It turns out that I was recently faced with a similar situation, so I 
implemented another MATPOWER extension to convert the limits on certain lines 
to soft limits, with a simple linear cost on line violations. I plan to include 
it in the final release of MATPOWER 5, but I will send it to you off-list now. 
Hopefully, it does exactly what you want.

Sorry for the lack of good clear examples in the manual of adding additional 
costs, constraints. I hope to remedy that at some point. For the time being, 
there is an example buried in the test suite, starting around line 185 in 
t/t_opf_mips.m.

-- 
Ray Zimmerman
Senior Research Associate
B30 Warren Hall, Cornell University, Ithaca, NY 14853  USA
phone: (607) 255-9645

> On Oct 29, 2014, at 11:03 AM, mohd <[email protected]> wrote:
> 
> Good Morning all,
>  
> I am using a DC OPF to be tested in a real case system. However, the problem 
> does not converge. However, if i remove transmission constraint, then the 
> problem is solved. Upon further inspection, i found some lines are violating 
> the constraint. When checking the high concentrated load area, i found the 
> least resistance path carries the most amount of the flow, while the high 
> resistance path carries less, which is logical and well-known. Now, what I am 
> trying to do is to add a penalty function when lines exceeds their capacity 
> to encourage the flow to the high resistance path, which is taken care of by 
> the OPF since it tries to minimize the obj function. Since line limits are 
> already included as part of my OPF in matpower, my understanding is that i 
> need to add penalty function to the objective function only. If so, when i 
> followed the manual, i kind of got lost with several matrices that needs to 
> be created and defined and i wish that matpower showed an example of 
> modifying the objective function, so i can follow and make an analogy. So, i 
> appreciate any help that can be provided or direction that can lead me to an 
> example that can be easily followed. Thanks.

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