SDP relaxation in PowerModelsAneex

Hi All,

I am wondering if there is an SDP relaxation of the OPF problem in PowerModelsAnnex? If there is no such function, I would appreciate any guide for implementing that in the PowerModelsAnnex.

I have noticed there are tow different SDP relaxations in PowerModels, including SDP and SparseSDP relaxations; can you please let me know how scalable are those relaxations?

All the best,
Rasoul

Hi Rasoul,

I have not yet ported the SDP relaxation to PowerModelsAnnex. However, the SOC relaxation there uses a similar variable space, so an extension of that model would be a good place to start.

The basic SDP model is the easiest to implement. It is very similar to most of the papers you would find about that model. The sparse version omits some entires in the W matrix and is hence more complex. But is also about 10 times more scalable.

In my experience, 100 buses is around the limit for the basic SDP model and about 1000 buses for the sparse version. In both cases you will want to use the MOSEK SDP solver. The open-source solvers are lagging far behind in terms of reliability compared to MOSEK.

FWIW, I generally do not use the SDP model in my work due to solver reliability challenges. Making SDP OPF formulation reliable in practice seems to be an open research topic.

I hope that helps!

Hi Dr. Coffrin,

Thank you so much for the response! I will look at the SOC relaxation in the PowerModelAnnex. It sure helps!

All the best,
Rasoul