Three-Phase Transformers -- part 4: Harmonics

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Harmonics are voltages or currents that operate at a frequency that is a multiple of the fundamental power frequency. If the fundamental power frequency is 60 hertz, for example, the second harmonic would be 120 hertz, the third harmonic would be 180 hertz, and so on. Harmonics are produced by nonlinear loads that draw current in pulses rather than in a continuous manner. Harmonics on single-phase powerlines are generally caused by devices such as computer power supplies, electronic ballasts in fluorescent lights, and triac light dimmers, and so on. Three-phase harmonics are generally produced by variable-frequency drives for AC motors and electronic drives for DC motors. A good example of a pulsating load is one that converts AC into DC and then regulates the DC voltage by pulse-width modulation.

Many regulated power supplies operate in this manner. The bridge rectifier changes the AC into pulsating DC. A filter capacitor is used to smooth the pulsations. The transistor turns on and off to supply power to the load. The amount of time the transistor is turned on as compared to the time it is turned off determines the output DC voltage. Each time the transistor turns on, it causes the capacitor to begin discharging. When the transistor turns off, the capacitor will begin to charge again. Current is drawn from the AC line each time the capacitor charges. These pulsations of current produced by the charging capacitor can cause the AC sine wave to become distorted. These distorted current and voltage waveforms flow back into the other parts of the power system.

+++++30 Pulse-width modulation regulates the output voltage by varying the time the transistor conducts as compared to the time it is turned off. Filter capacitor AC Bridge rectifier Transistor Voltage Regulator Load Width between pulses determines output voltage

+++++31 Harmonics cause an AC sine wave to become distorted. Typical sine wave Typical distorted current wave due to harmonics; Typical distorted voltage wave due to harmonics

Harmonic Effects

Harmonics can have very detrimental effects on electric equipment. Some common symptoms of harmonics are overheated conductors and transformers and circuit breakers that seem to trip when they should not. Harmonics are classified by name, frequency, and sequence. The name refers to whether the harmonic is the second, third, fourth, or so on of the fundamental frequency. The frequency refers to the operating frequency of the harmonic. The second harmonic operates at 120 hertz, the third at 180 hertz, the fourth at 240 hertz, and so on. The sequence refers to the phasor rotation with respect to the fundamental waveform.

In an induction motor, a positive-sequence harmonic would rotate in the same direction as the fundamental frequency. A negative-sequence harmonic would rotate in the opposite direction of the fundamental frequency. A particular set of harmonics called "triplens" has a zero sequence. Triplens are the odd multiples of the third harmonic (third, ninth, fifteenth, twenty-first, etc.). A chart showing the sequence of the first nine harmonics is shown in ====1.

====1 Name, Frequency, and Sequence of the First Nine Harmonics

+++++32 In a three-phase four-wire wye-connected system, the center of the wye-connected secondary is tapped to form a neutral conductor. Phase conductor; Phase conductor; Neutral conductor; Phase conductor:

Harmonics with a positive sequence generally cause overheating of conductors, transformers, and circuit breakers. Negative-sequence harmonics can cause the same heating problems as positive harmonics plus additional problems with motors. Because the phasor rotation of a negative harmonic is opposite that of the fundamental frequency, it will tend to weaken the rotating magnetic field of an induction motor causing it to produce less torque. The reduction of torque causes the motor to operate below normal speed. The reduction in speed results in excessive motor current and overheating.

Although triplens do not have a phasor rotation, they can cause a great deal of trouble in a three-phase four-wire system, such as a 208/120-volt or 480/277-volt system. In a common 208/120-volt wye-connected system, the primary is generally connected in delta and the secondary is connected in wye.

Single-phase loads that operate on 120 volts are connected between any phase conductor and the neutral conductor. The neutral current is the vector sum of the phase currents. In a balanced three-phase circuit (all phases having equal current), the neutral current is zero. Although single-phase loads tend to cause an unbalanced condition, the vector sum of the currents generally causes the neutral conductor to carry less current than any of the phase conductors. This is true for loads that are linear and draw a continuous sine wave current. When pulsating (nonlinear) currents are connected to a three-phase four-wire system, triplen harmonic frequencies disrupt the normal phasor relationship of the phase currents and can cause the phase currents to add in the neutral conductor instead of cancel. Because the neutral conductor is not protected by a fuse or circuit breaker, there is real danger of excessive heating in the neutral conductor.

Harmonic currents are also reflected in the delta primary winding where they circulate and cause overheating. Other heating problems are caused by eddy current and hysteresis losses. Transformers are typically designed for 60-hertz operation. Higher harmonic frequencies produce greater core losses than the transformer is designed to handle. Transformers that are connected to circuits that produce harmonics must sometimes be derated or replaced with transformers that are specially designed to operate with harmonic frequencies.

Transformers are not the only electric component to be affected by harmonic currents. Emergency and standby generators can also be affected in the same way as transformers. This is especially true for standby generators used to power data-processing equipment in the event of a power failure.

Some harmonic frequencies can even distort the zero crossing of the waveform produced by the generator.

Thermal-magnetic circuit breakers use a bimetallic trip mechanism that is sensitive to the heat produced by the circuit current. These circuit breakers are designed to respond to the heating effect of the true-RMS current value.

If the current becomes too great, the bimetallic mechanism trips the breaker open. Harmonic currents cause a distortion of the RMS value, which can cause the breaker to trip when it should not or not to trip when it should. Thermal magnetic circuit breakers, however, are generally better protection against harmonic currents than electronic circuit breakers. Electronic breakers sense the peak value of current. The peaks of harmonic currents are generally higher than the fundamental sine wave. Although the peaks of harmonic currents are generally higher than the fundamental frequency, they can be lower. In some cases, electronic breakers may trip at low currents, and, in other cases, they may not trip at all.

+++++33 Harmonic waveforms generally have higher peak values than the fundamental waveform.

Harmonic waveform Fundamental sine wave:

Triplen harmonic currents can also cause problems with neutral buss ducts and connecting lugs. A neutral buss is sized to carry the rated phase current.

Because triplen harmonics can cause the neutral current to be higher than the phase current, it is possible for the neutral buss to become overloaded.

Electric panels and buss ducts are designed to carry currents that operate at 60 hertz. Harmonic currents produce magnetic fields that operate at higher frequencies. If these fields should become mechanically resonant with the panel or buss duct enclosures, the panels and buss ducts can vibrate and produce buzzing sounds at the harmonic frequency.

Telecommunications equipment is often affected by harmonic currents.

Telecommunication cable is often run close to powerlines. To minimize interference, communication cables are run as far from phase conductors as possible and as close to the neutral conductor as possible. Harmonic currents in the neutral conductor induce high-frequency currents into the communication cable. These high-frequency currents can be heard as a high-pitch buzzing sound on telephone lines.

+++++34 Comparison of average responding and true-RMS responding ammeters. Sine wave response Ammeter type Square wave response Distorted wave response Correct Average responding Approx. 10% high As much as 50% low; Correct; True-RMS responding; Correct; Correct

+++++35 Average current values are generally less than the true-RMS value in a distorted waveform. RMS current value; Average current value

Determining Harmonic Problems on Single-Phase Systems

There are several steps to follow to determine if there is a problem with harmonics.

One step is to do a survey of the equipment. This is especially important in determining if there is a problem with harmonics in a single-phase system.

1. Make an equipment check. Equipment such as personal computers, printers, and fluorescent lights with electronic ballasts are known to pro duce harmonics. Any piece of equipment that draws current in pulses can produce harmonics.

2. Review maintenance records to see whether there have been problems with circuit breakers tripping for no apparent reason.

3. Check transformers for overheating. If the cooling vents are unobstructed and the transformer is operating excessively hot, harmonics could be the problem. Check transformer currents with an ammeter capable of indicating a true-RMS current value. Make sure that the voltage and current ratings of the transformer have not been exceeded.

It is necessary to use an ammeter that responds to true RMS current when making this check. Some ammeters respond to the average value, not the RMS value. Meters that respond to the true-RMS value generally state this on the meter. Meters that respond to the average value are generally less expensive and do not state that they are RMS meters.

Meters that respond to the average value use a rectifier to convert the AC into DC. This value must be increased by a factor of 1.111 to change the aver age reading into the RMS value for a sine wave current. True-RMS responding meters calculate the heating effect of the current. The chart in shows some of the differences between average-indicating meters and true RMS meters. In a distorted waveform, the true-RMS value of current will no longer be Average x 1.111. The distorted waveform generally causes the average value to be as much as 50% less than the RMS value.

Another method of determining whether a harmonic problem exists in a single-phase system is to make two separate current checks. One check is made using an ammeter that indicates the true-RMS value and the other is made using a meter that indicates the average value. In this example, it is assumed that the true-RMS ammeter indicates a value of 36.8 amperes and the average ammeter indicates a value of 24.8 amperes. Determine the ratio of the two measurements by dividing the average value by the true-RMS value:

Ratio = Average

________ RMS

Ratio = 24.8 A

______ 36.8 A

Ratio = 0.674

A ratio of 1 would indicate no harmonic distortion. A ratio of 0.5 would indicate extreme harmonic distortion. This method does not reveal the name or sequence of the harmonic distortion, but it does give an indication that there is a problem with harmonics. To determine the name, sequence, and amount of harmonic distortion present, a harmonic analyzer should be employed.

+++++36 Determining harmonic problems using two ammeters.

True-RMS meter indicates a value of 36.8 amperes Average meter indicates a value of 24.8 amperes

====2 Three-Phase Four-Wire Wye-Connected System

Conductor | True-RMS responding ammeter | Average-responding ammeter

Phase 1 365 A 292 A Phase 2 396 A 308 A Phase x 387 A 316 A Neutral 488 A 478 A

Determining Harmonic Problems on Three-Phase Systems

Determining whether a problem with harmonics exists in a three-phase system is similar to determining the problem in a single-phase system. Because harmonic problems in a three-phase system generally occur in a wye-connected four wire system, this example assumes a delta-connected primary and wye-connected secondary with a center-tapped neutral. To test for harmonic distortion in a three-phase four-wire system, measure all phase cur rents and the neutral current with both a true-RMS indicating ammeter and an average-indicating ammeter. It is assumed that the three-phase system being tested is supplied by a 200-kilovolt-ampere transformer, and the current values shown were recorded. The current values indicate that a problem with harmonics does exist in the system. Note the higher current measurements made with the true-RMS indicating ammeter and also the fact that the neutral current is higher than any phase current.

Dealing with Harmonic Problems

After it has been determined that harmonic problems exist, something must be done to deal with the problem. It is generally not practical to remove the equipment causing the harmonic distortion, so other methods must be employed. It is a good idea to consult a power quality expert to determine the exact nature and amount of harmonic distortion present. Some general procedures for dealing with harmonics follow.

1. In a three-phase four-wire system, the 60-hertz part of the neutral current can be reduced by balancing the current on the phase conductors. If all phases have equal current flow, the neutral current would be zero.

2. If triplen harmonics are present on the neutral conductor, harmonic filters can be added at the load. These filters can help reduce the amount of harmonics on the line.

3. Pull extra neutral conductors. The ideal situation would be to use a separate neutral for each phase, instead of using a shared neutral.

4. Install a larger neutral conductor. If it is impractical to supply a separate neutral conductor for each phase, increase the size of the common neutral.

5. De-rate or reduce the amount of load on the transformer. Harmonic problems generally involve overheating of the transformer. In many instances, it is necessary to de-rate the transformer to a point that it can handle the extra current caused by the harmonic distortion. When this is done, it is generally necessary to add a second transformer and divide the load between the two.

====3 Peak Currents Are Added to the Chart Conductor True-RMS responding ammeter Average responding ammeter Phase 1 365 A 292 A Phase 2 396 A 308 A Phase x 387 A 316 A Neutral 488 A Instantaneous peak current 716A 794 A 737 A 957 A 478 A

Determining Transformer Harmonic Derating Factor

Probably the most practical and straightforward method for determining the derating factor for a transformer is that recommended by the Computer and Business Equipment Manufacturers Association. To use this method, two ampere measurements must be made. One is the true-RMS current of the phases, and the second is the instantaneous peak phase current. The instantaneous peak current can be determined with an oscilloscope connected to a current probe or with an ammeter capable of indicating the peak value of current. Many of the digital clamp-on ammeters have the ability to indicate average, true-RMS, and peak values of current. For this example, it is assumed that peak current values are measured for the 200-kilovolt-ampere transformer discussed previously. These values are added to the previous data obtained with the true-RMS and average-indicating ammeters.

The formula for determining the transformer harmonic derating factor is

THDF = (1.414)(RMS phase current)


instantaneous peak current

This formula produces a derating factor somewhere between 0 and 1.0. Because instantaneous peak value of current is equal to the RMS value x 1.414, if the current waveforms are sinusoidal (no harmonic distortion), the formula produces a derating factor of 1.0. Once the derating factor is determined, multiply the derating factor by the kilovolt-ampere capacity of the transformer. The product is the maximum load that should be placed on the transformer.

If the phase currents are unequal, find an average value by adding the cur rents together and dividing by three:

The 200-kilovolt-ampere transformer in this example should be derated to 144.4 kilovolt-amperes (200 kVA x 0.722).

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