Dear MATPOWER developers,
My name is Piero Carlo dos Reis and I am the MAVT student who has previously
asked you for material on the courses in electrical engineering you hold at ETH.
Since my current semester project involves an optimization code for AC
newton Raphson procedure, I have been asked by my professor to validate it. I
have followed the procedure illustrated by Prof. Shahidehpour in his paper
"Security-Constrained Unit Commitment With AC Constraints" in order to model
the Jacobian matrix (in which I also included transformer variables such as tap
and transformer angle). A validation method advised to me by my Professor and
which I have tried to pursue is the use of AC opf with matpower to solve a case
study from internet (and to try to get same results with my code). I have
download matpower version 6. However, when solving case studies (such as case
WB5 which I am annexing together with a text file of the matpower solution), I
get that the sum of Q generation is different from the sum of Q load + sum of Q
losses (in WB5 matpower ac opf solution, it is evident due to the fact that the
result is sum Q generation is -7 p.u., sum Q load is 50 p.u. and sum Q losses
is 35.30 p.u.). Would you have an explanation to this results and to how
matpower solves the Q nodal balance of power/Q mismatch? In another case study
I choose to run, case5, I got the also that this equality was not true,
although the difference is not as evident as in WB5. I am also annexing the
results from my code and from matpower in text files (I evaluated the losses as
sum of Gen - sum of load for simplicity.)
I thank you for your attention, sincerely, Piero carlo dos Reis
function mpc = WB5
%% 5 bus case in MATPOWER format
% W. A. Bukhsh, Feb 2013
%% References:
% [1] W. A. Bukhsh, Andreas Grothey, Ken McKinnon, Paul trodden, "Local
Solutions of Optimal Power Flow Problem"
% submitted to IEEE Transactions on Power Systems, 2013
% [2] W. A. Bukhsh, Andreas Grothey, Ken McKinnon, Paul trodden, "Local
Solutions of Optimal Power Flow Problem"
% Technical Report ERGO, 2011
%% MATPOWER Case Format : Version 2
mpc.version = '2';
%%----- Power Flow Data -----%%
%% system MVA base
mpc.baseMVA = 100;
%% bus data
% bus_i type Pd Qd Gs Bs area Vm Va
baseKV zone Vmax Vmin
mpc.bus = [
1 3 0 0 0 0 0 0 0 345 1
1.05 0.95;
2 1 130 20 0 0 0 0 0 345 1
1.05 0.95;
3 1 130 20 0 0 0 0 0
345 1 1.05 0.95;
4 1 65 10 0 0 0 0 0 345
1 1.05 0.95;
5 2 0 0 0 0 0 0 0
345 1 1.05 0.95;
% 1 3 0 0 0 0 1 1.0 0 345
1 1.05 0.95;
% 2 1 130 20 0 0 1 1.0 0 345 1
1.05 0.95;
% 3 1 130 20 0 0 1 1.0 0
345 1 1.05 0.95;
% 4 1 65 10 0 0 1 1.0 0 345
1 1.05 0.95;
% 5 2 0 0 0 0 1 1.0 0
345 1 1.05 0.95;
% 2 1 130 20 0 0 1 1.0 -10
345 1 1.05 0.95;
% 3 1 130 20 0 0 1 1.0 -20
345 1 1.05 0.95;
% 4 1 65 10 0 0 1 1.0 -135 345
1 1.05 0.95;
% 5 2 0 0 0 0 1 1.0 -140
345 1 1.05 0.95;
];
%% generator data
% bus Pg Qg Qmax Qmin Vg mBase status Pmax
Pmin Pc1 Pc2 Qc1min Qc1max Qc2min Qc2max ramp_agc ramp_10
ramp_30 ramp_q apf
mpc.gen = [
1 263 30 1800 -30 1 100 1 5000 0
0 0 0 0 0 0 0 0 0 0
0;
5 30 30 1800 -30 1 100 1 5000 0
0 0 0 0 0 0 0 0 0 0
0;
];
%% branch data
% fbus tbus r x b rateA rateB rateC ratio
angle status angmin angmax
mpc.branch = [
1 2 0.04 0.09 0.0 2500 2500 2500 0
0 1 -360 360;
1 3 0.05 0.10 0.0 2500 2500 2500 0
0 1 -360 360;
2 4 0.55 0.90 0.45 2500 2500 2500 0
0 1 -360 360;
3 5 0.55 0.90 0.45 2500 2500 2500 0
0 1 -360 360;
4 5 0.06 0.1 0.0 2500 2500 2500 0
0 1 -360 360;
2 3 0.07 0.09 0.0 2500 2500 2500 0
0 1 -360 360;
];
%%----- OPF Data -----%%
%% area data
% area refbus
mpc.areas = [
1 5;
];
%% generator cost data
% 1 startup shutdown n x1 y1 ... xn
yn
% 2 startup shutdown n c(n-1) ... c0
mpc.gencost = [
% 2 2 0 3 0 4.00 0;
2 2 0 3 0 1.00 0;
2 2 0 3 0 1.00 0;
];
mpc.traf = [];
% return;
with P line limit type of constraint
MATPOWER Version 6.0, 16-Dec-2016 -- AC Optimal Power Flow
MATPOWER Interior Point Solver -- MIPS, Version 1.2.2, 16-Dec-2016
(using built-in linear solver)
Converged!
Converged in 0.30 seconds
Objective Function Value = 342.31 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 5 Total Gen Capacity 10000.0 -60.0 to 3600.0
Generators 2 On-line Capacity 10000.0 -60.0 to 3600.0
Committed Gens 2 Generation (actual) 342.3 -7.0
Loads 3 Load 325.0 50.0
Fixed 3 Fixed 325.0 50.0
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 6 Losses (I^2 * Z) 17.31 35.31
Transformers 0 Branch Charging (inj) - 92.3
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 0.988 p.u. @ bus 3 1.050 p.u. @ bus 1
Voltage Angle -6.66 deg @ bus 3 0.00 deg @ bus 1
P Losses (I^2*R) - 7.13 MW @ line 1-3
Q Losses (I^2*X) - 15.83 MVAr @ line 1-2
Lambda P 1.00 $/MWh @ bus 5 1.12 $/MWh @ bus 3
Lambda Q -0.05 $/MWh @ bus 4 0.01 $/MWh @ bus 3
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.050 0.000* 263.64 22.94 - - 1.000 -
2 0.992 -6.577 - - 130.00 20.00 1.116 0.007
3 0.988 -6.661 - - 130.00 20.00 1.124 0.007
4 1.019 -6.424 - - 65.00 10.00 1.075 -0.053
5 1.050 -2.494 78.67 -29.94 - - 1.000 -0.047
-------- -------- -------- --------
Total: 342.31 -7.00 325.00 50.00
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 138.59 13.55 -131.55 2.28 7.035 15.83
2 1 3 125.05 9.39 -117.92 4.87 7.132 14.26
3 2 4 -1.55 -24.20 1.59 -21.27 0.037 0.06
4 3 5 -8.98 -22.96 9.44 -23.06 0.460 0.75
5 4 5 -66.59 11.27 69.22 -6.88 2.634 4.39
6 2 3 3.11 1.92 -3.10 -1.91 0.009 0.01
-------- --------
Total: 17.307 35.31
================================================================================
| Voltage Constraints |
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
1 - 0.950 1.050 1.050 23.166
5 - 0.950 1.050 1.050 9.544
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Reactive Power Limits
# # Qmin mu Qmin Qg Qmax Qmax mu
---- ----- ------- -------- -------- -------- -------
2 5 0.047 -30.00 -29.94 1800.00 -
with S line limit type of constraint
> runopf(WB5)
MATPOWER Version 6.0, 16-Dec-2016 -- AC Optimal Power Flow
MATPOWER Interior Point Solver -- MIPS, Version 1.2.2, 16-Dec-2016
(using built-in linear solver)
MATPOWER Version 6.0, 16-Dec-2016 -- AC Optimal Power Flow
MATPOWER Interior Point Solver -- MIPS, Version 1.2.2, 16-Dec-2016
(using built-in linear solver)
Converged!
Converged in 0.27 seconds
Objective Function Value = 342.30 $/hr
================================================================================
| System Summary |
================================================================================
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 6 Losses (I^2 * Z) 17.31 35.30
Transformers 0 Branch Charging (inj) - 92.3
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 0.988 p.u. @ bus 3 1.050 p.u. @ bus 1
Voltage Angle -6.66 deg @ bus 3 0.00 deg @ bus 1
P Losses (I^2*R) - 7.13 MW @ line 1-3
Q Losses (I^2*X) - 15.82 MVAr @ line 1-2
Lambda P 1.00 $/MWh @ bus 5 1.12 $/MWh @ bus 3
Lambda Q -0.05 $/MWh @ bus 4 0.01 $/MWh @ bus 3
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.050 0.000* 263.55 22.97 - - 1.000 -
2 0.992 -6.574 - - 130.00 20.00 1.116 0.007
3 0.988 -6.658 - - 130.00 20.00 1.124 0.008
4 1.019 -6.394 - - 65.00 10.00 1.075 -0.052
5 1.050 -2.462 78.76 -29.98 - - 1.000 -0.046
-------- -------- -------- --------
Total: 342.30 -7.00 325.00 50.00
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 138.54 13.57 -131.51 2.25 7.030 15.82
2 1 3 125.01 9.41 -117.88 4.85 7.127 14.25
3 2 4 -1.59 -24.18 1.63 -21.29 0.037 0.06
4 3 5 -9.02 -22.93 9.49 -23.08 0.464 0.76
5 4 5 -66.63 11.29 69.27 -6.89 2.637 4.40
6 2 3 3.10 1.93 -3.09 -1.91 0.009 0.01
-------- --------
Total: 17.305 35.30
================================================================================
| Voltage Constraints |
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
1 - 0.950 1.050 1.050 23.410
5 - 0.950 1.050 1.050 9.461
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Reactive Power Limits
# # Qmin mu Qmin Qg Qmax Qmax mu
---- ----- ------- -------- -------- -------- -------
2 5 0.046 -30.00 -29.98 1800.00 - WITH P LINE LIMIT CONSTRAINT
MATPOWER Version 6.0, 16-Dec-2016 -- AC Optimal Power Flow
MATPOWER Interior Point Solver -- MIPS, Version 1.2.2, 16-Dec-2016
(using built-in linear solver)
Converged!
Converged in 0.91 seconds
Objective Function Value = 10067.77 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 5 Total Gen Capacity 1530.0 -1147.5 to 1147.5
Generators 5 On-line Capacity 1530.0 -1147.5 to 1147.5
Committed Gens 5 Generation (actual) 1006.8 387.4
Loads 3 Load 1000.0 328.7
Fixed 3 Fixed 1000.0 328.7
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 6 Losses (I^2 * Z) 6.78 67.77
Transformers 0 Branch Charging (inj) - 9.1
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 1.060 p.u. @ bus 3 1.100 p.u. @ bus 1
Voltage Angle -5.42 deg @ bus 3 0.00 deg @ bus 5
P Losses (I^2*R) - 3.71 MW @ line 1-2
Q Losses (I^2*X) - 37.11 MVAr @ line 1-2
Lambda P 10.00 $/MWh @ bus 5 10.20 $/MWh @ bus 3
Lambda Q 0.00 $/MWh @ bus 5 0.07 $/MWh @ bus 2
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.100 0.000* 568.89 171.04 - - 10.000 -
2 1.060 -5.022 - - 300.00 98.61 10.189 0.067
3 1.060 -5.424 40.00 29.99 300.00 98.61 10.204 0.067
4 1.085 -2.756 200.00 149.98 400.00 131.47 10.101 0.023
5 1.100 0.002 197.89 36.38 - - 10.000 -
-------- -------- -------- --------
Total: 1006.78 387.40 1000.00 328.69
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 376.71 133.33 -373.00 -97.05 3.711 37.11
2 1 4 192.71 38.59 -191.74 -29.66 0.971 9.71
3 1 5 -0.53 -0.88 0.53 -2.90 0.000 0.00
4 2 3 73.00 -1.56 -72.95 -0.01 0.051 0.51
5 3 4 -187.05 -68.61 188.10 78.32 1.049 10.49
6 4 5 -196.36 -30.14 197.36 39.29 0.995 9.95
-------- --------
Total: 6.777 67.77
================================================================================
| Voltage Constraints |
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
1 - 0.900 1.100 1.100 100.311
5 - 0.900 1.100 1.100 32.647
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
1 3 - 0.00 40.00 40.00 0.204
4 4 - 0.00 200.00 200.00 0.101
Gen Bus Reactive Power Limits
# # Qmin mu Qmin Qg Qmax Qmax mu
---- ----- ------- -------- -------- -------- -------
1 3 - -30.00 29.99 30.00 0.067
4 4 - -150.00 149.98 150.00 0.023
>>
WITH S LINE LIMIT CONSTRAINT
MATPOWER Version 6.0, 16-Dec-2016 -- AC Optimal Power Flow
MATPOWER Interior Point Solver -- MIPS, Version 1.2.2, 16-Dec-2016
(using built-in linear solver)
Converged!
Converged in 7.85 seconds
Objective Function Value = 10067.77 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 5 Total Gen Capacity 1530.0 -1147.5 to 1147.5
Generators 5 On-line Capacity 1530.0 -1147.5 to 1147.5
Committed Gens 5 Generation (actual) 1006.8 387.4
Loads 3 Load 1000.0 328.7
Fixed 3 Fixed 1000.0 328.7
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 6 Losses (I^2 * Z) 6.78 67.77
Transformers 0 Branch Charging (inj) - 9.1
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 1.060 p.u. @ bus 3 1.100 p.u. @ bus 1
Voltage Angle -5.42 deg @ bus 3 0.00 deg @ bus 5
P Losses (I^2*R) - 3.71 MW @ line 1-2
Q Losses (I^2*X) - 37.11 MVAr @ line 1-2
Lambda P 10.00 $/MWh @ bus 5 10.21 $/MWh @ bus 3
Lambda Q 0.00 $/MWh @ bus 5 0.07 $/MWh @ bus 2
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.100 0.000* 568.47 170.18 - - 10.000 -
2 1.060 -5.022 - - 300.00 98.61 10.190 0.068
3 1.060 -5.424 40.00 30.00 300.00 98.61 10.205 0.067
4 1.085 -2.756 200.00 149.99 400.00 131.47 10.101 0.023
5 1.100 0.003 198.31 37.23 - - 10.000 -
-------- -------- -------- --------
Total: 1006.78 387.40 1000.00 328.69
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 376.69 133.30 -372.98 -97.02 3.711 37.11
2 1 4 192.68 38.52 -191.71 -29.60 0.971 9.71
3 1 5 -0.90 -1.63 0.90 -2.15 0.000 0.00
4 2 3 72.98 -1.59 -72.93 0.02 0.051 0.51
5 3 4 -187.07 -68.63 188.12 78.35 1.049 10.49
6 4 5 -196.41 -30.23 197.41 39.38 0.995 9.95
-------- --------
Total: 6.777 67.77
================================================================================
| Voltage Constraints |
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
1 - 0.900 1.100 1.100 101.589
5 - 0.900 1.100 1.100 31.423
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
1 3 - 0.00 40.00 40.00 0.205
4 4 - 0.00 200.00 200.00 0.101
Gen Bus Reactive Power Limits
# # Qmin mu Qmin Qg Qmax Qmax mu
---- ----- ------- -------- -------- -------- -------
1 3 - -30.00 30.00 30.00 0.067
4 4 - -150.00 149.99 150.00 0.023
>>
MATPOWER Version 6.0, 16-Dec-2016 -- AC Optimal Power Flow
MATPOWER Interior Point Solver -- MIPS, Version 1.2.2, 16-Dec-2016
(using built-in linear solver)
Converged!
Converged in 1.70 seconds
Objective Function Value = 10067.77 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 5 Total Gen Capacity 1530.0 -1147.5 to 1147.5
Generators 5 On-line Capacity 1530.0 -1147.5 to 1147.5
Committed Gens 5 Generation (actual) 1006.8 387.4
Loads 3 Load 1000.0 328.7
Fixed 3 Fixed 1000.0 328.7
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 6 Losses (I^2 * Z) 6.78 67.77
Transformers 0 Branch Charging (inj) - 9.1
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 1.060 p.u. @ bus 3 1.100 p.u. @ bus 1
Voltage Angle -2.67 deg @ bus 3 2.76 deg @ bus 5
P Losses (I^2*R) - 3.71 MW @ line 1-2
Q Losses (I^2*X) - 37.11 MVAr @ line 1-2
Lambda P 10.00 $/MWh @ bus 5 10.21 $/MWh @ bus 3
Lambda Q 0.00 $/MWh @ bus 5 0.07 $/MWh @ bus 2
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.100 2.756 568.47 170.18 - - 10.000 -
2 1.060 -2.266 - - 300.00 98.61 10.190 0.068
3 1.060 -2.668 40.00 30.00 300.00 98.61 10.205 0.067
4 1.085 0.000* 200.00 149.99 400.00 131.47 10.101 0.023
5 1.100 2.759 198.31 37.23 - - 10.000 -
-------- -------- -------- --------
Total: 1006.78 387.40 1000.00 328.69
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 376.69 133.30 -372.98 -97.02 3.711 37.11
2 1 4 192.68 38.52 -191.71 -29.60 0.971 9.71
3 1 5 -0.90 -1.63 0.90 -2.15 0.000 0.00
4 2 3 72.98 -1.59 -72.93 0.02 0.051 0.51
5 3 4 -187.07 -68.63 188.12 78.35 1.049 10.49
6 4 5 -196.41 -30.23 197.41 39.38 0.995 9.95
-------- --------
Total: 6.777 67.77
================================================================================
| Voltage Constraints |
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
1 - 0.900 1.100 1.100 101.589
5 - 0.900 1.100 1.100 31.423
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
1 3 - 0.00 40.00 40.00 0.205
4 4 - 0.00 200.00 200.00 0.101
Gen Bus Reactive Power Limits
# # Qmin mu Qmin Qg Qmax Qmax mu
---- ----- ------- -------- -------- -------- -------
1 3 - -30.00 30.00 30.00 0.067
4 4 - -150.00 149.99 150.00 0.023
MATPOWER Version 6.0, 16-Dec-2016 -- AC Optimal Power Flow
MATPOWER Interior Point Solver -- MIPS, Version 1.2.2, 16-Dec-2016
(using built-in linear solver)
Converged!
Converged in 0.38 seconds
Objective Function Value = 10010.55 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 5 Total Gen Capacity 1530.0 -1147.5 to 1147.5
Generators 5 On-line Capacity 1530.0 -1147.5 to 1147.5
Committed Gens 5 Generation (actual) 1001.1 330.0
Loads 3 Load 1000.0 328.7
Fixed 3 Fixed 1000.0 328.7
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 6 Losses (I^2 * Z) 1.06 10.56
Transformers 0 Branch Charging (inj) - 9.3
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 1.090 p.u. @ bus 2 1.100 p.u. @ bus 1
Voltage Angle -0.38 deg @ bus 2 1.17 deg @ bus 5
P Losses (I^2*R) - 0.35 MW @ line 2-3
Q Losses (I^2*X) - 3.51 MVAr @ line 2-3
Lambda P 10.00 $/MWh @ bus 5 10.06 $/MWh @ bus 2
Lambda Q -0.00 $/MWh @ bus 5 0.01 $/MWh @ bus 2
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.100 1.161 196.28 24.85 - - 10.000 -
2 1.090 -0.384 - - 300.00 98.61 10.056 0.014
3 1.099 0.521 519.99 175.26 300.00 98.61 10.023 -
4 1.098 0.000* 200.00 132.98 400.00 131.47 10.041 0.000
5 1.100 1.167 84.79 -3.12 - - 10.000 -
-------- -------- -------- --------
Total: 1001.06 329.96 1000.00 328.69
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 117.82 27.11 -117.48 -24.56 0.340 3.40
2 1 4 80.47 -0.75 -80.30 1.58 0.163 1.63
3 1 5 -2.00 -1.51 2.00 -2.27 0.000 0.00
4 2 3 -182.52 -74.05 182.88 75.33 0.351 3.51
5 3 4 37.11 1.31 -37.08 -1.79 0.034 0.34
6 4 5 -82.62 1.71 82.79 -0.84 0.168 1.68
-------- --------
Total: 1.056 10.56
================================================================================
| Voltage Constraints |
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
1 - 0.900 1.100 1.100 12.134
3 - 0.900 1.099 1.100 1.874
4 - 0.900 1.098 1.100 0.511
5 - 0.900 1.100 1.100 4.964
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
3 3 - 0.00 519.99 520.00 0.023
4 4 - 0.00 200.00 200.00 0.041TT =
V_k tetha_k2 Pgennode Qgennode P_k Q_k
Pd Qd
_______ ________ ________ ________ _______
_______ __ ______
Bus n° 1 1.0163 0 3.2349 2.8365 -3.2349
-2.8365 0 0
Bus n° 2 0.97025 -5.8782 0 0 3
0.9861 3 0.9861
Bus n° 3 0.96908 -6.3348 0.4 0.3 2.6
0.6861 3 0.9861
Bus n° 4 0.99688 -3.0982 1.7003 1.5 2.2997
-0.1853 4 1.3147
Bus n° 5 1.0127 0.8699 4.7539 -0.38143 -4.7539
0.38143 0 0
TT2 =
Pgen_k Qgen_k
______ ________
Gen n°1 0.4 0.3
Gen n°2 0 0
Gen n°3 3.2349 2.8365
Gen n°4 1.7003 1.5
Gen n°5 4.7539 -0.38143
Total P losses are equal to 8.9152 MW
Total Q losses are equal to 96.8126 MVAr
Total cost of unit commitment is 10089.1522function mpc = case5
% function mpc = case5
%CASE5 Power flow data for modified 5 bus, 5 gen case based on PJM 5-bus system
% Please see CASEFORMAT for details on the case file format.
%
% Based on data from ...
% F.Li and R.Bo, "Small Test Systems for Power System Economic Studies",
% Proceedings of the 2010 IEEE Power & Energy Society General Meeting
% Created by Rui Bo in 2006, modified in 2010, 2014.
% Distributed with permission.
% MATPOWER
%% MATPOWER Case Format : Version 2
mpc.version = '2';
%%----- Power Flow Data -----%%
%% system MVA base
mpc.baseMVA = 100;
%% bus data
%bus_i type Pd Qd Gs Bs area Vm Va baseKV
zone Vmax Vmin
mpc.bus = [
% 1 2 0 0 0 0 1 1 0
230 1 1.1 0.9;
1 3 0 0 0 0 1 1 0 230
1 1.1 0.9;
2 1 300 98.61 0 0 1 1 0
230 1 1.1 0.9;
3 2 300 98.61 0 0 1 1 0
230 1 1.1 0.9;
% 4 3 400 131.47 0 0 1 1 0
230 1 1.1 0.9;
4 2 400 131.47 0 0 1 1 0
230 1 1.1 0.9;
5 2 0 0 0 0 1 1 0 230
1 1.1 0.9;
];
%% generator data
% modified version in which i put Qg compatible and nonzero values
% bus Pg Qg Qmax Qmin Vg mBase status
Pmax Pmin Pc1 Pc2 Qc1min Qc1max Qc2min Qc2max ramp_agc
ramp_10 ramp_30 ramp_q apf
mpc.gen = [
3 40 15 30 -30 1 100 1 40
0 0 0 0 0 0 0 0 0 0
0 0;
% 1 170 15.73 127.5 -127.5 1 100 1 170
0 0 0 0 0 0 0 0 0
0 0 0;
1 0 0 127.5 -127.5 1 100 1 170
0 0 0 0 0 0 0 0 0 0
0 0
1 323.49 194.65 390 -390 1 100 1 520
0 0 0 0 0 0 0 0 0 0
0 0;
4 0 184.12 150 -150 1 100 1
200 0 0 0 0 0 0 0 0 0
0 0 0;
5 466.51 -38.21 450 -450 1 100 1 600
0 0 0 0 0 0 0 0 0 0
0 0;
];
% % bus Pg Qg Qmax Qmin Vg mBase status Pmax
Pmin Pc1 Pc2 Qc1min Qc1max Qc2min Qc2max ramp_agc ramp_10
ramp_30 ramp_q apf
% mpc.gen = [
% 1 40 0 30 -30 1 100 1 40
0 0 0 0 0 0 0 0 0 0
0 0;
% 1 170 0 127.5 -127.5 1 100 1 170
0 0 0 0 0 0 0 0 0 0
0 0;
% 3 323.49 0 390 -390 1 100 1 520
0 0 0 0 0 0 0 0 0 0
0 0;
% 4 0 0 150 -150 1 100 1 200
0 0 0 0 0 0 0 0 0 0
0 0;
% 5 466.51 0 450 -450 1 100 1 600
0 0 0 0 0 0 0 0 0 0
0 0;
% ];
% %% branch data ORIGINAL VERSION!
% % fbus tbus r x b rateA rateB rateC ratio
angle status angmin angmax
% mpc.branch = [
% 1 2 0.00281 0.0281 0.00712 400 400 400 0
0 1 -360 360;
% 1 4 0.00304 0.0304 0.00658 0 0 0 0
0 1 -360 360;
% 1 5 0.00064 0.0064 0.03126 0 0 0 0
0 1 -360 360;
% 2 3 0.00108 0.0108 0.01852 0 0 0 0
0 1 -360 360;
% 3 4 0.00297 0.0297 0.00674 0 0 0 0
0 1 -360 360;
% 4 5 0.00297 0.0297 0.00674 240 240 240 0
0 1 -360 360;
% ];
%% branch data
% fbus tbus r x b rateA rateB rateC ratio
angle status angmin angmax
mpc.branch = [
1 2 0.00281 0.0281 0.00712 400 400 400 0
0 1 -360 360;
1 4 0.00304 0.0304 0.00658 400 0 0 0
0 1 -360 360;
1 5 0.00064 0.0064 0.03126 400 0 0 0
0 1 -360 360;
2 3 0.00108 0.0108 0.01852 400 0 0 0
0 1 -360 360;
3 4 0.00297 0.0297 0.00674 400 0 0 0
0 1 -360 360;
4 5 0.00297 0.0297 0.00674 240 240 240 0
0 1 -360 360;
];
%%----- OPF Data -----%%
%% generator cost data
% 1 startup shutdown n x1 y1 ... xn
yn
% 2 startup shutdown n c(n-1) ... c0
mpc.gencost = [
2 0 0 2 10 0;
2 0 0 2 10 0;
2 0 0 2 10 0;
2 0 0 2 10 0;
2 0 0 2 10 0;
% 2 0 0 2 14 0;
% 2 0 0 2 15 0;
% 2 0 0 2 30 0;
% 2 0 0 2 40 0;
% 2 0 0 2 10 0;
];
% % CORREZIONE DI PER UNIT PER IL BILANCIO DEL CODICE MAIN3
% mpc.bus(:,3)=mpc.bus(:,3)/mpc.baseMVA;
% mpc.bus(:,4)=mpc.bus(:,4)/mpc.baseMVA;
% mpc.gen(:,2)=mpc.gen(:,2)/mpc.baseMVA;
% mpc.gen(:,3)=mpc.gen(:,3)/mpc.baseMVA;
% mpc.gen(:,4)=mpc.gen(:,4)/mpc.baseMVA;
% mpc.gen(:,5)=mpc.gen(:,5)/mpc.baseMVA;
% mpc.gen(:,9)=mpc.gen(:,9)/mpc.baseMVA;
% mpc.branch(:,6)=mpc.branch(:,6)/mpc.baseMVA;
%
%
%
mpc.traf = [];
%
% % % BUS PARAMETERS
% Pd = mpc.bus(:,3);
% Qd = mpc.bus(:,4); % node vs time matrix
% Vmax= mpc.bus(:,12); %vector of mpc.bus (Node, column, time)
% Vmin= mpc.bus(:,13);
%
% % GENERATOR PARAMETERS
% refbus= find(mpc.gen(:,2)==3);
% Pg= mpc.gen(:,2)
% Qg= mpc.gen(:,3)
% Pmax=mpc.gen(:,9);
% Pmin=mpc.gen(:,10);
% Qmax=mpc.gen(:,4);
% Qmin=mpc.gen(:,5);
%
% % BRANCH PARAMETERS
% flow_lim=mpc.branch(:,6);
%
% % GENERATOR COST PARAMETERS
% c_startup=mpc.gencost(:,2);
% c_shutdown=mpc.gencost(:,3);
% ncost= max(mpc.gencost(:,4));
% % THE LINES UNDER ARE VALID IF MODEL IS 2 POLYNOMIAL
% costmodel=mpc.gencost(:,1);
% Ngen=length(mpc.gen(:,1));
% costgen=zeros(Ngen,ncost);
%
%
% for i=1:Ngen
% % if (mpc.gencost(i,1)==2)
% for j=1:ncost
% costgen(i,j)=mpc.gencost(i,4+j);
% end
% if ncost== 3
% c_A(i) =costgen(i,1);
% c_B(i) =costgen(i,2);
% c_C(i) =costgen(i,3);
% elseif ncost==2
% c_A(i) =0;
% c_B(i) =costgen(i,1);
% c_C(i) =costgen(i,2);
% end
% end
%
% onoff= zeros(Ngen,1);
% % alpha= [];
% % beta = [];
% alpha= zeros(Ngen,1);
% beta= zeros(Ngen,1);
% for i=1:Ngen
% if Pg(i)>0 | Qg(i)~= 0
% onoff(i,1)=1;
% else
% onoff(i,1)=0;
% end
% end
% onoff
%
% mpc
% disp (['The generator costs follow the model [row= gen]']);
% costmodel
% disp(['with number of coefficients']);
% mpc.gencost(:,4)
% disp(['The cost matrix (row=gen, column= cost coefficients) is']);
% costgen
%
% return
