I’m afraid I don’t have anything very concrete to offer in response to your
questions … but in my experience also I’ve been surprised at how well the
primal-dual interior point method converges even in the presence of fairly
ill-conditioned matrices.
My only suggestion in terms of approaches to wok around the ill-conditioning
would be to look for papers by the authors of the Artelys Knitro and IPOPT
packages which use similar algorithms, to see what approaches they have
implemented to deal with ill-conditioning. I don’t have the reference handy,
but I’m pretty sure I saw such a paper by the creators of Knitro.
There are probably others on this list with more experience and expertise on
this issue.
Ray
> On Jan 9, 2023, at 9:42 PM, Min Zhou <[email protected]> wrote:
>
> Dear Ray;
>
> I am a Ph.D. student working on power system optimization and have
> been matpower to solve optimal power flow problems recently. However,
> I got the following questions when I was running the algorithm:
>
> 1. In Newton's step, we need to solve a set of equations Ax = b. I
> found that the condition number of matrix A is very large (about 1e8).
> Thus, A is ill-conditioned. I was wondering why Newton's method can
> still get good numerical performance even when the equation Ax = b is
> ill-conditioned. Is 1e8 an acceptable condition number for Newton's
> method?
>
> 2. Is there any approach to solve the ill-condition problem of
> Newton's method when solving AC-OPF?
>
> Thank you for your time and consideration.
> --
> Min ZHOU
> School of Data Science
> City University of Hong Kong
>
