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 >> >> > >
