Photovoltaic Panels on Grid, Private Residence

Fig. 1. Photovoltaic panels for a household (Scheuten
5.07 kW, 39 square metres).

A household photovoltaic installation, which is smaller than or equal to 6 kilowatts, can use net metering in Denmark. The selling price of electricity is thus very good, it is tax free, and the administration is minimal. The simple payback period in this case study is 18 years or less and the internal rate of return is estimated at 3.6% (tax free).



A photovoltaic (PV) cell converts sunlight directly into electricity. A manufacturer wires multiple cells together and assembles them into a panel. The installation in Figure 1 consists of 26 panels, and the capacity is just over 5 kilowatts. It could drive 4 vacuum cleaners, just to give an idea of its power.

On sunny days the panels provide energy to the household. If there is more energy available, it is exported to the national electric grid (Samso has an electric cable to the mainland). It is a relatively simple installation, modular, and it is reliable since it is without moving parts.

The panels produce direct current (DC) electricity, but the electric grid is an alternating current (AC) system. An electronic inverter between the panels and the grid converts from DC to AC, and it is relatively expensive. It develops heat, therefore it must be cooled, either passively by a self-circulating flow of the surrounding air, or actively by a built-in electric fan (low noise, but audible). Running the fan costs a little bit of energy, therefore the inverter should be placed in a shady, cool location if possible. The whole inverter switches off at about 65 degrees C to prevent damage.

The panels are mounted on rails of aluminium profiles that are bolted onto the beams that carry the roof. Electric wires interconnect the panels in groups of fairly equal size. On Figure 1 there are three groups of 9, 8, and 9 panels each. If there is a fault in one group, the two other groups will still produce energy. The wires are kept as short as possible in order to minimise electric losses.

Losses directly affect the economy. The panels actually loose 87% of the energy coming from the sun, or in other words the utilisation of the available solar energy is only 13%. The inverter looses at least 3% of its incoming energy to heat, and there are additional heat losses in the wiring in the system. Furthermore, the panels perform poorer the warmer the weather is.

The overall efficiency of the whole system may be as low as 11-12%. On the other hand the lifetime is long — generally estimated at 30 years — so it may be an economically viable investment after all.

Fig. 2. Cost according to size. The installation cost is
stacked on top of the materials cost. The total cost is
almost linealy increasing with size in kilowatt (prices
from Brdr. Stjerne Feb 2012).

The installer Brdr. Stjerne offers five different packages of different capacities below the 6 kilowatt limit for net metering. The installer split the price of a package into materials and installation, see Figure 2. This is because the installation could become more expensive in case it is a complicated installation.

In each package the inverter determines the capacity, so the installer has fit the number of panels to the capacity of the inverter. It is important that the house owner selects the correct size of the system, because adding more panels later, would cost him a new inverter.

The figure shows that the total cost increases more or less linearly with the size of the system. The installation becomes a relatively smaller proportion of the total cost when the system is large. For a large system we could say that the materials cost dominates the installation cost, and since the panels generate the income, a larger system has to cover relatively less overhead. There is, after all, a benefit from economies of scale; that is, the larger the system the better the economy.

The electricity production depends on the number of sunny hours per year and the intensity of the sun. A combination of these affect the energy production. It also depends on orientation and slope; on Samso the optimal slope is 40 degrees, and the optimal orientation is 2 degrees east of South (PVGIS). If the panels face due West, the production will be 75% of due South.

Example (solar radiation potential) Assume the geographical location is good — relative to the average solar activity in the country — such that the number of sunny hours is 1.1 times the average (10% above average) and the intensity also 1.1 times the average (10% above average).

Then the available energy is 1.1 * 1.1 = 1.21 times the average, or 21% higher than average.

In the example two increases of 10% resulted in a bonus of 21% more energy. Islands and peninsulas in Denmark often have more sunny hours and more solar intensity as well; islanders may thus benefit from their remote location. The variation of the solar energy potential within Denmark is approximately +/- 5% (PVGIS).

Net Metering

On a sunny day, when the PV panels produce more than the home consumption, the surplus electricity is fed into the public grid. Due to the net metering arrangement the electricity meter is allowed to 'run backwards'. When the production is less than the home consumption, the public grid will deliver the deficit. When the production is larger than the domestic consumption, the public grid will accept the surplus production.

It is more sunny during summer time, so the production will be high. The meter is able to measure inflow and outflow, and it will accumulate the annual balance. If there is a net annual outflow to the grid the electricity price will be lower than the buying price. Normally the annual production is less than the home consumption, however, and the production thus helps to pay the household's electricity bill. The selling price for a kilowatt-hour is thus the same as the buying price, and it is tax free.

Since 2010 all renewable energy installations below 6 kilowatt are allowed to use net metering in Denmark.

Pre-Calculation from Sales Material

Fig. 3. Simple project balance. The size of the
installation is 5.16 kilowatts (data from Brdr. Stjerne
Feb 2012).
Fig. 4. Same as previous figure, but with marginal
electricity price 1.67 DKK/kWh (0.223 EUR/kWh) and
degradation due to ageing.

The installer uses for Samso the key figure 1 049 kilowatt-hours per installed kilowatt in order to estimate the annual energy production for a given size of installation. A maximum size installation of 6 kilowatt should then produce about 6 300 kilowatt-hours in a year. For comparison, a household wind turbine at 6 kilowatt produces nominally 11 000 kilowatt-hours in a year, but it is also more expensive to buy (Household Wind Turbine(external link)).

If we take the second largest package (5.16 kilowatt) from the installer the total investment is 18 100 EUR. The installer estimates that the annual production will be 5 460 kilowatt-hours. With an estimated electricity selling price at 1.87 DKK/kWh (0.25 EUR/kWh), Figure 3 shows the simple (without interest) project balance.

With the installer's assumptions, the simple payback period is 14 years and the internal rate of return (IRR) is 6.3%. At the end of the lifetime, after 30 years, the surplus is more than 22 000 EUR. It looks like a good investment, especially since the payback period is less than half of the lifetime; there is room for uncertainty and risk, for instance regarding the electricity price or the political regulations around net metering.

Even though it looks like a sound investment, the payback period is rather long for a private household. If the owner should wish to move to another home before the investment is paid back, he can hope for a better price for the home due to the PV panels, but there is no guarantee. Also the technical development may be such that panels with a better efficiency at a cheaper price may appear on the market in a few years. In that case the owner must again calculate whether it pays to switch to the new technology.

With a lower electricity price the picture changes somewhat. For a house with a large demand for electricity, for instance a house with an electric heat pump, there is a discount above 4 000 kilowatt-hours. The kilowatt-hours from the PV system reduce the electricity bill from the top end. If for instance the consumption before the PV system was 10 000 kWh, and after the PV system it is 5 000 kWh, then we have to use the price of the topmost 5 000 kWh, that is, the marginal price of a saved kilowatt-hour. In 2011 that price was 1.67 DKK/kWh (0.223 EUR/kWh), which is lower than what the installer assumed.

Furthermore, the PV panels degrade over the years due to ageing. Ultraviolet radiation, heat, frost, and corrosion erode the performance gradually over the years. The manufacturer guarantees at least 97.5% output for the first two years, then less than 0.63% linear performance reduction each year.

Figure 4 includes the lower electricity price and degradation. The simple payback period is now 16 years (up from 14) and the internal rate of return (IRR) is 4.7% (down from 6.3%).

Post-Calculation of Actual System

Fig. 5. Actual project balance in current prices.

The actual system (Fig. 1) is a little bigger than the previously treated installer package. It was also more expensive, because there were some complications and a price drop soon after the installation.

Figure 5 shows the actual project balance. The system was installed in 2010 and set into operation in the beginning of 2011. Therefore the time series is still very short.

The actual marginal price is the same as in Figure 4, but the production was higher than expected in the sales material. The electricity production in 2011 was 1075 kilowatt-hours per installed kilowatt. This is higher than expected, and it is due to a good location.

At the moment (end of 2011) the outlook is that the payback period will be 18 years and the internal rate of return (IRR) 3.6%.

Monthly Production

Fig. 6. Actual monthly kilowatt-hour production (kWh
2011) and estimate (kWh estimate).
Fig. 7. Energy counter. Cumulative actual production
(2011) in percentages of the full year production.

The first year of operation gives a good indication of the future production, naturally. Production numbers were collected every month to give an idea of the seasonal variation, see Figure 6. The figure shows that the maximal production was in May, which is perhaps a surprise since the Summer Solstice is not until late June. The reason is most likely that May is cooler, and the panels perform better in cool weather. Actually, a temperature drop of 10 degrees improves the performance by 4.8% according to the datasheet.

It is also possible to estimate the monthly production by means of the web-based Photovoltaic Geographical Information System (PVGIS). For a given geographical location, that the user picks on a map, PVGIS returns an estimate of the monthly production. PVGIS must know the system losses after the panels (3% in our case), the panel surface slope (45 degrees in our case), and the compass bearing (7.5 degrees westerly from south in our case).

The estimates are plotted in Figure 6, and the actual 2011 production fits well. The estimates are consistently higher during the winter period; this may be due to shade from nearby trees when the sun is low on the horizon. The actual annual production is only 0.2% off the estimated production.

Figure 7 shows how the kilowatt-hour counter grows month-by-month (2011). The numbers are normalised, and the diagram shows the production in percent of the full year production. The diagram shows that at the end of May, the panels had produced almost half of the production (42%), and by the end of August almost 80%.

By the end of August in future years, it should thus be possible to make a rather good guess at the final annual production.


Power rating 5.07 kWp
Production 2011 5 450 kWh (index 103)
Production per kWp 2011 1 075 kWh/kWp
Panels Scheuten Solar Multisol P6-54 UL series 195 watt
Inverter SMA Solar Technology, Sunny Boy 5000TL
Turn-key contractor energiTech, Samso
Dimensions 1 panel is 1-by-1.5 metres, 26 panels, 39 square metres
CO2 (greenhouse gas) 473 g/kWh 2 490 kg
CH4 (greenhouse gas) 0.24 g/kWh 1.260 kg
N2O (greenhouse gas) 0.006 g/kWh 0.032 kg
Greenhouse gases (CO2 equivalents) 480 g/kWh 2 530 kg
SO2 0.07 g/kWh 0.369 kg
NOx 0.34 g/kWh 1.790 kg
CO 0.15 g/kWh 0.791 kg
NMVOC (unburnt hydrocarbons) 0.05 g/kWh 0.264 kg
Particles 0.01 g/kWh 0.053 kg
Reference: NRGi Net 2010
Owner Private
Start-up date 1 Jan 2011
Nominal lifetime 30 years
Marginal electricity price 2011 1.67 DKK/kWh (0.223 EUR/kWh)
Investment (2010 prices)
Equipment and installation with tax 144 049 DKK (19 207 EUR)
Price per kWp 28 400 DKK/kWp (3 790 EUR)

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  4. %ScheutenSolar%
  5. %WikipediaNetMetering%
  6. %WikipediaPVsystem%
  7. %WikipediaSolarInverter%

Created by system. Last Modification: Thursday 05 July 2012 22:31:02 CEST by jj.