Model development 2012-2013: 4.165 kW Home Solar Array
Setting
The test house was located in the Australian city of Melbourne, the capital city of the south-eastern state of Victoria. The long axis of the house ran approximately east-west, making it convenient for the photovoltaic panel array to be located on the long north-facing roof. Roof pitch was 29.6 degrees, azimuth 8.3 degrees east of north. Approximate location is -37.78 (S) 144.97 (E), with the local East Australian Standard Time being GMT +10.0.
System
The system consisted of 17 REC245PE-BLK multicrystalline solar panels each rated at 245W nominal. See menu link for specifications from REC. The solar array's DC power was converted to the national 240V 50 Hz grid power by a SMA Sunny Boy 4000TL inverter rated at a nominal 4kW. Again, see menu link for specifications. 5 minute data on PV panel output was obtained from the Sunny Boy via its inbuilt Bluetooth interface.
The house power usage was monitored via a wifi-connected digital meter connected to the energy supplier's smartmeter (an i-Credit 500 unit installed in the house's electrical junction box). The smartmeter recorded the actual PV electricty export and grid electricty import data for the house, data accessible as 48 x 30 minute averages per day from the electricity distributor's web portal.
Actual vs Anticipated Performance – Summer Half-Year
Assessment of performance was carried out by calculating a “theoretical clear-sky” output from the solar array, to be compared with actual output on clear-sky days as the annual cycle unfolds. The theoretical calculation used was:
Theor_PV_out = ETRglobal x Panel_area x Panel_eff x De_rate_fact x AirMass_fact
where
ETRglobal = top of atmosphere estimate of global solar irradiance every 10 minutes
Panel_area = 28.05 m2
Panel_eff = 0.148 (14.8% efficiency)
De_rate_fact = 0.885
AirMass_fact = exp(-0.28 x AM0.45)
ETRglobal was obtained from the National Renewable Energy Laboratory's comprehensive irradiance calculator on the Solpos web site using the geographic location (lat., long.) and azimuth for the home. Panel properties were taken from the REC specifications sheet. The de-rate factor of 0.885 was calculated as shown in Table 1, based on the PVWatts formalism. The AirMass factor equation (representing attenuation due to changing pathlength of sunlight through the atmosphere) was empirically determined in this work, with the coefficients based on a least-squares fit of theoretical to observed PV output on a clear sky day just prior to the autumn solstice in 2013 (2nd March) using the 10 minute air mass data returned as part of the ETRglobal dataset from the Solpos web site.
Figure 1 shows comparisons between three-day sequences of theoretical clear-sky PV array output and actual output for the months of October, November and December 2012. The city of Melbourne rarely has cloud-free days, as is evident from the plots. Nonetheless, for the days on each of these months where cloud was minimal, the agreement between the theory and actual performance from month to month as sun angle and solar irradiance moved from near the equinox values (early October) through to the summer solstice values is very good. In summary – the PV array in its first 3 months performed just as anticipated, based on the specifications of the system components.
Effects of Shading in Winter
Figure 2 shows comparisons between three-day sequences of theoretical clear-sky PV array output and actual output for the months of March, April and May 2013. For the mid-day periods in these months as the sun now moved into the winter hemisphere, the theory-actual comparison remains just as good as it was approaching the summer solstice.
However with sun now lower in the sky, what is evident in the progression through these months is a growing “bite” being taken out of the actual output at the beginning and end of each day. In early March there is very little of this effect, which becomes very evident in April, and increases more into May.
Figure 3 shows the comparison for June, where the overall fidelity of the theoretical calculation continues to be evident despite the complicating presence of cloud every day this month. That said, the “bite” out of the actual output is very clear at each end of the day. It results from shading of the panels, which is caused by a worsening combination of factors as the sun declines daily towards the winter solstice. The initial shading evident from April onwards is caused by high trees on the horizon in neighbouring properties that begins to intrude as the sun moves north and sits lower and lower in the sky each day until the winter solstice. By May this has been added to by additional shading lasting for about 2 hours in the early morning from the immediate northern neighbour's TV aerial and chimney, with a similar 2 hour effect late afternoon from the test home's own TV aerial and chimney.
Using the data from the days in early June 2013 the shading effect was projected to reduce the maximum possible clear-sky daily production by about 3-3.5 kWh per day at the winter solstice, or in the range of 15 to 20% less than the theoretical maximum. Assuming that this shading effect comes and goes linearly with time from a value of zero at ± 90 days from the winter solstice to a maximum of about -3.25 kWh at the solstice, the overall, integrated loss of clear-sky potential annually is about 300 kWh. Given that the theoretical annual clear-sky production sums to 9100 kWh, this loss represents a 3.3% loss on that maximum annual clear-sky power for the system. The actual system output of course will be lower than the clear-sky theoretical output due to cloudiness, and proved to be 6272 kWh for the first full year of operation (October 2012 to September 2013). A 3.3% loss on this figure equates to 206 kWh as the projected actual loss under the “real-world” operating conditions for that year of operation, which in turn at $0.31 per kWh feed-in tariff lost, means a financial cost of about $64 for that year year due to the shading effect. Figure 4 provides a graphical comparison of the daily theoretical production with actual production for an extended period since the PV array began operation in late September 2012. The agreement between maximum (on clear sky days) actual output and theoretical is good for the summer half year, with the reduction of 2-3 kWh per day at mid-winter becoming qualitatively evident as the chart moves from about April onwards into the winter months of 2013.
Other Effects on Performance – Temperature and Wind Speed
One other effect qualitatively evident throughout the PV array output record is that of decreased array output on hot days. Figure 2 provides a nice example, where the 2nd and 3rd March were both (rare!) clear-sky days. On the 2nd, peak noon output of 3.75 kW was precisely what the theoretical calculation predicted, but next day on the 3rd only about 3.6 kW was obtained at noon. What was the difference? It appears to be temperature, as the air T records from the nearest Bureau of Meteorology observation site at Moorabbin Airport (4km to the East) show the 3pm afternoon reading to be 6.1C higher on the 3rd than the 2nd. The REC panel specifications note a decrease in efficiency of -0.43% per C, so an approximate decrease of a little over 2.6% in efficiency would be expected on 3rd March compared with the cooler 2nd March. This reduction applied to the 3.75 kW observed on 2nd March suggests that on 3rd March the temperature effect should have reduced the maximum noon output to 3.65 kW, which is very close to what was observed (see Figure 2).
A more systematic analysis is possible given the manner in which the specific arrangement of latitude and panel tilt yield an essentially invariant daily maximum array output for the 4 summer months centred on the summer solstice (Nov-Feb) – see Figure 4. By taking all days in this period where the sky was cloud-free for at least an hour either side of solar noon it was possible to amass a data record of 33 days for which nominally “invariant” maximum noon array power could be compared with 3pm air temperature (in Celsius) from Moorabbin Airport.
However the opportunity was also taken to add the 3pm wind speed (in km h-1) from the airport data record. The rationale for a wind speed hypothesis is that actual panel temperature will not be affected solely by daytime air temperature, but also by ventilation – wind speed. The hypothesis was that increased wind speed must effectively lead to increased “air cooling” of the panels, which would keep them cooler than on a day of the same air Temperature but lower wind speed.
Thus the final analysis was to carry out a multiple regression on the data set:
PV_noon_power = C1 + C2 x Air_T + C3 x Wind_Spd, for N = 33 samples, where the C's are unknown constants to be fitted by the regression.
Results were highly significant (p< 0.001), with the coefficient values as listed (std errors in brackets):
C1 = 3.894 (0.073)
C2 = -0.015942 (0.002199)
C3 = 0.006760 (0.001555)
multiple r2 = 0.703
Thus 70% of the variance is explained by the regression; a comparison of the resultant regression predictions with observed noon PV array power in Figure 5. Consistent with the original hypothesis, the temperature coefficient is negative – i.e. power output decreases as daytime air temperature increases (panels must be hotter on hotter days), while the opposite is true of wind speed – power increases with increasing wind speed (panels will be cooler than otherwise on windier days due to increased ventilation/cooling). Over the full ranges encountered in each of temperature and wind speed in this dataset the T effect varies by 0.35 kW, while the wind speed effect varies by 0.16 kW, suggesting that of the variance explained by these two effects 70% of would come from the daytime temperature variability, with 30% from wind speed variability.
Finally, it is worth comparing the empirically-determined T effect with the -0.43% per C given in the REC panel specification sheet. Taking the coefficient determined here, -0.015942 and dividing it by the upper limit (least T-affected) noon power value of 3.75 kW observed in the dataset, a value of -0.0042512 results, which expressed as a percentage is precisely -0.43%. It is hard to argue with that..
Effect on Electricity Import and Consumption
In the first months of operation the decrease in energy consumption from the grid was dramatic. There are two components to this: the first of course is the solar array which generates electricity; the second, however, was that at the same time a program to increasing the efficiency of energy use in the house was undertakene. This involved installation of smart switches on computer and video entertainment systems, which switch off when unused for a period of 20 minutes. In addition an old refridgerator used for drinks was removed from the garage - saving about 1.4 kWh per day. Third, all light globes in the house were replaced with low energy globes, resulting in about an 80% decrease in electricity use for lighting. To further save money the house moved to use of cheaper off-peak power (available from 2300-0700 overnight on weekdays; and for all hours of day and night on weekends) by moving elective activities such as dish and clothes washing, or oven roasting, more into off-peak periods. The changes in energy use are shown in the accompanying graph, which also shows the average household electricity use in the suburb. From being about average for the suburb (15.9 kWh per day), the test house moved to using less than half that average (averaging 6.9 kWh per day in total, with ony 4.3 kWh of that from the grid, the differnce being supplied by the PV panels), while at the same time exporting much more energy than the house uses (14.3 kWh per day exported, averaged over a year). In effect, to this point the installation of panels and efficiency increases in effect have taken one and a half houses off the grid.