It is true that when a lower generation limit is binding, as in this example,
the LMP at the bus will be lower than the generator’s marginal cost (or offer
in a market context). So, in a market you can’t get away with paying such a
generator only the LMP, you typically also pay them an “uplift” payment equal
to the shadow price on the lower generation limit in order to make them whole
financially.
Ray
> On Nov 19, 2015, at 1:19 PM, Victor Hugo Hinojosa M. <[email protected]>
> wrote:
>
> 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]
>> <mailto:[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]>
>> [mailto:[email protected]
>> <mailto:[email protected]>rnell.edu <http://rnell.edu/>] 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] <mailto:[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
>>
>>
>>
>>
>
>
