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 >> >> > >
