Being the stiffness of the grid its capability of maintaining the voltage constant despite small variations on load. Whereas, a weak grid would be easily affected by load variation and the voltage would change.
So here it comes my question, how do you quantify how stiff a grid? Is there any formula to calculate this?
If you model the power grid as a Thevenin source, then the "stiffness" is really the voltage drop across Zth with Vth being the nominal mains voltage at that point in the grid. Fortunately, this can be measured rather simply -- measure the mains voltage with a given load, then apply a load step to the grid and measure again. The resulting voltage drop is indicative of how stiff your grid source is, provided local long-lines (feeders) aren't dominating the measurement (since they will do so if present) -- as a result, you'll want to measure this at or very close to the service entrance if you're measuring this from a "customer's eye view".
The eigenvectors of the stiffness matrix are called modes and span a feature space. But this is never measured for the "grid" . However impedance and load regulation can be measured.
You can use the term loosely with analogies, but technically it is not measured or defined.
This is the same power supply impedance, that you also model/measure for other (e.g. onboard) power converters.
Grids have extremely low impedance at low frequencies (10 mHz and below) due to feedback through the power reserves.
At higher frequencies, the grid impedance becomes terribly high (several Ω) because the generators are too far away to react in time.
Here is an article with some curves.
One consequence is that the amplitude at nominal mains frequency is often rather constant, while the shape during the cycle can deviate 10s of V under heavy loads.
A consequence in turn is, that power factor correction is now mandatory for heavy loads. This forces most of the power consumption to be at low frequencies around the mains frequency and away from the several kHz frequencies.
My guess is that it would be quite a challenge to come up with a method that quantifies grid stiffness as a typical grid is a highly dynamic system with producers and consumers varying in load and attaching/detaching all of the time. You can measure the response of a specific outlet, for sure. But that might not tell you much about the grid as a whole.
Of course, you can try to quantify grid quality by finding measures for frequency stability, for example. Frequency might be one of the few parameters that quantify the grid as a whole, since most other parameters might be dependent on location.
