Understanding Insolation (W/m^2)

Re: Understanding Insolation (W/m^2)

The US government a few decades ago ran ~20 year solar isolation measurements around the US. They then put the data into a very simple to use program to calculate how much power (per month, or even per hour) you can get from XX kW array and yy% efficiency mounted on a 0/1/2 axis tracker.

Here is a link to the PV Watts program. Enter, for example Tucson, 10 kW of solar panels, 0.77 for Grid Tied, and defaults for everything else:

"Station Identification"
"City:","Tucson"
"State:","Arizona"
"Lat (deg N):", 32.12
"Long (deg W):", 110.93
"Elev (m): ", 779
"PV System Specifications"
"DC Rating:"," 10.0 kW"
"DC to AC Derate Factor:"," 0.770"
"AC Rating:"," 7.7 kW"
"Array Type: Fixed Tilt"
"Array Tilt:"," 32.1"
"Array Azimuth:","180.0"

"Energy Specifications"
"Cost of Electricity:"," 8.5 cents/kWh"

"Results"
"Month", "Solar Radiation (kWh/m^2/day)", "AC Energy (kWh)", "Energy Value ($)"
1, 5.70, 1282, 108.97
2, 6.11, 1212, 103.02
3, 7.03, 1550, 131.75
4, 7.50, 1561, 132.69
5, 7.29, 1513, 128.60
6, 7.15, 1418, 120.53
7, 6.44, 1316, 111.86
8, 6.85, 1411, 119.94
9, 7.06, 1434, 121.89
10, 6.72, 1444, 122.74
11, 5.99, 1287, 109.39
12, 5.27, 1199, 101.92
"Year", 6.59, 16627, 1413.30

You will get 1,199 to 1,561 kWHrs per month for Grid Tied solar.

Now, assuming that you want off grid system (batteries and AC inverter), change the derating factor to 0.52 (flooded cell batteries at 80% efficiency and 85% inverter efficiency * the 77% derating for a grid tied system):

"Station Identification"
"City:","Tucson"
"State:","Arizona"
"Lat (deg N):", 32.12
"Long (deg W):", 110.93
"Elev (m): ", 779
"PV System Specifications"
"DC Rating:"," 10.0 kW"
"DC to AC Derate Factor:"," 0.520"
"AC Rating:"," 5.2 kW"
"Array Type: Fixed Tilt"
"Array Tilt:"," 32.1"
"Array Azimuth:","180.0"

"Energy Specifications"
"Cost of Electricity:"," 8.5 cents/kWh"

"Results"
"Month", "Solar Radiation (kWh/m^2/day)", "AC Energy (kWh)", "Energy Value ($)"
1, 5.70, 853, 72.50
2, 6.11, 805, 68.42
3, 7.03, 1034, 87.89
4, 7.50, 1041, 88.48
5, 7.29, 1005, 85.42
6, 7.15, 941, 79.98
7, 6.44, 868, 73.78
8, 6.85, 935, 79.48
9, 7.06, 953, 81.00
10, 6.72, 963, 81.86
11, 5.99, 856, 72.76
12, 5.27, 797, 67.75
"Year", 6.59, 11049, 939.16

Now you are down to 856-1,041 kWHrs per month.

Your question was a bit confusing for me... You asked about battery bank sizing but talked about the amount of sun.

So, the above is an example of PV array sizing.

For Battery Bank Sizing, a good rule of thumb is to plan for 3 days of no-sun and a 50% maximum discharge. Or 6x your daily DC power needs (remember, the inverter is only 85% efficient, so you have to add more power to the battery bank). So, for 1,500 kWhrs per month:

• 1,500,000 Watt*Hour * 3 days * 1/0.50 * 1/0.85 inverter * 1/48 VDC bank = 220,588 Amp*Hours at 48 volts

That is one heck of a battery bank.

At this point in time, for home sized systems, lead acid battery banks tend to be the most cost efficient storage devices available. However, your energy usage is about 15x that what a "typical" off-grid home would aim for (try for 100 kWHrs or less).

Grid Tied is typically the best way to use Solar PV array for home type systems. There are variations that can include a Hybrid GT/Off-Grid inverter (Grid Tied for normal operations, battery bank + generator backup for emergency off-grid). Sort of depends on how much you want to spend and what it is you want to protect against. Also, not all utilities will allow a Grid Tied connection with 1 year net metering...

In the end, we usually try to convince people to spend their money first on conservation (insulation, double pane windows, energy star appliances, CFL lighting, downsizing loads such as a laptop instead of a desktop computer farm, turning things off, etc.)--because it is almost always more cost effective to conserve energy than to generate it.

Do you have more questions or more information on what you are trying to achieve?

-Bill

Re: Understanding Insolation (W/m^2)

Here is a nice I*V curve data sheet for a crystalline silicon panel.

The solar PV cell is basically a current source whose output current is proportional to the amount of solar energy falling on the surface. Once the panel is exposed to weak sunlight (or strong back scatter from the sky), Voc/Vmp is attained and the current above that point is pretty much proportional to the amount of sunlight. In fact, you can make a pretty decent sensor by just placing a silicon cell directly on an amp meter or low resistance shunt. Here is an example that can be home made--website also has some automated loggers available too (kit/turnkey).

When people type about "hours of sun"--they basically are assuming 1,000 Watts/sq.meter of "noon day" sun spread out over the entire day.

The output of the panel is defined on a 1,000 watt/sq.meter day, Standard Temperature and Wind. While the results are accurate, they are not really representative of real world average installations where there is not as much wind and the solar cells tend to run hotter, which depresses the Vmp (voltage maximum power). Imp does go up a little bit with temperature, but not near as much as Vmp goes down as temperature rises.

How much power can a panel output--on a sub-zero windy day with lots of white snow in the foreground / edge of cloud event, you can probably get upwards of 130% rated power. The NEC (current National Electric Code) has requiements on how to calculate the Isc and Voc with safety factors if you need those.

But assuming that the average V*I output + controller losses is in the range of 77% is not a bad place to start.

The PV Watts program has a list of deratings and the standard values they use here.

Because there is both an absolute value of solar radiation, plus mounting/tracking options and Cosine Error, you have a multitude of variables to address and integrate over.

The PV Watts Program (and other software/data) is open source (as I recall) if you hunt round in the website if you want to code something up yourself.

I would not count on much better than 10% accuracy given all of the variables out there (including weather, temperature, and specific equipment performance).

Regarding a GT/Off-Grid system... There are Hybrid systems out there that can do both. The Xantrex XW system is one very nice one. Up to 6kW 120/240 VAC of GT/Off-Grid power and a minimum of 600 Amp*Hour 48 Volt Battery Bank. With an Aux AC input for a backup Generator. Note that there are multiple components to the XW system (naming convention is a bit confusing). There is a Hybrid Inverter, a 60 amp MPPT solar charge controller, and a pre-wired panel to connect everything together. Plus other options (generator controller and such). You can price the major components from our host's website" Northern Arizona Wind and Sun.

A hybrid system is a great way to go... In general, it is best when you have lots or long power outages and generator fuel is difficult to store. Otherwise, a GT system + regular backup genset is hard to beat.

-Bill