While few would argue about of the wealth of information on the Internet, there isn’t a mechanism for qualifying its accuracy. Basically, anyone can post anything. Even such peer-reviewed sites as Wikipedia can fall short of the facts. A relatively simple concept in power is a good example. Online textbooks, PowerPoint presentations and numerous websites from some of the most reputable universities and companies (including electric utilities) still promote the “power triangle” as a method to describe the relationship between real power, reactive power and apparent power. Even the U.S. Department of Energy (DOE) contributes to this inaccurate information, as shown in Figure 1.

However, this and the aforementioned sources fail to account for harmonics, one of the most prevalent power quality phenomena. Harmonics have affected electric power systems for years, since the widespread use of fluorescent lights began in 1938 when GE introduced fluorescent Mazda lamps as a regular product line, selling about 200,000 in the first year. At conferences and in journals, people began to question the effect of harmonics on the accuracy of the traditional power measurements used in revenue meters.

The Institute of Electrical and Electronics Engineers (IEEE) organized a task force, chaired by Alex Emmanuel of Worcester Polytechnic Institute. This task force developed Standard 1459 2000, the “IEEE Trial Use Standard for Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions” (now IEEE 1459 2010).

The problem with using the old power triangle is in the reactive power leg of the triangle. Reactive power is the result of inductance or capacitance in the electrical system, which are both common in nearly every circuit. Nonlinear loads cause harmonic currents that result in harmonic voltage, which propagates to other system circuits. Voltage distortions of 5 percent or more are not uncommon anymore. In many locations, the replacement of incandescent lamps with compact fluorescent or light-emitting diode technology increases those numbers. Whereas a resistive load’s impedance is frequency insensitive, inductive and capacitive loads are affected. The higher the harmonic frequency, the higher the impedance of an inductor and the lower the impedance of a capacitor. The reactive power value is different for the fundamental, second harmonic, third harmonic, all the way to the nth harmonic, and must be computed separately.

To simplify the math, we typically compute the fundamental frequency reactive power as the other vector at 90 degrees to the real power vector and combine all of the harmonic power into a single vector called the “distortion power.” In Figure 2, the apparent power is kept at the same value as Figure 1, but the “nonworking power” now consists of the fundamental reactive power and distortion power vectors. The net result is that there is less “working” or real power for the same apparent power. In equine terms, less horsepower is applied to actually move the railcar down the tracks. In electrical terms, the power factor (PF) is lower since there are fewer watts in the numerator for the same volt-amperes in the denominator of the equation in Figure 1.

As I explained in “Imperfect Harmony” (October 2015, ELECTRICAL CONTRACTOR), some of the harmonics are effectively “negative sequence” components, which try to turn an electric motor in the opposite rotation from the fundamental frequency power. Others are zero-sequence components, generating no useful work. These values of the distortion power vector work against the “horse” to reduce its efficiency. In mechanical terms, bad bearings on the wheels or incorrectly aligned railroad tracks are horsepower losses.

An electric utility has to generate and distribute the volt-amperes the customer’s loads require, so they become less efficient as the PF decreases. Hence, tariffs or rate schedules for some industrial and commercial customers add a PF penalty or extra expense for inefficiently using their power. Some old electromechanical meters used to display the displacement power factor (DPF), or the cosine of the angle between the voltage and current, as the PF. It is possible for the DPF to be 1.0 and the true PF be significantly less, depending on the harmonic content.

Short of requiring all students and professionals to read ELECTRICAL CONTRACTOR, one must continue to exercise caution while surfing the web when it comes to PF (or just about anything else).

### About The Author

**BINGHAM**, a contributing editor for power quality, can be reached at 908.499.5321.