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First of all, IMHO their claim is as much about giving a compelling rhetorical framing as it is about giving the foundation for a shoddy calculation, so let's first attack that compelling framing.
Wrongly assuming that all variability on the power system is caused by wind energy, even though variability in electric demand has a far larger impact. Cherry-picking outlier events for wind variability and then extrapolating them as normal behavior. Cherry-picking an isolated instance of the pollution control technology at a coal plant failing, blaming wind energy for the emissions increase, and then extrapolating that as the normal impact of adding wind. Understating the emissions reduction benefits of wind energy in California by excluding the fact that wind is actually displacing the state's large imports of coal power. Greatly understating the emissions benefits of wind in the Pacific Northwest and California by ignoring the fact that displaced hydropower is stored behind the dam and used later to displace fossil fuel use and emissions. Only looking at hourly snapshots of the power system and therefore excluding the vast majority of the emissions savings when wind energy causes emitting power plants to turn off for an extended period of time. Failing to model the process by which grid operators actually choose which power plants to operate. That type of analysis is the only way to accurately assess the impact of adding wind, or any other resource, to the grid.
I suspect that the fourth and the before-last points are particularly potent tools of mis-estimation in a European setting, too.
The AWEA paper also references actual studies (not simulations) on the effect of wind power on electricity sector emissions, which found even greater reductions than direct replacement (that is, the net second-order effects are positive rather than negative), explained by a shift from coal to gas. On this front, it's worth to mention the situation in Ontario, where electricity sector greenhouse emissions reduced by more than 70% in eight years, all the while comsumption increased and Ontario turned from net importer to net exporter: coal's share dropped from 21% to 3% (and that's not counting coal's share in 2003 imports).
Another source they use is the thesis of B. Ummels. They don't mention the conclusions Ummels himself drew, which have been much more positive: he says large amounts of wind power can be integrated, and international exchange alone is a sufficient enabler for the Netherlands. They don't mention Ummels's disclaimer on the so-called load duration curves, either, which makes them unfit for the purpose Pair-Udo-de Groot use them:
...There are however important limitations to the application of duration curves for generation despatch, since duration curves incorporate neither chronology nor consider actual generation unavailabilities [106]. Since load levels are re-organised in a decremental order, all chronological aspects (minimum uptimes and downtimes, ramp rates etc.) are lost. This makes an analysis of power system operation difficult.
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