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Techno-economic evaluation of domestic solar water heating systems in India
Renewable Energy 29 (2004) 319–332 www.elsevier.com/locate/renene
Techno-economic evaluation of domestic solar water heating systems in India B. Chandrasekar, T.C. Kandpal Centre for Energy Studies, Indian Institute of Technology Delhi, Haus Khaz, New Delhi 110016, India Received 19 May 2003; accepted 11 June 2003
Abstract The most wide spread thermal use of solar energy, so far, has been for water heating. Solar water heating systems have been commercialized in many counties in the world. Though the technical feasibility of domestic solar water heating systems (DSWHS) has long been established, their financial viability needs to be carefully examined, particularly in tropical countries with relatively lower annual capacity utilization and poor purchasing power of potential users. The potential number of Indian households who can invest in DSWHS have been estimated based on the income distribution in the country, the capital cost of solar water heating systems, interest rate charged on the loan provided for the purchase of DSWHS etc. Using the seasonal and diurnal variation of ambient temperatures at many locations in the country, the periods with annual hot water requirement have been identified. A simple framework for financial evaluation of DSWHS has also been presented. The results of some typical exemplifying calculations have been presented and discussed. # 2003 Elsevier Ltd. All rights reserved. Keywords: Potential users; Domestic solar water heating systems; Capacity utilization; Technoeconomics
1. Introduction Significant efforts have been made towards the development and dissemination of domestic solar water heating systems (DSWHS) in India for the past two decades. The Government of India launched a demonstration program during 1980s
Corresponding author. Tel.: +91-11-265-91262; fax: +91-11-265-82037. E-mail address: [email protected] (T.C. Kandpal).
0960-1481/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0960-1481(03)00198-8
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for promoting DSWHS in the country. In order to promote the use of DSWHS, a variety of financial incentives have been offered to the end users [1]. These include capital subsidy, low interest loan, accelerated depreciation related benefit etc. However, the total collector area of DSWHS reportedly installed in the country so far (0.60 million square meters till December 2001) is below the expected levels of penetration. It is therefore critically important to study and analyze the role of different factors contributing to the dissemination and use of DSWHS in the country. A preliminary attempt to study the possible relationship between the seasonal and diurnal variations in ambient temperature at a place and the need of hot water for bathing has been made in this paper. The results obtained can be used to estimate the expected capacity utilization of DSWHS for different locations in the country. The income levels of the households directly affect their capacity to purchase DSWHS. Using the income distribution of households in the country, the capital cost of typical DSWHS, and the rate of interest on the loans provided to the users to purchase DSWHS, the potential number of households who can use DSWHS have also been estimated. From the above inputs as well as the prevailing estimates for the costs and benefits of DSWHS in India, a detailed financial evaluation has also been undertaken. The results of some typical calculations based on the above analysis are presented and briefly discussed.
2. Techno-economic evaluation One of the most critical factors in the dissemination of DSWHS is their financial viability. The monetary benefits accrued to the end users would depend on the amount and cost of fuel saved through the use of DSWHS. The efficiency of the DSWHS largely depends on the system design, the availability of solar radiation and ambient conditions. Another dimension of complexity in the financial evaluation of DSWHS is the seasonal variation in the hot water demand of the household for bathing purpose. In tropical areas, hot water may not be required during certain periods of the year. In such a situation, the effective capacity utilization of the water heating systems may be much lower resulting in increased unit cost of useful energy delivered by the DSWHS. 2.1. Determination of unit cost of useful thermal energy Unit cost of useful thermal energy provided by a DSWHS can be determined as the ratio of the total annual cost to the annual useful thermal energy delivered by the system, i.e., (" # ) d ð1 þ d ÞT þ m C0 ð1 þ d ÞT 1 UCute;s ¼ ð1Þ fV qCp ðTf Ti ÞN where q represents the density of water, C0 the capital cost of the DSWHS, Cp the specific heat of water, N the number of days in a year when the hot water is
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delivered and required by the user (usually this depends on the design of the system and its use), V the volume of daily hot water requirement of the household, f the fraction of total annual useful energy requirement for domestic water heating provided by the solar energy, Tf the outlet temperature of the hot water, Ti the temperature of inlet water to the tank, T the useful life of DSWHS, d the discount rate, and m the operation and maintenance cost as a fraction of the capital cost. The annual amount of fuel saved can be determined as Fs ¼
fV qCp ðTf Ti ÞN C v gf
ð2Þ
where Cv represents the calorific value of the fuel substituted (saved) by the DSWHS and gf the efficiency of utilization of the fuel for water heating. The monetary worth of annual fuel savings (Mwfs) can be calculated using the relation fV qCp ðTf Ti ÞN ð3Þ Mwfs ¼ pf Cv gf where pf is the unit price of fuel. The net annual monetary benefits (Bna) can be expressed as fV qVp ðTf Ti ÞN Bna ¼ pf mC0 C v gf
ð4Þ
2.2. Different financial figures of merit for DSWHS The cumulative present value of life cycle net benefits accrued to the end user due to purchase and installation of DSWHS can be determined using the following equation Bpv ¼ Bna PWFðd; TÞ
ð5Þ
where PWF(d,T) is the present worth factor for a discount rate d and the useful life T of DSWHS. The above expression assumes that the net annual monetary benefits accrued to the user is constant over the useful lifetime T of the DSWHS. However, it is expected that price of fuel saved (pf) would escalate in future resulting in increased monetary worth of annual fuel savings. The modified expression for the cumulative present value of net benefits can be expressed as "
# Bna 1þe T 0 Bpv ¼ 1 ð6Þ 1þd ðd eÞ where e is the annual rate of fuel price escalation. The following expressions can be derived for the various figures of merit used for evaluating the financial viability of an investment made on a DSWHS (without considering the escalation in the price(s) of fuel(s) saved by the DSWHS).
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2.2.1. Simple payback period The simple payback period (SPP) for a DSWHS can be determined as the ratio of the capital cost to the net annual benefits accrued to the user i.e., SPP ¼
C0 Bna
ð7Þ
2.2.2. Discounted payback period The discounted payback period (DPP) for a DSWHS can be determined using the relation DPP ¼
lnðBna Þ lnðBna dC0 Þ lnð1 þ dÞ
ð8Þ
2.2.3. Net present value The net present value (NPV) for DSWHS can be determined as the difference of present value of net annual monetary benefits to the capital cost of the system. For the case of uniform net annual benefits (Bna), the net present value (NPV1) can be expressed as NPV1 ¼ Bna PWFðd; TÞ þ
S C0 ð1 þ dÞT
ð9Þ
where S is the expected salvage value of DSWHS at the end of its useful life. For the case of non-uniform net annual benefits accrued to the user, the net present value (NPV2) can be expressed as ! T X Bna;j S NPV2 ¼ C0 ð10Þ þ j ð1 þ dÞT ð1 þ dÞ j¼1 where Bna,j represents the net annual benefits in the jth year. 2.2.4. Benefit to cost ratio The benefit to cost ratio (B/C) for a DSWHS can be determined as the ratio of net annual benefit to its capital cost. For the case of uniform net annual monetary benefits (Bna) the benefit to cost ratio, (B/C)1, can be expressed as S
Bna PWFðd; TÞ þ B ð1 þ dÞT ¼ C 1 C0
ð11Þ
For the case of varying net annual benefits due to the use of DSWHS the benefit to cost ratio (B/C)2 can be expressed as
PT Bna S
þ j¼1 j B ð1 þ dÞT ð1 þ dÞ ¼ ð12Þ C 2 C0 Eqs. (11) and (12) represent the ratio of net benefits to the capital cost. The following expressions can be used to determine the ratio of the present value of total
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life cycle benefits to the total life cycle costs. In the case of uniform annual monetary benefits and costs the expression is S
Mwfs PWFðd; TÞ þ B ð1 þ dÞT ¼ C 3 C0 ½1 þ mfPWFðd; TÞg In the case of varying annual monetary benefits, it is
PT Mwfs;j S
þ j¼1 j B ð1 þ dÞT ð1 þ dÞ ¼ C 4 C0 ½1 þ mfPWFðd; TÞg
ð13Þ
ð14Þ
where Mwfs,j represents the monetary worth of annual fuel savings, with subscript j representing the specific year and m the fraction of capital cost required for annual operation and maintenance of DSWHS. The annual operation and maintenance cost of the DSWHS is assumed to be constant over the useful life period in all the above four cases. 2.2.5. Internal rate of return The internal rate of return (IRR) on the investment made by the user on a DSWHS can be determined by equating the NPV to zero and then solving the equation for the discount rate. For the case of uniform net annual monetary benefits, it is determined by solving the equation ð1 þ IRRÞT 1 S Bna C0 ¼ 0 ð15Þ þ ðIRRÞ ð1 þ IRRÞT ð1 þ IRRÞT For the case of varying net annual monetary benefits accrued due to DSWHS the IRR is obtained by solving the following equation T X j¼1
Bna;j S þ C0 ¼ 0 j ð1 þ IRRÞT ð1 þ IRRÞ
ð16Þ
3. Hot water requirement based on seasonal variation of ambient temperature at different locations Hot water requirement for domestic purposes would essentially depend upon the prevailing temperatures at a location. One of the primary uses of hot water in the Indian households is for taking a bath in the early mornings or late evenings (in some locations). In the present study, the case of morning baths have been considered as majority of Indian households prefer early morning bath (5–7 a.m.). Though the water temperature required for taking the bath would vary with indiv vidual preferences, water temperatures in the range of 32–35 C is reportedly preferred by majority of households. It is with this assumption that an attempt has been made to determine the number of months in a year when hot water will be required by households for different locations in India using the temperature data
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available from the Indian Metrological Department [2]. In this study, it is assumed that if the average temperature between 5 and 7 a.m. is less than a pre-specified temperature (Tspc), the household would require hot water for taking a bath. As the value of Tspc would also vary from person to person, the analysis has been v made for six different values of Tspc. These are 20, 22, 24, 26 and 28 C.
4. Estimation of the potential number of households capable of investing in domestic solar water heating An attempt has also been made to estimate the potential number of households who can afford to purchase and install DSWHS in India. This would essentially depend upon the income levels of households in the country, capital cost of DSWHS, and the number and timings of repayment installments. It is assumed that the potential households would in general prefer availing the facility of low interest loan for the purchase and installation of DSWHS. It is also assumed that the loan is repaid in equal monthly installments. In such a case, the monthly repayment installment (MRI) would depend on the capital cost, rate of interest charged on the loan amount and the total number of repayment installments. The MRI can be determined as MRI ¼ FC0
de ð1 þ de ÞN ð1 þ de ÞN 1
ð17Þ
where C0, represents the capital cost of DSWHS, F the fraction of capital cost available as loan amount to the household, N total number of repayment installments, and de the monthly interest rate. If the annual loan repayment amount is less than a specified fraction of gross annual income of the household, it is considered capable of investing in the purchase of DSWHS.
5. Results and discussion Using simple formulations presented in the above sections, some exemplifying calculations have been made. Table 1 briefly presents the estimates of unit cost of useful thermal energy provided by some of the conventional domestic water heating options. Since the cost of the equipment has not been taken into the calculations, the values of Ucut,e presented in Table 1 always underestimate the corresponding actual values. However, the difference between the two values shall not be significant for most commonly used appropriate domestic water heating appliances. It may be noted from Table 1 that the unit cost of useful thermal energy provided by different conventional options varies considerably. The efficiency of fuel utilization and unit price of fuel used for water heating have maximum effect on the unit cost of useful thermal energy delivered. The estimates of unit cost of useful thermal energy delivered by the DSWHS are presented in Table 2. As expected, the
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Table 1 Unit cost of useful energy for different conventional domestic water heating options Fuel
Electricity LPG Kerosene Fuel wood Natural gas a
Unit (MJ/unit)
Calorific value Utilization efficiency
Unit price of fuel (Rs/unit)
a
kW h kW h kg kg kg kg kg kg m3 m3
3.6 3.6 45 45 45 45 16 16 39 39
3 5 16 25 7.5 14 1.5 1.5 2.0 2.5
0.93 1.54 0.59 0.93 0.42 0.78 0.94 0.38 0.08 0.11
0.9 0.9 0.6 0.6 0.4 0.4 0.1 0.25 0.6 0.6
Ucut,e (Rs./MJ)
Ucut,e represents unit cost of useful thermal energy.
Table 2 Unit cost of useful thermal energy delivered by a DSWHS Capital cost (Rs.) 15,000
20,000
25,000
Capacity utilization 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Unit cost of useful thermal energy delivered (Rs./MJ) d ¼ 0:06
d ¼ 0:08
d ¼ 0:10
d ¼ 0:12
2.55 1.27 0.85 0.64 0.51 0.42 0.36 0.32 0.28 3.40 1.70 1.13 0.85 0.68 0.57 0.49 0.42 0.38 4.25 2.12 1.42 1.06 0.85 0.71 0.61 0.53 0.47
2.87 1.43 0.96 0.72 0.57 0.48 0.41 0.36 0.32 3.82 1.91 1.27 0.96 0.76 0.64 0.55 0.48 0.42 4.78 2.39 1.59 1.19 0.96 0.80 0.68 0.60 0.53
3.21 1.60 1.07 0.80 0.64 0.53 0.46 0.40 0.36 4.28 2.14 1.43 1.07 0.86 0.71 0.61 0.53 0.48 5.34 2.67 1.78 1.34 1.07 0.89 0.76 0.67 0.59
3.56 1.78 1.19 0.89 0.71 0.59 0.51 0.45 0.40 4.75 2.38 1.58 1.19 0.95 0.79 0.68 0.59 0.53 5.94 2.97 1.98 1.48 1.19 0.99 0.85 0.74 0.66
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Fig. 1. Effect of discount rate on NPV and B/C.
unit cost of useful thermal energy delivered critically depends upon the total number of days when the DSWHS delivers hot water or is used by the investor. The unit cost is comparable to that for the cheapest of the conventional water heating options for high values of capacity utilization of DSWHS and/or low values of discount rates. The effects of discount rate used in the financial evaluation exercise, useful life of the DSWHS, capital cost and the fraction of capital cost spent annually on operation and maintenance on the NPV and IRR are shown in Figs. 1–4, respectively. The base values used in these calculations are given in Table 3. The curves showing the effect of discount rate (Fig. 1) and useful life period (Fig. 2) can also be used in analyzing the effect of availability of soft loan for the purchase and installation of
Fig. 2. Effect of useful lifetime on NPV and B/C.
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Fig. 3. Effect of capital cost on NPV and B/C.
DSWHS. Fig. 3 illustrates the effect of capital subsidy on the NPV and the B/C. As expected, there is a reduction in both the financial figures of merit with an increase in the capital cost. One of the key factors, which influences the penetration of new technologies, is the operation and maintenance cost of the system. Fig. 4 represents the effect of annual operation and maintenance cost (expressed as fraction of capital cost) on NPV and B/C. The effect of net annual benefits accrued to the end user of DSWHS on the NPV and IRR is illustrated in Fig. 5. One of the important issues in the financial viability of DSWHS is the capacity utilization of the system during the year. Due to seasonal change in the requirement of hot water in many areas of the country, the effective utility of DSWHS to some users may be limited (3–6 months of winter season only).
Fig. 4. Effect of annual operation and maintenance cost (as a fraction of capital cost) on NPV and B/C.
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Table 3 Base values used in calculations Input parameter
Symbol
Unit
Value
Capital cost Capacity Useful lifetime Discount rate Annual repair and maintenance cost (as a fraction of capital cost) Unit cost of electricity Initial temperature of water Final temperature of water Days of annual hot water requirement
C0 V T d
Rs. l/day Years Fraction
20,000 100 10 0.10
m
Fraction
0.02
– Ti Tf –
Rs./kW h v C v C Days
3 15 60 200
The effect of capacity utilization on the NPV and B/C is illustrated in Fig. 6. Fig. 7 represents the effect of capacity utilization factor on SPP and DPP. The results exemplify a linear reduction in the SPP and DPP with the increase in the capacity utilization factor. In urban areas, the DSWHS usually save electricity. Effect of cost of electricity to the user on the NPV due to investments made in DSWHS is shown in Fig. 8. The effect of varying fuel price escalation rate on NPV and IRR is shown in Fig. 9. Table 4 presents the variation of early morning (5–7 a.m.) ambient temperatures at different locations in the country. Obviously, the duration of the residential hot water demand for taking a bath in the morning varies with the location as well as the value of Tspc. For example, out of the 32 locations considered in the study, 19 v locations would need hot water for 6 months in a year if Tspc is assumed at 22 C. v If Tspc is increased to 28 C, the hot water will be required for 12 months in a year at 21 locations. The results presented in this table can be used for estimating the capacity utilization of the DSWHS for a specified value of Tspc at a location.
Fig. 5. Effect of annual net monetary benefits on NPV and IRR.
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Fig. 6. Effect of capacity utilization factor on NPV and B/C.
Fig. 7. Effect of varying the capacity utilization factor on SPP and DPP.
Fig. 8. Effect of varying the unit cost of electricity on NPV and B/C.
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Table 4 Estimated period (months) of DSWHS at different locations in India Locations
Elevation (in Latitude meters) msla (N)
Longitude (E)
Number of months in a year with temperature less than (during 5–7 a.m.) v
Agartala Ahmedabad Allahabad Amritsar Bangalore Bhavnagar Chennai Baroda Bhopal Gaya Goa Coimbatore Dibrugrah Hyderabad Imphal Indore Kolkatta Kodaikanal Lucknow Mangalore Mumbai Nandi Hills Nagpur New Delhi Patna Port Blair Pune Raipur Shillong Trivandrum Veraval Vizagpattnam a
16 55 98 234 921 5 12 38 523 116 55 397 111 545 781 567 6 2339 128 102 14 1479 310 216 60 79 559 298 1600 64 8 3
23 530 v 23 040 v 25 270 v 31 380 v 12 580 v 21 450 v 11 400 v 22 200 v 23 170 v 24 450 v 15 290 v 11 020 v 27 290 v 17 270 v 24 460 v 22 430 v 22 390 v 10 140 v 26 450 v 12 550 v 19 070 v 13 220 v 21 060 v 28 350 v 25 360 v 11 400 v 18 320 v 21 140 v 25 340 v 8 290 v 20 540 v 17 430 v
91 150 v 72 380 v 81 440 v 74 520 v 77 550 v 72 110 v 19 460 v 73 160 v 77 210 v 84 570 v 73 490 v 77 030 v 95 010 v 78 200 v 93 540 v 75 480 v 88 270 v 77 280 v 80 530 v 74 530 v 72 510 v 77 410 v 79 030 v 77 120 v 85 060 v 92 420 v 73 510 v 81 390 v 90 530 v 76 570 v 70 220 v 83 140 v
v
v
v
v
20 C
22 C
24 C
26 C
28 C
5 4 5 7 7 3 – 5 5 5 – 3 6 4 7 6 4 12 5 – 3 12 4 4 5 – 5 4 9 – 3 2
6 6 6 7 9 4 1 5 6 5 2 5 7 6 9 7 5 12 7 – 3 12 6 5 5 – 7 6 12 – 5 3
7 6 6 8 12 5 4 6 8 5 5 12 7 9 12 9 5 12 7 6 5 12 7 6 7 1 10 6 12 4 7 3
12 7 7 9 12 9 6 9 9 5 11 12 9 10 12 12 6 12 8 12 8 12 10 7 7 12 12 9 12 12 7 6
12 12 9 12 12 12 11 11 10 11 12 12 12 11 12 12 12 12 10 12 12 12 11 9 11 12 12 10 12 12 9 6
msl, mean sea level.
A nomograph for representing the effect of different input parameters on the potential number of households using DSWHS in India is shown in Fig. 10. It allows for a wide range of choices of the values of the input parameters and can be used for a quick estimation of the potential number of households who can use DSWHS in the country. The potential number of households using DSWHS depends on the cost of the DSWHS (and consequently the amount of loan to be taken by the end user), interest rate applicable on the loan amount, the number of loan repayment installments and other factors such as availability of space for
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Fig. 9. Effect of varying fuel price escalation rate on NPV and IRR.
installation, access to solar radiation, knowledge and motivation to purchase solar water heating system, etc. In order to decide about the capability of a household to purchase a DSWHS, the equated monthly installment as obtained in Fig. 10(a) is multiplied by a certain multiplication factor in Fig. 10(b) to provide the required annual income levels. The values of the multiplication factor can vary from household to household depending upon a variety of their socio-economic requirements and constraints. These required income levels are then compared with the household income distribution of the country [3] in Fig. 10(c) to provide the maximum number of household who can afford to invest in the purchase of a DSWHS. Finally Fig. 10(d) provides the estimates for the potential DSWHS used in the country in view of the fact that only a certain fraction of the total number of households obtained in Fig. 10(c) will be able to use the DSWHS due to limitations on availability and access to solar radiation, motivation, etc. An example of using the nomograph is also shown in Fig. 10 using thicker line with arrows. In this case loan of Rs. 20,000 with a repayment period of 4 years is considered, the corresponding equated monthly installment is found to be Rs. 450 for a multiplication factor of 60, the required annual income is Rs. 27,000 and the corresponding number of household in India (1998) is 75.02 millions. If it is assumed that only 60% of these households have access to solar radiation, the final potential number of households who can use DSWHS in India is estimated to be 45 millions.
6. Conclusions The study presented in this paper can be used to undertake a detailed technoeconomic evaluation of DSWHS. The paper also presents inputs for potential
332
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Fig. 10. Nomograph to determine the potential number of households who can use DSWHS in India.
assessment of using solar water heating system in India as well as for estimating their capacity utilization. References [1] Ministry of Non-conventional Energy Sources. Government of India. Annual report 2001–2002. p. 50. [2] Indian Metrological Department. Climatological tables 1951–1980, published by the Government of India, 1999. [3] National Council for Applied Economic Research (NCAER). India market demographics report 1998. p. 82.
Techno-economic evaluation of domestic solar water heating systems in India B. Chandrasekar, T.C. Kandpal Centre for Energy Studies, Indian Institute of Technology Delhi, Haus Khaz, New Delhi 110016, India Received 19 May 2003; accepted 11 June 2003
Abstract The most wide spread thermal use of solar energy, so far, has been for water heating. Solar water heating systems have been commercialized in many counties in the world. Though the technical feasibility of domestic solar water heating systems (DSWHS) has long been established, their financial viability needs to be carefully examined, particularly in tropical countries with relatively lower annual capacity utilization and poor purchasing power of potential users. The potential number of Indian households who can invest in DSWHS have been estimated based on the income distribution in the country, the capital cost of solar water heating systems, interest rate charged on the loan provided for the purchase of DSWHS etc. Using the seasonal and diurnal variation of ambient temperatures at many locations in the country, the periods with annual hot water requirement have been identified. A simple framework for financial evaluation of DSWHS has also been presented. The results of some typical exemplifying calculations have been presented and discussed. # 2003 Elsevier Ltd. All rights reserved. Keywords: Potential users; Domestic solar water heating systems; Capacity utilization; Technoeconomics
1. Introduction Significant efforts have been made towards the development and dissemination of domestic solar water heating systems (DSWHS) in India for the past two decades. The Government of India launched a demonstration program during 1980s
Corresponding author. Tel.: +91-11-265-91262; fax: +91-11-265-82037. E-mail address: [email protected] (T.C. Kandpal).
0960-1481/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0960-1481(03)00198-8
320
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for promoting DSWHS in the country. In order to promote the use of DSWHS, a variety of financial incentives have been offered to the end users [1]. These include capital subsidy, low interest loan, accelerated depreciation related benefit etc. However, the total collector area of DSWHS reportedly installed in the country so far (0.60 million square meters till December 2001) is below the expected levels of penetration. It is therefore critically important to study and analyze the role of different factors contributing to the dissemination and use of DSWHS in the country. A preliminary attempt to study the possible relationship between the seasonal and diurnal variations in ambient temperature at a place and the need of hot water for bathing has been made in this paper. The results obtained can be used to estimate the expected capacity utilization of DSWHS for different locations in the country. The income levels of the households directly affect their capacity to purchase DSWHS. Using the income distribution of households in the country, the capital cost of typical DSWHS, and the rate of interest on the loans provided to the users to purchase DSWHS, the potential number of households who can use DSWHS have also been estimated. From the above inputs as well as the prevailing estimates for the costs and benefits of DSWHS in India, a detailed financial evaluation has also been undertaken. The results of some typical calculations based on the above analysis are presented and briefly discussed.
2. Techno-economic evaluation One of the most critical factors in the dissemination of DSWHS is their financial viability. The monetary benefits accrued to the end users would depend on the amount and cost of fuel saved through the use of DSWHS. The efficiency of the DSWHS largely depends on the system design, the availability of solar radiation and ambient conditions. Another dimension of complexity in the financial evaluation of DSWHS is the seasonal variation in the hot water demand of the household for bathing purpose. In tropical areas, hot water may not be required during certain periods of the year. In such a situation, the effective capacity utilization of the water heating systems may be much lower resulting in increased unit cost of useful energy delivered by the DSWHS. 2.1. Determination of unit cost of useful thermal energy Unit cost of useful thermal energy provided by a DSWHS can be determined as the ratio of the total annual cost to the annual useful thermal energy delivered by the system, i.e., (" # ) d ð1 þ d ÞT þ m C0 ð1 þ d ÞT 1 UCute;s ¼ ð1Þ fV qCp ðTf Ti ÞN where q represents the density of water, C0 the capital cost of the DSWHS, Cp the specific heat of water, N the number of days in a year when the hot water is
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321
delivered and required by the user (usually this depends on the design of the system and its use), V the volume of daily hot water requirement of the household, f the fraction of total annual useful energy requirement for domestic water heating provided by the solar energy, Tf the outlet temperature of the hot water, Ti the temperature of inlet water to the tank, T the useful life of DSWHS, d the discount rate, and m the operation and maintenance cost as a fraction of the capital cost. The annual amount of fuel saved can be determined as Fs ¼
fV qCp ðTf Ti ÞN C v gf
ð2Þ
where Cv represents the calorific value of the fuel substituted (saved) by the DSWHS and gf the efficiency of utilization of the fuel for water heating. The monetary worth of annual fuel savings (Mwfs) can be calculated using the relation fV qCp ðTf Ti ÞN ð3Þ Mwfs ¼ pf Cv gf where pf is the unit price of fuel. The net annual monetary benefits (Bna) can be expressed as fV qVp ðTf Ti ÞN Bna ¼ pf mC0 C v gf
ð4Þ
2.2. Different financial figures of merit for DSWHS The cumulative present value of life cycle net benefits accrued to the end user due to purchase and installation of DSWHS can be determined using the following equation Bpv ¼ Bna PWFðd; TÞ
ð5Þ
where PWF(d,T) is the present worth factor for a discount rate d and the useful life T of DSWHS. The above expression assumes that the net annual monetary benefits accrued to the user is constant over the useful lifetime T of the DSWHS. However, it is expected that price of fuel saved (pf) would escalate in future resulting in increased monetary worth of annual fuel savings. The modified expression for the cumulative present value of net benefits can be expressed as "
# Bna 1þe T 0 Bpv ¼ 1 ð6Þ 1þd ðd eÞ where e is the annual rate of fuel price escalation. The following expressions can be derived for the various figures of merit used for evaluating the financial viability of an investment made on a DSWHS (without considering the escalation in the price(s) of fuel(s) saved by the DSWHS).
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2.2.1. Simple payback period The simple payback period (SPP) for a DSWHS can be determined as the ratio of the capital cost to the net annual benefits accrued to the user i.e., SPP ¼
C0 Bna
ð7Þ
2.2.2. Discounted payback period The discounted payback period (DPP) for a DSWHS can be determined using the relation DPP ¼
lnðBna Þ lnðBna dC0 Þ lnð1 þ dÞ
ð8Þ
2.2.3. Net present value The net present value (NPV) for DSWHS can be determined as the difference of present value of net annual monetary benefits to the capital cost of the system. For the case of uniform net annual benefits (Bna), the net present value (NPV1) can be expressed as NPV1 ¼ Bna PWFðd; TÞ þ
S C0 ð1 þ dÞT
ð9Þ
where S is the expected salvage value of DSWHS at the end of its useful life. For the case of non-uniform net annual benefits accrued to the user, the net present value (NPV2) can be expressed as ! T X Bna;j S NPV2 ¼ C0 ð10Þ þ j ð1 þ dÞT ð1 þ dÞ j¼1 where Bna,j represents the net annual benefits in the jth year. 2.2.4. Benefit to cost ratio The benefit to cost ratio (B/C) for a DSWHS can be determined as the ratio of net annual benefit to its capital cost. For the case of uniform net annual monetary benefits (Bna) the benefit to cost ratio, (B/C)1, can be expressed as S
Bna PWFðd; TÞ þ B ð1 þ dÞT ¼ C 1 C0
ð11Þ
For the case of varying net annual benefits due to the use of DSWHS the benefit to cost ratio (B/C)2 can be expressed as
PT Bna S
þ j¼1 j B ð1 þ dÞT ð1 þ dÞ ¼ ð12Þ C 2 C0 Eqs. (11) and (12) represent the ratio of net benefits to the capital cost. The following expressions can be used to determine the ratio of the present value of total
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life cycle benefits to the total life cycle costs. In the case of uniform annual monetary benefits and costs the expression is S
Mwfs PWFðd; TÞ þ B ð1 þ dÞT ¼ C 3 C0 ½1 þ mfPWFðd; TÞg In the case of varying annual monetary benefits, it is
PT Mwfs;j S
þ j¼1 j B ð1 þ dÞT ð1 þ dÞ ¼ C 4 C0 ½1 þ mfPWFðd; TÞg
ð13Þ
ð14Þ
where Mwfs,j represents the monetary worth of annual fuel savings, with subscript j representing the specific year and m the fraction of capital cost required for annual operation and maintenance of DSWHS. The annual operation and maintenance cost of the DSWHS is assumed to be constant over the useful life period in all the above four cases. 2.2.5. Internal rate of return The internal rate of return (IRR) on the investment made by the user on a DSWHS can be determined by equating the NPV to zero and then solving the equation for the discount rate. For the case of uniform net annual monetary benefits, it is determined by solving the equation ð1 þ IRRÞT 1 S Bna C0 ¼ 0 ð15Þ þ ðIRRÞ ð1 þ IRRÞT ð1 þ IRRÞT For the case of varying net annual monetary benefits accrued due to DSWHS the IRR is obtained by solving the following equation T X j¼1
Bna;j S þ C0 ¼ 0 j ð1 þ IRRÞT ð1 þ IRRÞ
ð16Þ
3. Hot water requirement based on seasonal variation of ambient temperature at different locations Hot water requirement for domestic purposes would essentially depend upon the prevailing temperatures at a location. One of the primary uses of hot water in the Indian households is for taking a bath in the early mornings or late evenings (in some locations). In the present study, the case of morning baths have been considered as majority of Indian households prefer early morning bath (5–7 a.m.). Though the water temperature required for taking the bath would vary with indiv vidual preferences, water temperatures in the range of 32–35 C is reportedly preferred by majority of households. It is with this assumption that an attempt has been made to determine the number of months in a year when hot water will be required by households for different locations in India using the temperature data
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available from the Indian Metrological Department [2]. In this study, it is assumed that if the average temperature between 5 and 7 a.m. is less than a pre-specified temperature (Tspc), the household would require hot water for taking a bath. As the value of Tspc would also vary from person to person, the analysis has been v made for six different values of Tspc. These are 20, 22, 24, 26 and 28 C.
4. Estimation of the potential number of households capable of investing in domestic solar water heating An attempt has also been made to estimate the potential number of households who can afford to purchase and install DSWHS in India. This would essentially depend upon the income levels of households in the country, capital cost of DSWHS, and the number and timings of repayment installments. It is assumed that the potential households would in general prefer availing the facility of low interest loan for the purchase and installation of DSWHS. It is also assumed that the loan is repaid in equal monthly installments. In such a case, the monthly repayment installment (MRI) would depend on the capital cost, rate of interest charged on the loan amount and the total number of repayment installments. The MRI can be determined as MRI ¼ FC0
de ð1 þ de ÞN ð1 þ de ÞN 1
ð17Þ
where C0, represents the capital cost of DSWHS, F the fraction of capital cost available as loan amount to the household, N total number of repayment installments, and de the monthly interest rate. If the annual loan repayment amount is less than a specified fraction of gross annual income of the household, it is considered capable of investing in the purchase of DSWHS.
5. Results and discussion Using simple formulations presented in the above sections, some exemplifying calculations have been made. Table 1 briefly presents the estimates of unit cost of useful thermal energy provided by some of the conventional domestic water heating options. Since the cost of the equipment has not been taken into the calculations, the values of Ucut,e presented in Table 1 always underestimate the corresponding actual values. However, the difference between the two values shall not be significant for most commonly used appropriate domestic water heating appliances. It may be noted from Table 1 that the unit cost of useful thermal energy provided by different conventional options varies considerably. The efficiency of fuel utilization and unit price of fuel used for water heating have maximum effect on the unit cost of useful thermal energy delivered. The estimates of unit cost of useful thermal energy delivered by the DSWHS are presented in Table 2. As expected, the
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Table 1 Unit cost of useful energy for different conventional domestic water heating options Fuel
Electricity LPG Kerosene Fuel wood Natural gas a
Unit (MJ/unit)
Calorific value Utilization efficiency
Unit price of fuel (Rs/unit)
a
kW h kW h kg kg kg kg kg kg m3 m3
3.6 3.6 45 45 45 45 16 16 39 39
3 5 16 25 7.5 14 1.5 1.5 2.0 2.5
0.93 1.54 0.59 0.93 0.42 0.78 0.94 0.38 0.08 0.11
0.9 0.9 0.6 0.6 0.4 0.4 0.1 0.25 0.6 0.6
Ucut,e (Rs./MJ)
Ucut,e represents unit cost of useful thermal energy.
Table 2 Unit cost of useful thermal energy delivered by a DSWHS Capital cost (Rs.) 15,000
20,000
25,000
Capacity utilization 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Unit cost of useful thermal energy delivered (Rs./MJ) d ¼ 0:06
d ¼ 0:08
d ¼ 0:10
d ¼ 0:12
2.55 1.27 0.85 0.64 0.51 0.42 0.36 0.32 0.28 3.40 1.70 1.13 0.85 0.68 0.57 0.49 0.42 0.38 4.25 2.12 1.42 1.06 0.85 0.71 0.61 0.53 0.47
2.87 1.43 0.96 0.72 0.57 0.48 0.41 0.36 0.32 3.82 1.91 1.27 0.96 0.76 0.64 0.55 0.48 0.42 4.78 2.39 1.59 1.19 0.96 0.80 0.68 0.60 0.53
3.21 1.60 1.07 0.80 0.64 0.53 0.46 0.40 0.36 4.28 2.14 1.43 1.07 0.86 0.71 0.61 0.53 0.48 5.34 2.67 1.78 1.34 1.07 0.89 0.76 0.67 0.59
3.56 1.78 1.19 0.89 0.71 0.59 0.51 0.45 0.40 4.75 2.38 1.58 1.19 0.95 0.79 0.68 0.59 0.53 5.94 2.97 1.98 1.48 1.19 0.99 0.85 0.74 0.66
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Fig. 1. Effect of discount rate on NPV and B/C.
unit cost of useful thermal energy delivered critically depends upon the total number of days when the DSWHS delivers hot water or is used by the investor. The unit cost is comparable to that for the cheapest of the conventional water heating options for high values of capacity utilization of DSWHS and/or low values of discount rates. The effects of discount rate used in the financial evaluation exercise, useful life of the DSWHS, capital cost and the fraction of capital cost spent annually on operation and maintenance on the NPV and IRR are shown in Figs. 1–4, respectively. The base values used in these calculations are given in Table 3. The curves showing the effect of discount rate (Fig. 1) and useful life period (Fig. 2) can also be used in analyzing the effect of availability of soft loan for the purchase and installation of
Fig. 2. Effect of useful lifetime on NPV and B/C.
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Fig. 3. Effect of capital cost on NPV and B/C.
DSWHS. Fig. 3 illustrates the effect of capital subsidy on the NPV and the B/C. As expected, there is a reduction in both the financial figures of merit with an increase in the capital cost. One of the key factors, which influences the penetration of new technologies, is the operation and maintenance cost of the system. Fig. 4 represents the effect of annual operation and maintenance cost (expressed as fraction of capital cost) on NPV and B/C. The effect of net annual benefits accrued to the end user of DSWHS on the NPV and IRR is illustrated in Fig. 5. One of the important issues in the financial viability of DSWHS is the capacity utilization of the system during the year. Due to seasonal change in the requirement of hot water in many areas of the country, the effective utility of DSWHS to some users may be limited (3–6 months of winter season only).
Fig. 4. Effect of annual operation and maintenance cost (as a fraction of capital cost) on NPV and B/C.
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Table 3 Base values used in calculations Input parameter
Symbol
Unit
Value
Capital cost Capacity Useful lifetime Discount rate Annual repair and maintenance cost (as a fraction of capital cost) Unit cost of electricity Initial temperature of water Final temperature of water Days of annual hot water requirement
C0 V T d
Rs. l/day Years Fraction
20,000 100 10 0.10
m
Fraction
0.02
– Ti Tf –
Rs./kW h v C v C Days
3 15 60 200
The effect of capacity utilization on the NPV and B/C is illustrated in Fig. 6. Fig. 7 represents the effect of capacity utilization factor on SPP and DPP. The results exemplify a linear reduction in the SPP and DPP with the increase in the capacity utilization factor. In urban areas, the DSWHS usually save electricity. Effect of cost of electricity to the user on the NPV due to investments made in DSWHS is shown in Fig. 8. The effect of varying fuel price escalation rate on NPV and IRR is shown in Fig. 9. Table 4 presents the variation of early morning (5–7 a.m.) ambient temperatures at different locations in the country. Obviously, the duration of the residential hot water demand for taking a bath in the morning varies with the location as well as the value of Tspc. For example, out of the 32 locations considered in the study, 19 v locations would need hot water for 6 months in a year if Tspc is assumed at 22 C. v If Tspc is increased to 28 C, the hot water will be required for 12 months in a year at 21 locations. The results presented in this table can be used for estimating the capacity utilization of the DSWHS for a specified value of Tspc at a location.
Fig. 5. Effect of annual net monetary benefits on NPV and IRR.
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Fig. 6. Effect of capacity utilization factor on NPV and B/C.
Fig. 7. Effect of varying the capacity utilization factor on SPP and DPP.
Fig. 8. Effect of varying the unit cost of electricity on NPV and B/C.
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Table 4 Estimated period (months) of DSWHS at different locations in India Locations
Elevation (in Latitude meters) msla (N)
Longitude (E)
Number of months in a year with temperature less than (during 5–7 a.m.) v
Agartala Ahmedabad Allahabad Amritsar Bangalore Bhavnagar Chennai Baroda Bhopal Gaya Goa Coimbatore Dibrugrah Hyderabad Imphal Indore Kolkatta Kodaikanal Lucknow Mangalore Mumbai Nandi Hills Nagpur New Delhi Patna Port Blair Pune Raipur Shillong Trivandrum Veraval Vizagpattnam a
16 55 98 234 921 5 12 38 523 116 55 397 111 545 781 567 6 2339 128 102 14 1479 310 216 60 79 559 298 1600 64 8 3
23 530 v 23 040 v 25 270 v 31 380 v 12 580 v 21 450 v 11 400 v 22 200 v 23 170 v 24 450 v 15 290 v 11 020 v 27 290 v 17 270 v 24 460 v 22 430 v 22 390 v 10 140 v 26 450 v 12 550 v 19 070 v 13 220 v 21 060 v 28 350 v 25 360 v 11 400 v 18 320 v 21 140 v 25 340 v 8 290 v 20 540 v 17 430 v
91 150 v 72 380 v 81 440 v 74 520 v 77 550 v 72 110 v 19 460 v 73 160 v 77 210 v 84 570 v 73 490 v 77 030 v 95 010 v 78 200 v 93 540 v 75 480 v 88 270 v 77 280 v 80 530 v 74 530 v 72 510 v 77 410 v 79 030 v 77 120 v 85 060 v 92 420 v 73 510 v 81 390 v 90 530 v 76 570 v 70 220 v 83 140 v
v
v
v
v
20 C
22 C
24 C
26 C
28 C
5 4 5 7 7 3 – 5 5 5 – 3 6 4 7 6 4 12 5 – 3 12 4 4 5 – 5 4 9 – 3 2
6 6 6 7 9 4 1 5 6 5 2 5 7 6 9 7 5 12 7 – 3 12 6 5 5 – 7 6 12 – 5 3
7 6 6 8 12 5 4 6 8 5 5 12 7 9 12 9 5 12 7 6 5 12 7 6 7 1 10 6 12 4 7 3
12 7 7 9 12 9 6 9 9 5 11 12 9 10 12 12 6 12 8 12 8 12 10 7 7 12 12 9 12 12 7 6
12 12 9 12 12 12 11 11 10 11 12 12 12 11 12 12 12 12 10 12 12 12 11 9 11 12 12 10 12 12 9 6
msl, mean sea level.
A nomograph for representing the effect of different input parameters on the potential number of households using DSWHS in India is shown in Fig. 10. It allows for a wide range of choices of the values of the input parameters and can be used for a quick estimation of the potential number of households who can use DSWHS in the country. The potential number of households using DSWHS depends on the cost of the DSWHS (and consequently the amount of loan to be taken by the end user), interest rate applicable on the loan amount, the number of loan repayment installments and other factors such as availability of space for
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Fig. 9. Effect of varying fuel price escalation rate on NPV and IRR.
installation, access to solar radiation, knowledge and motivation to purchase solar water heating system, etc. In order to decide about the capability of a household to purchase a DSWHS, the equated monthly installment as obtained in Fig. 10(a) is multiplied by a certain multiplication factor in Fig. 10(b) to provide the required annual income levels. The values of the multiplication factor can vary from household to household depending upon a variety of their socio-economic requirements and constraints. These required income levels are then compared with the household income distribution of the country [3] in Fig. 10(c) to provide the maximum number of household who can afford to invest in the purchase of a DSWHS. Finally Fig. 10(d) provides the estimates for the potential DSWHS used in the country in view of the fact that only a certain fraction of the total number of households obtained in Fig. 10(c) will be able to use the DSWHS due to limitations on availability and access to solar radiation, motivation, etc. An example of using the nomograph is also shown in Fig. 10 using thicker line with arrows. In this case loan of Rs. 20,000 with a repayment period of 4 years is considered, the corresponding equated monthly installment is found to be Rs. 450 for a multiplication factor of 60, the required annual income is Rs. 27,000 and the corresponding number of household in India (1998) is 75.02 millions. If it is assumed that only 60% of these households have access to solar radiation, the final potential number of households who can use DSWHS in India is estimated to be 45 millions.
6. Conclusions The study presented in this paper can be used to undertake a detailed technoeconomic evaluation of DSWHS. The paper also presents inputs for potential
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Fig. 10. Nomograph to determine the potential number of households who can use DSWHS in India.
assessment of using solar water heating system in India as well as for estimating their capacity utilization. References [1] Ministry of Non-conventional Energy Sources. Government of India. Annual report 2001–2002. p. 50. [2] Indian Metrological Department. Climatological tables 1951–1980, published by the Government of India, 1999. [3] National Council for Applied Economic Research (NCAER). India market demographics report 1998. p. 82.