Tuesday, May 12, 2015

What is the best tilt for solar PV?

We have a 2 kW solar PV system, and solar hot water. Our house is a net exporter of electricity (we don't use gas). This is by quite a margin: our average consumption is about 3 kWh/day and our average export is about 6.5 kWh/day.

Thus, we export more than double the power that we import from the grid.

However, at this time of year our import/export is about equal. We are using slightly more power than during the shoulder season (though we're yet to boost our solar hot water), but the production of our solar PV system has markedly decreased. There are two reasons for this:
  1. The angle of the sun is much lower at this time of year, resulting in lower irradiance to the panels
  2. Cloud cover
Clearly, there's nothing that can be done about cloud cover. But it is the sun's angle I want to talk about here.

PV tilt

There has been much discussion of the optimal tilt for PV panels. Back when there was a well-paying feed-in-tariff (FiT), people advocated installing the panels nearly flat. At Southern Australian latitudes, the annual production of clean panels is maximised when they are flat (note the word clean -- below ~10 degrees tilt, panels must be manually cleaned).

Now that there is no FiT, the equation has changed. For me, the FiT is less of a consideration -- my goal is to to live within my solar budget throughout the year. But why?

EDIT: It is worth mentioning that choosing the "best" tilt is important for all solar collectors: solar thermal, solar hot water, and solar PV. If anything, it is more important for solar thermal than solar PV, since solar PV collects diffuse light energy from the sky and not just the sun.

Your solar budget

Growing up in an age of cheap fossil fuels, we have been conditioned to the idea that gratification follows expectation. Want to heat your house to 35 C in the middle of winter? Sure. Want an outside spa in the snow? sure. This simply will not happen in the age of renewables. For a society powered on solar and wind, there will be times (sustained cloudy and calm periods) where power is significantly more expensive. By "significant", I imagine 10 times dearer or more.

This can be mitigated by installing battery storage, however batteries are expensive. To install sufficient storage to provide during prolonged periods of low production will be out of reach for many. I think in Australia a 3 kWh (usable) battery system would (currently) be affordable by the majority, and might cost $3000 including installation. Note that such a system would really only provide power for one day, and then only for the frugal.

This is a side issue, about which I will elaborate in another post, let's get back to the PV tilt.

It's all about winter production

If you want to live within your means, it is the winter production that is crucial. There is a solar bounty in summer, so there's no problem there. Therefore, we need to increase the tilt of the panels to increase winter PV production. Here comes some maths:

Let's imagine we have a solar panel that is directly facing the sun. We would say that its surface is normal or perpendicular to the sun. This maximises the production because it catches as much sun as is possible.
Now, let's imagine that we tilt the panel so that it is not directly facing the sun. Now it catches less sunlight (its shadow is smaller) and so it will produce less energy. If we keep turning it, eventually it will cast no shadow (it's sideways to the sun) and receive no direct sunlight [1] and produce little.

So, as we turn the panel from directly facing the sun, to being side-on to the sun, let's imagine a scaling factor that describes the production of the panel. This factor will be decreasing as we increase the angle away form the sun form 0 degrees (facing) to 90 degrees (side on). The curve that describes this is called the cosine curve.
The cosine curve, showing how production decreases as the PV panel is tilted away from direct sunlight. Remember, that this does not consider energy production from diffuse light (in practice a panel will still produce energy if oriented away form the sun, it will just produce a lot less). Note that for low angles (less than, say, 20 degrees) there is little effect on production, but by 40 degrees it is falling sharply. That is the characteristic of the cosine function.

Looking at the amount of power exported from my house since September 2014, this pattern is clearly visible as we approach winter.
These data start on December 20 2014 (summer solstice) and the decrease in production through Autumn 2015 is clear.

My panels are oriented at about 23 degrees, which means that at the winter solstice, my panels are oriented about 40 degrees from ideal, significantly effecting production.

Given that we have lots of available PV power in summer, I would happily sacrifice a little to gain extra winter production and I would do this by increasing the tilt of my panels. I think the optimum would be to increase their tilt to about 45 degrees, which would reduce the winter sun's angle to about 20 degrees and increase winter production (at the cost of some summer production).


Orienting PV panels to ensure optimal winter production is a strategy that will help maximise your self-consumption. This helps you get the most from your PV system during all seasons.

[1] PV panels also produce energy from diffuse light form the sky, but it is a lot less than direct sunlight. Here, we consider only the direct sunlight.


  1. Hi Angus.

    A very thoughtful discussion which not many people tend to consider. Yes, clean is a good idea, although a higher tilt on a panel helps keep them clean anyway - although it does depend on rainfall. Your mention of cosine started to make my head swim, so I glossed over that bit - you have to know your limitations. ;-)!
    The basic rule is to set the tilt for the panels at the latitude that you live. For example your panels being set at 20' from horizontal will optimise summer production, but reduce the output over winter considerably. It is all a compromise really, but around 34' should be OK for you and assist with winter power production. The summer loss will be insignificant.
    You can't deny the benefits of a tracker. They have downsides too - in that the actuators often fail and the wind loads on such a system can be extreme. A manual tilt frame is the most effective and possibly also the safest.
    Well done on the 3kWh/day. That is as good a result as here (my system eats 0.5kWh/day extra regardless and that is very efficient - cheaper inverters are a true energy monster).
    Batteries are funny beasts. Having a 3kW battery doesn't actually mean that you will be able to draw 3kWh from it. The faster you draw energy from a battery, the quicker it goes dead flat. Battery ratings are often provided as so many Amps at so many Volts. The thing is though that rating assumes that you only draw a constant charge from the battery say of about 5% of the total rating. People often express that as C (battery capacity in Amps) / 20. So you may see specifications quoting C/10 or C/20 or C/100. So for example with C/20 a 200Ah battery is rated to supply 10A for 20 hours. If you start drawing higher currents (Amps) from the battery, then the battery may be rated much lower as only a 150Ah or even a 100Ah battery. Remember batteries are a chemical reactor rather than a storage vessel. The new lithium batteries reduce that problem considerably, but no one really knows what their operating life spans will be and just how much punishment they can take. And remember the more you discharge from a battery they shorter it's life span will be. There are people living off grid and testing them now. They punish their batteries though. One guy I speak to takes his as low as 20% full. I get nervous when they reach 70% full.
    I'm asking people in the know about the Tesla battery units which are apparently rated to supply 3kW, but time will tell.
    Cheers. Chris

  2. Hi Angus,
    If you get the chance, have a look at this thread about the Tesla batteries that are being promoted. I've been speaking with these guys for years now about renewable energy things and they all live off grid. Their opinions carry some weight on that topic and a few of them even use lithium batteries in their households:



  3. Hi Chris,

    I think the rule of thumb you quoted puts panels at too shallow a tilt. Consider the winter solstice, where the sun is 60 degrees from zenith at midday. a 30 degree tilt is 30 degrees away from optimum (60 - 30 = 30) which, referring to the cosine curve above, shows a loss in production of 16%. For me, I would rather increase my winter production by having the panels at 45 degrees, at the expense of summer production (of which there is plenty anyway). This is what I did with the solar hot water system, and I'm glad -- I'm yet to boost it. I'm not saying everyone should do this, but it bears considering.
    I've seen seasonal trackers (north facing, allow the tilt to be adjusted). I'd love to have one, but as you say, the wind is the kicker. Having said that, I've now got a gigantic sail on the roof (solar space heater), so why not? ;-) It's running by the way -- need to write an article about it, but I want to get a better idea of performance first.

    Yes, batteries are an interesting beast. A very immature technology, really, and while I love the idea I hesitate to jump in... For me,I think I'd rather replace the fridge with a "eutectic" fridge first and try and cut down the night time consumption. See how low I can get it without storage before I look at batteries. (though, I've got the luxury of the grid ;-)

    I also followed your link. Interesting. The Tesla product sounds cheap in comparison to the competition. That has appeal. I've been thinking about your previous comment about cheap second hand systems and an tempted by that though. Second hand always appeals!

    Cheers, Angus

  4. Hi Angus,

    Yeah, great points. If 45 degrees and winter production is what you are after then that is a great idea. Give it a go and let us know how it goes. I get overshadowing from the ridge above me, which kills the winter production here... Not much i can do about that.

    Yeah, I'd love to hear how your solar hot water is doing at this time of the year. Interesting stuff.

    Sorry to correct you but, actually batteries are an extremely mature technology. Lead acid batteries have been around since the 19th century. Lithium batteries are more available now due to economic factors rather than technical factors.

    I know of a guy that uses Nickel Iron batteries in an off grid setup and he trades efficiency for longevity of the batteries. There ain't no such thing as a free lunch they tell me! ;-)!

    Yeah, some of the older locally made stuff is very cheap now - actually it is really good stuff. Have a look on eBay for Plasmatronics (regulators), Selectronics and Latronics (for inverters). All awesome bits of kit.



  5. Hi Chris,

    The solar hot water is performing extremely well. We had four consecutive mostly cloudy days last week, and the water was still very hot at the end (though we didn't use much). The little kitchen system performs well too. Had a sunny day on Sunday, and I couldn't put my hands in the water on Sunday night.

    Fair point about the batteries. I understand that Lead acid and Nickel Iron batteries are mature, in the sense that we've been making them a long time. I guess I see batteries in general as being immature, but perhaps I just have unrealistic expectations. I'd like to see a battery that performed more like a super-capacitor: rapid discharge ability, millions of cycles lifetime, no asymmetry in charge/discharge, etc... perhaps I should just be happy with (and live within the limitations of) the technology we do have!

    Thanks for the heads up regarding the regulators, etc. Food for thought...

    Cheers, Angus

  6. Hi Angus,
    No worries, everyone I meet thinks that batteries will get more efficient over time, but that is very unlikely.
    Cheers. Chris


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