Economic Viability Assessment of Active Building Envelope Systems

Economic Viability Assessment of Active Building Envelope Systems Flor Rivas Achille Messac Steven Van Dessel Corresponding Author Achille Messac, Ph.D. Distinguished Professor and Department Chair Mechanical and Aerospace Engineering Syracuse University, 263 Link Hall Syracuse, New York 13244, USA Email: messac@syr.edu Tel: (315) 443-2341 Fax: (315) 443-3099 https://messac.expressions.syr.edu/ Bibliographical Information Rivas, F., Khire, R. A., Messac, A., and Van Dessel, S., Economic Viability Assessment of Active Building Envelope Systems, 1st AIAA Multidisciplinary Design Optimization Specialist Conference, Paper No. AIAA-2005-2064, Austin, Texas, April 18-21, 2005.

Economic Viability Assessment of Active Building Envelope Systems Flor Rivas, Ritesh A. Khire, Achille Messac, and Steven Van Dessel, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A. Active Building Envelope (ABE) systems represent a new thermal control technology that actively uses solar energy to compensate for passive heat losses or gains in buildings or other enclosures. As a result, these systems are expected to eliminate the need to supply electricity to operate conventional air-conditioning systems and/or non-renewable energy sources to thermally condition buildings or other enclosures. This paper presents new findings pertinent to the development of ABE systems. Specifically, in this paper, we investigate the economic viability of ABE systems. A preliminary cost model of the ABE system is developed that combines individual cost models of its components. Different configurations of ABE systems, each comprising different heat absorbing component, are examined. The configuration that requires the least power unfortunately also results in the highest cost. A multi-objective optimization tool is used to resolve the trade-off between the power and the cost of ABE systems. Based on these optimization results, direction for future work is suggested. This paper represents an important step forward in obtaining a cost-effective ABE system that will provide an attractive alternative to current approaches. I. Introduction The built environment accounts for a significant fraction of the global energy consumption. A large fraction of this energy consumption is used to maintain a comfortable thermal indoor environment. This energy consumption comes in the form of use of electrical energy to operate conventional air-conditioning systems or that of non-renewable fossil fuels (such as coal, oil, and gas) for heating. Active building Envelop (ABE) systems represent a new technology that proposes to actively use solar energy to compensate for passive heat losses or gains in buildings or other enclosures. In ABE systems, solar radiation energy is converted into electrical energy by means of a photovoltaic unit (PV unit). Subsequently, this electrical energy is used to power a thermoelectric heat pump unit (TE unit), which is a collection of thermoelectric Masters Student, Department of Mechanical Engineering. PhD Candidate, Department of Mechanical Engineering, and AIAA student member. Professor, Department of Mechanical Engineering, and AIAA Fellow. Assistant Professor, School of Architecture. 1 of 17

coolers (heaters in winter). Among the key differences between ABE systems and conventional thermal control technologies are that the formers: (i) are intended to operate using solar energy, 1 (ii) are made of solid state devices and operate silently with no moving parts, (iii) use little or no fossil energy sources, and (iv) should result in important long-term environmental benefits. In this paper, we assess the economic viability of ABE systems using preliminary cost and engineering models of its components. A. Active Building Envelopes A brief description of the proposed ABE system is provided here (see Fig. 1). For more details, see. 1 As shown in Fig. 1, the ABE system is comprised of two basic components, a photovoltaic unit (PV unit) and a thermoelectric heat pump unit (TE unit). The PV unit converts solar radiation energy into electrical energy. The TE unit converts electrical energy into thermal energy, or the reverse. Both the PV and the TE units are integrated within the overall ABE enclosure. The TE unit can operate in a heating or a cooling mode, depending on the direction of the current. This feature allows for Thermoelectric Cooler Internal Heat Sink Thermal Mass Thermal Insulation External Heat Sink Air Flow Heat Dissipation Zone Photovoltaic System Figure 1. Active Building Envelope (ABE) system the ABE system to be used for heating as well as cooling applications. The PV unit forms an envelope surrounding the external wall such that a gap is maintained between the wall and the PV unit. This gap acts as an external heat dissipation zone for the TE unit (see Fig. 1). The external walls of the proposed ABE system consist of two layers. The external layer (facing the PV unit) is made of a good thermal insulating material, and the internal layer is made of a material with high heat storage capacity. In Fig. 1, the words Thermal Insulation and Thermal Mass pertain to the external and the internal layers of the ABE wall, respectively. TE coolers are dispersed inside the openings provided in the insulating layer. Each TE cooler consists of two heat sinks. The internal heat sink either absorbs or dissipates heat to the thermal mass layer. The external heat sink either absorbs heat from, or dissipates heat to, the surrounding air; through natural or forced convection. In the present study, we have neglected the internal heat sink in keeping with the scope of this preliminary study. B. Economically Viable ABE systems System design is a multifaceted process that involves taking into account important system features, such as the engineering feasibility and the economic viability of that system. Engineering feasibility is essential to ensure proper functioning of any system. In the current paper, we use an approximate analytical model of a TE cooler that takes into account the effect of a heat sink, to assess the engineering feasibility of ABE systems. The use of this computationally inexpensive approximate model is appropriate in keeping with the scope of this preliminary study. 2 of 17

Economic viability assessment of a system plays a key role in the design process. The cost of a specific system may govern the decision of an engineer, between alternate feasible designs. To assess the economic viability of ABE systems, we develop individual cost models of its components. These individual cost models are then combined to develop an overall cost model used to assess the economic viability of ABE systems. The input power for the TE unit and the cost of the ABE system are the two design objectives that we want to optimize simultaneously. Our preliminary investigation suggests that a tradeoff exists between these two design objectives. We use the multi-objective optimization tool to resolve the tradeoff between the two objectives of ABE systems (power and cost). This paper is organized as follows. Section II presents the overview of the study performed in this paper. Section III develops the approximate analytical models of the TE cooler and heat sink used to assess the engineering feasibility of ABE systems. Section IV develops the cost models for ABE systems. Section V presents the multi-objective optimization problem formulation used to design an appropriate ABE system configuration. Section VI presents the results of numerical optimization. In section VII we compare the ABE systems to conventional air-conditioning systems. Section VIII provides concluding remarks. II. Economic Viability Assessment of ABE systems In this section, we provide an overview of the economic viability assessment study of ABE systems, presented in this paper. Figure 2 depicts a flow chart that describes various models and the decision making tool used in this study. This assessment work involves three main aspects: the development of engineering models, the development of cost models, and the application of the multi-objective optimization tool. Design variables and parameters Engineering model Cost model TE unit TE cooler House Insulation TE cooler Solar cell Heat sink Heat sink Insulation Multi-objective optimization Optimal design Engineering Model Figure 2. Flow chart: overview As shown in Fig. 2, the engineering models of the TE unit and the house (for which the ABE system is designed) are combined to model the operation of ABE systems. The model of the TE unit includes the TE cooler model and the heat sink model. These two models are combined so as to allow the effect of the thermal resistance of the heat sink on the performance of the TE cooler to be considered. 1 The TE unit model is evaluated for the amount of heat load estimated from a preliminary house model considered in this paper (see Sec. III-D). 3 of 17

Cost Model In this paper, we develop individual cost models for the four main components of ABE systems that dictate it s fixed cost: TE cooler, heat sink, wall insulation, and solar cell. We note that in the current paper, we have not explicitly modeled the PV unit. Instead, we use the power required to operate the TE unit (which is supplied by the PV unit) to estimate the cost of PV unit (solar cells). We use the cost data available in product catalogs of these components to develop these models. These individual models are combined into an overall cost model that estimates the fixed cost of our ABE system. Multi-objective Optimization We use the cost of the ABE system and the input power required to operate the TE unit as the two design objectives that we minimize. Our preliminary investigation suggests that a trade-off exists between the two design objectives. That is, the cost of the ABE system increases as the input power decreases, and viceversa. We formulate a multi-objective optimization problem to simultaneously minimize these two conflicting objectives. The input power required to operate the TE unit is obtained from the engineering model, and the cost is obtained from the cost model. Different configurations of the ABE system are evaluated using the multi-objective optimization technique, details of which are provided in Sec. IV-A. III. Engineering Models This section develops computationally inexpensive models of the TE unit and the house. The model of the TE unit is composed of that of it s individual components. The individual component models are coupled, yielding a single integrated model that takes into account the effect of the heat sink on the TE cooler. This model is used to assess the engineering feasibility of the ABE system for the heat load estimated by the model of the house. A. Thermoelectric cooler Hot Junction Cold Junction Heat Absorbed (Q pc, T c ) Material 1 Material 2 L I Heat Released (Q ph, T h ) As shown in Fig. 3, when a current flows through the junction of V two dissimilar conductors (also called a thermocouple), heat is either liberated or absorbed (depending on the direction of the current) at that junction. This phenomenon is known as the Peltier effect; 2 4 Figure 3. Schematic of a thermocouple and it causes decrease in the temperature at the heat-absorbing junction, and in simultaneously increasing the temperature at the heat-releasing junction. When a current flows through a TE cooler, which contains n thermocouples, the amount of heat absorbed at the cold junction (Q pc ) is given by 5 7 Q pc = n[sit c K(T h T c ) 1 2 I2 R] (1) 4 of 17

where K = k 1A 1 L 1 + k 2A 2 L 2 (2) R = ρ 1L 1 A 1 + ρ 2L 2 A 2 (3) In Eqs. 1, 2, and 3, S is the relative Seebeck coefficient of the thermocouple; I is the input current flowing through the circuit; T c and T h are the temperatures of the cold and the hot junctions, respectively; K is the thermal conductance of the thermocouple; R is the electrical resistance of the thermocouple; k is the thermal conductivity; ρ is the electrical resistivity; and A and L represent the cross-sectional areas, and the lengths of the thermoelectric element, respectively. The subscripts 1 and 2 refer to the thermoelectric materials 1 and 2, respectively. B. Heat Sink Heat sinks lower or maintain the temperature of a device by dissipating heat into the surrounding medium. The primary requirement of an effective heat sink is to provide a low thermal resistance path for heat dissipation. In ABE systems, heat sinks are required to dissipate the heat generated at the hot side of the TE coolers, see Fig. 4. Failure to dissipate the required heat from the TE cooler may result in an increase in it s hot side temperature. The heat dissipated by a heat sink is given by 8 Q hs = T h T o R hs (4) TE cooler Figure 4. Ambient air, T o Heat sink Hot side, T h Schematic of a heat sink where Q hs is the heat dissipated by the heat sink, T h is the temperature of the heat source (in the ABE systems, the hot side of the TE cooler), T o is the ambient air temperature, and R hs is the thermal resistance of the heat sink. C. Estimating Effect of Heat Sink on TE Cooler As stated in the previous subsection, a heat sink is required to dissipate the heat generated at the hot side of the TE cooler. The heat generated at the hot side of the TE cooler (Q ph ) is given by 9 Q ph = Q pc + V I (5) Since the heat sink is required to dissipate this heat, we have Q hs = Q ph. Using Eqs. 4 and 5, we obtain the expression for the temperature at the hot side of the TE cooler as 9 T h = T o + (Q pc + V I)R hs (6) Substituting Eq. 6 into Eq. 1, to eliminate T h, we can determine the effect of a heat sink on a TE cooler; namely, the dependence of Q pc on R hs. 5 of 17

D. Estimating Heat Load for the House Figure 5 shows the schematic of the house used in this paper. We consider a 10 m wide 10 m long 3 m high house, with no windows or doors. We assume that conduction is the only mode of heat transfer for this house. Thus, the heat load for this house equals the 3 m 3 10 m 1 5 House 2 Conduction heat 4 amount of heat conducted through its four side walls and the roof. As shown in Fig. 5, surfaces 1 to 5 allows Ground 10 m conduction heat transfer. The amount of heat conducted through these surfaces is given by Fourier s law as Figure 5. Schematic of the house Q load = A(T o T i ) k t (7) where Q load is the heat load, A is the combined area of surfaces 1 to 5, T i is the inside temperature, k is the thermal conductivity of the wall insulation, and t is the thickness of the wall (we assume that all five surfaces have equal thickness). In the next section, we develop individual cost models for the components of the ABE system, and combine them into an overall cost model. IV. Cost Models The economic viability of any system is determined in part by its Life Cycle Cost (LCC), which includes 10, 11 the fixed cost (or the initial capital cost) and the recurring cost. The LCC is given as LCC = C F + C R (8) where C F is the fixed cost, and C R is the recurring cost. In conventional air-conditioning systems, the annual maintenance cost and the operating cost (electricity cost) are part of the recurring cost. In these systems, the wear and tear of the moving parts form a major fraction of the maintenance cost. Interestingly, ABE systems do not require external electricity nor do they have any moving parts. Hence, we expect that ABE systems will have low maintenance and operating costs. Based on this assumption, we consider only the fixed cost of the ABE system, in this paper. The fixed cost primarily consists of the fabrication cost and of the installation cost. In this paper, the fabrication cost includes the cost of: TE coolers, heat sinks, solar cells, and the volume of the wall insulation material. The installation cost primarily depends on the labor cost and the transportation cost. In keeping within the preliminary nature of this paper, we do not consider the installation cost. A. Development of Individual Cost Models First, we develop individual cost models for the ABE system components. We use the regression technique to develop these individual cost models. The cost data for these components is collected from product catalogs supplied by reputed manufacturers of these components. 12 15 6 of 17

Cost of a TE cooler, C TE ($) 60 50 40 30 20 C TE = 0.0008n 2-0.038n + 12.57 Regression model Manufacturers data 10 0 50 100 150 200 250 300 Number of thermocouples per TE cooler Cost of heat sink C hs ($) 22 18 14 10 6 C hs = -25.318R hs +38.643 Regression model Manufacturers data 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Heat sink resistance ( o C/W) (a) CP1.0-n-08L type TE cooler (b) Extruded fin heat sink Figure 6. Cost models developed using regression technique 1. Cost models for TE coolers In this paper, we select the CP1.0-n-zzL and CP1.4-n-zzL classes of TE coolers manufactured by Melcor Corporation, USA. 15 Here, n represents the number of thermocouples per TE cooler, and zz is a two digit number assigned by the Melcor Corporation to represent the value of λ (the ratio of the cross-sectional area, A, to the length, L, of the thermoelectric element). From each of these two classes, we select three types of TE coolers. A total of 2 3 = 6 types of TE coolers are evaluated in this study. These six types of TE coolers and their corresponding λ values (in m) are given in the first two columns of Table 1. The cost of a TE cooler depends on the number of thermocouples (n) included in one TE cooler. 15 Based on the cost data, the cost models of the TE coolers take the general form C T E = a n 2 + b n + c (9) where C T E is the cost of one TE cooler in US dollars ($). The values of the coefficients a, b, and c for the six types of TE coolers are given in Table 1. To obtain the total cost incurred by all TE coolers used in the ABE system, we multiply Eq. 9 by the number of TE coolers (N). Fig. 6(a) shows the cost data and the cost model for CP-1.0-08L type of TE coolers. Table 1. TE cooler cost model coefficients λ a b c CP-1.0-08L 5.0 10 4 0.0008-0.0384 12.572 CP-1.0-06L 6.1 10 4 0.0007-0.0358 12.37 CP-1.0-05L 7.9 10 4 0.0007-0.0464 11.956 CP-1.4-10 7.7 10 4 0.0004-0.0166 12.192 CP-1.4-06 11.8 10 4 0.0007-0.0502 12.24 CP-1.4-045 17.1 10 4-0.0002 0.0767 10.341 7 of 17

2. Cost model for Heat Sinks We use the extruded fin type heat sink, supplied by Melcor Corporation, USA. 15 The cost of the heat sink depends on it s thermal resistance (R hs ). The cost model for the extruded fin type heat sink is given by C hs = 21.947(R hs ) + 35.029 (10) where C hs is the cost of one heat sink in US dollars ($). Figure 6(b) shows the cost data and the regression model for the extruded fin heat sink. To obtain the total cost for heat sinks, we multiply Eq. 10 by the number of heat sinks (N). Cost of solar panel, C sol ($) 800 700 600 500 400 300 200 C sol = 3.3911(P ) + 70.279 in 100 Regression model Manufacturers data 0 0 50 100 150 200 Power developed by solar panel, P (W) (a) Solar cells in Cost of insulation m of wall area C ($) 2 ins 9 8 7 6 5 4 3 Regression model Manufacturers data C ins = 8.447(k/t) ins -0.2625 2 0 10 20 30 40 50 60 o 4 Thermal Conductivity/thickness, (k/t) (W /C m ) (b) Fiber glass insulation ins Figure 7. Cost models developed using regression analysis 3. Cost model for Solar Cells Figure 7(a) shows the cost model for solar cells. In ABE systems, solar cells generate the power required to operate the TE unit. The cost of solar cells is assumed proportional to the electrical power that they are 13, 14 required to generate. The data for the solar cell cost model is gathered from different manufacturers. The cost model for solar cells is given by C sol = 3.391P in + 70.279 (11) where C sol is the cost of solar cells in US dollars ($), and P in is the power generated by solar cells in W. This is the input power required to operate the TE unit (see Sec. V-C). 4. Cost model for Insulation Figure 7(b) shows the cost model for the fiberglass insulation. The cost of the insulating material depends on the ratio of it s thermal conductivity to the thickness (k/t) ins. The cost of insulating materials increases as this ratio decreased. The cost model for the fiberglass insulation is given by C ins = 8.477(k/t) 0.2625 ins (12) 8 of 17

where C ins is the cost of insulation per m 2 of wall area in US dollars ($). To obtain the total cost of the insulating material used in the ABE system, C ins is multiplied by the area of the insulated walls (A). B. Fixed Cost Model of ABE Systems The fixed cost of the ABE system (C F ) is equal to the sum of the costs of the ABE components, given by C F = N C T E + N C HS + C sol + A C ins (13) This fixed cost model is used to assess the economic viability of ABE systems. V. Multi-objective Optimization Strategy In this section we discuss the multi-objective optimization strategy used to assess the economic viability of ABE systems. Using multi-objective optimization, we determine: the optimal ABE system design that compensates the estimated cooling load, and the fixed cost associated with this design. In this paper, we consider two design objectives: (1) the electrical power required to operate the TE unit, and (2) the fixed cost of the ABE system. Both of these objectives are minimized simultaneously using the Normalized Normal Constraint method. 16 The following subsections describe the design variables, the design constraints, and the design objectives for the optimization problem. A. Design Variables The present optimization problem involves five design variables: the number of TE coolers (N), the number of thermocouples per TE cooler (n), the input current (I), the thermal resistance of the heat sink (R hs ), and the ratio of the thermal conductivity to the thickness of the insulating material (k/t) ins. In this formulation, the number of TE coolers is not allowed to become less than one or more than 10000. The input current is not allowed to exceed the maximum allowable current (I max ), which is specified in the Melcor product catalog. 15 The upper and the lower bounds on the number of thermocouples per TE cooler, the thermal resistance of the heat sink, and the thermal conductivity of the insulating material are the same as those on the sampling data for these components (Figs. 6(a), 6(b), and 7(b), respectively). B. Design Constraints The total heat absorbed by all the TE coolers is used as an equality constraint in the optimization problem. Equation 1 determines the amount of heat absorbed by a single TE cooler (Q pc ). The total heat absorbed by all the TE coolers is calculated by multiplying the amount of heat absorbed by a single TE cooler by the number of TE coolers (N). During the optimization process, the total heat absorbed by all the TE coolers is constrained to equal the estimated cooling load (Q load ). The temperature of the hot side of the TE cooler (T h ) is used as the first inequality constraint in the optimization problem. Equation 6 evaluates the temperature of the hot side of the TE cooler. This 9 of 17

temperature is not allowed to exceed the maximum allowable temperature for the TE cooler (T max ), which is specified in the Melcor product catalog. 15 The input voltage (V ) applied to a single TE cooler is used as the second inequality constraint in the optimization problem. The input voltage for a single TE cooler is given by V = S(T h T c ) + IR (14) This input voltage is not allowed to exceed the maximum voltage (V max ), which is specified in the Melcor product catalog. 15 C. Design Objectives Input power: The input power (P in ) required to operate the TE unit is used as the first design objective, and is given by P in = N V I (15) In ABE systems, the TE unit is powered by the PV unit (solar cells). The PV unit only produces electrical energy during the part of the day when solar radiation is available. 17 As a result, there may be a need to store power for use at night and at peak power demand periods. Hence, minimizing the input power is central to the feasibility of this system. Fixed cost: The second design objective is the fixed cost of the ABE system (C F ), which is given by Eq. 13. An ABE system with an excessive cost may not present a viable economical alternative to the conventional air-conditioning systems. Hence, we minimize the fixed cost in our search for a cost-effective ABE system configuration. D. Optimization Problem Statement The optimization problem statement for designing the optimal configuration of the TE unit is as follows. min (P in, C F ) (16) N, n, I, R hs, (k/t) ins subject to NQ pc Q load 1 = 0 (17) V V max 1 0 (18) T h T max 1 0 (19) 1 N 10, 000 (20) 0.01 I I max (21) R hsmin R hs R hsmax (22) 10 of 17

n min n n max (23) ((k/t) ins ) min (k/t) ins ((k/t) ins ) max (24) In the next section, we discuss the results of numerical optimization. VI. Results and Discussion We evaluate six different configurations of the ABE system in this paper. Each configuration includes a different type of TE cooler, as shown in Table 1. First, we discuss the trade-off characteristics between the two design objectives: the input power and the fixed cost. Input Power, P in (kw) 8 7 6 5 L 1 L 2 L 3 P 3 P 2 P 1 CP-1.0-08L CP-1.0-06L CP-1.0-05L Input Power, P in (kw) 8 7 6 5 L 4 L 5 L 6 P 6 P 5 P 4 CP-1.4-10L CP-1.4-06L CP-1.4-045L 4 H 3 H 2 H 1 4 H 6 H 5 H 4 0.5 1 1.5 2 2.5 3 Fixed cost in, C x 10 5 F ($) (a) Pareto Frontier of the CP-1.0 model 0.5 1 1.5 2 2.5 3 Fixed cost, C x 10 5 F ($) (b) Pareto Frontier of the CP-1.4 model Figure 8. Pareto frontiers for different ABE system configurations A. Trade-off Between Fixed Cost and Input Power Figures 8(a) and 8(b) show the trade-off characteristics (also called the Pareto frontiers) between the input power and the fixed cost, for all of the ABE system configurations evaluated in this study. Pareto frontiers shown in Figs. 8(a) and 8(b) are for the configurations of the ABE system that use CP-1.0 and CP-1.4 class of TE coolers, respectively. From these Pareto frontiers, we observe that the fixed cost increases as the input power decreases. The points marked L, on Figs. 8(a) and 8(b), represent the case where the fixed cost is minimized alone, and those marked H represent the case where the input power is minimized alone. For the CP-1.0 class (Fig. 8(a)), we observe that when the fixed cost is minimized alone, the ABE configuration with CP-1.0-05L type of TE coolers results in the lowest cost. However, when the input power is minimized alone, all three configurations result in similar fixed costs. For the CP-1.4 class (Fig. 8(b)), the difference between the design objectives for the configurations with CP1.4-06L and CP1.4-045L types of TE coolers is almost insignificant. We compare the performance of the six ABE system configurations at a point when the input power equals 5 kw. We note that this value of input power is selected purely for comparison purposes only. Details of the 11 of 17

Table 2. Comparison of different configurations of the ABE system at P in = 5 kw Notation TE cooler Fixed Insulation Heat Sink Thermocouples/ No. of TE I/p Current Type Cost (C F ) (k/t) ins R hs TE cooler (n) coolers (N) I U.S.$ W/C m 2 C/W Amp P 1 CP-1.0-08L 85,430 1.6084 1.3 94.4 2963 0.7805 P 2 CP-1.0-06L 76,970 1.6084 1.3 89.1 2745 0.7674 P 3 CP-1.0-05L 68,570 1.6084 1.3 77.9 2608 0.7346 P 4 CP-1.4-10L 74,090 1.6084 1.3 77.9 2799 0.6960 P 5 CP-1.4-06L 65,660 1.6084 1.3 55.8 2583 0.6748 P 6 CP-1.4-045L 70,120 1.6084 0.8 63.9 1614 0.6880 six design configurations at 5 kw are presented in Table 2. We observe that the ABE system configuration that uses the CP-1.4-06L type of TE coolers results in the lowest cost (Table 2-column 4) and is considered preferred among the six configurations evaluated in this study. However, it is important to note that the fixed cost of all of the design configurations is between $65,000 and $85,000. This appears to be a large investment for an air conditioning system. We note that for developing the cost models, we have used the cost data available in the product catalogs. The prices quoted in these catalogs are often for small quantities. The cost of the ABE system components is likely to decrease, when they are purchased in large quantities. This will result in lowering the fixed cost of ABE systems. However, the results reported in Table 2 lead to some interesting observations that may allow us to further reduce the cost of ABE systems. These observations are discussed in the following two subsections. B. Thermal conductivity of the insulation per unit thickness, (k/t) ins From the fourth column of Table 2, we observe that the optimal (k/t) ins value of the insulating material converges to 1.6 W/C m 2, for all of the ABE system configurations evaluated in this study. From Fig. 7(b), 1.6 W/C m 2 is the lower limit of the (k/t) ins values, for which the cost model is developed. We evaluate this behavior in detail. The multi-objective optimization problem attempts to find a balance between two competing objectives: the input power and the fixed cost of ABE systems. The cost of the insulation material increases as its thermal conductivity per unit thickness decreases, (Fig. 7(b)). For (k/t) ins = 1.6 W/C m 2, the cost of insulation is the highest. Interestingly, the optimization problem always converges to the lower limit of (k/t) ins. Although insulation materials with smaller (k/t) ins are more expensive, they reduce the heat load (Eq. 7). This behavior causes a decrease in the number of TE coolers (or the fixed cost) and in the input power. If we further reduce the (k/t) ins value of the insulating material, we can obtain a smaller heat load than that obtained by (k/t) ins = 1.6 W/C m 2. However, there would reach a point where the increase in the 12 of 17

insulation cost will overshadow the gains achieved through the smaller (k/t) ins value. Since (k/t) ins always converges to the lower limit, such a point has not been reached for the range of insulation materials evaluated in this study. Thus, we recommend the use of an insulating material with smaller (k/t) ins than the one used in this paper. C. Thermal resistance of the heat sink, (R hs ) From Fig. 6(b), a heat sink with high thermal resistance results in low cost. However, high thermal resistance also results in increased hot side temperature of the TE cooler (see Eq. 6). This increase in the hot side temperature increases the input power. However, from Table 2, the thermal resistance of the heat sink converges to 1.3 C/W, which is the upper limit for its cost model. Hence, the reduction in the cost related to using a heat sink with the highest thermal resistance is more significant than the corresponding increase in the input power. If we increase the heat dissipation capacity of the heat sinks, without significantly increasing its cost, an economically viable ABE system configuration can be designed. In this paper, we have considered heat sinks that dissipate heat through free convection. However, an external fan will be able to increase the heat dissipation capacity of the heat sinks. Since the external fan will add to the cost and the electrical power consumption, a detailed cost-based analysis will be required to select an appropriate fan. D. Number of TE coolers, (N) The number of TE coolers (which is also equal to that of the heat sinks) is one of the important factors in the design of ABE systems. To obtain a system with the lowest cost, the number of TE coolers should be minimized. However, an ABE system with the minimum number of TE coolers requires the highest input power. A viable approach to minimize both objectives, the input power and the fixed cost, is to make the heat transfer process efficient. In ABE systems, we can make the heat transfer process efficient by implementing the recommendations given in the previous two subsections. That is, we can reduce the heat load by using insulation materials with lower thermal conductivities, and improve the heat dissipation capacity of the heat sinks by incorporating a fan. From Table 2, the preferred ABE system configuration P 5 requires 2583 TE coolers of type CP-1.4-06. E. Number of Thermocouples per TE cooler, (n) The number of thermocouples per TE cooler has a direct impact on the number TE coolers. The number of TE coolers (N) decreases as the number of thermocouples per TE cooler (n) increases. However, as discussed in the previous subsection, the ABE system configuration with the smallest number of TE coolers is not necessarily the optimal one, for the bi-objective optimization problem considered in this paper. We observe this behavior from the results shown in Table 2. For the six ABE configurations evaluated in this study, the number of thermocouples per TE cooler never converges to the upper limit of 254 thermocouples. (The lower 13 of 17

and upper limits for n are 7 and 254, respectively, see Fig. 6(a)). For the preferred ABE system configuration, P 5, the optimal design requires CP-1.4-06 type of TE coolers, each containing 56 thermocouples. F. Input current (I) For the six ABE system configurations evaluated in this paper, the input current ranges from 0.68 Amp to 0.78 Amp. It may not be feasible for a single solar cell to produce this current at all times. In such cases, multiple solar cells connected in parallel can be used to generate the required input current. We note that, in the present paper, we have not used the input current as a design objective in keeping with the scope of this study. However, the input current may take significance, especially in the regions where ample sunlight is not available, as the current generated by the PV unit is proportional to the intensity of the incident solar radiation. 17 This ends the discussion of the results obtained from the numerical optimization. In the next section, we compare ABE and conventional air conditioning systems. VII. ABE and Conventional Air-conditioning system: Comparison Based on the results obtained from the numerical optimization, we mentioned in Sec. VI-A that ABE systems require a large initial investment. In this section, we compare the fixed cost of the ABE system with that of conventional air-conditioning systems. To determine the fixed cost of a conventional air conditioning system, we first determine its cooling load, which is discussed next. A. Cooling Load for Conventional System We estimate the cooling load for the same house described in Sec. III-D and shown in Fig. 5. Again, we assume that heat gain occurs through conduction only. To determine the cooling load, we use the American Society of Heating Refrigeration and Air-conditioning Engineers (ASHRAE) method. 18 The heat gain through the structure is calculated as Q = UA(CLT D) (25) where Q is the heat gain through the structure, U is the rate of heat transmission, and CLT D is the Cooling Load Temperature Difference for the applicable surface. Here, the rate of heat transmission is the reciprocal of the sum of all the individual thermal resistances of the structure. 19 Using the design temperatures for Albany, NY, listed in Ref, 18 we obtain the total heat load as 3362.3 W. Next, we select a conventional air-conditioning system for this heat load. B. Estimating the Cost of Conventional Air-conditioning System The smallest air-conditioning unit (in terms of heat load) commercially available is 1.5 Ton, which handles a heat load of approximately 5274 W. Considering the total heat gain obtained in the previous subsection, this value can be considered a good approximation for the conventional air-conditioning system (as several 14 of 17

heat adding factors are neglected in the evaluation). Thus, the fixed cost of the conventional system includes the cost of the 1.5 Ton air-conditioning unit and that of the insulation. Table 3 summarizes the fixed cost for the conventional system. The total fixed cost for a conventional air-conditioning system is approximately Table 3. Fixed cost of a conventional system Unit of measure Quantity $/Unit of measure $ Walls (Insulation) Area(m 2 ) 98.56 3.01 296.66 Roof (Insulation) Area(m 2 ) 100 8.07 807 Conventional heat pump Ton 1.5 676 1014 TOTAL 2115.06 $2100. C. Comparison of ABE versus Conventional System By comparing the fixed cost of the ABE system (Table 2) to that of the conventional system (Table 3), we observe that the former results in a extremely large fixed cost compared to the latter. Thus, based on the fixed cost comparison, the conventional system appears more attractive than the ABE system. However, we note that unlike conventional systems, ABE systems are expected to result in a lower operating cost, as discussed in Section IV. Thus, an accurate comparison of these two systems cannot be performed based on the fixed cost only. A Life Cycle Cost (LCC) analysis will be required in the future to compare these two systems in more detail. Also, ABE systems promise to offer significant environmental benefits, an important feature missing from the conventional systems. Other benefits such as reduction of toxic waste represent a noticeable advantage over conventional systems. In addition, ABE systems can potentially qualify for the federal and state governments special tax credits for using renewable sources of energy. Finally, the ongoing research in the field of solid state devices is expected to lower the costs of TE coolers and solar cells. Collectively, all these factors are expected to lower the cost of ABE systems, making them a cost-effective alternative to conventional system. D. Future Work Although the list of future work is extensive for ABE systems, we provide here few major items of importance. (1) Extend the range of the insulation cost model by incorporating insulations with lower thermal conductivity values. (2) Evaluate the effect of incorporating an external fan to improve the heat dissipation capacity of the heat sinks. (3) Refine the cost models: the cost modeling and estimating process is iterative and becomes more accurate as more information becomes available. (4) Perform Life cycle cost analysis of ABE systems. (5) Consider the environmental benefits of ABE systems. 15 of 17

VIII. Concluding Remarks In this paper, we have examined the economic viability of Active Building Envelope (ABE) systems. To do so, individual cost models of the components of the ABE system were developed. These individual cost models were combined into an overall cost model that estimates the fixed cost of ABE systems. To ensure the engineering feasibility of ABE systems, approximate analytical models of the TE cooler and heat sink were used. A multi-objective optimization strategy that simultaneously minimizes the input power and the fixed cost was used to evaluate different configurations of ABE systems. The results indicate that ABE systems require a large initial investment. However, it was noted that the cost of the ABE system can be significantly lowered by making the heat transfer process efficient. Two techniques were suggested to improve the efficiency of the heat transfer process without appreciably increasing the fixed cost: to use insulation material with lower conductivity, and to incorporate an external fan to dissipate heat from heat sinks. Finally, the ABE system was compared with the conventional airconditioning system. Although ABE systems result in a higher fixed cost, unlike conventional systems, they will have significantly less recurring cost. Also, ABE systems promise to offer important environmental benefits. A number of items for the future work were suggested. This paper represents the first step in developing cost-effective ABE systems. IX. Acknowledgement Support from the National Science Foundation, award numbers CMS-0333568 and DMI-0354733, is gratefully acknowledged. References 1 Van Dessel, S., Messac, A., and Khire, R., Active Building Envelopes: A Preliminary Analysis, Asia International Renewable Energy Conference, Beijing, China, Apr 2004. 2 Pollock, D. D., Thermocouples theory and practice, ISBN 0-8493-4243-0, CRC press Inc., Boca Raton, Florida 33431, U.S.A., 1991. 3 Ioffe, A. F., Semiconductor and Thermoelements and Thermoelectric Cooling, Infosearch Limited, London, 1957. 4 Rowe, D. M., CRC Handbook of Thermoelectrics, IEEE, CRC Press, July 1995, ISBN: 0-8493-0146-7. 5 Baird, J. R., Fletcher, D. F., and Haynes, B. S., Local condensation heat transfer rates in fine passages, International Journal of Heat and Mass Transfer, Vol. 46, No. 23, November 2003, pp. 4453 4466. 6 Seifert, W., Ueltzen, M., and Muller, E., One-dimensional modeling of thermoelectric cooling, phys. stat. sol. (a), Vol. 194, No. 1, 2002, pp. 277 290. 7 Chein, R. and Huang, G., Thermoelectric cooler application in electronic cooling, Applied Thermal Engineering, Vol. 24, No. 14-15, October 2004, pp. 2207 2217. 8 Holeman, J. P., Heat Transfer, ISBN 0-07-02961809, McGraw-Hill Inc., U.S.A., 5th ed., 1981. 9 Nagy, M. J. and Buist, R., Effect of Heat Sink Design on Thermoelectric Cooling Performance, AIP Conf. Proc., Vol. 316, No. 1, Aug. - Sep. 1994, pp. 147 149. 10 Barringer, H. P. and Weber, D. P., Life Cycle Cost Tutorial, Fifth International Conference on Process Plant Reliability, 16 of 17

Houston, TX, October 1996, Organized by Gulf Publishing Company. 11 Barringer, H. P., Life Cycle Cost And Good Practices, NPRA Maintenance Conference, San Antonio, TX, 1998, pp. May 19 22. 12 Owens Corning, Owens Corning catalog, www.owenscorning.com, 2005. 13 SANYO North America Corporation, SANYO catalog, www.sanyo.com, 2005. 14 BP Solar International LLC, BP Solar catalog, www.bpsolar.com, 2005. 15 Melcor Corporations, Melcor Thermal Solutions catalog, www.melcor.com, pp. 47 49. 16 Messac, A., Ismail-Yahaya, A., and Mattson, C. A., The Normalized Normal Constraint Method for Generating the Pareto Frontier, Structural and Multidisciplinary Optimization, Vol. 25, No. 2, 2003, pp. 86 98. 17 Green, M. A., Solar cells Operating principles, technology, and system application, ISBN 0-13-822270-3, Printice-Hall, Inc, Englewood Cliff, NJ 07632, U.S.A., 1982. 18 American Society of Heating, Refrigerating and Air-Conditioning Engineers, ASHRAE handbook, Fundamentals, 1985. 19 Martin, P. and Oughton, D., Heating and Air-Conditioning of Buildings, Butterworth & Co. Publishers Ltd., 7th ed., 1989. 17 of 17