1. The dummy buses are only connected to the line whose flow constraint you want to relax. 2. There is only one line in question. It was initially connected to X and Y, now it (the same line) is connected to X’ and Y’.
The idea is that we are essentially splitting the terminal buses of the line into two, X and X’ (and similarly for Y and Y’). X and X’ then are not physically connected by any branch, but the additional user constraints ensure they represent the same physical bus. Their voltages and angles are required to be the same, it’s just that at X the injection into the line is represented by a dummy generator and at X’ all of the other bus injections (which must be the negative of the line flow, since together all of the injections sum to zero) are represented by a dummy generator. As Álvaro points out, it is now easy to put costs on the injections of these dummy variables since they are simple optimization variables. I should mention that after looking again at the thread he linked to I realized I missed a constraint. You also need the equivalent of step 3 to constrain the reactive injections of the dummy generators as well. That is, Qg at X must equal -Qg at X’, and similarly at Y and Y’. Hope this helps, Ray -- Ray Zimmerman Senior Research Associate B30 Warren Hall, Cornell University, Ithaca, NY 14853 USA phone: (607) 255-9645 On Sep 24, 2014, at 9:50 AM, Jiazi Zhang <[email protected]> wrote: > Dear Dr. Zimmerman, > > Thank you so much for your approach. But I still have several questions. > > 1. For the two dummy buses, where should I add them? Are they directly > connected to the original bus X and Y? Or they are not connected to bus X and > bus Y, but have the same buses connection as X and Y? > 2. According to step 1, the relaxed line is reconnected to bus X' and bus Y', > but in step 6, it seems the line connected to X and Y still exists. Should > both the lines connected to X and Y, and X' and Y' exist in the system? > > Actually I'm not fully understanding why this approach can be equivalent to > relaxed the thermal limit constraints on a specific branch. Can you explain > the theory of the approach more in detail? > > Thank you! > > Best Regards, > Jiazi > > On Tue, Sep 23, 2014 at 1:20 PM, Ray Zimmerman <[email protected]> wrote: > There isn’t a really easy to solve what you want with the current version of > MATPOWER, but I think it should be possible to do it with a few “tricks”. > > For a branch between bus X and bus Y ... > > 1. Add two dummy buses X’ and Y’ and reconnect the line to X’ and Y’ instead > of X and Y. > 2. Add dummy generators at X, X’, Y and Y’ with PMIN = –M, PMAX = M, where M > is some value larger than the max flow on the line (even in the relaxed > solutions). > 3. Add user-defined linear constraints to enforce equality between the Pg of > dummy gen at X and -Pg of dummy gen at X’, and likewise for dummy gens at Y > and Y’. > 4. Set the cost on each of the dummy generators to a piecewise linear > function that is zero up to the original line limit value, and some large > value above that. > 5. Add user-defined linear constraints to enforce equality between the > voltages (magnitudes and angles) at X and X’ and at Y and Y’. > 6. Remove or relax the original line limit on the line itself. > > I don’t think I’ve never tried this, so I’d be interested in hearing how well > it works if you decide to attempt it. > > -- > Ray Zimmerman > Senior Research Associate > B30 Warren Hall, Cornell University, Ithaca, NY 14853 USA > phone: (607) 255-9645 > > On Sep 23, 2014, at 5:51 AM, Jiazi Zhang <[email protected]> wrote: > >> Dear all, >> >> I'm running AC OPF using Matpower for my project and for some cases, the OPF >> does not converge due to the capacities of several branches are not enough. >> I'd like to relax the thermal limit constraints on these branches with large >> penalty factors. But the power flow thermal limit constraints are nonlinear >> for AC OPF. I wonder if it is possible to do such branch limit relaxation in >> AC OPF program. >> >> Best Regards, >> Jiazi >> >> -- >> Jiazi Zhang >> Research Assisant >> School of Electrical, Computer & Energy Engineering >> Ira A. Fulton Schools of Engineering >> Arizona State University >> [email protected] > > > > > -- > Jiazi Zhang > Research Assisant > School of Electrical, Computer & Energy Engineering > Ira A. Fulton Schools of Engineering > Arizona State University > [email protected]
