A simple model: shaving off peaks to fill in the gaps

A bit later than I anticipated, a follow-up on previous post where I presented a simple model that gave the opportunity to learn about the mechanisms that determine an increase of intermittent energy sources (solar and wind). It confirmed that, when increasing in capacity, the production lows don’t grow much, but the production highs will steeply increase. Which is, mathematical speaking, rather logical. In practice this means that the need for backup will not decrease much with increasing capacity, but that at the same time measures need to be taken to top off those ever growing peaks.

That led to the next question: is it possible, at least theoretically, to save the surplus electricity from production highs and use it later when there is not enough electricity at production lows? I adapted the model to a scenario that when more solar and wind energy is produced than consumed, then the excess energy will be stored and when less solar and wind energy is produced than consumed, the system would try to retrieve this from storage.

I want to find out how big this storage needs to be, therefor I initially assume an unlimited storage capacity. This will most probably not happen in the near future (storage is very expensive), but I am not interested in predicting some state of the grid in the future, I just want to figure out the mechanisms that are working and how feasible such storage is.

Storing electricity is however not a free process. It involves conversion losses that need to be taken into account. So I added some more constraints to the model:

  • when less solar and wind energy is produced than consumed, the system would look at what is still in storage:
    • when enough charge → this amount plus the conversion losses are drawn from storage
    • when not enough charge → the storage is drained empty, but only the available energy minus the losses would flow back to the grid.
      In this case I will also calculate the shortage: the total shortage minus the amount available in storage (accounted for the losses)
  • when more solar and wind energy is produced than consumed → excess energy minus the conversion losses will be stored, no questions asked.

Therefor taking conversion losses on both sides into account.

I assume (Li-ion) battery storage (later in this post it will become clear why) and I will use a charging/discharging efficiency of 95%. I can later work with other levels of efficiency if necessary (the efficiency of the other storage devices will be (much) lower).

I also take the same assumption as explained in previous post (linear relationship capacity and production, converting production values to the capacity at the last day of 2018), timeslots with missing data are discarded, consumption of 2018,…).

In the previous runs of the model, there was as much surplus as shortage when multiplying the current solar + wind capacity with a number between 8 and 9. Some trial and error gave me 8.4. However this first version didn’t include any conversion losses, so the balance in this scenario will need a slightly higher multiplier. I will take 8.5, I have to start somewhere.

This is how it would look like without any storage:

simple energy model (charts007a) - belgium - solar and wind production x8.5 - reference year: 2018

When implementing an unlimited storage device and using the same y-axis, it looks like this:

simple energy model (charts007b) - belgium - solar and wind production x8.5 - reference year: 2018 - after

Hey, it doesn’t look that bad at first glance. The storage absorbed the surplus production and filled in almost all shortages (there were still 13 days 13 hours and 15 minutes of shortages). I assumed an unlimited storage device, so the times that the shortages couldn’t be filled are when not enough storage could be accumulated by that time. This is mostly at the beginning of the year (which I did expect), but apparently also at the end of the year (which I didn’t expect).

There are some problems though.

A first problem is that a minimum of 12,767 MW backup capacity is still needed (coming from 13,251 MW in the reference year 2018). That is the result of the small numbers multiplication effect described in previous post. In order to remove these shortages, the multiplier needs to be much, much higher. With trial and error, I found that at 10.1 all shortages were gone, but at the same time created a huge overproduction during the rest of the year.

One could now raise the objection that this need for huge capacities could be the result of the choice of starting point. The series starts at the beginning of the year (in winter when there is a high demand) and it might be a better choice to start later in the year, allowing for more buildup of electricity in the storage device during the months with lower demand.

There is some truth in it, but it is more nuanced than one would expect. I ran the model for the period July 2018 until June 2019 and the result was … even worse. There were 29 days, 15 hours and 45 minutes of shortage in total. What happened? Shouldn’t there be more buildup during summer?

I found that 2018 was a special year in the sense that it had above average wind production in the first three months of the year. This means that there was more solar and wind production than the next nine months. This then gave the opportunity to store decent amounts of energy in those first months. Unfortunately, it was not enough for some timeslots with (very) low production in those first months.

Also, in the July 2018 → June 2019 reference period, there wasn’t the peak production in May, therefor starting much lower and not enough could be build up during summer to account for the shortages in winter.

I started on January 1 with zero charge in the storage device and this might not be what happens in reality. Storage capacity will not be there at once, it will dynamically grow and chances are that there would still be some charge left in the storage device at the beginning of the year. That gave me the idea to start with some charge already in the storage device. But how much?

When I was testing the model, I used the month of December 2017 as test data and I recalled that there was also a lot of wind in that month. It also ended with a holiday week with traditionally a lower demand. Therefor there was a lot of charge in the storage device at the end of the month. I could use this value to start my 2018 run.

That is a lot better. Only 3 days, 10 hours and 15 minutes of shortages and these were situated only at the end of the year. The system was able to fill in all the largest shortages (in the beginning of the year) thanks to the charge already in the storage device. What was left were two small periods of shortage at the end of the year (end of November and end of December).

So I needed to increase my multiplier to get rid of them too. I was very close with my initial 8.5 value: there were no shortages anymore already at 8.57 times the current capacity. This is what happened in the storage device during the year at 8.57 times current (2018) capacity of solar and wind:

simple energy model (charts007b) - belgium - solar and wind production x8.57 - reference year: 2018 - storage state

Now the second problem is showing. Just take a closer look at the scale of the y-axis. The storage device stored 2,421 GWh at its maximum in summer, that is a huge number for storage. To put that in perspective, I will use an example of a real battery. This is the reason why I assumed batteries as a storage device. I decided to go for this kind of storage when I remembered a blog post of our previous Flemish Minister of Energy who breathlessly reported the installation of the first industrial “super battery” in Flanders. The capacity of those super batteries was not mentioned, it was only stated that such a battery delivered enough electricity for “200 families for one day”. A Belgian family consumes on average 3,500 kWh per year, so this battery could store:

3,500 kWh / 365 days * 200 families ≈ 2,000 kWh = 2 MWh

In order to store 2,421 GWh, we need more than 1 million of those super batteries. In that blog post, it was revealed that these batteries cost 1.5 million euros a pop, so at that price I don’t dare to think what the effect would be on the electricity price in Belgium (which is already one of the highest in the EU, just behind Germany and Denmark), even when the price of these batteries would drop by one order of magnitude, even when the price is spread over several years.

What we see is the need for seasonal storage. Belgium is located at 50 degrees North. This means our summers have roughly 8 hours of darkness and 16 hours of light. In winter it is the reverse, roughly 8 hours light and 16 hours dark. This means that our electricity demand is highest in winter and lowest in summer. Since wind more or less compensates for the lack of solar during winter and solar compensates for the lack of wind in summer, there will be a buildup of produced, but not used, energy in summer that is needed in winter. But as seen above this is not guaranteed. It depends on the weather and that is not controlled by us.

It is even more complex. We need most of our energy specifically during the evening peak in winter at working days (and less pronounced during the morning peak). In winter there is therefor one intermittent energy source missing at peak demand: solar. It is still dark/sun is rising during the morning peak and it is already dark/sun is setting during the evening peak. This means that it is (almost) completely on wind energy (and storage) to fill in the gap. On average there is more wind during the winter months and this will compensate for the limited solar, but that doesn’t guarantee that there will be wind when it is needed at peak demand. This is were a lot of these gaps (to be filled in by the charge in the battery) will be.

It doesn’t end here. To get to this point, there were already several assumptions that favored the use of storage as a means of stabilizing an intermittent system:

  • The previous year ended with at decent surplus (above average wind + low demand during the holidays)
  • The first three months of the year also had an above average for wind
  • There was unlimited storage available
  • The storage could get drawn completely empty (in reality this is not possible and if it was, the battery wouldn’t last for long)

Yet the year ended again with hardly any charge in the storage device (less than 100 GWh). There is no guarantee that it would be good months for wind in the first months of the following year. If I want to have at least as much charge in the storage device as there was at the end of 2017, then I need to increase the multiplier once again, also raising maximum storage value.

But then, is it really necessary that all this energy is stored? What if there is a limit on the capacity of the storage device? Can this be done without introducing shortages? Is curtailment necessary and, if so, how much? That is something for the next iteration of the model.


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