That is correct.
Ray
On Mar 30, 2012, at 10:10 AM, Hua Bowen wrote:
> I think each MU here (for PMIN, PMAX, VMIN, etc.) is one component of
> the Lagrangian multiplier μ in equation (A.32) in Appendix A. It is
> called Kuhn-Tucker multiplier, also known as shadow price. Am I right,
> Dr.Zimmerman?
>
> On Fri, Mar 30, 2012 at 9:36 PM, Ray Zimmerman <[email protected]> wrote:
>> 1. runmarket uses the offers and bids to determine the PMAX and PMIN from
>> generators and dispatchable loads respectively. So if you have a PMIN value
>> of -100 MW in the case file (for a dispatchable load) and you submit bid
>> quantities totaling 80 MW, it will set PMIN to -80 before calling the OPF to
>> solve for the market solution.
>>
>> 2, 3 and 4. I'm not sure why you think they are computed differently. All of
>> the shadow prices on constraints are computed the same way. All of them are
>> sensitivities of the objective to the constraint in question and all are
>> computed internally by the non-linear solver being used. As I mentioned in
>> my first response to you, in the case of the default MIPS solver, they are
>> included in the mu variable in equation (A.32) in Appendix A. The values are
>> computed in mips.m.
>>
>> --
>> Ray Zimmerman
>> Senior Research Associate
>> 419A Warren Hall, Cornell University, Ithaca, NY 14853
>> phone: (607) 255-9645
>>
>>
>>
>>
>> On Mar 29, 2012, at 4:12 PM, Carol Francesca wrote:
>>
>> Thank you.
>>
>> My questions are introduced as follows:
>>
>> 1.The value of Pmin in the case file and in the results are different while
>> they have to be the same. Why they are different when I am doing runmarket?
>> 2. The value MU_Pmin for dispatachable load and generators are computed in
>> different way, i.e. for generators it is calculated as explained in the
>> manual while for the dispatchable loads I don't know how they are
>> calculated. I want to know this(when I am doing runmarket).
>> 3. How MU_Pmax is calculated?
>> 4. Also, for voltage how they are calculated (MU_Vmin&max when I am doing
>> runmarket)
>>
>> I am so sorry for asking many questions.
>>
>> Best Regards
>>
>> C.F.
>>
>>
>>
>> On Thu, Mar 29, 2012 at 21:28, Ray Zimmerman <[email protected]> wrote:
>>>
>>> PMIN is a lower limit on the amount of generation PG in MW. This is an
>>> input value set in the case file. The value of MU_PMIN is the sensitivity of
>>> the objective to this constraint, a shadow price computed by the
>>> optimization. Similarly for PMAX and MU_PMAX. If you don't understand shadow
>>> prices you will need to get that from a course or book on optimization
>>> theory.
>>>
>>> When using the smart market code (runmarket.m) PMIN (for loads) and PMAX
>>> (for generators) are modified according to the bid and offered quantities
>>> before calling the OPF.
>>>
>>> Does that help?
>>>
>>> --
>>> Ray Zimmerman
>>> Senior Research Associate
>>> 419A Warren Hall, Cornell University, Ithaca, NY 14853
>>> phone: (607) 255-9645
>>>
>>>
>>>
>>>
>>> On Mar 29, 2012, at 12:27 PM, Carol Francesca wrote:
>>>
>>> Thank you for your response.
>>>
>>> My problem is the first: I don't understand how PMIN is computed in the
>>> result(it is different from the Pmin set in the case file)? MU_PMAX?
>>>
>>> MU_PMin for dispatchable loads and generators are calculated in a
>>> different way. I cannot understand this also why?
>>>
>>> Could you please explain these?
>>>
>>> Best Regards
>>>
>>> Carol Francesca
>>>
>>>
>>>
>>> On Thu, Mar 29, 2012 at 17:10, Ray Zimmerman <[email protected]> wrote:
>>>>
>>>> Are you saying you do not understand what a shadow price on a constraint
>>>> is? Or that you do not understand a specific optimization algorithm (such
>>>> as
>>>> the interior point method used by MIPS) and how these multipliers are
>>>> computed?
>>>>
>>>> If it is the first, I will just say, it is the sensitivity of the
>>>> objective function to the constraint. In other words, in the case of
>>>> MU_PMIN, for example, a shadow price of $X/MW means that the objective
>>>> function would decrease by $X*Y if you were to relax the PMIN limit by Y MW
>>>> for some tiny value of Y.
>>>>
>>>> If it is the second, I suggest that you take a course or read a book on
>>>> non-linear optimization. The algorithmic details of how these shadow prices
>>>> are actually computed is different for each algorithm and beyond the scope
>>>> of what I can explain in an e-mail.
>>>>
>>>> --
>>>> Ray Zimmerman
>>>> Senior Research Associate
>>>> 419A Warren Hall, Cornell University, Ithaca, NY 14853
>>>> phone: (607) 255-9645
>>>>
>>>>
>>>>
>>>>
>>>> On Mar 28, 2012, at 4:13 PM, Carol Francesca wrote:
>>>>
>>>> Dear Dr. Zimmerman,
>>>>
>>>> I read the manual but I didn't understand how Pmin mu for dispatchable
>>>> loads as well as Pmax for generators are calculated. I really confused. If
>>>> it is possible please explain, because It is not clear for me how it has
>>>> been computed.
>>>>
>>>> Best Regards
>>>>
>>>> Carol Francesca
>>>>
>>>>
>>>>
>>>> On Mon, Mar 26, 2012 at 15:16, Ray Zimmerman <[email protected]> wrote:
>>>>>
>>>>> MU_PMIN and MU_QMIN are shadow prices on the minimum generation limits
>>>>> for real and reactive power. Constraint shadow prices, also called
>>>>> Kuhn-Tucker multipliers, are a standard output of most all constrained
>>>>> optimization solvers. See any book on constrained optimization for a
>>>>> description of their meaning and how they are computed for any given
>>>>> algorithm.
>>>>>
>>>>> In MATPOWER, the shadow prices are computed by whichever solver is used.
>>>>> For example, in the case of the default MIPS solver, they are included in
>>>>> the mu variable in equation (A.32) in Appendix A. The value is computed in
>>>>> mips.m.
>>>>>
>>>>> I should probably mention also that in the case of trapezoidal generator
>>>>> capability curves (see Section 5.4.3 in the manual), if one of the sloped
>>>>> portions of the curve is binding, its shadow price is decomposed into
>>>>> components for the corresponding real and reactive limits.
>>>>>
>>>>> --
>>>>> Ray Zimmerman
>>>>> Senior Research Associate
>>>>> 419A Warren Hall, Cornell University, Ithaca, NY 14853
>>>>> phone: (607) 255-9645
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> On Mar 25, 2012, at 7:08 PM, Carol Francesca wrote:
>>>>>
>>>>> Dear Prof. Zimmerman,
>>>>>
>>>>> I have a question:
>>>>>
>>>>> When I do runmarkt sometimes price and Lambdas are not equal and its
>>>>> because of network congestion and losses.
>>>>> In MATPOWER, how MU_PMIN and MU_QMIN are calculated? Could you please
>>>>> address the m.file which calculates these?
>>>>> How they affect the prices? There is no sufficient explanation about it
>>>>> in the manual. I am sorry but I cannot understand how they are calculated.
>>>>>
>>>>> Best Regards
>>>>>
>>>>> Carol
>>>>>
>>>>>
>>>>
>>>>
>>>
>>>
>>
>>
>
>
