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When the voltage is produced on a properly functioning, three-phase generator, the voltage and current of such devices can be represented by a set of vectors or phasors that are equally spaced apart (120 degrees) and of equal magnitude. Like most other power quality problems, it is somewhere between the generator and the load (or the load itself) that turns these vectors in an unbalanced set in magnitude and phase angle, as seen in the illustration below from data taken at a distribution substation during a fault condition.

These unbalanced conditions can come from a blown fuse on one of the three PF cap banks, unevenly distributed single phase loads on the same power system, single phase-to-ground faults, overloaded transformers and other sources that result in unequal loading, unequal source impedance or an unequal source voltage. It is typical in today’s electrical environment to have a 1 to 3 percent voltage unbalance. The resulting current unbalance for the load may be up to 10 times that of the voltage unbalance.

There are two basic methods for calculating unbalance. A popular method in the United States is “deviation from average,” which can be estimated by using the difference in the rms values between the maximum deviation of any of the phases from the average of the rms values of the three phases, divided by the average. Normally, you should use the line-to-line voltages for the calculations.

Vunb = 100 * (max (Vrms Phase X – Vavg) / Vavg, where Vavg = (VrmsA + VrmsB + VrmsC / 3).

For example, with phase-to-phase voltage readings of 230, 232 and 225, the average is 229. The maximum deviation from the average among the three readings is 4. The percent imbalance is 100 * 4/229 = 1.7 percent. The NEMA-MG1 requires the motor to be derated for unbalanced conditions above 1 percent and will void many motor manufacturer’s warranties, whereas a 3 percent voltage unbalance results in a 10 percent derating.

This method is an approximation of the unbalance, where the error becomes significant when the unbalance exceeds 5 percent. A more accurate method is defined by the IEC standards, but it involves the use of sequencing components that not many people can readily calculate, but fortunately, many newer power quality monitors will do for you.

Sequence components are three sets of vectors that can be combined to represent an unbalanced set of three-phase vectors. The positive sequence components are three, 120-degree separated phasors of equal magnitude that rotate in the same direction that the motor would normally rotate. The negative sequence components are opposite-rotating vectors, whereas the zero sequence components have no 120-degree relationship. The ratio of the negative sequencing components to the positive sequencing compon-ents is the unbalance.

Three Phase Vectors equals the sum of the Positive Sequence + the Negative Sequence + the Zero Sequence vectors.

In many systems, the harmonic components are associated with the different sequencing vectors.

Positive sequence values (those that rotate the motor the correct way) are opposed by the negative sequencing components (which turn the motor in the wrong way) with the net result being heat in the motor, which again causes premature aging of the motor. The EPRI Distribution Power Quality survey, conducted on the distribution voltage system of 100 utilities throughout the United States during the 1990s, found that the most dominate harmonic out there on those systems is the 5th harmonic. This is referred to as a negative sequencing component, trying to turn the motor in the opposite direction and generating heat.

The source of this 5th harmonic is often the fact that many motors are being sold today powered from an electronic power converter. These systems are referred to as adjustable speed drives (ASDs) or variable frequency drives (VFDs). The power converter section of ASDs is usually made of diodes or SCRs that are used to rectify the AC into DC. A three-phase, full wave rectifier is referred to as a six pulse or pole converter. Such rectification results in nonlinear harmonic currents, as the conduction of the current does not take place throughout the complete 60Hz cycle. The six pulse converter will have harmonic currents (and voltages) of the 5th, 7th, 11th, 13th, 17th, 19th and so on.

Keeping the voltage in balance and the sequencing components rotating in the right direction will make life for motors a whole lot better. **EC**

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

### About The Author

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