Economic dispatch graph for a '4 units' system

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Hasan Ghorbani 2016-5-19

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https://ww2.mathworks.cn/matlabcentral/answers/284961-economic-dispatch-graph-for-a-4-units-system

编辑： Hasan Ghorbani 2016-5-19

Hi all, I have 4 generator in my system and I would like to plot the incremental cost graph vs system load (ranging from 250MW to 1200MW)

I can easily work out the values when all four units are in normal operation mode using following code:

a1=.004;b1=9;
a2=.002;b2=10;
a3=.006;b3=8;
a4=.006;b4=8;
aT = inv(inv(a1)+inv(a2)+inv(a3)+inv(a4))
bT = aT * (b1/a1 + b2/a2 + b3/a3 + b4/a4 )
for Pg = 250:50:1200;
    lambda = aT * Pg + bT;
    Pg1 = (lambda-b1)/a1;
    Pg2 = (lambda-b2)/a2;
    Pg3 = (lambda-b3)/a3;
    Pg4 = (lambda-b4)/a4;
    fprintf('\nPg=%4d \tlambda=%6.3f Pg1=%6.3f  Pg2=%6.3f Pg3=%6.3f  Pg4=%6.3f ',Pg,lambda,Pg1,Pg2,Pg3,Pg4)
end

And I know my graph should look similar to following diagram (with three breaking point perhaps):

But I don't know how to find out in which region, what unit should take more burden and which one can operate in its minimum. Can anyone help me on this please?

BTW, ignore losses.