The new HELM Powerflow in GridCal

This thread is a continuation of the discussion on the openmod list about the HELM power flow implemented in GridCal by @SanPen. To summarize:

@SanPen: do you have an idea why HELM fails here, even though it is supposed to be great for ill-conditioned systems? I tried to do debug into the HELM, but I know to little about the method to be able to check it…


After looking at the 11 bus iwamoto system, it was compiled from this very old paper by hand from the Ybus matrix: So it is very possible that there was a mistake in the conversion, and the system really doesn’t have a solution. Does anyone know of a data set with an ill-conditioned network in a more user friendly format?

#edit: I looked at the iwamoto system some more, and I don’t think we can rely on this network. The original paper does not give units for the admittance matrix (probably per unit, but who knows?) and also defines the power in per unit without giving the base power. Signs for the power (load/generation) are also not given. Its simply not possible to reliably compile the network from the given information.

Further discussion on the mailing list here (for some reason the original post seems to be missing).

And some references below (seeing I posted them to the mailing list). The Wikipedia article is also worth reading.


Trias, Antonio (July 2012). The holomorphic embedding load flow method. 2012 IEEE Power and Energy Society General Meeting. New Jersey, USA: IEEE. doi:10.1109/PESGM.2012.6344759.

Trias, Antonio (2015). “Fundamentals of the holomorphic embedding load-flow method”. arXiv. 1509.0242.


From what I can see a proper model of that 11-bus grid was not published, but rather the Ybus matrix directly… I observe that Ybus has no symmetry (not even close to symmetry) therefore I’d spend no time with this “grid” since I believe it was created to be non-solvable.

Best regards,

Well according to the paper it was created to be solvable, but difficult to solve. To test the superior convergence behaviour of HELM, we obviously need a network that is difficult to solve. Do you know of any ill-conditioned systems that NR might struggle with?

I can tell you right away that that grid is not only difficult to solve, it is probably impossible to solve.

A simple way to make it hard for NR is to set the specified voltage of some generators high (like 1.12) and others low (like 0.92). There NR will have a hard time solving the voltages since those are not very similar. On the other hand, HELM should work.

Something else that we must bear in mind is that any numerical method has boundaries. Helm included. The HELM convergence properties are supposed to be better but not infinite. Therefore a Y matrix without a symmetrical structure is not solvable by matrix methods. Maybe it is by BFS methods, but those are terrible is meshed grids anyway.