HARMONICS
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 Hz, for example, the second harmonic would be 120 Hz, the third harmonic would be 180 Hz, and so on. Harmonics are produced by nonlinear loads that draw current in pulses rather than in a continuous manner. Harmonics on single-phase power lines are generally caused by devices such as computer power supplies, electronic ballasts in fluorescent lights, 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 cur- rent into dc and then regulates the dc voltage by pulsewidth modulation (Figure 14–29). Many regulated power supplies operate in this manner. The bridge rectifier in Figure 14–29 changes the alternating current into pulsating direct current. 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 compared with 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 (Figure 14–30).
Harmonic Effects
Harmonics can have very detrimental effects on electrical 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, and so on of the fundamental frequency. The frequency refers to the operating frequency of the harmonic. The second harmonic operates at 120 Hz, the third at 180 Hz, the fourth at 240 Hz, 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, and so on). A chart showing the sequence of the first nine harmonics is shown in Figure 14–31.
Harmonics with a positive sequence generally cause overheating of conductors and 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-V or 480/277-V system. In a common 208/120-V, wye-connected system, the primary is generally connected in delta and the secondary is connected in wye (Figure 14–32).
Single-phase loads that operate on 120 V are connected between any phase conduc- tor and the neutral conductor. The neutral current will be the vector sum of the phase currents. In a balanced three-phase circuit (where all phases have equal current), the neutral current will be zero. Although single-phase loads tend to cause an unbalanced condition, the vector sum of the currents will generally cause 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, triplens 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-Hz 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 electrical component to be affected by harmonic cur- rents. Emergency and standby generators can 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.
CIRCUIT BREAKER PROBLEMS
Thermomagnetic 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. Thermomagnetic 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 (Figure 14–33). 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.
