## Economic Analysis

The cost of the conventional fuel energy is the the most important factor affecting the economic feasibility of the solar system. The economic calculations for this study are based on life cycle savings (LCS) method (Duffie and Beckman 1991). There are two variables which characterize the life cycle savings method: the duration of the analysis and the discount rate. The discount rate is defined as the rate of return which can be obtained from the best alternative investment. The life cycle savings of a solar system (LCS) over a conventional system can be defined as the difference between the reduction in fuel costs and the increase in expenses resulting from the additional investment for the solar system and is given by the following equation:

where P1 is the factor relating life cycle fuel cost to first-year fuel cost savings, P2 is the factor relating life cycle by additional capital investment to initial investmet, CA is the solar energy investment cost which is directly proportional to collector area, CE is the solar energy investment cost which is independent of collector area, CF is the unit cost of delivered conventional energy for the first year of analysis, L is the total load, and Ft is the total solar fraction of the solar system. For a particular locality and set of economic conditions, the economic analysis can be used to evaluate the economic feasibility of the solar system in terms of the life cycle savings. For example, optimization is made with respect to collector area to obtain the maximum life cycle savings for a given locality and a set of collector parameters. However, when two parameters were considered simultaneously, optimization was made in terms of the life cycle cost and not the life cycle savings.

A subroutine type compatible with TRNSYS is developed to calculate money savings due to using solar heating and cooling systems. The price of kW h generated by utility is constant and is equal to the tariff of Kuwait, which is subsidized by the government. It is supplied to the program on an hourly basis. The hourly load is assumed to be repeated each day and the inputs to the program are load in W and power generation. The hourly load values are read from a separate file and the output of the program is the life cycle solar savings (LCS). Life cycle solar savings is the money savings due to the use of solar heating and cooling systems. A FORTRAN program is developed based on the method proposed by Duffle and Beckman (1991) to evaluate the payback time of a solar system. The energy payback time is the minimum time it takes to recover investment costs. So, the number of years that a solar investment takes to pay off (NP) is given by the following expression:

for F^D

for F=D

where CS is the system cost, CE is the electrical saving, and CM is the annual operation and maintenance cost.

The gains or losses for the space heating and cooling system after a period of N years is given by f ( - \

for F=D

A positive value of P means a profit; on the other hand a negative result indicates a loss. The electrical load data are the electrical energy consumption over a period equal to the time step of TRNSYS simulation, which is at 15-min interval. 