Financial Return on Solar Panels

Financial Return on Solar Panels

We installed photovoltaic solar panels on 25 October 2010 and these notes are based on our experience so far. We generated our 20,000th unit in April 2017. Based on seven years experience the 4kWp of panels generate just over 3MWh of electricity per year, i.e. multiplying the installed power in kWp by 0.75 gives the annual output in MWh which is accurate enough to judge the economic feasibility of the project (1MWh is 1,000 units). We have received £9473 in generation tariff, £334 for exports, and saved £470 on consumption plus an extra £633 for domestic hot water and central heating, a total of £1103 at the end of 2016. If the installation costs are written off this income reduces our total energy costs including heating to just £104 per year averaged over the seven years.

We use electricity for lighting and cooking, and from January 2011 for all our heating. Prior to this our usage was 15 plus or minus 1 units per day and remarkably consistent. The cost was £0.1092 per unit (1kWh) or £1.64 per day (all monetary values exclude standing charges and the various discounts, but include VAT at 5%).

We live at about 51 degrees latitude. There are 18 solar panels, each with a nominal power of 220 watts giving 3.96 kWp (this is measured with an illumination of 1kW per square metre at 25 centigrade, rather optimistic for us). The panels are split equally across a SE and a SW facing roof, each with its own inverter with a capacity of 2kW. The inverter converts from the panels DC to the mains AC at the local voltage and frequency. The panels attached to one inverter are collectively called a string. Our panels are installed at an angle of approximately 40 degrees to the horizontal and hence are most efficient when the sun has an altitude of 50 degrees which can only occur around noon between 20 April and 23 August. There is some shade from trees especially in the late afternoon between October and February inclusive (the SW panel produces less electricity than the SE in winter), but are shade free in summer.

Each inverter requires at least 20 watts to function, and while 95% efficient at full load (2kW), this drops to 75% at 5% load (100 watts) and falls rapidly below that so the inverter goes into standby at 20 watts (and then consumes 1 watt from the mains).

In winter the inverter switches on 30 minutes after sunrise on a clear day and 1 hour after sunrise on a cloudy day with light grey clouds. It switches off 30 minutes before sunset on a clear day and 1 hour before on a cloudy day with light grey clouds. These times are extended in summer because the sun rises and sets behind the solar panels. With dark grey clouds switch on may be delayed until 3 hours after sunrise. On a few days it doesn't come on at all, especially if covered with snow. Using a digital camera set at ISO 100 the switch on light level corresponds to a sky exposure of 1/160 at f8 or landscape exposure of 1/30 at f3.5. However the power levels are extremely low for the 2 hours after dawn and before sunset. The following links give an idea of the power generated during a perfect sunny day in winter, spring/autumn and summer, and this spreadsheet has the actual values recorded.

A rule of thumb is that if you imagine looking out from the centre of the string of panels perpendicular to their plane and cannot at a minimum see the outline of the sun because of cloud, trees or other obstructions, or because the sun is not in that general direction, the inverter output is unlikely to be exceeding 10% of the panels nominal output (generating 200 watts per string in our case), and may well be much less. Thus a south facing panel in summer would start generating much later than our SE panel and likewise stop much earlier than our SW panel.

It also appears that while the statement that "direct sunlight is not required because any light will generate electricity" is true, it is also very misleading. With 2kWp of panels facing a clear blue sky with no direct sunlight on the string the output is about 25 watts (i.e. about 5% of that from a string facing the sun at the same time). On a cloudy day (light grey clouds) it does not matter whether the string is facing the sun or not - the output is about 10% of that which would be obtained if the sun was shining on the string. The conclusion is that if the sun is not shining on the string a cloudy sky is better than a clear sky. This is because the panels are not sensitive to blue light. A blue sky generates about as much electricity as dark grey clouds.

Any shadow on the panels has a significant effect - a 10% shadowed area reduces power by about 20%, and the difference between 100% shadow and 50% shadow is very small. Hence the requirement for unobstructed sunlight. Even a small shadow on one panel significantly reduces the power output of the inverter. This is because the inverter configures the DC circuit to maximise the power generated by the string of panels attached to it. It assumes that the illumination is constant over all the panels. If this is not the case the configuration will be suboptimal for all the panels resulting in a significant fall in efficiency. Additionally the non-illuminated cells act as resistances converting generated electricity into heat. This is the reason we have two inverters.

It should also be noted that this system does not give immunity from power failures. The inverter requires mains power to function. It synchronises its AC outout with that of the mains, and if there is no mains voltage it is synchronising with nothing. In fact for safety reasons if the mains goes outside the national specification for voltage or frequency the inverter will switch off. This is a legal requirement otherwise someone attempting to repair a faulty transmission line is likely to be electrocuted. (A different type of inverter for use with batteries is required for standalone systems).

It would be interesting to compare our SE-SW setup with a similar one facing due south. The maximum power should be 1.4 times what we are getting, but the maximum generation period would be about 10 hours a day against our 16 hours per day. We would generate less power in the winter, but should be better off once the day length exceeded 12 hours (18 March to 25 September) provided we generated an extra 1.14 units in those extra hours. Assuming a rate of 0.5 units per hour that would equate to a day length of greater than 14 hours or 18 April to 25 August. That implies that a 4 kWp south facing panel would be better than our split system, but not sufficienctly so to make replacement of the bungalow economic!

I am not convinced that solar power is particularly green (it takes over four years to produce more energy than that used to manufacture and install the panels), and the UK certainly could not run off solar even if all roofs were covered with solar panels. In fact it would require 12.5% of the UK's land surface to be covered in solar panels for a mid summer day, and even then there would be no electricity at night and very lttle in winter. However financially it was currently the best low risk investment that could be made provided the capital was available and the roof was suitable - (based on installation cost of £16867, a feed in tarriff of 41.3p and an export tarriff of 3p per unit increasing with the rate of inflation for 25 years). Based on the first four years it will take ten years to pay for the cost of the system ignoring loss of interest on the money invested. Assuming the panels last 25 years that leaves 15 years of profit (but the inverter will need to be replaced at least once in that time).

Note that all our monetary values are based on the the installation date of November 2010 and a feed-in tarriff of 41.3p. This rate has been and will continue to be reduced for newer installations. At the same time installation costs are also being reduced - currently about half of what we paid. I believe that the feed-in tarriff rates are too high and the export rate too low. We are being paid 3p for electricity which the power company is selling for 15p, at virtually no extra cost to themselves. This rate should be increased to the equal the maximum the power company is paying for its electricity, and the feed-in tarriff reduced accordingly. The power companies benefit significantly from small domestic installations because no additional equipment is required, and the power is generated close to where it is used, reducing transmission losses to a minimum.

The following gives an idea of the total power generated in units per day per 1kWp of nominal power for different weather conditions averaged over the 1 hour either side of noon in December/January (i.e. our figures are 4 times these):

The following gives an idea of the total power generated in units per day per 1kWp of nominal power for different weather conditions averaged over the 2 hours either side of noon in February and November (i.e. our figures are 4 times these):

The following gives an idea of the total power generated in units per day per 1kWp of nominal power for different weather conditions averaged over the 3 hours either side of noon in March and October (i.e. our figures are 4 times these):

The following gives an idea of the total power generated in units per day per 1kWp of nominal power for different weather conditions averaged over the 3 hours either side of noon in April and September (i.e. our figures are 4 times these):

The following gives an idea of the total power generated in units per day per 1kWp of nominal power for different weather conditions averaged over the 6 hours either side of noon in June and July (i.e. our figures are 4 times these):

This table gives the production for each month.

The second stage of the project was completed on 11 January 2011. This was the installation of an air source heat pump to provide hot water for radiators and domestic use, and the removal of the oil boiler.

The following explains the values in a spreadsheet which has detailed day by day values:
Date: The date of the readings, normally taken at 6am of the next day (i.e. the value for 1 January is taken at 6am on 2 January, but occasionally corrected to be approximately what would have been the values at 6am. There are also columns for the previous month's total, the total at the end of the previous month, the total for the current month, and the total at the end of the current month.

The first section is concerned with the income from the generation of electricity.
Internal meter end of period: This is one of only two raw values - the value on the generation meter at 6 am (or corrected to that value if taken at a different time, or estimated from the data on the inverter if we were away).
Units (Kw.hours) generated: The difference between the meter reading at 6am on the next day and 6am on this day giving the number of units generated (to 0.1 units). These units are used in the house (including domestic hot water and central heating from January 2011), and the excess if any exported.
Income from units generated: The number of units generated times the feed-in or generation tarriff per unit - the tarriff is adjusted on 1 April each year, and is in the range of 40-50p per unit.
External meter end of priod: The second raw data value taken from the import meter at 6am on the following day (and estimated if taken at a different time). This gives the whole number of units imported and used (including domestic hot water and central heating from January 2011). This provides the bulk of the income.
Units imported: The number of units imported (the difference between the import meter readings), but from January 2011 having a maximum value of 15 which is the estimated number of units used excluding hot water and central heating. The value varied between 10 and 19 prior to the installation of the heat pump. This maximum value allows estimation of the number of imported units used by the heat pump and hence its running cost.
Cost of imports: Number of units imported (maximum 15 after January 2011) times their unit cost (12 to 15p). The cost of additional units (over 15 from January 2011) is included in the Heat Pump section under Cost of Units.
Units exported: The actual number exported is unknown as we do not have an export meter; The value here is the government defined 50% of the units generated - this is a good approximation in the summer, but in the winter very few if any units are exported. The red indicator on our import meter is on continuously while exporting electricity.
Income from units exported: The number of units exported times the export tarriff which is in the range of 3-4p per unit and is the equivalent of adding half the export tarriff to the generation tarriff and using that to calculate the total income. This provides an insignificant part of the income.
Total income in day: The sum of the generation income and export income for that day.
Total income to date: The total income from when the solar panels were installed (25 October 2010).

The next section estimates the savings in the cost of elecitricity used (excluding hot water and heating).
Normal cost of imports: This assumes that 15 units are normally used (which is derived from previous measurements and confimed by some more recent values) and multiples that by the cost per unit (12-15p) to give a constant value for each day in the month (about £2).
Savings on imports per day: The difference between the normal cost of imports and the cost of imports - normally zero in the winter and up to half of the normal cost of imports in the summer. Thus the savings are not very much, a maximum of £1 per day.
Savings on imports to date: The total savings on imports to date. The savings are slightly greater than the income from the export tarriff, but do not amount to very much. The bulk of our savings comes from the use of the solar electricity to heat our domestic hot water, but these savings are included in the heat pump section.

The next section estimates the financial return.
Cost plus 0.013% per day: The installation cost was £16,867.62. This is increased by 0.013% per day compound to allow for inflation and lost of interest on the money invested.
Gain/loss in day: Income plus savings on imports less loss on depreciation and inflation or Total income + normal cost of imports - actual cost of imports + cost on previous day - cost on this day. Positive is a gain, negative a loss.
Total gain/loss to date: The gain/loss in this day added to the previous days value. When this equals the cost plus 0.013% per day we will will have covered the full cost.
Overall gain/loss This is the gain/loss based on the original price or the gain/loss to date - £16,867.62. Positive is a gain, negative a loss. When zero we will have covered the original purchase price but this will not take inflation into account.

The next section calculates the average unit cost to date of generated units at the end of the month.
Cost per unit (gross): This is cost to date (including inflation and loss of interest) divided by the number of units generated. We will be making a profit when this falls below the cost of imported units.
Cost per unit (net): This is cost to date (including inflation and loss of interest) less the income from generated units divided by the number of units generated. We will be making a profit when this falls below zero.

The next section records information about the day. The first four entries are taken from Time and Date for London.
Sunrise: The time at which the first part of the sun would appear if there was a flat horizon. Generation starts about an hour after this time on a fine day.
Sunset: The time at which the last part of the sun would disappear if there was a flat horizon. Generation ceases about an hour before this on a fine day.
Day length: The length of the day rounded down to 6 minutes (0.1 hours). It is important because it is a major influence on the length of time in which electricity is generated (in fine weather usually about two hours less than this value)
Sun altitude: The maximum height of the centre of the sun above a flat horizon measured in degrees. A major influence on the rate of electricity generation. This is a maximum when this angle plus the slope of the panels (50 degrees in our case) equals 90 degrees. The rate of generation decreases significantly when this angle is below 35 degrees, as the light has to travel further through denser air, and when less than 25 degrees tree shadows reduce the power generated even further.
Weather: This is a single number giving a very approximate indication of the amount of sun during the hours when most electricity is generated. It varies from 0 which indicates a very dark sky or snow covered panels so that no electricity is generated to 9 which is full sun with no clouds. The other values are described at the bottom of each worksheet. In practice it is difficult to decide which value is appropriate, and there is the danger of working backwards from the amount of electricity generated.

The next section gives more detailed information about the system.
System on: The earliest time at which the generating meter was known to be indicating that electricity was being generated (it may have been or probably was earlier). The inverter needs to be generating about 30 watts consistently (not neccessarily continuously) before the meter starts registering.
System off: The latest time at which the generating meter was known to be indicating that electricity was no longer being generated (it may have been or probably was earlier). The meter stops registering when the inverter's output falls below a consistent 25 watts. Note that on very dull days generation may cease several times during the day.
SE and SW Totals: The total power generated (in watt.hours or units/1000) by the SE and SW strings as indicated by the inverter. This keeps the last seven days readings so these values are estimated when we are away for a longer period. These values should be very similar on dull days. The SW string generates less electricity in the winter due to the shadow from an oak in our neighbour's garden. The sum of the two values is always slightly less than that from the generating meter (except in the case of estimates).
SE and SW Averages: The average number of watts generated by the two strings calculated at the end of the month by dividing the total watt.hours by the average generating period for that month (2 hours in January and December increasing in two hour steps to 12 hours in June and July). A total value for both strings of under 1200 watts indicates a dull month. Prior to July 2011 the maximum generation rate in each day was recorded instead - I stopped doing this as it became apparent that the values displayed on the inverter were incorrect - a sudden change in the sunlight level due to the edge of a cloud gave readings that were far too high to be plausible.

From January 2011 the very last section (below the heat pump) gives the net cost of electricity.
Income-cost of electricity in day: This is the income from the generation less the total cost of imports including that used by the heat pump.
Income-cost of electricity to date: That value added to the previous days value - positive is income, negative is cost.

Note that the rate at which units are passing through a meter can be estimated by the red indicator light found on most models - this normally flashes once every watt.hour - there are 1000 flashes per unit. Thus 1 flash per second is 3.6 kilowatts, 2 seconds between flashes is 1.8 kW, 10 seconds between flashes 360 watts, and a minute between flashes 60 watts. If the external/import meter's red light is on continuously electricity is being exported. If the internal/generation meter light is on continuously no electricity is being generated (the invertor's output voltage is lower than mains voltage).

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