Guest post by Roger Andrews:
In the recent Efficiency of Solar Photovoltaics post Euan Mearns presented some solar PV load factors calculated from BP 2012 installed capacity and generation data that made no sense, such as 7% for the US and 30% for Spain. So I did some work to find out whether these numbers were isolated instances. I calculated more load factors using 2012 data from other sources, such as Wikipedia, Observ’ER and Photovoltaic Barometer, added a few more countries and plotted the results against latitude. They are all over the map (Figure 1):
[Image – World’s northernmost solar PV system – Kotzebue, Alaska. Latitude 66.9N, load factor 8.9%]
Figure 1. Load factors vs. latitude calculated from national solar PV statistics, 2012.
And the reason they are all over the map is that different data sources give conflicting estimates for 2012 solar PV generation and installed capacity. Here are some examples:
- Chinese government agencies give three different estimates of of installed solar PV capacity in China at the end of 2012 (7,970, 7,000 and 3,500mWp) and four different estimates of the amount of solar PV capacity added during 2012 (5,040, 4,500, 3,500 and 1,090mWp).
- US government agencies give two wildly conflicting estimates of 2012 solar PV generation in the US (3,451gWh from the Energy Information Agency and 12,557gWh from the National Renewable Energy Laboratory, which, interestingly, is a branch of the EIA.)
- According to the BP 2013 Statistical Review solar PV generation in Canada in 2012 was 0.7 terawatt-hours and according to Observ’ER it was 0.262 terawatt-hours. According to BP solar PV generation in Australia was 2.8 terawatt-hours and according to Observ’ER it was 1.483 terawatt-hours.
- According to Wikipedia installed solar PV capacity in Spain at the end of 2012 was 5,166mWp, according to Photovoltaic Barometer it was 4,517mWp and according to the Red Eléctrica de España it was 4,298mWp.
And the reason different data sources give such different estimates is that national solar PV statistics are basically guesses. There are too many solar PV systems coming on line too quickly (one every four minutes in the US) to keep proper track of installed capacity and it’s impossible to compile accurate generation totals when output from most PV systems is unmonitored. So different people take their best guesses and come up with totally different answers.
Which means that we can’t calculate meaningful solar PV load factors from national installed solar PV capacity and generation statistics. So assuming it would be nice to get some meaningful numbers, how do we get them?
Here I do it by calculating load factors for individual solar PV systems for which monitored output data are available and by using the arithmetic mean of the load factors to define the average load factor for the country. (I use arithmetic means because solar PV load factors don’t change with the size of the system, all other things being equal, and because production-weighted means often lead to a large number of small systems getting swamped by one large one.)
The monitored output data I used comes from two sources:
- http://en.wikipedia.org/wiki/List_of_monitored_photovoltaic_power_stations gives data for approximately 450 solar PV systems in different parts of the world (although mostly in Europe and the US) ranging in size from 200 watts to 13 megawatts. In roughly half the cases there are enough metered output data to allow load factors to be estimated with good confidence.
- http://www.sunnyportal.com/Templates/PublicPagesPlantList.aspx lists approximately 40,000 solar PV systems, with the major contributors being Germany (13,637), US (4,847), Australia (2,821), Netherlands (2,523) and France (1,523). Many of the systems, however, contain no usable monitored data or are too recent to have completed a year of operation.
I calculated load factors for approximately 200 systems from data set 1 using a minimum of one complete year of generation data (some systems gave as much as five years). Working through all the entries in data set 2 would undoubtedly have yielded some useful results but would have taken years, so I confined my activities to calculating load factors for an additional ~200 systems from this data set to fill in gaps in the data set 1 coverage.
Figure 2 illustrates the type of metered output data provided, although it’s not always this complete. The data can also be downloaded in numerical form, usually to fractions of a kWh:
Figure 2: Metered generation data. Slepe Farm solar PV system, Dorset
With data like these load factors can be calculated precisely (the example above gives 12.43% in 2012 and 12.48% in 2013 at the listed system capacity of 492kWp).
Figure 3 plots all ~400 (actually 4o9) of my load factor estimates against latitude:
Figure 3: Load factors at 409 monitored solar PV systems
The results are a good deal more plausible than those shown in Figure 1. Load factors in the Northern Hemisphere peak somewhere between 15 and 35 degrees latitude, i.e. in desert areas where solar irradiance is highest, and decline rapidly towards the Pole (decreasing solar irradiance and increasing cloud cover) and more slowly towards the Equator (increasing cloud cover overcomes increasing solar irradiance). The pattern in the Southern Hemisphere is similar. The scatter around the mean (red line) can be attributed to differences in the type and quality of the installation – tracking arrays, optimally-aligned fixed panels, non-optimally aligned fixed panels etc. and to variations in cloudiness between countries/regions at the same latitude. (Tracking arrays are not always identified in the data sets but they invariably show appreciably higher load factors in cases where they can be identified. The point at 65N that gives a 14.1% load factor is a tracking array, as are at least some of the points that give the plus 20% load factors between 25N and 41N.)
Figure 4 plots average load factors against latitude for the countries and regions (six in the US and three in Australia) where I had enough data to calculate load factors with reasonable confidence:
Figure 4: Average load factors by country/region versus latitude
The results are remarkably consistent (note how the Northern and Southern Hemisphere load factors mirror each other), and with a few exceptions the scatter can be explained by variations in cloudiness. Fewer clouds explain why load factors are higher in the Southwest USA and Israel than in Japan and China and higher in Spain, Portugal and Greece than in the Northeast USA. Fewer clouds in summer also explain why the Baltic region has a higher average load factor than the UK even though it is seven degrees farther north, and also why it has a significantly higher average load factor than Norway, which is at the same latitude. And the low load factors in Malaysia and Indonesia? These countries are in the intertropical convergence zone, which is arguably even cloudier than Scotland.
However, not all the differences in load factors can be explained by clouds. Average load factors for Alaska, Spain, Portugal and Greece are likely biased high relative to the other countries/regions by a disproportionate number of tracking arrays (the average load factor for Alaska decreases from 10.1% to 8.9% when tracking arrays are deleted) and the somewhat low average load factor for China may be at least partly a result of unexplained gaps in the records, examples of which are shown in Figure 5.
Figure 5: Gaps in Chinese records
Table 1 summarizes the Figure 4 results with countries/regions sorted by decreasing load factor. The champion is the US Desert Southwest, which will come as no surprise to anyone who has lived there. However, there are as yet no monitored solar PV systems in the Sahara, or at least none for which I have data.
World’s southernmost solar PV system – Ushuaia, Argentina. Latitude 54.8S, load factor unknown