For a case where branch limits make the AC OPF infeasible, this is a clever way to get a solution that is close to feasibility, however, it does so by relaxing the power balance constraints, not the flow limit constraints. I'm not sure that's what you want.
When you say that sometimes it doesn't work, do you mean that the OPF doesn't converge? If so, it may be due to numerical issues stemming from a large range of costs (assuming you are using very large costs on these virtual generators). It's possible that a different solver or less extreme costs on these virtual generators would be more successful. Let me mention that just because you are using an AC OPF does not mean that you can't apply penalty costs to a linear approximation of the flows. If you iterate, you could improve the linear approximation of the flows at each iteration and probably get quite close to the solution you are looking for (penalties on violated AC flows). You could start by approximating the AC flows with the DC flows, assigning a penalty to violations of these linear approximations to the flows. Then you could linearize each line flow around the current operating point, reconstruct the violated flow penalties based on the new flows and re-run, repeating until you have convergence. Just an idea … -- Ray Zimmerman Senior Research Associate 419A Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On Apr 10, 2013, at 3:11 AM, Roman Korab <[email protected]> wrote: > Hi Ray, > > Thank you for your reply. In my current research I use AC OPF, so the problem > is not easy. I tried to solve this issue by adding in every bus two virtual > generators - the first one with positive and the second with negative > generation, both with very high costs. In consequence virtual generators > produce power only when there is no any other way to meet branch limits. But > it sometimes works fine, and sometimes not. I wonder what can be the reason > of such behaviour? > > Best regards > Roman > ----- Original Message ----- > From: Ray Zimmerman > To: MATPOWER discussion forum > Sent: Tuesday, April 09, 2013 8:58 PM > Subject: Re: Branch limits as "soft" constraints > > Hi Roman, > > In the current version of MATPOWER there is no easy way to do this for AC OPF > problems, since the flows are non-linear functions of the optimization > variables. It is possible to add user-defined costs on the DC model flows > using the mechanism described in sections 5.3.1 and 6.1 of the User's Manual, > since they are linear functions of optimization variables. > > -- > Ray Zimmerman > Senior Research Associate > 419A Warren Hall, Cornell University, Ithaca, NY 14853 > phone: (607) 255-9645 > > > > > On Apr 9, 2013, at 11:26 AM, Roman Korab <[email protected]> wrote: > >> Hello Matpower users! >> >> I wonder if is possible to treat the thermal branch limits as a "soft" >> constraints in Matpower OPF procedures? For example, when I make some OPF >> calculations in order to determine effectivness of cross-border real power >> flow control by using phase shifting transformers, for some settings of PST, >> OPF don't converge. The main reason is that some branches have not enough >> capacity to transmit more power. Is there any simple way to overcome >> mentioned problem, for example, by automatic treatment the thermal limits of >> such branches not as a strict constraints, but as constraints that can be >> exceeded? >> >> Best regards >> Roman > >
