<font size=2 face="sans-serif">Hi:</font>
<br>
<br><font size=2 face="sans-serif">I went over and looked at my calculations
whereby I arrived at the simple expression that the change in harvested
solar energy is bounded by the sin of the angle of tilt to the North.</font>
<br>
<br><font size=2 face="sans-serif">As I was doing it however, it became
clear that the reason this simple result popped up, is simply because,</font>
<br>
<br><font size=2 face="sans-serif">1. The effect of tilting an array North
is exactly the same as if the system was physically relocated farther North
by that amount of degrees latitude.</font>
<br><font size=2 face="sans-serif">2. There is a linearly decreasing amount
of annual insolation which is a linear function of latitude.</font>
<br>
<br><font size=2 face="sans-serif">Latitude versus Average
Annual Insolation</font>
<br><font size=2 face="sans-serif">30 degrees latitude has 8.7 kWh-m2</font>
<br><font size=2 face="sans-serif">40 degrees latitude has 7.8 kWh-m2</font>
<br><font size=2 face="sans-serif">50 degrees latitude has 6.7
kWh-m2</font>
<br><font size=2 face="sans-serif">60 degrees latitude has 5.6
kWh-m2</font>
<br>
<br><font size=2 face="sans-serif">3. The SIN function is very linear for
small angles up to about 40 degrees</font>
<br><font size=2 face="sans-serif">Angle versus sin</font>
<br><font size=2 face="sans-serif">sin(10) = 0.17 </font>
<br><font size=2 face="sans-serif">sin(20) = 0.34</font>
<br><font size=2 face="sans-serif">sin(30) = 0.5</font>
<br><font size=2 face="sans-serif">sin(40) = 0.64</font>
<br>
<br><font size=2 face="sans-serif">The sin expression describing the effect
of north tilt is a bounding function, whereby it bounds the maximum reduction
in energy harvest as a function of tilt. It is a bounding analysis
as it does not take into account the effect of atmospheric diffuse radiation
which has the effect of making the "tilt loss" less than it would
be if the earth had no atmosphere.</font>
<br>
<br><font size=2 face="sans-serif">For example if an array was tilted north
by 40 degrees in Vancouver, with no atmosphere the modules would see no
sunlight for 6 months of the year. With an atmosphere, there is still
a lot of light to be gathered.</font>
<br>
<br><font size=2 face="sans-serif">Regardless, my intent with the exercise
from the beginning was to find a bound for the potential "loss effect"
of North tilt so that I could continue to advocate the maximum use of roof
space even when that roof is North facing.</font>
<br>
<br><font size=2 face="sans-serif">JARMO<br>
</font><font size=3 color=#008000>_____________________________________________________________________________________</font><font size=3>
<br>
</font><font size=1 face="Arial"><b><br>
Jarmo Venalainen</b> | </font><font size=1 color=#008000 face="Arial"><b>
Schneider Electric </b></font><font size=1 face="Arial"><b> | Xantrex
Brand</b> | <b>CANADA</b> | <b>Sales Application
Engineer</b> <b><br>
Phone:</b> +604-422-2528 | <b>Tech Support:</b> 800-670-0707
| <b>Mobile:</b> +604-505-0291 <b><br>
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<b>Address:</b> 3700 Gilmore Way, Burnaby, BC V5G4M1 <br>
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<td><font size=1 color=#5f5f5f face="sans-serif">From:</font>
<td><font size=1 face="sans-serif"><billbrooks7@sbcglobal.net></font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="sans-serif">To:</font>
<td><font size=1 face="sans-serif">"'RE-wrenches'" <re-wrenches@lists.re-wrenches.org>,
</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="sans-serif">Date:</font>
<td><font size=1 face="sans-serif">07/28/2015 12:20 PM</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="sans-serif">Subject:</font>
<td><font size=1 face="sans-serif">Re: [RE-wrenches] Using the North Facing
Roof</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="sans-serif">Sent by:</font>
<td><font size=1 face="sans-serif">"RE-wrenches" <re-wrenches-bounces@lists.re-wrenches.org></font></table>
<br>
<hr noshade>
<br>
<br>
<br><font size=2 color=#004080 face="Calibri">Jarmo,</font>
<br><font size=2 color=#004080 face="Calibri"> </font>
<br><font size=2 color=#004080 face="Calibri">Unfortunately, simple is
wrong in this case—and detrimental to the PV industry that needs all the
roof real estate it can find.</font>
<br><font size=2 color=#004080 face="Calibri"><br>
Bill.</font>
<br><font size=2 color=#004080 face="Calibri"> </font>
<br><font size=2 color=#004080 face="Calibri">Bill Brooks, PE</font>
<br><font size=2 color=#004080 face="Calibri">Principal</font>
<br><font size=2 color=#004080 face="Calibri">Brooks Engineering</font>
<br><font size=2 color=#004080 face="Calibri"> </font>
<br><font size=2 color=#004080 face="Calibri"> </font>
<br><font size=2 face="Calibri"><b>From:</b> RE-wrenches [</font><a href="mailto:re-wrenches-bounces@lists.re-wrenches.org"><font size=2 face="Calibri">mailto:re-wrenches-bounces@lists.re-wrenches.org</font></a><font size=2 face="Calibri">]
<b>On Behalf Of </b>Jarmo.Venalainen@schneider-electric.com<b><br>
Sent:</b> Tuesday, July 28, 2015 10:43 AM<b><br>
To:</b> RE-wrenches <re-wrenches@lists.re-wrenches.org><b><br>
Subject:</b> Re: [RE-wrenches] Using the North Facing Roof</font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=2 face="Arial">Hi:</font><font size=3 face="Times New Roman">
<br>
</font><font size=2 face="Arial"><br>
Granted that the description is very simple, but that is the intent. </font><font size=3 face="Times New Roman">
<br>
</font><font size=2 face="Arial"><br>
The essence of it is that the "loss" for small variations in
angle of incidence is approximately bounded by, (less than), the sin of
the angle between the orientations of two panels/arrays in question.</font><font size=3 face="Times New Roman">
<br>
</font><font size=2 face="Arial"><br>
10 degrees ---> minus 17%</font><font size=3 face="Times New Roman">
</font><font size=2 face="Arial"><br>
20 degrees ---> minus 33%</font><font size=3 face="Times New Roman">
</font><font size=2 face="Arial"><br>
30 degrees ---> minus 50%</font><font size=3 face="Times New Roman">
<br>
</font><font size=2 face="Arial"><br>
If you go through the detailed math and take into account atmospheric
effects, especially when the sun is near the horizons, temperature, location,
weather, etc., the result will vary, but will not be worse than the sin
of the angle.</font><font size=3 face="Times New Roman"> <br>
</font><font size=2 face="Arial"><br>
I'll draw out better picture with more detail for Vancouver. We're
at a fairly high latitude, so overall array orientation is a more sensitive
factor than farther south.</font><font size=3 face="Times New Roman"> <br>
</font><font size=2 face="Arial"><br>
JARMO</font><font size=3 face="Times New Roman"> </font><font size=2 face="Arial"><br>
</font><font size=3 color=#008000 face="Times New Roman"><br>
_____________________________________________________________________________________</font><font size=3 face="Times New Roman">
</font><font size=1 face="Arial"><b><br>
<br>
Jarmo Venalainen</b> | </font><font size=1 color=#008000 face="Arial"><b>
Schneider Electric </b></font><font size=1 face="Arial"><b> | Xantrex
Brand</b> | <b>CANADA</b> | <b>Sales Application
Engineer</b> <b><br>
Phone:</b> +604-422-2528 | <b>Tech Support:</b> 800-670-0707
| <b>Mobile:</b> +604-505-0291 <b><br>
Email:</b> </font><a href="mailto:jarmo.venalainen@schneider-electric.com"><font size=1 color=blue face="Arial"><u>jarmo.venalainen@schneider-electric.com</u></font></a><font size=1 face="Arial">
| <b>Site:</b></font><a href=http://www.xantrex.com/ target=_blank><font size=1 color=blue face="Arial"><u>
www.Xantrex.com</u></font></a><font size=1 face="Arial"> |
<b>Address:</b> 3700 Gilmore Way, Burnaby, BC V5G4M1 </font>
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<table width=100%>
<tr valign=top>
<td width=12%><font size=1 color=#5f5f5f face="Arial">From:</font><font size=3 face="Times New Roman">
</font>
<td width=87%><font size=1 face="Arial">Brian Mehalic <</font><a href=mailto:brian@solarenergy.org><font size=1 color=blue face="Arial"><u>brian@solarenergy.org</u></font></a><font size=1 face="Arial">></font><font size=3 face="Times New Roman">
</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="Arial">To:</font><font size=3 face="Times New Roman">
</font>
<td><font size=1 face="Arial">RE-wrenches <</font><a href="mailto:re-wrenches@lists.re-wrenches.org"><font size=1 color=blue face="Arial"><u>re-wrenches@lists.re-wrenches.org</u></font></a><font size=1 face="Arial">>,
</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="Arial">Date:</font><font size=3 face="Times New Roman">
</font>
<td><font size=1 face="Arial">07/28/2015 09:48 AM</font><font size=3 face="Times New Roman">
</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="Arial">Subject:</font><font size=3 face="Times New Roman">
</font>
<td><font size=1 face="Arial">Re: [RE-wrenches] Using the North Facing
Roof</font><font size=3 face="Times New Roman"> </font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="Arial">Sent by:</font><font size=3 face="Times New Roman">
</font>
<td><font size=1 face="Arial">"RE-wrenches" <</font><a href="mailto:re-wrenches-bounces@lists.re-wrenches.org"><font size=1 color=blue face="Arial"><u>re-wrenches-bounces@lists.re-wrenches.org</u></font></a><font size=1 face="Arial">></font></table>
<br><font size=3 face="Times New Roman"> </font>
<div align=center>
<hr noshade></div>
<br><font size=3 face="Times New Roman"><br>
<br>
<br>
The analysis of 50% of south facing production is too simplistic; running
some modeling shows that, depending on the latitude, the difference can
be much smaller, approaching 25% less for the north facing. I think
this layout could become more common especially on low slope commercial
roofs, where the north facing module would occupy space that was already
unused due to interrow shading. Of course the closer to the equator
the less difference between production of the north and south arrays...and
you better be careful when stringing them in series so as not to mix N
and S facing..plus filling in all those gaps between rows could make servicing
the array a bit problematic! <br>
<br>
Cheers, <br>
<br>
<br>
Brian Mehalic <br>
NABCEP Certified Solar PV Installation Professional™ R031508-59 <br>
<br>
PV Curriculum Developer and Instructor <br>
Solar Energy International</font><font size=3 color=blue face="Times New Roman"><u><br>
</u></font><a href=http://www.solarenergy.org/ target=_blank><font size=3 color=blue face="Times New Roman"><u>http://www.solarenergy.org</u></font></a><font size=3 face="Times New Roman">
<br>
<br>
On Tue, Jul 28, 2015 at 10:24 AM, <</font><a href=mailto:billbrooks7@sbcglobal.net target=_blank><font size=3 color=blue face="Times New Roman"><u>billbrooks7@sbcglobal.net</u></font></a><font size=3 face="Times New Roman">>
wrote: </font><font size=2 color=#004080 face="Calibri"><br>
Jarmo,</font><font size=3 face="Times New Roman"> </font>
<p><font size=2 color=#004080 face="Calibri"> </font><font size=3 face="Times New Roman">
</font>
<p><font size=2 color=#004080 face="Calibri">The sun’s geometry is not
nearly that simple. To understand the impact of north-facing arrays, you
have to perform a simulation. PV:WATTS does this just fine and it is easy
to show that a 18-degreed North-facing tilt produces 75% of a perfect 30-degree
south-facing array. Far more than your assumption of 50%.</font><font size=3 face="Times New Roman">
</font>
<p><font size=2 color=#004080 face="Calibri"> </font><font size=3 face="Times New Roman">
</font>
<p><font size=2 color=#004080 face="Calibri">To compare 15-degrees South
to 15-degrees North, the numbers are slightly better at 77%. We are going
to see a lot of north-facing arrays once people understand that low tilt
angles are very forgiving on North slopes. Steep slopes are a totally different
story and you have to run the numbers….</font><font size=3 face="Times New Roman">
</font>
<p><font size=2 color=#004080 face="Calibri"> </font><font size=3 face="Times New Roman">
</font>
<p><font size=2 color=#004080 face="Calibri">Bill.</font><font size=3 face="Times New Roman">
</font>
<p><font size=2 color=#004080 face="Calibri"> </font><font size=3 face="Times New Roman">
</font>
<p><font size=2 face="Calibri"><b>From:</b> RE-wrenches [mailto:</font><a href="mailto:re-wrenches-bounces@lists.re-wrenches.org" target=_blank><font size=2 color=blue face="Calibri"><u>re-wrenches-bounces@lists.re-wrenches.org</u></font></a><font size=2 face="Calibri">]
<b>On Behalf Of </b></font><a href="mailto:Jarmo.Venalainen@schneider-electric.com" target=_blank><font size=2 color=blue face="Calibri"><u>Jarmo.Venalainen@schneider-electric.com</u></font></a><font size=2 face="Calibri"><b><br>
Sent:</b> Tuesday, July 28, 2015 8:04 AM<b><br>
To:</b> RE-wrenches <</font><a href="mailto:re-wrenches@lists.re-wrenches.org" target=_blank><font size=2 color=blue face="Calibri"><u>re-wrenches@lists.re-wrenches.org</u></font></a><font size=2 face="Calibri">><b><br>
Subject:</b> Re: [RE-wrenches] Using the North Facing Roof</font><font size=3 face="Times New Roman">
</font>
<p><font size=3 face="Times New Roman"> </font>
<p><font size=2 face="Arial">I did a slide on the effect of North facing
modules. For even a fairly aggressive rotation North as shown, the
effect is "only" a 50% reduction.</font><font size=3 face="Times New Roman">
</font><font size=2 face="Arial"><br>
<br>
The questions of whether or not to do it, are,</font><font size=3 face="Times New Roman">
</font><font size=2 face="Arial"><br>
<br>
- is the mounting structure simpler, lower cost</font><font size=3 face="Times New Roman">
</font><font size=2 face="Arial"><br>
- security against wind</font><font size=3 face="Times New Roman"> </font><font size=2 face="Arial"><br>
- can I put a larger array on the roof (typically yes, if you make
back to back pyramid shaped structures)</font><font size=3 face="Times New Roman">
</font><font size=2 face="Arial"><br>
- overall, what is the cost versus benefit</font><font size=3 face="Times New Roman">
<br>
</font><img src=cid:_1_0E1740680E1739DC007DB2B388257E93><font size=2 face="Arial"><br>
JARMO</font><font size=3 color=#008000 face="Times New Roman"><br>
_____________________________________________________________________________________</font><font size=3 face="Times New Roman">
</font><font size=1 face="Arial"><b><br>
<br>
Jarmo Venalainen</b> | </font><font size=1 color=#008000 face="Arial"><b>
Schneider Electric </b></font><font size=1 face="Arial"><b> | Xantrex
Brand</b> | <b>CANADA</b> | <b>Sales Application
Engineer</b> <b><br>
Phone:</b> </font><a href="tel:%2B604-422-2528" target=_blank><font size=1 color=blue face="Arial"><u>+604-422-2528</u></font></a><font size=1 face="Arial">
| <b>Tech Support:</b> </font><a href="tel:800-670-0707" target=_blank><font size=1 color=blue face="Arial"><u>800-670-0707</u></font></a><font size=1 face="Arial">
| <b>Mobile:</b> </font><a href="tel:%2B604-505-0291" target=_blank><font size=1 color=blue face="Arial"><u>+604-505-0291</u></font></a><font size=1 face="Arial">
<b><br>
Email:</b> </font><a href="mailto:jarmo.venalainen@schneider-electric.com" target=_blank><font size=1 color=blue face="Arial"><u>jarmo.venalainen@schneider-electric.com</u></font></a><font size=1 face="Arial">
| <b>Site:</b></font><a href=http://www.xantrex.com/ target=_blank><font size=1 color=blue face="Arial"><u>
www.Xantrex.com</u></font></a><font size=1 face="Arial"> |
<b>Address:</b> 3700 Gilmore Way, Burnaby, BC V5G4M1 </font>
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<table width=100%>
<tr valign=top>
<td width=12%><font size=1 color=#5f5f5f face="Arial">From:</font><font size=3 face="Times New Roman">
</font>
<td width=87%><font size=1 face="Arial">"Peter Parrish" <</font><a href=mailto:peter.parrish@calsolareng.com target=_blank><font size=1 color=blue face="Arial"><u>peter.parrish@calsolareng.com</u></font></a><font size=1 face="Arial">></font><font size=3 face="Times New Roman">
</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="Arial">To:</font><font size=3 face="Times New Roman">
</font>
<td><font size=1 face="Arial">"'RE-wrenches'" <</font><a href="mailto:re-wrenches@lists.re-wrenches.org" target=_blank><font size=1 color=blue face="Arial"><u>re-wrenches@lists.re-wrenches.org</u></font></a><font size=1 face="Arial">>,
</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="Arial">Date:</font><font size=3 face="Times New Roman">
</font>
<td><font size=1 face="Arial">07/28/2015 12:22 AM</font><font size=3 face="Times New Roman">
</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="Arial">Subject:</font><font size=3 face="Times New Roman">
</font>
<td><font size=1 face="Arial">[RE-wrenches] Using the North Facing Roof</font><font size=3 face="Times New Roman">
</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="Arial">Sent by:</font><font size=3 face="Times New Roman">
</font>
<td><font size=1 face="Arial">"RE-wrenches" <</font><a href="mailto:re-wrenches-bounces@lists.re-wrenches.org" target=_blank><font size=1 color=blue face="Arial"><u>re-wrenches-bounces@lists.re-wrenches.org</u></font></a><font size=1 face="Arial">></font></table>
<p><font size=3 face="Times New Roman"> </font>
<div align=center>
<hr noshade></div>
<p><font size=3 face="Times New Roman"><br>
</font><font size=2 color=#004080 face="Calibri"><br>
<br>
I recently read a short piece that caught me up short, and I quote:<br>
<br>
“The fast dropping cost of solar, while a huge boon to the adoption of
solar PV, has counter-intuitively altered design parameters. No longer
is the north-facing roof considered unusable because limited application
in less-than optimal orientations can still show a positive net benefit.
Arrays are thus designed now with elements or sub-arrays in these locations,
increasing overall kW installation while reducing the energy production
per capacity installed. This might have been anticipated based on sheer
economic analysis from a users perspective, but so long has solar been
expensive that these less optimal orientations were never seriously considered.”</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Calibri"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Calibri"><br>
I doubt that the individual who wrote this piece came to these conclusions
him/herself. Does anyone know of a recent article that argued this perspective?
Is this an emerging design practice? If so, I’d like to know more about
it. <br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Calibri"><br>
- Peter <br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Calibri"><br>
Peter T. Parrish, Ph.D.</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Calibri"><br>
President, SolarGnosis</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Calibri"><br>
1107 Fair Oaks Ave., Suite 351</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Calibri"><br>
South Pasadena, CA 91030</font><font size=3 face="Times New Roman"> </font><font size=3 color=blue face="Times New Roman"><u><br>
</u></font><a href="tel:%28323%29%20839-6108" target=_blank><font size=2 color=blue face="Calibri"><u>(323)
839-6108</u></font></a><font size=3 face="Times New Roman"> </font><font size=3 color=blue face="Times New Roman"><u><br>
</u></font><a href=mailto:petertor@pobox.com target=_blank><font size=2 color=blue face="Calibri"><u>petertor@pobox.com</u></font></a><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Calibri"><br>
</font><font size=3 face="Times New Roman"> </font>
<p><font size=3 face="Times New Roman"><br>
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