How much storage do you need in a wind+solar grid ?

Motivation

Andrew Jennings Blocked Unblock Follow Following Jan 15, 2017

The transition to renewable energy is controversial. In Australia we recently had the complete failure of power to the whole of a state (South Australia). The local grid is a combination of wind power and fuel generators, with a link to the national grid, which is mostly coal generators. Critics argued that the coal generators are essential for grid stability. I wondered how much storage might be needed to replace the coal and I could not find a study that helped.

A statistical approach.

This is not how we think about electricity grids at the moment. If we say that we accept 1% probability of failure to supply, does that mean we can tolerate 3 days a year without power? When isolated locations run fully renewable, they usually have a backup generator for those rare occasions where the sun doesn’t shine and the wind doesn’t blow, sometimes for days at a time. What is the equivalent for a national grid?

A statistical approach gives us an understanding of the tradeoffs. There is no such thing as a never-failing system.

Models.

The models for wind generation are well established. Unfortunately, the data is also expensive. Here I have adopted a Weibull distribution for wind, with a typical wind farm power curve. If there are significant time of day effects for wind, if the wind dies down every night, then the results here will have to be reconsidered.

Solar statistical models are less often discussed, which I find surprising. Clearly if we just model solar output as a random variable over the day, regardless of the time then we hide the deterministic variation due to both time and seasons. The solar power available at midday is quite different to what is available at 6pm. I take the distribution of power as conditional on the time of day, so we have a different distribution for each hour. There is no practical reason why we couldn’t go to ten minute interval distributions. I have used the excellent Australian Bureau of Meteorology 1 minute data for Alice Springs.

I have assumed that the solar power statistics are independent of the wind statistics. Given they are in widely differing locations, I think this is reasonable. However this needs testing.

Markets

Today’s electricity markets are fuel based, if you consider dammed water as a fuel. Each supplier makes a choice to bid and use fuel. If you are a wind supplier, or a solar supplier then you have no real choice to defer supply. At the moment wind and solar disturb the market significantly. When the wind is blowing strongly it drives down the market cost, similarly solar. At what point does it become uneconomic to continue to operate a fuel based generator? It’s hard to stay. One thing is certain, they will cease operation well before we reach 100% renewable.

There seem to be two stable regimes: mostly fuel based, and mostly renewable. In the middle its hard to see how the market will work.

Perhaps it is possible to imagine a renewable market where each supplier has vast quantities of storage, and decides to store or supply. With today’s storage costs this is hard to imagine. Typically the capital cost for storage is roughly equivalent to the cost of generation (wind or solar), so a generate and store solution will be twice the cost of a generate only grid.

I have assumed that all suppliers are working on fixed supply prices. So there is no renewable bidding market. Suppliers establish long term contracts with a fixed price. This raises the issue of how to ensure emergency supplies. Clearly we would like to do it with storage, but how much is needed?

Situation

With wide variation in locations and seasons it is hard to be comprehensive. Instead I have attempted to imagine the worst case situation from the solar power point of view. A solar power station in Alice Springs together with a wind farm in southern Australia. In the middle of winter. Roughly equal solar and wind power generation.

On the demand side, I assume a simplified two peak model:

Solar plus wind daily variation.

The early morning regime is clearly a cloudy/clear split. Even in the middle of winter, clouds are rare in Alice Springs. This graph shows the probability distribution of power at 9am: the vertical axis is the probability of occurrence and the horizontal axis is the power level. For example the probability of 5Gw is about 0.09. The “two humps” reflect the combination of the solar and wind distributions.

Power probability density of wind + solar

Later, the middle of the day is simpler:

Power probability density of wind + solar

As the sun sets the two regimes again merge as the sun weakens:

Power probability density of wind + solar

In this scenario, having a deficit of power is fairly rare until we get to the evening. There are still some artefacts in these distributions, but the general shape is clear.

Storage

So how much storage is needed? Taking as a target less than 1% probability of failure to supply for a particular hour, we need to shift the probability distribution to the right until less than 1% is at the left of zero.

The critical times are at the onset of the morning and evening peak. We need enough stored overnight (from wind) and enough during the day (from both solar and wind) to meet the peaks. In the case we study here the evening peak is more difficult, as we have assumed an equal split between solar and wind power.

The case illustrated is described in terms of peak supply (at midday) divided by background demand. The peak supply ratio is 9.3 and the storage equal to only 1. The dynamics of storage is quite complex, and I have simplified it here to look only at the average case. To be more comprehensive a Monte Carlo simulation will give us the distribution of storage trajectories.

The morning peak balance between supply and demand:

and the evening peak:

Withdrawals from storage are shown here:

There are heavy withdrawals at the onset of both the morning and the evening peak.

The amount energy in storage shows the relative difficulty of the two peaks, and how close to exhaustion of stored energy during the evening peak. Here the stored power available drops below 0.1.

Energy in storage versus time

It is clear even from this simple example that a solar only grid is quite difficult. The requirement to meet both the evening peak and the long night demand stretches storage requirements. Wind and solar complement each other. Overnight the available wind assists in meeting the morning peak. Here we have roughly 2.3GW peak power and only 1.0GW of storage, roughly half of the suggested 1:1 generation to storage ratio.

Conclusions

Quite modest storage can stabilise a combined solar and wind generating grid.

What now? More detailed analysis would help us understand the grid behaviour. There is also the big question of how we design a purely renewable energy market.

The R code for the model, the data and results is available on github.