Thank you so much for the information Prof. Zimmerman.
I’d like your explanation about the simulation for the 6-bus system (Wood &
Wollemberg). When I run a DCOPF with the original case (rundcopf(case6ww)), the
LMP shown for Matpower are the same (11.899 $/MWh) for all buses because there
isn’t congestion in the transmission lines. Despite of the fact that the
Lagrange multiplier for generator 1 is active (0.303 $/MWh), the LMP are the
same. In my opinion, the LPM from bus 1 should be 12.202 $/MWh.
I’ll wait for your comments.
Regards,
Vh
MATPOWER Version 5.1, 20-Mar-2015 -- DC Optimal Power Flow
Gurobi Version 6.0.4 -- automatic QP solver
Converged in 0.16 seconds
Objective Function Value = 3046.41 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 6 Total Gen Capacity 530.0 0.0 to 0.0
Generators 3 On-line Capacity 530.0 0.0 to 0.0
Committed Gens 3 Generation (actual) 210.0 0.0
Loads 3 Load 210.0 0.0
Fixed 3 Fixed 210.0 0.0
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 11 Losses (I^2 * Z) 0.00 0.00
Transformers 0 Branch Charging (inj) - 0.0
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 1.000 p.u. @ bus 1 1.000 p.u. @ bus 1
Voltage Angle -3.67 deg @ bus 5 0.00 deg @ bus 1
Lambda P 11.90 $/MWh @ bus 3 11.90 $/MWh @ bus 4
Lambda Q 0.00 $/MWh @ bus 1 0.00 $/MWh @ bus 1
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.000 0.000* 50.00 0.00 - - 11.899 -
2 1.000 -0.299 88.07 0.00 - - 11.899 -
3 1.000 -0.278 71.93 0.00 - - 11.899 -
4 1.000 -2.986 - - 70.00 0.00 11.899 -
5 1.000 -3.666 - - 70.00 0.00 11.899 -
6 1.000 -3.087 - - 70.00 0.00 11.899 -
-------- -------- -------- --------
Total: 210.00 0.00 210.00 0.00
================================================================================
| 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 2.61 0.00 -2.61 0.00 0.000 0.00
2 1 4 26.06 0.00 -26.06 0.00 0.000 0.00
3 1 5 21.33 0.00 -21.33 0.00 0.000 0.00
4 2 3 -0.15 0.00 0.15 0.00 0.000 0.00
5 2 4 46.91 0.00 -46.91 0.00 0.000 0.00
6 2 5 19.59 0.00 -19.59 0.00 0.000 0.00
7 2 6 24.33 0.00 -24.33 0.00 0.000 0.00
8 3 5 22.75 0.00 -22.75 0.00 0.000 0.00
9 3 6 49.03 0.00 -49.03 0.00 0.000 0.00
10 4 5 2.97 0.00 -2.97 0.00 0.000 0.00
11 5 6 -3.37 0.00 3.37 0.00 0.000 0.00
-------- --------
Total: 0.000 0.00
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
1 1 0.303 50.00 50.00 200.00 -
De: [email protected]
[mailto:[email protected]] En nombre de Ray Zimmerman
Enviado el: jueves, 19 de noviembre de 2015 12:03
Para: MATPOWER discussion forum
Asunto: Re: Question about LMP
The LMPs for a DC OPF problem do incorporate any generator limits as well as
generation cost. Consider the case with no congestion, where the LMPs are
uniform at all nodes. For nodes with generators that are dispatched between
their lower and upper limits, the LMP equals their marginal cost of generation.
For a node with a generator at a binding upper (lower) limit, the LMP will
equal the marginal cost of generation plus (minus) the shadow price on the
binding upper (lower) generation constraint.
Ray
On Nov 19, 2015, at 8:27 AM, Victor Hugo Hinojosa M. <[email protected]>
wrote:
Dear Jovan and Sarmad,
I agree with your comments about LMP. In this analysis I’m not considered the
congestion. If the generation inequality constraints aren’t active, Matpower
prints this information correctly, and It’s possible to realize different
prices when the lines is congested. Sarmad, I’ve verified your idea. Despite
the fact that the shadow price for the minimum or maximum is active, the LMP
shown are the same for all buses.
My question is about why LMP doesn’t include the Lagrange multipliers related
to generation inequality constraints. I did a model using the dual problem for
the DCOPF, and I realized that dual constraints are the prices for each buses.
It’s very clear in those constraints that those “prices” take into account the
marginal cost, the congestion cost through the partial transmission
distribution factors (PTDF) and the generation constraints.
In the technical literature for the DCOPF (losses are neglected), the LPM are
modeled considering energy cost and congestion cost. However, in the book “Spot
pricing of electricity” from F. Schweppe et all, authors include these shadow
prices in order to compute the spot prices.
I’d like to know your feedback about these comments.
Regards,
Vh
De: [email protected]
[mailto:[email protected]] En nombre de Jovan Ilic
Enviado el: jueves, 19 de noviembre de 2015 1:13
Para: MATPOWER discussion forum
Asunto: Re: Question about LMP
Dear Victor,
If there is no congestion in the network, there is the same LMP at all the
nodes.
The LMP consists of loss, congestion, and energy costs. DCOPF has no
losses, and if there is no congestion only the energy cost is accounted for.
You can think of it as if since there is no congestion or loss cost the energy
can
be distributed to all nodes at the same price.
Regards,
Jovan Ilic
On Wed, Nov 18, 2015 at 4:37 PM, Victor Hugo Hinojosa M.
<[email protected]> wrote:
Dear Prof. Zimmerman,
I have a question about Local Marginal Prices (LMP) that are shown in
Matpower.
The definition of the LMP is the marginal cost of supplying, at least cost,
the next increment of electric demand at a specific location (node) on the
electric power network, taking into account both supply (generation/import)
bids and demand (load/export) offers and the physical aspects of the
transmission system including transmission and other operational
constraints.
When it is performed a DCOPF, Matpower shows LMP for each bus considering
the marginal cost (energy cost) and the congestion cost so that I'd like to
know why the generation constraints (maximum and minimum power) aren't
considered in the LMP.
Thank you so much for your ideas and comments.
Regards,
Vh
