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).

Conclusion

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.

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[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.

bits that fall through cracks

As I've described in how much do we use and renewable energy as investment, we have made an effort to reduce our power consumption, without going to absurd lengths. We regularly export about 8 kWh/day to the grid from our 2 kW solar PV system, and draw about 2 - 4 kWh/day from the grid. This is changing as we approach winter (read on).

As I said quite bluntly in Solar PV: opinions, merits, challenges, I am a believer in using the grid where it exists, because a battery storage system must be greatly oversized when off-grid to cope with the worst possible conditions -- conditions that are encountered only rarely [1]. Despite this, Australian utilities seem determined to cause grid defection: the process where people decide that they're economically better-off without the grid and leave it. I believe this will be a bad thing for Australia, because a lot of investment has already gone into the grid, and this will be wasted if people defect from it [2].

However, I'm also unhappy about our patterns of power use as they are. We don't have any fancy monitoring installed at our meter, I just take regular meter readings. I usually take a meter reading just before going to bed at about 10pm. Sometimes I check the meter again in the morning, just to see what has been used overnight. Without any intervention, we used about 1 kWh overnight.

Overnight power use

What's using all this power? Here's what I estimate/measure:

	Consumption (W)
microwave	0 (5)
mini oven	0 (5)
fridge (continuous equiv)	33
clock radio	5
master bedroom cd player	5
kids' bed cd	5
computers-office	10
macbook	8
old laptop	5
router	10

Our Electrolux ETM4200SB fridge is one of the most efficient consumer fridges (we bought it second-hand for $500), and uses about 800 Wh daily, when the fridge's environment is about 24 C.  800 Wh/day is the same as 33 W (continuous equivalent) [3]. All the other values in the table are standby power consumption that I measured myself with a plug in Watt-meter. If you add all these values up, and multiply by 12 (hours), you get about 1 kWh used overnight. Note that I've counted the microwave and mini oven as having a standby power (also known as a phantom load) of zero -- that's because I switch off the microwave at the wall.

Clearly, if we want to draw less power from the grid, this is what needs to be reduced. Particularly at night when solar PV isn't producing. On windless nights, those electrons are supporting coal power, even though we buy GreenPower [4].

The fridge is the big one, and it would be good to get a fridge like the ozefridge, that can "store coldness" for use overnight (so that it doesn't use electricity at night time), but it's too expensive to justify right now -- if we were considering going off-grid it would be a no-brainer though (because storing energy in batteries is less efficient, with greater maintenance, than storing the energy as coldness in the fridge). 

I will install proper switches on the supply cables to the two CD players, and I want to put a timer on the office computers and router (so that they're properly off at night time). EDIT: I have found that the timers consume a significant amount of power and are unreliable, so I have just been switching things off or unplugging them.

Doing this reduces our overnight power consumption to about 0.5 kWh overnight (10pm to 7am).

Data:

(Note that the resolution of these measurements is 0.1 kWh, so they are a bit approximate)

• I turned off the router and the two CD players overnight. Instead of using 1 kWh overnight, we used 0.7 kWh.
• Then I turned off the study computers and washing machine too, which reduced our consumption to 0.6 kWh overnight (I bought cheap powerboards for the study PCs (~$10 each) that have a switch on them that turns off the whole board)
•  If I turn off the router overnight our consumption is about 0.5 kWh overnight.
• We've unfortunately needed to run a night-light for the kids, which is using almost 0.1 kWh overnight

In looking to save power, this is a significant saving for us (about 20% of our total grid draw), for very minimal effort and no sacrifice.

Solar -- Winter

This is a sun path diagram. It slows the path of the sun through the sky in Adelaide across the year. The upper green line (top of the yellow area) is the path taken at the Winter solstice. The lower blue line (bottom of the yellow area) is the path taken at the Summer solstice. The red line is the path taken on May 5th (today) -- you can see it is not far from the Winter solstice path, even though the Winter solstice is nearly two months away (this is because the path the sun takes is a sinusoidal curve, and the time of greatest rate-of-change is behind us (that occurs at the Autumn/Spring equinoxes) -- the rate of change occurring near the Solstices is small (for example, if you pay attention to the time of sunrise and sunset, you'll notice it changes most rapidly at the equinox, and most slowly at the solstice).

Sun path diagram. The original is here

Below are meter reading data that I have collected. In these data, look at the date and the pattern of solar PV production and electricity consumption is clearly variable as the seasons progress. In particular, the decrease in solar PV production (green line) during Winter is marked.
Also obvious is the large change in grid-draw (red line) that occurred on September 1st, 2014. That was when we switched off our electric storage hot water heater and went to solar hot water.
There is also a further reduction that occurs in early February 2015 -- this is the reduction that resulted from my targeting of phantom loads! It is subtle on this graph, but is clearer on the next graph which shows the cumulative data. The switch to solar hot water is also apparent in this graph, as an inflexion point at September 1st 2014, and a second inflexion point is visible at early February 2015. This shows that the savings from our reduction in phantom loads are significant.

Conclusion

Once the main areas of energy reduction are targeted,  it is very worthwhile to reduce phantom loads, particularly overnight. For essentially no effort, we're saving money every day, and reducing our support for coal and gas fired electricity.

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[1] Another alternative is that off-gridders accept that sometimes they run out of power, and use candles for light, fire for cooking, and nothing else. This is fairly widely accepted by rural off-gridders, but something tells me that city folk will be less inclined to accept this.

[2] Note the idea of a proposal being "economical" -- I don't believe that economics adequately captures many of the most important elements in a decision, and that this is due to economic externalities (economic costs being imposed on non-players). Let's take an example. It is widely considered that cheaper to install a larger solar PV system and use the excess electricity to heat water. It costs less money. This is because solar panels are artificially cheap (their cost to society is much higher than the price paid for them -- I won't substantiate this claim here, it's an article to itself, but there are many such articles written already). In comparison, the monetary cost to install a solar hot water system (that uses sunlight to heat water directly, without converting it to electricity) is higher but the cost to society much lower.

This shows that "economic considerations" are not necessarily indicative of overall merit.

[3] I have considered playing with the fridge's thermostat. My idea was to run the fridge much colder during the day, then raise the thermostat so it didn't work as hard at night time. This would make a dent in our night-time consumption. I haven't done anything with this idea yet (there are clearly food-hygiene considerations here!)

[4] This is probably a somewhat contreversial statement. We buy 100% Greenpower, so in theory our power is all sourced from renewables. However, if there is a windless night, then any power consumption increases the electricity spot price, which aids coal/gas fired power stations (currently there is almost no storage of renewable energy in the grid).

This article was written by Angus Wallace, and first appeared at guesstimatedapproximations.blogspot.com.au