Last month, we reviewed the basics of the power parameters as affected by inductive, capacitive and resistive loads as well as a mixture of two or more of those elements. While that background information is important for understanding the system as a whole, the real issue to many people is, “What am I being billed for, and is the bill accurate?” With today’s mixture of loads as they interact with unbalanced and distorted voltage supplies, the answer may seem vague: “It all depends on what you are looking for.”

The old power triangle from last month has been replaced by the new distorted power triangle. The difference is the addition of the distorted power leg. Volt-amperes reactive (VARs) take into account the power flow related to inductors and capacitors. The impedance of these components depends on the current’s frequency.

In the old days, this current was composed of almost entirely the fundamental power frequency (50 or 60 Hz in most cases). Therefore, there was only one vector to include in the triangle for this. If one added the vectors of the resistive-based power component (real or active power) to the reactive-based component (VAR), the combination would be equivalent to the volt-amperes vector or apparent power that the generators had to produce. Depending on how big the reactive component was, the electric utility would bill you on the watts and VARs. Or it would use the parameter called power factor, which was related to the amount of VARs or power the utility had to produce but was not being measured by a watt-hour meter. Adding a couple more coils and a bit of magic to the revenue meter would produce measurements for both, along with the demand or maximum usage within the average value over the demand interval, which typically was 15 minutes. This additional billable parameter exists because the utility must provide for the maximum demand, whether you use it once a day, once a week or once a year.

Then, along come the harmonic and interharmonic currents from today’s loads. The simple method for determining the VAR value is no longer valid, as there is not just one frequency in the current. There sometimes are dozens or more. Each of those frequencies results in a different impedance value at a given current level. For inductive loads, the impedance grows as the frequency goes up, while it gets smaller for capacitive loads. It makes for a bunch of little contributors at various phase angles and magnitudes that we lump together into the distortion power vector. The electric utility still must provide this total power, even though it did not fall into the old power triangle model. In other words, volt-amperes has gotten larger for the same amount of billable watts.

It resulted in a change in how the consumer’s effective power usage was measured. The power factor (PF) parameter mentioned above usually was measured using the equivalent of the trigonometric function, called cosine of the phase angle, between the voltage and current. That method is more correctly known as the displacement power factor (DPF). What most of the newer power-monitoring instruments and meters use now is often labeled as “true” power factor, which is the ratio of the watts to the volt-amperes, or W/VA. In cases where there is no distorted power, PF is equal to DPF.

What about the customer who wanted to know if he was being billed the correct amount? This story illustrates the point. The electric utility replaced the under-glass electromagnetic induction-type watt-hour meter (with the disk that rotates around at the speed of power consumption) at a commercial facility with a newer electronic one, which has the telltale numerical display to indicate the different measured (and sometimes billable) parameters.

The next month’s electric bill was significantly larger. The customer’s reaction was: “The meter is broken. Replace it, for I am not paying.” Replacements had the same results. The customer asked that the old meter be put back. “I have the same equipment, running at the same rate as before the meter was changed, so my bill shouldn’t be any different.”

The utility’s response was that the old meter did not accurately measure the real energy burden since it did not account for the distorted power. This opens up another dangerous discussion: Do the old meters even measure the real watts correctly under such conditions? The University of Texas and others have conducted studies with mixed published results, but you can probably guess which the utilities would support.

The electronic meters usually measure wattage by multiplying the instantaneous sample of the voltage waveform by the sample of the current waveform. They then mathematically combine those values together for the watts value. The fundamental VAR value (as it is more accurately known) requires some fancier math. The easiest calculation is volt-amperes, which is the Vrms value (root mean sum of the squares of all those instantaneous samples over one cycle) multiplied by the Irms value. But even the calculations can be inaccurate if the sampling rate is not high enough to account for the various harmonic and interharmonic frequencies present in the system.

So, does an electric bill accurately reflect the demand and energy burden consumed by a facility? It depends (see the figure). __EC__

**BINGHAM**, a contributing editor for power quality, can be reached at 732.287.3680.