With help from Peter Dudfield and Stephanie Willis. Code is on Github.
All of the graphs in this piece are interactive: you should be able to zoom and hover on them. They’re made and hosted by Plotly, my favourite Python plotting library and a brilliant company based in Montreal 🇨🇦⚜️
- Electricity demand in the UK peaks in the evening, when it’s not very sunny
- You can generate more solar power in the evening by orienting your solar panels West, towards the setting sun
- However, South facing panels still generate more electricity in total, and this outweighs the smaller quantity of more valuable electricity generated by West facing panels
The problem: the UK needs more 6pm power
Like many countries, the UK has made stiff commitments to reach Net Zero by 2050, with a goal of 70% emissions reduction by 2030. We’re actually doing quite well (largely due to the death of coal power), hitting 51% below 1990 levels for 2020.
However, several nuclear power plants are retiring, and we need to replace them. Because electricity is hard to store, electricity generation has to be designed to meet the maximum demand throughout the year. Unfortunately, these periods of maximum usage don’t always align with when the wind is blowing or the sun is shining, so simply installing more renewable power isn’t a good solution. Instead, the UK is is contemplating building new gas power plants to plug the gap.
The primary advantage that gas still has over renewables is its controllability. Generation from gas can be ramped up quickly during moments when renewable generation is low and demand is high, such as the famous “kettle peak” at around 6pm when lots of people finish watching TV and head into the kitchen to put on the kettle and switch the oven on for dinner. The National Grid reported that the Queen’s Address on COVID on April 5th 2020 was immediately followed by a surge in demand equivalent to 300’000 households popping the kettle on.
How can we meet peak demand with renewables?
Despite its reputation as a gloomy place, the UK has been enthusiastically installing solar PV since 2010, when it was incentivized by a generous feed in tariff. We’re now at about 4% of total electricity generation:
The vast majority of solar installation is on South facing roofs, because as we all know, South-facing surfaces receive the most light as the sun moves from East to West throughout the day.
But if we want more power at 6pm, how about putting solar panels on West facing surfaces? Let’s take a look at whether this makes sense.
Optimizing the positioning of solar panels
Here are the ingredients we’ll need for our optimization:
- The price of electricity at different times of day throughout the year. This defines how valuable the electricity we generate from our solar panels will be, and whether we can make an economic case for West facing panels.
- The amount of sunlight throughout the year, measured on a horizontal surface in the UK. This is what we’d capture if we just laid a solar panel flat on the ground.
- The position of the sun in the sky throughout the year. This allows us to use a bit of trigonometry to convert the measurement of horizontal irradiance and estimate how much more or less energy we’d get if we oriented the solar panel in different ways
UK electricity data is available from Nordpool. The cost of electricity in the UK 1 is characterized by a “double hump”: it’s expensive in the morning and the evening. In this graph, each line is a day in 2019, with the average in blue:
On a monthly basis, energy is most expensive in the winter months, when it’s coldest.
These graphs tell a pretty clear story: energy is most valuable in the evening hours of the winter months. In fact, we can combine the two to see this more clearly:
Sunlight on a horizontal surface
We’ve grabbed some data from the CEDA Archive. These measurements are sunlight falling on a horizontal surface in Filton, near Bristol. As you’d expect, we get the most energy in midsummer.
Summing across the year, we get a very pleasing normal distribution per hour, peaking at midday.
Where is the sun?
In order to calculate the impact of positioning our panels, we need to know where in the sky the sun is at any point in time.
The language here gets a bit confusing, so let’s take a quick primer. Azimuth is the orientation you’d read off a compass – North, South etc. Altitude is height in the sky,
We can get altitude and azimuth data for anywhere we care about from this helpful tool. The resulting data is slightly dazzling:
This shows altitude and azimuth, both in radians. What we’re looking at here is the altitude fluctuating smoothly as the sun rises and falls, and the azimuth changing drastically at midnight because we’re plotting a circular phenomenon in a linear way.
We don’t need to worry too much about the raw data here, because what we really care about is using the sun’s position to estimate the energy captured by panels of different orientations.
From horizontal to vertical
If you don’t like maths, you should probably skip this section.
We’ll estimate the impact of azimuth and altitude in two steps. First we’ll calculate the sunflower intensity, assuming that our inclined panel rotates to face the sun – like a sunflower. We’ll then fold in the azimuth data to understand the energy captured by a panel of fixed orientation.
In both cases we’ll be calculating a weighting to apply to irradiance measured on the horizontal.
I’m going to gloss over the derivation and refer you to Steph’s article on solar heating of houses or the code for details of the trigonometry. We can derive the intensity of sunlight on an inclined surface (Iɑ) from the angle of the incline (ɑ), the altitude of the sun (θ) and the intensity as measured on a horizontal surface (IH):
I<sub>ɑ</sub> = I<sub>H</sub> * sin(θ+ɑ) / sin(θ)
Which leaves us with weightings that look like this for mid June:
As you might intuit, more vertical panels are better in the morning and evening (remember, this assumes they’re rotating to face the sun), but at midday the weighting for the vertical panel dips below 1, meaning that it’s worse than a horizontal panel. Interestingly the 45o panel outperforms the horizontal one at all times, because the sun doesn’t spend much time directly overhead in the UK.
We can multiply through with some of the recorded data we have for horizontal irradiance to complete the picture of how tilt affects energy capture:
Conclusion: a 45o tilt is better than a horizontal or vertical panel, assuming it rotates to track the sun’s position in the sky. That’s obviously not an option most homeowners have, so let’s tackle the orientation next.
Orienting our panels
We can use some more trigonometry to work out how much sun is captured by panels of different orientations. Again, checkout Steph’s article for details. If the sun’s azimuth is at ɣ and our panel is oriented at β, we can take
to work out the intensity falling on the panel. This peaks when
β is 90o: when the sun’s rays are perpendicular to the orientation of the panel, we capture the full sunflower intensity.
Again, this yields a weighting which we can apply to our sunflower intensity to describe what fraction of sunlight is captured by a panel with a fixed orientation. These weightings look like:
And once more, we can multiply through by our measured data and our adjustment for panel tilt to get the irradiance that would be captured by a 45o panel facing in different directions!
Averaging over the whole year, we can see that West facing panels generate more energy after 2pm, but the total energy generation is lower than a South facing one.
So: is this evening energy worth enough to justify the lower total energy production?
Pulling it all together
We can now simulate the electricity generation for a panel of any orientation and angle, and ask how much that electricity is worth 2. Here’s the simulated revenue from South and West facing panels in Bristol throughout 2017:
In fact, a South facing beats West facing every month of the year:
Despite the fact that a West facing panel does indeed make more in the evenings:
This is a pretty clear rejection of the idea that it’s time to start building West facing solar panels.
So what is the best orientation?
Since we’ve done all this work, we can now simply perform a search over panel tilts and orientations to define the most valuable setup for a solar panel.
We can start by assessing the total energy capture, which is greatest for a South facing panel at 60o
Counterintuitively, multiplying through by price to work out the value of generation from each panel suggests that the optimal rotation is slightly to the East, not the West:
Morning peaks align better with sunshine hours
We started with a theory that West facing panels might make sense, and we’ve ended up concluding that a slight rotation to the East is better. What’s going on?
Because of the double hump, prices at 9am are not that much lower than those at 6pm. The available sunlight is, however, much greater: it’s light by 9am throughout the year, but it’s dark by 6pm in Winter. So orienting your solar panel to go after the morning peak is a better idea, even if the peak is lower!
There have been lots of moving pieces, so let’s quickly recap what we did:
- We took the amount of sunlight (irradiance) falling on horizontal plane, as measured empirically
- From that, we estimated the irradiance falling on panels of different orientations and tilts, using the position of the sun (azimuth, altitude) and some trigonometry
- We combined this irradiance data with the price of electricity for each hour of 2019 in order to calculate how much money solar panels of different orientations and tilts could have made
Our conclusion: it’s better to orient your solar panel slightly to the East, because you can help meet the morning peak. It’s simply too dark by 6pm during the winter for solar to be very useful for meeting the evening peak, and so West facing panels don’t make much money.
Other avenues to explore
- Does this vary across the country? I’d like to understand how representative Bristol is
- What’s the tipping point? We could simulate various price fluctuations to understand what would have to happen to prices to justify a departure from South facing panels
- What about split arrays? Would an East + West combo beat a South facing monolith?
- We could incorporate the cost of storage and ask whether different orientations become preferable with different storage costs. For instance, if you can store electricity for 2 hours cheaply but it’s expensive to store it for 6 hours, West facing panels might be attractive for hitting the 6pm peak even in the winter months when it’s dark by 4pm
The impact of carbon pricing
Grid carbon intensity fluctuates throughout the day in much the same way as demand, peaking at 10am and 6pm. This is because the additional demand is primarily met by gas plants increasing their output:
If the UK imposed a substantial carbon price, this would further drive up prices during peak hours, because meeting that demand with gas would become more expensive. This might further tip the balance towards non-South facing panels, but since it would affect the morning and evening peaks similarly, it’s unlikely to affect our conclusions here.
How might this conclusion change in the future?
As more and more renewables are added to the grid, their marginal value tend towards zero. In plain speak: we’ll start having too much electricity when the sun is shining and the wind is blowing, and we still won’t have enough for that 6pm kettle rush.
This might end up providing another argument for arranging solar panels in unconventional ways: simply to add some diversity to the grid.
So what do we do about peak demand?
Luckily, unconventional arrangement of solar panels is not the leading solution to peak demand and grid intermittency. In fact Steph and Peter, my collaborators in this project, both work on far more promising solutions (energy efficiency and batteries, respectively).
In North America, where the doctrine of “electrification of everything” is gathering steam, overcapacity is one solution: just add a boatload of renewables until even at peak, we have more than enough. This is the approach proposed by Saul Griffith’s in his excellent (and free!) Rewiring America.
I’m not sure how well this logic applies to the UK, and I’d be curious about how much excess capacity would be required to meet those winter evening peaks. The legendary David MacKay was fairly bearish on the ability of solar to meet UK energy needs in his iconic Sustainable Energy Without the Hot Air. However, I think even he would have been shocked at the radical decline in solar costs since the book’s publication: I would love to see an updated version of those calculations with today’s numbers.
The UK government’s 10 Point Plan outlines a few other options. Although a full discussion is the beyond the scope of this article, the ambition to push next-generation nuclear is conspicuous and somewhat against the international trend.
If you’re interested in this topic and would like to explore it further, I’d love to chat.
All of the data and the code for this post is available on Github.
- We’re using the Day Ahead Price here, which is the cost of buying electricity for a specified 30 minute interval, 24 hours in advance
- There are a couple of extra approximations we need to make about solar panel size and efficiency, but these don’t change the conclusions, they just scale all of the numbers up or down