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Economic evaluation of a solar water heating system
Energy Convers. Mgmt VoL 27, No. 2, pp. 197-204, 1987 Printed in Great Britain. All rights reserved
0196-8904/87 $3.00+0.00 Copyright © 1987 Pergamon Journals Ltd
ECONOMIC EVALUATION OF A SOLAR WATER HEATING SYSTEM M. N. A. H A W L A D E R 1, K. C. NG l, T. T. C H A N D R A T I L L E K E 1, D. S H A R M A I and K E L V I N KOAY H. L. 2 1Department of Mechanical and Production Engineering, National University of Singapore, Kent Ridge, Singapore 0511 2Manager, Facilities and Engineering Projects, Cliangi International Airport Services (CIAS), Singapore 9181 (Received 26 March 1986)
Abstract--This paper describes different methods of analysis of a solar water heating system to determine its economic viability. The solar fraction, required for this analysis, has been calculated with a stimulation program using hourly meteorological data of Singapore. A measured load profile, representing the average condition, was used for this program. The economic variables have been selected from the trends shown in previous years. When different economic optimization criteria were applied to the CIAS solar system, it was seen that both the life cycle saving and the annualized life cycle cost lead to the prediction of the same optimum collector area of 1200 m2. The payback period and the internal rate of return analyses also predicted the same optimum collector area of 1000 m 2, which is smaller than that predicted by the method of life cycle costing. For the economic variables used in this analysis, the minimum payback period is about 14 years. Solar water heating Payback period
Industrial process heating Economic optimization Annualized cost Internal rate of return
NOMENCLATURE A = CoUector area b = Constant relating tank storage volume to collector area Cc = Collector cost ($/m2) Cr = Fuel costs (g/M J) C ~ = Capital recovery factor
Cr = e= F= i= i'=
Tank cost ($/m2) Fuel escalation rate Solar fraction (Qs/Qo) Discount rate Effective discount rate
i " = Effective discount rate for fuel
j -- Inflation rate n = Life cycle of system np = Minimum payback period Q,--Solar heat gain (M J) Qo = Load (M J) S = Collector area/load (m2/MJ) INTRODUCTION The conversion of solar energy for useful applications
Life-cycle savings
requires a considerable initial investment compared to a conventional system. In the majority of solar processes, a source of auxiliary energy is required so that the system includes both solar and conventional equipment to meet the desired load. Solar systems are normally characterized by a high initial investment followed by low operating costs. It is, therefore, necessary to determine whether such an investment is economically competitive when compared with conventional systems. The economic analyses are performed based on several figures of merit such as, annualized system cost, net life cycle savings, payback period, internal rate of return, and a few others. Wijeysundera and Ho [1] have shown that the above four methods can be broadly grouped into two. The annualized system cost and the net life cycle savings methods of analyses lead to identical optimum conditions, predicting the same collector area, as shown in a later section. Similarly, the payback period and internal rate of return lead to an exactly identical expression for the optimum condition. Barley and W i n n [2], Brandemuehl and Beckman [3], and Lunde [4] have used life cycle savings as the figure of merit in the optimization of solar systems. Chang and Minardi [5] used annualized system cost as the optimization criteria for a solar hot water system. In the life cycle savings and annualized system cost analyses, the future expenses and benefits are expressed in terms of dollars in hand, 197
198
HAWLADER et al.: ECONOMIC EVALUATION OF SOLAR WATER HEATER
which requires assumptions, on future discount rate, inflation rate and fuel escalation rate. Thus, the conversion of all future earnings to present worth dollars involves a certain degree of uncertainty. Moreover, most customers are interested in the payback period of the system. Michelson [6] and Boer [7] used the minimum payback period for economic optimization of solar systems which requires fewer assumptions about future costs. Gordon and Rabl [8] used the internal rate of return as the criterion for the optimization of a solar process heat plant. This paper described the results of an economic analysis of an existing solar system at the Changi International Airport Services (CIAS) which supplies hot water in the temperature range of 60-80°C for the flight kitchen. In the economic evaluation, various figures of merit have been used to determine if the existing system is operating at its optimal level. This requires knowledge of the thermal performance of the system, which is normally expressed in terms of annual solar fraction and collector area. The annual solar fraction for different collector areas has been calculated using a simulation program developed in the department [9]. The program was run with the hourly meteorological data and the measured load profile. THE SOLAR SYSTEM One of the many services, which the Changi International Airport Services provides, is the kitchen facilities for airlines. Its flight kitchen requires large quantities of hot water for cooking and washing purposes. A large fraction of this heating requirement is met by solar energy. A schematic diagram of the solar system is shown in Fig. 1. The water in the collector loop is heated via 630 m 2 of Yazaki blue panels which are mounted on the roof top. Energy incident on these collectors heats the water circulated through the collectors by the primary pumps. The collector loop is separated from the load loop via heat exchangers. The secondary circuit is an open circuit. There are four storage tanks, each of 10 m 3 vol. The water in the storage tanks is circulated through the heat exchangers by secondary pumps. When there is a demand, hot water is drawn from storage tank 1, and an equal amount of make up water is supplied from the mains and enters into tank 4 at the bottom. When the temperature of the water is below the desired value, a calorifier is used to provide auxiliary energy. Two air cooling units are also provided for cases when thermal overloading occurs in the storage tanks, and the excess energy, under these circumstances, is discharged to the atmosphere. During operation, the fluid, circulated by the primary pump through the collectors, absorbs a fraction of the solar energy incident on the panels. The water in the secondary circuit receives a large part of this energy via heat exchangers. The operation of the
system is controlled by an automatic controller. When water is delivered to the storage tanks, the controller gives priority to tank l, followed by 2, 3 and 4, when more than one tank is eligible for energy input. A tank is eligible for energy input when its temperature is <70°C. This allows tank 1 to be always at a higher temperature, unless all of them are thermally full, in order to minimize the use of auxiliary energy. The storage tanks are considered thermally full when all of them are at 70°C. When this occurs, the secondary pumps are switched off. However, the fluid in the primary circuit may still be receiving solar energy, resulting in a temperature rise. When the fluid temperature in the collectors exceeds 85°C, the secondary pumps are switched on and the water from the heat exchangers is circulated through the air cooling unit (ACU), instead of the storage tanks. At the air cooling unit, this energy is vented to the atmosphere, preventing damage to the collectors. ECONOMIC EVALUATION METHODOLOGY The economic optimization of solar energy systems involves multiple variables. In general, all the components in the system will have some effect on the thermal performance of the system and thus on costs. In practice, the problem often reduces to a simpler one of determining the size of a solar system for a known load, with storage capacity and other parameters fixed in relation to collector area. For solar systems, the performance is more sensitive to collector area than to any other variable [10]. Therefore, in this analysis, the primary index of the size of the solar system is chosen to be the area of the collectors. The following are the types of cost encountered in the solar system analysis [10]: capital equipment cost, acquisition cost, operating cost, interest charges, if money for capital is borrowed, maintenance, insurance and miscellaneous charges, taxes, sales and national, recurring or one time cost associated with the system and salvage value. The above types of cost can be simplified broadly as collector area related cost, Co and collector area independent cost, C~. Therefore, Cs = CoA + C,
(1)
where C, is the total cost of the system. Investment analysis uses a present value approach, whereby initial investment, annual expenses and annual savings are discounted to their present value, and the sum of the first two is compared with the latter. The reason that the cash flow must be discounted lies in the time value of money. Process of optimization The optimization of solar heating systems can be broadly divided into three stages [6]. (i) Optimization criterion. This may be technical,
i
'
Temperature sensor
Temperature transmitter
FLow meter
Heat quantity meter
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Fig. 1. Schematic diagram o f solar hot water system at CIAS.
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HAWLADER et al.: ECONOMIC EVALUATION OF SOLAR WATER HEATER
e.g. the thermal performance of the system is to be optimized, or economic, e.g. one year's cost, life cycle cost, etc., is to be minimized. (ii) Thermal performance evaluation. The thermal performance of the system can be evaluated by using hour-by-hour simulation over a long period of time. It can also be estimated by using reduced weather data or the f-chart method [10]. (iii) Optimization procedure. The influence of one variable on the function can be considered at a time and the maximum/minimum can be evaluated. This can be applied to two variables at a time to give contours from which the optimum can be determined. Alternatively, a differential expression can be developed for the function and the maximum/minimum can be estimated by obtaining the point at which the partial derivative is zero. In this study, economic optimization is carried out according to method (i) by writing a differential expression, and the minimum/maximum is obtained by finding the point where the partial derivative is zero. The thermal performance of the system for a given load is evaluated by using hour-by-hour simulation of the system [9]. The typical values of the economic parameters, used in this study, are given in Table 1, whereas the system parameters are given in Table 2. A typical average load profile of the CIAS system is shown in Fig. 2.
Economic figures of merit
(B) (C)
Life cycle costing: (i) annualized life cycle cost, and (ii) net life cycle savings. Payback period. Internal rate of return.
Life cycle cost includes the sum of all costs over the life of the system or selected period of analysis, in today's dollars, taking into account the time value of money. This is done by using the annualized life cycle costs method or the life cycle savings (LCS) method. Boer [4] defines the payback period as the time at which first costs and annual expenses with compounded interest equal the total saving on energy costs with compounded interest. There are other definitions of payback period, as outlined in Ref. [10]. The internal rate of return is the discounted rate when life cycle savings are zero. Table 1. Economic parameters Consumer inflation rate Fuel inflation rate Life cycle of system Loan interest rate Loan term Discount rate
1°22'N 10° 0 0.02 0.93 16°1 ' 1 630.0 m 2 0.92 0.76 22.076 m3/la 4130 J/kg K 990 kg/m~ 10,000J/m2 K 5000 J/m 2 K 0.4646 W/m K 27,500 W/K 0.81 65°C 19.296 m3/h 0.4646 Wire K
It can be seen from analysis [1] that the governing equation describing the optimum condition becomes identical for annualized life cycle cost and the net life cycle saving and predicts the same collector area. Similarly, the analysis of internal rate of return and payback period lead to an identical equation, giving the same collector area, which is different from the one described earlier. For this reason, the life cycle cost and payback period will be investigated in this study.
Net life cycle savings
Several economic figures of merit have been used as the criteria for the evaluation and optimization of a solar system, as described below. (A)
Table 2. System date Latitude (~) Collector tilt angle (#) Collector azimuth orientation (~) Ground albedo Collector absorptivity *Longitude correction from standards meridian Number of glass covers Collector area Collector efficiency factor Collector transmission coefficient for diffuse radiation Primary circuit flow rate Water specific heat Water density at operating temperature Collector and water content heat capacity Heat capacity of water in pipes for total collector-beat exchanger circuit Pipe heat loss coefficient for pipes in primary circuit Conductance-area product Heat exchanger efficiency Hot water demand temperature Flow rate in secondary circuit Heat loss coefficient of pipes in secondary circuit
0.02 0.13 20 years 0.09 8 years 0.07
Life cycle savings (LCS) are the difference between a reduction in fuel cost and an increase in expenses incurred as a result of the additional investment for the solar energy system.
Q,c~
L C S = - -
C~(i", n)
C~.
(2)
Equation (2) represents the total cost of the energy replaced by solar energy less the system cost. The annualized life cycle costs, as derived in the Appendix, are given by
Ce.e(i', n) Ca = CsCe.e(i',n) + Q.~CF~-~,.,,-Sq ~e.e[l ,nJ or
CA = C~(i', n~)
C~ + ( Q o - Q~)
C~.(i', n) C r ~
QnCe C~(i", n)
QsCr Ce~(i",n)
or
QDCe C~(i", n)
CA C~(i', n) = -Cs+
- QsCF C~(i", n)
= LCS.
(3)
HAWLADER et al.: ECONOMIC EVALUATION OF SOLAR WATER HEATER
201
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33
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Q ,(
o
_J
1.$ 1.2
-1
0.9 0.6 0.3 i
2
4
22 TIME,
26
HOUR
Fig. 2. A typical hourly hot water demand pattern.
Differentiating equation (3) with respect to A and equating it to zero gives
8C~ OA
aCA = O. CRr(i', n) aA
a (LCS)
Differentiating with respect to A
1
~A
Cr 8Q, C~(i", n,) aA
or
Using equation (A4)
CD=
O
aQ,
Cr
&4 C~(t "",np) "
From equation (5)
a---.4(LCS) = - CoC~(i', n)
8Q,
CRr(i', n) + - ~ CF CRF(i., n~) = O.
Cs
Ce
Q,
C~(i", np)
Therefore, Rearrangement of the above equation gives
OF
CoC~(i", n)
as
G
(4)
aQs
Q, CD
ax
c,
Q,Co c~ +G
or where F = Qs/Q, and S = A/QD. It is seen from equations (4) and (A5) that the annualized cost method and the LCS method are equivalent and yield identical optimum results.
Payback period The minimum payback period, using discounted auxiliary fuel cost, is given by the following equation [10]:
Q,G c,
E.C.M. 27/2--F
-
-
-
C RF(i", rip)
(5)
~F aS
F CI
(6)
S+-QoC~
The maximum internal rate of return gives [1] an optimum condition which is exactly similar to equation (6). Equations (1)--(6) are used for the economic optimization study of the solar system considered here. A set of assumptions have been made for the load distribution, determination of solar fraction from the system simulation model, and estimation of costs.
202
H A W L A D E R et al.:
ECONOMIC EVALUATION OF SOLAR WATER HEATER
There is always a certain amount of uncertainty in the prediction of future expenses and benefits, which is sometimes magnified by the existing international energy situation. Results of optimization must, therefore, be treated with considerable discretion.
RESULTS AND DISCUSSION
For a given set of conditions, such as hot water requirements, economic situation, geographical location, it is possible to determine the optimal design variables to give maximum life cycle savings. Although there are many variables having considerable influence on the performance of the solar system, the most important variable in the design of a solar system is the collector area. Figure 3 shows the life cycle savings as a function of the collector area. For a collector area < 350 m E, the curve shows a negative saving and reflects the fixed cost of the solar energy system. With increasing collector area, an increased saving can be achieved, until a maximum at some optimum collector area is reached. Further increases in collector area causes higher fuel savings, but the system cost increases excessively, forcing the solar saving to decrease. The optimum collector area which yields maximum savings is characterized by a point where the gradient of life cycle savings against collector area is zero. Equation (4) represents this condition. The optimum collector area predicted by this
method, under the economic conditions considered, is 1200 m 2. Figure 4 shows the variation of annualized cost with collector area. This cost decreases with increasing collector area, approaches a minimum value, and then rises. This phenomenon can be explained by the fact that the increased collector area reduces auxiliary fuel costs, but once the optimum area is exceeded, the decrease in auxiliary energy cost is less than the collector area related costs, resulting in increased annualized cost. The minimum cost occurs at an optimum collector area and is represented by equation (A5). The optimum collector area, without loan interest, is 1200 m 2, which is exactly similar to that shown in Fig. 3, indicating that the life cycle method and annualized method of analyses yield the same optimum collector area. As shown in Fig. 3, this optimum area is slightly lower when loan interest is taken into account. The variations of payback period with collector area for different economic parameters are shown in Fig. 5. The payback period is seen to decrease sharply with the increase in collector area, since the auxiliary fuel savings are far greater than the increase in cost due to increased collector area. It passes through a minimum and then increases. The collector area corresponding to this minimum payback period is the optimum collector area which gives maximum fuel savings. Further increase in area causes a sharp increase in cost which is higher than the savings on
700000 500O00 5000O0 /,00000 300000 ell
200O0O < U'l
U >, LAJ LI. -J
I0000C 0 -100000 -20000~
0
500
IO00
1500
2000
2500
3000
COLLECTOR AREA, m 2 Fig. 3. Variation o f life cycle savings as a function of collector
area.
HAWLADER et al.: ECONOMIC EVALUATION OF SOLAR WATER HEATER
210000 !
ANNUAL COST WITHOUT LOAN
//
INTEREST
200000
203
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1200OO 110OOO 100000 0
,
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.
ISO0
.
2O00 COLLECTOR AREA, m 2
,I
,
2.~10
~00
Fig. 4. Annualized cost as a function of collector area.
fuel. The minimum payback period without loan interest is about 14 years. It is also seen from Fig. 5 that the inclusion of discount and interest causes an increase in the payback period. The optimum collector area corresponding to the minimum payback period is found to be 1000 m 2, which is lower than that obtained from an analysis based on life cycle savings. The smaller value of the optimal collector area predicted by the payback period is partly due to
the fact that this model fails to consider cash flows which occur after the point where payback is reached. The optimization methods discussed previously give a measure of risk and illiquidity. Risk is involved because the estimates of economic figures of merit are based on the amount of fuel saved and the future price of fuel, which together with estimates of economic parameters are uncertain. Illiquidity arises because the solar energy investments are uncertain.
40.0 UNDISCOUNTED PAYBACK WITHOUT LOAN INTEREST DISCOUNTED PAYBACK WITHOUT lOAN INTiSqEST - - . - - UNDISCOUNIED PAYBACI< WITH LOAN INTEREST --DISCOUNTED PAYBACK WITH LO.6bl INTEREST ....
35.0
3Z S 30.0
w > . 27.S x
U 4[
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S
/ I "
17.5 1S.0 I I?~S 10.0 0
SO0
1000
IS00
2000
~500
3000
COLLECTOR AREA, m2 Fig. 5. Payback period as a function of collector area with interest on loan as a parameter.
204
HAWLADER et al.:
ECONOMIC EVALUATION OF SOLAR WATER HEATER
Since the prime concern of most investors is not to incur losses, the payback period gives an estimate of exposure to risk and illiquidity. The use of the different methods of economic optimization are thus governed by investor motives. An investor looking for long term investments will try to maximize life cycle savings. Gordon and Rabl [8] propose that maximizing LCS is a more appropriate choice based on the fact that buying energy is an operating expense which is justified only by the profit from the activity the energy is used to run. It is seen from the anlaysis that the optimum collector area for the given conditions is 1200m 2 which should provide about 80% of the hot water load. At present, as mentioned earlier, the CIAS solar system uses 630 m 2, giving a solar fraction of 0.58 [9]. The collector area can be increased to 1200 m 2 without any additional storage facility. The system was built at a cost of about S$800,000 and the experiment measurements indicate a savings of S$100,000 per annum in fuel cost.
2. C. D. Barley and C. B. Winn, Sol. Energy 21, 279 (1978). 3. M. J. Brandemuehl and W. A. Beckman, Sol. Energy 23, 1 (1979). 4. P. J. Lunde, Sol. Energy 28, 197 (1982). 5. K. K. Chang and A. Minardi, Sol. Energy 24, 99 (1980). 6. E. Michelson, Sol. Energy 29, 89 (1982). 7. K. W. Boer, Sol. Energy 20, 225 (1978). 8. G. M. Gordon and A. Rabl, Sol. Energy 28, 519 (1982). 9. M. N. A. Hawlader, K. C. Ng, T. T. Chandratilleke and H. L. Kelvin Koay, Renew. Energy Rev. J. 6, 40 (1984). 10. W. A. Beckman and J. A. Duffle, Solar Engineering o f Thermal Processes. Wiley, New York (1980).
APPENDIX Annualized Life Cycle Costs
The annual cost is the annualized cost of the system plus the annual cost of auxiliary energy, which is represented by the following equation: Cm~(i', n) C A = CsCm~(i', n) + Q a C p - C t ~ i ' , n)
(Al)
where CONCLUSION Several economic figures of merit have been applied for the analysis of a solar system in Singapore. It shows that the annualized life cycle cost method and the life cycle savings approach of analysis lead to prediction of the same collector area. Similarly, the payback period and internal rate of return predict an optimal collector which is smaller than the other two methods. It should be noted that this optimum will change if the economic variables are altered. The economic evaluation of the existing solar system at CIAS for the required load and the meteorological conditions of Singapore indicates that the optimum collector area of the system should be about 1200m 2, providing about 80% of the load. Although the system was designed for this collector area, it actually installed 630 m 2 of collector area with provision for future expansion. The performance of the system, which provides about 58% of the total load, may be considered reasonably well.
(A2) Here, all costs are brought to capital cost using the relevant capital recovery factor. Using equations (1) and (A2), equation (Al) becomes QA = Qo - Q,.
C A = (CDA + Ct)Cm~i',n)
c,,Ai' n)
+ (Qo - Q,)Ce - ~ . . . . . Ctu~(i", n)
where CD = Cc + bC r.
For cost optimal area, dC A ., dQs ~ C ~ ( i ' , n) dA = CoCe.At , n) - -ff~ c r CRAi", n) = 0 (A4) or
aQ,
c o c ~ ( i " , n)
aA
C~
or
OF coc~(i", n) as
REFERENCES
1. N. E. Wijeysundera and J. C. Ho, Energy Convers. M g m t 25, 331 (1985).
(A3)
c~
where F = Q~/Qo and S = A J Q o.
(a5)
0196-8904/87 $3.00+0.00 Copyright © 1987 Pergamon Journals Ltd
ECONOMIC EVALUATION OF A SOLAR WATER HEATING SYSTEM M. N. A. H A W L A D E R 1, K. C. NG l, T. T. C H A N D R A T I L L E K E 1, D. S H A R M A I and K E L V I N KOAY H. L. 2 1Department of Mechanical and Production Engineering, National University of Singapore, Kent Ridge, Singapore 0511 2Manager, Facilities and Engineering Projects, Cliangi International Airport Services (CIAS), Singapore 9181 (Received 26 March 1986)
Abstract--This paper describes different methods of analysis of a solar water heating system to determine its economic viability. The solar fraction, required for this analysis, has been calculated with a stimulation program using hourly meteorological data of Singapore. A measured load profile, representing the average condition, was used for this program. The economic variables have been selected from the trends shown in previous years. When different economic optimization criteria were applied to the CIAS solar system, it was seen that both the life cycle saving and the annualized life cycle cost lead to the prediction of the same optimum collector area of 1200 m2. The payback period and the internal rate of return analyses also predicted the same optimum collector area of 1000 m 2, which is smaller than that predicted by the method of life cycle costing. For the economic variables used in this analysis, the minimum payback period is about 14 years. Solar water heating Payback period
Industrial process heating Economic optimization Annualized cost Internal rate of return
NOMENCLATURE A = CoUector area b = Constant relating tank storage volume to collector area Cc = Collector cost ($/m2) Cr = Fuel costs (g/M J) C ~ = Capital recovery factor
Cr = e= F= i= i'=
Tank cost ($/m2) Fuel escalation rate Solar fraction (Qs/Qo) Discount rate Effective discount rate
i " = Effective discount rate for fuel
j -- Inflation rate n = Life cycle of system np = Minimum payback period Q,--Solar heat gain (M J) Qo = Load (M J) S = Collector area/load (m2/MJ) INTRODUCTION The conversion of solar energy for useful applications
Life-cycle savings
requires a considerable initial investment compared to a conventional system. In the majority of solar processes, a source of auxiliary energy is required so that the system includes both solar and conventional equipment to meet the desired load. Solar systems are normally characterized by a high initial investment followed by low operating costs. It is, therefore, necessary to determine whether such an investment is economically competitive when compared with conventional systems. The economic analyses are performed based on several figures of merit such as, annualized system cost, net life cycle savings, payback period, internal rate of return, and a few others. Wijeysundera and Ho [1] have shown that the above four methods can be broadly grouped into two. The annualized system cost and the net life cycle savings methods of analyses lead to identical optimum conditions, predicting the same collector area, as shown in a later section. Similarly, the payback period and internal rate of return lead to an exactly identical expression for the optimum condition. Barley and W i n n [2], Brandemuehl and Beckman [3], and Lunde [4] have used life cycle savings as the figure of merit in the optimization of solar systems. Chang and Minardi [5] used annualized system cost as the optimization criteria for a solar hot water system. In the life cycle savings and annualized system cost analyses, the future expenses and benefits are expressed in terms of dollars in hand, 197
198
HAWLADER et al.: ECONOMIC EVALUATION OF SOLAR WATER HEATER
which requires assumptions, on future discount rate, inflation rate and fuel escalation rate. Thus, the conversion of all future earnings to present worth dollars involves a certain degree of uncertainty. Moreover, most customers are interested in the payback period of the system. Michelson [6] and Boer [7] used the minimum payback period for economic optimization of solar systems which requires fewer assumptions about future costs. Gordon and Rabl [8] used the internal rate of return as the criterion for the optimization of a solar process heat plant. This paper described the results of an economic analysis of an existing solar system at the Changi International Airport Services (CIAS) which supplies hot water in the temperature range of 60-80°C for the flight kitchen. In the economic evaluation, various figures of merit have been used to determine if the existing system is operating at its optimal level. This requires knowledge of the thermal performance of the system, which is normally expressed in terms of annual solar fraction and collector area. The annual solar fraction for different collector areas has been calculated using a simulation program developed in the department [9]. The program was run with the hourly meteorological data and the measured load profile. THE SOLAR SYSTEM One of the many services, which the Changi International Airport Services provides, is the kitchen facilities for airlines. Its flight kitchen requires large quantities of hot water for cooking and washing purposes. A large fraction of this heating requirement is met by solar energy. A schematic diagram of the solar system is shown in Fig. 1. The water in the collector loop is heated via 630 m 2 of Yazaki blue panels which are mounted on the roof top. Energy incident on these collectors heats the water circulated through the collectors by the primary pumps. The collector loop is separated from the load loop via heat exchangers. The secondary circuit is an open circuit. There are four storage tanks, each of 10 m 3 vol. The water in the storage tanks is circulated through the heat exchangers by secondary pumps. When there is a demand, hot water is drawn from storage tank 1, and an equal amount of make up water is supplied from the mains and enters into tank 4 at the bottom. When the temperature of the water is below the desired value, a calorifier is used to provide auxiliary energy. Two air cooling units are also provided for cases when thermal overloading occurs in the storage tanks, and the excess energy, under these circumstances, is discharged to the atmosphere. During operation, the fluid, circulated by the primary pump through the collectors, absorbs a fraction of the solar energy incident on the panels. The water in the secondary circuit receives a large part of this energy via heat exchangers. The operation of the
system is controlled by an automatic controller. When water is delivered to the storage tanks, the controller gives priority to tank l, followed by 2, 3 and 4, when more than one tank is eligible for energy input. A tank is eligible for energy input when its temperature is <70°C. This allows tank 1 to be always at a higher temperature, unless all of them are thermally full, in order to minimize the use of auxiliary energy. The storage tanks are considered thermally full when all of them are at 70°C. When this occurs, the secondary pumps are switched off. However, the fluid in the primary circuit may still be receiving solar energy, resulting in a temperature rise. When the fluid temperature in the collectors exceeds 85°C, the secondary pumps are switched on and the water from the heat exchangers is circulated through the air cooling unit (ACU), instead of the storage tanks. At the air cooling unit, this energy is vented to the atmosphere, preventing damage to the collectors. ECONOMIC EVALUATION METHODOLOGY The economic optimization of solar energy systems involves multiple variables. In general, all the components in the system will have some effect on the thermal performance of the system and thus on costs. In practice, the problem often reduces to a simpler one of determining the size of a solar system for a known load, with storage capacity and other parameters fixed in relation to collector area. For solar systems, the performance is more sensitive to collector area than to any other variable [10]. Therefore, in this analysis, the primary index of the size of the solar system is chosen to be the area of the collectors. The following are the types of cost encountered in the solar system analysis [10]: capital equipment cost, acquisition cost, operating cost, interest charges, if money for capital is borrowed, maintenance, insurance and miscellaneous charges, taxes, sales and national, recurring or one time cost associated with the system and salvage value. The above types of cost can be simplified broadly as collector area related cost, Co and collector area independent cost, C~. Therefore, Cs = CoA + C,
(1)
where C, is the total cost of the system. Investment analysis uses a present value approach, whereby initial investment, annual expenses and annual savings are discounted to their present value, and the sum of the first two is compared with the latter. The reason that the cash flow must be discounted lies in the time value of money. Process of optimization The optimization of solar heating systems can be broadly divided into three stages [6]. (i) Optimization criterion. This may be technical,
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HAWLADER et al.: ECONOMIC EVALUATION OF SOLAR WATER HEATER
e.g. the thermal performance of the system is to be optimized, or economic, e.g. one year's cost, life cycle cost, etc., is to be minimized. (ii) Thermal performance evaluation. The thermal performance of the system can be evaluated by using hour-by-hour simulation over a long period of time. It can also be estimated by using reduced weather data or the f-chart method [10]. (iii) Optimization procedure. The influence of one variable on the function can be considered at a time and the maximum/minimum can be evaluated. This can be applied to two variables at a time to give contours from which the optimum can be determined. Alternatively, a differential expression can be developed for the function and the maximum/minimum can be estimated by obtaining the point at which the partial derivative is zero. In this study, economic optimization is carried out according to method (i) by writing a differential expression, and the minimum/maximum is obtained by finding the point where the partial derivative is zero. The thermal performance of the system for a given load is evaluated by using hour-by-hour simulation of the system [9]. The typical values of the economic parameters, used in this study, are given in Table 1, whereas the system parameters are given in Table 2. A typical average load profile of the CIAS system is shown in Fig. 2.
Economic figures of merit
(B) (C)
Life cycle costing: (i) annualized life cycle cost, and (ii) net life cycle savings. Payback period. Internal rate of return.
Life cycle cost includes the sum of all costs over the life of the system or selected period of analysis, in today's dollars, taking into account the time value of money. This is done by using the annualized life cycle costs method or the life cycle savings (LCS) method. Boer [4] defines the payback period as the time at which first costs and annual expenses with compounded interest equal the total saving on energy costs with compounded interest. There are other definitions of payback period, as outlined in Ref. [10]. The internal rate of return is the discounted rate when life cycle savings are zero. Table 1. Economic parameters Consumer inflation rate Fuel inflation rate Life cycle of system Loan interest rate Loan term Discount rate
1°22'N 10° 0 0.02 0.93 16°1 ' 1 630.0 m 2 0.92 0.76 22.076 m3/la 4130 J/kg K 990 kg/m~ 10,000J/m2 K 5000 J/m 2 K 0.4646 W/m K 27,500 W/K 0.81 65°C 19.296 m3/h 0.4646 Wire K
It can be seen from analysis [1] that the governing equation describing the optimum condition becomes identical for annualized life cycle cost and the net life cycle saving and predicts the same collector area. Similarly, the analysis of internal rate of return and payback period lead to an identical equation, giving the same collector area, which is different from the one described earlier. For this reason, the life cycle cost and payback period will be investigated in this study.
Net life cycle savings
Several economic figures of merit have been used as the criteria for the evaluation and optimization of a solar system, as described below. (A)
Table 2. System date Latitude (~) Collector tilt angle (#) Collector azimuth orientation (~) Ground albedo Collector absorptivity *Longitude correction from standards meridian Number of glass covers Collector area Collector efficiency factor Collector transmission coefficient for diffuse radiation Primary circuit flow rate Water specific heat Water density at operating temperature Collector and water content heat capacity Heat capacity of water in pipes for total collector-beat exchanger circuit Pipe heat loss coefficient for pipes in primary circuit Conductance-area product Heat exchanger efficiency Hot water demand temperature Flow rate in secondary circuit Heat loss coefficient of pipes in secondary circuit
0.02 0.13 20 years 0.09 8 years 0.07
Life cycle savings (LCS) are the difference between a reduction in fuel cost and an increase in expenses incurred as a result of the additional investment for the solar energy system.
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(2)
Equation (2) represents the total cost of the energy replaced by solar energy less the system cost. The annualized life cycle costs, as derived in the Appendix, are given by
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= LCS.
(3)
HAWLADER et al.: ECONOMIC EVALUATION OF SOLAR WATER HEATER
201
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Differentiating equation (3) with respect to A and equating it to zero gives
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a (LCS)
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or where F = Qs/Q, and S = A/QD. It is seen from equations (4) and (A5) that the annualized cost method and the LCS method are equivalent and yield identical optimum results.
Payback period The minimum payback period, using discounted auxiliary fuel cost, is given by the following equation [10]:
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-
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The maximum internal rate of return gives [1] an optimum condition which is exactly similar to equation (6). Equations (1)--(6) are used for the economic optimization study of the solar system considered here. A set of assumptions have been made for the load distribution, determination of solar fraction from the system simulation model, and estimation of costs.
202
H A W L A D E R et al.:
ECONOMIC EVALUATION OF SOLAR WATER HEATER
There is always a certain amount of uncertainty in the prediction of future expenses and benefits, which is sometimes magnified by the existing international energy situation. Results of optimization must, therefore, be treated with considerable discretion.
RESULTS AND DISCUSSION
For a given set of conditions, such as hot water requirements, economic situation, geographical location, it is possible to determine the optimal design variables to give maximum life cycle savings. Although there are many variables having considerable influence on the performance of the solar system, the most important variable in the design of a solar system is the collector area. Figure 3 shows the life cycle savings as a function of the collector area. For a collector area < 350 m E, the curve shows a negative saving and reflects the fixed cost of the solar energy system. With increasing collector area, an increased saving can be achieved, until a maximum at some optimum collector area is reached. Further increases in collector area causes higher fuel savings, but the system cost increases excessively, forcing the solar saving to decrease. The optimum collector area which yields maximum savings is characterized by a point where the gradient of life cycle savings against collector area is zero. Equation (4) represents this condition. The optimum collector area predicted by this
method, under the economic conditions considered, is 1200 m 2. Figure 4 shows the variation of annualized cost with collector area. This cost decreases with increasing collector area, approaches a minimum value, and then rises. This phenomenon can be explained by the fact that the increased collector area reduces auxiliary fuel costs, but once the optimum area is exceeded, the decrease in auxiliary energy cost is less than the collector area related costs, resulting in increased annualized cost. The minimum cost occurs at an optimum collector area and is represented by equation (A5). The optimum collector area, without loan interest, is 1200 m 2, which is exactly similar to that shown in Fig. 3, indicating that the life cycle method and annualized method of analyses yield the same optimum collector area. As shown in Fig. 3, this optimum area is slightly lower when loan interest is taken into account. The variations of payback period with collector area for different economic parameters are shown in Fig. 5. The payback period is seen to decrease sharply with the increase in collector area, since the auxiliary fuel savings are far greater than the increase in cost due to increased collector area. It passes through a minimum and then increases. The collector area corresponding to this minimum payback period is the optimum collector area which gives maximum fuel savings. Further increase in area causes a sharp increase in cost which is higher than the savings on
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area.
HAWLADER et al.: ECONOMIC EVALUATION OF SOLAR WATER HEATER
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Fig. 4. Annualized cost as a function of collector area.
fuel. The minimum payback period without loan interest is about 14 years. It is also seen from Fig. 5 that the inclusion of discount and interest causes an increase in the payback period. The optimum collector area corresponding to the minimum payback period is found to be 1000 m 2, which is lower than that obtained from an analysis based on life cycle savings. The smaller value of the optimal collector area predicted by the payback period is partly due to
the fact that this model fails to consider cash flows which occur after the point where payback is reached. The optimization methods discussed previously give a measure of risk and illiquidity. Risk is involved because the estimates of economic figures of merit are based on the amount of fuel saved and the future price of fuel, which together with estimates of economic parameters are uncertain. Illiquidity arises because the solar energy investments are uncertain.
40.0 UNDISCOUNTED PAYBACK WITHOUT LOAN INTEREST DISCOUNTED PAYBACK WITHOUT lOAN INTiSqEST - - . - - UNDISCOUNIED PAYBACI< WITH LOAN INTEREST --DISCOUNTED PAYBACK WITH LO.6bl INTEREST ....
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2000
~500
3000
COLLECTOR AREA, m2 Fig. 5. Payback period as a function of collector area with interest on loan as a parameter.
204
HAWLADER et al.:
ECONOMIC EVALUATION OF SOLAR WATER HEATER
Since the prime concern of most investors is not to incur losses, the payback period gives an estimate of exposure to risk and illiquidity. The use of the different methods of economic optimization are thus governed by investor motives. An investor looking for long term investments will try to maximize life cycle savings. Gordon and Rabl [8] propose that maximizing LCS is a more appropriate choice based on the fact that buying energy is an operating expense which is justified only by the profit from the activity the energy is used to run. It is seen from the anlaysis that the optimum collector area for the given conditions is 1200m 2 which should provide about 80% of the hot water load. At present, as mentioned earlier, the CIAS solar system uses 630 m 2, giving a solar fraction of 0.58 [9]. The collector area can be increased to 1200 m 2 without any additional storage facility. The system was built at a cost of about S$800,000 and the experiment measurements indicate a savings of S$100,000 per annum in fuel cost.
2. C. D. Barley and C. B. Winn, Sol. Energy 21, 279 (1978). 3. M. J. Brandemuehl and W. A. Beckman, Sol. Energy 23, 1 (1979). 4. P. J. Lunde, Sol. Energy 28, 197 (1982). 5. K. K. Chang and A. Minardi, Sol. Energy 24, 99 (1980). 6. E. Michelson, Sol. Energy 29, 89 (1982). 7. K. W. Boer, Sol. Energy 20, 225 (1978). 8. G. M. Gordon and A. Rabl, Sol. Energy 28, 519 (1982). 9. M. N. A. Hawlader, K. C. Ng, T. T. Chandratilleke and H. L. Kelvin Koay, Renew. Energy Rev. J. 6, 40 (1984). 10. W. A. Beckman and J. A. Duffle, Solar Engineering o f Thermal Processes. Wiley, New York (1980).
APPENDIX Annualized Life Cycle Costs
The annual cost is the annualized cost of the system plus the annual cost of auxiliary energy, which is represented by the following equation: Cm~(i', n) C A = CsCm~(i', n) + Q a C p - C t ~ i ' , n)
(Al)
where CONCLUSION Several economic figures of merit have been applied for the analysis of a solar system in Singapore. It shows that the annualized life cycle cost method and the life cycle savings approach of analysis lead to prediction of the same collector area. Similarly, the payback period and internal rate of return predict an optimal collector which is smaller than the other two methods. It should be noted that this optimum will change if the economic variables are altered. The economic evaluation of the existing solar system at CIAS for the required load and the meteorological conditions of Singapore indicates that the optimum collector area of the system should be about 1200m 2, providing about 80% of the load. Although the system was designed for this collector area, it actually installed 630 m 2 of collector area with provision for future expansion. The performance of the system, which provides about 58% of the total load, may be considered reasonably well.
(A2) Here, all costs are brought to capital cost using the relevant capital recovery factor. Using equations (1) and (A2), equation (Al) becomes QA = Qo - Q,.
C A = (CDA + Ct)Cm~i',n)
c,,Ai' n)
+ (Qo - Q,)Ce - ~ . . . . . Ctu~(i", n)
where CD = Cc + bC r.
For cost optimal area, dC A ., dQs ~ C ~ ( i ' , n) dA = CoCe.At , n) - -ff~ c r CRAi", n) = 0 (A4) or
aQ,
c o c ~ ( i " , n)
aA
C~
or
OF coc~(i", n) as
REFERENCES
1. N. E. Wijeysundera and J. C. Ho, Energy Convers. M g m t 25, 331 (1985).
(A3)
c~
where F = Q~/Qo and S = A J Q o.
(a5)