iv. harmonics in power systems

7/29/2019 IV. Harmonics in Power Systems

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4.1

IV. HARMONICS IN POWER SYSTEMS

4.1 Introduction

Power system harmonics have been presented since the invention of AC as a means of power

transmission. However, harmonic problems became more critical mainly due to the

substantial increase of non-linear loads due to the technological advances, such as the use of

power electronic circuits and devices, in ac/dc transmission links or loads in the control of

power systems using power electronics or microprocessor controllers. Prior to the appearance

of power semiconductors, the main sources of waveform distortion were electric arc furnaces,

the accumulated effect of fluorescent lamps and to a lesser extent electrical machines and

transformers.

Sources of harmonics can be classified as:

Traditional harmonic sources

Transformers

Rotating Machines (Motors and generators)

Arcing devices: Arc furnaces and fluorescent lamps

Modern (power electronic) harmonic sources

Electronic controls and switch-mode power supplies and office electronic

equipment

Thyristor-controlled devices (Electronic and Power Electronic Devices)

Rectifiers

Inverters

Static VAR compensators

Cycloconverters

HVDC power transmission systems

Surge arresters

Photovoltaic systems,

Electronic ballasts,

Welding machines,

Electrical Communication systems.

4.2 Transformers

Coils that have iron core will cause harmonics in electrical power systems. Transformers are

the most commons between those. As being one of the most important elements in power

systems, transformers are the oldest nonlinear elements known. The magnetization

characteristic of a transformers core is non-linear and will produce harmonics as it issaturated.


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4.2

The equivalent circuit of a transformer is given below. Here Rp and Xp shows the primary

circuit resistance and the leakage reactance, Rs and Xs shows the secondary resistance andleakage reactance that is transferred (referred) to the primary respectively. RFe is the

resistance which symbolizes the iron losses and IFe is the current related to this losses. In

parallel to this resistance, Xm shows the magnetization reactance and Im is the related current

passes through.

At no-load conditions:

ttN

Edt

N

e

dt

dNtEev mmm

coscossin

11

1111

A sinusoidal primary voltage produces a sinusoidal flux at no-load. The primary current,

however, will not be purely sinusoidal, because the flux is not linearly proportional to the

magnetizing current. The magnetizing current harmonics often rise to their maximum levels in

the early hours of the morning, in example, when the system is lightly loaded and the voltage

high.

For 3-phase transformers, let,

I1: Effective value of the fundamental component of a nonlinear and balanced load current

w1: angular frequency for the fundamental frequency

The instantaneous value of the fundamental component of the load current for phases a,b and

c is equal to

)3/2sin(2)(,)3/2sin(2)(,)sin(2)( 111111 tItitItitIti cba

For the nth harmonic component, instantaneous value of the phase currents will be


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4.3

)3/2sin(2)(,)3/2sin(2)(,)sin(2)( 111 ntnItintnItitnIti ncnnbnnan

For triplen harmonics; k=1,2,3, and n=3k

)3sin(2)()()( 13333 tkItititi kkckbka

As seen from the equation above, under balanced load and network conditions, triplen

harmonic components of the phase currents are equal to each other.

a) Star-Connected Transformers:

The Transformers Star Point is connected to Earth:

The current flows through the neutral conductor will be zero because of the sum of thebalanced fundamental component currents belong to the three phases is zero. This

situation is not valid for triplen harmonics. The sum of the three phase currents flows

through the neutral conductor as shown in the figure below.

The triplen harmonics may cause extra heat on the neutral conductor so during the

consideration of the neutral conductors cross section, triplen harmonics should taken intoaccount.

All the remaining harmonics besides the triplen ones have 120

of phase difference so

that their sum will be zero at the star point. As easily be seen, if the star point of thetransformer is connected to Earth, triplen harmonics passes to the secondary circuit

(network).

Transformers Primary Circuit Star Point is Disconnectedfrom Earth:

Triplen harmonics cannot pass to the secondary circuit as the star point of the primary

circuit is not connected to Earth.

b) Delta-Connected Transformers:

Primary Circuit is Delta-Connected:


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4.4

Triplen harmonics occur in magnetization currents but they cannot get out of the delta

connected coils. Other harmonic components pass to the network side.

Secondary Circuit is Delta-Connected:As the total current at the nodal points of the delta connection is equal to zero, triplen

harmonics do not flow through the network.

If the nonlinear load is unbalanced, whatever the transformer design is, triplen harmonics

will also flow through the network.

4.3. Rotating Machine Harmonics

Rotating machines produce harmonic due to the field distribution of salient poles, the

magnetic permeance is related with slots and the saturation of the main circuit. These

harmonics induce an electromotive force (emf) on the stator windings at a frequency equal to

the ratio of speed/wavelength. The resultant distribution of magnetomotive forces (mmfs) in

the machine produces harmonics that are a function of speed. Additional harmonic currents

can be created upon magnetic core saturation.

Harmonics produced by a synchronous generator will not be taken into consideration if the

generators power rating is smaller than 1000 kVA. If the magnetic flux of the field system isdistributed perfectly sinusoidal around the air gap, the e.m.f. generated in each full-pitched

armature coil is 2f

sin wt volts per turn. Where

is the total flux per pole and f is

frequency related to the speed and pole pairs. However the flux is never exactly distributed in

this way, particularly in salient pole machines.

4.4 Arcing Devices

The voltage-current characteristics of electric arcs are highly non-linear. Following an arc

ignition the voltage decreases due to the short-circuit current, the value of which is only

limited by the power system impedance. The main harmonic sources in this category are the

electric arc furnaceand discharge type lighting with magnetic ballasts.

Arc furnaces may range from small units of a few ton capacities, power rating 2

3 MVA, to

larger units having 400-ton capacity and power requirement of 100 MVA. The harmonics

produced by electric arc furnaces are not definitely predicted due to variation of the arc feed


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4.5

material. The arc current is highly nonlinear, and reveals a continuous spectrum of harmonic

frequencies of both integer and non-integer order. The arc furnace load gives the worst

distortion, and due to the physical phenomenon of the melting with a moving electrode and

molten material, the arc current wave may not be the same from cycle to cycle.

There is a vast difference in the harmonics produced between the melting and refining stages.

As the pool of molten metal grows, the arc becomes more stable and the current becomes

steady with much less distortion. Figure below, shows erratic rms arc current in a supply

phase during the scrap melting cycle, and table below, shows typical harmonic content of two

stages of the melting cycle in a typical arc furnace. The values shown in this table cannot be

generalized.

Both the odd and the even harmonics are produced. Arc furnace loads are harsh loads on the

supply system, with attendant problems of phase unbalance, flicker, harmonics, impact

loading, and possible resonance.


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4.6

Discharge lighting is highly nonlinear and gives rise to considerable odd-ordered harmonic

currents. This effect is illustrated in figures below, which shows the current waveform and

harmonic spectrum of a high-efficiency lamp.

This effect is particularly important in the case of fluorescent lamps, given the large

concentration of this type of lighting. Additional magnetic ballasts are needed to limit the

current to within the capability of the fluorescent tube and stabilize the arc. These type of

lamps shows nonlinear voltage-current characteristics because of their negative resistance

property.

Also the lighting ballasts connected to the lamp may produce large harmonic distortions and

third harmonic currents in the neutral. The newer rapid start ballast has a much lowerharmonic distortion and can be filtered with a filter circuit implementation. Table below

shows the harmonic spectrum of a fluorescent lamp with magnetic ballast. Harmonic currents

are shown as the percentage of the fundamental component.


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4.7

Harmonic Order (n)

1 3 5 7 9 11 13 15 17 19 21

%In/I1 100 19,9 7,4 3,2 2,4 1,8 0,8 0,4 0,1 0,2 0,1

Lighting circuits often involve long distances and have very little load diversity. With

individual power factor correction capacitors, the complex LC circuit can approach a

condition of resonance.

4.4. Electronic and Power Electronic Devices/Systems

The increasing use of the power electronic devices in which the voltage and/or the frequency

are varied to adapt to specific industrial and commercial processes has made power converters

the most widespread source of harmonics in distribution systems. Converters can be grouped

into the following categories:

Small power rectifiers used in residential entertaining devices, including TV sets and

personal computers, battery chargers

Medium-size power converters like those used in the manufacturing industry for motor

speed control and in the railway industry.

Large power converters like those used in the metal smelter industry and in HVDCtransmission systems.

Single-Phase Rectifiers

Rectifiers are used in all sorts of power system and power electronic subsystems to convert

AC power to DC power. In low-power applications using single-phase power, rectifiers are

used as the front-end of switching power supplies and small motor drives. A single-phase,

full-wave rectifier is shown below.

Two cases can be analyzed separately, namely, continuous conduction mode and

Discontinuous conduction mode. Waveforms for continuous conduction mode are givenbelow.


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4.8

As L line current approaches to a square wave. For this idealized case, the first harmonichas amplitude 1.0, the third harmonic has amplitude 1/3, the fifth harmonic has amplitude 1/5,

and so on. Note that the line current drawn by this rectifier circuit is very harmonic-rich, with

a THD of 48.3 percent.

Waveforms for discontinuous conduction mode are given below. As L0 line currentapproaches to impulse functions. Typical THD values are around 130%.

Example: Assume that a 120-V AC source consumes a DC load of 5 A through a single-phase

full-wave rectifier with and a capacitive output filter. With a 1000 F bus capacitor,

the load voltage ripple is about 25-V peak-peak. Load voltage and line currents are

shown below.


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4.9

Example: In order to decrease the ripples in DC voltage of the previous example to 4 V, filter

capacitance is increased to 10000 F. The waveforms for the new system areshown below.


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4.10

Harmonic contents of the two configurations are given below.

Harmonic

order

Line current Magnitude of the

system with C = 1000 F

Line current Magnitude of the

system with C = 10000 F

13

5

7

9

11

13

15

17

19

21

2325

27

100.094.0

69.0

48.0

30.0

22.0

21.0

20.0

16.5

13.4

12.5

12.011.0

10.0

100.0100.0

98.0

95.0

90.0

82.5

77.5

70.0

65.0

63.0

50.0

45.038.0

33.0

THD 140 % 265 %

Three-Phase Rectifiers (The six-pulse rectifier)

A typical application using a three-phase, six-pulse rectifier is an adjustable speed drive.

Three-phase power is full-wave rectified by the six-pulse rectifier. The rectified voltage is

filtered by the high-voltage bus capacitor, generating a DC voltage, which is used by the

subsequent inverter. The three-phase inverter generates the three-phase currents necessary todrive the motor.

Typical waveform for a 6-pulse rectifier is given below.


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4.11

If L, then the resulting line current becomes a quasi-square waveform. THD of such awaveform is 31 percent. It is less than of the single phase one due to absence of triplen

harmonics.

Waveforms for discontinuous conduction mode will be as follows.


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4.12

Some useful observations:

1. The absence of triple harmonics.

2. The presence of harmonics of orders 6k+/-1 for integer values of k3. Those harmonics of orders 6k+1 are of positive sequence and those harmonics of

orders 6k-1 are of negative sequence.

4. The rms magnitude of the fundamental frequency is

LI6

5. The rms magnitude of the nth harmonic is ..6

n

IL

Example: A six-pulse 3 diode rectifier operating as a DC power supply has the followingcurrent spectrum.. Calculate the THD and sketch the current waveform.

h 1 5 7 11 13 17 19

Ih % 100 72.3 51.5 16 9 7.5 5.4< Ih -12 -241 -88 16 -235 -172 -42

rmsIrmsrms

h

hI

ITHDII

II

THD

,1

2

,1

2

2

1

*353.11

%1.911


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4.13

The twelve-pulse rectifier

The twelve-pulse rectifier is comprised of two six-pulse rectifiers fed from separate

transformers. One six-pulse is fed from a Y/Y transformer, and the other is fed from a /Y

transformer. The two rectifier voltages are phase shifted 30 than in the six-pulse case. This isbecause the 12-pulse topology eliminates the 5th, 7th, 17th, and 19th harmonics, leaving the

11th, 13th, 23rd, and 25th harmonics.


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4.14

Variable Frequency Drives

VFDs are, in reality, power converters. The reason to further address them under a separate

section is because, by themselves, VFDs constitute a broad area of application used in diverseand multiple industrial processes. In a very general context, two types of VFDs can be

distinguished:

those that rectify AC power and convert it back into AC power at variable frequency and

those that rectify AC power and directly feed it to DC motors in a number of industrial

applications.

In both cases, the front-end rectifier, which can make use of diodes, thyristors, IGBTs, or any

other semiconductor switch, carry out the commutation process in which current is transferred

from one phase to the other. This demand of current in slices produces significant currentdistortion and voltage notching right on the source side, i.e., at the point of common coupling.Motor speed variations, which are achieved through firing angle control, will provide

different levels of harmonic content on the current and voltage waveforms.

Variable frequency drive designs also determine where harmonic currents will predominantly

have an impact. For example, voltage source inverters produce complex waveforms showing

significant harmonic distortion on the voltage and less on the current waveforms. On the other

hand, current source inverters produce current waveforms with considerable harmonic

contents with voltage waveforms closer to sinusoidal. None of the drive systems is expected

to show large distortion on both voltage and current waveforms, in line with Finneysobservations.

The Static VAR Compensators (SVC)

Static var compensators (SVCs) are very flexible and have many roles in power systems.

SVCs can be used for power factor correction, flicker reduction, and steady-state voltage

control, and also have the benefit of being able to filter out undesirable frequencies from the

system. SVCs typically consist of a TCR in parallel with fixed capacitors.


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4.15

The fixed capacitors are usually connected in ungrounded wye with a series inductor to

implement a filter. The reactive power that the inductor delivers in the filter is small relative

to the rating of the filter (approximately 1 to 2 percent).

The controls in the TCR allow continuous variations in the amount of reactive power

delivered to the system, thus increasing the reactive power during heavy loading periods and

reducing the reactive power during light loading. SVCs can be very effective in controlling

voltage fluctuations at rapidly varying loads. Unfortunately, the price for such flexibility is

high. Nevertheless, they are often the only cost-effective solution for many loads located in

remote areas where the power system is weak. Much of the cost is in the power electronics on

the TCR. Sometimes this can be reduced by using a number of capacitor steps. The TCR then

need only be large enough to cover the reactive power gap between the capacitor stages.

TCR generates the 3th,5th,7th,9th harmonics. Normally three phase TCRs are deltaconnected to prevent the triplen harmonics.


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4.16

Another possibility is the use of a thyristor-switched capacitor (TSC). TSCs usually

consist of two to five shunt capacitor banks connected in series with diodes and thyristors

connected back to back. In this case, each capacitor bank is switched on and off by means of

thyristors. With this, a discrete variation of the reactive power can be achieved, but never a

continuous variation as in the TCR.

Cycloconverters

A cycloconverter is actually a variable frequency AC motor drive composed of two, three

phase bridges supplying a single phase output. It converts AC power to a lower frequency ACpower. A typical application of a cycloconverter is as an AC traction motor speed control and

other high-power, lowfrequency applications, generally in the MW range.


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iv. harmonics in power systems

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