I use this blog as a soap box to preach (ahem... to talk :-) about subjects that interest me.

Wednesday, September 8, 2010

Photovoltaic Panels

Advertisements for solar panels have begun appearing on Australian television. At least, they have become frequent enough that I noticed them. Obviously, the purpose of the ads is to encourage the viewer to buy solar panels, but they tend to be misleading. By selling the electricity you generate, you eventually repay the acquisition price of the photovoltaic system. That’s true. It is also true that your electricity bill is reduced and can even go negative (which means that you get money from the utility). But you shouldn’t consider the two facts simultaneously true. After all, the utility pays you only once!

In this post, I will describe what I think is the financially correct way to look at the photovoltaic panels. But to start, I will first tell you what system my wife and I have bought.

We have on the roof eighteen panels manufactured by Sharp (model NT-N5E3E), as shown in Figure 1.
Figure 1: Our panels.

Each panel can nominally generate up to 175 W of power. Therefore, our maximum generating capacity is 3,150 W.

The panels generate Direct Current. To connect them to the grid, you need an inverter that converts DC to Alternate Current. We have a Fronius IG60 (see Figure 2), which has a maximum power output of 5 kW. We bought it over-dimensioned because we wanted to keep open the possibility of buying more panels at a later date.
Figure 2: Our inverter.

The roof faces North, which obviously is the best orientation for a house in the Southern Hemisphere. Canberra is located at a latitude of 35.5 degrees South, and our roof is pitched at 24.5 degrees (not much snow around here). As a result, at the equinoxes, the sun illuminates the panels with an angle of 35.5 - 24.5 = 11.0 degrees. The ideal angle would obviously be 0 degrees, because then, the amount of solar irradiation per square meter of panels would be maximum. But with 11 degrees of difference one only misses [1 - cos(11 deg)] = ~1.8% of the energy. Not enough to justify mounting the panels at an angle from the face of roof.

At the Summer solstice, the sun is 23.5 degrees higher and at the Winter solstice, the sun is 23.5 degrees lower (because the earth’s axis is tilted by that angle). Therefore, in high Summer, we miss [1 - cos(11-23.5 deg)] = ~2.4% of the energy, and in high Winter, we miss [1 - cos(11+23.5 deg)] = ~17.6%. It is good that we are more efficient in Summer, when there is more energy to capture. See Figure 3 for a graphical representation of what I am talking about. It is the scan of a free-hand sketch. Perhaps, one day, I will make a proper diagram...
Figure 3: Latitude, roof pitch, and all that.

Figure 4 shows a plot of the monthly amount of energy generated in the twenty-three full months of operation between October 2008 and August 2010.
Figure 4: kWh generated.

In total, we generated more than 9.7 MWh, corresponding to an average of 422.5 kWh/month (min: 280 kWh in May 2009; max: 570 kWh in Jan 2009), or 13.9 kWh/day (min: two days with 1kWh; max: twelve days with 23 kWh). In the ACT (Australian Capital Territory), the incumbent utility (ActewAGL) pays AUD 0.5005 for each kWh generated and fed into the grid (FYI, the cost for consumption is AUD 0.1560/kWh). This means that we have earned an average of AUD 2,538/year.

And now, let’s talk about money.

The contract we have with ActewAGL guarantees the feed-in tariff of 0.5005 $/kWh for twenty years, paid quarterly. Let’s suppose to place all the earnings into a savings account that pays interests monthly and with an average yearly interest of, say 3%/year. With a simple spreadsheet, it is easy to calculate that the total amount of money generated with the panels over twenty years plus compound interests is approximately $69,200 (for simplicity, I ignored the fact that the quarterly revenue depends on the season).

On the other side of the balance sheet, we have to consider the price to acquire the photovoltaic system. We paid for our 3 kW system approximately $37,300, but we received $8,000 subsidy from the Australian government and also got Renewable Energy Certificates that we sold for approximately $2,700. Therefore, all in all, the system cost us $26,600. We could have kept that money in a term deposit with interest of, say 6% paid yearly, and saved the interests in a savings account. If we had done so, at the end of the twenty years, we would have had $69,700. With an interest rate of 7% on the term deposit, we would have had $76,800.

Note that with a smaller system we would have been worse off, because there are costs that don’t scale down very well, like the inverter and the installation.

It seems that, at least from a financial point of view, it doesn’t pay to invest in solar panels. But before you arrive to the conclusion that the solar panels are good for the environment but not for your pocket, you have to consider one more thing: what is your marginal tax rate? You see: money earned by generating electricity is not taxable (at least for now), while the interests in the bank are. For example, if your marginal rate is 30%, at the end of the twenty years of savings, you would end up with something like $57,800 if the term deposit pays 6%, and $63,000 if the term deposit pays 7%, not the $69,700 and $76,800 that I calculated before.

And if your marginal tax rate is higher, the solar panels become even more profitable in the long term. Obviously, you could invest in the stock exchange with a long-term historical return of 12%, rather than in a fixed-term deposit, but the 12% rate is historical. It doesn’t mean that it will be maintained after the Global Financial Crisis.

All considered, my wife and I are happy to have bought the photovoltaic system. Perhaps it will pay in the long run, perhaps it will not. But the investment is in the past, while the electricity bills that put money into our bank keep coming. And what about the warm and fuzzy feeling we get from reducing our carbon footprint? Actually, as our inverter can take it, we are probably going to buy another kW.

The price of the panels is going down. Solar Online Australia sells our panels for $890 each, and Energy Matters for $1,088. If we buy six panels, add $200 for delivery and $300 for installation (figures out the hat), we reach a very rough price estimate of $7,000. Those panels would add to our current capacity 1/3 of what we are currently producing. Therefore, at the end of twenty years, they would give us a return of $69,200/3 = ~$23,000. If we kept the $7,000 and locked them up in a term deposit at 6%, we would get 63,000/26,600*7,000 = ~$16,600 in interests. And all this without even considering taxes. It definitely pays to expand the system. We could probably integrate into our system more modern and cheaper panels, which would further enhance our earnings.

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