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**** >> **** >> ** ** >> >> >> > >
