Energy Loss due to low power factor in a residence
Here are the assumptions:
1) Residential power meters measure real power. The Oscillating power (the reactive component) that is generated by inductive motors travels through the wires between the motor and the utility grid, passing back and forth through the residential meter.
2) Capacitors can be used to intercept the reactive power from inductive motors, and return it to the source on the next cycle. However, if the capacitors are at the service entrance or utility panel, they will do nothing to reduce I2R losses in the wiring between the panel and the motor. In order to eliminate line losses, the power factor correction device must be mounted at the inductive load.
3) If the resistance of the wiring was zero, then the power losses due to the reactive components would also be zero. However, residential wire does have a resistance as we will calculate below.
Now for some tests with a top fill washing machine on a regular cycle:
Make Whirlpool
Model LCR7244JQ3
Rated 9.8A 120 Volts
Age: 3 years
First the fill cycle:
Real power: 3W
Current: 0.4A
Voltage: 121.3VAC
Apparent power: 5VA
Power factor: 0.68
Length of fill 5 min
Next the wash cycle:
Real power 630W
Current: 9.54A
Voltage: 120.2 VAC
apparent power: 1144VA
Power factor: 0.53
Length of wash: 25 minutes
Finally the spin cycle while water still draining:
Real power: 689W
Current: 9.11A
Apparent power: 1106VA
Power factor: 0.58
And the spin when it gets up to full speed:
Real power 513W
Current 8.94A
Apparent power: 1081VA
Power factor: 0.47
The complete cycle took 41 minutes. Total real energy used (the part we pay for) 0.23 kWh.
From the data above, we can do the following:
Ignore the fill cycle since it is 200 time smaller than the wash and spin.
Lump the wash and spin together since they both use a similar amount of energy (another reason to get a front loader. They use about 22 watts on the wash cycle because they don't have to slosh around gallons of water). We will be conservative and use the worst numbers, those of the spin cycle:
That leaves us with:
30 minutes
Power Factor: 0.47
Current: 8.94A
Real power: 513W
Apparent power: 1081VA
From this we can calculate the following:
Impedance phase angle is arcos(True power / apparent power) = 62 degrees
Reactive power = Real power * atan(phase angle) = 423 VAR
The above is easier to conceptualize as a power triangle, a right angle triangle where the apparent power is the hypotenuse, and the other two sides are the reactive and real powers. The reactive part does not do work. The real part only does work.
The apparent power is what you get when you measure the voltage and current as measured with a meter.
Now, we will assume that 513W of real work can wash and spin the clothes. Had the power factor been 1, we would have needed 513W/110V = 4.66A. However, because of the poor power factor, we drew an extra (8.94 - 4.66) = 4.27A
Stage Two:
We need to calculate the energy loss between the washing machine and the service panel. Let's assume the following:
1) The distance between the machine and the panel is less than 40 feet. I think that is generous in most cases.
2) 110V machines are usually wired with 14AWG copper. Looking on the net, we can find some values:
2.524 Ohms/1000 feet http://www.mwswire.com/barecu5.htm
2.525 Ohms/1000 feet
http://en.wikipedia.org/wiki/American_wire_gauge
2.6 Ohms/1000 feet
http://www.engineersedge.com/copper_wire.htm
Let's take the highest value. Using this, we can calculate the resistance of a 40 length of wire to be 40ft * (2.6Ohms/1000ft) = 0.104 Ohm.
There are also connections, a screw clamp on the circuit breaker, possible a few spring connectors if the wall boxes are daisy chained, and a screw connection on the wall plug. So let's calculate it directly. When the washer moved from fill to wash, the voltage dropped (121.3 - 120.2) = 1.1 volts. This occurred at a load increase of 9.41A. V = I/R so R = V/I = 1.1v/9.41 = 0.11 Ohms. The washer above is located on the 3rd floor, the breaker panel is on the garage.
So, it appears that both methods of calculation give us similar results for resistance. Let's use the higher value, 0.11 Ohms.
Stage Three:
We want to know the energy loss by heating the wires between the washing machine and the utility power meter. We really don't care what happens on the other side of the meter, although the power company does.
Power = I2R = 4.27A * 4.27A * 0.11Ohms = 2 Watts.
Energy = (2W/(1000W/Kwh)) * 1/2 hour = 0.001 kWh
Cost of this power: 0.001 * 12 cents/kWh = 0.012 of a penny
Finally, let's assume you run a wash every day of the year (perhaps true if you have children). Annual power cost: $0.00438
Stage Four the Economics:
1) The unit must be installed at the source, not the panel or we defeat the purpose of eliminating the I2R losses.
2) We will use an interest rate of 7%, the inflation adjusted average growth of the stock market over the last 200 years.
3) Life of capacitors is 15 years. After this, you will discard the power factor unit, or perhaps it will just become useless.
Let's calculate the present value of a hypothetical power saving device:
PV(7%,15years,$0.00438) = $0.04
Provided that MS Excel's PV calculation is still accurate with fractional cents, it looks like the investment is worth 4 cents.
Maybe.
I live in a very cold climate and heat with electricity because natural gas it not available and trees are scarce. All the wiring in the house aside from exterior lighting, is in heated spaces. Most of the year, the "wasted heat" is actually useful to me.
Hope this helps. If you see a mistake here, please let me know and I will correct it.
Regards,
Peter