Optimization of a residential solar combisystem for minimum life cycle cost, energy use and exergy destroyed

Optimization of a residential solar combisystem for minimum life cycle cost, energy use and exergy destroyed

Available online at www.sciencedirect.com ScienceDirect Solar Energy 100 (2014) 102–113 www.elsevier.com/locate/solener Optimization of a residentia...

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Available online at www.sciencedirect.com

ScienceDirect Solar Energy 100 (2014) 102–113 www.elsevier.com/locate/solener

Optimization of a residential solar combisystem for minimum life cycle cost, energy use and exergy destroyed Jason Ng Cheng Hin, Radu Zmeureanu ⇑ Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canada Received 24 April 2013; received in revised form 5 September 2013; accepted 1 December 2013 Available online 22 December 2013 Communicated by: Associate Editor Ursula Eicker

Abstract This paper presents the optimization of a model of a solar combisystem in an energy efficient house in Montreal (Qc), Canada. A hybrid particle swarm and Hook–Jeeves generalized pattern search algorithm is used to minimize the life cycle cost, energy use and exergy destroyed of the combisystem. The results presented include four different optimal configurations depending on the objective function used. The optimizations were able to reduce, compared with the base case combisystem, the life cycle cost of the combisystem by 19%, the life cycle energy use by 34%, the life cycle exergy destroyed by 33% and 24% using the technical boundary and physical boundary, respectively. Due to the high cost of the solar collector technologies and the low price of electricity in Quebec, none of the optimal configurations have acceptable financial payback periods. However, they all have energy payback times between 5.8 and 6.6 years. The use of technical boundary in the exergy analysis favors the use of electricity over solar energy due to the low exergy efficiency of the solar collectors. The use of the physical boundary, on the other hand, favors the use of solar energy over electricity, and all of the combisystem configurations have exergy payback times between 4.2 and 6.3 years. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Solar combisystem; Optimization; Life cycle cost; Life cycle energy; Life cycle exergy destruction

1. Introduction A solar combisystem is defined as a solar heating system that is configured to provide heat for space heating as well as for domestic hot water production for a residential household. Combisystems normally consist of five sub-systems: solar collector loop, heat storage, heat distribution, controls, and auxiliary power supply. Combisystems have been extensively studied in the last 15 years, with numerous international and collaborative research efforts taking place. The International Energy Agency Solar Heating and Cooling Programme devoted one of their working ⇑ Corresponding author. Tel.: +1 514 848 2424/3203; fax: +1 514 848 7965. E-mail addresses: [email protected] (J.N. Cheng Hin), [email protected] (R. Zmeureanu).

0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.12.001

tasks, Task 26, to solar combisystems (IEA, 2002). The project, which lasted from 1998 to 2002, involved a thorough analysis of different combisystem designs which were generalized into 21 different configurations. From 2001 to 2003, the European Commission, under the Altener programme and in collaboration with Task 26, studied over 200 combisystems in seven European community countries, monitored 39 different systems and developed guidelines for installation and design (Ellehauge, 2003). Furthermore, from 2007 to 2010, Intelligent Energy Europe (IEE) commissioned a project known as Combisol (Papillon, 2010). The objectives of this project were to develop best practices, standards, and recommendations for manufacturers, installers, authorities and technical experts. A few examples of other combisystem related research efforts are given in (Jordan and Vajen, 2001; Lund, 2005; Anderson and Furbo, 2007; Streicher and Heimrath, 2007).

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103

Nomenclature BCSCS Cp DHWHX DHWT EE EPR EPT F HUSP LCC LCE LCX LCXp LCXt PSO PW RFT T V X XPR XPT

base case solar combisystem specific heat domestic hot water heat exchanger domestic hot water tank embodied energy energy payback ratio energy payback time primary energy factor hours under set point life cycle cost life cycle energy life cycle exergy life cycle exergy considering the physical boundary life cycle exergy considering the technical boundary particle swarm optimization algorithm present worth radiant floor tank temperature volume exergy exergy payback ratio exergy payback time

Several recent studies have used optimization techniques to optimize solar thermal systems. The most popular optimization technique lately for solar water heating systems has been the Genetic Algorithm (GA). Loomans and Visser (2002) used a GA to minimize the payback time of a large scale solar domestic hot water heating system. Kraus et al. (2002) also used a GA to optimize large solar domestic hot water systems to minimize solar heat cost. Kalogirou (2004) combined artificial neural networks (ANN) with GA to optimize an industrial solar water heater for maximum life cycle savings. Bales (2002) and Calise et al. (2011) used a deterministic optimization algorithm, known as the Hooke–Jeeves (HJ) generalized pattern search algorithm, instead. Bales maximized the fractional energy savings of a solar combisystem using the HJ algorithm and the TRNSYS simulation software while Calise et al. used a modified HJ algorithm to minimize the payback period and annual costs of three different solar heating and cooling systems. Bornatico et al. (2012) used a particle swarm optimization (PSO) to optimize a solar combisystem to minimize a weighted combination of solar fraction energy use and cost. Dincer and Rosen (2007) pointed out that an energy analysis of a thermodynamic system can be misleading since it does not necessarily explain how closely the system is performing to ideality. An exergy analysis can make up

g

efficiency

Subscripts a aux col comp CS d emb f HX II L p phys r repl S Sol St Tech W

ambient auxiliary collector component combisystem destroyed embodied collector fluid heat exchanger second law or exergy efficiency leaked absorber plate physical room replacement stored solar storage technical water

for this shortcoming by using the second law of thermodynamics. There are numerous studies that used exergy to characterize solar collector systems including (Altfeld, 1988a,b; Luminosu and Fara, 2005; Gunerhan and Hepbasli, 2007). In general, solar collectors tend to have low exergy efficiencies, mostly between 2% and 11%, due to the conversion of high quality solar heat at 6000 K for low quality heating purposes at low indoor air temperature around 293 K. Also, the solar collectors tend to be responsible for the majority of the overall thermal system’s irreversibilities, where they often represent up to 95% of the exergy destroyed by the whole system. Fraisse et al. (2009) compared various energy, exergy and economic optimization criteria for a solar domestic hot water system by computer simulation with TRNSYS and GenOpt programs. They concluded that it is better to oversize the collector area and reduce the storage tank volume. This paper, an extension of a study by Leckner and Zmeureanu (2011), that presented the performance of a base case solar combisystem (BCSCS), focuses on the search for the optimal configurations of a residential solar combisystem for minimum life cycle cost, life cycle energy use, and life cycle exergy destroyed in Montreal. The comparison with the BCSCS configuration in terms of performance is also presented.

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2. Methodology The following methodology is followed in this study: (1) The model of a combisystem installed in a residential building is developed. (2) The optimization variables are selected and objective functions are defined. (3) The optimization algorithms are selected. (4) The optimizations are completed and results analyzed.

2.1. House model and combisystem design The house was initially developed by Leckner (2008), using the TRNSYS software (Klein, 2012). The house model was designed to represent a typical house built in the mid 1990s in Montreal, Canada, that had been renovated to be a very energy efficient house. The building is a two-story, wood framed detached house with a total heated floor area of 208 m2. The house also includes a partially heated basement and an un-heated attic space. The walls and windows of the house are constructed to comply with the minimum requirements of the R-2000 building standard in terms of thermal resistance. Electricity is used as the auxiliary power supply due to the abundance of relatively inexpensive hydroelectricity in Quebec. More details of the house model can be found in Leckner (2008) and Leckner and Zmeureanu (2011). The house is equipped with a solar combisystem which supplies heat to the domestic hot water heating system as well as the radiant floor heating system. Fig. 1 shows a schematic diagram of the original base case solar combisystem (BCSCS) design. The BCSCS uses four SOL 25 solar collectors (Stieble Eltron, 2011) in parallel, each having an area of 2.73 m2.

The collectors are installed on the roof of the house which is oriented due south. The collector fluid travels to a flow diverter where the flow is directed towards the radiant floor tank (RFT) or the domestic hot water tank (DHWT) depending on the control parameters. The flow of collector fluid to the two storage tanks is controlled by two separate pumps located after the diverter. Each tank contains an internal heat exchanger through which the collector fluid circulates before returning to the collectors. The collector fluid is composed of a 60% glycol–water mixture. The collector fluid flow rate is set at a constant 100 kg/h. Both the RFT and the DHWT are 300 L vertical cylinder tanks. The flat plate solar collectors are modeled in TRNSYS with the TESS Type 1b, Quadratic Efficiency, 2nd Order Incidence Angle Modifier Solar Collector, that uses a standard equation for the efficiency of the collector in terms of: (i) the temperature of fluid entering the collector, (ii) the ambient temperature, (iii) the incident solar radiation on the collector, and (iv) three coefficients based on manufacturer’s tests. Both the radiant floor tank (RFT) and the DHW tank are simulated in TRNSYS with Type 534, Cylindrical Storage Tank with Immersed Heat Exchangers, which allows for stratification in a user defined number of layers; in this case four layers were used. These layers are defined as nodes, with node 1 being the top node where water exits the tank. Each tank contains one coiled tube heat exchanger located in the bottom half of the tank, with the heat transfer fluid flowing in at node 3 and out at node 4. Water enters the tank at the bottom into node 4. Auxiliary energy is provided directly to the tanks via internal electric heating elements when the available solar energy is insufficient to cover the demand of the house. The DHWT contains one element of 1 kW while the RFT contains two elements of 2 kW and 4 kW. Hot water is supplied to the house straight from the DHWT. A thermostatic mixing valve is used to mix the

Fig. 1. Schematic diagram of the combisystem design (Leckner and Zmeureanu, 2011).

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hot water from the tank with cold city water in order to provide hot water to the house at a constant 49 °C. The DHWT is replenished with city water that has passed through a drain water heat exchanger (DWHX) to preheat the city water using the warmer drain water. Simulation results of the house equipped with the BCSCS show that the house uses a total of 11,217 kW h of electricity annually. Electricity used for space heating accounts for 30% of the overall annual electricity use, or 3315 kW h, while domestic hot water preparation accounts for 3%, or 330 kW h. The two collector fluid pumps use only 53 kW h of electricity per year and the remaining electricity is split up between lighting (6%), major appliances (15%), other appliances (20%), ventilation (17%), and the heat recovery ventilator (9%). 2.2. Optimization variables Table 1 shows the selected design variables to be optimized and the corresponding limits of the design space. 2.3. Objective functions There are four independent objective functions used for the optimization of the combisystem: (1) the life cycle cost (LCC); (2) the life cycle energy use (LCE); and (3 and 4) the life cycle exergy destroyed (LCX) calculated by using two different approaches. The goal is to find four different combisystem configurations based on the objective function being minimized. The life cycle is taken as 40 years, which is the expected life of the house before major renovations are generally required. In this case, some of the combisystem equipment will need to be replaced within the life of the house. Table 2 shows the replacement times of the combisystem equipment, after which the component is replaced with a new one. 2.3.1. Life cycle cost The life cycle cost (LCC) of the combisystem is made up of three separate components: (1) the initial cost of all of the components upstream of the two tanks, including the tanks; (2) the replacement costs of this equipment and (3) the annual operating costs which include the cost of the

Table 1 Optimization variables. Variable

Range

Units

Number of solar collectors RFT volume DHWT volume DHWT auxiliary power RFT auxiliary power high RFT auxiliary power low Collector tilt Collector flow rate per collector area

1–22 300–30,000 100–1000 0.5–5 0.5–10 0.5–15 0–90 10–115

Number l l kW kW kW ° kg/h/m2 of collector

105

Table 2 Combisystem component replacement times. Component

Replacement time (years)

Solar collectors Radiant floor tank Domestic hot water tank Glycol Pumps Controller

25 15 15 3 10 15

auxiliary energy used for the heaters of both tanks as well as the electricity used for the two collector fluid circulating pumps upstream of the two tanks. Items 2 and 3 are calculated as present worth (PW) of future expenditures, with the financial parameters presented in Table 3. The radiant floor heating system and the drain water heat recovery system are not included in the cost of the combisystem. The cost of disposing each component is not considered in this study since there is presently little information in the literature about the disposal costs of these technologies. The LCC objective function is calculated, in Canadian Dollars, as follows: Minimize : LCC ¼ Initial Cost þ PWrepl;cost þ PWEnergy cost

ð1Þ

Due to the stochastic nature of the PSO algorithm, it is possible that the algorithm selects a combisystem configuration that cannot adequately heat the house (e.g. small collector area, storage tanks and auxiliary electricity inputs). In order to ensure that the combisystem is capable of maintaining adequate temperatures in the house, a new metric is created: hours under the heating set point (HUSP). The operative air temperature of each zone is monitored such that the number of hours in each room under the heating set point temperature is counted over the heating season and while set-back temperatures are not in effect. The HUSP is the sum of the total number of hours that each zone spends under the heating set point throughout the year. Due to the sudden change in set point temperatures immediately after the set-back temperature is no longer in effect, a certain amount of HUSP is inherent depending on the heater capacity. The HUSP takes into account, along with other factors, how quickly the system is capable of raising temperatures to comfortable levels when the house occupants wake up. The BCSCS has a HUSP of approximately 510 h for all heated rooms. For the purpose of the optimization, the acceptable number of HUSP is increased to 550. This value is used as a baseline for adequate thermal comfort performance of the combisystem. In order to modify the objective function such that any design that allows more than 550 HUSP is omitted, a penalty function is added to the objective function, which adds an arbitrarily large amount to the objective function value such that the underperforming configuration can never be selected as optimal. The LCC objective function (Eq. (1)) is modified as follows:

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J.N. Cheng Hin, R. Zmeureanu / Solar Energy 100 (2014) 102–113 Table 3 Financial parameters for PW calculations. Parameter

Value

Reference

Inflation rate Discount rate Price of electricity

2.0% 6.0% $0.0776/ kW h 2.15%

Bank of Canada (2012) MNECCB (1997) Average price of electricity for customers using an average of 1000 kW h per month (Hydro Quebec, 2010) Average rate of increase in electricity prices in Quebec between 2006 and 2010 (Hydro Quebec, 2006, 2010)

Increase rate of electricity price

Table 4 Embodied energy of solar thermal collectors. Area of collectors (m2)

Embodied energy (kW h)

Embodied energy (kW h/m2 of collector area)

Source

Kalogirou (2009) Ardente et al. (2005) Gurzenich and Mathur (1998) Gurzenich and Mathur (1998) Streicher et al. (2004) Streicher et al. (2004)

1.4 2.13 2

740 976 1000

548 458 500

98.4

74,167

754

1780 2398

356 480

5 5 Average

Table 5 Embodied energy coefficients for typical materials used to fabricate hot water storage tanks.

516

Minimize : LCC ¼ Total Initial Cost þ PWrepl;cost þ PWenergy

cost

þ ltð550; HUSPÞ  200; 000

ð2Þ

where the function lt(550, HUSP) returns 1 if 550 is less than HUSP and 0 otherwise. Included in the cost assumptions is a reduction in the cost of solar collectors of 35% (IEA, 2007) by the time the collectors need to be replaced (after 25 years).

Material

Density (kg/m3)

Embodied energy (MJ/kg)

Aluminum Polyisocyanurate EPDM Copper Stainless steel Steel

2700 40 860 8940 7740 7850

207 (Yang, 2005) 70 (Kibert, 1999) 183 (Scheuer et al., 2003) 48.7 (Yang, 2005) 16.3 (Yang, 2005) 28.8 (Yang, 2005)

the energy of the collector materials, the energy required for transportation, the energy of the materials for the pipes connecting the solar collectors on the roof to the tanks in the basement, and also the energy embodied in the glycol fluid. Table 4 shows a summary of the embodied energy of flat plate collectors from current literature. The data in this table represents only the embodied energy for the solar collectors and does not include the shipping, piping or glycol. The embodied energy of the propylene glycol fluid is taken as 21.5 kW h/kg (Ardente et al., 2005). The embodied energy, EEcol, of the solar collectors, piping and glycol, in kW h, including replacements during the 40 year life cycle of the house, is calculated as follows: EEcol ¼ 3592:7  N col þ 6946:1

2.3.2. Life cycle energy use The life cycle energy (LCE) objective function contains two separate parts: (1) the embodied energy of the equipment and the replacement equipment and (2) the operating energy use over the life cycle of the house. The energy used to maintain and dispose of the equipment is disregarded since there is insufficient information available for disposal energy of this kind of equipment in current literature, and determining this is outside of the scope of this paper. Few studies have attempted to estimate the embodied energy of solar combisystems. Therefore, average values of primary embodied energy from different studies for similar equipment will be used whenever such data is available. When such data is not available in published literature, the materials used to fabricate the component is estimated from actual available products, and the embodied energy is calculated from the quantities of materials used. For the solar collectors, several factors are taken into account for the estimation of embodied energy including

ð3Þ

where Ncol is the number of solar collectors. For the two hot water storage tanks, embodied energy values from literature (Ardente et al., 2005; Gurzenich and Mathur, 1998; Hugo, 2008), are combined with estimates based on the materials required to fabricate the tanks to produce a correlation between embodied energy and tank volume. Table 5 shows the density and embodied energy coefficients of the materials used to fabricate the storage tanks. The embodied energy of storage tanks EEstorage tanks, in kWh, including replacements during the 40 year life of the house, is calculated as follows: EEstorage

tanks

¼ 93:21  V 0:61 storage

tanks

ð4Þ

where Vstorage tanks is the storage tank volume in litres. The collector fluid pumps and the controller are ignored for the embodied energy calculation because there is insufficient information in literature and in product specifica-

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tions for these components to obtain a reasonable estimation of their embodied energy. The operating energy of the combisystem, estimated using the simulations in TRNSYS v16, is the sum of the auxiliary electricity used in the RFT and the DHWT, and the electricity used for the two collector fluid pumps. It is assumed that the electricity used in the first year of operation is the same as the remaining 39 years of the life of the house. A primary energy factor Fprimary of 1.37 (Hugo, 2008) is used to convert the site electricity use to primary energy use, considering the electricity mix in Quebec and the transportation and distribution losses. The LCE used by the solar combisystem is calculated, including the same penalty function used with the LCC objective function: Minimize : LCE ¼ EEcol þ EERFT þ EEDHWT þ LCEoperating þ ltð550;HUSPÞ  200;000 ð5Þ

2.3.3. Life cycle exergy destroyed The exergy destroyed by each component is summed to determine the exergy destroyed by the whole combisystem. 2.3.3.1. Solar collectors. Torio and Schmidt (2010) observed in current literature a common issue with the calculation of the exergy destroyed in solar thermal systems. Usually, to calculate the exergy destroyed by the conversion of solar radiation into usable heat, the sun is considered as an infinite heat source at 6000 K. This approach is called “technical boundary” where a technical intervention is required to convert some form of energy into a usable form. Torio and Schmidt proposed a new definition of the system boundary to express the advantages of using solar thermal systems over other energy forms. The proposed approach, called the “physical boundary considers the thermal energy at the collector temperature as the primary energy source. The maximum possible collector temperature, given the available solar radiation, is considered when determining the exergy efficiency rather than the radiation exergy at the temperature of the sun. The use of these two different boundary assumptions only affects the calculation of the exergy destroyed by the solar collectors. Technical boundary. The exergy rate flowing into the solar collector, using the technical boundary, is calculated (Eq. (6)) by adding the exergy rate flowing into the solar collector with the glycol and the exergy rate of the solar radiation, which is calculated using the Patela formula (1964) (Eq. (7)): X_ in;col ¼ X_ in;f þ X_ in;sol

ð6Þ

where "  4  # 1 Ta 4 Ta _ X in;sol ¼ I  gcol  Acol  1 þ    3 T sol 3 T sol

ð7Þ

   T in;col X_ in;f ¼ m_ f  C p;f  T in;col  T a  T a  ln Ta

107

ð8Þ

where Ta is the reference temperature, equal to the outdoor air temperature (K) at every time step. The exergy rate flowing out of the solar collectors is the exergy in the glycol at Tout,col:    T out;col X_ out;col ¼ m_ f  C p;f  T out;col  T a  T a  ln ð9Þ Ta The exergy rate of destruction by the solar collector using the technical boundary is calculated in kW as: X_ d;col;tech ¼ X_ in;col  X_ out;col

ð10Þ

Physical boundary. The exergy rate flowing out of the solar collector, using the physical boundary, is considered as the exergy rate of the glycol assumed to be at the absorber plate temperature. To calculate the absorber plate temperature, the collector energy efficiency, at given inlet fluid temperature, is considered to be equal with the ratio of the actual energy output over the ideal energy output of the collector. The ideal energy output is determined assuming that the outlet fluid temperature reaches the absorber plate temperature, Tp. gcol ¼

m_ f  C p;f  ðT out;col  T in;col Þ m_ f  C p;f  ðT p  T in;col Þ

ð11Þ

Given that gcol, Tout,col, and Tin,col are already known for each time step in the simulation, Eq. (12) is re-arranged to solve for Tp: Tp ¼

T out;col  T in;col þ T in;col gcol

ð12Þ

The exergy of the absorber plate is then calculated using the calculated absorber plate temperature Tp:    Tp _ X p ¼ m_ f  C p;f  T p  T a  T a  ln ð13Þ Ta The exergy efficiency is formulated as follows: gII;col;phys ¼

X_ out;f  X_ in;f X_ p  X_ in;f

ð14Þ

Finally, the exergy efficiency, calculated with Eq. (14) is input in Eq. (15), and the exergy rate of destruction is calculated with Eq. (16), which is a rearrangement of: X_ d;col;phys X_ p  X_ in;f

ð15Þ

X_ d;col;phys ¼ ð1  gII;col;phys Þ  ðX_ p  X_ in;f Þ

ð16Þ

gII;col;phys ¼ 1 

2.3.3.2. Collector fluid flow pumps. These mechanical and heat transfer losses are accounted for in the electric power input that is supplied to the pumps in order for them to operate: X_ d;pumps ¼ F primary  E_ pumps

ð17Þ

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where Fprimary is the primary energy factor described in Section 2.3.2. 2.3.3.3. Storage tanks. Since the calculation for the two storage tanks is similar, only the formulation for the DHWT is presented here. Exergy flows into the tank with the glycol and with the incoming city water. The exergy flows out of the tank with the glycol at the outlet temperature, and with the water leaving the tank to the sinks and showers; in addition, exergy is lost due to heat losses through the tank wall. The exergy that is stored in the tank at any given time step and the auxiliary electricity supplied to the tanks are also taken into consideration. The exergy destroyed by the storage tanks is calculated as follows, where Dt = 10 min: X X X X X_ in;HX þ X_ in;st  X_ out;HX  X_ out;st X d;st ¼ Dt   X X  X_ L þ F primary  E_ aux þ X s ð18Þ where    T in;st X_ in;st ¼ m_ w;st  C p;w  T in;st  T a  T a  ln Ta    T out;st X_ out;st ¼ m_ w;st  C p;w  T out;st  T a  T a  ln Ta    T in;HX _ X in;HX ¼ m_ f  C p;f  T in;HX  T a  T a  ln Ta    T out;HX _ X out;HX ¼ m_ f  C p;f  T out;HX  T a  T a  ln Ta

ð19Þ ð20Þ ð21Þ ð22Þ

The exergy leaked from the storage tank is calculated as:   Ta _ X L;RFT ¼ U L;RFT  ARFT  ðT RFT  T r Þ  1  ð23Þ T RFT The exergy stored, Xs, in the storage tank is calculated based on the difference between average temperature of the tank at any given time step, and the average temperature in the tank in the previous time step (/ = 0.00028 kW h/kJ): t1 X ts;RFT ¼ X tRFT  X RFT

ð24Þ

where    T RFT X RFT ¼ a  mw;RFT  C p;w  T RFT  T a  T a  ln Ta

ð25Þ

2.3.3.4. Whole combisystem. The annual exergy destroyed by each component is summed to calculate the exergy destroyed by the combisystem under the technical boundary and the physical boundary, respectively: X d;cs;tech ¼ X d;col;tech þ X d;RFT þ X d;DHWT þ X d;pumps

ð26Þ

X d;cs;phys ¼ X d;col;phys þ X d;RFT þ X d;DHWT þ X d;pumps

ð27Þ

Table 6 Maximum temperature of combisystem component materials. Component

Material

Maximum temperature (K)

Solar collector Storage tanks Glycol Pipes

Aluminum Steel Propylene glycol Copper

1373 (IALI, 2012) 2000 (Green et al., 2013) 490 (Chan and Seider, 2004) 1773 (EPA, 1995)

2.3.3.5. Embodied exergy. The embodied exergy lost is estimated under the assumption that there existed a potential for work from the embodied energy of a component, EEcomp, used by the manufacturing processes to produce the component at a given temperature relative to the environment:   Ta X emb;comp ¼ EEcomp  1  ð28Þ T The heat source temperature is assumed to be the maximum temperature during the manufacturing of a given component of the combisystem (Table 6). The environmental temperature is more problematic to estimate, since the proper temperature to use would be the outdoor temperature at the time and place that the maximum temperature of the manufacturing process occurred. In this study, we used the average yearly outdoor temperature of 6 °C from the closest airport (Environment Canada, 2012). 2.3.3.6. LCX objective functions. The life cycle exergy destroyed by the solar combisystem is found by summing the annual exergy destroyed from operation of the system over the life of the house (40 years), the embodied exergy of the combisystem components, and the penalty function. LCXt denotes the life cycle calculations using the technical boundary while LCXp denotes the physical boundary. Minimize : LCXt ¼ 40  X d;cs;tech þ X emb;CS þ ltð550; HUSPÞ  500; 000 ð29Þ Minimize : LCXp ¼ 40  X d;cs;phys þ X emb;CS þ ltð550; HUSPÞ  500; 000

ð30Þ

2.4. Optimization algorithm A hybrid particle swarm optimization (PSO) and Hooke–Jeeves (HJ) generalized pattern search algorithm is used in this study. The PSO, a stochastic search algorithm, is used as a global search, and then the optimal solution found by the PSO is used as a starting point for the HJ deterministic algorithm. The use of the stochastic search algorithm followed by a deterministic algorithm could reduce the risk of stopping the search in a local minimum. To reduce the risk of getting trapped in a local minimum, the hybrid algorithm is started three independent times with a random initial population (solution). This hybrid algorithm was found to be a good compromise between its ability to find an optimal solution and the computation

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time required (Wetter and Wright, 2004). The algorithm is available as a standard option in the software GenOpt (Wetter, 2011), which was designed to facilitate the application of several different deterministic and probabilistic optimization algorithms for building simulation optimization problems that use text based input and output files, such as TRNSYS. 3. Results and discussion Table 7 shows the configurations of the four optimized combisystems and the corresponding objective function values, compared with the BCSCS. The optimizations were able to reduce, compared with the base case combisystem, the life cycle cost of the combisystem by 19% ($21,461 vs. $26,628), the life cycle energy use by 34% (150,350 kW h vs. 228,475 kW h), the life cycle exergy destroyed by 33% (358,424 kW h vs. 533,327 kW h) for technical boundary and 24% (179,736 kW h vs. 236,486 kW h) for physical boundary, respectively. The LCC and LCXt optimal configurations have very close values for each objective function (e.g., $21,461 vs. $21,489; and 359,753 kW h vs. 358,424 kW h). Both configurations minimize the area of the collector array, while the LCXt optimal combisystem sets greater collector slope (70 vs. 57.5°) and collector fluid flow rate ð32:5 vs: 20 kg=h=m2collector Þ. The LCE and LCXp optimal configurations have very close objective function values (e.g., 150,350 kW h vs. 165,161 kW h; and 180,839 kW h vs. 179,736 kW h), mostly because of the high number of solar collectors. The BCSCS configuration is a non-inferior solution when its life cycle performance is compared to the four optimized configurations. For example, the BCSCS has LCC of $26,628, which is greater than the $21,461 or the $21,489 of the LCC or LCXt optimal configurations, respectively; however, its LCC is lower than the $33,479

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or the $36,641 of the LCE or LCXp optimal configurations, respectively. For comparison purposes, the annual solar fraction was also included in Table 7. As expected, the LCE and LCXp optimal configurations, which use more solar collectors, have greater solar fraction values of 0.72 and 0.74, compared with the LCC and LCXt optimal configurations with values of 0.21 and 0.26, respectively. All of the optimal combisystems minimize the size of the storage tank volumes to the minimum allowed (see constraints in Table 1), except for the LCXp optimal configuration. In the three other cases the savings incurred by increasing the volume of the storage tanks, to attempt to store more heat, do not compensate for the financial, energetic or exergetic losses that come with larger volumes. So in the case of this house, type of combisystem, climate and occupant behavior, it is not beneficial to make use of longer storage periods unless the goal is to attempt to minimize the LCX destroyed using the physical boundary. The optimum tilt of solar collectors was about 58–75° such that they are able to collect and deliver more solar energy/exergy for heating purposes during the winter months, when the sun is lowest in the sky. The results show that for a steeper collector, which collect more solar energy, the mass flow rate is smaller for the same amount of heat delivered to the system. This is demonstrated by the 13:75 kg=h=m2collector flow rate at 75° (for the minimum LCE) versus the 20 kg=h=m2collector flow rate at 57.5° (for the minimum LCC). A similar trend is observed for the optimum solutions at minimum LCX. 3.1. Financial payback The simple financial payback of the BSCS and the four optimal configurations is calculated as the initial cost of the

Table 7 Comparison of base case and optimal combisystem configurations. Component

Configuration based on BCSCS

Minimum LCC

Minimum LCE

Minimum LCXt destroyed

Minimum LCXp destroyed

Number of solar collectors Collector slope (°) Collector fluid flow rate ðkg=h=m2collector Þ DHWT volume (L) RFT volume (L) DHWT auxiliary power (kW) RFT auxiliary power high (kW) RFT auxiliary power low (kW)

4 45 9.1 300 300 1 2 4

1 57.5 20.0 100 300 0.5 3.0 0.5

9 75 13.8 100 300 0.75 0.5 3.0

1 70 32.5 100 300 0.5 2.6 6.0

8 68.1 40.8 1000 300 1.3 1.0 0.8

Objective function value LCC ($) LCE (kW h) LCXt (kW h) LCXp (kW h)

26,628 228,475 533,327 236,486

21,461 307,253 359,753 286,805

33,749 150,350 801,404 180,839

21,489 308,515 358,424 285,009

36,641 165,161 749,888 179,736

Solar fraction

0.51

0.21

0.74

0.26

0.72

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Table 8 Simple financial payback analysis. Configuration

Annual reduction of electricity use (kW h)

Annual electricity cost at $0.0776/kW h ($)

Annual cost savings ($)

Total initial cost ($)

Simple payback (years)

No system BCSCS LCC optimal LCE optimal LCXt optimal LCXp optimal

0 2667 1006 4394 983 4145

492 285 414 151 415 170

0 207 78 341 76 322

0 13,302 8060 20,575 8060 21,482

– 64 103 60 106 67

Fig. 2. Cumulative cash flow analysis for the BCSCS and the four optimal configurations.

system divided by the annual cost savings incurred by using the solar combisystem. The scope of this paper was the optimization of a solar combisystem; however, for the purpose of financial comparison only, the case of the house without a solar collector system is included in Table 8. Financially speaking, all of the optimal configurations perform quite poorly compared to the case without the combisystem because of the high initial cost of such a solar system, and the low cost of electricity in Quebec. The simple payback times of all of the configurations are considerably longer than the assumed life of the house (40 years). There are significant limitations of the simple payback analysis that make the results even more optimistic. First, the simple payback analysis does not consider the time value of money and second, it does not consider that the components of the combisystem need to be replaced at certain time intervals over the life of the house. These terms can be taken into account with a cumulative cash flow analysis. Fig. 2 shows the cumulative cash flow analysis for all of the combisystem configurations. None of the systems ever completely pay back the required investment when the time value of money, the rising price of electricity, and the cost of replacing the equipment are considered. Even after the assumed 40 year life of the house, the cumulative cash flow of all of the configurations hardly changes (see Fig. 3).

Fig. 3. Annual site electricity use of the BCSCS and the four optimal configurations.

A previous study by Leckner and Zmeureanu (2011) concluded that, for the climatic conditions of Montreal, the price of electricity needs to be $0.24/kW h for a 40 year payback and $0.32/kW h for a 25 year payback to make the solar combisystem cost-effective when all other parameters are held constant. Although $0.24/ kW h is significantly more than the current $0.0754/ kW h in Montreal, it is not totally unreasonable in other cities in North America such as New York City, where the price of electricity was approximately $0.2532/kW h at the time of the study. 3.2. Energy payback The LCE and LCXp optimal configurations use significantly less electricity than the other configurations due to the higher number of solar collectors. In the case of the LCC and LCXt optimal configurations, the results promote the use of electricity rather than the conversion of solar energy under the conditions of this study (climate and price of electricity in Quebec). This does not take into account, however, that solar energy is relatively inexhaustible and clean. The energy payback analysis indicates if installing a combisystem is beneficial by comparing the amount of energy it could save over its life and the amount of energy that is used to manufacture, transport and install this

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Table 9 Energy payback analysis. Configuration

Embodied energy (kW h)

Difference in embodied energy from no collectors (kW h)

Annual primary electricity use (kW h)

Annual primary energy reduction (kW h)

Life cycle primary energy saved (kW h)

Energy payback time (EPT) (years)

Energy payback ratio (EPR)

No collectors BCSCS LCC optimal LCE optimal LCXt optimal LCXp optimal

6046 27,363 15,109 43,850 15,109 45,012

0 21,317 9063 37,804 9063 38,966

8682 4998 7279 2588 7294 2805

0 3684 1403 6094 1388 5877

– 147,357 56,115 243,750 55,512 235,077

– 5.8 6.5 6.2 6.5 6.6

– 6.9 6.2 6.4 6.1 6.0

Table 10 Exergy payback time and exergy payback ratio for all five configurations using the physical boundary. Configuration

Embodied exergy (kW h)

Difference in embodied exergy from no system (kW h)

Annual exergy destroyed (kW h)

Annual reduction in exergy destroyed from no system (kW h)

Exergy payback time (XPT) (years)

Exergy payback ratio (XPR)

No system BCSCS LCC optimal LCE optimal LCXt optimal LCXp optimal

5202 18,707 9575 30,541 9575 32,011

0 13,505 4373 25,339 4373 26,809

7920 5444 6931 3757 6886 3693

0 2475 989 4162 1034 4226

– 5.5 4.4 6.1 4.2 6.3

– 7.3 9.0 6.6 9.5 6.3

Table 11 Exergy efficiency of combisystem components for BCSCS and LCC, LCE and LCX optimal configurations. Configuration

Exergy efficiency (%) Combisystem

BCSCS LCC optimal LCE optimal LCXt optimal LCXp optimal

Solar collectors

Technical boundary

Physical boundary

Technical boundary

Physical boundary

7.4 9.3 5.0 9.3 5.8

15.7 11.4 20.3 11.4 20.2

7.7 11.4 5.7 10.5 5.6

46.8 50.8 45.9 52.1 44.4

system (Table 8). Two different metrics are used for each configuration (Table 9): the energy payback time (EPT) and the energy payback ratio (EPR). The EPT is calculated by dividing the embodied energy of the solar collectors by the annual reduction in primary electricity use compared to having no collectors. The EPR is calculated by multiplying the annual primary energy savings by the number of years for the life of the house (i.e. 40) and then dividing by the embodied energy of the system. All optimum configurations have EPTs between 6.2 and 6.6 years, compared with 5.8 years for BCSCS. Similarly, the EPRs of the optimum configurations are also fairly consistent, between 6.0 and 6.4, compared with 6.9 for BCSCS. These results show that although the combisystem never pays back financially regardless of the configuration, they all pay back in terms of energy.

Radiant floor tank

Domestic hot water tank

14.5 10.8 23.4 11.0 21.8

40.2 16.8 51.8 15.9 68.9

3.3. Exergy payback The exergy payback analysis determines if the system can save more exergy from being destroyed than is embodied within its components during the manufacturing. The exergy payback time (XPT) and exergy payback ratio (XPR) are calculated similarly to EPT and EPR (Table 10). All optimum configurations have XPTs between 4.2 and 6.3 years, compared with 5.5 years for the BCSCS, and XPRs between 6.3 and 9.0, compared with 7.3 for the BCSCS. The exergy efficiency of the solar collectors of the optimal configurations under the physical boundary approach are much higher (44.4–52.1%) compared with the collectors of the configurations under the technical boundary approach (5.6–11.4%) (Table 11). As a result, the exergy

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efficiency of the whole combisystem is also higher for the physical boundary than for the technical boundary approach. The high efficiency of 44.4% for the solar collectors in the LCXp optimal configuration is due to the large collector area, which allows for a reduction of exergy destruction of 4226 kW h (Table 10). However, the increase in embodied exergy of 26,809 kW h due to the increase in collector area makes the exergy payback time almost equal to the other configurations. For all three components of the combisystem using both boundaries, the BCSCS is a non-inferior solution and falls in between the other configurations in terms of exergy efficiency. The comparison between a tank with thermal stratification and a tank with uniform water temperature was not performed in this study. The actual amount of exergy stored in the tank is relatively low due to the relatively low average tank temperature. The tanks can be considered as exergy transition tanks rather than storage tanks since, in fact, very little exergy is stored.

optimizations, and between the energy and physical exergy optimizations. Due to the current high cost of solar collector technologies and the low price of electricity in Quebec, none of the configurations have acceptable financial payback periods. However, all of the configurations have energy payback times between 5.8 and 6.6 years. The use of technical boundary in the exergy analysis favors the use of electricity over solar energy due to the low exergy efficiency of the solar collectors. The use of physical boundary, on the other hand, favors the use of solar energy over electricity, and all of the combisystem configurations have exergy payback times between 4.2 and 6.3 years.

4. Conclusions

References

The results prove the advantage offered by the use of optimization techniques for the design of solar combisystems. The optimizations resulted in reductions of 19–34% for the four objective functions, when compared with the base case combisystem that was designed based on current practices. Although the study was based on conditions specific to Montreal such as the initial cost of the equipment, energy cost, embodied energy, inflation rate or escalation rate of energy cost, there are some general conclusions that can be drawn from this study. Certainly, the use of site-specific parameters might lead to different absolute values of design variables and optimization criteria; however, we expect that the trend of variation would remain similar. The optimal configurations of the solar combisystem obtained from the LCC and LCXt optimizations are similar, with only one solar collector, while the optimal configurations from the LCE and LCXp optimizations have 8–9 solar collectors. In addition, the LCXp optimal configuration has a large domestic hot water tank. The LCC optimal configuration would be preferable if the financial goal is the main criterion of the decision maker, since this configuration contains the minimum number of solar collectors; however, the economic parameters (e.g., inflation rate) might change over the expected life of the system, with positive or negative impacts on the cost-effectiveness of the selected design solution. The LCE optimal configuration would be preferable if the decision maker has the goal of increasing the contribution of solar energy in housing, since this configuration uses more solar collectors. Certainly, the LCE could help in designing systems with a longer-term vision. It is also interesting to note the similarity between the cost and technical exergy

Acknowledgements The authors acknowledge the financial support from the National Science and Engineering Research Council of Canada, and the Faculty of Engineering and Computer Science of Concordia University.

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