Victor, Just formulate a DCOPF with whatever constraints and cost function you'd like and pick the best (LP/IP/QP/SQP) algorithm for the formulation. The line flow constraints are now just a product of DF and bus injections. If your objective function is linear you are done. It could be a very good formulation if you have to run it very many times without changing the system topology or parameters because DF matrix needs to be calculated only once.
By the way, note that B from Y=R+jB is very likely non-singular for a real system so you might not even need a slack bus. Jovan Ilic On Mon, 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**** > > **** > > ** ** >
