Effects of running a state estimation with initialized load elements

[davidcano90]

Hello PGM Community!

I want to do a (asymmetric) state-estimation (SE) of a meshed network with 193 nodes, 202 lines, 2 transformers (just to give you an idea). There are enough power and voltage sensors. Considering a random seed number generator to be able to reproduce the scenarios, I have realized the following with the corresponding effects:

1. SE execution with load elements in the model for each node. The values for each phase are set to zero:
   There is a successful convergence of the SE.

2. SE execution with load elements in the model for each node. The values for each phase are set to a non-zero value - e.g. P = 1 kW; Q = 0 Var:
   There is a successful convergence of the SE, but the results are not exactly the same as in case 1).

3. SE execution without load elements:
   _There is no convergence. "power_grid_model.core.errors.IterationDiverge: Iteration failed to converge after 2000 iterations! Max deviation: 2.59437e-06, error tolerance: 8e-07."

4. SE execution without load elements with error tolerance set to 2.6 e-06:
   There is a convergence, but the results vary significantly with respect to case 1) and 2).

For all cases the algorithm used was “iterative linear”.

From the above I have two questions that I would appreciate if you could help me to solve them:

1. What role do the load elements play in PGM during the execution of a SE?
2. In the dictionary that contains the results of the SE, what does the key associated to the loads represent?

Thank you in advance for your help!

Best regards

David

[mgovers]

Hi David,

Thank you for opening this topic. I think I understand your question, but to make sure, can you please elaborate a little bit more?

• Which component do you mean by "load element"? Is that sym_load/asym_load?
  • If so, in the case of state estimation, sym_load and asym_load function as an indicator to tell the PGM that "there is a load connected here". I.e.:
    • If there is no load provided, then the PGM will assume a zero-injection constraint (Kirchoff's Laws hold for the connected branches alone).
    • If there is a load connected at a node, then it introduces an additional unknown, because there is no zero-injection constraint: it is not known how much the load consumes/produces - that's up to the state estimation algorithm to deduce.
  • That may explain the difference seen between the first 2 and last 2 scenarios (but not the difference within the first 2 and within the last 2, resp.).
• Concerning the 2nd part of your question, it contains the deduced loads from state estimation. The deduction is taken from the added unknown in Kirchoff's Laws in the previous bullet points.
• Is there a possibility you could share your data and/or your test code?
  • That way, it is a little bit easier to understand your question. We will also be able to investigate where the difference comes from.
  • To speed up the investigation, it would be great if you can share it in the form of a test case (see also https://power-grid-model.readthedocs.io/en/stable/examples/Make%20Test%20Dataset.html)
  • It would be even better if you can make it a minimal example (e.g. you can try to remove the amount of nodes and lines in steps and until you find a different behavior, and then share the last configuration before it changed behavior).
  • The smaller a test case is, the easier and quicker the investigation will go and the better we can pinpoint the exact problem if there is any.