Solar Panel Efficiency in SAP 2009 – Products with
High Second Order Coefficients
3rd May 2011
Stuart Elmes MA, Viridian Solar
For simplicity, SAP 2009 uses only first-order efficiency value for solar
heating panels. This works well for most solar panels that have a relatively
straight-line efficiency characteristic, however solar panels with poorer
insulation and a more curved efficiency characteristic are unfairly
rewarded. A simple enhancement of the current calculation is put forward
to remedy this anomaly and make the calculation in SAP Appendix H more
accurate.
Table 1 shows performance characteristics of two flat plate solar panels2.
These panels were selected for comparison due to their similar zero loss
coefficients and aperture areas (2.5 and 2.35 m2), but very different heat loss
coefficients.
Background
The UK government publishes a methodology for estimating the energy
performance of dwellings, the Standard Assessment Procedure1 (SAP).
Given a set of input data such as U values of building fabric and
performance of heating systems, the calculation estimates the energy
consumption and carbon dioxide emissions from any given dwelling.
In the 2005 revision the calculation was modified to include a more refined
estimate of energy savings from the use of solar water heating. Where
previous versions of SAP assumed a flat rate of energy benefit from solar
heating panels (per square metre installed), SAP 2005 captured the
diminishing return produced by solar water heating systems as they increase
in size.
The calculation was also structured to reflect the better energy outcome from
higher performing solar panels by using accredited test data from EN12-975
part 1, the European standard for testing the thermal performance of solar
heating panels.
These tests describe the performance of a solar heating panel using three
values: zero loss efficiency (η0), first order heat loss coefficient (a1) and
second order heat loss coefficient (a2).
The efficiency of a solar heating panel can be calculated at any operating
point using an equation in the following form:
η = η0 – a1.{(Tm – Ta)/ GT} – a2.GT.{ (Tm – Ta)/ GT}2
where
η is the panel operating efficiency
Tm is the average temperature in the panel (°C)
Ta is the ambient temperature (°C)
GT is the incident light energy (W/m2)
For the SAP calculation, it was decided to use the zero loss efficiency (η0)
and the first order heat loss coefficient (a1) parameters to characterise panel
performance. This was understood to be an approximation to real-world
performance but, after analysis of published test data from a number of solar
panel products, it was decided that this was sufficiently accurate.
“Hook-Nosed” Solar Curves
There are a growing number of solar heating panels in the market where an
attractively low first order heat loss coefficient conceals a poorer overall
thermal performance. These products have a solar efficiency curve with
high curvature - their efficiency fades more quickly as the operating
temperature rises above ambient. The decision to use only the first order
coefficient for simplicity means that SAP does not properly reflect the
performance of such panels. Although they are still few in number, products
with efficiency figures which can exploit this “loophole” are rapidly gaining
favour with SAP assessors.
Aperture
η0
2.35
2.50
0.790
0.795
(m2)
Panel A
Panel B
a1
a2
ceff
(W/m2.K)
(W/m2.K2)
(kJ/m2K)
2.414
3.90
0.0490
0.0125
8.09
6.30
Table 1 Efficiency characteristics and heat capacity Ceff for two similar size flat plate solar panels.
Figure 1 Panel A has a better first order heat loss coefficient than Panel B, but by virtue of its
higher second order heat loss coefficient is of overall lower performance than Panel B.
Figure 1 shows a graph of the efficiency of the two panels at an irradiation of
800W/m2 as the average panel temperature increases from ambient. As can
be seen, Panel A has a far greater curvature in its efficiency plot due to its
higher second order coefficient, resulting in a generally lower overall
performance across the typical operating range for solar water heating.
In SAP 2009, only the first order coefficient is used, whereas T*Sol, a
commercial solar modelling package takes both first and second order
coefficients into account. A solar energy calculation was made using
Appendix H of SAP and using T*Sol for each of the two panels.
In SAP the floor area of the building was set to 85 m2, producing a daily hot
water demand of 100 l/day. The total panel area was set at 5.0m2 for both
panel A and B to remove differences except those due to their relative
efficiencies. Other settings: South facing, 30 degrees inclination, shading –
none or very little, 200 litre twin coil cylinder with 70 litres of solar
dedicated volume.
In T*Sol the daily demand was set to 100 l/day at 50C, Detached House
(evening max) water use pattern. The panel performance characteristics
shown in Table 1 were entered for each panel, but the aperture area was set
to 2.5 m2 for both types. Other settings: 2 panels (for a total area of 5 m2),
Location –London, South facing, 30 degrees inclination (1084 kWh/m2 panel
irradiation), 200l twin-coil cylinder.
Panel A
Panel B
SAP Qs (kWh/year)
1,135
1,058
T*Sol (kWh/year)
1,350
1,390
Table 2 Panel A produces 7% more solar energy in SAP Appendix H than Panel B. T*Sol, taking
account of the second order efficiency coefficient predicts 3% more energy from Panel B.
Table 2 shows the results. Ignoring the differences in total energy between
the two methodologies and considering only the relative energy produced by
each of the two panels, it can be seen that under SAP Panel A produces 7%
more energy than Panel B. By taking the second order coefficient into
account, in T*Sol Panel B produces 3% more energy than Panel A. By
ignoring the second order coefficient, SAP produces an overall 10%
inaccuracy in favour of Panel A.
Suggested New Treatment in SAP 2009
A suggested refinement of SAP Appendix H is offered that would be simple
to implement, but would remove the anomaly caused by solar panels with
high second order coefficients.
It is proposed that a new linear coefficient a1* is derived from the a1 and a2
test values. In this way the main body of the calculation can be left as it is,
with a1* being used instead of a1. This reduces the testing required before
making the change and lowers the risk of introducing unforeseen
consequences.
In preparation for the derivation of a1*, a representative value for GT is
needed, as well as an understanding of the distribution of operating
conditions for a solar panel.
A study3 conducted in collaboration with the Building Research
Establishment describes results from a test rig simulating an average hot
water load on a hot water cylinder heated by solar and an auxiliary heat
source. A water use pattern equivalent to 100 litres per day of hot water at
60C in a pattern according to EU M324EN tapping cycle 2 was applied to
the hot water cylinder, and the heating system set up to simulate a
“disinterested” or non-optimising household.
Data from this study includes a record of irradiation in the plane of the panel,
cylinder and panel temperatures and solar energy collection at three-minute
intervals covering a 12 month period.
If:
η = η0 – a1.{(Tm – Ta)/ GT} – a2.GT.{ (Tm – Ta)/ GT}2
and for simplicity we set b = {(Tm – Ta)/ GT}, and choose GT = 600 W/m2,
then:
η = η0 – a1.b – 600a2.b2
[1]
A straight line that passes through η0 has the form:
η = η0 – a1′.b
If
a1′ = a1 + αa2
η = η0 – a1.b – αa2.b
[2]
then:
[3]
A best fit value of α was found by numerical methods such that the
weighted difference between [1] and [3] was minimised over the range of
operating points from 0.0 – 0.22. For panels A and B the value of α which
achieved this was found to be 45. As a check a high performance tube was
considered (η0 0.76, a1 2.12, a2 0.0077). A value of α equal to 45 also
produced the best fit between the straight line and the curve.
a1′ = a1 + 45 a2
[4]
The energy collected in the year at different values of irradiation during this
study is shown in Figure 3.
Figure 5 A straight line approximation to the curve is found where the weighted difference
between the two lines is minimised. Weighting values are shown in Figure 4
Figure 3 Annual energy collected by a solar water heating system
at different levels of in-plane irradiation
It was found that the panel collected around half the energy in the year at an
in-plane irradiation below 600W/m2 and around half the energy at irradiation
levels above 600W/m2. The representative value of GT used to derive a1* is
therefore set to 600 W/m2.
The operating point {(Tm – Ta)/ GT} was found for each three minute interval
for the year, and the total number of minutes spent at each point summed.
The results are shown in Figure 4.
This new linear coefficient a1′ is always greater than the value of a1, so
adopting this as the new coefficient for SAP would mean that the energy
produced by all solar heating systems would be reduced. Consequently, a
scaling value, s is found that reduces a1′ in such a way that the energy
produced by a solar panel with an average performance is unaffected by the
overall change.
a1* = s.a1′ = s(a1 + 45 a2)
[5]
The performance characteristics from solar panels tested by SPF and
published on their web site4 were analysed. The sample was randomly
selected as the first 100 panels in the list, plus panels A and B. It included
23 evacuated tube collectors and 79 flat plate collectors, a proportion which
is broadly representative of the breakdown of the solar market in the UK5.
Figure 6 shows a frequency distribution for second order coefficients in the
population considered.
When equation [4] was used to calculate a1′ for each of the 100 panels, the
average value of a1′/ a1 was found to be 1.121. To correct the average panel:
s = 1/1.121 = 0.892, and
a1* = 0.892 (a1 + 45 a2)
Figure 4 Time spent at each operating point by a solar water heating panel
during a one year monitoring study
The profile in Figure 4 was used to create a weighting factor for each
operating point and derive a straight-line approximation to the second order
curve that minimised the weighted difference between the two curves.
[6]
Figure 6 Distribution of second order coefficients from test results of 102 solar panels.
Effect of the Proposed Change
The comparison calculations performed previously were repeated using the
proposed new calculation with a1* in the Appendix H calculation instead of
a1
For Panel A
a1* = 0.892 (2.414 + 45 x 0.0490) = 4.12
For Panel B
a1* = 0.892 (3.90+ 45 x 0.0125) = 3.98
The solar energy yield calculated by Appendix H is as follows:
Panel A
Panel B
Proposed SAP Qs (kWh/year)
1,045
1,054
Panel A now produces 0.8% lower energy yield than Panel B and is therefore
in better agreement with more sophisticated solar simulations that take the
second order coefficient into account.
Conclusion
A simple modification to SAP Appendix H is recommended, where a new
linear heat loss coefficient is derived:
a1* = 0.892 (a1 + 45 a2)
This would increase the accuracy of SAP solar energy estimates, particularly
with respect to solar panels with a high second order heat loss coefficient.
Although the number of these is small relative to the general population of
panels, the significant benefits the current “loophole” offers means that they
are increasingly favoured by SAP assessors and building designers who are
often seeking only slight improvements in building performance to achieve
compliance.
1
2
3
4
5
See http://www.bre.co.uk/sap2009
Panel A, Keymark number 011-7S516F, Panel B Keymark Number 011-7S652F
See http://www.viridiansolar.co.uk/Assets/Files/BRE_Report_Viridian_Solar_Average_House_Simulation.pdf
See http://www.solarenergy.ch/Collectors.111.0.html?&L=6
See solar thermal statistics compiled by HHIC.
http://www.centralheating.co.uk/news/category/market-reports