ECE421POWER SYSTEM ANALYSIS
Homework #7
6.12a / 6.12b / 6.12c / 6.13a / 6.13b / 7.6 / 7.9a / 7.9b / 7.9c / 7.9M / 7.11 / 7.11M / totalECE421 / 10' / 10' / 5' / 10' / 5' / 10 / 15' / 15' / 15' / 5’ / 15' / 5’ / 120
6.12(a)
Bus admittance matrix,
6.12(b)
Determine Jacobian matrix,
Initial condition,
First iteration,
Second iteration,
6.12(c)
Run the following code,
%Problem 6.12(c)
clear
basemva = 100;
accuracy = 0.00001;
accel = 1.0;
maxiter = 100;
%bus data
% Bus Bus Voltage Angle -Load------Generator--- Injected
% No code Mag Degree MW MVAR MW MVAR Qmin Qmax MVAR
busdata=[1 1 1.0 0.0 0.0 0.0 0.0 0.0 0 0 0
2 2 1.05 0.0 0 0 400 0.0 0 600 0
3 0 1.0 0.0 500 400 0.0 0.0 0 0 0];
%line data
% Bus Bus R X 1/2 B Line code
% nl nr pu pu pu
linedata=[1 2 0.0 0.025 0.0 1
1 3 0.0 0.05 0.0 1
2 3 0.0 0.05 0.0 1];
lfybus
lfnewton
busout
The result agrees with calculation,
> ECE599HW8_6_12_c
Power Flow Solution by Newton-Raphson Method
Maximum Power Mismatch = 6.65779e-12
No. of Iterations = 5
Bus Voltage Angle ------Load------Generation--- Injected
No. Mag. Degree MW Mvar MW Mvar Mvar
1 1.000 0.000 0.000 0.000 100.000 4.723 0.000
2 1.050 1.611 0.000 0.000 400.000 537.059 0.000
3 0.905 -6.919 500.000 400.000 0.000 0.000 0.000
Total 500.000 400.000 500.000 541.782 0.000
6.13(a)
First iteration,
The power residuals,
Second iteration,
6.13(b)
Run the following code,
%Problem 6.13(b)
clear
basemva = 100;
accuracy = 0.00001;
accel = 1.0;
maxiter = 100;
%bus data
% Bus Bus Voltage Angle -Load------Generator--- Injected
% No code Mag Degree MW MVAR MW MVAR Qmin Qmax MVAR
busdata=[1 1 1.0 0.0 0.0 0.0 0.0 0.0 0 0 0
2 2 1.05 0.0 0 0 400 0.0 0 600 0
3 0 1.0 0.0 500 400 0.0 0.0 0 0 0];
%line data
% Bus Bus R X 1/2 B Line code
% nl nr pu pu pu
linedata=[1 2 0.0 0.025 0.0 1
1 3 0.0 0.05 0.0 1
2 3 0.0 0.05 0.0 1];
lfybus
decouple
busout
The result agrees with calculation,
> ECE599HW8_6_13_b
Power Flow Solution by Fast Decoupled Method
Maximum Power Mismatch = 2.25093e-06
No. of Iterations = 10
Bus Voltage Angle ------Load------Generation--- Injected
No. Mag. Degree MW Mvar MW Mvar Mvar
1 1.000 0.000 0.000 0.000 100.000 4.723 0.000
2 1.050 1.611 0.000 0.000 400.000 537.059 0.000
3 0.905 -6.919 500.000 400.000 0.000 0.000 0.000
Total 500.000 400.000 500.000 541.782 0.000
7.6
7.9(a)
For loading condition
The optimal dispatch is,
For loading condition
The optimal dispatch is,
For loading condition
The optimal dispatch is,
7.9(b)
Start with initial value
For loading condition, first iteration,
Second iteration,
The equality constraint is met in two iterations.
For loading condition, first iteration,
Second iteration,
The equality constraint is met in two iterations.
For loading condition, first iteration,
Second iteration,
The equality constraint is met in two iterations.
7.9(c)
For loading condition, when 3 generator share load equally,
For the optimal dispatch,
The saving is
For loading condition, when 3 generator share load equally,
The saving is
For loading condition, when 3 generator share load equally,
The saving is
Run the following code to check the result,
%ECE521 Problem 7.9
cost = [350 7.2 0.004
500 7.3 0.0025
600 6.74 0.003];
disp('(i) Pdt = 450 MW')
Pdt = 450;
dispatch
gencost
disp('(ii) Pdt = 745 MW')
Pdt = 745;
dispatch
gencost
disp('(iii) Pdt = 1335 MW')
Pdt = 1335;
dispatch
gencost
The results agree with calculation,
> ECE599HW8_7_9
(i) Pdt = 450 MW
Incremental cost of delivered power (system lambda) = 8.000000 $/MWh
Optimal Dispatch of Generation:
100.0000
140.0000
210.0000
Total generation cost = 4828.70 $/h
(ii) Pdt = 745 MW
Incremental cost of delivered power (system lambda) = 8.600000 $/MWh
Optimal Dispatch of Generation:
175.0000
260.0000
310.0000
Total generation cost = 7277.20 $/h
(iii) Pdt = 1335 MW
Incremental cost of delivered power (system lambda) = 9.800000 $/MWh
Optimal Dispatch of Generation:
325.0000
500.0000
510.0000
7.11
The real power loss,
First iteration,the initial condition ,
The real power loss,
The error,
Second iteration,
The real power loss,
The error,
Run the following code,
%Problem 7.11
cost = [320 6.2 0.004
200 6.0 0.003];
mwlimits =[ 50 250
50 350];
Pdt = 412.35;
B=[0.0125 0
0 0.00625]
basemva=100;
lambda = 7.0;
dispatch
gencost
The result is,
> ECE599HW8_7_11
B =0.0125 0
0 0.0063
Incremental cost of delivered power (system lambda) = 7.803862 $/MWh
Optimal Dispatch of Generation:
161.1765
258.6003
Absolute value of the slack bus real power mismatch, dpslack = 0.6118 pu
Total generation cost = 8193.13 $/h
So, the optimal dispatch finally converge to,