Further to my recent post about the intermittency of solar power, I thought I’d tackle some of you more mathematically challenged and hopefully bring more light (no pun intended) to the problems facing those who believe in 100% renewables running complex civilisation.
If on a perfect cloudless sunny day you plot the output of a solar array between sunrise and sunset you’ll end up with a perfect bell curve. This rarely happens of course. Clouds come and go, and depending on where your panels are installed all sorts of things can shade your panels, like trees. The curve then comes out looking rather less perfect, a bit like this…:
The pale blue area is the cloudless curve, the darker one is real life. Around 8am there’s a dip, could be caused by a cloud or a tree; and by the way, it only takes partial shading of a single panel to cause s drop off in production for the entire array. So a shadow caused by a stink pipe protruding through one’s roof could cause this….
Back to the curve. The AREA under this curve is important. It represents the ENERGY generated by the power shown on the y axis multiplied by the time on the X axis. Energy is power X time, hence kWh is the preferred unit of energy when discussing electricity.
The variability of the sun’s input plus all the shading issues make measuring the energy generated on any one day kind of difficult. Luckily, we have technology….
Maximum Power Point Trackers (MPPTs) have white man’s magic built into them to not just measure energy but even store the data so that nerds like us can talk about it and even blog about it…!
PEAK SUN HOURS
As you can see from the above curve, power output peaks at solar noon. Unless of course a big black cloud is overhead at the time and peak power happens some other time….. I hope you’re starting to grapple WHY it’s difficult to sometimes work out exactly what’s going on with this, when compared to a coal fired generator whose output is both controllable and predictable….
So theoretically, full sun beaming at right angles to one’s panels at midday should be giving us 1000W/m² which is the maximum power available. If you have a 2kW array like ours it means we should be producing the full 2,000 Watts. You can pretty much expect this for an hour, ½ hour before noon, and ½ hour after.
Now think of drawing a thin strip one hour wide from the top of the curve down. You now have a thin rectangle 1 hour wide by 2,000 W high, and the area of that rectangle is 2kWh….. Still with me….?
Now it’s possible, using calculus or more simply white man’s magic to squeeze all the curvy bits of our more than likely complicated generation curve into a rectangle with a flat top.
If you know that the top is 2000W like our system because it’s the highest possible output, then you can work out how wide (how many hours) to make your rectangle. These ‘hours’ are your PEAK SUN HOURS….
If you go back to my phone app screenshot, you’ll see that on June 4 we generated 4kWh. This is equivalent to our system running flat out for two hours.
2kW × 2hours = 4kWh
Therefore on June 4 we had 2 hours of peak sun, equivalent to the rest of the day being completely dark…. Now just think about all those zero days…. it’s tantamount to the sun never rising like it does at the poles in winter. Obviously, on those days I could walk around in the rain to feed the animals and see them, but unlike solar panels, human eyes have irises that can open wide to compensate. Maybe that’s the next challenge for PV developers.
Our very best generation numbers around the equinox on cloudless sunny days is 11.9kWh or nearly six hours of peak sun. And bear in mind we’ve had zero days and 5 PSH days in a row….
So can someone please explain how we run industry on intermittent energy like that…..? Solar’s power factor is all over the place….. It can even be affected by temperature, as I wrote up here years ago..
Now I’m not saying we should continue burning fossil fuels to run complex civilisation, far from it. As far as I’m concerned we should have abandoned fossil fuels yesterday, just don’t expect life to continue as usual when we do, because it won’t. As Marc Janvovici says, if renewables are so good why have we been trying to get rid of them for the past 250 years? Peak Sun hours is but one reason….
Damn the Matrix 
Thanks Mike. Good explanation. I tried to paste a screen shot of my solar generation from last Dec, courtesy of my electricity provider’s web app, showing energy to and from the grid, but it won’t paste. Anyway….a perfect parabola from 7am to 7pm producing 18.8 kWh net energy going to the grid…. the difference between what was actually generated and what was taken from the grid….for which, incidentally, I received the lousy credit of $1.92.
You might want to rethink using the phrase “white man’s magic” for possible racism, even if you mean it in jest. As for your findings on the efficacy of solar power, I think some of us are prepared for less than total resilience, but it will still be hard to get used to.
Your question on baseload for industry is very different from the problems of getting power from a single set of rooftop panels in mid-winter in Tasmania. I am awaiting the growth of solar thermal power stations, which will use molten salt to stay hot enough over long periods actually boil the water to turn the turbines. A helio-centric system that followed the sun could also give better results.
I recently saw an article on AIMN on the desire for gas powered plants which pointed out that “baseload” is not just about the minimum power needed to keep things going, but originally more about the level that had to be maintained to keep the coal fired boilers from having to be shut down. The article was shared on the CANWin Facebook page
Good luck with that…
Ok, I found where you state that your from Tasmania. A different planet then. In North America, in June, or most any month but especially June your solar production would be questioned.
Not a different planet, just a different hemisphere…
The real problem is that a bloke in Tasmania, with a small solar installation and a small blog (sorry I am a regular reader and love your blog) has to point this out. What has happened to professional engineers – where are they, why are they silent. The pubic is more than happy to be sold a lie that their energy intensive lives can be powered by wind/solar – but why aren’t the leading engineering institutes exposing the lie. Those engineers have children and grandchildren, they know it can’t work, what future do they think they are building ?. Instead the snake oil peddling Elons of the world get all the headlines. Rational reasoning is dying along with our civilization.
I’m in the south of the UK, at midwinter the sun gets to 16 degrees above the horizon at midday, the daylight portion of the day is 8hrs,
midwinter is the maximum demand for electricity, I just can’t see solar working for us here,
the UK needs to harvest energy in the summer to use in the winter, electricity is difficult to store, and expensive,
instead of covering farmland with solar PV I’d grow crops, say wheat, store the grain and straw which is easy,
come demand in winter put the milled grain through anaerobic digesters to generate biogas and put the straw through pyrolisation kilns to make more biogas,
use the gas for space heating and electricity generation,
mix the slurry from the digester with the charcoal from the kilns and apply it to the grain fields as a fertilier, soil ammendment and also a form of carbon sequestration,
I’ve no idea how much energy could be generated this way but it’s better than nothing and it’s practical,
the carbon released burning the biogas would be recaptured by the next years crop and you’d always be sequestering more carbon than you released using the charcoal as a soil ammendment,
it’s all pretty low tech, food waste and human effluent can also go through the anaerobic digesters year round,
all anaerobic digester slurry is top liquid fertiliser, dilute and apply,
Cuba has dual use sugar cane mills, after processing the cane into sugar they switch to generating electricity by burning the bagasse,
pyrolisation of crop waste does use some of the potential energy but it also creates charcoal for carbon sequestration and minimises the co2 released by just burning biogas not the entire crop waste,
this approach could never produce the power we currently enjoy from fossil fuels but it is a strategy to produce a predictable flow of energy and also a steady carbon sequestration stream,
I hear you, but the problem with biomass energy is that you’re stealing resources from your soil, eventually depleting it to uselessness. We currently grow wheat unsustainably thanks to fossil fuels.
There’s no free lunch I’m afraid. It’s actually much simpler to grow trees and burn the wood. The unusable parts of the trees can be returned to the Earth along with the ashes….
There is a major difference between what works well financially for a single off grid system and for a country or region as a whole. When looking across a country there is variation in solar and wind output and also in demand. The grid control people are used to managing this and in the past would just call up more gas fired output if the demand was predicted to rise above predicted supply. Now the aim is to manage the system with a range of options. One is to reduce demand – through contracts with large users and for example supermarket fridges and freezers which can be shut off for various periods of time without problems. Secondly they now aim to call up more storage – either short term or long term storage – batteries, pumped storage, hot gravel batteries etc. In some areas the grid managers can also call on adjacent regions with different demand profiles and vice versa. In the UK the grid company now says it does not want “base load” large scale new fossil generation as it is set up for renewables and storage with demand side management. Several studies now show this is also much cheaper than trying to do fossils anymore.
http://energystoragereport.info/eroi-energy-return-on-investment-energy-storage/
As soon as you add storage to renewables, their ERoEI falls through the floor…
There’s so many people high on hopium when it comes to this eh Mike? I’ve been telling people for years – you *can* run a society on 100% renewables – just not the society we presently live in.