How do you calculate voltage unbalance?

Electrical Apparatus, Nov 2004 by Nailen, Richard L

It is important for an understanding of equipment performance

WHETHER YOU CALL IT "unbalance" (the NEMA standard term) or "imbalance," equality of all three phase voltages is the basis for design and rating of three phase systems and apparatus, including motors. Whether you attempt to reduce a motor's horsepower output when unbalance exists; adjust other electrical loads to improve balance; or complain to the utility about perceived unbalance-you recognize that unbalance causes motors to overheat and lose torque. It can also greatly complicate the selection of suitable overcurrent protective devices (fuses, circuit breakers, starter overloads, and relays).

To deal with the problem, the first step is to determine the amount of unbalance. Several different calculations have been used. All of them result in a figure labeled "percent voltage unbalance." The values are all in the same ballpark-but only one is accepted as the standard basis for judging the effect on connected motors or other apparatus.

The starting point for any evaluation is measurement of the three-phase voltage. Since the reason for doing so is to evaluate the performance of, for example, a motor, readings should be taken as close to the motor terminals as possible, on the load side of any starter or contactor controlling the machine.

Also, they should be taken while the motor is running under normal load. That's because phase voltage unbalance is often caused by varying contact resistance in switching devices, fuse clips, or wiring terminations. A set of well-balanced voltages far upstream, or with little or no current flowing, may become significantly unbalanced at the load with normal current. Finally, some motors when unloaded will inherently exhibit a degree of measurable current unbalance even when voltage measurements indicate balance; the condition largely disappears under full load.

Phase currents are naturally easier to measure, using clamp-on meters. Such readings are subject to significant error, however. Furthermore, although motor performance problems are the direct result of unbalanced winding currents, the industry standards for evaluating unbalance are all based on voltage rather than current.

As an example of the variation in voltage unbalance percentage calculated by various methods, suppose the readings in a nominal 480 volt circuit are 468, 480, and 482 volts. Percent unbalance might then be defined in any of the ways shown in Figure 1.

The answers differ significantly. To correlate with NEMA standards (MG 1 Section 14), and support useful conclusions about the effect on motor performance, only the method shown in Figure 2 should be used

When phase unbalance is calculated that way, it can be properly related to current unbalance, winding overheating, and load derating, as recognized within the motor industry.

By Richard L. Nailen, P.E., EA Engineering Editor