The Jacobean can certainly provide useful information, but it is always this issue of the predicting capability of state-based indices. Close to point-of-collapse they may give a good indication but it may be too late. Given state-based vs Margin-based indices is still an issue.

In CIGRE it was done much work on this topic in the 1990ies and followed up later.

Some work it could be useful to take a look at again are (reports available for free):

CIGRE WG/TF 38.02.11 Indices predicting voltage collapse including dynamic phenomena.

https://e-cigre.org/publication/091-indices-predicting-voltage-collapse-including-dynamic-phenomena

CIGRE WG/TF 38.02.10 Modelling of voltage collapse including dynamic phenomena.

https://e-cigre.org/publication/075-modelling-of-voltage-collapse-including-dynamic-phenomena

CIGRE WG/TF 38.02.12 Criteria and countermeasures for voltage collapse.

https://e-cigre.org/publication/101-criteria-and-countermeasures-for-voltage-collapse

I read these referances, thank you very much

I believe that voltage instability is not an issue in distribution networks (if you disagree try to figure out how this could happen) and hence any kind of voltage stability prediction index developed for the transmission system is purposeless.

The transformer is the source for the distribution network (DN). The transformer is supplied from a theoretical infinite power system. So, the voltage in the whole DN is given by the transformer. The conductors cross-sectional areas are chosen in such way to achieve acceptable voltage value at any extremity of the network for both directions of the power flow. Any DG connected into the DN should not be set to control the voltage because it might work against the transformer voltage. This is why voltage margins should be defined and the control is in terms of Q. The problem then is to correlate the controls.

In the case of DG, for sudden changes in the generated power, the influence on the voltage level is within +/-5%. Otherwise, the network was not correctly designed.

So, the most important is the voltage setting to the transformer secondary.

With radial distribution networks which receive power from the distribution transformer, voltage stability would not be an issue - thus I share Florin Capitanescu's opinion.

If you are however still interested in the theoretical idea of voltage stability based on Jacobian matrix, experiment your self with various metrics that can be derived from this matrix:

- The determinant

- The max / min singular value ratio

- The eigenvalues

In my experiences, all the metrics above are not particularly useful because they don't have a linear relationship with the distance to the point of voltage collapse. The PV curve or V-Q curve methods are more simple to implement and also give an exact distance to the maximum loading point.

The responses so far seem to refer to the traditional distribution systems with non or limited DG-penetration. Today many distribution systems experience a significant penetration of DG, many loads will be behind PE-converters and EV-charging is becoming a challenge. In some areas the flow may be to and not from the main grid in periods. Different kinds of stability issues seem to appear. The indices of the past may not be too useful and need to be adapted to fit the new topologies, components, models and control strategies. The thinking of margins and knowledge about what type of information the different indices give, may still be useful as a starting point. I agree with the previous response on the challenges to use the given state based indices for prediction due to the non-linearity of the problem.

Are there examples of published work reflecting stability issues in the new environment?

Thanks

Due to high Resistance to Reactance ratio

I see number of works on voltage stability in distribution network with distributed generation. I request Florin to provide more details about his answer as it is creating some confusion at least for people like me who are new to the field. A few references areas follow:

[1] M. Ettehadi, H. Ghasemi and S. Vaez-Zadeh, "Voltage Stability-Based DG Placement in Distribution Networks," in IEEE Transactions on Power Delivery, vol. 28, no. 1, pp. 171-178, Jan. 2013.

[2] K. K. Mehmood, C. Kim, S. U. Khan and Z. M. Haider, "Unified Planning of Wind Generators and Switched Capacitor Banks: A Multiagent Clustering-Based Distributed Approach," in IEEE Transactions on Power Systems, vol. 33, no. 6, pp. 6978-6988, Nov. 2018.