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 >>>>> >>>>> >>>> >>> >> >
