Kaytto6 En

7/28/2019 Kaytto6 En

1/44

Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering6.1

6. MAIN CIRCUIT POWER ELECTRONIC TOPOLOGIES APPLIED TO THE CONTROL OF

ROTATING-FIELD MOTORS ........................................................................................................... 1

6.1 Cycloconverter ..................................................................................................................... 1

6.2 LCI Drive ........................................................................................................................... 10

6.3 Voltage Source Inverter Power Stages .............................................................................. 11

6.3.1 Generation of Voltage Vectors as the Combined Effect of the Inverter and Winding .. 19

6.3.2 Space Vector Modulation (SVM) .................................................................................. 246.3.3 Dimensioning of a DC Link Capacitor .......................................................................... 31

6.4 Matrix Converter ................................................................................................................ 32

6.5 Structure and Interfaces of a Frequency Converter ........................................................... 37

6.6 Multi-Level Inverters ......................................................................................................... 39

6. MAIN CIRCUIT POWER ELECTRONIC TOPOLOGIES APPLIED TO THE CON-TROL OF ROTATING-FIELD MOTORS

In principle, the motors can be controlled either by direct converters or by converters with interme-

diate DC links (DC link converters). In the case of the direct converters, alternating current is con-

verted directly into new alternating current, whereas in the case of the DC link converters, either

direct current (by a current source inverter, CSI) or direct voltage (by a voltage source inverter,

VSI) is produced from an AC voltage source.

In the early history of frequency converters, the current source inverters were quite popular, howev-

er, their commercial role has constantly been reducing. The frequency converters presently on the

common market are without exception voltage source inverters.

Defects of direct current link converters are, in the case of the CSI, the relatively large coil func-

tioning as an energy storage, or in the case of the VSI, the relatively large DC link capacitor. Late-

ly, the target has been to reduce the capacitance of the DC voltage link capacitor and thus also itssize, basically in order to bring cost savings. When the capacitance is reduced to the minimum, the

VSI begins to resemble a direct converter. In that case, the control technology must focus on con-

trolling the voltage of the DC link. When a large capacitance is used, the voltage of the DC link can

be considered almost constant, whereas in the case of a minimized capacitance, also the voltage of

the DC link behaves very unsteadily.

In the direct converters, the DC link and the components related to it can be avoided, however,

something else is often lost instead. A cycloconverter applying thyristors used to be quite a popular

frequency converter in slow motor drives, but it has also been losing markets for high-voltage VSIs.

Of the current source inverters, the load commutated inverter (LCI) has managed to keep its posi-tion basically as the frequency converter of large, high-speed synchronous machine drives.

The matrix converter represents a research branch, in which the target is to completely avoid the

DC link in small drives. The problem in this application is the need for bidirectional switches; in the

matrix converter, each input phase can be connected to each output phase, and thus it is in principle

possible to always select the desired input voltage for the output. Figure 6.1 illustrates the basic

topologies of these different frequency converter types.

6.1 Cycloconverter

A cycloconverter is a so-called direct frequency converter, which converts the constant-frequency

and constant-voltage alternating current of the power line directly without an intermediate DC link


2/44


into AC of varying frequency and varying voltage to the output side of the converter, as shown in

Fig. 6.2, which in turn illustrates the topology of the frequency converter with an intermediate DC

link.

Figure 6.1 Topologies of frequency converters. As shown in the figure, each converter type produces a three-phase

output system from the three-phase input system. The numbers of phases may naturally be other than in the illustration;

for instance, the input of small voltage source inverters is usually a single-phase system.

Figure 6.2 Topology of a cycloconverter: a direct AC-AC conversion. f1 is the line frequency and u1 is the line voltage.f2 is the output frequency and u2 is the output voltage of the cycloconverter.

f1, u1 f2, u2

direct converter

1, u1 f2, u2

current source inverter

1, u1 f2, u2

voltage source inverter

f1, u1

f2, u2

L

C

matrix converter

cycloconverter


3/44


The connection of the topology of the cycloconverter to other power converters as well its operation

principle can be investigated by the six-pulse thyristor bridge of Fig. 6.3a; this bridge can be consi-

dered a basic component of the cycloconverter. The line-commutated six-pulse thyristor bridge is

applied either to inversion or rectification, since the bridge can be employed to generate a DC vol-

tage UDC, the (short-term) mean value of which is either positive or negative. The currentIDC of the

bridge can flow only into one direction determined by the thyristors. Hence the bridge may operate

in two quadrants of the current-voltage plane, as shown in Fig. 6.3b.

IDC

UDC

UDC

IDC

a) b)

Figure 6.3 a) Six-pulse thyristor bridge.IDC is the direct current conducted by the bridge, and UDC is the generated DC

voltage. b) Current-voltage plane and those quadrants in which the six-pulse thyristor bridge is operating.

If there are two bridges connected antiparallel, as shown in Fig. 6.4, we obtain another flow direc-

tion for the currentIDC which is negative when compared with the current in the figure as well as

both polarities of the voltage UDC when the current is flowing in this direction.

IDC

DCUDC

Figure 6.4 Antiparallel thyristor bridges in the supply of a DC machine. IDC is the direct current conducted by the anti-

parallel connection, and UDC is the generated DC voltage.

Thus we have created a converter that can operate in a four-quadrant current-voltage plane, as

shown in Figure 6.5a. Figure 6.5b depicts the schematic diagram of the antiparallel six-pulse thyris-

tor bridges. By using the antiparallel connection, the direction and magnitude of current and voltage

may change freely independent of each other. Since power is a product of current and voltage, also

its direction may change freely. Thus, the converter with the antiparallel connection can be used to

supply power to the load, or an active load may supply power through the converter to the grid.

This converter is used in DC drives to implement the four-quadrant operation of the DC machine.


4/44


U

I

a) b)

Figure 6.5 a) The quadrants of the current-voltage plane, in which the antiparallel six-pulse bridges are operating. b)

The block diagram symbol of the antiparallel converter.

In the DC drives, the output voltage is regulated to be a DC voltage; however, nothing prevents

from converting the output voltage of the four quadrant converter also into a low frequency AC vol-

tage. The converter becomes thus an AC voltage source, in which the directions of current and vol-

tage may settle independently with respect to each other, as shown in Fig. 6.6. The phase angle be-

tween the current and the voltage is determined by the impedance of the load. Also the flow direc-

tion of the effective and reactive power may settle according to the load, in other words, the drive

operates completely in four quadrants also at direct current.

The frequency and amplitude of the output voltage is altered by changing the frequency and ampli-

tude of the voltage reference. These properties make the switching a frequency converter, in which

the conversion is performed directly from AC to AC without an intermediate DC link. The conver-

ter is known as a single-phase cycloconverter or a direct frequency converter. The converter oper-

ates without a circulating current, if only one of the six-pulse bridges of the antiparallel connection

operates at a time, while the other is blocked. Between the bridge switch over, there has to be a

short currentless period before the current moves from one bridge to the another. If both the bridgesreceive control pulses, one of the bridges is kept in the rectification state and the other in the inver-

sion state. However, in the converter, there flows a so-called circulating current, since the instanta-

neous values of the output voltage of different bridges are not exactly equal, although the target is

to keep their instantaneous mean values equal. Now a short pause is not required between the

bridge changes, but the current may change its direction immediately. The circulating current has to

be restricted by a choke in order for the current not to increase excessively. The cycloconverters are

usually manufactured as configurations operating without a circulating current.

U I

U, I

P>0 P0 P0

P

Figure 6.6 The phase difference between the voltage Uand the currentIwhen supplying a reactive load. This requires

a four-quadrant operation, in other words, the directions of the current and the voltage may settle independently, in

which case also the flow direction of the powerP is free.


5/44


A three-phase frequency converter is obtained by applying three converters of this kind one for

each phase. The converters for each phase are usually star-connected, or they may supply the phas-

es of the load separately. The star connection and the separate-phase connection are illustrated in

Fig. 6.7. The phase-specific converters are usually supplied via transformers, as shown in Fig. 6.8.

Transformers or phase windings separated from each other have to be used, since the formation of

the star point by interconnecting the negative buses of the cycloconverters would mean a short-circuit between the phases always when there would be a different phase of the grid connected to

the negative bus in different cycloconverters. This problem is avoided by using transformers, since

the transformers form a galvanic separation between the different phases of the grid. Unfortunately,

transformers naturally add to the costs, weight and space requirement of the machine configuration.

A cycloconverter with transformers seems however to be a more popular solution than a separately

wound machine.

When separate phase windings are applied, the drive usually requires a separate choke for the zero-

sequence current, through which all the phase currents are transferred. In the choke, the target is to

maintain the zero-sequence flux linkage, which simultaneously attempts to guarantee the instanta-

neous zero sum of the phase currents, which is important for the operation of the rotating-field ma-

chines.

a) b)

Figure 6.7 A three-phase cycloconverter: a) the phases are connected in star (star configuration), b) the phases are gal-

vanically separated. The drive has yet been equipped with a zero current choke.

The topology of an ordinary three-phase cycloconverter is illustrated in Fig. 6.8.


6/44


usa

sb

sc

u

u

Figure 6.8 A cycloconverter, in which there are antiparallel thyristor bridges in each phase. The galvanic separationbetween the phases is obtained by a supply transformer. usa, usb, and usc are the phase voltages.

The curve form of the output voltage of each phase is constructed of the cycles of different line-to-

line voltages of the supply voltage, as shown in Figures 6.9 and 6.10, based on simulations. In the

figures, the frequency of the power line is 50 Hz. In Figure 6.9, a sine control is applied, in other

words, the instantaneous mean value of the output voltage of the cycloconverter is desired to vary

sinusoidally on average. The control principle for the sine modulation can be simply expressed as

U u td0 vcos cos 2 . (6.1)

Here Ud0 is the DC voltage of the six-pulse bridge corresponding to the control angle = 0. By ad-

justing the control angle the instantaneous DC voltage of the left-hand side is made equal tothe slow AC voltage of the right-hand side. The modulation reference becomes thus

arccos cosu t

U

v

d0

2. (6.2)

-1.5

-1

-0.5

0

0.5

1

1.5

0 10 20 30 40 50 60 70 80 90

time t / ms

2

2

u1

u

i

Figure 6.9 The curve form of the output voltage u2 and the output current i2 of a cycloconverter when applying sine

control. Also the curve form of one of the line-to-line voltages u1 of the grid supply voltage is presented, when the

supply frequency isf1 = 50 Hz and the output frequency isf2 = 8 Hz.

Another control method is the trapezoidal method. In the method, the target is to make the instanta-

neous mean value of the output voltage to change according to the trapezoidal curve, Fig. 6.10.


7/44


-1.5

-1

-0.5

0

0.5

1

1.5

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

time t / ms

uu

1

2

Figure 6.10 The curve form of the phase voltage u2 of the cycloconverter, when applying trapezoidal control, and thecurve form of the line-to-line voltage u1 of the supply grid voltage, when the supply frequency is f1 = 50 Hz and the

output frequency isf2 = 24 Hz.

The output frequency of the cycloconverter is in practice limited to a half of the frequency of the

supply grid at maximum, since at higher frequencies, the current increasingly deviates from the sine

form. Both in the output voltage and the input current of the cycloconverter there occur also sub-

harmonic frequency components in addition to the usual harmonics. The target is thus that the out-

put voltage is sinusoidal or trapezoidal on average. With trapezoidal voltage, the control reactive

power can be made lower than by the sine control, since the thyristors are in that case longer con-

ducting at the peak value of the voltage. Due to the control reactive power, the power factor of the

cycloconverter is always inductive irrespective of the power factor of the load. The power factor of

the whole cycloconverter drive is 0.707 by the sine control, when applying the modulation index of

1.0. As the output voltage decreases and the modulation index becomes smaller, the power factor

reduces rapidly. These values hold for a single-phase and a three-phase case supplied with a six-

pulse and twelve-pulse cycloconverter; they are valid also with a six-pulse cycloconverter in the

case of a separate winding. The machine in that case is a synchronous machine, the power factor of

which has been set to one. When applying trapezoidal control, a power factor higher than 0.707 can

be achieved for the drive.


8/44


The basic configuration comprises a six-pulse-

cycloconverter-fed three-phase synchronous

machine, Fig. 6.11. When we desire to increase

the power, either the voltage or the current has

to be increased. However, due to the limited

withstanding to voltage and current, the increase

in power would require the connection of thyris-tors either in series or in parallel.

When connecting the thyristors in series, the dis-

tribution of voltages evenly over all thyristors is

problematic, and in the parallel connection, also

the even current division between the thyristors

is uncertain. Therefore, various new connection

alternatives have been developed for the cyclo-

converters.

Figure 6.11 Six-pulse-cycloconverter-fed three-phase mo-

tor

By connecting two cycloconverters in series we obtain almost a double common voltage. Since the

cycloconverters connected in series to the same phase of the machine are supplied from different

secondary windings of the three-winding transformer, the voltages are evenly distributed between

the cycloconverters. Furthermore, the difference in the vector groups of the secondary windings of

the three-winding transformer causes a phase difference between the voltages, thus making the se-ries connection of the cycloconverters a twelve-pulse one. This means an improved curve form of

both the output voltage and the phase current of the power line, since there are less harmonics in

both the voltage and the current. The twelve-pulse connection improves also the operation of the

current control when compared to the six-pulse one, since in the twelve-pulse connection, there are

twice as many voltage control alternatives than in the six-pulse connection, Fig. 6.12.

The power can be increased by constructing the winding of the machine of two parallel windings,

which are both fed with an individual six-pulse cycloconverter. The current flowing into the ma-

chine is increased by constructing two separate stator windings to the machine, into which current

is supplied independently by own cycloconverters. The connection is called a double star connec-

tion. A direct parallel connection of the cycloconverters is not applied to the supply of a single sta-tor winding. Figure 6.13 illustrates the respective cycloconverter connection.

The output frequency of the cycloconverter is rather low, being a half of the supply frequency at the

maximum. Since the rotation speed of the synchronous machine is directly proportional to the

supply frequency, the rotation speed remains rather low in cycloconverter-fed drives. The power

range is usually 1.530 MW. As the drive motor, both synchronous and asynchronous motors are

used. When using a synchronous machine, a better power factor is usually achieved for the configu-

ration, since the power factor of the machine can be regulated to be one. The cycloconverters are

applied to slow-speed high-power drives, such as propeller motor drives in ships (e.g. icebreakers,

multi-purpose vessels, and cruise ships). In various fields of industry, cycloconverters are applied

for instance to the rotation speed control of ore and cement mills, pumps, blowers, or to lifts andhoists in the mining industry, as well as to the rolling-mill drives in the metal industry.

SM Magnetizing


9/44


Figure 6.12 A three-phase motor fed by a twelve-pulse

cycloconverter

Figure 6.13 2 3-phase motor fed by a six-pulse cyclo-converter

The cycloconverter drive and the VSI drive that will be introduced later in this chapter provide

good possibilities for accurate motor control. Both drives can be applied to the implementation of

the vector control; however, the properties of the VSI are far more versatile than the ones provided

by a cyclo drive.

SMMagnetizing

SMMagnetizing


10/44


6.2 LCI Drive

Considering the power electronics, the simplest power stage is the LCI drive (Load Commutated

Inverter). The LCI drive is completely based on thyristor bridge technology; however, in the drive,

the six-pulse bridge is used as an inverter, similarly as in the line converter. In this case, the syn-

chronous machine forms the electrical power grid, which can produce the commutation reactive

power for the thyristor bridge acting as the inverter. Figure 6.14 illustrates a drive of this kind. Thelarge inductanceLd included in the bridge connection has to be designed so large that it appears as a

current source to the machine. The coil ensures the magnitude of the direct current, and the bridge

acting as the inverter guides this direct current to the over-magnetized synchronous machine, which

is thus able to take care of the commutation power required by the bridge. A LCI drive is thus a CSI

drive, in which the pole voltage of the machine is determined indirectly. The current of the DC link

is regulated by controlling the input bridge.

Ld

Id

SM

Figure 6.14 LCI drive of a synchronous motor. The motor operates over-magnetized and produces the required commu-

tation reactive power for the motor bridge. From the point of view of the thyristor bridge inverter, the motor forms an

electrical power grid that provides the commutation reactive power.

An LCI drive is somewhat difficult to start up, since the non-rotating machine does not naturally

produce electromagnetic force, and cannot thus generate the required commutation reactive power.Starting is therefore performed by controlling the bridge on the line side so that the direct currentId

of the DC link is cut at appropriate instants, and the thyristors of the inverter bridge can be switched

off naturally. When the machine has been brought to rotate at an appropriate speed (10 % of the

rated speed), the current of the DC link can be kept continuous, and the inverter bridge commutates

assisted by the over-magnetized synchronous machine. Figure 6.15 represents the principal curve

forms of the current and the voltage in a LCI drive.

ia

ib

ic

ua

Figure 6.15. Idealized curve forms of a LCI drive.

Thanks to the properties described above, an LCI drive is applicable to drives of simple dynamics,

such as pump or blower drives; however, also some rolling mill drives have been built up with this


11/44


technology. There is information that in 1998, ABB supplied NASA with a 101 MW LCI drive for

a wind tunnel installation; this drive could thus be the largest motor drive in the world. An LCI

drive is applicable as such also as a generator drive. In that case, the motor bridge operates a rectifi-

er, and the input bridge as an inverter.

6.3 Voltage Source Inverter Power Stages

At present, the voltage source inverter (VSI) drives are commercially the most significant applica-

tions. There are mainly two types of VSI drives available, namely the so-called two-level and three-

level devices. Nowadays, with the three-level technology, it is possible to reach such a high power

level that for instance cycloconverters and the LCI technology are gradually exiting the market.

Constructed without a DC link, a cycloconverter is yet still more compact in size than a VSI, and

therefore it is preferred in restricted-space environments, as for instance in ships, where the physi-

cal size of the device is a critical factor. Two-level VSI technology is generally applied to the in-

dustrial and marine drives in the power range of 100 W to 5 MW and above (e.g. ABB 0.125,600

kW).

The VSIs are applied to the control of all kinds of rotating-field machines. By applying a three-level

IGCT or GTO thyristor technology, the medium-voltage range and a power up to 30 MW can be

reached. Figure 6.16 illustrates the basic topologies of the three-level and two-level inverters.

A B C

N

A B C

Figure 6.16 Topologies of the inverter sections of the two-level and three-level VSIs and the most common topology of

a two-level frequency converter with line connectors, a diode bridge for rectification, a DC voltage link, an IGBT in-

verter, and motor connectors. A single symbolic switch in the upper illustration includes in the lower illustration an

IGBT transistor and an antiparallel diode.

N

grid

rectification inversion

motor

n

iA

UDC A B C


12/44


A two-level VSI produces, by applying pulse width modulation (PWM), a three-phase output vol-

tage, as shown in Fig. 6.17. The figure illustrates the application of the so-called sine-triangle com-

parison technique to construct the output voltage. There is a reference value curve for each phase in

the figure, as well as a triangular wave for all phases, into which the reference value curves have in

this case been synchronized. This modulation method was quite common in the days of analog

technology. Since then, also digital versions of the method have been introduced, yet comprehend-

ing the modulation is easiest by investigating the analog curves.

mf2mf+12mf 3mf+23mf

mf= 15

ma= 0.8

10

0.20.40.6

0.8

ULLUDC

UUN

UVNUDC

uref,U uref,V uref,W

ULL

UDC

+UDC

-UDC

N

N

+UDC/2

-UDC/2

0

Figure 6.17 Modulation based on sine-triangle comparison, the produced voltages and the harmonic content of the line-

to-line voltage ULL. The amplitude modulation ratio is 0.8 and the frequency modulation ratio is 15. The harmonic con-

tent of the line-to-line voltage, appears, in addition to the fundamental harmonic, also in the vicinity of the switching

frequency and its multiples. (Mohan, Undeland, Robbins)

The function of the comparator is to form the switch references for the change-over switches of the

two-level inverter so that the output is connected to the upper voltage UDC of the DC link or to the


13/44


negative bus N. Together with the modulation method, the frequency modulation ratio is deter-

mined as the ratio of the switching frequency and the fundamental (output) frequency

1

sw

f

fmf . (6.3)

Ifmf < 21, the so-called synchronous modulation is recommended to avoid subharmonic compo-

nents. In synchronous modulation, the frequency of the triangular wave varies along with the refer-

ence value, being its multiple of three. Furthermore, it is required in the synchronous PWM that at

the common zero positions of the curves, the derivatives (slopes) have to be of opposite polarity.

The switching frequency is determined by the frequency of the triangular wave, and therefore it va-

ries constantly with the frequency. When applying low switching frequencies, to reach the best

overall result, the frequency modulation ratio is usually lowered as the frequency increases.

Nowadays, the switching frequencies of frequency converters are so high that synchronous modula-

tion is not required, but the switching frequency can be kept constant. In that case, the modulation

ratio is no longer an integer. Further, it is constantly changing together with the increasing outputfrequency.

In addition to the frequency modulation ratio, also the amplitude modulation ratio is determined in

the sine-triangle comparison

triangle

refa

u

um . (6.4)

In the linear modulation range, the modulation ratio ma 1. The peak value for the fundamental

voltage between the phase and the negative bus is determined as

2 DCaN,1A,

Umu . (6.5)

The above yields the effective value of the line-to-line voltage

DCaDCainvLL, 612.022

3UmUmU . (6.7)

If the DC voltage link is supplied by a diode bridge, the mean value of the voltage of the DC link iswritten as

LLLL6

6

LLDC 35.1

23dcos2

3

1UUttUU

. (6.8)

The maximum voltage in the linear modulation based on the sine-triangle comparison is thus

LLLLinvLL,83.0612.035.1 UUU . (6.9)


14/44


In a frequency converter operating in the 400 V grid, the output voltage in this phase is 330 V. In

sine-triangle modulation, in order to reach a voltage corresponding to the line voltage, the so-called

overmodulation (ma > 1) is required. In the overmodulation, in the middle region of the pulse pat-

tern that forms the phase voltage, a uniform block is created, which results in plenty of low-

frequency odd harmonics to the output voltage. This situation of overmodulation is illustrated in

Fig. 6.18.

The modulator based on sine-triangle comparison produces an output voltage that is directly pro-

portional to the amplitude modulation ratio as long as ma remains 1. However, in that case, the

output voltage of the inverter bridge is still low when compared with the line voltage, and overmo-

dulation is required in order for e.g. a frequency converter connected to the 400 V grid to produce a

400 V output voltage. When applying sufficient overmodulation, a two-level inverter produces

square wave to its output, the fundamental harmonic of which already exceeds the supply voltage.

mf= 15

ma= 1.25

UUN

UVNUDC


ULL

mf= 15

ma= 3.24

UUN

UVNUDC


ULL+UDC

2

4 DCU

UDCUDC

Figure 6.18 Overmodulation of a two-level inverter in two cases of overmodulation when applying sine-triangle com-

parison. With a full square wave, the peak value of the phase voltage is 2/UDC. A full square wave is realized at theamplitude modulation ratio ma = 3.24, when the frequency modulation ratio is mf= 15

In the case of the full square wave of Fig. 6.18, we obtain by the Fourier analysis the maximum

value 2/UDC for the fundamental harmonic of the phase voltage. Consequently, the maximumvalue of the effective value of the line-to-line voltage becomes

LLDCLLDCDC

LL 053.178.0

6

23

6

2

4

2

3UUUU

UU . (6.10)

This square voltage contains harmonics, the order of which is

,...3,2,1,16 nn (6.11)

The magnitudes of the amplitudes of the harmonics are inversely proportional to the order of theharmonic


15/44


DCLL,78.0

UU

. (6.12)

Let us consider further, what does a voltage of a star-connected motor look like in these drives. Ac-

cording to Figure 6.16, we may write for the phase voltages

Nn,NC,nC,Nn,NB,nB,Nn,NA,nA, ,, uuuuuuuuu . (6.13)

For a three-phase system, we may write

0nC,nB,nA, uuu . (6.14)

Eq. (6.13) yields

NC,nC,Nn,

NB,nB,Nn,

NA,nA,Nn,

uuuuuu

uuu

(6.15)

We substitute (6.14) to the topmost expression of (6.15) and then apply the two expressions below

nC,nB,nA,Nn,

Nn,nC,Nn,nB,nA,nA,nC,nB,NA,nA,Nn,

3

1uuuu

uuuuuuuuuuu

(6.16)

The information of (6.16) is applied in (6.13); thus we obtain

NC,NB,nA,nA,3

1

3

2uuuu . (6.17)

The respective equations can be created also for the voltages of the phases B and C. Figure 6.19 il-

lustrates two different cases for the curve forms of the phase voltage of a star-connected motor. The

lower illustration depicts square wave modulation according to Eq. (6.12).

uA,n

t

t

DC

2U

DC3

1U

DC3

2U

uA,n

0

1 3.24 ma

a b c

0.612

0.78

DC

LL

U

U


16/44


Figure 6.19 Waveforms of the voltage produced by the modulation in a two-level PWM frequency converter. The right-

hand illustration shows the ratio of the output voltage fundamental to the DC link voltage as a function of modulation

index.

As a result of overmodulation, a pure square wave is obtained, the effective value of the fundamen-

tal harmonic of which is 0.78 1.35 ULL = 1.053 ULL. In the 400 V grid, the effective value of thefundamental harmonic produced by the square wave is U

LL= 421 V. Respectively, the phase vol-

tage obtains the value of 243 V. Different voltage losses naturally reduce the magnitude of the out-

put.

Since in the sine-triangle comparison, the upper limit of the linear range is already at 330 V, differ-

ent variations of the system have been developed in order to avoid the number of low-frequency

harmonics in the overmodulation. By adding a significant amount of the third harmonic to the refer-

ence value curves, it is possible to extend the range of linear modulation to approach the square

wave modulation. Figure 6.20 shows the sine-triangle modulation modified by the third harmonic.

The third harmonic can be applied without problems in the supply of three-phase systems, since the

third harmonic waves are in the same phase and cannot thus produce currents in the motor wind-

ings, when the star point of the motor is disconnected. Since it is now possible to avoid the longuniform voltage block in the waveform of the voltage, caused by the overmodulation of the system

based on the sine-triangle comparison, also the low-frequency harmonics harmful to the operation

of the motor can be avoided. Consequently, also a 400 V output voltage can be achieved.

UUN

uref, U

Figure 6.20 Modulation based on sine-triangle comparison; third harmonic has been included in the reference harmonic

wave. It is now possible to reach the same voltage level as in the supply grid without the voltage containing a large

amount of low-frequency harmonics.

Next, a three-level voltage source inverter is investigated.

A three-level inverter is nowadays typically implemented with GTO or IGTC switches. An IGB

transistor is usually employed as the switch of a two-level inverter. The term two-level or three-

level results from the fact that in these inverter types, each of the phase conductor to the motor can

be connected to three or two different potentials. In the three-level inverter, the options are + (posi-

tive pole), 0 (zero point), ornegative pole), and in the two-level inverter + or.

The circuit diagram of a three-level NPC (neutral point clamped) inverter is shown in Figure 6.21.

In a NPC inverter, there are three input poles, and the connection resembles the series connection of

two two-level inverters; the difference being the clamping diodes used in the NPC inverter. The DC

link voltage is divided into two parts by series-connected capacitors. The successful realization ofthe voltage division has to be controlled in these inverters. As switching components, GTO thyris-


17/44


tors of IGCT switches are usually employed. There are also low-voltage three-level inverters

equipped with IGBT switches in the market.

In the GTO inverter of Figure 6.21, the energy of the protection capacitors is fed to the main circuit

with two choppers that are in the potentials of the positive and negative buses. The rated voltages of

NCP inverters are typically 2400 V and 3300 V, and the power range is 130 MW.

Figure 6.22 illustrates the implementation of one phase of a three-level inverter by using GTO thy-

ristors. It comprises four legs similar to the ones in the two-level inverter, as well as two clamping

diodes V9 and V10.

Figure 6.21 Schematic circuit diagram of a NPC inverter (SAMI Megastar) according to ABB Industry. The switchcomponent is GTO. CH choppers restore the energy of protection circuits to the DC link.

PULSE AMPLIFIERS

CONTROL CARD

TERMINAL BLOCK CARD (I/O) CONTROLPANEL

VOLTAGESOURCE

CH

IU

A B C

0 0 0

CH

12

12

230 V~

0

IU

IU


18/44


V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

+

0

- Figure 6.22. Implementation of a three-level inverter by GTO thyristors or IGC thyristors, V1V4 and fast switch dio-

des, V5V10.

The operation of a three-level three-phase inverter can be demonstrated by the change-over switch

illustrated in Fig. 6.16. By appropriately controlling the switches A, B, and C, a three-phase vol-tage can be generated to the poles of the motor. Figure 6.23a illustrates the voltage patterns

achieved by the NPC inverter with pulse number 1, and in Figure 6.23b with pulse number 3.

u A

u B

u C

u AB

u An

2UDC

UDC1

2UDC

2

3UDC1

2UDC1

3U

DC

uA

uB

uAB

a) b)

Figure 6.23 (a) The potentials UA, UB, and UC connected to the motor phases by the change-over switches as well as the

line-to-line voltage UAB. Also the motor phase voltage UAn is illustrated with pulse numb er 1; (b) the potentials con-

nected to the motor phases by the change-over switches as well as the line-to-line voltage with pulse number 3.

Let us next investigate the operation of one phase of an inverter topology according to Fig. 6.22,

when the load of the inverter is a three-phase motor. The phase A is connected to the positive (+)

pole of the DC voltage source, when the thyristors V1 and V2 are switched on. Now the motor cur-

rent may flow away from the inverter through the thyristors V1 and V2 into the direction of the in-

verter through the diodes V5 and V6 (Fig. 6.24a). Next, the thyristor V1 is switched off, and the

thyristor V3 is switched on. Now the phase A is connected to the centre point of the DC voltagesource, and the current flows to the motor through the diode V9 and the thyristor V2, or if the cur-

rent is flowing to the opposite direction, through the thyristor V3 and the diode V10 to the centre


19/44


point (Fig. 6.24b). The phase A is connected to the negative pole () of the DC voltage source,

when the thyristor V2 is switched off and the thyristor V4 is switched on, in which case the current

flows to the direction of the inverter through the thyristors V3 and V4, and when the current direc-

tion is opposite, through the diodes V7 and V8 (Fig. 6.24c).

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

+

0

-

A

Figure 6.24a The current directions of the phase A of the

NPC-PWM inverter when the thyristors V1 and V2 or the

diodes V5 and V6 are switched on.

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

+

0

-

A

Figure 6.24b The current directions of the phase A of the

NPC-PWM inverter when the diode V9 and the thyristor

V2 or the diode V10 and the thyristor V3 are switched on.

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

+

0

- Figure 6.24c The current directions of the phase A of the NPC-PWM inverter when the thyristors V3 and V4 or the

diodes V7 and V8 are switched on.

6.3.1 Generation of Voltage Vectors as the Combined Effect of the Inverter and the Winding

Voltage vectors in the two-level inverter

So far, we have discussed the inverter bridge as a voltage source applying pulse width modulation;

however, considered together with the winding, the inverter can also be regarded as the generator of

the voltage vectors. The voltage vectors generated together by the inverter and the motor can be

defined by the state vector representation. In a two-level three-phase inverter, there are 23 = 8 com-

binations of switch positions (SA, SB, SC), given in Table 6.1. There are six actual voltage vectors

and two zero-sequence vectors.

Table 6.1 The combinations of switch positions for the switches of a two-level inverter.


20/44


switch combinations of switch positions

SA SB SC

Figure 6.25 represents the eight different states of the change-over switches of the inverters and the

respective voltage vectors. The voltage vector is calculated by the familiar equation

u a a a 2

30 1 2u u uA B C , (6.18)

where the phase shift operator (unity vector)a is

3

2j

ea . (6.19)

In Figure 6.25, to generate the voltages uA, uB, and uC, the switches are connected to the potentialsof the DC link. When considering the windings of an electrical machine, we may state that the poss-

ible voltages acting in the windings are in principle depending on the switching situation 2/3uDC, 1/3 uDC, and 0. The output voltage vector now obtains the values:

.0

,3

2

,3

2

,3

2

,3

2

,3

2

,3

2

,0

7

1DC6

2DC5

0DC4

1DC3

2DC2

0DC1

0

u

au

au

au

au

au

au

u

u

u

u

u

u

u

(6.20)


21/44


Figure 6.25 The switching alternatives of a three-phase inverter with a VSI and the directions of the possible output

voltage vectors, which are the positive and negative directions of the magnetic axes of the phase windings. The zerovalue of the output voltage has no direction. Note that the right-hand column determines the direction of the voltage

experienced by the windings, which is signed positive, when the direction corresponds to the direction of the voltage of

the motor winding according to the figure (uA). The voltage signs of the switch positions are thus exactly opposite to

the signs of the voltages experienced by the windings. This distinction has to be made in order for the positive voltage

vector to produce a parallel current vector in the windings.

We notice that there is a slight theoretical problem in the generation of the voltage vector: the vol-

tages of the switches are often substituted to Eq. (6.18) directly according to the voltage levels of

the DC link, in which case for instance the voltage vectoru1 is obtained by substituting the relative

voltages (+1, 0, 0) or (+, -, -) or (+2/3, -1/3 , -

1/3). The latter series is probably the best represen-

tation of the physical situation. In practice, this is always a possible method, as long as it is ensured

that the voltage vector generates the corresponding current vector in parallel direction. This can be

guaranteed in practice with the directions of the current measurement.

From a theoretical point of view, the above substitution leads into a problem, in which the voltage

vector points into opposite direction than the current vector it has generated. In the figure, this has

been taken into account by signing the voltage from the star point towards the line terminal as the

positive voltage; this voltage creates a current that is parallel to the voltage vector. Now the voltage

vectoru1 is created when the switches are connected to the buses as follows: (SA, SB, SC) (0, +1,

+1) or (-, +, +) or (-2/3, +1/3, +

1/3). The implementation is thus exactly the opposite to the

above case, cf. Figure 6.26.

SA, SB, SC

SB SC

a0

a2

a1

a0

-a 2

-a 1

a 2

-a 0

a1

0

0

direction

uA

voltage

u6u5

u4

u3 u2

u1

u7

u0

uA, uB, uC

switches

SA

SA, SB, SC


22/44


The right-hand notations of Figure 6.25 represent those values that have to be substituted to the eq-

uation of the voltage vector in order for the directions of the current and voltage vectors to be con-

vergent.

u6u5

u4

u

3u

2

u1

u7

u0

2/3UDC1/3U

DC

1/3UDC

Figure 6.26 Generation of the voltage vector of a two-level inverter by applying the directions of the magnetic axes of

the stator of a three-phase machine. In the figure, the notations of the real switch positions have been used; these nota-

tions have to be multiplied by 1 to obtain the voltage quantities required in the formation of the voltage vector.

Thus, when investigating the generation of the voltage vector, we noticed that also several possible

voltage combinations produce parallel voltage vectors. We may think rightfully that the voltage

vector is generated as the forward ends of the windings touch the potentials + and - or +1 and 0.

This is checked by finding u1

u a a a a a a a

a a a a

a a a a

1

0 1 2 0 1 2 0

0 1 2 0

0 1 2 0

2

3

2

3

2

3

1

3

1

3

2

3

2

3

1

2

1

2

1

2

2

3

2

31 0 0

2

3

u u uA B C

.

(6.21)

Voltage vectors in a three-level NPC inverter

Figure 6.27 illustrates a model for a change-over switch of a three-level three-phase inverter and the

possible voltage levels , 0, + of the line-to-line voltage UAB.


23/44


+

UDC0

UDC

UAB

A B C

Figure 6.27 Topology of a three-phase three-level inverter and the voltage division between the DC capacitors in an

ideal situation.

Since in the NPC inverter, the output voltage may obtain three different values, its switches have

33=27 combinations of switch positions (Tables 6.2 and 6.3). These combinations generate 19 dif-

ferent vector directions (Figure 6.28). The definition of the vectors is carried out similarly as in the

case of the two-level inverter. Here, we neglect the above theoretical problem, and apply the switch

information directly to the generation of vectors.

Table 6.2 Combinations of switch positions for a three-level NPC inverter

combinations of switch positions

A

B C

Table 6.3 Alternatives for the generation of the line-to-line voltage UAB of the three-level NPC inverter

UAB combinations of switch positions

+UDC +UDC

0 UDC UDC


24/44


1

2

345

6

7

8

9 10 11

1213

1415

16

17 18

+UDC

+UDC

UDC

UDC

a) b)

Figure 6.28 (a) The vector phasors of the three-phase three-level inverter, (b) an example of the curve form of the line-

to-line voltage. In the figure, the quantities common in literature are used as the switching positions. By substituting

these to the voltage vector equation, the desired vectors are obtained.

NPC inverters are best adapted to high-power electrical drives; their power range reaches 30 MVA.

The most typical applications are high-power pumps, blowers, compressors, propeller drives, loco-

motive drive systems, rolling mill drives in metal industry, high-power hoists and cranes, and in-

duction heaters. A special application of NPC inverters is fast induction motors; these are used for

instance in high-speed trains and metal machining tools. A frequency converter, the inverter section

of which is implemented by the NPC-PWM technology, is a real alternative to high-power electric-

al drives in which good controllability is required. An NPC inverter can be modulated in a more

versatile way than a traditional two-level inverter, which results in a reduced harmonic content.

Furthermore, the voltage stress of the main components in the NPC inverter is a half of the voltage

stress in the two-level inverter, and thus the NPC inverter can be constructed for a double voltage

when compared with the two-level inverter without the requirement of actual series connection ofthe switches.

If three-level technology is applied to 400 V inverters, the inverter bridge can be constructed by

employing 600 V IGBT modules. In a common 400 V two-level inverter, to ensure sufficient with-

standing voltages, 1200 V IGBT switches have to be applied; in the case of 690 V, 1700 V switches

are required. The losses of 600 V switches are considerably lower and the switches are faster than

in the versions that can better withstand voltages, and therefore, in addition to the achieved beauti-

ful curve form, at least the same efficiency can be reached by the three-level inverter as by the two-

level ones, although several more components are required. Considering the motor, the curve forms

of the three-level inverter are far more favourable than the corresponding curve forms of two-levelinverters.

6.3.2 Space Vector Modulation (SVM)

It was shown previously that the inverter bridge generates the voltage vectors together with the mo-

tor windings. These vectors can now be employed instead of the sine-triangle modulation directly in

the so-called space vector modulation, which is nowadays a commonly used method. The reference

vector of the modulator for the voltage is written as

ref,ref,j

refref je uuu u . (6.22)


25/44


Figure 6.29 illustrates the principle of space vector modulation.

Figure 6.29 Voltage vectors u0u7 of the VSI. Figure illustrates the active vectors and zero vectors of a static frame of

reference. Also the reference vector (uref) and its generation from active vectors at an instant of time is shown. The out-

er hexagon indicates the maximum length of the voltage vector at each point. The circle inside the hexagon represents

the locus plotted by the point of the voltage vector when producing maximum sinusoidal voltage. The length of the

voltage vector is 2/3 UDC. The maximum length for the amplitude of the sinusoidal voltage is

DC6...1DC6...1 577.0866.03/12/3 UU uu . This yields for instance in a 400 V systemV31278.0

6

23

3

2

2

3 LLLLLL UUUu . The value corresponds to a ca. 220 V voltage, which is thus 95.9

% of the line voltage (230 V). The drop is due to the fact that in diode rectification, not the peakLL2U of the line-to-

line voltage is reached, but a value ofLL

23U . The ratio of these values is 3/ = 0.95

The operating range of space vector modulation is divided into three sections:

linear modulation. In this range, the phase angle of the voltage vector in a steady statetravels at a constant speed . tjref

jrefref ee

uu u , and the length of the voltage vector

is according to Fig. 6.29 DC3/1 U at maximum. When operating in the linear modulationrange, zero vectors are typically applied.

overmodulation range I (mode; cf. Holtz (1997); Bolognani and Zigliottopuolestaan kyttvt kai ran-gea, kumpi valitaan). Also in this range, the phase angle of the voltage vector in a steady state

travels at a constant speed . tjrefj

refref ee

uu u . However, the amplitude varies, sincethe voltage vector is too short in the center portion of the hexagon side. The zero vectors are

not used at the lower limit of the overmodulation range.

overmodulation range II. In this range, the state corresponding to the full overmodulationof the sine-triangle comparison is gradually reached, that is, the square wave. The process

progresses in such a way that the full voltage vector is kept locked (the vector remains

fixed) at the hexagon corners for a certain time duration. As the lock-in angle increasesalong with the modulation index M, the voltage vector is kept on non-modulated until the

angular frequency has produced an angle that corresponds to a half of the arc (hexagon

u6u5

u4

u3 u2

u1u7

u0

uref

I

II

III

IV

V

VI

upper limit of the overmodulation

range IM= 0.951


26/44


side). Now, it is changed over to the next voltage vector. Naturally, no zero vectors are used.

Thus, the voltage vector always jumps non-modulated from one sector edge to another; this

corresponds to the full overmodulation of the sine-triangle comparison. The phase voltage

of the motor appears as a square wave.

Next, the different ranges (modes) of modulation are discussed somewhat further. In the linear

range, the length of the reference voltage vectorref depends in the steady operation on the induc-tion law, and obtains the value s ; whereas in dynamic states, rapid changes may occur. The an-

gle is determined by the desired rotation speed of the voltage vector. In the steady state = t+

0. Here 0 represents the initial angle of modulation.

The time duration of the modulation sequence Tswcan be determined as dependent on the switching

frequencyfsw

sw

subsw

12

fTT . (6.23)

Here Tsub is the duration of the subsequence of the modulation. The voltage vector according to thesampling of the reference vector is constructed by the space vectors illustrated in Fig. 6.29. The

complex plane is subdivided according to Fig. 6.29 into six sectors of equal sizes, the active vectors

acting as the sides of the sectors. Modulation in the sector I is based on the equation

021sub7,002211subref tttTtttT uuuu . (6.24)

The construction of the reference vector by modulation requires two active vectors and possibly

some zero vectors. In each sector, two vectors defining the sector as well as both the zero vectors

are selected as the active vectors. In Figure 6.29, the reference vector is generated in the sector I by

selecting the active vectors u1and u2and both the zero vectors u0and u7. Switching durations t1 and t2are calculated for the selected active vectors, the on-duration t1 being the switching duration of the

vector on the leading edge, and t2 being the on-duration on the trailing edge. The formulas for the

switching durations for active vectors are given in Table 6.4. For instance in the sector I, the on-

duration t1 can be calculated by the sine rule from the triangle of Fig. 6.29, defined by the voltage

vectors u1 and u2.

The symbol M in the definitions denotes the modulation index determined for instance by Holtz

(1994), this modulation index being now different from the modulation index of the modulation

based on the sine-triangle comparison

DC16p,

DC

ref

16p,

ref

2;

2U

U

M . (6.25)

refis the length of the reference vector (i.e., the peak value of the respective phase voltage curve)

and UDC is the voltage of the intermediate DC link. Mis thus now the ratio of the peak voltage to

the peak value of the fundamental harmonic of the phase voltage obtained by the six-pulse modula-

tion.

When the modulation index reaches the valueM= 1, only active vectors are employed, and the time

functions of the voltage are square waves we are now at the operating point that produces themaximum voltage of the overmodulation range II .


27/44


Table 6.4. The switching durations of the active voltage vectors in the space vector modulation.

Sector The location angle

of the reference

vector

Active voltage

vectors used in

modulation

Switching durations of the active voltage vectors

I 0

Documents

Kaytto6 En