On the subject of Dinorwig power station (and similar pumped storage stations), and their contribution to grid stability, I understand Dinorwig was specified to be big enough to cope with a PWR nuclear power station going off line suddenly.
At a massive coal power station like Drax, there are several boilers, several steam turbines, and several sets of pylons carrying power away from the plant. However they are grouped into individual grouped systems of about 600MW each (Drax has 6 of them), so one boiler feeds one turbine feeds one three-phase power line. If a fault develops somewhere in the power station only one 600MW system is lost to the grid and all the rest of the 600MW systems carry on regardless. On average the UK is using about 35GW, so loss of one generating set at any of the big power stations in the UK amounts to only about 1.7% of UK usage. If left uncorrected, grid frequency would suffer, but by having a few power stations running at less than 100% output the grid could cope by opening the valves at those stations.
At the time that Sizewell B PWR was designed, it was found that a reactor size big enough to produce steam for about 1200MW of electricity was most efficient, so to avoid designing new turbines the decision was made to simply use two turbines of the existing design. However, the national grid now had to be able to cope with losing two generating sets simultaneously if for some reason the reactor had to be shut down suddenly. A sudden loss of 3.4% of grid capacity was thought to be too much for the existing spinning spare capacity to deal with, so Dinorweg was conceived. In the event that a PWR shut down suddenly, Dinorweg would switch on (or refrain from pumping) for an hour or two while a cold power station was gently coaxed into life.
Sizewell was built, and then privatisation happened and the follow-on PWR reactors to the same design were sadly never built. Now, Dinorweg is still sometimes factored into the cost of Sizewell when people want to paint a picture of nuclear being expensive, whereas in reality it was already required for black start purposes and to deal with short term fluctuations dues to the likes of Coronation Street and deaths amongst royalty.