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May 25th, 2020
The thermal analysis of collector storage walls is presented in Section 6.2.1, Chapter 6, where a diagram of the wall and the thermal gains and losses are given. The unutilizability concept, developed by Monsen et al. (1982), can also be applied in this case to determine the auxiliary energy required to cover the energy supplied by the solar energy system. Again here, two limiting cases are investigated: zero and infinite capacitance buildings. For the infinite thermal capacitance case, all net monthly heat gain from the storage wall, Qg, given by
Life cycle analysis is performed annually and the following are evaluated according to Eq. (12.10) to find the solar savings:
• Fuel savings.
• Extra mortgage payment.
• Extra maintenance cost.
• Extra insurance cost.
• Extra parasitic co...
Read MoreDue to the nature of the economic analysis, i. e., predicting the way various costs will occur during the life of a solar energy system, a number of uncertainties are involved in the method. The person responsible for the economic analysis of a solar energy system must consider a number of economic parameters and how these will develop in the years to come. A usual technique is to find how these parameters were modified during the previous years and expect that the same behavior will be reflected in the future years. These two periods are usually equal to the expected life of the system. Additionally, the prediction of future energy costs is difficult because international oil prices change according to the quantity supplied by the oilproducing countries...
Read MoreAs we have already seen in solar energy system design, the collector area is considered as the primary parameter for a given load and system configuration. The collector area is also the optimization parameter, i. e., the designer seeks to find the collector area that gives the highest life cycle savings. A method for the economic optimization was given in Section 12.2.3, in which life cycle savings
FiGURE 12.3 Optimum collector area determination from the slope of the Fversus Ac curve. 
are plotted against the collector area, Ac, to find the area that maximizes savings. The optimization procedure can be simplified if life cycle savings (LCS) can be expressed mathematically in terms of the collector area. Therefore, the optimum is obtained when
d(LCS) = 0
dAc
or, by using Eq. (12...
Read MoreAnother way of viewing the calculations of Example 12.7 is to obtain the present worth of each column and sum them to obtain the present worth of solar savings, using appropriate signs for each column. Therefore, the life cycle savings (LCS) of a solar energy system over a conventional system is expressed as the difference between a reduction in the fuel costs and an increase in expenses incurred as a result of the additional investment required for the solar energy system, given by
LCS = PjCF1FL – P2Cs
where
Pi = ratio of life cycle fuel cost savings to firstyear fuel savings.
P2 = ratio of life cycle expenditure incurred from the additional investment to the initial investment.
The economic parameter P1 is given by
P1 = (1 – Cte) PWF(ne, iF, d) (12.32)
where
te = effective income ta...
Read MoreWhen a solar energy system is designed, the engineer seeks to find a solution that gives the maximum life cycle savings of the installation. Such savings represent the money that the user/owner will save because of the use of a solar energy system instead of buying fuel. To find the optimum size system that gives the maximum life cycle savings, various sizes are analyzed economically. When the present values of all future costs are estimated for each of the alternative systems under consideration, including solar and nonsolar options, the system that yields the lowest life cycle cost or the maximum life cycle savings is the most cost effective.
As an example, a graph of life cycle savings against the collector area is shown in Figure 12.1...
Read MoreThe example in this section considers a complete solar water heating system. Although different solar energy systems have different details, the way of handling the problems is the same.
A combined solar and auxiliary energy system is used to meet the same load as in Example 12.5. The total cost of the system to cover 65% of the load (solar fraction) is $20,000. The owner will pay a down payment of 20% and the rest will be paid over a 20year period at an interest rate of 7%. Fuel costs are expected to rise at 9% per year. The life of the system is considered to be 20 years, and at the end of this period, the system will be sold for 30% of its original value...
Read MoreThe first example is about the fuel cost of a nonsolar or conventional energy system. It examines the time value of an inflating fuel cost.
Calculate the cost of fuel of a conventional (nonsolar) energy system for 15 years if the total annual load is 114.9 GJ and the fuel rate is $17.2/GJ, the market discount rate is 7%, and the fuel inflation rate is 4% per year.
Solution
The firstyear fuel cost is obtained from Eq. (12.4) as
t
CL = CFL JLdt = 17.2 X 114.9 = $1,976.30
0
(because the total annual load is given, the integral is equal to 114.9 GJ).
The fuel costs in various years are shown in Table 12.4. Each year’s cost is estimated with Eq. (12.13) or from the previous year’s cost multiplied by
Table 12.4 Fuel Costs in Various Years for Example 12.5

In life cycle cost analysis, all anticipated costs are discounted to their present worth and the life cycle cost is the addition of all present worth values. The cash flow for each year can be calculated, and the life cycle cost can be found by discounting each annual cash flow to its present value and finding the sum of these discounted cash flows. Life cycle costing requires that all costs are projected into the future and the results obtained from such an analysis depend extensively on the predictions of these future costs.
In general, the present worth (or discounted cost) of an investment or cost (C) at the end of year (n) at a discount rate of (d) and interest rate of (i) is obtained by combining Eqs. (12.11) and (12.13):
Equation (12...
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