Saturday, July 31, 2010

What does power mean? Or, more #@%* math




Many times when I describe how much power a solar array makes, the common question is "just what does that mean, how can I relate to the amount of power produced?"
When talking about power, there are two basic types of power measurement. One is the solar array rating and the other is what it makes over time.
The array rating is usually stated as watts under Standard Test Conditions or STC. These conditions are shining 1000watts of light energy onto one square meter at 25 degrees Celsius. When PV modules are made, the manufacturer "flashes" this amount of energy upon the module being tested. If it falls within tolerance, it passes the test and is labeled as so many watts STC.
The rating therefore is an instantaneous reading of energy output. It really hasn't done any work, since it takes power over time to arrive at an understandable unit of work or power.
Common output instantaneous ratings are described as:
Watt (W, after James Watt, inventor of the steam engine and definition of horsepower)
Kilowatts (KW; 1000 watts)
Megawatts (MW; 1,000,000 watts, 1000KW)
Gigawatts (GW; 1,000,000,000 watts, 1,000,000KW, 1000MW)
and so on.
When describing practical power, you must add the element of time. On average, on a SE West Virginia Summer day, you can expect 5.2 peak sun-hours per day. This unit goes back to the STC thing, 1000 watts per square meter. This is how we quantify solar energy through the seasons with all the clouds, rain, snow, and shorter days thrown in.
So, say you have an array rated at 2000 watts STC on a 5.2 peak sun-hour day. simply multiply 5.2 x 2000 and to get 10,400 watt-hours or 10.4 Kilowatt-hours for the day.
Now, we have something to grab on to, a quantity of useful, practical power.
So, what the hell does a kilowatt-hour mean to ME? Its surprising in this day and age that we are so used to having so much energy at our fingertips. Why, I remember in the old days, (not really) how little power was available to us. Back in days of yore, we had muscle power (human and animal), water and wind power to accomplish our work.
If you had a 1 horsepower electric motor, it would take about 1 kilowatt of electricity to run it. A horsepower is actually 746 watts, but with inefficiencies, it takes about a thousand watts. OK, so a Kilowatt-hour is worth one horsepower-hour, so what? When James Watt experimented with rating horsepower, he used big ol' draft horses, working at peak power over short time frames. When I say peak, the horse was working at levels that were not sustainable. I'm sure you are starting to get a handle on this power.
For you geeks, I'll explain what a horsepower is worth: it is 33,000 ft-lbs per minute. In other words, a horse could lift 33, 000 pounds a distance of one foot in one minute. Conversely, it could also lift one pound, 33,000 feet in one minute or any combination between. That's a bunch of work! In WV, we pay about 9 cents worth of electricity to do the same work. No wonder we have become so detached from the understanding of power and how cheap (artificially) it is.
So, back to the quantity of power from a 2000 watt array. Over the course of a Summer month, you could expect 312 KWh to be produced. You must subtract some power loss from inefficiencies of the inverter, line losses, and the fact that Summer heat reduces output compared to the STC rating. By observation, I determined the Summer efficiency rate of 90-92% for a complete high quality PV system, so my guess you would net 290 KWh.
What are the energy equivalents of that 290 KWh? You could do one the following activities:
>You could run your toaster for 8 days straight and make 4640 slices of toast
>The Budweiser Clydesdale hitch could pull a fully loaded beer wagon, up grade, for 48 hours straight.
>You could vacuum your house for 232 hours straight or 9.6 days, whew!
>Heat 2000 gallons of water from 60 to 120 degrees F.
>Run a large room air conditioner for 6 days, around the clock.
>Drive your car at 40 MPH on a level road for 19 hours and go 773 miles.
>Burn 8 CFL lamps rated at 100 watts of light (23w actual) for 65 days.
> Watch TV (LCD type) around the clock for 80 days, snacks not included.
Now let's look at what the equivalents are when you throw the switch:
>You turn on 4 CFL lamps- a healthy person works at maximum power for a while and the lights go dim as he becomes exhausted.
>Toast a bagel- A large draft horse pulls all it can for about 5 minutes.
>Turn on the room AC-A team of 2 to4 draft horses pull all they can for as long as the AC is on.
>Turn on all electric heat- Your 24hp lawn tractor runs at full bore mowing tall wet weeds.
I hope all this helps you to form some mental images as you go about living and realize how plush we have it, for now.

3 comments:

  1. Wow, that puts things in a different light. Thanks for the clarifications. AC seems very inefficient/expensive in this power use evaluation. There are many ways to passively reduce energy use in a house, from insulation and weatherizing after the fact, to designing an energy efficient home. Just seems that it is taking a long time for these practices to become mainstream.
    http://www.pueblo.gsa.gov/cic_text/housing/energy-eff/energy.html

    Just a couple of questions - are you going to be doing that vacuuming? and how much energy and time does it take to harness the Budweiser Clydesdale team?

    ReplyDelete
  2. You know the answer to the vacuum question, it really sucks.
    I pose a question to you: How many bales of hay, gallons of water, and pounds (tons) of oats would it take to get full output from 6 one ton horses for 48 hours? You can have rest stops, but must work 48 hours total.

    ReplyDelete
  3. My guess is that 1 horse can work 6 hours in 24, so it would take 8 days to get 48 hours.

    8 days x 15gal water x 6 = 720gal water
    8 days x 45 lbs hay x 6 = 2160 lbs of hay
    8 days x 15 lbs grain x 6 = 720 lbs grain

    This would not be "full output" as that exerted by pulling horses during their all out pull, or what a racehorse would do in a few minute race...

    ReplyDelete