Published on *EC Mag* (http://www.ecmag.com)

One power quality steady-state condition is known by two names: imbalance or unbalance. Given that the latter seems to be more commonly used in power quality and electrical motor documentation, I use “unbalance” in this article, with the caveat that “imbalance” can be substituted for those who prefer it.

As there are two words for the same problem, there also are two mathematical definitions for it. In North America, the most often-quoted sources for these mathematical definitions are the NEMA standard MG1, Motors and Generators, and ANSI C84.1-2006, American National Standard for Electric Power Systems and Equipment—Voltage Ratings (60 Hertz). They use the “maximum deviation” method to determine either voltage or current unbalance. First the arithmetic average of the three phases is computed, and then the same is done for the difference or deviation of each phase from the average. Whichever deviation is the largest is divided by the average value and converted into a percentage value. Though this has served the industry as the method for determining unbalance, it has shortcomings (inaccuracies) when making such calculations for electrical systems with significant harmonic distortion.

A mathematical process called “sequence components” is involved in the method that most of the rest of the world uses. Just like a distorted waveform can be broken down into a sum of harmonic frequencies, a three-phase unbalanced waveform can be recreated using the vectorial sum of three sets of equipotential phasors—one rotating in the positive direction (that which makes the motor turn the way that is intended), another negative sequence set of phasors (that which makes the motor turn the opposite way than intended), and a set of zero-sequence phasors that are 0 degrees apart from each other. Depending on the extent of the phase angle and amplitude unbalance between the three phases, the negative and zero sequence will increase and can even exceed the positive sequence value in a reverse-rotation scenario.

While it is unusual to find a significant deviation in the three-voltage phasors from being 120 degrees apart from each other in an unfaulted system, current unbalance can be found with both phase-angle and magnitude unbalance, depending on the systems’s load characteristics and the voltage unbalance. Unbalance is calculated as the ratio of the negative-sequence value to the positive-sequence value as well as the zero-sequence value divided by the positive-sequence value. The former is the more accurate equivalent with distorted waveforms than the maximum deviation method. As recommended in IEEE 1250, IEEE Guide for Identifying and Improving Voltage Quality in Power Systems, line-to-line voltage measurements should be used when calculating unbalance using the maximum deviation method, to improve the accuracy and more closely match the sequence component method of voltage unbalance determination.

Though voltage unbalance and current unbalance are related, we usually look at the voltage unbalance first, as it can have a more widespread effect, and the generally accepted limits on them are much tighter than current. For example, the general rule of thumb is that an unbalanced voltage at motor terminals of a fully loaded motor will result in phase-current unbalance, ranging from six to 10 times the percent of voltage unbalance. There also can be damaging effects on motors, power supply wiring, transformers and generators.

Once again, there are two recommended voltage unbalance limits, with 3 percent being the ANSI C84.1 limit. IEC 61000-2-2 recommends 2 percent. Voltage unbalance will increase the heat in motors (18 percent rise at 3 percent unbalance), especially in high-efficiency motors. NEMA MG-1 recommends derating the motor based on the level of unbalance (see Figure 2). Voltage unbalance can also result in unbalanced currents and noncharacteristic harmonics for electronic equipment such as adjustable speed drives.

There are many possible sources of unbalance. In general, look upstream toward the source for voltage unbalance and downstream toward the load(s) for current unbalance. Unbalance can be due to problems or faults on the utility system (such as a blown fuse on the power-factor correction capacitor), incorrect tap setting on the transformer, open delta connected transformer, unequal impedance in the wiring, unequal loading (especially large single-phase loads). Some circuits can benefit from having unbalance protection relays, useful for motors, where the unbalance can affect both running at full load as well as locked-rotor torque and breakdown torque.

Many of the latest power quality monitors will perform the necessary unbalance calculations for you. It is a quick and easy measurement to make that can keep the process from going askew and equipment from aging prematurely.

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