### Published Sunday September 2, 2012

**Power Factor**

Power factor can be kind of confusing. If 10 X 120 = 1200, how can a circuit that draws 10 amps at 120 volts not draw 1200 Watts?

For DC current, the math is that simple but in AC circuits, voltage can lag the current and vice versa. This causes both real power and imaginary (or reactive power) to be present. There really is negative imaginary power and positive imaginary power. It happens every day in almost all our electronics.

Power factor is a ratio of real power to imaginary power. For a resistive load the power factor is 1. For capacitive or inductive loads the power factor is between 0 and 1. There are weird cases where the power factor is greater than 1.

To the home user, power factor can be ignored for the most part. It is only when the current draw starts to max out the circuit long before the power rating is reached does it become a problem. For example, at 240VAC, the capacitive charger in my EV truck draws 30Amps but only 2500 watts of real power is being sent into the batteries. Because of the low power factor of the capacitive charger, the 30 Amp circuit (which is capable of delivering 7200 watts) is being maxed out pre-maturely. Only 1/3rd of its capacity is being utilized because it is hitting its max current rating long before it reaches its max power rating.

Residential customers are only billed for watts consumed and not for the volt-amps delivered. Most of the time, this isn't a problem.

To demonstrate this phenomenon, I set up an experiment were I ran a 120 volt inverter off of a 12V battery. I connected up an incandescent light-bulb and measured its power consumption and power factor with a Kill-A-Watt meter. I also measured the DC current draw from the 12V battery. I then connected up a CFL and measured its power draw and power factor while it was running off of the inverter. I again measured the DC current on the 12V battery.

Measurement | 15 Watt CFL | 60 Watt Incandescent |

12V DC Amps | 1.50 Amps DC | 5.3 Amps DC |

12V DC Volts | 12.85 V | 12.85 V |

12V DC Watts | 19.3 Watts DC | 69.1 Watts DC |

120V AC Watts | 15.0 Watts AC | 55 Watts AC |

120V AC VA | 28.0 VA | 58 VA |

Power Factor | 0.53 | 0.95 |

calc. inverter loss | 4.25 Watts | 13.1 Watts |

calc. inverter efficiency | 77.8% | 80.1% |

From the above chart, we can see that even though the CFL has a poor power factor, it is indeed drawing less power from the battery. Going off of the volt-amp reading alone, it looks like the CFL is only 1/2 as efficient as the incandescent bulb where in reality it is over 4 times as efficient.

It is only when looking at the DC watts do we see that the battery merely has to work as hard as the real watt draw of the light bulb and nothing extra. If reactive power were real, the battery would have to deliver over 30 watts in order to power a 15 watt CFL and inverter. But imaginary power is not real power, so the battery only draws about 19 watts to power the 15 watt CFL and inverter.

The inefficiency of the inverter has to be accounted for but that is external to the issue of power factor.

The home consumer never pays for volt-amps, only watts. We are only billed for real power which is watts.

For industrial customers, large, inductive loads like motors cause grief for the electric utility. As such, they are billed by the volt-amp.

**We must be wise to the tricks of power factor.**

FYI: My place of employment is charged 4 cents per kVA (not kWh). Whenever I plug in my EV truck at work, the capacitive charger actually cancels out some of their electric bill. The capacitive reactance of my truck's capacitive battery charger cancels out some of the inductive reactance of large inductive loads (like motors) at my work.