Insolation, and a solar panel’s true power output

The standard figures quoted for a solar plant’s “peak power” and “installed capacity” assume that the solar panels are illuminated by 1 kilowatt per square metre of incoming sunlight. The average insolation in northern Europe is about ten times lower than this, so the electricity output from solar panels in northern Europe is around ten times lower than the figures in the data sheets.

Insolation (INcoming SOLar radiATION) is a measure of the solar energy striking a unit surface area in a unit time. It determines how much electrical power a photovoltaic solar panel will deliver – the more sunlight you have, the more power you get.

Mean solar power above the Earth’s atmosphere is 1366 Wm^{−2  [1]}, but sunlight is attenuated on its way through the atmosphere, so the insolation has fallen to 1000 Wm⁻² by the time the light has reached the Earth’s surface. This is the incoming solar power on a clear day, at sea level, with the sun overhead. This illumination level has been adopted by the solar energy industry as a standard operating condition for quoting the peak output power of a solar panel.

The solar power industry has agreed a set of Standard Test Conditions for rating the output power of photovoltaic solar panels ^[2]. This standardised approach allows a like-for-like comparison to be made between products. The industry has chosen the figure of 1000 Wm⁻² as the standard illumination level for measuring and quoting a solar panel’s power output. The electrical power produced by a panel when it is illuminated by 1 kWm⁻² of solar radiation is called the “peak output power” of the panel. This is the figure that’s normally listed in product brochures and data sheets. Likewise, when the “installed capacity” of a solar power plant is quoted, this also refers to the peak power at an insolation level of 1 kWm⁻².

Insolation Level In Europe

How does this theoretical “peak” insolation level of 1 kWm⁻² compare with real insolation values? Figure 1 shows how insolation varies across Europe. It comes as no surprise to see that the south is a lot sunnier than the north.

Figure 1.  Insolation map of Europe. The map shows the total solar energy falling on each square metre. Values depicted are worst case at optimum tilt. Units are kilowatt-hours/m2/day.   (1 kWh/day = 41.7 W)

Looking at this in more detail, Table 1 shows monthly and annual average insolation levels for various cities in Europe. The data are from the NASA Atmospheric Science Data Center ^[3] at the NASA Langley Research Center. The numbers are day-night averages, they are affected by the number hours of daylight, cloud cover, and sun angle.

Table 1.  Insolation levels for European cities – monthly and annual averages

City	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	Year
	W m−2
Limassol	105	136	189	250	285	325	325	299	255	185	126	96	215
Malaga	105	135	188	225	265	295	318	284	225	154	108	89	199
Athens	83	105	153	217	266	313	317	288	232	146	90	68	190
Lisbon	95	125	179	215	255	269	287	264	213	143	95	77	185
Madrid	80	115	170	201	244	272	296	263	205	128	82	66	177
Rome	74	105	155	203	249	285	295	264	201	128	83	65	176
Toulouse	58	89	133	168	201	215	244	211	170	103	66	52	143
Bern	46	74	114	150	196	211	237	206	153	91	53	38	131
Paris	37	68	109	165	204	201	223	192	139	83	47	30	125
Munich	44	75	118	165	202	194	214	186	133	83	43	33	124
Brussels	31	55	95	153	195	187	201	175	119	72	38	23	112
London	28	53	93	145	189	188	198	167	119	69	37	22	109
Hamburg	23	46	87	153	203	186	186	162	108	62	29	17	105
Dublin	23	45	82	138	183	179	179	142	112	60	32	18	99
Oslo	13	36	70	130	194	202	191	140	93	43	18	8	95
Edinburgh	18	39	78	133	180	181	172	142	101	50	25	13	94
Units are watts per square metre. Ref: “NASA Surface Meteorology and Solar Energy Data Set for Renewable Energy Industry Use” [2] Notes: Data show monthly and annual averaged insolation incident on a horizontal surface. Data show the insolation averaged over the 10-year period July 1983 – June 1993. The highest (Limassol, July) and lowest (Oslo, December) monthly insolation values have been highlighted in yellow. The global average insolation is approximately 250 watts per square metre.

The sunniest places in Europe, such as Limassol (average insolation 215 Wm⁻²), get about five times less solar power than the theoretical peak level assumed in solar panel specifications. The least sunny cities, such as Edinburgh (average insolation 94 Wm⁻²), receive nearly eleven times less solar radiation than the theoretical peak value.

As well as these geographical variations, there is also a large seasonal variation. Limassol gets three times less solar power in December than in July; Oslo gets twenty-five times less insolation in midwinter than in midsummer (onto a horizontal surface).

A Concrete Example

To see how this works in practice, let’s go through a concrete example, a domestic rooftop photovoltaic (PV) solar installation in northern Europe.

The example I’ve chosen is a residential property with thirty square metres of rooftop solar PV panels located in South East England. I’ll assume the panels operate at 19% efficiency, the highest efficiency commercially available. The manufacturer would quote the “peak power” or “installed capacity” of this 30m² solar array as 5.7 kW_p. This is the power the panels would generate if they were illuminated by 1000 Wm⁻² of solar radiation. In fact, London and the South East get an average insolation of 109 Wm⁻², about nine times less than the peak value. That means the 30m² solar roof will generate not 5.7 kW, but 621 W of power averaged over the year.

There’s a very large seasonal variation as well. The panel generates more power during the summer, but much less during the winter, when energy needs are greater. The insolation for London in December is 22 Wm⁻², so the power from this solar roof will be 125 W averaged over the month of December. The figures are summarised in Table 2.

Table 2.  Power output of a rooftop solar PV installation in London

	Power   output
Peak power, or “installed capacity”:	5700 W
Annual average power:	621 W
Monthly average power for July:	1129 W
Monthly average power for December:	125 W
These figures are based on the following example: Mean insolation: 109 watts per square metre (London value); Solar panel is horizontal; Solar panel area: 30 square metres; Solar panel efficiency: 19%

There’s a very large difference between the headline “peak power” figures quoted in the datasheets and the true average power output of a solar panel. It’s important not to confuse the “installed capacity” or “peak power” ratings provided by the solar panel manufacturers with the mean power that will actually be generated at a given location. In northern Europe, the mean power output is about ten times lower than the theoretical “peak power” rating.

In London in midwinter, a thirty square metre rooftop solar installation will generate an average of 125 W of electricity, enough for about ten low-energy light bulbs, or one incandescent bulb.

References

1. The sun’s total and spectral irradiance for solar energy applications and solar radiation models, C.A. Gueymard, Solar Energy 76, 423–453 (2004)
2. Handbook of Photovoltaic Science and Engineering, page 295, A. Luque and S. Hegedus, John Wiley and Sons (2000)
3. Release 3 NASA Surface Meteorology and Solar Energy Data Set for Renewable Energy Industry Use, C.E. Whitlock et al., Rise & Shine 2000, the 26th Annual Conference of the Solar Energy Society of Canada Inc. and Solar, Oct. 21–24, 2000, Halifax, Nova Scotia, Canada. (requires login)

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