a, is defined as:

a ¼ JCO � JCGSJCO

� 100 (16)

where JCO denotes the annual primary energy consumption of aconventional energy supply system, in which the electric powerdemand is met only by purchasing electric power, and the heatdemand is met only by supplying from a conventional gas-firedboiler. The hot water supply and heating efficiencies of the con-ventional gas-fired boiler based on the higher heating value ofnatural gas are assumed to be 80 and 75%, respectively. The positivevalue of this reduction rate indicates the energy savings by utilizingthe residential cogeneration system.

The reduction rate of the annual primary energy consumption,a, by utilizing the optimal structure is plotted in Fig.11, showing therelationship between the annual electric power and heat demands,and the heat-to-power supply ratio of the three types of cogene-ration units at the rated electric power output. All the results for ahave positive values; thus, all the optimal structures reduce theannual primary energy consumption as compared with the con-ventional energy supply system. The system in which no cogene-ration unit is selected has also an advantage in the energy savingsbecause the latent heat recovery type gas-fired boiler is installedunlike the conventional energy supply system. a increases withboth the annual electric power and heat demands because of thechange in the energy-saving effect of the three types of cogenera-tion units with different heat-to-power supply ratios and opera-tional restrictions. a has high sensitivity to the annual energydemands in low electric power and heat demands. On the otherhand, a slightly decreases in considerably high annual electric po-wer and heat demands because the amount of the purchasedelectric power and hot water supplied from the gas-fired boiler isincreased to compensate for the shortage in the supplies from thecogeneration unit. The highest value of a in the case of the winterheating by electric air conditioners, i.e., 19.2%, is derived in theenergy demands where the annual electric power and heat de-mands are 17.6 and 14.8 GJ/y, respectively, and a in the case of thewinter heating by hot water, i.e., 19.0%, is derived in the energydemands where the annual electric power and heat demands are

16.1 and 24.3 GJ/y, respectively; these energy demands are plottedin Fig. 11. For the highest value of a, the SOFC-CGU is selected alongwith the air-cooled heat exchanger in the both winter heatingmethods, as shown in Fig. 6 and Table 3.

3.3.4. Energy-saving analysis of suboptimal structuresTo conduct the sensitivity analysis for the optimal structure of

the residential cogeneration system, the energy-saving effect ofits suboptimal structures is also investigated. First, the subopti-mal structures for the cogeneration units are focused on. Table 4shows the reduction rate of the annual primary energy con-sumption, a, of the optimal structure in the case where eachcogeneration unit is intentionally selected and the energy supplysystem without the cogeneration units, for the original energydemands (rE ¼ 1.0 and rQ ¼ 1.0); the results are derived bypreliminarily fixing the binary variable to select the corre-sponding system components.

For both the winter heating methods, the difference in a be-tween the SOFC-CGU (the optimal cogeneration unit) and the PEFC-CGU is around one percentage points. The GE-CGU also greatlyreduces the annual primary energy consumption as compared withthe energy supply system without the cogeneration units, espe-cially in the case of the winter heating by hot water. However, a ofthe GE-CGU is smaller than those of the SOFC-CGU and PEFC-CGUfor both the winter heating methods. This is due to limiting theoperation of the GE-CGU under low electric power demands, asshown in Fig. 10. In the case where the SOFC-CGU is selected, theair-cooled heat exchanger is selected, but the electric water heateris not selected because theminimum electric power demand on therepresentative days exceeds the minimum electric power output.

Table 4Energy-saving effect and optimal structure of preliminarily selected cogeneration unit in original energy demands.

Winter heating Cogeneration unit Reduction rate of annualprimary energy consumption %

Selected (S)/not selected (NS)

EH AC

Electric air conditioners SOFC-CGU (optimal) 18.3 NS SPEFC-CGU 17.3 S NSGE-CGU 10.4 S NSNo CGU 2.81 NS NS

Hot water SOFC-CGU (optimal) 18.8 NS SPEFC-CGU 17.5 S NSGE-CGU 13.1 S NSNo CGU 4.49 NS NS

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On the other hand, in the case where the GE-CGU or the PEFC-CGUis selected, the electric water heater is selected, but the air-cooledheat exchanger is not selected. This system structure aims at theoperation of the cogeneration units under a low electric powerdemand and at the effective utilization of the hot water producedby the cogeneration units with high heat-to-power supply ratios.

Second, the energy-saving effect of the suboptimal structuresfor the peripheral devices is investigated. a of the residentialcogeneration systems with the preliminarily selected peripheraldevices for each cogeneration unit is listed in Table 5; the originalenergy demands, in which the winter heating is conducted by theelectric air conditioners, are focused on. In the case where theSOFC-CGU is selected, installing the air-cooled heat exchanger in-creases the reduction rate of the annual primary energy con-sumption by two percentage points. This is because the load factorof the SOFC-CGU without the air-cooled heat exchanger is reducedso that surplus hot water is not generated. However, installing theelectric water heater does not influence the reduction rate at all.This means that the electric water heater is not operated. On theother hand, in the case where the GE-CGU or PEFC-CGU is selected,a is slightly increased by installing the electric water heater. Thisresult shows that the operating time of the GE-CGU and PEFC-CGUwithout the electric water heater is limited so that surplus electricpower is not generated. However, installing the air-cooled heatexchanger scarcely increases the reduction rate because the GE-CGU and PEFC-CGU with high heat-to-power supply ratios needto effectively utilize the produced hot water in order to achieveenergy savings. Although the result is not shown, it was confirmedthat the result in the case of thewinter heating by hot water has thesame tendency as that of the winter heating by electric airconditioners.

Table 5Energy-saving effect of residential cogeneration system with preliminarily selectedperipheral devices in original energy demands (Winter heating by electric airconditioners).

Cogenerationunit

Reduction rate of annualprimary energyconsumption %

Selected (S)/not selected (NS)

EH AC

SOFC-CGU 18.3 NS S16.3 S NS18.3 S S16.3 NS NS

PEFC-CGU 17.0 NS S17.3 S NS17.3 S S17.0 NS NS

GE-CGU 9.78 NS S10.4 S NS10.4 S S9.76 NS NS

These sensitivity analyses reveal that not only the cogenerationunits but also the peripheral devices should be appropriatelyselected for a high energy-saving effect.

4. Conclusions

An optimal structural design model of residential cogenerationsystems that considers various kinds of operating restrictions wasdeveloped from the energy-saving viewpoint. As principal oper-ating restrictions of cogeneration units, a constant power outputoperation, a daily startestop operation, and a continuous operationwere focused on.Moreover, the variation in the generation and heatrecovery efficiencies of cogeneration units under partial-load con-ditions was formulated using piecewise linear equations. Thedeveloped model results in a mixed-integer linear programmingproblem and the selection and multi-period operation are simul-taneously optimized. The suboptimal structure could be alsoanalyzed by preliminarily fixing the binary variables to select thecorresponding system components.

Thedevelopedmodelwas then applied to the structural design ofa residential cogeneration system, consisting of a cogeneration unitwithout the electric power export, a storage tank, a gas-fired boiler,and peripheral devices, for simulated energy demands in a Japaneseresidence. The candidates for a cogeneration unit are a GE-CGUemploying the constant power output operation, a PEFC-CGUemploying the daily startestop operation, and an SOFC-CGUemploying the continuous operation, and the candidates for pe-ripheral devices are an electric water heater and an air-cooled heatexchanger. The results revealed that the selection of the optimalcogeneration unit is influencedmore by the operating restrictions ofthe cogenerationunits than by the consistency in the heat-to-powerratios of the cogeneration unit and energy demands. In addition, itwas revealed that the selection of the peripheral devices varies withthe selected cogeneration unit and energy demands. Furthermore,the energy-saving analysis of the residential cogeneration systemswith the optimal and suboptimal structures showed that theoptimal structural design of the residential cogeneration system isimportant to achieve a high energy-saving effect and that thedevelopedmodel is a powerful tool for theoptimal structural design.

In a further study, the optimal structure of the residentialcogeneration system, inwhich a battery is newly considered to be acandidate, will be analyzed because a residential cogeneration unitwith a battery can operate more flexibly even without the electricpower export. The fuel cell-based cogeneration units focused in thisstudy have high energy-saving effects for a wide range of theannual energy demands; however, a total cost reduction by utiliz-ing them is not currently expected due to their high initial costs.Moreover, the optimal structural design from only the energy-saving viewpoint may select many peripheral devices that areoperated on limited days. Hence, the important issue of future

T. Wakui, R. Yokoyama / Energy 64 (2014) 719e733 733

studies is to develop the optimal structural design model consid-ering the capital recovery constraint of the system components;this method can also optimize the sizing of the system components.

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