Just thinking out loud here: From what you quoted, the imbalance appears to have been in the generator frequencies to start with? I imagine they need to stay synchronized in frequency if they are sharing loads. Otherwise you set up a beat frequency at the difference frequency between the two generating systems, and their voltages will move from being in phase to being out of phase, back to being in phase again at the rate of the beat frequency. I don't know how power grids really work, but I imagine this will cause intolerable voltage variations as they sum in phase and out of phase. Did that happen? It's a simple graph to add two sine waves of equal amplitude but with a slight difference in phase to show what happens.

But upon closer inspection of the article you mentioned it looks like the real complaint was simply that having a slightly lower frequency than the assumed 50 Hz, kitchen equipment that assumes 50 Hz and some kind of zero crossing counter as a clock reference will get a long term clock drift.

As an aside, when we talk about load impedances being a function of frequency, unless the load has a very high Q (lossless resonance), they don't change very much in the vicinity of the frequency of the stimulus. Bio-mechanical systems (a cool topic) are inherently lossy and must have low Qs. To a first order it would be surprising to see much sensitivity to the frequency of the stimulus. But I can see additions and cancellations of multiple stimulus playing a role. And our internal body clocks seem to get reset every day according to the motion of the sun.

Hello. I'm registered for the Daily Study Group!

In early 2018, there was an incident in the European electrical power grid. From the Ars Technica reporting on the incident European grid dispute resolved, lost 6 minutes returned to oven clocks:

Last month, the European Network of Transmission System Operators (ENTSO-E) publicly admonished Serbia and Kosovo for not properly balancing their grids according to previous agreements. "This average frequency deviation, that has never happened in any similar way in the CE [Continental Europe] Power system, must cease," the group wrote. "ENTSO-E is urging European and national governments and policymakers to take swift action."

Two days later, on March 8, the Transmission System Operators (TSOs) from Serbia and Kosovo confirmed that they were back to balancing their grids appropriately.

The incident piqued my curiosity: it's a unique example where load influenced the frequency of the AC power grid. Even though the 50Hz grid never dropped below 49.996Hz, this remains (to the best of my knowledge) a unique deviation from that most-important frequency. Technically, what happened? What was the imbalance, and how could it have this significant an impact on the entire European grid? My understanding is that a 1% drop in the line frequency of a grid could have serious impact on some old (stodgy) generators. Is it possible to have a Wolfram Language simulation showing what happened for the class? What was this imbalance, and how much of an imbalance would it take to produce a 1% drop in the frequency? I'd love to hear a brief discussion about this incident during the class, but realize it may be a bit late to change the presentation. Perhaps a homework example?

The dynamics of electricity is a secondary interest to me. Many other systems -- including mechanical systems like our musculoskeletal system -- use stored energy in their oscillating cycles. The same impedance model used in electrical systems can be applied to many mechanical systems. Impedance is inherently dependent on frequency, but most don't understand the frequency-dependent dynamic in biomechanics. That must change.

Since electricity is discussed far more than any other domain studying impedance, I pay attention when Wolfram Research is discussing such things. Thank you for this WSG.