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the width. Another important constraint is a side constraint or bound. This sets the range for which the independent variables are to be evaluated within. The program used to perform the optimization for the system is EES. EES has a min/max function built in the program which uses numerical optimization methods to minimize or maximize a function based on 1 to x number of variables. The two methods available are the direct search method and the variable metric method. The direct search method is also called a conjugate-direction method; specifically EES uses Powell’s Method for direct search optimization. The basic premise of this method is to search for the optimum value using one independent variable while holding the others constant. Once the optimum value is found for that variable the process is repeated for the next set of variables. The advantage of this method is that it is useful when functions are not easily differentiable, which may be the case for the thermodynamic functions involved for this project. Also this method is ideal for when the optimum value may be on one of the bounds which is entirely possible with Rankine cycle systems. The algorithm of Powell’s Method is given as follows (Antoniou et al., 2007): Step 1 Input x00 = [x01 x02 . . . x0n]T and initialize the tolerance ε. Set d01 =[x01 0...0]T d02 =[0x02 ...0]T 28PDF Image | Exergoeconomic Analysis and Optimization of ORC
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