I run a number of mains clocks, but the frequency of UK mains over the last few years has become more unstable (apparently due to the rise of unpredictable supplies from wind farms). It 'evens out' over time, but there can be a few days in a row where the clocks are as much as 1.5 minutes slow.
Would it be possible to design something to ensure the frequency is a constant 50Hz?
The only way to do this is to use a time standard independent of the mains frequency. This is usually done with a crystal oscillator which has been used in watches for years since they don't connect to mains power. These oscillators are more stable than the mains frequency over short periods but will eventually drift significantly over long periods (months to years depending on the quality of the crystal). You can also use the time signals transmitted by several different national laboratories (US, Germany, Japan, China) which rely on atomic clocks. These will not have any drift with time. Many low cost clocks are available with this feature.
Perhaps you could use a UPS which is connected to the mains normally but produces its own sine wave output (i.e. does NOT pass the mains AC through during normal operation). This isolates any variances in frequency in the grid from the clocks incoming AC power. However this could be quite expensive if all you're using it for is to keep clocks accurate. It might be easier to replace the clock with one that can sync to the Internet or radio controlled clocks, which as Barry mentions, are relatively low cost. The obvious caveat is that you lose the original clock you wanted to keep synchronised so if you have some reason to use that specific clock, then it might not be cheap or easy.
If your clocks could be controlled by computer somehow, NTP (Network Time Protocol) provides a traceable standard time reference.
If you're feeling ambitious, and your clocks are on their own feed, here's a pointer to some accurate 50Hz inverter solutions: https://bestengineeringprojects.com/crystal-controlled-inverter-verified-inverter-circuit/
Combine this with an NTP client to make the 50Hz to close the loop.
Maybe a UPS could do this as well, provided it uses an accurate time reference. This solves a secondary problem of power loss.
There's a time signal broadcast from Rugby, UK, and you should be able to find "motor" modules which pick this up. It may be possible to retrofit these to your clocks but I suspect that mounting and fitting hands will be problematic - unless there are some standard sizes that I'm not aware of.
The signal, also known as the MSF signal (and formerly the Rugby clock), is broadcast at a highly accurate frequency of 60 kHz and can be received throughout the UK, and in much of northern and western Europe. The signal's carrier frequency is maintained at 60 kHz to within 2 parts in 1012, controlled by caesium atomic clocks at the radio station. Source: Wikipedia.*
The article goes on to explain the time encoding which is also transmitted on the carrier. This is used to synchronise clocks and clock systems.
