Mechanical Engineering

optimization and generator loss curves

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Many engineering problems come down to optimization, whether is the most output, least cost, or best fit. Many of these tasks can be performed in Excel. Two powerful tools that come with Excel are LINEST and Solver. These can even be used together. The attached spreadsheet shows a common problem: generator loss curves. These are most often provided as a fan of curves for various power factors. These can be reduced to a single curve by a transformation of variables: x=kW/PF^n, where n=1.5 to 3. The same transformation will work to reduce transformer loss curves to a single curve, although the range of n is different. The Solver can be used to find the best n, while LINEST is finding the best polynomial fit. See it all in this spreadsheet. A trick you will also find useful is creating columns of powers of x without actually changing the spreadsheet. The values of x^1 in this case are given by cells D4:D99. You can create x^2, x^3, ... with this statement range^{list} as in =LINEST(C4:C99,D4:D99^{1,2},TRUE,TRUE).

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