Thanks for the insight. On Sun, Jun 5, 2016 at 12:20 AM, Ray Zimmerman <[email protected]> wrote:
> The lambdas are sensitivities of the objective function to changes in > demand. So a positive LAM_Q means that an increase in reactive demand will > increase the total system cost. A negative value means it will decrease the > system cost. So a generator injecting power at a bus with a positive LAM_Q > is reducing the system cost (providing value for which they should, > arguably, be paid). A generator that is absorbing reactive power at a bus > with a positive LAM_Q is increasing system cost and should pay for the > reactive power. When the price is negative, it means that absorbing > provides value (reduces cost) and you should have to pay to inject reactive > power since it increases system cost. > > Ray > > > > On Jun 4, 2016, at 3:40 AM, Saranya A <[email protected]> wrote: > > > > 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] > > > > > >
