Rusko A., Thompson M. Power Quality in Electrical Systems

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capacitor bank is switched. The ripple in the load voltage is due to the capac-

itor current that rings at the resonant frequency of the LC circuit.

Interruption

An interruption is defined as a reduction in line-voltage or current to

less than 10 percent of nominal, not exceeding 60 seconds in length.

Interruptions can be a result of control malfunction, faults, or improper

breaker tripping. Figure 3.13 shows an interruption of approximately

1.7 seconds in length.

Notching

Another common power-quality event is “notching.” Notching can occur

during current “commutation” in single-phase and three-phase rectifiers.

Shown in Figure 3.14a is a three-phase rectifier with the line inductance

of each phase shown. Note that in the rectifier, if we assume that the

Voltage Distortion 35

Voltage (%)

100

120

0.05 0.1 0.15 0.2

Time (ms)

rms variation

0.25 0.3

−150

−100

−50

Voltage (%)

100

150

25 50 75 100

Time (ms)

125 175150 200

Figure 3.13 An interruption of approximately 0.17 seconds duration

[3.1].

The top trace is the rms line-voltage. The bottom trace is the first 200 mil-

liseconds of the interruption.

The ring frequency is radians/second, or 1591 Hz.

From IEEE Std. 1159-1995, p. 16.

1>2p 2LC

parasitic inductances are zero, then the diodes turn on and off instan-

taneously. With a finite line inductance, there is a finite switchover

time from diode pair to diode pair.

Example 3.5: Voltage notching in a single-phase full-wave rectiﬁer. In this

example, we’ll see how line-side inductance can result in voltage notch-

ing in rectifiers. First, let’s consider an ideal single-phase full-wave

rectifier with a 208-V line-voltage and a 200 A DC load (Figure 3.15a).

If we assume the line inductance is zero, how will this circuit operate?

Looking at the rectifier output voltage (Figure 3.15b), we see a full-

wave rectified sine wave, as expected. In this circuit, D1 and D4 are on

for the positive half-wave of the sine wave, and D2 and D3 are on for

the negative half-wave. At the sine wave zero crossing, the switchover

from diode pair to diode pair occurs instantaneously.

36 Chapter Three

(a)

(b)

−1000

−500

0.020 0.025 0.030 0.035 0.040 0.045 0.050

500

1000

Figure 3.14 Notching in a three-phase rectifier. (a) A three-phase rectifier

that has commutation due to line inductances L

and which produces

notching. (b) A waveform

showing notching.

From IEEE Std. 1159-1995, p. 23.

Next, let’s consider what happens if there is a finite line inductance. In

Figure 3.16a, we see the same circuit, but this time assuming there is 100

microhenries of line inductance. The effect of the inductor is to introduce

a finite switchover time from one pair of diodes turning off to the other pair

turning on. During this switchover time, all four diodes are on and the

output of the rectifier is zero. This effect is shown in Figure 3.16b where

we see notches near the sine wave zero crossing. This notching adds unde-

sirable harmonics to the load voltage, and also reduces the average value

of the load voltage.

Voltage Fluctuations and Flicker

Voltage fluctuations are relatively small (less than 5 percent) varia-

tions in the rms line-voltage. Shown in Figure 3.17 is a system setup

Voltage Distortion 37

(a)

D3 D4

200 A

Vout+

Vout−

D1 D2

−

−50 V

0 V

50 V

0 s 2 ms 4 ms 6 ms 10 ms

8 ms 14 ms 16 ms 18 ms12 ms

Time

(b)

20 ms

100 V

150 V

200 V

250 V

300 V

Figure 3.15 An ideal single-phase full-wave rectifier with a 208-V line-neutral volt-

age and loaded by a constant current of 200 A DC. (a) Circuit; (b) output voltage wave-

form. There is no notching, since in this exercise we’ve assumed the line inductance

is negligible.

(a)

D3 D4

200 A

Vout+

Vout−

100 uH

−

−50 V

0 V

50 V

0 s

V(V

OUT

+) −V(V

OUT

−)

2 ms 4 ms 6 ms 10 ms

8 ms 14 ms 16 ms 18 ms12 ms

Time

(b)

20 ms

100 V

150 V

200 V

250 V

300 V

Ls = 11 uH

−50V

50V

5.0ms

V(V

OUT

+) −V(V

OUT

−)

5.5ms 6.0ms 6.5ms 7.5ms

7.0ms 8.5ms 9.0ms 9.5ms8.0ms

Time

(c)

10.0ms

100V

150V

200V

250V

300V

Figure 3.16 A nonideal single-phase full-wave rectifier with finite line inductance.

(a) Circuit; (b) the output voltage waveform. Note the notching in the output voltage wave-

form. (c) Close-up of the waveform in the 5ms to 10ms time range showing the notching

in the full-wave rectified wave.

that can cause voltage variations. A varying source of harmonic cur-

rents includes welders and capacitor banks. Voltage variation created

by this setup couples to residential lighting through the distribution

system.

Figure 3.18 displays typical harmonic levels during arc furnace oper-

ation. The harmonics produced by an arc furnace are unpredictable due

to the variation of the arc during metal melting. We see that during ini-

tial melting, the harmonic content (both even and odd harmonics of the

line-voltage) are relatively high. During the latter part of the arc furnace

melt cycle, the arc is more stable and the harmonic current has dimin-

ished. Shown in Figure 3.19 is an example of line-voltage fluctuations

caused by the operation of an arc furnace. Such voltage fluctuations can

cause a further phenomenon known as “flicker.” The waveform of a flicker

event is shown in Figure 3.19.

Flicker is the human perception of light intensity variation. In

Figure 3.20, we see a “flicker curve,” which shows that the human

perception of flicker depends on the amplitude and frequency of the event.

Voltage Distortion 39

R + jX

−

A.C.s

dryer

washers

Lamps

Residences:

Internal

sources

Residences

External

sources

External

sources

Capacitor

banks

Rolling

mills

Welders

Figure 3.17 A circuit capable of flicker propagation to a residence [3.4].

Figure 3.18 Harmonic content of arc furnace current [3.5].

Table 4.1

Harmonic Content of Arc Furnace Current

at Two Stages of the Melting Cycle

Harmonic Current

% of Fundamental

Harmonic Order

Furnace condition 2 3 4 5 7

Initial melting (active arc) 7.7 5.8 2.5 4.2 3.1

Refining (stable arc) 0.0 2.0 0.0 2.1 0.0

40 Chapter Three

1 2 3 6 10 20 30 1 2 4 6 10 20 30 60 2 3 4 6 1015

% Voltage fluctuation

Fluctuation per hour Fluctuation per minute

Fluctuation per

second

House pumps

Sump pumps

A/C equipment

Theatrical lightning

Domestic refrigerators

Oil burners

Reciprocating

pumps

Compressors

Automatic

spot-welders

Arc furnaces

Flashing signs

Arc-welders

Manual spot-

welders

Drop hammers

Saws

Group elevators

Single elevator

Hoists

Cranes

Y-delta changes on

elevator-motor-

generator sets

X-ray equipment

Solid lines composite curves of voltage flicker studies

by general electric company. General electric review

August 1925; Kamsas city power & light company,

Electrical world. May 19, 1934; T & D committee, EEI.

October 24, 1936. Chicago; Detrcit Edison company;

West Pennsytwanie Power Company; Public Service

Company of Northern [i]inois.

Dotted lines voltage flicker allowed by two utlities, referen-

ces electrical world november 3, 1959 and June 26, 1961

Border line

of visibility

Border line

of irritation

Figure 3.20 Voltage fluctuation limits, from [3.5], p. 81.

−1.5

−1.0

−0.5

0 50 100

Time (ms)

Voltage (Vpu)

100 DN > NC35KA(Type 1)

150 200

0.5

0.1

1.5

Figure 3.19 Voltage fluctuations [3.1].

Voltage Imbalance

A voltage “imbalance” is a variation in the amplitudes of three-phase volt-

ages, relative to one another. Figure 3.21 shows a three-phase voltage

waveform where the phases a, b, and c have different amplitudes. This

imbalance can be caused by different loads on the phases, resulting in

different voltage drops through the phase-line impedances.

A voltage imbalance can cause a reverse-rotating airgap field in induc-

tion machines, increasing heat loss and temperature rise.

Summary

To summarize voltage distortion types and causes, see Figure 3.22.

Voltage Distortion 41

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

−500

−400

−300

−200

−100

100

200

300

400

500

VLL = 480

Time (s)

Voltage (V)

Figure 3.21 Voltage imbalance.

Disturbance type

Narrow pulse with fast rise and

exponential or damped oscillatory

decay; 50 V to 6 kV amplitude,

0.5 µs to 2 ms duration

Repetitive low-energy disturbances

in the 10 kHz to 1 GHz band, with

100 µV to 100 V amplitude

Low voltage (typ. less than 80%),

for more than one periord

High voltage (typ. more than 110%),

for more than one period

Load switching, fuse clearing, utility

switching, arcing contacts, lightning

Normal equipment opeation

(switching power supplies, motor

speed controllers, etc.), carrier power-

line communication, wireless

broadcasting

Starting heavy load, utility switching,

ground fault

Load reduction, utility switching

Impulse

EMI

SAG

Swell

Description Causes

Figure 3.22 Overview of power disturbances [3.6].

Disturbance type Description Causes

References

[3.1] IEEE, “IEEE Recommended Practice for Monitoring Electric Power Quality,” IEEE

Std. 1159-1995.

[3.2] K. J. Cornick and H. Q. Li, “Power Quality and Voltage Dips: Problems,

Requirements, Responsibilities,” Proceedings of the 5th International Conference on

Advances in Power System Control, Operation, and Management, APSCOM 2000,

Hong Kong, October 2000, pp. 149–156.

[3.3] IEEE, “IEEE Recommended Practice for Emergency and Standby Power Systems

for Industrial and Commercial Applications,” IEEE Std. 446-1995 (The Orange

Book).

[3.4] C.-S. Wang and M. J. Devaney, “Incandescent Lamp Flicker Mitigation and

Measurement,” IEEE Transactions on Instrumentation and Measurement, vol. 53,

no. 4, August 2004, pp. 1028–1034.

[3.5] IEEE, “IEEE Recommended Practices and Requirements for Harmonic Control in

Electrical Power Systems,” IEEE Std. 519-1992, revision of IEEE Std. 519-1981.

[3.6] R. Redl, R. and A. S. Kislovski, “Telecom Power Supplies and Power Quality,”

Proceedings of the 17th International Telecommunications Energy Conference, INT-

ELEC ‘95, October 29 to November 1, 1995, pp. 13–21.

42 Chapter Three

Figure 3.22 (Continued)

Small repetitive fluctuations in the

voltage level

Repetitive dips in the line voltage,

with short durations

Deviation from ideal sine wave due

to the presence of harmonics or

interharmonics

Deviation of the frequency from the

nominal value

Zero-voltage condition of a single

phase or several phases in a multi-

phase system, for more than a half-

period

Pulsating load

Current commutation in controlled or

uncontrolled three-phase rectifier

circuits

Rectifiers, phase-angle controllers,

other nonlinear and/or intermittent

loads

Poorly regulated utility equipment,

emergency power generator

Load equipment failure, ground fault,

utility equipment failure, accidents,

lightning, acts of nature

Flicker

Notches

Waveform distortion

Frequency variation

Outage

Chapter

Harmonics and Interharmonics

In this chapter, we shall discuss harmonics (frequency

components that are integer multiples of the fundamental line

frequency) and interharmonics (high-frequency components).

For most of what we shall do in this chapter, the fundamental

frequency used will be 60 Hz.

Background

As we mentioned in previous chapters, harmonics can adversely affect

the operation of cables, capacitors, metering, and protective relays. To

summarize, a brief listing of some systems and the effects of harmon-

ics is shown in Table 4.1 [4.1].

Periodic Waveforms and Harmonics

The notion that any periodic waveform can be broken up into a series

of sine waves at the proper amplitudes and phase relationships was first

worked out by Joseph Fourier, the French mathematician and physicist

[4.2]. He showed that any periodic waveform can be expressed as a sum

of sine and/or cosine waves, with the proper amplitude, frequency, and

phase relationships between the waves. For instance, a square wave

(Figure 4.1a) can be represented by the infinite Fourier series:

where v is the frequency in radians per second. Note that the amplitude

of the first harmonic is (4/), the amplitude of the third harmonic is

vstd 5 a

bsin svtd 1 a

bsin s3vtd 1 a

bsin s5vtd 1 ???

one-third as much the first, the amplitude of the fifth harmonic is one-

fifth as much as the first harmonic, and so on. Also, note that the square

wave has only odd harmonics (that is, harmonics of the order 1, 3, 5...,

and so on). The spectrum of the square wave is shown in Figure 4.1b.

Likewise, a triangle wave (Figure 4.2a) can be represented by the

infinite Fourier series:

vstd 5 a

bsinsvtd 2 a

bsins3vtd 1 a

bsins5vtd 1 ???

44 Chapter Four

At Effect

Circuit breakers Malfunction

Capacitor banks Overheating

Insulation breakdown

Failure of internal fuses

Protection equipment False tripping

No tripping

Measuring devices Wrong measurements

Transformers, reactors Overheating

Motors Increased noise level

Overheating

Additional vibrations

Telephones Noise with the respective harmonic

frequency

Lines Overheating

Electronic devices Wrong pulses on data transmission

Over-/undervoltage

Flickering screens

Incandescent lamps Reduced lifetime

Flicker

TABLE 4.1 Some Effects of Harmonics

−1

(a)

Figure 4.1 Periodic waveforms. (a) A square wave

with peak values 1 and period T. (b) The spec-

trum of a square wave. The square wave has only

odd harmonics.