Economy & Energy
Year VIII -No 47:
December 2004  January 2005
ISSN 1518-2932

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 Promotion of solar energy for water heating in the Residential Sector

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Omar Campos Ferreira.

Advisor S&T Management. of the

Secretariat of Science and Technology of  Minas Gerais, Brazil


                The objective of the present article is to analyze the difficulties regarding the generalized use of solar energy for water heating and to present suggestions to circumvent them.

                The use of solar energy reduces both the cost of water heating at low temperature and the investment relative to electricity generation and distribution and therefore it is advantageous to the user and to the electric energy utility. However, the initial investment for the installation is larger than that corresponding to other heating modalities, inhibiting the initiative of the user to substitute the electric shower by solar heating. The apparent solution would be to combine the investment capacity of the electricity companies with the user’s willingness to pay.

                It is suggested that the concessionaires takes on the investment, at interest charges, to be paid by the user,  equivalent to the investment for generation capacity, considering the lifetime of the solar installation..

1 - Introduction

The use of electricity for water heating at low temperature (40-50o C)  is a peculiarity of the Brazilian  energy system, that is historically explainable by the low cost of hydroelectric generation and by the shortage of fossil fuels. From the physical point of view, this use is considered as energy dissipation since the generation of one electric energy unit  via thermodynamic cycle requires between 2 to 4 heat units.

However, the convenience of electricity use makes it difficult to break the national habit of using electrical showers, faucets and ovens, which  could be substituted by fueled appliances. In the case of electrical showers and faucets, the most rational electricity substitution would be by solar energy that is clean, safe and of low cost.

In spite of all these advantages, the electricity user remembers solar energy only in time of crisis such as the 2001 rationing.  Initiatives to break this impasse have been taken but the results are still modest. However, the growing electricity participation in energy demand at growing costs imposes measures regarding the incentive of solar energy use.

2 – Use of electricity for water heating  in the Residential Sector.

                 It is estimated by CEMIG (Companhia Energética de Minas Gerais) that in 1996 about 4.5% of its total load (34.5 TWh) was used for water heating: on the average, each residence of Minas Gerais used 37 kWh/month for this purpose (“CEMIG in Números/2002”).,  It was estimated that In 1999 670l/apartment were consumed, corresponding to 615kWh/apartment/month (“Utilização de Aquecimento Solar para a Redução da Demanda no Horário de Ponta – Informações para Participação no Projeto”, CEMIG,1999). In this large consumption value one can find situations where substitution is economically viable vis-à-vis the concessionaire’s tariff. As a starting point  for evaluating the viability, we have estimated, just for shower purposes, an average consumption of 300l/day at 40o C[1]. The alternatives are electric shower, LPG heater and solar installation. The corresponding costs for the user, at retail prices, were calculated and are  shown in the following table.


Costs R$/day

Electric shower

LPG Heater

Flat-plate Solar Collector

Investment R$




Lifetime - years




Investm. cost (*)





7,33 kWh

0,71 kg

1,83 kWh (#)









(*) interests rate: 12% annually, exchange rate 3,20 R$/US$.  (#) it is assumed that solar energy substitutes 75% of the electricity used.  (+) efficiency is substituted by  the commercial parameter : 100l/day of hot water / m2of flat-plate solar collector.


The calculation shown above has considered only the direct factors, and it should be also taken into account the architectural project adaptation, the implementation of hot water supply piping and other less important factors in new projects but that are important when dealing with built houses and structures.

However, the cost difference of solar energy in the studied case is sufficiently large to absorb these additional factors without considerably changing the sketched scenery.

In the case of apartment buildings, there are other favorable and unfavorable components regarding the solar cost. There are rather complete studies for these cases that show the competitiveness of the solar installation.[2]

As a first approximation, the main obstacle for using solar energy is the financial one, since the initial cost for the user is larger than that of the other modalities, whereas the operation and maintenance cost is practically zero. The main ways to circumvent this difficulty would be: a) make very expensive the use of electricity for water heating at on-peak hours (between 17 and 23hs); b) fix taxes for the fabrication of undesired electrical appliances; c) motivate the use of solar energy by financing the user with interest rates equal to those paid to the market by the concessionaires.

We think that restrictive measures should be avoided if there is a constructive solution, as neither the Government nor the concessionaires have been disturbed by the peak load consumption before the 2001 supply crisis. The special tariff for the peak load would rather be another protective measure concerning the concessionaires’ economy  than attending the users’ convenience. We are considering in the present study the possibility of a cooperative solution between concessionaire and user.


 3 – Proposal for the creation of a “solar energy investment fund”.

The structure of the present proposal aims at conciliating the interest of both the concessionaire and the electricity user and so the points of view of those involved in the question should be examined. From the concessionaire’s point of view the parameters of interest are:

a – Investment in electricity generation, transmission and distribution.

The process of the Electric System restructuring makes it difficult, to a certain measure, the evaluation of these investments as the three basic functions would be executed by different entities. In the past, when only one agent was responsible for these functions, the investment structure was known: 59% for generation, 25% for transmission, 11% for distribution and the remaining 5% for general installations. In the last invitation to bid carried out by ANEEL, the average direct investment  was estimated as 770 US$/kW; including the interests during construction, generation investment reaches US$ 1.000/kW[3]  and the total investment is close to  1.700 US$/kW.

b – Power reserve for supplying peak load.

From the daily residential sector load (of August 1996) and the number of residences served, one infers that the peak load due to shower was about 300 Wh/h.res. In round numbers, between 1996 and 2000 the residential consumption in the CEMIG System has grown 26% and the population in Minas Gerais grew 6% and so, as we do not have updated figures, consumption per residence grew 20%. Assuming that the residential consumption structure has not been substantially changed, it is estimated that consumption for water heating has grown proportionally to the total consumption by residence (20%), reaching 360 Wh/h.res. Taking into account the energy loss in transmission and distribution (15%, according to BEN/2000), the reserved power[4] has been calculated to be 415 W/res. Therefore, the load reserve investment  is about US$ 705/residence, equivalent to about R$ 2,470/residence, at an exchange rate at the time when the prices of the solar installation were collected (R$ 1,800 for flat-plate collectors, stainless steel reservoir, piping, isolation and electric complementation).

It should be observed that the unit investment in hydroelectric power plants tends to grow and investment in solar installation tends to decrease due to scale production, if the adequate financing mechanism is found. So, one may consider that investment in power reserve already exceeds investment in solar energy  and the difference tends to increase.[5]

c -capacity factor in the peak load.

The capacity factor can be calculated from the daily curve of the residential load, shown below, but it is necessary to weight the average monthly curves. Furthermore, the peak capacity does not  exclusively supply to water heating as the system is operationally flexible to accommodate the different load curves of the other sectors (industrial, commercial, public illumination, etc.). Therefore, it seems more appropriate to use a historical series of the capacity factor concerning the Public Service thermoelectric power plants, usually employed for complementing the hydroelectric power plants. Between 1984 and 1999, the average value of this factor was 0.25 which is used in the following calculation.

d - generation, transmission and distribution costs  at on-peak hours in the Residential Sector

For calculating the electricity supply cost at the residential on-peak load hours (except charges and taxes), we have adopted a simplified procedure based on the generation cost structure (financial costs, operation, maintenance and others) assuming that the structure is approximately the same in the three functions. Using the global cost previously calculated (US$ 1,700/kW), 12% annual interest rate and the historical capacity factor for peak generation (0.25) and excluding the public goods use, one obtains the cost below:


Costs – R$/MWh

Investment                                                                            371

Operation / maintenance                                                    22


                              Total                                                         393


The generation cost at residential on-peak load hours is considerably higher than the residential tariff, which is R$ 262/MWh (less taxes). Therefore, the concessionaire would economize if it could eliminate supply at on-peak  hours.

It is the interest of the user to reduce water heating charges as most of them have no access to financial investment that could be more attracting than the economy obtained by using solar energy; the interest of the concessionaire is to avoid investment with a lower interest rate and get rid of supplying electricity at a tariff lower than its cost. Therefore, it seems that, considering the lower cost possibility for both parts, an initial encouragement  would suffice to attain the desired substitution.

4 – The “solar fund”  investment.

One of the ways to give an initial impulse would be to establish a solar energy investment fund with an initial financial resource equivalent to the unused investment for reserve capacity to supply the peak load due to electric shower. Concessionaires with power company characteristics (not limited to electricity generation) could administer the fund, by modifying the legislation of public service concession which would impose the use of solar installation for new users. This scheme would permit linking  the amortization collection paid by the user to the electricity bill, using the existing administrative structure and this amortization would be a fraction of the tariff, guaranteeing the benefits along time for both the concessionaire and the user. For the concessionaire, the electricity cost  at on-peak  hours (in the new situation), on the average, would be about R$0.13/kWh or about 50% of the residential tariff (less tax). Therefore, the fund’s administration cost can be considered as well paid as long as the tariff  is not changed as a function of the solar energy incorporation to the social objective of the concessionaire. Otherwise, the tariff could be revised to accommodate the different cost changes.[6] 

Let us assume that an investment fund has been established with an initial allocation equivalent to N0 solar installations with a feedback equal to the amortization paid by the user. One assumes a linear financial chronogram so that half of the amortization corresponding to the annual installation increment is reinvested in the same year. Let a (R$/residence.year) and p (R$/residence) be the amortization value and the installation price, respectively. The fund evolution is described by the equation:

Ni –Ni-1 = [N0 + (Ni –Ni-1)/2 ]a/p

At the end of the solar installation lifetime, estimated as 15 years, it is necessary to incorporate a progressive “withdrawal” term : 

Ni –Ni-1 = [N0 + (Ni –Ni-1)/2 ]a/p - Ni-15

The calculation is exemplified in Graphic 1 from the results of the following table for the minimum amortization, corresponding to the user’s expenses regarding water heating (a = 365 x R$ 1,35 = R$ 493/year), retail price of the solar installation (p = R$ 1.800) and fund allocation equivalent to the price of 1,000 solar installations (No = 1.000).

Graphic 1 – Evolution of the “ Solar Investment Fund ”.







(Ni-Ni-1- Ni-15)

































































































 It can be noted in the graphic that the withdrawal of 15-year old installations only produces a small drop in the 16º year that is readily regained. Therefore, the investment fund can be self-sustained and after 30 years the installation cost for the financer would be 4% of the present cost for the user. Other amortization and price (that one hopes will decrease with scale production) schemes could be adopted to evaluate a better solution.

5 – Modalities of solar energy absorption.

The calculations presented have as reference the absorption by flat-plate solar collectors but  they are equally valid  for heat pumps whose cost and useful life are comparable to that of flat-plate collectors.[7] The pump has the advantage of operating without direct solar radiation with a better performance.  Regarding  peak load reduction, these installations have rather different performances. Solar panel absorption has a more drastic reduction than the pump in periods of faint sun light which could bring back the peak load; in the case of the pump, the effect would be  extending its operation time that would occur outside the on-peak hours if the device is adequately designed.

It is possible to associate collector and pump in series or in parallel but data for cost calculation are insufficient.

In any case, the generalized use of solar energy is confronted with the apparently trivial problem of adapting residences that have no hot water line. Considering that the Brazilian population and that the urbanization process have already surpassed their inflection points, this problem limits the solar energy market.  It seems that there is room for the  development of remote control systems for hot and could water fluxes using a mixer upstream the existing valve. Regarding collectors, there still are requirements for the flat-plate positioning and water reservoirs.


6 – Effect of substitution on  capacity factor of the electric sector.

The proposed substitution effect can be evaluated considering the CEMIG’s daily load curve in August 1996, adopting the following simplifications:

-                       the peak demand was satisfied by importing energy from other concessionaires (in the considered year, CEMIG’s thermal generation was negligible and imports were 43% of the total offer, exceeding exports);

-                       the load factor in the CEMIG system, relative to the energy supplied to the market, was equal to the average factor in the Brazilian interconnected system, about 0.57;

-                       the power “reserved” for supplying the peak load was  1.370 MW, the  total load was 108,800 MWh/day (numerical integration  of the total load curve) and the energy absorbed by the electric showers  was 5.830 MWh/day, as shown in graphics 2 e 3, obtained from CEMIG’s publications;


Solar water heating

Graphic 2 –Residential load curve.


Graphic 3 –Total daily load and shower daily load.
(constructed using CEMIG’s data).

Calculations were carried out with the following data:

-                       Effective power (considering electric energy imports and exports) for supplying the  total daily load:

Pef = 108.800 MWh/day / (24 h/day x 0,57) = 7.953 MW.

-                       Effective power reduction, assuming that the solar installation will supply  75% of the showers load:

ef = 7.953 – 0,75 x 1.370 = 6.926 MW.

-                       Reduced daily load:

W´ = 108.800 – 0,75 x 5.830 = 104.400 MWh/day.

-                       Modified capacity factor :

FC´= 104.400 MWh/day / (24 h/day x 6.926) = 0,63

-                       Efficiency gain (lato sensu) of the electrical system:

∆FC/FC = (0,63-0,57) / 0,57 = 10,5%.

The calculation gain should be considered as a preliminary information about the maximum expected benefit since the fund implementation would be gradual; furthermore, it should be noticed that  the data used are not the average ones for the whole interconnected system and that they are limited to an atypical month (end of winter) when consumption for water heating is naturally larger than the average consumption. However, it seems that it is worthwhile to follow this objective because it is generally difficult to obtain such gains in a system that is rather developed in its operational and economic aspects.


7 - Conclusion.

There is a potential for financing the acquisition of solar installations in favorable conditions both for the user and the concessionaire. One of the possible forms would be to incorporate solar energy absorption to the social objective of the concessionaire , once the necessary legal changes are made. So the concessionaire would finance the user with resources equivalent to the unused investment for load capacity, charging in the electricity bill an amortization equal to the cost of solar energy absorption and reinvesting the collected resources in new solar installations

The advantage for society  would be the better use of renewable energy resources, at a lower cost and in a distributed form, avoiding the frequent residential tariff increase  and creating occupations (if not jobs) for a larger numbers of workers.

Therefore, it seems that the “Solar Fund” can make the  “Paretian optimum” dream come true, that is, it would allow to  modify the energy system for the benefit of all involved in the  “energy business”.


[1] Prices used in the calculation were collected by phone and the electricity tariff is that of  CEMIG plus 30% taxes. 

[2]  See for example : “Seminário sobre Aquecimento Solar como Alternativa de Conservação de Energia”, CEMIG, 1987.

[3] The interest rates were assumed as 12% annually. The 2001-2011 Decennial Plan considers an interest rate of 15% annually.

[4] For the consuming upper category the value can reach 700 W/residence.

[5] It would be more appropriate to compare investments in different modalities of solar energy absorption, since water accumulation reservoirs above the average level of  oceans is also a form solar energy absorption.

[6] This report does not intend to solve all the details regarding substitution  but only to show its viability.


[7] I thank  Prof. Mauri Fortes for the information about the development of the thermal pump model for residential use.

Graphic Edition/Edição Gráfica:
Editoração Eletrônic

Tuesday, 11 November 2008

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