5200_A08 - EE 5200 - Assignment DISPATCH Fall Semester 2009...

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EE 5200 - Assignment “DISPATCH” Due: Fri Dec 11 th , 5pm Fall Semester 2009 - Mork (Don’t wait to begin !) Objectives : Constrained minimization via LaGrange multipliers, lossless optimal dispatch, correcting unacceptable bus voltages with shunt capacitor banks or shunt reactors. 1) Using the method of LaGrange multipliers, minimize the function f(x,y) = x 2 + y 2 , subject to the constraint y = 2x + 8. Sketch out the function and the constraint, and explain in practical terms what you’ve done. 2) After running a load flow simulation, the voltage magnitude at a load bus is found to be 1.10 per unit. (Hint: since you will need to address 2 cases here and you may need to do this calculation again in the future, consider writing a Matlab program to do this calculation.) a) What type of shunt impedance should be added at this bus to pull the voltage down to 1.0 per unit? b) If the Thevenin impedance at this bus is Z = 4.0 + j6.0 per unit, calculate the value of this shunt impedance. If your calculation indicates more than one mathematical solution, indicate
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