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86 Integrated system design of the inputs in the calculation methodology can be used in economical/thermodynamical optimizations, as shown in the next section. 4-3 Optimization of the net present value of a solar tower power plant This section deals with the formulation of an optimization problem which takes into account both the thermodynamic cycle parameters and dimensioning of the main components. The solution to this problem is left for future investigations due to its high computational costs. The optimization problem is oriented to the design of the solar tower power plant, and it is focused on the maximization of the thermal efficiency and simultaneously on the minimization of the investments associated with the system components. The net present value is a parameter commonly used to analyze the profitability of an investment project. It is the difference between the present value of all future cash inflows produced by a property and the present value of the cash investment required to obtain the property. It can be calculated by means of the next equation NPV =N Λi −Γ0, (4-65) i=1 (1+k)i where N is generally the number of years considered, Λi is the cash flows produced in a specific year i, k discount rate and Γ0 is the initial investment. Higher net present values mean better projects and therefore its maximization is an important target in economical analysis. In this regard, equation (4-65) shows that decreasing the initial investment Γ0 increases the NPV. Additionally, for a fixed power output, increasing the efficiency of the system decreases the collected power from the solar field, which will need a lower number of heliostats and consequently will have a lower cost. Thus, increasing the system thermal efficiency and decreasing the equipment investment can be considered the targets of these optimization problem. Since two variables are of interest in the problem, a multi-objective optimization procedure is needed from a mathematical point of view. This problem can be stated as maximize F(x) = [ηTH(x), ς(x)] , subject to jk(x) ≤ 0, k = 1,2,...,n, (4-66) where ηTH is the thermal efficiency as a function of the design variables x, and ς is a function related with the calculation of the components cost. The set of constrains is represented by jk and n the number of functions in this set. The function ς calculates the inverse of the normalized cost of the components, where ς′(x) is the function that calculates the cost and |ς′ MAX ς(x) = 1 − ς′(x) , |ς′ | (4-67) | is the maximum investment allowable. The cost of the components can be calculated as a function of their mass, J.S. Bahamonde Noriega ς′(x) = Ψ[Φ(x)], (4-68) Master of Science Thesis MAXPDF Image | Design method for s-CO2 gas turbine power plants
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