By J. Barry Cooke, James L. Sherard
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Extra resources for Concrete Face Rockfill Dams Design, Construction, and Performance: Proceedings of a Symposium
There are strategies discussed below to reduce the amount of spinning reserve required due to solar energy generators on the utility system during the day, due to intermittent clouds. Utility system operation occurs at several time scales: Power quality: Power quality refers to power factor (phase alignment of current and voltage waves), harmonic distortion (frequencies other than 60 Hz), and tolerances in voltage and frequency. The time scale of interest in power quality is less than one second.
Substitution of equations 1-9 and 1-10 into 1-12 and taking the derivative with respect to Prated produces the expression that will be set to zero to ascertain the optimal value of Prated that minimizes life cycle cost. dLCC = 0 = (Cpv + (CO&M*pwf) f + (cretial*pwf*((T*(−1 + dP Prated ((1 + n)^(−1)) + EXP(( P LN((1 − (Pload /Prated)))/n)))) − ((Pload − Prated)*T*((((1 − (Ploadd/Prated))*n)^(−1))*Pload*(Prated^ (−2))*(EXP( P LN((1 − (Pload /Prated)))/n)))) − ((T^( T −n))/(1 + n)* ((T*EXP(( P LN((1 − (Pload /Prated)))/n)))^(1 + n))) − (Prated* (T^(1 T − n))*((T*EXP(( P LN((1 − (Pload /Prated)))/n)))^n)* (((1 − (Pload /Prated))*n)^(−1))*Pload *(Prated^(−2))*(EXP( P LN ((1 − (Pload /Prated)))/n)))))) − (cwhsl*PWF*((T*EXP(( P LN((1 − (Pload /Prated)))/n))) + ((Prated − Pload)*T*((((1 − (Pload /Prated))*n)^ (−1))*Pload*(Prated^(−2)*(EXP( P LN((1 − (Pload /Prated)))/n)))) − ((T^ T (−n))/(1 + n)*((T*EXP(( P LN((1 − (Pload /Prated)))/n)))^(1 + n))) − (Prated*(T^(1 T − n))*((T*EXP(( P LN((1 − (Pload /Prated)))/n)))^n)* (((1 − (Pload /Prated))*n)^(−1))*Pload*(Prated^(−2)*(EXP( P LN((1 − (Pload /Prated)))/n))))))))) (1-13) This is a transcendental equation, which means that the variable Prated appears both in exponential terms and as a product multiplied by the exponential term, and may be solved by iteration (guess a value of Prated and check to see if the equation equals zero, if not guess a higher or lower value), or software products, such as the “goal seek” function in Microsoft Excel spreadsheet may solve for Prated.
06/kWh for every kWh put back onto the utility system by Linear programming refers to computer programs which solve a system of simultaneous equations to explicitly calculate the optimal solution. The objective function of life cycle cost and each of the constraints are written as linear equations of the design variables to be optimized. This requirement is accommodated by making curved dependencies piecewise linear. For example, a curve of cost versus size might be approximated by three straight-line segments.
Concrete Face Rockfill Dams Design, Construction, and Performance: Proceedings of a Symposium by J. Barry Cooke, James L. Sherard