But it doesn't need to be _more_ energy than before, just at different times. If you have 5% of your fuel need filled by wind, that's 5% you didn't need to burn. If it can only do 5% because of clouds, then the gas that need to be burned is still 5% less gas than before the wind turbine contributed 5%. Why would there be an INCREASE in gas burning because wind is taking some of the burden?
So now you only need gas on cloudy days. Before, you needed it every day. That's less overall gas.
It doesn't work that way, because gas and renewables are not the only players.
As more wind and solar are built, they displace non-dispatchable power, such as coal, nuclear and 'run of the river' hydropower. These baseload providers cannot operate profitably in a world where sometimes they are needed, and sometimes not.
Say you need 1000GW of power all the time, and another 300GW for peak loads. Before renewables, you might have:
500GW coal
500GW nuclear
0-300GW gas
Now a 100GW of wind power and 100GW of solar are added to the mix.
The gas plant has to run at 1/3 capacity at peak times on windy, sunny days; and at full capacity on calm, cloudy days. All is good; Exactly as you predicted, less gas is burned, with wind and solar offsetting its use. Yay!
So now you add more wind and solar. Let's double the installed capacity. Now on a windy day with little cloud, the gas plant doesn't run at all. But there's 100GW more power than is needed - so someone else has to shut down. But the coal and nuclear plants cannot just shut down - and if they do, and the wind drops or the clouds roll in, then someone is getting a power outage, because they take a long time to start back up once you take them offline.
So you need more gas to cover the gap, while whichever of the baseload plants ramps back up. So now you have:
0-200GW Wind
0-200GW Solar
500GW Coal
500GW Nuclear
0-900GW Gas
And either the coal or the nuclear plant (or both) is running in a very expensive way - stop-start means more maintenance costs - and they are selling far less than their nameplate capacity of electricity, so they are in a double-bind, with less revenue and increased costs. Meanwhile, the gas plant is running at well below its nameplate capacity (which is fine - they only burn gas when they are up and online, so they don't mind so much if they are only at full power on still, overcast afternoons).
At this point, the anti nuclear lobby will point out that the plant is making a huge loss, runs far less frequently than it should, and with a collective cry of 'Fukushima!!'*, will demand that it be decommissioned forthwith.
So now you have:
500GW coal
500-900GW gas
0-200GW wind
0-200GW solar
You are burning far more gas than before, and total CO
2 emissions have gone UP. For the exact same supply of 1000-1300GW.
And that's pretty much exactly what happened in California. Only the actual numbers are different to keep the maths simple.
Notice that a small amount of wind/solar is not a problem, as it just offsets gas burning as long as the contribution stays below the threshold where it starts to displace baseload power. It's larger installed unreliable capacities that cause a problem. Which is why it's taken a while to get to this point, even though wind and solar have been around for a while.
The principle that "If a little is good, a lot must be better" was never a wise approach to life, and this and alcohol consumption are two prime counterexamples.
Of course, if your population are smarter than the Californians, they shut the coal plant; that way carbon dioxide emissions will fall (gas is about half as bad per GWyear as coal); But note that demand for gas still goes up in this scenario. So you might save the environment from climate change, but you are still going to need to tell the people to get fracked.
*Death toll - zero