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:

simple energy model (charts007d) - belgium - solar x10 and wind x19.05 - reference year: 2018 - with_unlimited_storage

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.

I first modified the model by disconnecting solar and wind capacities, assigning their own multiplier that I could manipulate independent from each other. I then tried numerous runs with different combination of shares of solar and wind, but I couldn’t find storage requirements below 2,400 GWh. That didn’t go well.

Just before I was about to give up, I got the idea to look whether I could find something in the scientific literature on the optimal mix of solar and wind. To my surprise, I found a scientific paper titled Seasonal optimal mix of wind and solar power in a future, highly renewable Europe. It is a paper from the time of the dinosaurs however, published in 2010. The authors also start from the observation of seasonal differences and have the same question as I have (could solar and wind balance each other at 100% share).

This is the abstract:

The renewable power generation aggregated across Europe exhibits strong seasonal behaviors. Wind power generation is much stronger in winter than in summer. The opposite is true for solar power generation. In a future Europe with a very high share of renewable power generation those two opposite behaviors are able to counterbalance each other to a certain extent to follow the seasonal load curve. The best point of counterbalancing represents the seasonal optimal mix between wind and solar power generation. It leads to a pronounced minimum in required stored energy. For a 100% renewable Europe the seasonal optimal mix becomes 55% wind and 45% solar power generation. For less than 100% renewable scenarios the fraction of wind power generation increases and that of solar power generation decreases.

They have two approaches to find this sweet spot. The first is theoretical (a formula), the second is a simple storage model. They find an optimal share of 40% – 50% solar production and 50% – 60% wind production for 100% supply by solar and wind (in the conclusion they state 45% solar and 55% wind, probably they just took the average).

That is interesting, they look at it from a different perspective than I did. Until now I worked in multiples of current capacities, they work with production.

Time to adapt the model once again. The starting point of the new version is the total target production of one year and then calculating what this would mean for solar and wind production in that year. Because I know what production of solar and wind actually did, I can calculate a conversion factor and apply this to the production in the reference year. That way, I can tweak the model using the total target production until I get to the point where there are no shortages for the selected shares of solar and wind. Then I could read the resulting maximum storage capacity. This in the assumption that, in a situation of no shortages, the lower the production is for a certain share of solar and wind, the less power will end up in storage.

This is what I got when running a 45%/55% split of solar/wind and the same production that could balance 8.57x the current capacities (with a small surplus at the start of the reference year 2018):

simple energy model (charts007e) - belgium - solar 45% and wind 55% - reference year: 2018 - with unlimited storage

There are now 6.5 days of shortages in this scenario, minimum required backup is still 12,880.72 MW (of 13,251 MW in the reference year) and storage is also already much higher than 2,421 GWh. This scenario is not better than the initial 8.57x scenario where solar and wind balance their load.

Running other splits between 50-60 wind and 40-50 solar all gave required storage higher than 2,421 GWh. No luck there either.

Then I got the idea to try scenarios with shares larger than 60% for wind and a smaller than 40% for solar. Wind correlates better with demand at our latitude and solar has the most extremes, therefor the optimal split might be outside the proposed range. That finally worked. I found a share of 35% solar and 65% wind the most optimal, supported by “only” 2,389 GWh of storage. Our current capacity of solar and wind (34.4% solar and 65.6% wind) is close to that sweet spot, that is why I had problems finding scenarios with less required storage.

Solar and wind are intrinsically intermittent, so this sweet spot might well be 35/65 in the reference year 2018, but it might differ in previous and next years. Also demand is changing from one year to the next. Making that sweet spot an ever moving target.

That sweet spot is in fact a probability area and that area might be bigger than the authors of the paper found.

The biggest problem that I see is the storage requirement. Although 2,389 GWh is a huge improvement over solar and wind separately, it is still an insanely high storage capacity.


5 thoughts on “A simple model: an optimal mix of solar and wind?

  1. oiltranslator

    Timorously, but still, to a barbarian from the former Colonies an disadvantage clangs with dissonance not unlike that which accompanies exposure to an horrible concession to dropped aitches.


  2. Frode Kjærvik

    What you need is just a single Tesla Megapack.
    Check out what you have to pay for one of those. ;–)



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