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Performance Index - BusBar optimization

Performance Index - BusBar optimization - 2 e 2 e 2 e Total...

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Maximum temperature rise < 90 o C Adequate strength Adequate oxidation resistance Constraints minimize Life Cost [capital plus resistive heating losses] Objective carry electrical current Function
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Current-carrying capacity limited by temperature rise Temperature rise determined by heat balance between resistance heating [I 2 R] and heat losses through convection and radiation [sound familiar?] Typical temperature rise limited to ~ 50 o above ambient Current densities on the order of 2 A/mm 2
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Capital Cost Capital Cost For C m = cost per kilogram [or pound] of the material, ρ = its density, A the cross section area of the bus bar and L its length: C 1 = C m AL ρ Costs Due to Resistive Heating [Power] Losses Costs Due to Resistive Heating [Power] Losses For C e = cost per kilowatt hour of electricity, t = operating life of the bus bar [hours], I the current and ρ e the resistivity of the material from which it is made:
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Unformatted text preview: 2 e 2 e 2 e Total Operating Cost Total Operating Cost C = C 1 + C 2 = C m AL ρ + C e I 2 [ ρ e L/A]t Differentiating cost with respect to area and setting the derivative equal to zero gives the optimum value for cross sectional area for the minimization of total operating cost: A opt = [C e ρ e I 2 t/(C m ρ )] 1/2 Substituting A opt back into the total cost equation gives the objective function : e 2 1/2 m e 1/2 “Cost is minimized by selecting the material with the greatest value of”: M 1 = 1/[C m ρ e ρ ] “Strength is important when a bus-bar of large span is unsupported or is exposed to other loads . Then we require a minimum value for the elastic limit.” graphite • For cost and strength, bronzes are best • Without strength, would have selected graphite...
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Performance Index - BusBar optimization - 2 e 2 e 2 e Total...

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