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 <r...@cornell.edu> 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 <r...@cornell.edu> 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 <r...@cornell.edu> 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 <r...@cornell.edu> 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 >>>> >>>> >>> >>> >> >> > >
