When the wind is blowing really hard? Wind turbines?
The texas winter was a bit of an anomaly. It got so cold that every power source ending up failing because none were set up to deal with it even though all of them in theory could have (& would have if they were in, say, alaska).
It'll take time to shift to using green energy and there will be problems but the same would be true for any other kind of shift to any new sources of power.
Probably not 16 years like the new UK nuclear plant will take though :/
If you don't believe me go back and have a look at how big the batteries were. The 500 million dollar project installed 130 MWh worth of electricity storage. That is enough to produce the same energy as a power station for 10 minutes before being fully drained.
California has more than 1.5 GW of utility-scale chemical batteries interconnected to it's grid with another 1 GW anticipated to enter service by the end of the year. Most of these batteries can sustain full output for four hours. This is in addition to the more than 3.0 GW of pumped hydro "batteries."
1 GW is roughly the output of one nuclear power plant.
Source: I develop power plants in the western US.
We'll need at least half a day's worth of storage, likely much more if we want to use wind for a significant portion of power generation.
Then over the course of a few years there was a lot.
All that really matters is A) is it cost effective B) will there be scaling problems C) will there be political impediments.
Either way, conservatively speaking, $50-60/MwH for battery backed wind/solar on the mainland seems fairly doable. Prices will likely keep dropping too.
By contrast, in the UK Hinkley Point C is being paid $124/MwH guaranteed for 20 years. It doesn't exist because it's a cost effective way of supplying green energy that's for sure, but it does bolster the nuclear economy. The military do like to hire nuclear technicians and buy parts for PWRs in nuclear subs, etc. and somebody has to pay for these things. Rate payers, I guess.
Assume enough energy is supplied to charge the batteries. So lets say we want 1kWh during 4 hours, that puts our capital cost at 4 kWh*200$/kWh = 800$. Now we assume this system runs every day for 4 hours during ten years. Ten years sounds reasonable, but it could be less. 7 years maybe? So about 1kWh*365,25*10=14610kWh in total. That gives us 800$/14610kWh = 0,0548$/kWh or 54,8 $/MWh in 2030 if I didn't make a major mistake somewhere and assuming no efficiency losses. That's pretty good.
It'll take time to build out capacity but it'll take more time AND cost to build new nuclear plants.