The concept of Peak Sun Hours

6 07 2021

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….