Have you looked at the User's Manual? See section 5.5 and 5.6, in particular Table 5-2.
-- Ray Zimmerman Senior Research Associate B30 Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On Aug 6, 2013, at 11:35 AM, Aftognosia Aftognosia <[email protected]> wrote: > Doctor Zimmerman, > > I would like to study how the different algorithms work in the local minima. > In other words, how the different algorithms give different results, and how > this affect the local/global optimum. > > Could you please make me aware of where I can find a list of all the > algorithms supported by matpower and how can I set matpower to operate on > each one? > > Thank you ver y much > > > From: Ray Zimmerman <[email protected]> > To: MATPOWER discussion forum <[email protected]> > Sent: Monday, August 5, 2013 6:07 PM > Subject: Re: DC-OPF on matpower > > Thanks, Jovan, for this interesting discussion. You've convinced me. After a > bit more thought, I believe I agree with you after all. The formulations > should be equivalent. > > -- > Ray Zimmerman > Senior Research Associate > B30 Warren Hall, Cornell University, Ithaca, NY 14853 > phone: (607) 255-9645 > > > > On Aug 5, 2013, at 11:34 AM, Jovan Ilic <[email protected]> wrote: > >> >> Ray, >> >> No and yes. >> >> No, I am not sure what you mean by "line constraints will be affected by the >> choice >> of slack bus". A line constraint is either binding or not and slack bus >> choice will not >> affect it. It can be shown mathematically and is clear intuitively, once you >> show it >> mathematically, I suppose. :-) >> >> Yes, this formulation will give you a single LMP (at the slack bus) and line >> Lagrange multipliers (mus) and then you use the found LMP, DF and mus to >> calculate the rest >> of LMPs: >> >> LMPs = ones(Nb-1,1)*LMP + transpose(DF)*mu >> >> You can derive this from KKT conditions. You can also find a hint of it in >> Felix Wu's >> paper "Folk Theorems in Power Systems" or something like that. If I >> remember the >> paper, Felix uses relative LMPs or something like that, stopped half way if >> you ask >> me. >> >> Jovan Ilic >> >> >> >> On Mon, Aug 5, 2013 at 11:12 AM, Ray Zimmerman <[email protected]> wrote: >> For an unconstrained network, I agree that the slack is irrelevant and the >> problems are equivalent. >> >> However, I don't think the problems are equivalent when you have binding >> line constraints. Then I'm pretty sure the line constraints will still be >> affected by the choice of slack used when forming the PTDF. >> >> Another clue that the problems are not equivalent in this case is that it >> seems there is no way to recover the nodal prices from the PTDF-based >> approach. In a case with a single binding line limit you only have two >> non-zero constraint shadow prices in the problem (using PTDF), but you can >> have many different nodal prices from the traditional DC OPF. >> >> -- >> Ray Zimmerman >> Senior Research Associate >> B30 Warren Hall, Cornell University, Ithaca, NY 14853 >> phone: (607) 255-9645 >> >> >> >> On Aug 5, 2013, at 10:52 AM, Jovan Ilic <[email protected]> wrote: >> >>> >>> Ray, >>> >>> Yes, as I mentioned in my original post, dense PTDF is the drawback of this >>> approach and you might want to know bus angle differences to draw some >>> conclusions about the system but if you code it carefully you already have >>> what you need to quickly calculate the angles. >>> >>> However, there is no approximation introduced by the slack bus, with or >>> without the slack bus the result is the same. >>> >>> I coded it with both LP and QP and the results are the same, well if the >>> cost >>> functions are all linear of course. It takes about an hour to code it in >>> any >>> language and test it if you already have decent LP/QP functions. >>> >>> I actually expected people to question the method because I said that nodal >>> equations are not needed, just the global supply demand balance constraint. >>> It seems that I underestimated the audience. :-) >>> >>> Jovan Ilic >>> >>> >>> >>> On Mon, Aug 5, 2013 at 9:59 AM, Ray Zimmerman <[email protected]> wrote: >>> MATPOWER does not use the dense distribution factor matrix (PTDF) to >>> formulate the DC OPF. One other important distinction is that a PTDF matrix >>> is an approximation that requires an assumption about the slack. The sparse >>> formulation that includes the voltage angles does not require this >>> assumption. So the two formulations are not quite equivalent. >>> >>> In MATPOWER, the DC OPF is formulated as an LP or QP problem and the >>> algorithm used to solve it varies depending on the solver chosen via the >>> OPF_DC_ALG option. >>> >>> -- >>> Ray Zimmerman >>> Senior Research Associate >>> B30 Warren Hall, Cornell University, Ithaca, NY 14853 >>> phone: (607) 255-9645 >>> >>> >>> >>> >>> >>> On Aug 5, 2013, at 9:17 AM, Victor Hugo Hinojosa M. >>> <[email protected]> wrote: >>> >>>> Dear Jovan, >>>> Thank you so much for your message. >>>> I agree with your comment. Considering that >>>> [Y_bus]*[theta_angles]=[Power_injections], the balance nodal constrained >>>> can be formulated as a global balance power equation. Hence, the balance >>>> nodal matrix is reduced to one single equation. >>>> In addition, the power transmission constraint depends on the angles, but >>>> the angles can be transformed using the equation >>>> [theta_angles]=[Y_bus]^-1*[Power_injections], so the transmission >>>> constraint depends on the power injections, and it’s easy to find out >>>> about the distribution factors. With this proposal, it’s possible to model >>>> the DC-OPF problem using only the power generation as decision variable. >>>> Therefore, there are many advantages of this proposal. >>>> Do you address the DC-OPF problem with this proposal? >>>> I’d like to know which algorithm is applied by you to solve the OPF >>>> problem? >>>> Best Regards, >>>> Víctor >>>> >>>> De: [email protected] >>>> [mailto:[email protected]] En nombre de Jovan Ilic >>>> Enviado el: jueves, 01 de agosto de 2013 20:11 >>>> Para: MATPOWER discussion forum >>>> Asunto: Re: DC-OPF on matpower >>>> >>>> >>>> Victor, >>>> >>>> Yes, you can do it without bus angles but you'd end up with a formulation >>>> with >>>> a dense distribution factors matrix which could be a problem for large >>>> systems. >>>> One place where you can speed up such DCOPF is by using a global power >>>> balance equation instead of nodal equations. You do not need nodal >>>> balance >>>> equations if you have the distribution factors matrix. An added benefit >>>> of >>>> using the distribution matrix would be loss estimation. >>>> >>>> I rarely use Matpower so I am not sure which algorithm Ray uses. Maybe I >>>> should've let Ray answer the question since it was addressed to him. >>>> >>>> Jovan Ilic >>>> >>>> >>>> >>>> >>>> >>>> On Thu, Aug 1, 2013 at 7:06 PM, Victor Hugo Hinojosa M. >>>> <[email protected]> wrote: >>>> Dear Dr Zimmerman, >>>> I’d like to ask you a question about the DC optimal power flow (DC-OPF). >>>> The optimization problem in Matpower is modeled using as decision >>>> variables the active power generation and the bus voltage angles. These >>>> variables are solved using the primal-dual interior point solver (MIPS) >>>> considering that both variables are independent. When the AC transmission >>>> system is transformed using the DC approach, the voltage angles and the >>>> active power injections are related through the Y_bus matrix, so the >>>> decision variables are dependent. It’s possible to model the DC-OPF >>>> problem using only the power generation as decision variable? >>>> Thank you so much for your comments in advance. >>>> Best Regards, >>>> Víctor >>>> >>>> >>> >>> >> >> > > >
