1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
|
//Chapter 7
//Example 7.1
//page 246
//To find incremental cost and load sharing
clear;clc;
///Let us use the program given in the Appendix G in the textbook to write
//a function that returns the value of lamda and Loading of each generator
//when the total load on the plant is sent to the function
function [lamdaprev,Pg]=optimum(Pd)
n=2; //number of generators
Alpha=[0.2 0.25];
Beta=[40 30];
lamda=35; //initial guess for lambda
lamdaprev=lamda;
eps=1; //tolerance
deltalamda=0.25; //increment in lamda
Pgmax=[125 125];
Pgmin=[20 20];
Pg=100*ones(n,1);
while abs(sum(Pg)-Pd)>eps
for i=1:n
Pg(i)=(lamda-Beta(i))/Alpha(i);
if Pg(i)>Pgmax(i) then
Pg(i)=Pgmax(i);
end
if Pg(i)<Pgmin(i) then
Pg(i)=Pgmin(i);
end
end
if (sum(Pg)-Pd)<0 then
lamdaprev=lamda;
lamda=lamda+deltalamda;
else
lamdaprev=lamda;
lamda=lamda-deltalamda;
end
end
endfunction
//to draw the table 7.1
printf('Table 7.1 Output of each unit and plant output for various values of lamda\n')
printf('--------------------------------------------------------------\n');
printf('Plant Lamda, Unit 1 Unit 2 Plant Output \n');
printf('Rs/MWh Pg1,MW Pg2,MW (Pg1+Pg2),MW \n');
printf('--------------------------------------------------------------\n');
Pd_matrix=[40 76 130 150 175 220 231.25 250];
for i=1:8
[lamda,Pg]=optimum(Pd_matrix(i));
printf('%0.2f %0.2f %0.2f %0.2f\n',lamda,Pg(1),Pg(2),Pg(1)+Pg(2));
end
printf('--------------------------------------------------------------\n');
//To draw the Graphs 7.3 and 7.4
Pd_test=40:3.75:250;
[Pd_ro,Pd_co]=size(Pd_test)
for i=1:Pd_co
[lamda,Pg]=optimum(Pd_test(i));
lamda_test(i)=lamda;
Pg1_test(i)=Pg(1);
Pg2_test(i)=Pg(2);
end
Pg1_test=Pg1_test.'; //transposing without conjugating
Pg2_test=Pg2_test.';
lamda_test=lamda_test.';
subplot(211)
plot(Pd_test,lamda_test);
title('Incremental Fuel cost versus plant output');
xlabel('Plant output,MW');
ylabel('Incremental fuel cost,Rs/MWh');
set(gca(),"grid",[0,0])
get("current_axes");
subplot(212)
plot(Pd_test,Pg1_test,Pd_test,Pg2_test);
title('Output of each unit versus plant output');
xlabel('Plant output,MW');
ylabel('Unit output,MW');
legend(["Unit 1";"Unit 2"],[2]);
set(gca(),"grid",[0,0])
get("current_axes");
|
