A simple model: an optimal mix of solar and wind?

When comparing seasonal characteristics of solar and wind in previous post, there was one graph that got my attention:

It shows wind got shortages (visible orange lines) during the summer months, while solar had its best production at the same time. Solar got shortages in the beginning and end of the year, while wind had a decent production at the same time. Then it is tempting to assume that solar and wind are complementary. I understand that solar and wind are only complementary on average. When it comes to individual timeslots, they are certainly not complementary. That is an disadvantage when production and demand need to be in balance at all times.

What if we throw in storage? Is there an optimal mix of solar and wind that can deliver as much as possible direct power from solar and wind, therefor minimizing storage requirements? Separately, both solar and wind have dizzying storage requirements. Yet they could be balanced by means of 2,421 GWh storage in my first post on storage. This tells me that quite some gain is possible combining them both. Can we go even lower by varying both capacities? Maybe even in a storage range that is feasible? However, at a higher multiplier both drifted apart and solar was left far behind, so it might not be as simple as it looks.

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A simple model: solar versus wind

Recently, I learned that that demand response (a change in energy consumption in order to deal with intermittency) would be more problematic for increasing solar capacities and easier for increasing wind capacities. Initially, that seemed a bit contra-intuitive to me. Solar is doing best during the day when most power is needed, so until then I assumed that it would be easier for demand to follow solar power (coinciding with the demand pattern) than wind power (which is more erratic).

However, there are some things that might interfere with that reasoning. For example, sunny weekends or holidays could spell trouble (high production, yet low demand). More, at our latitude, solar produces most power in summer when least power is needed and least in winter when most power is needed. This however allows for building backup during the summer months to be used later when there is a shortage.

The dynamics of wind power is different. At our latitude, there is more wind in winter when we need most power and less in summer when we need least power. It is however not guaranteed to blow when demand is high and then it also requires some kind of backup/storage.

Looking at it over a longer time frame, demand should follow wind better, potentially decreasing the need for demand response. Time to adapt my simple energy model to find out.

A simple model: limiting storage capacity

In my series on the impact of intermittent power sources, I got to the point where I was working with a unlimited battery capacity to find out how big that storage needs to be to fill in the gaps of less production with stored power from earlier excess production. I came to the (surprising) conclusion that almost 2,500 GWh was needed to fill in all the gaps. To recap, this is how the stored power looked like over the year:

Which I found an awful high number for storage. Therefor my question back then was: is it really necessary to store all that power? What would happen when storage is limited to a value below the optimal capacity?

A simple model: the amazing November dip

This post is a follow-up to the previous post, where I looked into the scenario of an unlimited storage device topping off the excess electricity at peaks and filling in the gaps when there is a shortage. I found that a storage capacity of about 2,500 GWh was needed to fill in all the gaps. That number seemed very high to me, so I wanted to check whether other people also found such large numbers.

I quickly found a back-of-the-envelope-calculation by the late David MacKay. He proposes that 33 GW of wind power, delivering on average 10 GW, needs roughly 1,200 GWh backup. This is his calculation:

10 GW × (5 × 24 h) = 1,200 GWh.

He starts from the assumption that it is necessary to bridge five consecutive days of no wind. The difference is that he only considers wind, while I also include another intermittent energy source (solar).

The average delivered power is rather similar in both cases. In my scenario I have ((3,369.05 MW x 0.12) + (3,157.185 MW x 0.24)) x 8.57 = 9,957.95 MW.

Which is a tad below the 10 GW of MacKay is working with. Yet, my result is almost twice as high. Is this the influence of another intermittent power source in the mix? Or just a coincidence? Or did I do something wrong?