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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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