Failed to converge due to adjacent links

[noelhuang]

Hello everyone,

I am trying to calculate a loadflow on a grid I received, but unfortunately I receive the following error messages:

I have heard that this can apparently be caused by two or more adjacent links (i.e., link-node-link) which can lead to failure to converge. The grid I am trying to use does have many adjacent links, a small excerpt:

What would be the best approach to getting the loadflow to work on this grid?
I have tried two approaches, but perhaps I am missing something:

1. Removing adjacent links, but it seems not all adjacent links can be removed from my grid due to multiple 'dead-end' nodes being connected to a single node via links. See example part of my grid, with links highlighted:

2. Converting links to lines, and assigning some small value of x1 and r1 and i_n to them (small, but still larger than the hardcoded default used for links) to prevent the numerical instability. However, I am not sure what values for x1, r1, and i_n would be good to choose in this case.

Thanks in advance for any help!

[mgovers]

Hi @noelhuang,

Thank you for your question. Links are indeed a well-known potential source of instabilities (see e.g. PowerGridModel/power-grid-model#1217 which may be related to the edge case you're facing). We are working on improving this (see e.g. PowerGridModel/power-grid-model#35 , which is currently under active development), but for the time being, a workaround is indeed required.

1. What is the reason you need the "dead nodes" in your grid? Would you be able to remove those dead nodes as well?
2. If that is not possible, you can indeed try to replace the links with lines with a fixed impedance.
   • The PGM uses a default admittance for lines of $$10^6 (1 + \text{j})\text{ Siemens}$$ for a 10 kV node, which can be mapped onto other voltage levels using Ohm's law: $$Z_{link} = \frac{1-j}{2} \frac{u_{\text{rated}}}{10\text{ kV}} * 10^{-6} \text{ Ohm}$$.
   • As a good starting point, you can therefore try to set $$\text{r1} = k * 10^{-11} * \text{u rated}$$ where $k$ is a relative factor, e.g. $10$. For the sake of consistency, you can set x1 = r1 and you can leave i_n empty (it's not a required value by PGM cfr. https://power-grid-model.readthedocs.io/en/stable/user_manual/components.html#line)
   • If that doesn't work, you can try $100$.
   • If that still doesn't work, there may be something else going on. Please make sure to double-check your data. It may help to try to make a minimal reproducible case.

[figueroa1395]

Hello @noelhuang,

To add to this answer, usually link elements give problems when performing a state estimation calculation (but that's not a rule), so my gut feeling is that this is a case of bad data somewhere.

Nevertheless, I would recommend you to send us a minimum reproducible case, so we can track the issue more easily. You can try making a small grid that contains a representation of what you think is potentially causing the issue (like the links of links hypothesis); for this, I highly recommend you use power-grid-model-ds if the initial grid is too hard to manage. You can try to visualize the grid, and start "chopping" bits until you get the smallest grid for which this is an issue, then it would be easier for us to investigate and give you more input on.

[noelhuang]

Hi! Thank you for replying, and I apologize for the slow follow-up. I took a look at the grid using power-grid-model-ds as you suggested.

I have applied multiple of your suggestions:

1. Remove leaf nodes and their link (nodes that were connected via only a single link).
2. Excised a small-ish suspicious portion of the grid (42 nodes) (the part downstream from the transformer, where many edges branch out from a single node, presumably this is an installation/bus bar),
3. Replace any remaining links with lines where x1 and r1 are both equal to 0.00001.
   But unfortunately PGM seems to still fail to converge.

Sadly, the grid we received is from Enexis and as such I cannot publicly share it on this discussion page. I will contact you directly, if that's OK?

[figueroa1395]

Hello @noelhuang,

As I understand it, the issues have now been resolved. The main problem, besides what has been mentioned here already, was that the u_ref for the source was set in V instead of p.u.. Once that and the other things were addressed, not only the convergence was successful, but the results were accurate.

If this is true, please let us know and mark the answer as correct, so other users can potentially pinpoint. Feel free to add anything else needed :).

[noelhuang]

Hi @figueroa1395 ,

Indeed the issues have been resolved, and as you summarized, after setting the u_ref of the source to 1, and combining it with the other above mentioned suggestions (remove leaf nodes that are connected via a link, and interpret links as lines with small x1 and r1 of 0.00001), the load flow now works correctly.

Thanks again for your help!