Hourly modelling of conversion of USA48 to wind/solar, with costing and optimisation - Updated.

Update note - I made an error which inflated the build costs of S&W by 8.76. That greatly inflated the resulting optima, by about that amount. I have rewritten this post; you can see the original here.

Update 2 (two hours later). I realised that I used the mean GW to cost, rather than the built faceplate GW. I have fixed that; optima are approximately doubled.

Update 3 (four hours later). I realised that The first estimate wasn't bad, because I had multiplied the cost by 3 for the capacity factor. Working with faceplate installed, that isn't appropriate. So it's back in the range of 5-6 $T.

Update 4. Not a mistake this time, but an improvement. I've costed wind and solar separately, with wind the same at $1.647/W, but solar is cheaper at $1/Watt. This is preparatory to improve by changing proportion of solar, as per next post. The difference here is small , saving maybe $0.5T.

In a post earlier this month, I looked at a currently circulating claim, most recently from CFACT, that replacement of fossil fuel (FF) generation with wind and solar (W&S) would require impossible amounts of storage. Costs of hundreds of trillions of dollars were mentioned. That earlier posts has links.

The original analysis of hourly IEA data was done by Ken Gregory, of Friends of Science. I pointed out the problem, which was that they had allowed too little generation capacity, so the hypothetical grid was relying on storage to cope with annual fluctuations in demand. No system, FF or otherwise, can reasonably do this. You must have enough generation to cover the annual peak periods.

So I adapted Ken's spreadsheet to allow variable amounts of generation. Bringing it up to adequate levels hugely reduces the storage requirement. Building more quickly makes it very small.

Now increasing the generation also has costs, but nothing like the huge costs of Gregory and CFACT. A small number of trillions. The US grid is big business.

A commenter at WUWT, Old Cocky, suggested that costing would be interesting. Being the sum of a rising cost of build with rapidly falling storage costs, there must be an optimum. Ken's model was that W&S would increase proportionally (factor H) to meet the demand formerly met by FF, while nuclear and hydro would remain unchanged (and so not in the analysis). You can analyse hourly data for just one year to get the minimum storage that would get through the year.

Data collection

I have recently been able to extend the data to the four years 2019-2022, which seem to be all the full years IEA has. It would be tempting to use a multi-year set, but the problem is that wind has been growing rapidly, so if the expansion of 2019 is sufficient, then later years are wastefully more than sufficient. I could have tested one year of wind on four years of variable demand, but that misses the point, which is looking for the effect of rare bad wind episodes.

Costs

There are basically just two costs that matter for this optimisation, and I've used Ken's numbers, for which he gives the source. The capital cost of building W&S is set at $1647 per KW. And for storage, $347 per KWh. To cost the build, we need the currently installed base (to be multiplied by H). I had to look that up in Wikipedia; the values (for all USA, W&S) for 2019-2022 are 0.1821 0.2190 0.2563 0.2813 TW.

Optimising

A small change from the last post (and KG). H is now the ratio of new (not old+new) W&S to old W&S. So values are one less than in that post.

As shown in that post, the storage requirement and cost reduces rapidly (exponentially) with H. But the build cost increases linearly with H. So somewhere there is an optimum. Here is a table of computed values around the optimum, for the years 2019-2022. The first column is H, the second is minimum storage needed, computed as in the earlier post. The third is the build cost in $B, formed by multiplying the faceplate GW by the cost per GW. The fourth is storage (col 2) multiplied by storage cost/TWh, and the fifth is the sum, for which we want the minimum (bolded).

For any H, as years progress the build cost increases and the storage cost decreases. This is because the base W&S level is increasing. So the optimum moves to lower H. Y

2019	Storage TWh	Cost(H*S&W) $T	Storage $T	Sum Costs $T
12	26.551	3.005	2.521	5.526
13	18.724	3.256	1.778	5.033
14	15.606	3.506	1.482	4.988
15	13.226	3.756	1.256	5.012
16	10.935	4.007	1.038	5.045
2020	0	0	0	0
10	26.514	2.983	2.372	5.354
11	15.274	3.281	1.366	4.647
12	9.506	3.579	0.85	4.429
13	7.163	3.877	0.641	4.518
14	6.091	4.176	0.545	4.72
2021	0	0	0	0
10	33.56	3.442	3.13	6.571
11	17.073	3.786	1.592	5.378
12	9.635	4.13	0.899	5.029
13	7.142	4.474	0.666	5.14
14	6.153	4.818	0.574	5.392
2022	0	0	0	0
9	18.396	3.354	1.751	5.105
10	8.13	3.727	0.774	4.501
11	3.302	4.1	0.314	4.414
12	1.967	4.473	0.187	4.66
13	1.117	4.845	0.106	4.952

Discussion

The amounts are much less that the hundreds of trillions in the CFACT report, and now around $5T (US GDP is about $22T). How should we think about this? Well, electricity generation is big business, and this represents renewal over, say, 27 years. That would have cost a lot in any technology, and of course produces a system with much reduced fuel costs. But here are some factors which might increase or reduce it

• The obvious big thing that might increase it is the need to be more conservative about storage. The criterion for each year was to get through that year with storage not drained. There will be worse years.
• The obvious big thing that might decrease it is continued reduction in costs, which have been coming down a lot.
• Another big reduction comes from the artificial requirement that the dips in W&S that drain storage are proportional to H. That would be true if the original sites were each expanded by that factor. But new sites will be found, and their diversity will smooth out the dips in W&S.
• A very big reduction comes if cheaper forms of storage than battery are used, as they will be, particularly pumped storage.
• In Europe at least, a big reduction will come from improved interconnection, allowing trade in surpluses, and also rationalisation in location. It is much better to spend on solar in Spain (or Morocco) than in Germany. And in Mexico rather than Maine.
• The model assumed hydro would continue as before. But there will be a continued market-led shift of hydro to drain dams only when W&S are low (and prices high). This has the effect of a big storage increase.

Incidentally, storage costs at the optima are less than build costs.

Conclusion

As before, the very high levels of storage in the reports by Ken Gregory and CFACT are ridiculous. You have to optimise, and then the costs come down to manageable levels (about $5T) as capital cost to replace FF with W&S and battery storage. And there are many ways of ameliorating them.

Postscript

I have added the csv files for each of the years 2019-2022 to the earlier zipfile.

I thought about ways to test all years in a continuous optimisation. The problem is that W&S has been increasing rapidly, so how should it be expanded. If uniformly, the storage troubles of 2019 will dominate. There isn't any point in using one W&S year expanded for 2019-22; the point is to test the variability of W&S over four years.

I tried detrending W&S (and FF), so 2019 was in effect pre-expanded. But this was still not good enough; 2019 was still the limiting year, because exaggerated expansion leads to exaggerated variability. So I'm stuck, for the moment, with doing individual years.