Homework #8\ 7.6. Find the minimum value of the function\

f(x,y)=x^(2)+y^(2)

\ subject to one equality constraint\

g(x,y)=x^(2)-5x-y^(2)+20=0

\ and one inequality conslriant\

u(x,y)=2x+y>=6

\ 7.8. The fuel-cost functions in

$

th for three thermal plants are given by\

C_(1)=350+7.20P_(1)+0.0040P_(1)^(2)\ C_(2)=500+7.30P_(2)+0.0025P_(2)^(2)\ C_(3)=600+6.74P_(3)+0.0030P_(3)^(2)

\ wherc

P_(1),P_(2)

, and

P_(3)

are in MW. The governors are set such that generators share the loud equally. Neglecting tine losses and generator limits, find the total cost in

$h

when the total losd is\ (i)

P_(D)=450MW

\ (ii)

P_(D)=745MW

\ (iii)

P_(D)=2335MW

\ 7.9. Neglecting line losses and generator limits, determine the optimal acheduling of generation for each loading condition in Problem 7.8\ (a) by analytical technique, using (7.33) and (7.31).\ (b) using lterative method. Start with at initial estimate of

\\\\lambda =7.5($)/(M)Wh

. (c) find the stavings in $h for each case compared to the costs in Problem 7.8 when the generators shared load equally.\ 7,10. Repeat Problem 7,9 (a) and (b), but this time consider the following generator limits (in MW)\

122

7.6. Find the minimum value of the function f(x,y)=x2+y2 subject to one equality constraint g(x,y)=x25xy2+20=0 and onc inequality conslraint u(x,y)=2x+y6 7.8. The fuel-cost functions in S/h for three thermal plants are given by C1=350+7.20P1+0.0040P12C12=500+7.30P2+0.0025P22C3=600+6.74P3+0.0030P32 wherc P1,P2, and P3 are in MW. The governors are set such that generators share the loud equally. Neglecting line losses and generator limits, find the total cost in Sh when the total load is (i) PD=450MW (ii) PD=745MW (iii) PD=2335MW 7.9. Neglecting line losses and generator limits, determine the optimal acheduling of generation for each loading condition in Problem 7.8 (a) by analytical technique, using (7.33) and (7.31). (b) using Iterative method. Start with at initial estimate of =7.5s/MWh. (c) find the savings in $Sh for each case compared to the costs in Problem 7.8 when the generators shared load equally. 7.10. Repent. Problem 7.9 (a) and (b), but this time consider the following generator limits (in MW) 12226050P1400P2600P3445