A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges

Energy xxx (2014) 1e18

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A mixed-integer linear programming approach for cogenerationbased residential energy supply networks with power and heat interchanges Tetsuya Wakui*, Takahiro Kinoshita, Ryohei Yokoyama Department 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

a b s t r a c t

Article history: Received 15 February 2013 Received in revised form 28 January 2014 Accepted 30 January 2014 Available online xxx

The feasibility on a residential energy supply network using multiple cogeneration systems, known as combined heat and powers, is investigated by an optimization approach. The target residential energy supply network is based on a microgrid of residential cogeneration systems without electric power export, and featured by power and heat interchanges among cogeneration systems and hot water supply network where produced hot water is supplied to multiple residence units through networked pipes. First, an optimal operational planning model is developed on the basis of mixed-integer linear programming, where energy loss characteristics of connecting pipes between storage tanks are originally modeled by considering the influence of hot water retention. Second, a hot water demand calculation model considering energy loss from networked pipes is developed to reduce the solution space of the optimization problem. The developed models are then applied to a residential energy supply network for a housing complex composed of multiple 1-kWe gas engine-based cogeneration systems and 20 residence units. The results show that the energy-saving effect of the residential energy supply network is dominated by the power interchange and decreases with an increase in the number of residence units involved in the hot water supply network.
2014 Elsevier Ltd. All rights reserved.

Keywords: Cogeneration Gas engine Microgrid Operational planning Optimization Energy saving

1. Introduction 1.1. Background and concept of residential energy supply network Cogeneration systems have been extended to residential sector because of the development of small-scale, high-performance energy-conversion machines [1]. In Japan, a 1-kWe gas enginebased cogeneration system (GE-CGS) [2] and 1-kWe [3] and 0.75kWe [4] polymer electrolyte fuel cell-based cogeneration systems (PEFC-CGSs) are available for residential use. Recently, a 0.7-kWe solid oxide fuel cell-based cogeneration system (SOFC-CGS) has been released [5]. These residential cogeneration systems (R-CGSs) have different heat-to-power supply ratios and operational restrictions. The GE-CGS has a high heat-to-power supply ratio and must be operated under a constant power output to maintain a high generation efficiency. The PEFC-CGSs have higher generation efficiencies than the GE-CGS; however, they adopt a daily starte

* Corresponding author. Tel.: þ81 72 254 9232; fax: þ81 72 254 9904. E-mail address: [email protected] (T. Wakui).

stop operation, in which they can be started and stopped up to once a day. This is due to thermal degradation of stacks and input energies for start-up. The SOFC-CGS has the highest generation efficiency and must be operated continuously because its high operating temperature requires a long warm-up time and a high level of input energies. Moreover, in Japan, surplus electric power generated by R-CGSs cannot be exported to commercial electric power systems. Thus, to obtain benefits such as energy savings, CO2 emission reduction, and cost reduction, R-CGSs must be appropriately operated in response to variations in electric power and heat demands. A storage tank is also indispensable for intermittent hot water supply. However, if energy demands of a residence unit do not match capacity and operational restriction of an R-CGS, then the R-CGS may not fully achieve its potential benefits. The present study focuses on a residential energy supply network (R-ESN) using multiple R-CGSs to improve the energysaving effect of R-CGSs. The R-ESN is based on a microgrid [6] of R-CGSs without electric power export; this microgrid is referred to as power interchange. Hot water produced by R-CGSs is stored in storage tanks and stored hot water is interchanged among storage tanks; this is referred to as heat interchange. Moreover, the stored

http://dx.doi.org/10.1016/j.energy.2014.01.110 0360-5442/
2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

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Nomenclature

Indices/sets f˛F floors in housing complex h˛H residence units involved in hot water supply network k˛K sampling times on each representative day m˛M representative days in typical year n˛N residential cogeneration systems on each floor Objective functions JESN total daily primary energy consumption of residential energy supply network [MJ/d] Binary variables for mixed-integer linear programming model z binary variable vector expressing operating status of devices dIH operating status of pump for heat interchange dR retention status of hot water in connecting pipe dRl retention status of hot water longer than maximum duration time dRs retention status of hot water shorter than maximum duration time Continuous variables for mixed-integer linear programming model T continuous variable vector expressing duration time of hot water retention x continuous variable vector expressing energy flow rates of inputs and outputs of energy conversion devices y continuous variable vector expressing energies stored in energy storage devices B EPC electric power purchased in bulk [kWh/h] natural gas consumption in cogeneration unit [m3/h] GCGU GGB natural gas consumption in gas-fired backup boiler [m3/h] QIH energy flow rate of interchanged hot water [kWh/h] QL energy flow rate lost from connecting pipe [kWh/h] in QST out QST

SST TR

zIH xR

energy flow rate of hot water stored to storage tank [kWh/h] energy flow rate of hot water supplied from storage tank [kWh/h] stored energy [kWh] duration time of hot water retention [h] continuous variable to linearize nonlinear term continuous variable to linearize nonlinear term [h]

Equations for mixed-integer linear programming model gCD linear equation vector expressing inputeoutput characteristics of energy conversion devices gEB linear equation vector expressing energy balance and supplyedemand relationships gST linear equation vector expressing inputeoutput characteristics for storage tanks hCP nonlinear equation vector expressing inputeoutput characteristics for connecting pipes Variables for hot water demand calculation model gd mass flow rate of hot water at each residence unit [kg/ h] gPP mass flow rate of hot water in hot water pipe [kg/h]

Qd QSP SPP SRPP UPP

hSPP qPP qSPP sPP

hot water demand at each residence [kWh/h] energy flow rate of hot water at supply point [kWh/h] energy of hot water in hot water pipe [kWh] energy lost from hot water pipe [kWh] overall heat transfer coefficient of hot water pipe [kW/ (m2  C)] hot water supply efficiency hot water temperature in hot water pipe [ C] hot water temperature in hot water pipe during hot water supply [ C] time constant during hot water retention [h]

Parameters c specific heat of water [kWh/(kg  C)] outside diameter of insulator [m] doIS diPP doPP

inside diameter of hot water pipe [m] outside diameter of hot water pipe [m]

R ECGU L sIH

rated electric power output of cogeneration unit ength of hot water pipe [m] hot water energy added during heat interchange [kWh] sampling time [h] maximum duration time of hot water retention available for heat interchange [h] volume of hot water pipe [m3] weighted number of representative days for each month heat transfer coefficients inside hot water pipe [kW/ (m2  C)] heat transfer coefficients outside hot water pipe [kW/ (m2  C)] heat interchange efficiency of connecting pipe energy loss rate from storage tank ambient temperature [ C] feed water temperature [ C] hot water supply temperature [ C] hot water temperature in storage tank [ C] heat conductivity of insulator [kW/(m  C)] heat conductivity of hot water pipe [kW/(m  C)] water density [kg/m3] conversion factor for primary energy of purchased electric power [MJ/(kWh)] conversion factor for primary energy of natural gas [MJ/m3] upper and lower limits

Dt TRM VPP W

ai ao hIH hST qA qF qS qST lIS lPP r fE fG ðÞ; ðÞ

Performance criteria total daily primary energy consumption of JCO conventional energy supply system [MJ/d] JSE total daily primary energy consumption of separate operation of each residential cogeneration system [MJ/ d] PE electric capacity factor of residential cogeneration systems [%] RE electric power supply rate [%] RIH interchanged hot water rate [%] RQ hot water supply rate [%] gESN reduction rate of primary energy consumption for residential energy supply network relative to that for conventional energy supply system [%]

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

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gSE

reduction rate of primary energy consumption for separate operation of each residential cogeneration system relative to that for conventional energy supply system [%]

Abbreviation CO conventional energy supply system GE-CGS gas engine-based cogeneration system IE residential energy supply network employing power interchange

hot water is supplied to multiple residence units through networked pipes; this is referred to as hot water supply network. Thus, the R-ESN under study is featured by the power and heat interchanges and the hot water supply network. By employing the power interchange, surplus electric power generated by an R-CGS can be transmitted to other residence units; this increases capacity factor of R-CGSs that have the above-mentioned operational restrictions. The heat interchange and the hot water supply network can also increase the capacity factor because effective utilization of hot water produced by R-CGSs is indispensable for energy savings.

1.2. Review of previous works Benefits of microgrids including R-ESNs have already been studied numerically and experimentally. Some of previous studies [7e9] were conducted on the basis of simulation, in which R-CGSs were operated in a heat-led mode and surplus electric power was exported. Many studies based on optimization approaches are related to two issues: optimal operational planning and optimal design. Most of the former studies were based on mixed-integer linear programming (MILP). Aki et al. developed a multi-objective optimization model for an R-ESN using PEFC-CGSs; they analyzed the effects of operational strategies of PEFC-CGSs [10] and the numbers of PEFC-CGSs and natural gas reformers [11] on the operational cost and CO2 emission reductions. The authors of the present study developed an optimization model for a microgrid using multiple R-CGSs, in which electric power generated by RCGSs was interchanged among residence units. They analyzed the effects of the number of GE-CGSs [12] and SOFC-CGSs [13], operational strategies of SOFC-CGSs [14], and sizing of GE-CGSs [15] and SOFC-CGSs [16] on energy savings. Kopanos et al. also developed an optimization model for an R-ESN using multiple 1-kWe Stirling engines, in which electric power and hot water were interchanged. They analyzed reduction in the operational cost for 64 residence units [17]. A multi-objective optimization model for a microgrid incorporating a demand response program was also developed [18]. Moreover, an adaptive learning algorithm [19] and an evolutionary algorithm [20] for multi-objective optimization models with nonlinear objective functions were proposed. In studies on the optimal design, sizing and structure as well as operational planning were simultaneously optimized. The linear programming approaches [21,22], MILP approaches [23e30] as well as intelligent algorithms [31,32] were used. R-ESNs were demonstrated in Japan. Yamaguchi et al. [33] demonstrated an R-ESN consisting of a GE-CGS and a single-loop hot water supply network for a housing complex with seven residence units. Aki et al. [34] demonstrated an R-ENS using three PEFC-CGSs in a housing complex with six residence units. Both the demonstrations revealed that the R-ESNs are highly effective in reducing CO2 emission and saving energy, but they are seriously

3

IEH

residential energy supply network employing power and heat interchanges MILP mixed-integer linear programming PEFC-CGS polymer electrolyte fuel cell-based cogeneration system R-CGS residential cogeneration system R-ESN residential energy supply network SE separate operation of each residential cogeneration system SOFC-CGS solid oxide fuel cell-based cogeneration system

affected by energy losses due to long networked pipes [33] and hot water retention because of an intermittent hot water supply [34]. 1.3. Objective of the study With such a background and review of previous works, the present study develops an analysis model for the energy-saving effect of R-ESNs using multiple R-CGSs and then investigates their feasibility by analyzing the optimal operational planning. The developed analysis model is basically an extension of our MILP approach [12], by newly considering the heat interchange and the hot water supply network. Unlike previous works based on linear programming [21,22], MILP approach can consider various operational restrictions of system components including R-CGSs, e.g., oneoff status and nonlinear variations in their energy conversion efficiencies in response to their load factors by using piecewise linear equations [35]. Moreover, energy loss from networked pipes is an important issue to consider R-ESNs, as pointed out in the demonstrations [33,34]. Some research ignored the energy loss [7e9,18e 23,26,30,32], some research treated the energy loss as a constant rate [10,17,24,29], and other research considered the energy loss to be proportional to the pipe length [25,27,28,31]. The present study uniquely models the energy loss characteristics of connecting pipes between storage tanks by considering the influence of hot water retention. A more realistic optimal operational planning can be conducted based on the proposed model. The further novelty of the approach is to treat energy loss from networked pipes calculated by considering hot water retention as hot water demand, to reduce the solution space of the optimization problem. The developed analysis model is applied to an R-ESN for a housing complex composed of multiple 1-kWe GE-CGSs and 20 residence units. Consequently, the effects of the power and heat interchanges and the hot water supply network on energy savings are revealed. 1.4. Framework of the study The framework of energy-saving analysis of R-ESNs is shown in Fig. 1. In this study, the following two models are developed: the MILP model for the optimal operational planning problem and the hot water demand calculation model considering the energy loss from the networked pipes. The configuration of R-ESN is the common input to both the MILP model and the hot water demand calculation model. The specifications of the devices and electric power demands of the housing complex are the input to the former model, while the specifications of the networks pipes and hot water demands of the housing complex are the input to the latter model. Moreover, the hot water demand calculated by using the hot water demand calculation model and the conversion factors from the primary energy are the input to the MILP model. This paper consists of five sections. Following the introduction, the configurations of the target R-ESN and reference systems are

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

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Fig. 1. Framework of energy-saving analysis of residential energy supply network.

stated in Section 2. Section 3 describes the energy-saving analysis model consisting of the MILP model and hot water demand calculation model. Section 4 reports a case study by applying the proposed model to a hypothesized housing complex and the energy savings are compared with the reference systems. Finally, the derived results and future studies are summarized in Section 5. 2. Residential energy supply network (R-ESN) using multiple R-CGSs The R-ESN has various kinds of configurations based on the type and capacity of cogeneration unit as well as the installation or non-

installation and the capacity of peripheral devices. In the present study, the configuration is preliminarily fixed and the R-ESN is applied to a housing complex, as shown in Fig. 2. In a housing complex, power interchange of R-CGSs without electric power export can be easily conducted under the Japanese electricity regulation and the energy loss from hot water pipes for heat interchange and hot water supply network can be reduced. The same numbers of R-CGSs, which have the same capacity, are installed on each floor of the housing complex. The hot water supply network is constructed on only the same floor. The number of the residence units involved in the hot water supply network is also fixed to be identical for any RCGS and treated as an analytical parameter.

Fig. 2. Energy flow-based configuration diagram of residential energy supply network using multiple R-CGSs in housing complex.

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

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Fig. 3. Actual configuration of heat interchange between storage tanks on the same floor.

To analyze the effect of the power and heat interchanges, the two typical configurations of the R-ESN are focused on: the R-ESN employing both the power and heat interchanges (IEH) and that employing only the power interchange (IE). The hot water supply network is employed in both configurations. An R-ESN employing only the heat interchange is not effective because the operational restriction of R-CGSs due to electric power demand of each residence unit limits their capacity factor [12]. 2.1. Energy flow in R-ESN 2.1.1. Power interchange The power interchange is conducted by forming a microgrid of R-CGSs without electric power export in the housing complex. Actually, an on-line controller manages load dispatching of each RCGS so as to maximize benefits. Sensors to monitor the energy stored in each storage tank, energy demands of the housing complex, and purchased electric power, and communication network among R-CGSs are also required. For this kind of microgrid, the electric stability is often an important subject. However, in the previous demonstration [34], no instability of the microgrid using multiple PEFC-CGSs and connected electric power system was reported during operation.

5

line controller. As an example, an actual configuration of heat interchange between the adjacent storage tanks on the same floor, which can be seen in Fig. 2, is shown in Fig. 3. Generally, a household storage tank is always filled with water and have temperature stratifications to its vertical direction [36]; i.e., the water temperature at the top of the storage tank is close to the outlet water temperature of the cogeneration unit, while that at the bottom is close to the feed water temperature. Thus, the two adjacent storage tanks are actually connected through the two connecting pipes. In the upper connecting pipe, two pumps with opposite flow directions are installed, and an electromagnetic valve is installed in the bottom connecting pipe. Additionally, the pipes to supply hightemperature water from the cogeneration unit and to the hot water supply network are installed at the top of the storage tank, and the pipe to supply low-temperature water to the cogeneration unit and the pipe to supply feed water to the storage tank are installed at the bottom of the storage tank. As an example, the heat transfer from the left-side storage tank to the right-side storage tank is focused on. After receiving the command signal, the electromagnetic valve installed between the two storage tanks is opened and only the pump for sending hot water rightward is operated. Consequently, the high-temperature water is sent from the left-side storage tank to the right-side storage tank through the upper connecting pipe, while the lowtemperature water with the same flow rate as the hightemperature water is automatically sent in the opposite flow direction through the bottom connecting pipe. The heat interchange between the adjacent storage tanks on the upper and lower floors can also be conducted in the same manner as that on the same floor. 2.1.3. Hot water supply network The hot water supply network can be flexibly formed for multiple residence units on the same floor and the upper and lower floors. An actual configuration of the hot water supply network on the same floor, which can be seen in Fig. 2, is shown in Fig. 4, as an example. Hot water supplied from a storage tank passes through a gas-fired backup boiler and then is distributed to multiple residence units through hot water pipes; they are collectively called a networked pipe. A shortage of energy of the hot water supplied from the storage tank is supplemented for by the gas-fired backup boiler. The distributed hot water is mixed with feed water at a mixing valve, to obtain a given hot water supply temperature. 2.2. Configuration of reference systems

2.1.2. Heat interchange between storage tanks The heat interchange can be flexibly conducted between adjacent storage tanks on the same floor and the upper and lower floors. The command signal is sent from the above-mentioned on-

The following reference configurations are also considered: (1) separate operation of each R-CGS that is installed at each residence unit and independently operated without the power and heat

Fig. 4. Actual configuration of R-CGS and hot water supply network.

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

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interchanges, hot water supply network, and electric power export (SE), and (2) conventional energy supply without R-CGS, where at each residence unit, the electric power is purchased from an electric power company and hot water is supplied from a gas-fired boiler (CO). By comparing the energy-saving effect of SE with that of IE, the effect of the power interchange on energy savings can be investigated. CO is the benchmark to analyze the energy-saving effect of SE, IE, and IEH. 3. Energy-saving analysis model for R-ESN As shown in Fig. 1, the MILP model and hot water demand calculation model are developed in the present study. Their details are described in this section. 3.1. MILP model for optimal operational planning problem To evaluate the theoretical upper limit of saving energy by the RESN, the optimal operational planning is conducted by the developed MILP model. In this model, operational strategies of devices in the R-ESN are determined so as to minimize daily primary energy consumption. The target housing complex has F floors, and N R-CGSs are installed on each floor. The hot water in each storage tank is supplied to H residence units. Moreover, to consider seasonal and hourly variations in energy demands, a typical year is divided into M representative days, and each representative day is divided into K sampling times, with a period of Dt, i.e., Dt ¼ 24/K. The operational strategy in each representative day is separately determined to reduce the solution space. As is the case with the previous study [12], a daily cyclic operation is considered, assuming that energy demands change cyclically with a period of 24 h on each representative day. 3.1.1. Problem formulation In the optimal operational planning problem under study, the objective is to minimize daily primary energy consumption in the R-ESN, JESN(m) while satisfying the constraints regarding the inputeoutput characteristics of the devices and the energy balance. The problem is formulated as below.

Fig. 5. Energy flow rate-based modeling of storage tank with heat interchange.

the inputeoutput characteristics of the connecting pipes; gEB is the linear equation vector expressing the energy balance and supplye demand relationships; X and X are the lower and upper limits of x(k,m); and Y and Y are the lower and upper limits of y(k,m). The eighth equation in Eq. (1) means that z(k,m) is the binary variable vector consisting of I elements; this number corresponds to the number of the binary variables [37].

9 > > > > > B ðk; mÞ þ f > fE ðkÞEPC D min: JESN ðmÞ ¼ ðn; f ; k; mÞ þ G ðn; f ; k; mÞg t fG > CGU GB G > > > n ¼ 1 k¼1 f ¼1 > > > > > ðm ¼ 1; 2; .; MÞ > > 9 > > > > g CD ðxðk; mÞ; zðk; mÞÞ ¼ 0 > > > > > > > > > > g ST ðxðk; mÞ; yðk; mÞ; yðk  1; mÞÞ ¼ 0 > > = > > > > hCP ðxðk; mÞ; Tðk; mÞ; Tðk  1; mÞ; zðk; mÞ; zðk  1; mÞÞ ¼ 0 = > > > > > g EB ðxðk; mÞÞ ¼ 0 > > > > s:t: > > > > > X  xðk; mÞ  X > > > > > > > > > > > Y  yðk; mÞ  Y > > > > > > ; > I > > zðk; mÞ˛f0; 1g > > > > > ðk ¼ 1; 2; /; K; m ¼ 1; 2; /; MÞ ; K P

"

F P

N P

where gCD is the linear equation vector expressing the inpute output characteristics of the energy conversion devices; gST is the linear equation vector expressing the inputeoutput characteristics of the storage tanks; hCP is the nonlinear equation vector expressing

#

(1)

The objective function, JESN(m), is calculated from the purchased electric power and natural gas at each sampling time and their conversion factors for the primary energy. The detailed formulation of gCD is referred to Eqs. (2)e(5), (9), and (10) of

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9 P P ðn; f ; k; mÞ  Q dP ðn; f ; k; mÞ > > Q IH dIH ðn; f ; k; mÞ  QIH > IH IH > = N N N ðn; f ; k; mÞ  Q d ðn; f ; k; mÞ Q IH dIH ðn; f ; k; mÞ  QIH IH IH > > > > ; dPIH ðn; f ; k; mÞ þ dNIH ðn; f ; k; mÞ þ dR ðn; f ; k; mÞ ¼ 1

Ref. [35] and Eq. (8) of [38]. The detailed formulation of gEB is referred to Eqs. (9) and (12) of Ref. [15]. gCD is formulated by piecewise linear equations divided into multiple intervals to express nonlinear inputeoutput relationships of the energy conversion devices including the cogeneration units, electric water heaters, gas-fired backup boilers, and radiators. In case of the cogeneration unit employing the constant power output operation, e.g., a gas engine-based cogeneration unit, the number of the intervals is set to be 1 [12]. For gEB, the supplyedemand relationships of the electric power and hot water are considered in the housing complex and at the supply point to the networked pipe, indicated in Fig. 4, respectively. The energy flow rate of the hot water at the supply point is preliminarily calculated by using the hot water demand calculation model stated in Section 3.2. The energy balance relationship is also considered at each connecting point between the devices. Moreover, gST consists of the energy balance relationships of the storage tanks between the two consecutive sampling times. They are an extension of the ideal stratification model defined by Celador et al. [39] and formulated on the basis of the energy flow rates shown in Fig. 5. The detailed formula is expressed as follows:

ðn ¼ 1; 2; .; N  1; f ¼ 1; 2; .; F  1; k ¼ 1; 2; .; K; m ¼ 1; 2; .; MÞ (3) where dIH is the binary variables expressing the oneoff status of the pump to send the interchanged hot water and an element of z. The duration time of the hot water retention, TR, is calculated by using dR as follows:

TR ðn; f ; k; mÞ ¼ fTR ðn; f ; k  1; mÞ þ DtgdR ðn; f ; k; mÞ ðn ¼ 1; 2; /; N  1; f ¼ 1; 2; /; F  1; k ¼ 1; 2; /; K; m ¼ 1; 2; /; MÞ (4) TR and dR are elements of T and z, respectively. The daily cyclic operation is applied to TR. If the duration time in a connecting pipe is longer than its maximum time, TRM , in which the hot water temperature inside the connecting pipe is usable for the heat

9 > > > > > > > > > > n o> > > P N N > þQIH ðn  1; f ; k; mÞ  QIH ðn  1; f ; k; mÞ þ QL ðn  1; f ; k; mÞ > > > > > > > > > > o n > > P P N =  Q ðn; f ; k; mÞ þ Q ðn; f ; k; mÞ þ Q ðn; f ; k; mÞ

SST ðn; f ; k; mÞ  SST ðn; f ; k  1; mÞ in ðn; f ; k; mÞ  Q out ðn; f ; k; mÞ  h ðk; mÞS ðn; f ; k  1; mÞ ¼ QST ST ST ST Dt

IH

L

IH

> > o> > > > U D þQIH ðn; f  1; k; mÞ  QIH ðn; f  1; k; mÞ þ QLD ðn; f  1; k; mÞ > > > > > > > > > > o n > > U U D >  QIH ðn; f ; k; mÞ þ QL ðn; f ; k; mÞ þ QIH ðn; f ; k; mÞ > > > > > > > ; S ðk; mÞ  S ðn; f ; k; mÞ  S ðk; mÞ

ð2Þ

n

ST

ST

ST

ðn ¼ 1; 2; /; N; f ¼ 1; 2; /; F; k ¼ 1; 2; /; K; m ¼ 1; 2; /; MÞ in and Q out are where SST is the stored energy and an element of y; QST ST the energy flow rate of hot water supplied to and from the storage tank, respectively, and elements of x; QIH is the energy flow rate of the interchanged hot water and an element of x; and the superscript P, N, U, and D denote the positive (from the nth storage tank to the n þ 1th storage tank on the same floor), negative (from the nth storage tank to the n  1th storage tank on the same floor), upward (from the fth floor to the f þ 1th floor), and downward (from the fth floor to the f  1th floor) directions in Fig. 5, respectively. In this equation, the flow rate of energy of the hot water lost from the connecting pipes, QL, is uniquely considered when the hot water is extracted from the storage tank. The daily cyclic operation is applied to SST. Furthermore, hCP consists of the following Eqs. (3)e(6). The hot water retention in the horizontal connecting pipes is expressed by the binary variable dR as follows:

interchange, the energy flow rate to make up for the decrease in the hot water temperature is added to QL. TRM is treated as a parameter. This operating condition is expressed by using the binary variables, dRI and dRS, in the following equation:

0TRs ðn;f ;k;mÞTRM ðn;f ;k;mÞdRs ðn;f ;k;mÞ n o TRM ðn;f ;k;mÞþ Dt dRl ðn;f ;k;mÞTRl ðn;f ;k;mÞT Rl dRl ðn;f ;k;mÞ > > > > > > ; dRs ðn;f ;k;mÞþ dRl ðn;f ;k;mÞ ¼ 1 ðn ¼ 1;2;.;N 1;f ¼ 1;2;.;F 1;k ¼ 1;2;.;K;m ¼ 1;2;.;MÞ (5) where the subscript l and s denote the duration time longer and shorter than TRM , respectively. As a result, QL is expressed by the following equation:

sIH ðk; mÞ dRl ðn; f ; k  1; mÞdIH ðn; f ; k; mÞ Dt ðn ¼ 1; 2; .; N  1; f ¼ 1; 2; .; F  1; k ¼ 1; 2; .; K; m ¼ 1; 2; .; MÞ QL ðn; f ; k; mÞ ¼ hIH ðk; mÞQIH ðn; f ; k; mÞ þ

9 > > > > > > =

TR ðn;f ;k;mÞ ¼ TRs ðn;f ;k;mÞþTRl ðn;f ;k;mÞ

(6)

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where hIH is the heat interchange efficiency and treated as a parameter; and sIH is the hot water energy added during heat interchange and treated as a parameter. dRl applies the daily cyclic operation. dRl is also an element of z; thus, hCP is a nonlinear equation vector with respect to T(k  1,m), z(k,m), and z(k  1,m). The constraints for the vertical connecting pipes are formulated in the same manner as the horizontal ones.

3.1.2. Solution method The above formulation of the optimal operational planning problem results in a mixed-integer nonlinear programming one. As the number of the binary variables, I, increases, this problem becomes large scale and it is difficult to solve it directly. Hence, this problem is reformulated as a MILP one. First, the nonlinear terms in hCP, which are the product of TR(n,f,k  1,m) and dR(n,f,k,m) in Eq. (4) and that of dRl(n,f,k  1,m) and dIH(n,f,k,m) in Eq. (6), are replaced with the following continuous variables, xR(n,f,k,m) and zIH(n,f,k,m):

xR ðn; f ; k; mÞ ¼ TR ðn; f ; k  1; mÞdR ðn; f ; k; mÞ ðn ¼ 1; 2; .; N  1; f ¼ 1; 2; .; F  1; k ¼ 1; 2; .; K; m ¼ 1; 2; .; MÞ (7)

zIH ðn; f ; k; mÞ ¼ dRl ðn; f ; k  1; mÞdIH ðn; f ; k; mÞ ðn ¼ 1; 2; .; N  1; f ¼ 1; 2; .; F  1; k ¼ 1; 2; .; K; m ¼ 1; 2; .; MÞ (8) respectively. The product of dR1 and dIH is also replaced with the continuous variable to reduce the total number of the binary variables. For xR and zIH, the following constraints are additionally considered:

9 T R dR ðn; f ; k; mÞ  xR ðn; f ; k; mÞ  T R dR ðn; f ; k; mÞ > > =

3.2. Hot water demand calculation model considering energy loss from networked pipes In the hot water demand calculation model, the energy flow rate of the hot water at the supply point to the networked pipe, QSP, is calculated by considering the energy loss not only during the hot water supply but also due to the hot water retention. If the hot water temperature in the hot water pipe during the hot water retention becomes lower than the hot water supply temperature, the energy to make up for its decrease is regarded as the energy loss. The addition of this energy loss depends on the hot water supply condition at the two consecutive sampling times.

3.2.1. Mathematical formulation The hot water demand calculation model consists of the following equation as well as Eqs. (A1)e(A6) of Appendix A.

QSP ðn; f ; k; mÞ ¼

hSPPh ðn; f ; k; mÞ ¼

H P



h¼1

Qdh ðn; f ; k; mÞ SRPPh ðn; f ; k; mÞ þ Dt hSPPh ðn; f ; k; mÞ



qSPPh ðn; f ; k; mÞ  qF ðk; mÞ qST qF ðk; mÞ

SRPPh ðn; f ; k; mÞ 8 0 ðgPPh ðn; f ; k; mÞ ¼ 0Þ > > >   9 > > S > > > q ðn; f ; k  1; mÞ  qPPh ðn; f ; k; mÞ 0 > > PPh > > > > > > > > > > = < S ðn; f ; k; mÞ  S ðn; f ; k  1; mÞ PPh PPh ¼   > > > qS < qPPh ðn; f ; k  1; mÞ < qSPPh ðn; f ; k; mÞ > > > > > > > > > > > ; > > > ðqPPh ðn; f ; k  1; mÞ < qS Þ > SPPh ðn; f ; k; mÞ > > : ðgPPh ðn; f ; k; mÞ > 0Þ

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

(11)

TR ðn; f ; k  1; mÞ þ T R fdR ðn; f ; k; mÞ  1g

> >  xR ðn; f ; k; mÞ  TR ðn; f ; k  1; mÞ ;

ðh ¼ 1; 2; /; H; n ¼ 1; 2; /; N; f ¼ 1; 2; /; F; k ¼ 1; 2; /; K;

ðn ¼ 1; 2; .; N  1; f ¼ 1; 2; .; F  1; k ¼ 1; 2; .; K; m ¼ 1; 2; .; MÞ (9) 9 dRl dIH ðn; f ; k; mÞ  zIH ðn; f ; k; mÞ  dRl dIH ðn; f ; k; mÞ > > = dRl ðn; f ; k  1; mÞ þ dRl fdIH ðn; f ; k; mÞ  1g > > ;  zIH ðn; f ; k; mÞ  dRl ðn; f ; k  1; mÞ

m ¼ 1; 2; /; MÞ First, QSP is calculated from the sum of the actual hot water demand of each residence unit, Qd, and the energy lost from each hot water pipe, SRPP . Second, the hot water supply efficiency, hSPP , is calculated from the hot water temperature at the outlet of the hot water pipe S

ðn ¼ 1; 2; /; N  1; f ¼ 1; 2; /; F  1; k ¼ 1; 2; /; K; m ¼ 1; 2; /; MÞ (10) respectively, where T R and T R are set as 0 and KDt, respectively; and

dRl and dRl are set as 0 and 1, respectively. In Eq. (9), if dR ¼ 0, xR ¼ 0, or else, if dR ¼ 1, xR ¼ TR. In Eq. (10), if dIH ¼ 0, zIH ¼ 0, or else, if dIH ¼ 1, zIH ¼ dRI. Thus, this procedure can linearize Eqs. (7) and (8) without any approximation [40] and transform the problem into the MILP one. The reformulated problem is coded using the algebraic modeling language, GAMS distribution 23.1 [41], and is solved using the optimization solver for large-scale MILP problems, CPLEX version 12.2 [42]. The solver can evaluate the lower bound of the objective function by using linear relaxation during computation. All of the solutions in this study are derived under the condition that the gap between the actual value of the objective function and its lower bound is within 0.02%.

during the hot water supply, qPP , the hot water temperature in the S

storage tank, qST, and the feed water temperature, qF. qPP is calculated by Eq. (A1) of Appendix A derived by solving the heat balance equation and Eq. (A2) of Appendix A to calculate the overall heat transfer coefficient, UPP. qST and qF are treated as parameters. Third, SRPP is calculated from SPP that is the energy of the hot S

water in the hot water pipe, the temperature of which equals to qPP , and SPP that is the energy of the actual hot water in the hot water pipe. SPP and SPP are calculated from Eqs. (A3) and (A4) of Appendix A, respectively. The calculation of SRPP depends on the hot water temperature at the outlet of the hot water pipe, qPP, at the previous sampling time and the mass flow rate of the hot water in the hot water pipe, gPP, at the current sampling time. qPP is calculated from Eqs. (A5) and (A6) of Appendix A; the time constant in the latter equation, sPP, is derived by considering the heat balance during the hot water retention. If the hot water is retained in the hth hot water pipe at the kth sampling time, i.e., gPPh(n,f,k,m) ¼ 0, no energy is

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T. Wakui et al. / Energy xxx (2014) 1e18

added as SRPPh . If the hot water is supplied through the hth hot water pipe at the kth sampling time, i.e., gPPh(n,f,k,m) > 0, the energy to S

make up the decrease in qPPh from qPPh is added. Moreover, if qPPh is lower than the hot water supply temperature qS, the energy, the S

temperature of which coincides with qPPh , is added because lowtemperature hot water in the hot water pipe cannot be used for the hot water supply. 3.2.2. Solution method Qd is calculated from the flow rate of the hot water supplied to each residence, gd, and the given qS. hSPP and SRPP are calculated by setting the boundary conditions including qST, qF, the ambient temperature qA, and Qd, and then QSP is calculated. This calculation procedure does not require any convergence algorithm. Thus, QSP is preliminarily calculated and substituted as the input data for the MILP model. 4. Case study As a case study, the developed model for the energy-saving analysis of the R-ESN is applied to a housing complex in Japan. First, the input data are stated and then the derived results are discussed. 4.1. Input data 4.1.1. Configuration of R-ESN The R-ESN is applied to a hypothesized housing complex to analyze its energy-saving effect. The R-ESN under study employs GE-CGSs because the power and heat interchanges and the hot water supply network can increase the capacity factor of GE-CGSs with the operational restrictions stated in the introduction. The radiator is not installed because effective utilization of produced hot water is indispensable for energy savings by operating a gas engine with a high heat-to-power supply ratio [43]. The targeted housing complex has five floors, i.e., F ¼ 5, and four residence units on each floor; thus, the total number of residence units is 20. The number of residence units involved in the hot water supply network, H, is parametrically set to be 1, 2, and 4. Hereafter, IE and IEH in the case of H residence units per GE-CGS are referred to as IE-H and IEH-H, respectively. For H ¼ 1 and 2, the heat interchange is conducted on the same floor, while for H ¼ 4, the heat interchange is conducted between the adjacent floors. Hereafter, the hth GE-CGS on the fth floor is referred to as GE-CGS-fh. For SE, H

9

Table 2 Specifications of connecting and networked pipes. Item

Value

Pipe inside/outside diameter [46]

20.6/22.22 20.6/22.22 26.8/28.58 5.0 1.0 3.0 2.0 5.0 20 388 0.045 11.63

Connecting pipe, mm Networked pipe (H ¼ 1, 2), mm Networked pipe (H ¼ 4), mm Pipe length Connecting pipe (H ¼ 1), m Connecting pipe (H ¼ 2), m Connecting pipe (H ¼ 4), m Networked pipe (h ¼ 1), m Networked pipe (h ¼ 2, ., H), m Insulation thickness [46], mm Heat conductivity of copper pipes [46], W/(m  C) Heat conductivity of rock wool insulator [46], W/(m  C) Heat transfer coefficient on surface of insulator [46], W/(m2  C)

is fixed to be 1, and the objective function is formulated as is the case with Ref. [12]. For SE and IE without the heat interchange, all the binary variables expressing the oneoff status of pumps for the heat interchange are set to be 0. 4.1.2. Specifications of devices and pipes The specifications of the devices, including those of the 1-kWe GE-CGS estimated on the basis of Ref. [44], are listed in Table 1. The lower limit of the stored energy is set to be 10% of its upper limit [38] to consider unusable hot water due to actual temperature stratification. The energy loss rate from the storage tank is calculated by using the overall heat transfer coefficient. Unlike the released 1-kWe GE-CGS [44], a latent heat recovery type of gasfired backup boiler [45], which is more efficient than a conventional type, is employed. The specifications of the connecting and networked pipes are listed in Table 2. The pipe length is originally estimated from residence unit arrangements of a typical housing complex in Japan. All of the pipes are assumed to be copper pipes surrounded by rock wool insulation [46]. For the connecting pipes, TRM is set to be shorter than the sampling time of this study (Dt ¼ 1 h) because of the high hot water temperature in the storage tank. 4.1.3. Energy demands for R-ESN The demands for electric power and hot water of 20 residence units were measured in the other housing complex located in the Kansai region of Japan; they were reported by Tsuji et al. [47]. These energy demands are estimated at 24 sampling times for a representative day in each month, i.e., M ¼ 12, K ¼ 24, and Dt ¼ 1 h. The total daily demands for electric power and hot

Table 1 Specifications of devices in residential energy supply network. System component

Item

Value

Gas engine cogeneration unit [44]

Rated electric power output, kW Rated hot water output, kW Rated natural gas consumption, m3/h Power consumption at water pump, kW Hot water temperature,  C Heating efficiency, % Maximum input electric power, kW Volume, L Surface area, m2 Hot water temperature,  C Overall heat transfer coefficient for energy loss [35], W/(m2  C) Thermal efficiency based on higher heating value, % Rated energy flow rate of interchanged hot water, kW Rated power consumption, kW

1.00 2.50 0.337 0.050 75 90 0.95 90H 1.20H2/3 75 0.80

Electric water heater [44] Storage tank [44]

Gas-fired backup boiler [45] Pump for heat interchange [44]

90 2.50 0.050

Fig. 6. Total daily energy demands of 20 residence units on representative day in each month.

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10

T. Wakui et al. / Energy xxx (2014) 1e18 Table 3 Conversion factors for primary energy. Purchased energy source

Value

Electric power (8:00 to 22:00), MJ/kWh Electric power (22:00 to 0:00), MJ/kWh Natural gas, MJ/m3

9.97 9.28 45.0

Table 4 Scale of mixed-integer linear programming problem.

Fig. 7. Ambient and feed water temperatures on representative day in each month.

water of the 20 residence units on each representative day are shown in Fig. 6. The characteristics of these demands are described in [48]. The electric power demand for IE and IEH is calculated by aggregating the electric power demands of 20 residences units. The hot water demand is calculated by using the model described in Section 3.2. The energy loss from the networked pipes is considered for H ¼ 2 and 4 because the hot water pipe for H ¼ 1 is vanishingly short. The ambient and feed water temperatures use the monthly mean temperatures at the location near the target housing complex, as shown in Fig. 7; they were reported by the Japan Meteorological Agency and in [49], respectively. On any representative day, qS is fixed to be 42  C. Moreover, the hot water flow rates during the hot water supply and heat interchange is assumed to be the constant value of 10 L/min, based on [50]. The increase in the hot water demand for the R-ESN relative to the total hot water demand of the 20 residence units is shown in Fig. 8. The energy loss from the networked pipes increases with H due to the increase in the pipe length. The increasing rates of the hot water demand are high in the summer and low in the winter because of the amount of the total hot water demand, as shown in Fig. 6. 4.1.4. Conversion factors for primary energy The conversion factors for the primary energy of the purchased electric power and natural gas are listed in Table 3. For the purchased electric power, an average thermal power conversion factor is introduced [51]. For natural gas, the value of the conversion factor is reported by Japanese gas companies [52].

Fig. 8. Increasing amount and rate of total hot water demand due to energy loss on representative day in each month.

Energy supply configuration

Total number Equation

Continuous variable

Binary variable

SE IE-1 & IEH-1 IE-2 & IEH-2 IE-4 & IEH-4

76,540 76,060 37,070 19,075

52,414 51,934 25,994 13,024

16,920 16,920 8460 4230

4.2. Results and discussion By using the above-mentioned input data, the energy-saving effect of the R-ESN is analyzed. The scale of the MILP model is listed in Table 4. It decreases with the increase in H because the number of the GE-CGSs is decreased.

4.2.1. Effect of power and heat interchanges on optimal operational strategy of GE-CGSs First, the effect of the power and heat interchanges on the optimal operational strategy of the GE-CGSs is investigated in the case of H ¼ 1. The optimal operational strategies of the GE-CGS-44 for SE and IE-1 on the representative day in December are shown in Figs. 9 and 10, respectively. Both the gas engines in SE and IE-1 are operated in the evening and nighttime when the hot water demand increases, so as to reduce the energy loss from the storage tank. In SE, the surplus electric power generated by each gas engine cannot be transmitted to other residence units; thus, most of the electric power output is consumed in the electric water heater. On the other hand, in IE-1 with the power interchange, the surplus electric power is supplied to other residence units. Moreover, the operating time of the gas engine in IE-1 is longer than that in SE by 2 h. The increase in the operating time of the gas engine contributes to the increase in the amount of produced hot water. Thus, the hot water supply from the gas-fired backup boiler in IE-1 is reduced relative to SE. The optimal operational strategies of the hot water supplied from/to the two adjacent storage tanks for IE-1 and IEH-1 are shown in Figs. 11 and 12, respectively. These results are for the GECGS-43 and GE-CGS-44 on the representative day in December. Positive and negative values indicate the energy flow rate of the hot water stored in and supplied from the storage tank, respectively. The hot water demand of the corresponding residence unit is also shown in the negative value; the difference between the hot water demand and the energy flow rate of the hot water supplied from the storage tank shows the hot water supply from the gas-fired backup boiler. The operating time of the gas engine in the GECGS-44 for IEH-1 with the heat interchange is longer than that for IE-1 by 1 h and is partially shifted to the morning to sent the hot water to the GE-CGS-43. Consequently, all of the hot water demands of both residence units are met by the supply from the storage tanks, while in IE-1, the shortage of the hot water supply from the storage tanks is compensated for by the gas-fired backup boilers.

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

T. Wakui et al. / Energy xxx (2014) 1e18

11

Fig. 9. Optimal operational strategy of GE-CGS-44 in SE on representative day in December.

Fig. 11. Optimal operational strategy of GE-CGS-43 and GE-CGS-44 in IE-1 for hot water stored in and supplied from storage tank on representative day in December.

Fig. 10. Optimal operational strategy of GE-CGS-44 in IE-1 on representative day in December.

Fig. 12. Optimal operational strategy of GE-CGS-43 and GE-CGS-44 in IEH-1 for hot water stored in and supplied from storage tank on representative day in December.

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

12

T. Wakui et al. / Energy xxx (2014) 1e18

4.2.2. Optimal operational strategy of R-ESN Moreover, the optimal operational strategy of the R-ESN in the case of H ¼ 1 is investigated. Fig. 13 shows the optimal strategy of the total electric power supplied to the 20 residence units on the representative day in December for SE, IE-1, and IEH-1. For any energy supply configuration, the operation of the gas engines is concentrated in the nighttime with a high demand for hot water. The amounts of the electric power supplied from the gas engines in IE-1 and IEH-1 increase as compared with SE because of the power interchange. It was confirmed that the electric power generated by the gas engine is not consumed at the electric water heater in any GE-CGS. The additional introduction of the heat interchange (IEH-1) slightly increases the amount of the electric power supplied from the gas engines relative to IE-1. Moreover, Fig. 14 shows the optimal strategy of the total hot water supplied to the 20 residence units on the same representative day for SE, IE-1, and IEH-1. For any energy supply configuration, a large portion of the hot water demand of the 20 residence units is met by the supply from the storage tanks. With the increase in the operating time of the gas engines by employing the power interchange (IE-1), the amount of total hot water supplied from the gas-fired backup boilers is reduced. It is also slightly reduced in the daytime by additionally conducting the heat interchange (IEH-1). These results are consistent with those derived in Section 4.2.1. To quantitatively evaluate the effect of the power and heat interchanges, the total daily amounts of the purchased electric power and natural gas and total daily primary energy consumption for SE, IE-1, and IEH-1 on the representative day in December are listed in Table 5. The amount of the purchased electric power decreases by employing the power and heat interchanges, while the amount of the purchased natural gas increases relative to SE; these are caused by increasing the operating time of the gas engines. The total daily primary energy consumption in IE-1 is less than that in SE, and that in IEH-1 is slightly less than that in IE-1. This is because the reduction in the purchased electric power surpasses the increase in the natural gas consumption in the perspective of saving energy.

PM RIH ¼

PK

m¼1 WðmÞ

k¼1

PF

f ¼1

PN

primary energy consumption for IEH-1, IEH-2, and IEH-4 on the representative day in December are listed in Table 6. Due to the significant increase in the operating time of the gas engines, the amount of the purchased electric power in IEH-2 is slightly smaller than that in IEH-1, while the amount of the purchased natural gas in IEH-2 is slightly larger than that in IEH-1. However, the daily primary energy consumption in IEH-2 is slightly more than that in IEH-1 because of the energy loss from the networked pipes and storage tanks. The amount of the purchased natural gas in IEH-4 is slightly smaller than that in IEH-1, while the amount of the purchased electric power is larger than that in IEH-1. Thus, in IEH-4, the purchased electric power increases the daily primary energy consumption. Moreover, it was confirmed that the effects of H for IE have almost the same tendency as those for IEH. 4.2.4. Energy-saving analysis of R-ESN 4.2.4.1. Performance criteria. Based on the above analyses, energy-saving effect of the R-ESN is investigated. First, following four performance criteria are defined: the electric pacity factor of the R-CGSs, PE, electric power supply rate, RE, water supply rate, RQ, and interchanged hot water rate, RIH.

PK PF PN N m¼1 WðmÞ k¼1 f ¼1 n¼1 ECGU ðn; f ; k; mÞDt PM R m¼1 WðmÞKFNECGU ðn; f ; k; mÞDt

PM PE ¼

 100 (12)

PM

PK

PF

PN

N n¼1 ECGU ðn; f ; k; mÞDt  100 PK PF PN PH m¼1 WðmÞ k¼1 f ¼1 n¼1 h¼1 EDh ðn; f ; k; mÞDt

RE ¼ PM

m¼1 WðmÞ

k¼1

f ¼1

(13) PK PF PN out m¼1 WðmÞ k¼1 f ¼1 n¼1 QST ðn; f ; k; mÞDt PK PF PN PH PM m¼1 WðmÞ k¼1 f ¼1 n¼1 h¼1 QDh ðn; f ; k; mÞDt PM

RQ ¼

 100 (14)

n

P N U n¼1 QIH ðn; f ; k; mÞ þ QIH ðn; f ; k; mÞ þ QIH ðn; f ; k; mÞ PK PF PN PM m¼1 WðmÞ k¼1 f ¼1 n¼1 QCGU ðn; f ; k; mÞDt

4.2.3. Effect of number of residence units involved in hot water supply network on optimal operational strategy Furthermore, the effect of H on the optimal operational strategy is analyzed. The optimal strategies of the total electric power and hot water supplied to the 20 residence units on the representative day in December for IEH-2 and IEH-4 are shown in Figs. 15 and 16, respectively. In comparison to Fig. 13(c), the operating time of each gas engine drastically increases with H because the hot water demand to each gas engine increases with H. For IEH-2, the hot water demand is almost met by the supply from the storage tanks as is the case with IEH-1. The gas engines for IEH-4 are operated most of the day; however, the hot water supply from the gas-fired backup boilers increases in the nighttime. The limitation of the operation of the gas engines is due to the increase in the energy loss from the storage tanks until the evening with high hot water demand. The increase in the storage time is also found in IEH-2, relative to IEH-1. To quantitatively evaluate the effect of H, the total daily amounts of the purchased electric power and natural gas and total daily

the the cahot

o D þ QIH ðn; f ; k; mÞ Dt

 100

(15)

Moreover, the energy-saving effect is evaluated by the following reduction rates of the annual primary energy consumption for RESN and SE relative to that for CO, gESN and gSE, respectively:

PM m¼1 WðmÞJCO ðmÞ  m¼1 WðmÞJESN ðmÞ PM WðmÞJ CO ðmÞ m¼1

PM

gESN ¼

PM m¼1 WðmÞJCO ðmÞ  m¼1 WðmÞJSE ðmÞ PM WðmÞJ CO ðmÞ m¼1

 100

(16)

PM

gSE ¼

 100

(17)

where JCO and JSE denote the total daily primary energy consumption of the housing complex for CO and separate operation of each residential cogeneration system, respectively. JCO is calculated from the purchased electric power and natural gas consumption for the conventional gas-fired boiler, whose thermal efficiency calculated by using the higher heating value is 80%, at each residence unit. For both the reduction rates, a positive value indicates saving energy by

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13

Fig. 13. Optimal strategy of total electric power supply to 20 residence units on representative day in December for SE, IE-1, and IEH-1.

introducing the R-ESN and SE. The above quantitative evaluation is also applied for the analysis on each representative day. 4.2.4.2. Energy-saving analysis on representative day in each month. First, the effect of the power and heat interchanges on energy savings is quantitatively analyzed on the representative day in each month. The results for SE, IE-1, and IEH-1 are shown in Fig. 17. gSE and gESN have the same tendency for seasonal changes as PE; PE increases in winter but decreases in summer. Thus, the energysaving effect by the GE-CGSs strongly correlates with the total amount of the hot water demand. From the comparison between SE

and IE-1, the power interchange increases PE, RE and RQ, and they contribute to the increase in gESN. The comparison between IE-1 and IEH-1 shows that the heat interchange increases RQ, but the increases in PE and RE are slight because of the small amount of RIH; thus, the increase in gESN by the heat interchange is slight. Second, the effect of H on energy savings quantitatively analyzes on the representative day in each month. The results for IEH-1, IEH2, and IEH-4 are shown in Fig. 18. The seasonal changes in PE and RE are almost the same for three cases of H; however, PE is much increased with H. Although RE and RQ have almost the same value for three cases of H, those for IEH-4 are decreased only on the

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T. Wakui et al. / Energy xxx (2014) 1e18

Fig. 15. Optimal strategy of total electric power supply to 20 residence units on representative day in December for IEH-2 and IEH-4.

of little difference in RE and RQ. gESN for IEH-4 is smaller than that for IEH-1 and IEH-2 on the winter representative days due to the decrease in RE and RQ.

Fig. 14. Optimal strategy of total hot water supply to 20 residence units on representative day in December for SE, IE-1, and IEH-1.

winter representative days. This is because of limiting the operating time of the gas engines, as shown in Fig. 15. RIH for IEH-4 is almost equal to 0 on any representative day. Furthermore, gESN for IEH-1 and IEH-2 is almost the same on any representative day because Table 5 Total daily amount of purchased electric power and natural gas and primarily energy consumption in SE, IE-1, and IEH-1 on representative day in December. Energy supply configuration

Total daily amount Purchased electric power kWh/d

Purchased natural gas m3/d

Primary energy consumption MJ/d

SE IE-1 IEH-1

189.75 165.25 162.49

35.92 38.13 38.68

3454.15 3304.49 3302.52

4.2.4.3. Annual energy-saving analysis. Based on the analysis in each month, the annual results are analyzed. The results for all of the target configurations are listed in Table 7. gESN for IE-1 increases by 3.3 percentage points relative to SE due to the power interchange. The additional introduction of the heat interchange increases gESN for IEH-1 by only 0.2 percentage points relative to IE-1. The same energy-saving effects of the power and heat interchanges are also seen for H ¼ 2, while only the power interchange contributes to energy savings for H ¼ 4. Moreover, gESN decreases with an increase in H. The decrease in gESN for IE-2 and IEH-2 is only 0.1 percentage points relative to IE-1 and IEH-1, respectively, because the increase in the energy losses from the networked pipes and storage tanks surpasses the slight increase in RE and RQ. The substantial increase in PE under the slight changes in RE and RQ for H ¼ 2, relative to H ¼ 1, indicates that the hot water supply capacity of the 1-kWe gas engine is sufficient for two residence units. The decrease in gESN for H ¼ 4 is mainly caused by its decrease in the winter representative days as shown in Fig. 18. Due to the significant decrease in RIH, there is no difference in gESN between IE-4 and IEH-4; however, gESN for IE-4 and IEH-4 is larger than gSE. From these results, IE-2 and IEH-2, in which the number of GE-CGSs is reduced by half of that for IE-1 and IEH-1, can be strong candidates for the R-ESN because of little difference in gESN between H ¼ 1 and 2. IE-4 may be a cost-effective candidate because the number of GECGSs is reduced by quarter of that for IE-1 and its energy-saving effect surpasses that for SE.

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T. Wakui et al. / Energy xxx (2014) 1e18

15

Fig. 16. Optimal strategy of total hot water supply to 20 residence units on representative day in December for IEH-2 and IEH-4.

4.2.5. Sensitivity analysis on energy losses from connecting and networked pipes Finally, the sensitivity analysis on energy losses from the connecting and networked pipes due to hot water retention, which are features of the developed analysis model, is conducted. First, the simple MILP model where the energy loss due to hot water retention in the connecting pipes is neglected (simple model-1) is focused on by omitting the second term in the right side of Eq. (6). gESN for IEH-1, IEH-2, and IEH-4 by the developed model and simple model-1 is listed in Table 8. The difference in the models is found only for IEH-1; gESN by the simple model-1 is larger than that by the developed model. Although the heat interchange is conducted for IEH-2 in both the models, the energy loss due to the hot water retention in the connecting pipes is small because of the short length of the connecting pipes, as shown in Table 2. For IEH-4, the heat interchange is hardly conducted. Second, the simple hot water demand calculation model where the energy loss due to the hot water retention in the networked

Table 6 Total daily amount of purchased electric power and natural gas and primarily energy consumption in IEH-1, IEH-2, and IEH-4 on representative day in December. Energy supply configuration

Total daily amount Purchased electric power kWh/d

Purchased natural gas m3/d

Primary energy consumption MJ/d

IEH-1 IEH-2 IEH-4

162.49 160.70 171.92

38.68 39.03 37.98

3302.52 3303.64 3378.29

Fig. 17. Performance criteria and reduction rate of primary energy consumption on each representative day for SE, IE-1 and IEH-1.

pipes is neglected (simple model-2) is focused on by omitting the second term in the summation operation in the first equation of Eq. (11). gESN for IE-2, IE-4, IEH-2, and IEH-4 by the developed model and simple model-2 are listed in Table 9. For any configuration, gESN by the developed model is smaller than that by the simple model-2. These sensitivity analyses show that the simple analysis models neglecting the hot water retention overestimate the energy-saving effect of the R-ESN. 5. Conclusions An analysis model for the energy-saving effect of R-ESNs using multiple R-CGSs, which are featured by the power and heat interchanges and the hot water supply network, was developed, and then the feasibility of an R-ESN was investigated. In the developed mixed-integer linear programming model, the hot water retention in the connecting pipes was uniquely modeled, and the heat loss in response to the hot water retention was calculated. The developed

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

16

T. Wakui et al. / Energy xxx (2014) 1e18 Table 8 Impact of energy loss model from connecting pipes between storage tanks on energy savings. Energy supply configuration

Reduction rate of annual primary energy consumption gESN % Developed model

Simple model-1

IEH-1 IEH-2 IEH-4

12.8 12.7 11.4

13.1 12.7 11.4

Table 9 Impact of energy loss model from networked pipes on energy savings. Energy supply configuration

IE-2 IE-4 IEH-2 IEH-4

Reduction rate of annual primary energy consumption gESN % Developed model

Simple model-2

12.5 11.4 12.7 11.4

12.6 11.7 12.9 11.7

supply network (IE) and the power and heat interchanges and hot water supply network (IEH), for a housing complex composed of multiple 1-kWe GE-CGSs and 20 residence units. The derived results are summarized as follows:  The energy-saving effect considerably increases by employing the power interchange.  The power interchange contributes to energy savings rather than the heat interchange.  The energy-saving effect of IE and IEH decreases with the increase in the number of residence units involved in the hot water supply network, H.  The difference in the energy-saving effect between H ¼ 1 and 2 is slight; thus, IE-2 and IEH-2 can be strong candidates for the RESN.  Neglecting the energy loss from the pipes due to the hot water retention overestimates the energy-saving effect.

Fig. 18. Performance criteria and reduction rate of primary energy consumption on each representative day for IEH-1, IEH-2 and IEH-4.

hot water demand calculation model, in which the energy loss from the networked pipes is preliminarily regarded as the hot water demand of the R-ESN, reduce the solution space of the optimization problem. The developed analysis model was then applied to two configurations of the R-ESN, i.e., the power interchange and hot water

The developed model can be applied to other types of configurations by appropriately setting the configuration parameters, i.e., F, H, and N, and their corresponding specifications. The above results offer some suggestions for further feasibility studies. First, the feasibility from the cost reduction perspective must be investigated. Second, an R-ESN with the combined use of the 1-kWe GE-CGS and a PEFC-CGS or SOFC-CGS can be an effective configuration because a relatively small amount of hot water produced by fuel cells can be supplemented by a large amount of hot water produced by gas engines. Moreover, a comparison between an R-ESN and a central energy supply configuration using a largescale cogeneration system is very important. Finally, the optimal

Table 7 Annual performance criteria and reduction rate of annual primary energy consumption. Energy supply configuration

Electric capacity factor PE %

Electric power supply rate RE %

Hot water supply rate RQ %

Interchanged hot water rate RIH %

Reduction rate of annual primary energy consumption gSE, gESN %

SE IE-1 IE-2 IE-4 IEH-1 IEH-2 IEH-4

12.8 17.3 35.1 65.8 17.8 36.2 65.8

22.8 30.8 31.3 29.3 31.7 32.3 29.4

91.6 95.2 95.8 88.8 97.9 98.7 88.9

e e e e 2.69 3.35 0.05

9.30 12.6 12.5 11.4 12.8 12.7 11.4

Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110

T. Wakui et al. / Energy xxx (2014) 1e18

structure of R-ESN, in which various design parameters are determined so as to maximize benefits, is an important issue for future studies.

[3]

Appendix A. Formulation of hot water demand calculation model

[4]

The additional formulation for the hot water demand calculaS tion model is presented. qPP is calculated by the following equations:

[5]

9 > > > > > gPPh ðn; f ; k; mÞc =

UPP pdiPP



qSPPh ðn; f ; k; mÞ ¼ qA ðk; mÞþfqST  qA ðk; mÞge gPPh ðn; f ; k; mÞ ¼

H P j¼h

P

h j¼1 Lj

> > > > > ;

gdj ðn; f ; k; mÞ

(A1) ðh ¼ 1; 2; .; H; n ¼ 1; 2; .; N; f ¼ 1; 2; .; F; k ¼ 1; 2; .; K;

[6]

[7] [8]

[9]

[10]

[11]

m ¼ 1; 2; .; MÞ [12]

UPP ¼ 1

ai þ

diPP 2lPP

 ln

doPP diPP



1

 o d do di þ 2lPP ln doIS þ doPPa IS

PP

IS

(A2)

[13]

o

[14]

SPP and SPP are calculated as follows:

n o S SPPh ðn; f ; k; mÞ ¼ rcVPPh qPPh ðn; f ; k; mÞ  qF ðk; mÞ

(A3)

[15]

[16]

ðh ¼ 1; 2; .; H; n ¼ 1; 2; .; N; f ¼ 1; 2; .; F; k ¼ 1; 2; .; K; m ¼ 1; 2; .; MÞ

[17]

SPPh ðn; f ; k  1; mÞ ¼ rcVPPh fqPPh ðn; f ; k  1; mÞ  qF ðk  1; mÞg

[18]

(A4) [19]

ðh ¼ 1; 2; .; H; n ¼ 1; 2; .; N; f ¼ 1; 2; .; F; k ¼ 1; 2; .; K; m ¼ 1; 2; .; MÞ

[20]

qPP is calculated from the following equations:

[21]

qPPh ðn; f ; k; mÞ

¼

8 > qSPPh ðn; f ; k; mÞ > > > > <

[22]

ðgPPh ðn; f ; k  1; mÞ > 0Þ s Dt

(A5)

qA ðk; mÞ þ fqPPh ðn; f ; k  1; mÞ  qA ðk; mÞge PPh > > > > > : ðgPPh ðn; f ; k  1; mÞ ¼ 0Þ

[24] [25]

ðh ¼ 1; 2; /; H; n ¼ 1; 2; /; N; f ¼ 1; 2; /; F; k ¼ 1; 2; /; K; m ¼ 1; 2; /; MÞ

sPPh ¼

rcVPPh UPP pdiPP Lh

ðh ¼ 1; 2; .; HÞ

[23]

(A6)

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Please cite this article in press as: Wakui T, et al., A mixed-integer linear programming approach for cogeneration-based residential energy supply networks with power and heat interchanges, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.01.110