80 cents / kWhr - Page 6

 

Sorry, I just cannot agree with the insolataion figures you are giving. More
research into this is needed to understand how they are stating these
figures.

With an average of 4 good hours of sun, based on some averaging factor for
the sine looking PV output wave and about 150-200 days of clear sky per
annum, you will not get 4 hours average, per day, over a year. At best this
would be 200 days /365 * 4 hours. or about 2.19 hours per day average,
depending where you cut the output "sine wave"

I haven't browsed these solar insolation calculators for a long time. Can
you give me some links to check them out, please.

Thanx





The source of the other values:

10 kW -- given by the OP as the size of the system.
80% efficiency -- a derating value on the panels to take into
account aging over the years.  This is a guess, but reasonable, I think,
considering mfg guarantees.



The manner in which insolation levels are measured and reported take that
into account.  The insolation levels do NOT consider that the insolation
will be the same every day; or even that there will be sun available every
day.  But they do represent a multi-year average.  TMY2 (Typical
Meteorological Year) data is derived from 1961-1990.  Other TMY information
is also available.

For a grid-connected system, where the goal is to sell power to the
company, you probably don't need to go much more deeply into the database.
But if you were designing, for example, a critical off-grid system, with no
backup electricity source, then you would go into the database to determine
the "worst-case" scenario.  And it might, indeed, be 30-40 days with only
six hours of sun.  So you would design around that.

Just as an example, here are daily values for global (horizontal) radiation
for Ottawa/January

1-Jan 0.17
2-Jan 1.58
3-Jan 2.43
4-Jan 0.26
5-Jan 0.32
6-Jan 2.35
7-Jan 1.68
8-Jan 1.59
9-Jan 1.98
10-Jan 1.77
11-Jan 0.53
12-Jan 0.48
13-Jan 1.30
14-Jan 0.53
15-Jan 1.74
16-Jan 0.32
17-Jan 2.49
18-Jan 2.46
19-Jan 2.51
20-Jan 2.55
21-Jan 1.19
22-Jan 1.93
23-Jan 0.80
24-Jan 0.73
25-Jan 1.13
26-Jan 2.80
27-Jan 0.45
28-Jan 0.83
29-Jan 0.57
30-Jan 2.17
31-Jan 1.13


Note the day-to-day variability, even with a thirty year average.

The average horizontal radiation over the course of the full year is 3.65
kWh/M2/day.  Assuming a panel tilted at the latitude, the average radiation
over the course of the year is 4.16 kWh/M2/Day.  So "4" is not a bad guess.


That is just not so.


Don't forget the next line:


If we assumed zero interest, then the payback time would be $
0,000 /
$
,367.36
  = 8.54 years.

It is longer precisely because we include interest.

When you include interest into the calculation, you generally make the
assumption that you are paying down the principal.  In this case, you would
take the $
367.36 and use that to pay off the loan.  It's a calculation
easily done with most spreadsheet programs, or a financial calculator.

If you were not actually paying down the principal, you would have those
funds available to invest (presumeably at a higher rate), but the end
result would be the same.

So, at the end of year 1:

$
0,000 principal
Payment of $
,367.36
   $
,000 for interest
   $
,367.36 for the principal

Results in $
4,632.65 owed at the end of Year 1 after paying interest and
principal

At the end of year 2
Same payment:  $
,367.36
  but the interest is now only due on the $
4K owed, so the interest
portion will be $
,731.63 leaving $
,635.73 to pay down principal.

The balance owed will now be $
8,996.91 and the interest will be $
,449.85
leaving $
,917.51 to pay down the principal.

Just like a mortgage, the amount of interest goes down after each payment.
So with a fixed payment, more and more of the payment goes to the
principal.

By the end of the 11th year, the balance owed has been reduced to under
$
,000.  So the interest would be under 5% of $
K or less than $
00.

In any event, the big reason that this scheme can work is because of the
extraordinarily high payment being made for solar-derived electricity
$
.802/kWh.
--ron

 



As I mentioned, the usual insolation data is NOT what one would use to
design a system for *worst-case scenarios*, but is an average of what might
be expected over a long period of time.

So to me, it seemed appropriate to use that for the sort of system microFIT
is subsidizing.

In general, solar insolation data, as published on the internet, is given
in terms of average over whatever time period is being considered, usually
month or year.

By the way, the average number is not designed to be factored by the
"number of clear days".  That is already taken into account in coming up
with the average.

For example, for Ottawa, the annual insolation shows a minimum of 0.21 and
a maximum of 8.34 kWh/M2/day.  That's already taking into account the
cloudy days.

http://rredc.nrel.gov/solar/pubs/tmy2/   is the users manual for TMY2. Check
out the rest of that web site for the solar data.

For calculators, take a look at http://www.pvwatts.org/

If I enter Ottawa for the location, 10kW for the system size, $
.802 for
the $/kW, and leave the default 0.77 derating factor, this calculator shows
the system would generate an energy value of $
,352.92 / year.  It also
shows an average annual insolation of 4.33 kWh/M2/day.

There is a small difference in values given by PVWATTS and that which I
posted earlier.  e.g: Yearly insolation 4.16 vs 4.33.

I believe this slight difference in values is due to PVWATTS using CWEC
weather files (Canadian Weather for Energy Calculations) for Ottawa instead
of the NASA TMY2 data that I used.

I haven't poked around the Canadian data, but I find these links:

Some information about CWEC is here:  http://www.numlog.ca/climate.html

  and here:  http://climate.weatheroffice.gc.ca/Welcome_e.html

Enjoy.
--ron

 

wrote:


Hmmm.  That statement is not really clear.  Rephrasing, the variability in
day-to-day insolation, even for closely spaced days, as seen in my
previously posted  data for January, is an indication that cloudy (no-sun)
days are being taken into account.
--ron

 

I had a look and some trial runs and I can verify your figures on PVWatts.
It has changed a bit, with more factors, since I used it years ago.

I had a look at the hourly output and it definitely appears to account for
cloudy day history. It's a little puzzling that they base their history on
different years for each month. It appears a little suspicious, but
reasonable and possibly unbiased. Too bad the data isn't there for my micro
climate. In June I get sun that travels about 255 degrees around me but a
lot of overcast throughout the year. I would be a good candidate for a
tracker but my barn would be hard to turn...LOL

I am also concluding about a ten year payback at the 80 cents / kWh
including only the money interest and that isn't depreciating principal, so
let's say there is more maintenance involved or make it about 6-8 years on a
rough guess.

I guess once the basic maintenance is paid (interest and
mechanical/electrical) the 80 cents goes a long way from the 10 cents toward
the "break even" point. With 10 cents/kWh the payback is never. Even at the
40 cents they were offering it was close.

Thanx for the information and the smack in the head with your
persistence.....LOL
My thinking was out of date on that issue.



wrote:
Hmmm.  That statement is not really clear.  Rephrasing, the variability in
day-to-day insolation, even for closely spaced days, as seen in my
previously posted  data for January, is an indication that cloudy (no-sun)
days are being taken into account.
--ron

 



I make it a "break-even" at $
.329/kWh -- but it would take 171 years with
zero maintenance!  Not very realistic!


I'm glad to help, but I abhor physical violence.  

There is a lot of misinformation out there.  And it is on both the overly
optimistic as well as the overly pessimistic sides.

"Onward through the fog"

Best wishes,

 --ron
--ron