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Energy and Buildings 49 (2012) 200–208

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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild

A linear programming approach to household energy conservation: Efficient allocation of budget Fehmi Görkem Üc¸tu˘g ∗ , Ergün Yükseltan Bahcesehir University, Department of Energy Systems Engineering, 34353 Besiktas, Istanbul, Turkey

a r t i c l e

i n f o

Article history: Received 20 July 2011 Received in revised form 20 December 2011 Accepted 5 February 2012 Keywords: Energy conservation Household energy consumption Linear programming Optimization Building energy efficiency Turkey Insulation Photovoltaic cells Energy labels

a b s t r a c t Linear programming method was used to optimize the allocation of budget in order to maximize the energy savings of a hypothetical household in Turkey. The energy conservation methods involved in this study were installing photovoltaic solar cells, replacing regular windows with double-glazed ones, replacing incandescent bulbs with compact fluorescent light bulbs and replacing C-Energy Class household appliances with A-Energy Class ones. The costs of these different energy conservation methods were obtained from the manufacturers’ or distributors’ websites. The annual energy savings of these methods were either obtained from available sources or calculated when necessary. The results showed that installing double-glazed windows and purchasing compact fluorescent light bulbs are the proper choices for low budgets. When budget increased, solar panel installation emerged as the feasible choice. The findings indicated that replacing household appliances should be considered only when a budget greater than D20,000 is available. Payback periods were found to be less than one and a half years, even at the highest budget. A budget decision of D800 was found to be the optimum decision for short term investments, whereas a budget decision of D24,000 was found to be the optimum decision for long term investments. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Efficient use of energy is a very important concept, not only because it favors a more stable economy, but it also helps prevent environmental pollution, and the combination of these two facts is essential for sustainable development. Buildings are responsible for the consumption of approximately 40% of all commercial energy supplied as processed fuels or electricity in developed countries [1,2]. For thousands of years, mankind has tried to improve the energy efficiency of buildings via simple methods such as choosing the ideal geographic location or by using appropriate building and insulating materials depending on the climate. As the technology developed, the measures to minimize energy loss have become more complex. However, it was the 1973 global energy crisis that triggered a worldwide pursuit in designing buildings with less energy consumption, by incorporating energy efficiency

Abbreviations: CFL, compact fluorescent light; DSW, dishwasher; LED, lightemitting diode; RFG, refrigerator; TRY, Turkish Lira; WMC, washing machine. ∗ Corresponding author at: Bahcesehir University, Department of Energy Systems Engineering, Ciragan Caddesi, 34353 Besiktas, Istanbul, Turkey. Tel.: +90 0 212 381 5691; fax: +90 0 212 381 0550. E-mail address: [email protected] (F.G. Üc¸tu˘g). 0378-7788/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2012.02.020

and renewable energy resources [3]. Since then, many countries adopted laws and regulations on how to use energy more efficiently and energy efficiency in residential and commercial buildings have become a common area of interest [4–8]. Above-mentioned laws and regulations impose certain targets and deadlines regarding both residential and commercial buildings with the aim of reaching specified energy consumption limits. For instance, in Turkey the Energy Efficiency Law came into effect in May 2007, aiming to minimize the high level of energy intensity so as to achieve productive and effective use in every field of energy, prevention of wasteful expenditure and protection of the environment. This law, which was revised recently in February 2011, comprises the principals and procedures in order to increase the energy efficiency in industrial, building and transport sectors. With this law, Turkey aims to accomplish an energy saving of 30% in the next decade [9]. In order to achieve this goal, home-owners or tenants must take suitable actions to reduce their energy consumption without having to compensate from their quality of living. Therefore, the solution must satisfy energy-related, environmental and financial aspects of the problem. When the great number of possible actions that can reduce the energy consumption of a building is concerned, using a sophisticated method to determine the optimum choice(s) is inevitable. Before proceeding with linear programming, which is our choice of method, we would like to briefly review similar studies in the field.

F.G. Üc¸tu˘g, E. Yükseltan / Energy and Buildings 49 (2012) 200–208

1.1. Review of computer-aided techniques for building energy efficiency improvement Several decision analysis methods have been put forward in the field of energy, and building energy efficiency in particular, recently. In his study, Al-Homoud reviewed a significant variety of computer-aided building energy analysis methods, ranging from simple steady-state methods to detailed hourly analysis techniques [10]. He concluded that “available energy simulation models are useful and powerful tools for the evaluation of the thermal performance of buildings and they can provide extensive performance information on the selected building considering the dynamic behavior of the system, as well as part load behavior”. He also stated that “optimization techniques can also be useful in providing designers and decision makers with prescriptive information that cannot be easily achieved using simulation models alone”. In a more recent study, Kolokotsa et al. analyzed various decision support methods for energy management in buildings [11]. They concluded that several constraints such as environmental, social, financial and energy-related aspects must be taken into account in order to make an optimum choice. As far as multiobjective methodological approach is concerned, the following studies attracted our attention: Wright et al. investigated that application of a multi-criterion genetic algorithm in the search for a non-dominated set of solutions to pay-off between energy cost and occupant discomfort [12]. Their results showed that multi-criterion genetic algorithm was able to identify the pay-off characteristic between daily energy cost and zone thermal discomfort. Alanne et al. proposed a multi-criteria “knapsack” model to determine the most feasible renovation actions in the conceptual phase of a renovation project [13]. Amongst the 27 different options, radiator network adjustment via the installation of thermostatic valves emerged as the most feasible action. Chen et al. used an energy-time consumption index in order to maximize energy utilization efficiency in intelligent buildings, via an approach called analytic network process, which is a multicriterion decision method [14]. The distinctive feature of this study is the allocation of priority values to each criterion by taking the opinions of property owners, property managers, occupants and visitors. Verbeeck and Hens developed a global methodology to optimize concepts for extremely low energy dwellings, taking into account energy use, environmental impact, and financial costs over the life cycle of the buildings [15]. They used a software called TRNSYS to execute their energy simulations. The ecological impact was evaluated through a life cycle inventory of the whole building, whereas costs were evaluated through a cost–benefit analysis. Verbeeck and Hens reached two important conclusions regarding the economic implications of energy efficiency improvement in buildings. Firstly, they concluded that without financial support or incentives, building energy efficiency improvement will be limited to a small number of consumers with a high environmental consciousness that are willing to invest large budgets. However, they also stated that the energy payback time is extremely low for energy efficient dwellings and is, in most cases, less than two years. Diakaki et al. suggested a considerable number of energy efficiency improvement options to choose from, such as door and window types, insulation thickness and type of heating system [16]. Their model calculated not only the energy consumption but also the CO2 emission of the building. And for the last but not the least, Magnier and Haghighat described an optimization methodology based on a combination of an artificial neural network and a multiobjective evolutionary algorithm, by using Latin Hypercube sampling and GenOpt automation engine in order to create the database of cases [17]. Their study produced the energy impact of the thermal comfort choice made by the user as the output.

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1.2. Justification of the method In this study, linear programming method was used to optimize the allocation of budget in order to maximize the energy savings of a hypothetical household in Turkey. Linear programming is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for a list of requirements represented as linear relationships [18]. A linear programming model simply contains an objective function (to be maximized or minimized) and a constraint function. Linear programming method is a very convenient tool that it is used extensively to solve and optimize various types of economical and industrial problems. Our model, whose details will be presented in the following Section 3.3, accepts energy savings (W) as the objective function and the budget as the constraint function. There are various actions that result in energy savings in a house, each with a specified unit cost. The aim of the algorithm is to allocate the budget to these actions in order to obtain the maximum energy savings. Different budget values were used as constraint to get energy saving values as a function of budget. While developing the method, our main idea was to analyze the issue of building energy efficiency from the household consumer’s point of view. We wanted to create a simple, yet effective algorithm. Our algorithm was designed to answer the question of “how much energy would be saved if certain amount of money was spent”. After obtaining the maximum possible energy savings values for each different budget, we calculated payback periods and profitability values to convert the output into a more understandable form for the consumer. A further strength of this study is the realization of a detailed market research in order to get approximate cost values for each particular energy-saving measure. The readers can simply check the references listed at the end to get the actual cost values for any given item or method. 2. Energy conservation methods in buildings The materials and techniques employed in order to improve the energy efficiency in buildings vary greatly. Jaber and Ajib [19] listed the main steps to achieve energy conservation in residential buildings as follows: i. Passive design by considering climate effects so as to decrease heating, cooling, dehumidification, lighting, equipment and hot water loads. ii. Improving the efficiency of the mechanical and electrical equipment used in the building. iii. Replacing fossil fuels with renewable sources for the supply of primary energy Heating and cooling systems make up for a significant portion of the total expenditure of households. Heating systems like boilers, heat pumps and cooling systems like air conditioners are expensive to install and operate; consequently the entire energy requirement of a building cannot solely be met by using such equipment as far as energy efficiency is concerned. Therefore, using insulation materials to minimize heat loss (or gain) is essential to achieve meaningful energy conservation. Windows lose energy more readily than walls or a floor, therefore using insulation materials in windows is the most straightforward approach to minimize heat loss. The most common technique applied for insulating windows is double glazing, in which double or triple glass window panes separated by an air-(or other gas)-filled space are used to reduce heat transfer across a part of the building envelope. Double glazing is not only an

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effective method to reduce heat losses but it also promotes acoustic insulation. Thermal conductivity, k (W/m ◦ C) and cost are two important properties of insulation materials as far as performance is concerned [20]. Solar energy is the most abundant, inexhaustible and clean of all the renewable energy resources. Solar energy can be used in buildings by installing thermal solar collectors on the roof and then using the absorbed energy to heat utility water [21]. Solar energy can also be directly converted into electricity via photovoltaic cells. Photovoltaic cells are designed to transfer the energy contained in individual photons penetrating the panel to electrons that are channeled into an external circuit for powering an electrical load [22]. Photovoltaic cells can be connected in series to form a module and then placed on the roofs, or where available, to provide electricity to households. Unlike thermal solar collectors, photovoltaic cells do not require a continuous and abundant reception of sunlight; therefore they can be employed more generally as far as location is concerned. In addition to being used to provide power for buildings, they are also used for water pumping, communications, satellites and space vehicles, reverse osmosis plants, and for even large power plants [21]. One disadvantage of photovoltaic cells is their high initial cost, and this slows down the penetration of photovoltaic technology into building sector. Ever since electricity was first used as the primary source to provide lighting around at the end of the 19th century, incandescent bulbs have always been the most common type of bulb in the market. However, approximately 90% of the power consumed by an incandescent light bulb is emitted as heat, rather than as visible light. Thus, in the recent years consciousness has risen on the low efficiency of incandescent light bulbs in international scale. For instance, the European Commission gradually prohibits the usage of incandescent light bulbs via decree. Starting September 1, 2009, Regulation 244/2009 introduced a gradual phase-out for almost all kinds of incandescent bulbs until September 2012. As of September 2012, only energy-efficient lighting sources will be allowed for sale. Among these are halogen light bulbs, light-emitting diodes (LED), or compact fluorescent light bulbs (CFL) – often referred to as energysaving light bulbs [23]. CFL bulbs consume 25% of the electricity incandescent bulbs consume in order to provide the same level of illumination, and their approximate lifespan is 6 times of that of incandescent light bulbs. Nonetheless, CFL bulbs are significantly more expensive than incandescent light bulbs, with an approximate price ratio of 7:1. A considerable portion of residential electricity consumption belongs to major household appliances. Mills and Schleich [24] claim that refrigerators and freezers alone are responsible for 15% of residential electricity end-use, with washing machines accounting for 4% and dishwashers accounting for 2%. Increasing the energy efficiency of these appliances is crucial for realizing energy efficiency policy objectives. In order to encourage both the manufacturers and the customers toward a more energy-efficient future, labeling systems have been introduced. Energy efficiency labels are informative tags that are added on to fabricated products and describe a product’s energy performance (generally in the form of energy use, efficiency, or energy cost) to provide consumers with the data necessary for making informed purchases. The most common labeling program is the “Energy Star” program, which was initiated in U.S.A. in 1992, creating a labeling system to promote the use of energy efficient devices. Today, Australia, Canada, Japan, New Zealand, Taiwan and the European Union (EU) have also adopted the program. Augmented utilization of Energy Star appliances can potentially generate substantial energy savings. In fact, it is estimated that if consumers only bought new Energy Star labeled dishwashers, refrigerators, and washing machines, greenhouse gas emissions would decrease by 4.5 billion pounds per year, equivalent to reducing emission levels by 370,000 cars [25]. The generation of

consumer information on appliance energy efficiency is, in turn, expected to create market incentives for appliance manufactures to design more energy-efficient products, and may reinforce priceinduced technological innovation [26]. Before proceeding to the next section, we would like to emphasize that while there are many other possible methods that can be applied to improve energy efficiency in households, the ones mentioned above were particularly chosen as they are available to the common user, regardless of his/her socioeconomic status or the location of the building the user resides in.

3. Methodology 3.1. Definition of the problem This study aimed at employing linear programming technique for optimizing the allocation of budget to be spent on improving energy conservation in a domestic household in Turkey. All the data regarding the costs of each method was obtained from local sources, with the cost units being Turkish Lira (TRY). The costs were then converted to Euro (D), that is why cost values shown in the tables or mentioned in the text are not all rounded figures. As of December 20th 2011, 1 TRY is equivalent to 0.53 U.S. Dollar and 0.40 Euro. While the general accommodation trend in Turkey is living in multi-storey apartment buildings, we preferred to select our hypothetical building as a two-floor detached house. This choice was made mainly for the sake of convenience, as heat loss calculations would have been much more difficult in the case of an apartment, since the environment would be non-uniform in terms of temperature. Furthermore, it would also be difficult to calculate energy savings per household when more than one household would benefit from that particular investment. In terms of the dimensions of the building, total roof area and window area must be known. These values would be the physical constraints for the maximum number of solar cells and maximum area of double-glazed windows, respectively. Persson et al. claimed that total window area of a two-floor house is nearly 16% of the total floor area [27]. For a realistic approximation of 200 m2 total floor area, the total window area can then be approximated as 32 m2 . Since Turkey is in the subtropical climate region, harsh winters and heavy snowfall is not common, with the exception of Eastern Anatolia region. Hence, a low pitch roof would be adequate. From available literature, it has been found that a roof height of 4 m is necessary for 12 m width when the roof is low pitch [28]. Thus, for an estimated basal area of 100 m2 (10 m × 10 m), total roof area can be calculated approximately as 140 m2 , by taking into account the fact that the width of the roof needs to be slightly greater than the base width, approximately by 1 m. However, due to reasons related to the strength and durability of the construction, it would be hazardous to cover the entire roof with solar panels. A realistic approach would be to allocate a maximum area of 50% of the total roof area for solar panel installation. Therefore the area available for solar panel installation was found as 70 m2 . If the house is assumed to have one living room, three bedrooms, two bathrooms and one kitchen, a total of ten 100-W incandescent light bulbs would be enough to provide sufficient lighting in the initial stage. Table 1 below contains the physical characteristics and layout details of the house that would be included in the linear model as constraints.

3.2. Costs and energy savings In this study, the following methods were chosen to improve the energy conservation in a household:

F.G. Üc¸tu˘g, E. Yükseltan / Energy and Buildings 49 (2012) 200–208 Table 1 Physical characteristics and layout details of the house. House characteristic

Value

Total basal area, m2 Total roof area available for solar panel installation, m2 Total window area, m2 Total number of rooms

100 (10 m × 10 m) 70

dglass , thickness of glass layer, m kglass , thermal conductivity of glass layer, W/(m ◦ C) dair , thickness of air layer, m kair , thermal conductivity of air layer, W/(m ◦ C) In the equation above, Q defines the heat flux through a doubleglazed window unit. However, we are interested in calculating the savings when compared to regular windows. Hence, we also need to calculate the heat flux value without the presence of any air (dair = 0) and then the difference between those two values would give us the saving in terms of flux. The average winter temperature of Istanbul region was obtained from the website of Turkish State Meteorological Service as approximately 7 ◦ C [35]. If the ideal living temperature inside a house is taken as approximately 22 ◦ C (72 ◦ F), then T value can be found as 15 ◦ C. Surface area of total window installation is a variable in this study. As stated above, the glass thickness is 4 mm (0.004 m) and air thickness is 12 mm (0.012 m). Thermal conductivity and heat transfer coefficient values were gathered from available literature [36]. Table 3 below summarizes the calculation parameters, energy saving in terms of heat flux rate and cost of double-glazed window purchase and installation. The prices and power consumptions of CFL light bulbs were obtained from a distributor company’s website [37]. The brands whose products were investigated were OSRAMTM , PhilipsTM , GreengoTM , and WellmaxTM . While choosing the CFL bulbs that would replace the existing incandescent bulbs, the criterion was to achieve the same level of lighting as in the case of a 100-W incandescent bulb. The average power consumption of a CFL bulb that would provide the same level of lighting as that of a 100-W incandescent light bulb (≈1400 lumens) was found as 19.5 W. Hence the energy gain by replacing incandescent bulbs with CFL bulbs was found as 80.5 W per bulb. The average cost of a single CFL bulb was found as D2.32 (≈5.8 TRY). The prices and power consumptions of home appliances (refrigerator, washing machine, and dishwasher) were obtained by calculating averages via using data from five different local manufacturers’ websites [38–42]. The brands were Arc¸elikTM , ProfiloTM , VestelTM , BoschTM and SiemensTM . The classification of the appliances, which normally have a very wide range of types according to size, technology or material, was done as follows:

32 7 (one living room, three bedrooms, two bathrooms and one kitchen) 10 × 100 W incandescent bulbs

Lighting requirements

Table 2 Capacities, areas and average prices of photovoltaic solar modules.a Capacity (W)

Area (m2 )

Price (D)

Performance (W/D)

50 65 120 140 180 200

0.43 0.53 0.91 1.03 1.32 1.45

181.2 226.4 329.2 413.2 450.4 543.2

0.275 0.288 0.365 0.340 0.400 0.368

a

All prices belong to monocrystalline solar cells.

• Installing photovoltaic cells on the roof where the area occupied is a variable • Installing double-glazed windows where the window area is a variable • Replacing incandescent bulbs with compact fluorescent bulbs where the number of bulbs is a variable • Replacing the C-Energy Class appliances by A-Energy Class ones The prices, areas and power outputs (capacities) of solar panels were obtained from three different distributors’ websites [29–32]. The brands were EvergreenTM , BPTM , KyoceraTM , SanyoTM , SharpTM , KanekaTM , Bright WattsTM , and MitsubishiTM . The price values of different products with same capacities (in Watts) were gathered and their averages were taken to calculate the final price. The values are tabulated below in Table 2. Prices of double-glazed window units were also obtained from local manufacturers’ websites [33,34]. In double-glazing technology, the thickness of the glass and the layer of air (or other gas) can vary, and in this study we decided to select the air layer thickness as 12 mm and the glass thickness on either side as 4 mm. Then, the average purchase and installation cost for 1 m2 of double-glazed window was found to be approximately D24 (≈60 TRY). The energy saving calculations was performed by taking into account both conductive and convective heat transfer mechanism while neglecting any possible contribution of radiation. The calculations are given below: Q =

203

T 1/A(1/h + dglass /kglass + dair /kair + dglass /kglass + 1/h)

• All the refrigerators were selected as No-Frost type with approximate storage space of 500 l (±4%). The energy class was A. • All the washing machines had capacities of 7 kg. The energy class was A-20%. • All the dishwashers were 5 programme. The energy class was A-10%.

(1) At this stage it is worth mentioning that when it comes to household appliances, power itself does not have a significant meaning regarding financial return. We are aware that electricity unit cost is based on kWh, and the duration of use of the equipment must be known to switch from Watts (power) to kWh (energy). Yet, in this study the energy savings have been calculated in terms of watts up to this point, as the energy gains (or losses) from photovoltaic cells, double-glazed windows and lighting are

where Q, heat transfer rate through the window unit, W T, average temperature difference between inside and outside during winter, ◦ C A, surface area of double-glazed window to be installed, m2 h, heat transfer coefficient of air, W/(m2 ◦ C) Table 3 Energy saving calculation parameters for double-glazed windows. T (◦ C)

h W/(m2 ◦ C)

dglass (m)

kglass W/(m ◦ C)

dair (m)

kair W/(m ◦ C)

Qreg (W/m2 )

Qdg (W/m2 )

Qsave (W/m2 )

Cdg (TRY/m2 )

15

50

0.004

0.96

0.012

0.026

310.3

29.4

280.9

60

Qreg is the heat transfer flux through regular windows, Qdg is the heat transfer flux through double-glazed windows, Qsave is the energy saving as a result of installing double-glazed windows (Qsave = Qreg − Qdg ) and Cdg is the cost of double-glazed window purchase and installation per square meter.

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continuous processes. However, it would be inaccurate to follow the same approach for household appliances. Refrigerators operate almost 365 days a year, 24 h a day while dishwashers and washing machines are operated once in every few days on an average basis, depending on the number of people living in the house. It had already been stated that refrigerators consume more energy when compared to washing machines and dishwashers combined on an annual basis [24], however the power requirement of a refrigerator is much lower than that of a washing machine or a dishwasher. For that reason, the manufacturers express the energy consumption of their refrigerators as kWh per year, whereas for washing machines or dishwashers the energy consumption values are given as kWh per run. If the power requirement values had been used as inputs for our mathematical model, the results would not have been reliable. Thus, we decided to develop a novel approach in order to get comparable values for the power consumptions of household appliances. Instead of using the actual power requirements of all these three appliance types, we only decided to use the actual power requirement of a refrigerator. For the washing machine and the dishwasher, we decided to define a new term, called the “adjusted power requirement”. Adjusted power requirement is a hypothetical quality and it is calculated by assuming that the appliance (washing machine or dishwasher) is operated continuously during the year, just like a refrigerator. The calculation details of adjusted power requirements of washing machines and dishwashers are as follows: PR =

1000 ER 365 × 24

PW a = PDa

=

T 1000 × EW × NW

365 × 24

1000 × ED × NDT 365 × 24

Table 4 Power requirements, energy savings and costs of A-energy class home appliances.

Refrigeratora Washing machineb Dishwasherc a b c d

Power requirement (W)

Energy savings (W)

Cost (D)

57.6 17.98d 17.33d

40.4 11.99 5.79

784 501.2 521.2

No Frost Type, 500 L (±4%) capacity, A energy class. 7 kg capacity, A-20% energy class. 5 programme, A-10% energy class. Based on adjusted power requirement values.

C-Energy Class washing machine and a C-Energy Class dishwasher were found as 98 W, 29.97 W and 23.12 W, respectively. Table 4 below summarizes the average prices and average power requirements of A-Energy Class appliances as well as the energy savings when compared to C-Energy Class. 3.3. Linear programming model

(2)

In this study, Lingo 12.0 software was used to obtain the results. The linear model, which was created by using the costs and savings data and considering the physical constraints, all of which were presented in the previous sections, is given below. x, yi , z, r, p, t are the decision variables of the model

(3)

Max Z = (Qx ∗ x) +

(4)

where PR , actual power requirement of a refrigerator, W ER , actual energy consumption of a refrigerator per year, kWh a , adjusted power requirement of a washing machine, W PW EW , actual energy consumption of a washing machine per run, kWh T , number of times a washing machine is operated in a year NW a PD , adjusted power requirement of a dishwasher, W ED , actual energy consumption of a dishwasher per run, kWh NDT , number of times a dishwasher is operated in a year ER , EW and ED values were obtained from the manufacturers’ websites, as mentioned above. During the calculation of adjusted T and N T values are taken as 150. The power requirements, both NW D constants 365, 24 and 1000 denote the number of days in a year, number of hours in a day and the conversion factor from kW to W, respectively. While calculating the price values, the average of the prices of similar products was taken. The same approach was also followed while calculating the power consumptions. Since companies do not produce lower energy class (such as C-Energy Class) products anymore, it has not been possible to acquire any data regarding the energy consumptions of such appliances from the manufacturers’ websites. Thus, we had to make an approximation. The maximum acceptable energy consumption (kWh) values of each appliance with different energy labels were obtained from available literature [43]. Then, the average of the maximum acceptable energy consumption values of C and B-Energy Class appliances was taken and that value was assumed as the approximate energy consumption of a given C-Energy Class appliance. The “adjusted power requirement” approach was also followed to calculate the average power requirement of C-Energy Class appliances. With that approach, the average power requirements of a C-Energy Class refrigerator,

(Cx ∗ x) +

 n 

 n 



Qyi ∗ yi

+ (Qz ∗ z) + (Qr ∗ r) + (Qp ∗ p) + (Qt ∗ t)



i=1

Cyi ∗ yi

+ (Cz ∗ z) + (Cr ∗ r) + (Cp ∗ p) + (Ct ∗ t) ≤ w

i=1

x≤k n 

(yi ∗ ai ) ≤ q

i=1

z≤v x, yi , z, r, p, t are non-negative and yi is Integer r, p, t are binary Variables and i = 1, 2, 3, . . . , n

where x, double-glazed window area yi , the number of ith type photovoltaic solar panel to be purchased z, number of incandescent light bulbs to be replaced with CFL bulbs

 r=

 p=

1 if C-class washing machine is replaced with A-class washing machine 0 otherwise

 t=

1 if C-class dishwasher is replaced with A-class dishwasher 0 otherwise

1 if C-class refrigerator is replaced with A-class refrigerator 0 otherwise

where Qx , energy savings rate by installing 1 m2 of double-glazed window, W QYi , electricity production rate of solar panel type i, W Qz , energy consumption rate difference between incandescent and CFL light bulbs, W Qr , adjusted energy consumption rate difference between CEnergy Class and A-Energy Class dishwashers, W

F.G. Üc¸tu˘g, E. Yükseltan / Energy and Buildings 49 (2012) 200–208

205

Table 5 Budget optimization and energy savings, low range budgets. Budget (D)

400 800 1200 1600 2000 2400 2800 3200 3600 4000 a b c

Double-glazed windows (m2 )

15.7 32 32 32 32 32 32 32 32 32

Solar panel installation (#)

CFL bulbs (#)

Type 1

Type 2

Type 3

Type 4

Type 5

Type 6

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0

0 0 1 1 1 0 2 0 0 0

0 0 0 0 1 0 0 0 0 0

0 0 0 1 1 3 3 4 5 7

0 0 0 0 0 0 0 1 1 0

Appliances

Total energy savings (W)

RFG.a

WMC.b

DSW.c

10 10 10 10 10 10 10 10 10 10

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

CFL bulbs (#)

Appliances

5215.3 9793.7 9913.8 10,093.7 10,233.8 10,398.7 10,564.4 10,713.7 10,893.7 11,053.7

Refrigerator. Washing machine. Dishwasher.

Table 6 Budget optimization and energy savings, medium range budgets. Budget (D)

6000 8000 10,000 12,000 14,000 16,000 a b c

Double-glazed windows (m2 )

32 32 32 32 32 32

Solar panel installation (#)

Type 1

Type 2

Type 3

Type 4

Type 5

Type 6

0 0 1 0 0 0

1 0 0 0 0 0

0 0 0 1 0 1

0 0 0 0 0 0

11 16 20 24 28 33

0 0 0 0 1 0

10 10 10 10 10 10

Total energy savings (W)

RFG.a

WMC.b

DSW.c

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

11,838.7 12,673.7 13,443.7 14,233.7 15,033.7 15,853.7

Refrigerator. Washing machine. Dishwasher.

Qp , adjusted energy consumption rate difference between CEnergy Class and A-Energy Class washing machines, W Qt , energy consumption rate difference between C-Energy Class and A-Energy Class refrigerators, W Cx , average purchase and installation cost of 1 m2 double-glazed window, D CYi , average purchase and installation cost of solar panel type i, D Cz , average cost of one CFL light bulb, D Cr , average cost of one A-Energy Class dishwasher, D Cp , average cost of one A-Energy Class washing machine, D Ct , average cost of one A-Energy Class refrigerator, D k, total window area (physical constraint for double-glazed window installation), m2 ai , area of solar panel type i q, total available roof area (physical constraint for solar panel installation), m2 v, maximum number of CFL light bulbs that can be purchased for the house

All the energy saving parameters, cost terms and physical constraint values expressed in the model above have been presented in Tables 1–4. 4. Results and discussion During the allocation analysis, three budget regions were defined: (i) Low budget: budgets up to D4000 (≈10,000 TRY) (ii) Medium budget: budgets between D4000 and D16,000 (≈10,000–40,000 TRY) (iii) High budget: budgets between D16,000 and D40,000 (≈40,000–100,000 TRY) The increment between budget values for the low budget range was selected as D400 (≈1000 TRY) whereas the increment for

Table 7 Budget optimization and energy savings, high range budgets. Budget (D)

20,000 24,000 28,000 32,000 36,000 40,000 a b c

Double-glazed windows (m2 )

32 32 32 32 32 32

Refrigerator. Washing machine. Dishwasher.

Solar panel installation (#)

CFL bulbs (#)

Type 1

Type 2

Type 3

Type 4

0 0 0 0 0 0

0 1 1 1 1 1

1 0 0 0 0 0

1 0 0 0 0 0

Type 5 41 51 1 1 1 1

Type 6 0 0 47 47 47 47

10 10 10 10 10 10

Appliances

Total energy savings (W)

RFG.a

WMC.b

DSW.c

0 0 1 1 1 1

0 0 0 1 1 1

0 0 0 1 1 1

17,433.7 19,038.7 19,479.7 19,496.9 19,496.9 19,496.9

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Fig. 1. Energy savings as a function of budget and budget utilization percentages.

medium budget range was selected as D2000 (≈5000 TRY) and the increment for high budget range was selected as D4000 (≈10,000 TRY). The optimum allocation of the budget amongst available options is given in Tables 5–7 below: When the data in Table 5 is analyzed, it can be seen that at low budgets the most feasible methods to improve energy efficiency are purchasing CFL bulbs and having double-glazed windows installed. Once all the bulbs in the house are replaced and all the windows are renewed, the next logical step appeared to be installing solar panels. Amongst the six different types of solar panels, “type v” emerged as the most preferable one as its performance value (capacity/price – W/D) is the highest. It was interesting to see that renewing the appliances did not appear to be a profitable choice. This result mainly arose from the fact that solar panels offer a significant amount of energy saving, despite their high cost when installed in multiple units. Table 6 reveals similar results to those tabulated in Table 5. Again, renewing the appliances did not seem to be an economical option, and installing most of the excess budget that remained after double-glazing and lighting improvements on “type v” solar panels returned the highest energy savings. It was only at very high budgets (around D28,000) that renewing the appliances started to emerge as reasonable options. As it can be seen in Table 7, the maximum amount of energy saving (19,496.9 W) that can be obtained when the pre-defined physical constraints are concerned was reached in a budget range of D28,000–D32,000. The combination that yields to the maximum energy saving is as follows: • • • •

32 m2 of double-glazed window installation purchasing 10 CFL light bulbs installing 1 “type ii”, 1 “type v” and 47 “type vi” solar panels renewing the refrigerator, washing machine and the dishwasher

This combination cost a total amount of D28,804.8 (≈72,012 TRY), which is the maximum amount of money that can be spent to improve the energy efficiency our hypothetical house. Fig. 1 below shows the energy savings as a function of budget as well as the budget utilization (actual money spent divided by the given budget).

As expected, energy savings increase with respect to budget up to a maximum point. Budget utilization is approximately 100% with a clear exception of D1200 budget, where only 93% of that much budget (≈D1120) would yield the maximum possible energy saving. Since this particular study aims at developing a consumerfocused approach to maximize energy savings as a function of budget, the payback period of the investment and the profitability rather than the energy savings would be more accurate indicators of feasibility. Therefore the payback period for each budget value was calculated by converting the power values to kWh via assuming that energy gain processes involved in this study are continuous throughout the year. Average cost of electricity in Turkey (neglecting the slight variation between day-time and night-time rates) was obtained as D0.12 (≈0.30 TRY) per kilowatt-hour from the work of Celik [44]. Time value of money was neglected. The calculation of the payback period is given in Eq. (5) below. PP =

1000 × B 365 × 24 × ES × 0.12

(5)

where PP is the payback period (in years); 1000 is the conversion factor from kW to W; B is the budget (D); 365 and 24 denote the numbers of days in a year and hours in a day, respectively; ES is the energy savings (W); and 0.12 is the cost of electricity in Turkey (D/kWh). The results of payback period calculations can be seen in Fig. 2. Fig. 2 shows that even the highest investment would reach its break-even point before one and a half years. Such a quick payback proves that investing on energy-efficient buildings would be a sound investment. As part of a developing a customer-focused approach, the final step was to calculate profitability. Profitability was calculated by assuming the same level of financial savings as a result of energy saving measures each year. The maintenance and operation costs of the measures were neglected. The calculation details of profitability can be found in Eq. (6) below: PR =

n × (ES × 365 × 24 × 0.12) 1000 − B

(6)

where PR is the profitability (in D); n is the number of years; ES is the energy savings (W); 365 and 24 denote the numbers of days in a year and hours in a day, respectively; 0.12 is the cost of electricity

F.G. Üc¸tu˘g, E. Yükseltan / Energy and Buildings 49 (2012) 200–208

207

Table 8 Profitability results over 5 years as a function of budget. Budget (D) 400 800 1200 1600 2000 2400 2800 3200 3600 4000 6000 8000 10,000 12,000 14,000 16,000 20,000 24,000 28,000 28,804.8 a

1st year profit (D)

2nd year profit (D)

5082.32 9495.14a 9221.39 9010.50 8757.77 8531.11 8305.30 8062.24 7851.46 7619.65 6444.84 5322.59 4132.02 2962.47 1803.43 665.41 −1673.69 −3986.52 −7522.94 −8309.66

10,564.65 19,790.28a 19,642.77 19,620.99 19,515.54 19,462.23 19,410.59 19,324.48 19,302.91 19,239.30 18,889.68 18,645.19 18,264.03 17,924.93 17,606.85 17,330.82 16,652.61 16,026.96 12,954.12 12,185.48

3rd year profit (D) 16,046.97 30,085.41 30,064.16 30,231.49 30,273.31 30,393.34 30,515.89 30,586.72 30,754.37 30,858.95 31,334.52 31,967.78 32,396.05 32,887.40 33,410.28 33,996.23 34,978.92 36,040.44a 33,431.18 32,680.62

4th year profit (D) 21,529.29 40,380.55 40,485.55 40,841.99 41,031.08 41,324.45 41,621.19 41,848.97 42,205.83 42,478.60 43,779.37 45,290.37 46,528.07 47,849.86 49,213.70 50,661.64 53,305.22 56,053.92a 53,908.24 53,175.77

5th year profit (D) 27,011.62 50,675.69 50,906.93 51,452.49 51,788.85 52,255.57 52,726.49 53,111.21 53,657.29 54,098.25 56,224.21 58,612.97 60,660.09 62,812.33 65,017.13 67,327.05 71,631.53 76,067.41a 74,385.30 73,670.91

The maximum profit for that particular number of years.

bulbs, installing double-glazed windows and replacing C-Energy Class appliances (refrigerator, washing machine and dishwasher) with A-Energy Class versions. The physical constraints of the house in regards to the above-mentioned methods were as follows: • a total window area 32 m2 • total roof area allocated for solar panel installation: 70 m2 • total number of light bulbs to be replaced: 10

Fig. 2. Payback periods of energy saving investments as a function of budget.

in Turkey (D/kWh); 1000 is the conversion factor from kW to W; and B is the budget (D). The profitability analysis results are given in Table 8 below. The values in Table 8 indicate that instead of a steady trend, there is a maximum profit value for every budget. For short term, investing D800 seems to be the optimum decision, returning a profit of D9495.14 at the end of the first year and D19,790.28 at the end of the second year. For longer terms, D24,000 budget emerges as the optimum decision, returning profits of D36,040.44, D56,053.92 and D76,067.41 at the end of the third, fourth and fifth years, respectively. It must not be overlooked that Fig. 2 and Table 8 were prepared by assuming all the financial outputs regarding the energy savings were calculated in electricity units (D per kWh of electricity), however the energy savings from double-glazing would compensate for central heating, for which natural gas or coal rather than electricity is used. This assumption can be expected to introduce a slight error as far as payback periods and profitability values are concerned. 5. Conclusions In this study, linear programming method was used to maximize energy savings subject to budget for a hypothetical household in Turkey. The subject house was selected to be a two-floor, detached building. The methods involved to decrease the building’s energy consumption were installing photovoltaic solar panels on the roof, replacing incandescent light bulbs with compact fluorescent light

The energy savings were calculated in power units (Watts). Energy savings induced by each individual method were either obtained from manufacturer or distributor companies’ websites, or calculated where applicable. The purchase and installation costs of each of the energy saving methods were obtained by taking the averages of various values gathered from the manufacturer or distributor companies’ websites. Lingo 12.0 software was used to for linear optimization. The energy savings were calculated as a function of total allowable budget, and budgets ranging between D400 and D40,000 were used as inputs for the model. The results indicated that installing photovoltaic solar panels is the optimum choice throughout the entire budget range, as a result of the high energy saving opportunity. Renewing household appliances did not emerge as very profitable options, due to the low energy savings when compared to other techniques. Doubleglazed window installation and purchasing compact fluorescent light bulbs was the optimum combination because of the relatively low cost. For the given constraints the maximum amount of energy savings was found to be 19,496.9 W, at a budget of D28,804.8 As the authors, we believe that the most significant contribution of this particular work to building energy research is the methodology developed rather than the results themselves. The model we presented can be modified as desired for different households, climate conditions, or countries so that the final results would be completely different. The reason we decided to implement the model by using data obtained from local sources was to ensure consistency, yet we believe the model can be applied globally as long as the required data can be provided.

Acknowledgments The authors would like to thank Assoc. Prof. Dr. Yıldız Arıkan and Mr. Sami Eskenazi of Bahcesehir University, Energy Systems

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