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] >
