SOLAR ECONOMIC ANALYSIS Although the resource of a solar energy system, that is, the solar irradiation, is free, the equipment required to collect it and convert it to useful form (heat or electricity) has a cost. Therefore, solar energy systems are generally characterized by high initial cost and low operating costs. To decide to employ a solar energy system, the cost of collectors, other required equipment, and conventional fuel required as backup must be lower than the cost of other conventional energy sources to perform the same task. Thus, the economic problem is to compare an initial known investment with estimated future operating costs, including both the cost to run and maintain the solar energy system and auxiliary energy used as backup. Other factors that need to be considered include the interest paid on money borrowed, taxes if any, insurance cost if any, and resale of equipment at the end of its life. The objective of the economic analysis is to find the right size of a system for a particular application that gives the lowest combination of solar and auxiliary energy cost.

Since the availability of solar energy is intermittent and unpredictable, it is generally not cost effective to provide 100% of the energy requirements of a thermal system with solar energy year round. This is because, when the system satisfies fully the requirements under the worst operating conditions, it will be greatly oversized during the rest of the year, requiring the dumping of thermal energy, which is not cost effective. Usually, the other way around is effective, i.e., size the system to satisfy 100% the thermal energy requirements under the system’s best operating conditions, usually during summertime, and use auxiliary energy for the rest of the year to back up the solar energy system. The actual size is usually decided by following an economic analysis

Use of solar energy is in conjunction with the type and cost of the conventional fuel used as backup. The target is to design a solar energy system that operates at full or nearly full capacity most of the time and uses auxiliary energy for the rest of the year, although the total percentage of annual demand covered is less than 100%. It can easily be proved that such a system is much more economical than a larger system satisfying fully the thermal load year round. The auxiliary system can also cover the load in extreme weather conditions, thus increasing the reliability of the solar energy system. The annual load factor covered by solar energy compared to the total annual thermal load is called the solar fraction, f. It is defined as the ratio of the useful solar energy supplied to the system to the energy needed to heat the water or the building space if no solar energy is used. In other words, F is a measure of the fractional energy savings relative to that used for a conventional energy system. This is expressed in percentage, given by

Life cycle analysis The economic analysis of solar energy systems carried out to determine the least cost of meeting the energy needs, considering both solar and non-solar alternatives is called life cycle analysis. This method takes into account the time value of money and allows detailed consideration of the complete range of costs. It also includes inflation when estimating future expenses. Some of the criteria used to evaluate and optimize solar energy systems are: 1. Life cycle cost (LCC) is the sum of all costs associated with an energy delivery system over its lifetime in today’s money, taking into account the time value of money. LCC can also be estimated for a selected period of time. The idea of LCC is to bring back costs that are anticipated in the future to present-day costs by discounting, i.e., by calculating how much would have to be invested at a market discount rate. The market discount rate is the rate of return of the best alternative investment, i.e., putting the money (to be invested) in a bank at the highest possible interest rate.

2. Life cycle savings (LCS), for a solar plus auxiliary energy system, is defined as the difference between the LCC of a conventional fuel-only system and the LCC of the solar plus auxiliary system. This is equivalent to the total present worth of the gains from the solar energy system compared to the fuel-only system. 3. Payback time is defined as the time needed for the cumulative fuel savings to become equal to the total initial investment, i.e., it is the time required to get back the money spent to erect the solar energy system from the fuel savings incurred because of the use of the system. This time can be obtained with and without discounting the fuel savings. Other definitions of payback time are the time required for the annual solar savings to become positive and the time required for the cumulative solar savings to become zero. 4. Return on investment (ROI) is defined as the market discount rate that results in zero life cycle savings, i.e., the discount rate that makes the present worth of the solar and non-solar alternatives equal.

Life Cycle Costing Life cycle analysis, in fact, reflects the benefits accumulated by the use of solar energy against the fuel savings incurred. Compared to conventional fossil fuel systems, solar energy systems have relatively high initial cost and low operating cost, whereas the opposite is true for conventional systems. Therefore, in a naive selection, based on the initial cost alone, the solar energy system would have no chance to be selected. This is not the case when a life cycle analysis is employed, because it considers all costs incurred during the life of the solar energy system. Additionally, one should consider that, as the resource becomes scarce, oil prices will rise, and the higher the fuel cost replaced by the solar energy system, the better are the economic factors, such as the life cycle savings and the payback times.

In life cycle analysis, both the initial cost and the annual operating costs are considered for the entire life of the solar energy system. These include the initial purchase cost of the system, operating costs for fuel and electricity required for the pumps, interest charges on money borrowed, maintenance costs, and taxes paid, if applicable. There is also a salvage value, which is returned at the end of the life of the system, when the components are sold as scrap metal for recycling. The initial purchase cost should include the actual equipment cost, designer fee, transportation cost, labor cost to install the system, cost of brackets and any other modifications required to install the system, the value of space required to install the system if this is not installed on the roof of the building, and the profit of the installer. The actual equipment cost includes the solar collectors, storage tank, pumps or fans, piping or ducting, insulation, heat exchangers, and controls.

As the solar energy system size increases, it produces more energy but costs more. It would, therefore, be required to determine the optimum size of the solar energy system that has the maximum life cycle savings or the quickest payback time. The total cost of the solar equipment, cs, is given by the sum of two terms: one is proportional to the collector area, ac, called area-dependent costs, ca, and the other is independent of the collector area, called area-independent costs, ci, given by The area-dependent cost, ca, includes not only costs related to the purchase and installation of the collector system, such as collector panels, brackets, and piping, but also other costs that depend on the size of the collector system. Area-independent cost includes the cost of components not related to the collector area, such as the cost of controls and electrical installation.

Operating costs, Co, include maintenance, parasitic, and fuel costs. Maintenance costs are usually considered to be a percentage of the initial investment and are assumed to increase at a certain rate per year of the system operation to account for the system aging. Parasitic costs accounts for the energy required (electricity) to drive the solar pump or blower, depending on the type of system. Fuel savings are obtained by subtracting the annual cost of the conventional fuel used for the auxiliary energy from the fuel needs of a fuel-only system. The integrated cost of the auxiliary energy use for the first year, that is, solar backup, is given by the formula The integrated cost of the total load for the first year, that is, the cost of conventional fuel without solar energy, is where CFA and CFL = cost rates (in $/GJ) for auxiliary energy and conventional fuel, respectively

If the same type of fuel is used by both systems, CFA = CFL. Both values are equal to the product of fuel calorific value and heater efficiency. Equation (12.4), gives the fuel costs for the conventional (non-solar) system. In Eq. (12.3), instead of LAUX, the total thermal load, L, can be used, multiplied by (1 - F). In equation form, the annual cost for both the solar and conventional backup systems to cover the energy need of the thermal load is given by For non-income-producing systems,

For income-producing systems Solar savings can also be obtained by the difference between the cost of conventional and solar energy systems: If savings are negative, then they are deficits (expenses) instead of savings.

Time value of money A sum of money at hand today is worth more than the same sum in the future. Therefore, a sum of money or cash flow in the future must be discounted and worth less than its present-day value. A cash flow (F) occurring (n) years from now can be reduced to its present value (P) by Equation (12.11) shows that a present worth of a given amount of money is discounted in the future by the factor (1 + d)-n for each year in the future. Therefore, the fraction (1 + d)-n can be used to estimate the present worth at any year (n), PWn, given by

The present worth can be estimated from Eq. (12 The present worth can be estimated from Eq. (12.12) or obtained directly from Table 12.1. The present worth can be multiplied by any cash flow in the future at time (n) to give its present value. Its use in a life cycle analysis allows all calculations to be made at present by discounting costs and savings incurred during the life of the system

The amount of money needed to purchase an item increases because the value of money decreases. Thus, an expense (C), when inflated at a rate (i) per time period, equals (C) at the end of the first time period, equals C(1 + i) at the end of the second time period, equals C(1 + i)2 at the end of the third time period, and so on. Therefore, with an annual inflation rate (i), a purchase cost (C) at the end of year (n) becomes a future cost (F) according to

Description of the life cycle analysis method 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 (12.14) gives the present worth of a future cost or expenditure at the end of (n) years when the cost or expenditure at the end of first year is (C). This equation is useful for estimating the present worth of any one payment of a series of inflating payments. Equation (12.14) gives the present worth of a single future payment. Summing up all the present worth values of (n) future payments results in the total present worth (TPW), 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 cost. Extra property tax. Extra tax savings. Solar savings for each year are the sums of the items shown above, as shown in Eq. (12.10). The savings are positive and the costs are negative. The present worth of each year’s solar savings is determined using Eqs. (12.11) and (12.12). The results are estimated for each year. These annual values are added up to obtain the life cycle savings, according to the equation:

Payback Time The time needed for the cumulative fuel savings to equal to the total initial investment, i.e., It is the time required to get back the money spent to erect the solar energy system from the fuel savings incurred because of the use of the system. This time can be obtained with or without discounting the fuel savings. Not discounting fuel savings Initially, we consider that the fuel savings are not discounted. The fuel saved in a year (j) is given by

The product FL represents the energy saved because of the use of solar energy. Summing the fuel saved in year (j) over the payback time (np) and equating to the initial system cost, (cs), given by eq. (12.2), gives The summation gives Solving Eq. (12.25) for the payback time, nP, gives

Another way to determine the payback time is to use the PWF values tabulated in Appendix 8. Here, the sum of the fuel savings is given by the multiplication of the first year’s saving, FLCF1 and PWF at zero discount rate. In equation form, this is given by

Discounting fuel savings The procedures followed to equate discounted fuel costs to initial investment are similar. For discounted fuel costs, Eq. (12.27) becomes

Other definitions of payback time are the time required for the annual solar savings to become positive and the time required for the cumulative solar savings to become 0.

The P1, P2 method 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

Optimization Using P1, P2 Method 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. life cycle savings 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

Rearranging, the maximum savings are obtained when the relationship between the collector area and solar fraction satisfies the following relation:

Uncertainties In Economic Analysis Due 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 oil-producing countries. Therefore, it is desirable to be able to determine the effect of uncertainties on the results obtained from an economic analysis.