Dear Ray,
When I run optimal power flow for a 6-bus system using MATPOWER 5.1, this
is the result which I obtain.
1. Here, I observe that Lambda values of Q is negative. What does this
signify?
I understand positive value of lambda means the generator gets paid for
supplying reactive power. On the other hand, what happens when a generator
consumes reactive power from the system?
2. At bus 2, the generator supplies Q and at bus 3 the generator consumes Q
but in both cases the lambda is negative.I dont clearly understand what
signal lambda is giving. Please clarify my doubt.
-----------------------------------------------------------------------
MATPOWER Version 5.1, 20-Mar-2015 -- AC Optimal Power Flow
MATLAB Interior Point Solver -- MIPS, Version 1.2, 20-Mar-2015
(using built-in linear solver)
Converged!
Converged in 0.10 seconds
Objective Function Value = 2454.85 $/hr
================================================================================
| System Summary
|
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- -------------
-----------------
Buses 6 Total Gen Capacity 530.0 -300.0 to 420.0
Generators 3 On-line Capacity 530.0 -300.0 to 420.0
Committed Gens 3 Generation (actual) 159.3 28.5
Loads 6 Load 158.0 82.8
Fixed 6 Fixed 158.0 82.8
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 11 Losses (I^2 * Z) 1.29 3.90
Transformers 0 Branch Charging (inj) - 58.2
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 1.044 p.u. @ bus 4 1.070 p.u. @ bus 2
Voltage Angle -2.31 deg @ bus 6 0.00 deg @ bus 1
P Losses (I^2*R) - 0.39 MW @ line 2-4
Q Losses (I^2*X) - 0.77 MVAr @ line 2-4
Lambda P 11.45 $/MWh @ bus 2 11.70 $/MWh @ bus 5
Lambda Q -0.06 $/MWh @ bus 2 0.10 $/MWh @ bus 4
================================================================================
| Bus Data
|
================================================================================
Bus Voltage Generation Load
Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P
Q
----- ------- -------- -------- -------- -------- -------- -------
-------
1 1.067 0.000* 50.00 9.35 16.00 10.00 11.450
-0.003
2 1.070 -0.533 62.76 19.61 8.00 4.80 11.449
-0.064
3 1.063 -0.883 46.53 -0.45 12.00 4.00 11.522
-0.028
4 1.044 -1.469 - - 40.00 32.00
11.676 0.097
5 1.051 -2.049 - - 34.00 20.00
11.698 0.010
6 1.053 -2.306 - - 48.00 12.00
11.674 -0.012
-------- -------- -------- --------
Total: 159.29 28.51 158.00 82.80
================================================================================
| 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 3.65 -5.60 -3.63 1.08 0.021
0.04
2 1 4 16.37 6.06 -16.22 -9.92 0.148
0.59
3 1 5 13.98 -1.11 -13.84 -5.09 0.141
0.53
4 2 3 3.28 -0.95 -3.27 -5.84 0.007
0.04
5 2 4 25.70 13.76 -25.31 -15.22 0.385
0.77
6 2 5 11.01 1.00 -10.90 -5.15 0.115
0.35
7 2 6 18.41 -0.08 -18.20 -4.95 0.212
0.61
8 3 5 9.08 -2.09 -8.99 -3.30 0.088
0.19
9 3 6 28.72 3.49 -28.57 -4.97 0.150
0.75
10 4 5 1.53 -6.85 -1.52 -1.90 0.016
0.03
11 5 6 1.24 -4.56 -1.24 -2.07 0.003
0.01
--------
--------
Total: 1.287
3.90
================================================================================
| Voltage Constraints
|
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
2 - 0.950 1.070 1.070 28.097
================================================================================
| Generation Constraints
|
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
1 1 0.752 50.00 50.00 200.00 -
case1offpeak =
version: '2'
baseMVA: 100
bus: [6x17 double]
gen: [3x25 double]
branch: [11x21 double]
gencost: [6x7 double]
order: [1x1 struct]
om: [1x1 opf_model]
x: [18x1 double]
mu: [1x1 struct]
f: 2.4549e+03
var: [1x1 struct]
nln: [1x1 struct]
et: 0.0970
success: 1
raw: [1x1 struct]
