1. Manually execute one iteration of the Lambda Iteration Method.

2. Write a program to solve the load dispatch by the Lambda Iteration Method

Given:

Helpful Matlab example

A 2-Generator Example:

clear all Pd=412.35 %Cost Coefficients a1=320; a2=6.2; b1=200; b2=6; %Loss Coefficients x1=0.000125; x2=0.0000625; %Initialization with losses ignored 

PL=0;lamda=(Pd+PL+(a2/(2*a3))+(b2/(2*b3)))/((1/(2*a3))+(1/(2*b3))) P1=(lamda-a2)/(2*a3) P2=(lamda-b2)/(2*b3)

 err=(P1+P2-Pd)-PL 

for i=1:2 Iteration=i 

 PL=x1*P1*P1+x2*P2*P2 PGen_Loss=[P1 P2 PL] dpl1=2*x1*P1 dpl2=2*x2*P2 L1=1/(1-dpl1) L2=1/(1-dpl2) y1=1/(2*a3*L1) y2=1/(2*b3*L2) 

lamda=(Pd+PL+(a2/(2*a3))+(b2/(2*b3)))/(y1+y2) P1=((lamda*(1-dpl1)-a2))/(2*a3) P2=((lamda*(1-dpl2)-b2))/(2*b3) err=(P1+P2-Pd)-PL

end

% Final Results (Book solution:P1=161.1765, P2=258.6003, Lambda=7.80386

lamda PL=x1*P1*P1+x2*P2*P2 err=(P1+P2-Pd)-PL C=(a1+a2*P1+a3*P1*P1)+ (b1+b2*P2+b3*P2*P2)

Results:

Pd = 412.3500 lamda = 7.4995 P1 = 162.4357 Iteration = 1

PL = 7.2017 L1 = 1.0423 lamda = 7.7991 P1 = 160.3025 Iteration = 2 PL = 7.4127 L1 = 1.0417 lamda = 7.8034 P1 = 161.3377 lamda = 7.8034 PL = 7.4277

P2 = 249.9143

PGen_Loss = L2 = 1.0322

P2 = 259.2492

err = 1.1369e-13 162.4357 249.9143 7.2017

err = -1.7941e-13

a3=0.004; b3=0.003; 

PGen_Loss = 160.3025 259.2492 7.4127 L2 = 1.0335

P2 = 258.4250 err = 5.5067e-14 err = -0.0150 C = 3.3753e+03

7.8. The fuel-cost functions in S/h for three thermal plants are given by C1 350+7.20P 0.0040Pi 25007.30P2 0.0025P where Pi, P2, and Ps are in MW. The governors are set such that generators share the load equally. Neglecting line losses and generator limits, find the total cost in $/h when the total load is Gi) PD 450 Mw 7.9. Neglecting line losses and generator limits, determine the optimal scheduling 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 an initial estimate of -7.5 S/MWh. (c) find the savings in S/h for each case compared to the costs in Problem 7.8 when the generators shared load equally. (case (i) P =450 MW only. Use the dispatch program to check your results. 7.8. The fuel-cost functions in S/h for three thermal plants are given by C1 350+7.20P 0.0040Pi 25007.30P2 0.0025P where Pi, P2, and Ps are in MW. The governors are set such that generators share the load equally. Neglecting line losses and generator limits, find the total cost in $/h when the total load is Gi) PD 450 Mw 7.9. Neglecting line losses and generator limits, determine the optimal scheduling 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 an initial estimate of -7.5 S/MWh. (c) find the savings in S/h for each case compared to the costs in Problem 7.8 when the generators shared load equally. (case (i) P =450 MW only. Use the dispatch program to check your results