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Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering11.1

11. ASYNCHRONOUS MACHINE ............................................................................................. 1

11.1 Industrial Motor Types ........................................................................................................ 2

11.2 Machine Structures and Norms ............................................................................................ 3

11.3 Starting Current .................................................................................................................... 7

11.4 Electricity Consumption and Losses of Asynchronous Motors ........................................... 7

11.5 Loss Reduction by Appropriate Motor Selection .............................................................. 10

11.6 Selection of the Motor Size ................................................................................................ 1211.7 Losses in an Inverter Drive ................................................................................................ 16

11.8 Load Capacity and Efficiency of an Inverter Drive ........................................................... 17

11.9 Control Methods of an Induction Motor ............................................................................ 25

11.9.1 Scalar Control ............................................................................................................ 25

11.9.2 Field Weakening ........................................................................................................ 27

11.9.3 Vector Control ........................................................................................................... 32

11.9.4 Direct Torque Control ................................................................................................ 39

11.9.5 Motor Model in a DTC Drive .................................................................................... 41

11.9.6 Flux Linkage Correction in the Induction Machine DTC .......................................... 44

11.9.7 The Outer Control Systems of the DTC..................................................................... 46

11.9.8 Torque Control ........................................................................................................... 47

11.10 Summary ........................................................................................................................ 51

11. ASYNCHRONOUS MACHINE

An induction motor is the most common motor type in industrial use. Industrial motors are usually

three-phase configurations. The machine is stator-fed, since the stator winding has to excite the

machine and also to take care of the energy conversion together with the short-circuited rotor

winding. When supplying the machine with three-phase current, a rotating field is generated into

the air gap of the motor together by the stator and rotor winding, the flux lines of which intersectthe rotor bars when the rotor runs with slip. In an asynchronous machine, slip is necessary for

torque production; thanks to the slip, an electromotive force, which produces the rotor current, is

induced to the rotor bars. According to the Lorentz force, the force effect between the current and

the rotating magnetic field produces the torque of the machine, which makes the rotor rotate. The

motor starts to rotate, when the electric torque is higher than the torque of the load braking the

rotor. As the rotor speed increases, the speed between the rotor bars and the field decreases, and

consequently, the rotor voltage reduces and its frequency decreases. The rotor rotates slower than

the magnetic field, and thus its speed deviates from the synchronous speed; therefore, an induction

motor is called an asynchronous motor. Figure 11.1 illustrates an asynchronous machine.

The rotation speed n of an asynchronous motor is

n f s 2 1 (11.1)

and the synchronous speedns

nf

ps

60. (11.2)

The frequencyfis the line frequency andpis the number of pole pairs in the machine. The slip sof

the motor expresses the percentual difference of the synchronous speed nsdetermined by the line

frequency and the rotor speed n

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sn n

n

s

s

100 % (11.3)

Figure 11.1 Assembly of an ABB M2BA 280 motor (shaft height 280 mm). 75 kW 3000 min-1.

A part of the electric power taken by the motor is converted into heat in the stator, yet most of the

power is transferred as the air gap power through the rotating magnetic field to the rotor. The

mechanical power Pmgenerated by the motor at the rotation speed nis

P nTp

s T Tm 1 21

, (11.4)

where T is the torque, is the electric angular speed of the grid and is the mechanical angularspeed of the rotor.

An asynchronous machine is adapted for modest drives supplied directly from the grid. However, in

this case, the means to control the machine are almost nonexistent. Previously, slip-ring

asynchronous machines were a common choice; by adjusting the external rotor resistance, the static

torque curve of the machine could be affected so that it was possible to reduce the rotation speed of

the drive when necessary. However, the control method is lossy, and therefore no longer in wide

use. The rotation control of an asynchronous machine can be implemented by a voltage control only

in certain specific cases. An asynchronous machine has initially been the simplest machine type for

an inverter control drive, since the machine operates well scalar controlled in such a way that the

inverter takes care only of the ratio of the supply voltage and the frequency in compliance with the

requirements of the induction law. However, when aiming at a demanding vector control, we see

that an asynchronous machine is extremely challenging machine for the control drive. In particular,

the slip typical of the machine makes the control difficult especially if an accurate rotation speed

control without a speed feedback is required. In spite of their complex structure, the synchronous

machines discussed in the previous chapters are, after all, easier to control than asynchronous

machines.

11.1 Industrial Motor Types

In Finland, approximately 80 % of the industrial electricity is consumed in electrical motors, thenumber of which in various industrial processes is about 600,000. If all the small-scale motors of

auxiliary devices are included, the total number adds up to 34 million [6]. At the moment, the

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Finnish industry operates based on three conventional electrical machine types. The largest group in

number consists of induction motors. In control drives, there are still plenty of DC machines, and

the large constant-speed drives are often implemented by synchronous machines. A typical example

of this type of use are the large synchronous machines operating the wood grinders in groundwood

plants in the forest industry. Figure 11.2 presents the distribution of electrical motors in a typical

forest industry plant in South-Eastern Finland.

DC machines 3 % synchronous machines 0.1 %

asynchronous machines 97 %

Figure 11.2 Distribution of motors by quantity at the Enso Gutzeit Kaukop mill (now owned by Stora Enso) in 1994

[1].

The corresponding power distribution of the motors at the Kaukop mill is presented in Figure

11.3. The estimated dissipation power distribution is presented in Figure 11.4.

Synchronous motors 1 %DC-motors 8 %

asynchronous motors 91 %

Figure 11.3 The installed power distribution of electrical

motors at the Kaukop mills in 1994 [1].

DC-motors 8.5 %

nduction motors 91 %

synchronous motors 0.5 %

Figure 11.4 The dissipation power distribution at the

Kaukop mills by motor types in 1994 [1].

Asynchronous machines constitute thus clearly the largest industrial energy consumption group.

Their share also among the control drives is constantly increasing along with the novel controltechnology. The asynchronous machine is now probably in its heyday, and may in the future lose

ground to other machine types, such as permanent magnet machines and synchronous reluctance

machines.

11.2 Machine Structures and Norms

The structures and characteristics of electrical machines are regulated by various international and

national norms. Induction machines in particular are regulated by several standards. The most

important international standards have been published by IEC (International Electrotechnical

Commission) and CENELEC. The German VDE standards are largely congruent with the IECnorms. The British Standard norms are widely applied to in the area of the former British Empire,

whereas throughout North America, NEMA motor standards are applied to; the NEMA standards

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define notably tighter limits for instance for the starting current of induction motors than the IEC

norms.

Totally enclosed induction motors constitute the most significant motor group. In the following,

their structure and characteristics are discussed in brief. According to the manufacturer information

[2], the domestic totally enclosed induction motors comply with the following norms

The structure compliant with the standard IEC 34-1 The rated powers and dimensions are compliant with CENELEC HD 231

The enclosure class complies with the standard IEC 34-5. Totally enclosed machines in the

enclosure class IP55 are dust tight and water resistant

The type of cooling is IC 01 41, in compliance with IEC 34-6, in which the frame-surface

cooling takes place with an external shaft mounted blower. Machines are also supplied with

a separate blower.

The mounting position is compliant with the standard IEC 34-7. The mounting position is

indicated in the IEC standard only by two codes, of which the code I covers only the motor

and its bearing end shield, and a single shaft extension. The code II is a general code. The

motor mounting positions are identified by an IM code; there are dozens of different codes

for foot-mounted motors and for flange-mounted motors with a small flange or a large

flange. Different code variants are obtained by mounting the machines in different positions

either horizontally or vertically and by simultaneously indicating whether there are one or

two free shaft ends in the motor. An ordinary foot-mounted motor for normal floor

mounting is designated IM B3 or IM 1001. A horizontal flange-mounted machine, large

flange, is designated IM B5 or IM 3001.

D-end and N-end. The motor ends in compliance with the standard IEC 34-7 are designated

by the codes D (Drive end) and N (Non drive end).

The positive rotation direction for the motors is the clockwise direction when looking from

front of the machine towards the D-end.

Insulation and insulation classes. Insulation materials are categorized into insulation classesin compliance with the standard IEC 85. The insulation class expresses the upper limit of the

operating ambient temperature range for the insulation material under normal operating

circumstances. The dimensioning of the motors is carried out with the ambient temperature

at 40 C, and the motors may be operated at their rated power up to 1000 m above sea levelat maximum, Table 11.1.

Table 11.1 The effect of temperature and mounting level on the load capacity.

Ambient temperature C 40 45 50 55 60 70Allowed power in per cent of the rated power 100 96.5 93 90 86.5 79

Altitude above sea level / m 1000 1500 2000 2500 3000 3500 4000

Allowed power in per cent of the rated power 100 97 94.5 92 89 86.5 83.5

Insulating materials are classified according to their ability to resist high temperatures without

failures. Table 11.2 shows the temperatures according to IEC standard, and the previous, although

still commonly used temperature classes with letter codes. The hot spot allowance gives the highest

permitted temperature the warmest part of the insulation may reach. Temperature rise allowance

denotes the highest permitted temperature rise of the winding at rated load.

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Table 11.2 Temperature (insulation) classes of insulating materials (IEC 34-1)

Insulation

Class

Hot spot allowance / C Permitted design temperature rise

/C, when the ambient temperature

is 40 C

Permitted average winding

temperature determined by

resistance measurement /C

Y 90

A 105 60

E 120 75

B 130 80 120

F 155 100 140

H 180 125 165

C >180

The most common temperature class in electric machines is 155 (F). Also the classes 130 (B) and

180 (H) are of common occurrence.

The aging of the insulation sets a limit to its long-term thermal resistance, i.e. to its temperature rise

allowance. When evaluating long-term thermal resistance of a single insulator, the concept of

thermal index is employed. Thermal index is the maximum temperature at which the insulator can

be operated based on specified controlled test conditions (e.g. IEEE) to yield an average life of 20

000 hours. Short-term thermal resistance refers to thermal stresses the duration of which is a few

hours at maximum. During this stress the insulator may melt, or bubbles may occur, or the insulator

may shrink or become charred. The insulation should not be damaged in any of the mentioned ways

if the temperature is moderately exceeded in any situation in normal operation circumstances. In

Table 11.2, temperature rise refers to a permitted temperature rise of a winding at rated load. This

temperature rise does not yet cause premature aging of the insulator. An excessive temperature

fluctuation may cause development of brittleness and cracks in the insulator. In certain operation

situations, also the frost resistance may decide the selection of insulating material.

The tolerances in compliance with the standard IEC 34-1:Power factor is measured at rated power. The tolerance limit compliant with the standard is

(1/6)(1-cos), yet the error has to be in the range of [0.02, 0.07].

Voltage and frequency. The tabular values hold for rated power and frequency. The motor may be

constantly loaded at its rated power, if the voltage deviates from the rated value 5 % at maximum.In that case, the temperature rise may be 10 K. The voltage may deviate only temporarily 510 %

from the rated value.

The tolerance ofslip is 20 %.The tolerance of efficiency is 10 %(1-), when the motor power is > 50 kW and 15 %(1-),when the motor power is 50 kW.Rotation speed. AC motors have to withstand at least 1.2 times the rated speed.

Instantaneous overcurrent. AC generators have to withstand 1.5 times the rated current for the

duration of 30 s. (15 s for generators above 1200 MVA). Three-phase AC generators below 1 kV

and 315 kW have to withstand 1.5 times the rated current for the duration of 2 min. Withstanding to

instantaneous overcurrent is not determined for three-phase motors larger than this, neither for any

single-phase motors.

Torque is the most important motor parameter; the standard IEC 34-12 defines the torque

requirements for various induction motors with three different torques. There are four motor types:

N (normal torque), H (high torque), and NY and HY (star-delta starting). The locked rotor torque

Tl, the saddle torque Tu, and the pullout torque Tb are given for the machines producing normal

torque as a relative value of the rated torque according to Table 11.3. These values are minimum

values at the rated voltage (UN690 V). The torque values required of the H-type machines arenotably higher than these. The relative starting torque has to vary from the value of 2 for largemachines to the value of 3 for small machines. Correspondingly, the saddle torque varies between

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1.42.1. In the start-up of NY-motors, Tland Tuhave to be 25 % of the values of corresponding N-

motors.

Table 11.3 Torque requirements of a three-phase induction motor producing normal torque (N-type) in compliance with

IEC 34-12

Number of polesPower range 2 4 6 8

(kW) Tl Tu T Tl Tu T Tl Tu T Tl Tu T

0.4

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11.3 Starting Current

In starting, DC braking, or reversing the rotation direction of an induction motor operating direct-

on-line, the ratio of the machine current to the rated current increases multifold. The magnitude of

the ratio is inversely proportional to the short-circuit impedance of the machine. The magnitude of

the current also has an effect on the voltage drop of the line and the temperature rise of the machine.

The voltage drop also reduces the starting torque of the motor and, in a frail grid in particular, may

disturb other devices operating direct-on-line. The excessive temperature rise of the motor in turn

weakens the insulation structures and thus reduces their service life.

The international standards delimit the starting torque of induction motors by defining a maximum

apparent power or a maximum current for a motor at stall. Table 11.4 presents the maximum

permitted starting apparent powers proportioned to the motor shaft output power in compliance

with the IEC standard.

Table 11.4 The maximum permitted starting apparent powers in compliance with the IEC standard when the motor is at stallsupplied at its rated voltage.

motor size [kW] Sst/P

0.4 < P6.3 136.3 < P25 1225 < P 100 11100 < P 630 10

For instance the starting apparent power of a 4 kW motor may thus be 53 kVA, which at 400 V

yields the permitted starting current of 75 A. The rated current of a 4 kW motor is typically 7.5 A,

and thus the maximum current could be ten-fold to the rated current of the motor. The American

NEMA standard is tighter than the IEC standard. The following table is compiled by interpolating a

permitted starting current for the 4 kW (5.36 hp) machine.

Table 11.5 Comparison of the IEC and NEMA standards with respect to the locked rotor current.

voltage 400 V, 50 Hz 460 V, 50 Hz

power / hp

NEMA

Ist/A Ist/In

IEC

Ist/A Ist/In

NEMA

Ist/A Ist/In

IEC

Ist/A Ist/In

5 58.08 8.2 69.58 9.9 50.5 8.2 60.5 9.9

5.36 * 61.23 * 8.2 73.92 * 9.9 53.24 * 8.2 64.28 * 9.9

10 101.78 8.2 129.95 9.9 88.5 8.2 113 9.9* interpolated values

11.4 Electricity Consumption and Losses of Asynchronous Motors

In Finland, industry consumes more than a half of all produced electricity (51 % in 1992 [3]). More

than 80 % of the industrial electricity is consumed in motors; the share of asynchronous motors

amounts to 7580 %, that is, over 20 TWh. In average, 6 % of the electricity consumption of the

asynchronous machines is consumed in losses in the machine.

In the wood processing industry, asynchronous motors are by far the largest electric energy

consumer group. For example, at Stora Enso Kaukop mills and UPM Kymmene Kaukas mills in

Lappeenranta, there are about 15,000 asynchronous motors in total. At the Kaukop mills, 85 %

of the asynchronous motors are with power of 37 kW or below; the corresponding figure forKaukas is 89 %. Figure 11.5 illustrates the distribution of induction motors by power levels at the

Kaukop and Kaukas mills. The figure shows that the installed base of motors of these two

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different wood processing mills are almost identical. At the Kaukop mill, fine paper and board are

produced of chemical pulp. Kaukas mills differ from Kaukop mills by having a sawmill; this

explains the difference in the number of motors in the 47.5 kW power class. Furthermore, Kaukas

also produces a considerable amount of mechanical pulp. The electricity consumption of these

example mills is approximately 8001000 GWh for both mills. Almost all of the synchronous

motors are induction motors. Previously, no special attention was paid to selecting small induction

motors best adapted to the purpose, or to the efficiency of the motors. Figure 11.6 presents thepower balance of a typical 4 kW induction motor. 15 % of the electric energy is converted into heat

when operating at the rated power of the machine. The proportion of the copper (load) losses is

quite large 77 % of the total losses. The situation is basically due to commercial factors, chiefly

the high copper prices. The machines are designed for general-purpose use, and therefore they are

not dimensioned for the demands of the drives operating constantly close to their rated power. As a

matter of fact, drives of this kind would require a machine type of their own.

0

5

10

15

20

2530

35

shareofall[%]

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Ps 100 %, 4.7 kW

Pa 85 %, 4.0 kWPCus6,9%

PFe

1,9%

Pl 0,5%P

PCur4,7%

P

255

300

Figure 11.6 A Sankey diagram of a 4 kW constant induction motor. PFe, iron losses, PCus, stator copper losses, Pl,

additional losses, P, air gap power, PCur, rotor copper losses, P, friction losses

An induction motor is very well adapted to industrial drives thanks to its simple and durable

configuration and good loading characteristics. Asynchronous motors account for 83 % of the total

electric energy consumption at Kaukop, and 69 % of the consumption at Kaukas. The difference

is chiefly due to synchronous drives used for the production of mechanical pulp at the Kaukas mill;

the energy consumption of these drives is considerable. Small-scale motors (37 kW) account for16 % of the share of asynchronous motors of the total electricity consumption at Kaukop, and 19

% at Kaukas. Figure 11.7 illustrates the percentage distribution of the electrical energy consumption

of asynchronous motors at the investigated mills.

0

5

10

15

20

25

30

35

40

45

shareofel.

consumption[%]

250

kW

power class [kW]

Kaukas

Kaukop

Figure 11.7 Percentage distribution of the electric energy consumption of asynchronous motors at Enso GutzeitKaukop mills (currently owned by Stora Enso) and at UPM Kymmene Kaukas mills in Lappeenranta [3].

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Losses account for about 6 % of the electric energy consumed by asynchronous motors. Motors

with a rated power of 37 kW or below account for 33 % of all losses at the Kaukop mills and 38

% at the Kaukas mills. When comparing the ratio of losses to the electricity consumed by the motor

group in question, we can see that the relative amount of energy consumed in losses in the motors

with a rated power of 37 kW or below is 2.5 times higher than in the motors above 37 kW.

Therefore, improving the efficiency of small-scale asynchronous motors in continuous operation

can be justified. Figure 11.8 shows the percentage distribution of the losses in asynchronous motorsby power classes at the investigated mills.

0

5

10

15

20

25

30

shaseoflosses[%]

250 kW

power class [kW]

Kaukas

Kaukop

Figure 11.8 The percentage distribution of the losses in asynchronous motors by power classes at Enso-Gutzeit Oy

Kaukop mills in Imatra and UPM Kymmene Kaukas mills in Lappeenranta [3].

11.5 Loss Reduction by Appropriate Motor Selection

When selecting a motor for the asynchronous motor drive, a motor that is best adapted for the

purpose has to be chosen. The selection criteria in order of importance are the technicalfunctionality and the economical efficiency of the motor. A prerequisite of technical functionality is

correct dimensioning, based on the loading caused by the machine to be operated. Economical

efficiency in turn is based on long-term optimization, in which the sum of purchase price and

operating costs is minimized. The efficiency of the standard asynchronous motors improves as the

rated power of the motor increases. This makes it possible to improve the efficiency of the motor

drive in some power ranges by selecting a motor with somewhat higher power than actually

required for the duty. Figure 11.9 illustrates the efficiency of the motors as a function of both

relative and absolute power.

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0

10

20

30

40

50

60

70

80

90

100

20 40 60 80 100 120 1400

P/Pn [%]

0.55 kW1.1 kW4 kW22 kW55 kW

20

40

60

80

90

70

2 4 6 8 10 12 14 16 18

P [kW]

0

0

5.5 kW7.5 kW

11 kW15 kW

Figure 11.9 Efficiencies of three-phase four-pole standard induction motors as a function of load at rated voltage [3].

The efficiency remains quite constant when the power reduces from the rated load to the 50 % load.By the present dimensioning criteria, the efficiency reaches its maximum value usually at the 75 %

load. Thus, to achieve the best efficiency, considering the limitations of the drive, it is advisable to

choose a motor such that it operates at approximately power. If we select a motor at one power

level higher than required by the load, we can exploit the high efficiency of the large motor, the

motor operating in that case at a 6784 % load. Particularly in the case of small-scale motors, the

efficiency at a rated power improves rapidly along with the machine size.

The figure shows clearly which machine should be chosen for a certain duty to maximize the

efficiency. Bearing this in mind, we should always select a motor with the topmost efficiency curve

at the shaft output power in question. The figure shows clearly that it is advisable to dimension the

machine to operate at about power, which, in practice, means over-dimensioning of one powerlevel (i.e., selecting a machine at the next power level). Selecting a machine larger or smaller than

this will yield a poor efficiency. Let us next consider an example of over-dimensioning: the power

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required by the power tool is 5 kW. We could select a 5.5 kW motor for this drive, the efficiency of

which at the power in question would be 86 %. However, considering the efficiency of the drive, it

is preferable to select a motor over-dimensioned by one power level (7.5 kW), the efficiency of

which is 88 %. The losses can now be reduced by 14 %. Next, an example of excessive over-

dimensioning is discussed briefly: a 15 kW motor operates constantly at a 25 % (3.75 kW) load. Its

efficiency is thus about 82 %. We replace the motor by a 7.5 kW motor, and thus the efficiency of

the motor is increased to 87 %. The losses can be reduced by 26 %.

At the moment, the EU recommendations on the motor efficiencies are complied with throughout

Europe. Figure 11.10 how the motors provided by different manufacturers are placed on the curves.

70

75

80

85

90

95

100

1 10 100Output power [ kW ]

Efficiency

[%]

EFF1

EFF2

EFF3

Figure 11.10 The EU efficiency classes EFF1, EFF2, and EFF3 as well as the efficiencies of standard asynchronousmotors of different manufacturers (Haataja 2003).

Figure 11.11 emphasizes the importance of the correct selection of the manufacturer when selecting

the motor. We can see that the dissipation power is almost doubled between the best and the

weakest alternative.

11.6

Selection of the Motor Size

In electric machines, a part of the supplied energy is always converted into heat. For instance, when

the efficiency of a 4 kW standard induction machine at a rated power is 85 %, the followingpercentages of the energy supplied to the poles of the machine turn into heat: 6.9 % in the stator

copper losses, 1.9 % in the stator iron losses, 0.5 % in the additional losses, 4.7 % in the rotor

losses, and finally, about 1 % in the friction losses. The rest of the supplied energy is converted to

mechanical energy of the shaft. The heat generated in the machine has to be led to the medium

surrounding the machine. The cooling methods of the electric machines are defined in the standard

IEC 34-6, and the enclosure classes in the standard IEC 34-5. The enclosure class depends on the

cooling method. For instance, the enclosure class IP 44 designates a good mechanical and moisture

protection that are not compatible with the cooling method IC 01, since it requires an open machine.

Table 11.6 introduces the most common IC classes.

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Table 11.6 The most common IC classes of electric machines.

Code Definition

IC 00 The coolant surrounding the machine cools the inner parts of the machine. The ventilating effect of

the rotor is insignificant. The coolant is transferred by free convection.

IC 01 Like IC 00, but there is an integral fan mounted on the shaft or the rotor to circulate the coolant.

This is a common cooling method of open induction motors.

IC 03 A method similar to IC 01, but with a separate motor mounted blower having same power source

with the machine to be cooled.

IC 06 A method similar to IC 01, but the coolant is circulated with separate motor mounted blower with

different power source. There can also be a single extensive blower system supplying the coolant

for several machines.

IC 11 The coolant enters the machine via a ventilating duct and passes freely to the surrounding

environment. The circulation of the coolant is carried out with a motor or shaft mounted blower.

IC 31 The rotating machine is inlet and outlet pipe ventilated. The circulation of the coolant is carried out

with a motor or shaft mounted blower.

IC 00 41 Totally-enclosed internal circulation of the coolant by convection and cooling through the frame

with no separate blower.

IC 01 41 Like IC 00 41, but the frame-surface cooling takes place with a separate shaft mounted blower

causing the circulation of the coolant. This is a cooling method of ordinary enclosed inductionmotors.

IC 01 51 Totally-enclosed internal cooling by convection. The heat is transferred through an internal air-to-

air heat exchanger to the surrounding medium, which is circulated by a shaft mounted blower.

IC 01 61 Like IC 01 51, but the heat exchanger is mounted on the machine.

IC W37 A71 Totally-enclosed internal cooling by convection. The heat is transferred through an internal water-

to-air heat exchanger to the cooling water, which is circulated either by supply pressure or an

auxiliary pump.

IC W37 A81 Like IC W37 A71, but the heat exchanger is mounted on the machine.

The duty types of electric machines are designated according to IEC 34-1 (1983) and VDE 0530

Teil 1/12.84 as S1, S2, S3,...S9.

Duty type S1 Continuous running duty

Operation at constant load maintained for sufficient time to allow the machine to reach thermal

equilibrium. A machine for this kind of operation is stamped with the abbreviation S1. This is the

most common duty type.

Duty type S2 Short time duty

Operation at constant load for a given time, less than that required to reach thermal equilibrium.

Each operation period is followed by a time at rest and de-energized, of sufficient duration to re-

establish the temperature of the surrounding air. For machines of short time duty, the recommended

durations of the duty are 10, 30, 60, and 90 minutes. The appropriate abbreviation is S2, followedby an indication of the duration of the duty, stamping e.g. S2 60 min.

Duty type S3 Intermittent periodic duty

A sequence of identical duty cycles, each including a time of operation at constant load and a time

at rest and de-energized. Thermal equilibrium is not reached during a duty cycle. Starting currents

do not significantly affect the temperature rise. The cyclic duration factor is 15, 25, 40, or 60 % of

the 10 minute duration of the duty. The appropriate abbreviation is S2, followed by the cyclic

duration factor, stamping e.g. S3 25 %.

Duty type S4 Intermittent periodic duty with starting

A sequence of identical duty cycles, each cycle including a significant starting time, a time ofoperation at constant load and a time at rest and de-energized. Thermal equilibrium is not reached

during a duty cycle. The motor stops by naturally decelerating, and thus the motor is not thermally

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stressed. The appropriate abbreviation for stamping is S4, followed by the cyclic duration factor,

the number of cycles in an hour (c/h), the moment of inertia of the motor (JM), the moment of

inertia of the load (Jext) referred to the motor shaft, and the permitted average counter torque Tv

during a change of speed given by means of the rated torque. Stamping e.g. S4 - 15% - 120 c/h -JM

= 0,1 kgm -Jext= 0,1 kgm - Tv= 0,5 TN.

Duty type S5 Intermittent periodic duty with electric brakingA sequence of identical duty cycles, each cycle consisting of a starting time, a time of operation at

constant load, a time of braking and a time at rest and de-energized. Thermal equilibrium is not

reached during a duty cycle. In this duty type, the motor is decelerated with electric braking, e.g.

counter-current braking. The appropriate abbreviation for stamping is S5, followed by the cyclic

duration factor, the number of cycles per hour (c/h), the moment of inertia of the motor JM, the

moment of inertia of the loadJext, and the permitted counter torque Tv. Stamping e.g.

S5-60%-120 c/h-JM= 1,62 kgm -Jext= 3,2 kgm - Tv= 0,35 TN.

Duty type S6 Continuous-operation periodic duty

A sequence of identical duty cycles, each cycle consisting of a time of operation at constant load

and a time of operation at no-load. Thermal equilibrium is not reached during a duty cycle. The

cyclic duration factor is 15, 25, 40, or 60 % and the duration of the duty is 10 min. Stamping e.g. S6

60 %.

Duty type S7 Continuous-operation periodic duty with electric braking

A sequence of identical duty cycles, each cycle consisting of a starting time, a time of operation at

constant load and a time of electric braking. The motor is decelerated by counter-current braking.

Thermal equilibrium is not reached during a duty cycle. The appropriate abbreviation is S7,

followed by the moment of inertia of the motor, the moment of inertia of the load and the permitted

counter torque (cf. S4). Stamping e.g. S7 - 500 c/h-JM= 0,06/kgm - Tv= 0,25 TN.

Duty type S8 Continuous-operation periodic duty with related load/speed changes

A sequence of identical duty cycles, each cycle consisting of a time of operation at constant load

corresponding to a predetermined speed of rotation, followed by one or more times of operation at

other constant loads corresponding to different speeds of rotation (carried out, for example, by

means of a change in the number of poles in the case of induction motors). There is no time at rest

and de-energized. Thermal equilibrium is not reached during a duty cycle. The appropriate

abbreviation is S8, followed by the moment of inertia of the motor, the moment of inertia of the

load, and the number of duty cycles in an hour. Also a permitted counter torque and the cyclic

duration factor have to be given. Stamping e.g.

S8 -JM= 2.3 kgm -Jext35 kgm

30 c/h - Tv= TN- 24 kW - 740 r/min - 30 %

30 c/h - Tv= 0,5 TN- 60 kW - 1460 r/min - 30 %

30 c/h - Tv= 0,5 TN- 45 kW - 980 r/min - 40 %

Load and combinations of rotation speeds are stamped in the order in which they occur in the duty.

When choosing the motor, the torque profile of the load and the thermal time constant of the

machine have to be known. When the duty comprises different periods, which are clearly shorter

than the thermal time constant of the motor it is possible to overload the motor during short periodsof time if the average losses are smaller than the rated losses of the motor. The thermal time

constants of totally enclosed induction motor vary depending on the machine size from tens of

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minutes to an hour, or even to several hours. For instance, a 30 kW induction motor, operating at

the rated load, reaches its end temperature in about half an hour, and thus the thermal time constant

is about twenty minutes. In the dimensioning of the motor, a rms value has to be determined for the

power; this value is according to the definition of the rms value

P Pt

P t t

t

N E

je 0

d

j

12 . (11.5)

The duty types S1 (continuous running duty), S3 (intermittent periodic duty), and S6 (continuous-

operation periodic duty) in particular allow the dimensioning based on Eq. (11.5) as long as the

cycle time tj is short when compared with the thermal time constant of the machine. The motor

selection in compliance with the duty type S2 requires more specific knowledge on the machine.

Heavy starting and braking duties require an in-depth techno-economical dimensioning analysis.

In the rated duty, rated losses are removed from the motor. From the thermal point of view, the

motor selection in the periodic duties is based for instance on the definition of dissipation energy

balance. In that case, a dissipation power corresponding to the rated duty is removed from themachine during the equivalent cooling time tje of the cycle. Thus, it is possible to base the

dimensioning of the motor on the determination of the rated current corresponding to the load. The

rated currentINof the motor corresponding to the load has to be at least

It

I t t

t

N

jE

d

j

1 2

0

( ) , (11.6)

tjis the current-carrying cycle time and tjEis the equivalent cooling time.

In dimensioning the rated current, the current is divided into sub-currents, which are used tocalculate the total current.

It

I t t I t t I t t I t tt

t

t

t

t

tt

N

jE

nd d d d

j(n-1)

jn

j2

j3

j1

j2j1

1

1

2

2

2

3

2 2

0

( ) ( ) ( ) ( ) (11.7)

The stator current of an asynchronous machine also includes inductive current, and therefore the

power factor of the motor is included in the calculation. In the case of partial loads, the respective

power factor of the motor has to be employed.

Determining the equivalent cooling time is somewhat problematic, since the cooling properties of

the motor are highly dependent on the rotation speed. We can estimate that the cooling power of a

machine at rest and de-energized is about 20 % of the rated cooling power. Thus, for instance in the

duty type S3, 20 % of the standing time is included in the equivalent cooling time. Next, we check

whether a motor, in which the motor power complying with S1 is exceeded by 30 %, can be applied

to the duty S3-25 %. The power factor at a 130 % power is cos= 0.87 and at the rated power cos

= 0.85. The equivalent cooling time is tje= 0.25 + 0.200.75 = 0.4. The current is thusI= 1.30IN0.85/0.87 = 1.27 IN. The values are substituted to Eq. (11.7), which yields for the rated current of

the machine

I t tN d d

1

0 4127 0 102

0

0 25

2

0 25

1 0

.. .

.

.

.

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We can see that the same peak temperature is reached and the machine cools closely as in the rated

S1 duty. The dimensioning is checked with Eq. (11.5)

P P t t N E0

d 1

0 4

13 10320 25

.

. .

.

.

According to this result, we would need a slightly larger machine than initially dimensioned.

11.7 Losses in an Inverter Drive

Induction machine inverter drives are becoming increasingly common. The sine-triangle

comparison, still commonly used in connection with the PWM technique, produces pulse-width

modulated pulse trains for the voltage references between the points U and N and V and N as

shown in Figure 11.11. The voltage ULL

between the phases U and V is obtained by subtracting the

voltages of the pulse trains from each other. A voltage of this kind includes, depending on the

voltage modulated stage mf and the amplitude modulated stage ma, for instance the frequency

spectrum illustrated in Figure 11.11.

As shown in Figure 11.11, in the vicinity of the multiples of the inverter switching frequency, there

occur sidebands of the harmonics of the motor supply voltage. The lowest harmonics of the PWM

inverter can thus be found in the vicinity of the switching frequency. When the target is to obtain as

sinusoidal current as possible to the motor, the switching frequency has to be raised. The state-of-

the-art motor control systems (e.g. the DTC by ABB) do not have a fixed modulation method, and

thus the frequency spectrum does not remain constant. However, there occur harmonics in

somewhat similar manner as in Figure 11.11. The difference is that the frequency spectrum isspread over a wider range, and the peaks are not as clear as in the sine modulation.

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mf2mf+12mf 3mf+23mf

mf= 15

ma= 0.8

10

0.20.40.60.8

ULLUDC

UUN

UVNUDC

uref,U uref,V uref,W

ULL

UDC

+UDC

-UDC

N

N

+UDC/2

-UDC/2

0

Figure 11.11 Sine-triangle comparison for generating the PWM pulse pattern; the line-to-line voltage and its harmonics

[4].

The rate of current change in an inverter-driven induction motor at the inverter switching frequency

is limited basically by the transient inductance Ls' of the machine. The transient inductance

characterizes the inductance experienced by the fast pulse fed to the stator. The rotor manages to

react to the fast pulse only by its leakage inductance. This transient inductance can be determined

for instance by employing the short pulses obtained from the inverter.

11.8 Load Capacity and Efficiency of an Inverter Drive

A phase voltage of a star-connected motor in sine modulation follows the pulse pattern of Figure11.12. In the modern vector-controlled inverters, the pulse pattern does not necessarily have a fixed

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modulation scheme, but in the steady state, the pulse pattern is selected such that it is possible to

produce a current as sinusoidal as possible to the inductive load.

uA,n

t

Figure 11.12 The pulse pattern of the phase voltage of a star-connected motor produced by a double-layer inverter, and

the fundamental harmonic of the phase voltage.

Considering the induction motor, an inverter drive is not completely unproblematic. When the

inverters entered the markets, it was considered a great advantage that an ordinary induction motor

could be applied to control drive. However, thyristor PWM inverters operating with a low switching

frequency caused so large additional losses in the electrical machine that the rated power at the

rated speed was recommended to be lowered by 1020 % in the continuous duty. In the thyristor

inverters, the switching frequencies were in the range of only a few hundred Hertz. The low

switching frequency and the resulting slow voltage-rise rates were also an advantage, since the

arrangement made it possible to avoid the problem of matching the motor cable and the motor

characteristic impedances; with the present technology, when using a long motor cable, this may

cause overvoltages in the windings that damage the motor insulations. The switching frequencies ofinverters applying GTO thyristors are still so low, and consequently, the curve forms of the currents

are so distorted that the motors can be loaded at the rated rotation speed only with a 9095 % load

when compared with the sinusoidal supply.

Irrespective of the switching frequency of the inverter, in the inverter-driven motor, distortion is

caused by the distortion voltages to the phase current of the motor. The high-frequency phenomena

experience the transient inductance Ls' of the motor. The number of flux components of the

switching frequency occurring in the air gap is quite small, and their penetration to the iron circuits

is quite limited. Nevertheless, switching-frequency loss components of the inverter are created in

the induction motor. The higher switching frequency is used, the better the motor current can bemade to resemble pure sinusoidal form and the smaller become the additional losses caused by the

inverter drive.

An inverter drive causes losses in the induction motor basically by the following ways:

High-frequency current components cause skin effect in the windings of the machine. The

stator winding of small machines, however, is usually made of so thin wire that the losses

caused by the skin effect are quite insignificant. If the winding of the machine is made of

preformed copper, the losses caused by the skin effect will increase.

In spite of the damping effect of the leakage inductances, the high-frequency current

components cause small high-frequency components also to the main flux of the machine,thus increasing the iron losses of the machine.

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The rotor surface of the machine is particularly susceptible to losses in the inverter drive.

Depending on the ratio of the rotor flux leakage and the magnetizing inductance, a small

part of the fast transient passes even through the magnetizing inductance, causing rapid

oscillation of the main flux. When the amplitude of the main flux of the machine oscillates

as an effect of the current harmonics, the eddy currents induced to the cage winding of the

induction motor tend to damp this oscillation. Consequently, losses occur both in the rotor

aluminium and the in the iron in the region of the rotor slot opening, Figure 11.13.

high frequency

leakage flux

pvuon vrin

Figure 11.13 As the amplitude of the main flux oscillates at the frequencies caused by the inverter, currents resisting the

ripple of the main flux are created in the rotor winding; for their part, these currents cause high-frequency leakage flux

components that cross the rotor slot opening. In the region of the slot opening, considerable losses occur in the

saturating iron particularly in the case of closed slots.

To reduce the losses in the rotor slot opening, the slot opening illustrated in Figure 11.4 has been

introduced for inverter motors. A slot opening of this kind provides a smaller leakage flux in the

rotor slot opening than the traditional solutions, since the saturating slot wedge is rather long.

Simultaneously, also the losses caused by eddy currents in the iron of the rotor slot opening are

reduced. In the 100 kW power class, with this slot opening type, the efficiency is improved byseveral per cents when compared with the conventional solution.

Figure 11.14 The shape of the slot opening applied to

inverter motors when using an aluminium pressure-cast

rotor. This configuration provides a good path for the

leakage flux, and thus the losses in the long iron bridge

remain lower than in the case of ordinary rotor bars [7].

rotor bar

rotor lamination

An open rotor slot would best prevent the problems of the surface losses in the inverter motor.

Therefore, the rotor winding of motors intended for inverter drive is nowadays often manufactured

of preformed copper. The slot opening of the rotor can now be left slightly open. This, on the other

hand, reduces the transient inductance of the machine, and may thus cancel the effect of the open

rotor slot.

Already in the 1990s, in the Laboratory of Electric Drives Technology at LUT, test measurements

were carried out for a 22 kW induction motor fed through an ABB ACS 501 inverter. Figure 11.15

depicts the largest voltage and current harmonic components illustrated by the frequency spectrum.We can see that the phase voltage is considerably distorted; however, the phase current is almost

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sinusoidal including only very small-amplitude harmonic components when applying a switching

frequency of 2 kHz.

176 78 80 82 84

157 159 161 163 233 235 237 239 241 243 245 316 318 320

0

20

40

60

80

100

120

140

160

V,A

176 78 80 82 84

157 159 161 163 233 235 237 239 241 243 245 316 318 320

order of the harmonic

voltage

current x 10

Figure 11.15 The measured phase voltage and current spectrum of the motor. The switching frequency of the inverter is

2 kHz [3].

In the following, the behaviour of the efficiency of the ACS 501 inverter and the 22 kW motor is

presented based on the measured results. Figure 11.6 represents the measured efficiencies of the

components of the electrical motor drive and of the whole electrical drive at different frequencies at

the rated torque. The maximum efficiency 88 % is achieved at the rated frequency of 50 Hz of the

motor.

Figure 11.16 The efficiency

of an electrical motor drive

at the rated torque of the

motor, when the switching

frequency of the ACS 501

inverter is 1 kHz. The rated

frequency is 50 Hz, therated current is 62 A; the 22

kW 4-pole induction motor

(HXUR 368G2 B3 380 V

43 A cos = 0.86, 1460min-1) [8].

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2

supply frequency, p.u.

inverter

motor

drive

Since the information on the efficiency of the electrical drive at different torques and rotation

speeds is required for the determination of the efficiency of the complete drive system (pump,blower, etc.), the efficiency measurements of the electrical drive and its components are next

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presented in compliance with Figure 11.6 at 1.2, 0.75, 0.5, and 0.25-fold rated torque of the motor.

The differences are not significant, yet clearly detectable.



at a 1.2-fold rated torque of

the motor, when theswitching frequency of the

ACS501 inverter is 1 kHz.

The rated frequency is 50

Hz [8].

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1


inverter

motor

drive



at a 0.75-fold rated torque

of the motor, when the

switching frequency of the

ACS501 inverter is 1 kHz.The rated frequency is 50

Hz [8].

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2


drive

motor

inverter

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Figure 11.19 The efficiency of

an electrical motor drive at a

0.5-fold rated torque of the


frequency of the SAMI GS

inverter is 1 kHz. The rated

frequency is 50 Hz [8].

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2


drive

motor

inverter

Figure 11.20 The efficiency of

an electrical motor drive at a

0.25-fold rated torque of the


frequency of the SAMI GSinverter is 1 kHz. The rated

frequency is 50 Hz [8].

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2


drive

motor

inverter

Since the switching frequency of the inverter impacts on the efficiency of the motor and the

inverter, the changes in the efficiency of the entire drive are presented as a function of the inverter

switching frequency in Figure 11.21. The figure shows that as the switching frequency increases,

the efficiency of the inverter decreases, and the efficiency of the motor improves. The decrease in

the inverter efficiency is clearly due to the increased switching losses. In our example case, as the

switching frequency increases, the motor losses decrease faster than the inverter losses, and thus the

efficiency of the whole drive improves together with the increased switching frequency.

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Figure 11.21 The effect of the

switching frequency on the

efficiency of an inverter drive at a

75 % torque and a rated supply

frequency of 50 Hz. 12 kHz is the

maximum switching frequency of

the inverter in question. By thisswitching frequency, almost a

sinusoidal motor current is

achieved, and the motor efficiency

becomes almost as high as when

operating at a sinusoidal line

voltage. The measurement is

carried out at the highest efficiency

1 of the motor at about 75 %

power at the rated frequency. The

information of the figure can be

applied to the IGBT inverters

operating at a high switching

frequency [8].

0.88

0.90

0.92

0.94

0.96

0.98

0 2 4 6 8 10 12switching frequency [kHz]

inverter

motor

drive

Finally, Figure 11.22 sums up the total efficiencies of the assembly as a function of supply

frequency with switching frequency as a parameter, when the motor is let to run at its rated torque.

The figure shows that the efficiency of the drive does not significantly depend on the switching

frequency of the output stage of the inverter. In our example case, the changes in the inverter and

motor losses nearly cancel each other. In general, we may state that the PWM inverter and

induction motor combination can provide a quite high efficiency at different frequency and torque

ranges.

Figure 11.22 The efficiency of the

example drive as a function of

supply frequency at the rated

torque with switching frequency

as a parameter, The bars are

presented in the order of 1 kHz, 3

kHz, 6 kHz, 12 kHz. We can see

that in our example case, the

switching frequency is of minor

significance for the efficiency of

the whole drive. As the efficiency

of the electrical machine improves

together with the increasedswitching frequency, the

efficiency of the inverter is

decreased correspondingly due to

the high switching frequency. In

general, we may state that a

switching frequency of 3 kHz

suffices well to bring the motor

current so close to sinusoidal

form that the losses of the

machine are not significantly

reduced by an increased switching

frequency [8].

0

0.2

0.4

0.6

0.8

1

0.2 0.4 0.6 0.8 1 1.2


As the frequency diminishes, the efficiency of the induction motor starts to decrease. If the torque

of the machine is kept constant when the speed decreases, the machine produces almost a constant

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thermal loss during its operation. If the machine is self-ventilated, the cooling of the machine

declines crucially as the speed decreases. Hence it is not possible to load the machine constantly at

its rated constant torque, if the machine speed is clearly below the rated speed. The situation is

illustrated by Figure 11.23.

T/Tn

0

0.5

1.0

0 1 2f/fn

ACS 501ACS 350DTC

SAMI STAR

ACS 502...ACS 504

Figure 11.23 Load capacity of the motor with different inverter types (ABB 2000). In the case of DTC inverters and

inverters with a high switching frequency, at rated speed, the machine can be operated at rated torque without

overheating of the machine. The topmost curve may be used for ACS 501 and ACS 400 as well as ACS 300 inverters

when operating at a switching frequency above 5 kHz. The middle curve relates to the ACS 502ACS 504 inverters at

3 kHz switching frequency. This curve has to be applied also to ACS 300, ACS 400 and ACS 500 inverters when

operating at low switching frequencies. The optimum switching applied to by the ACS 600 DTC inverter produces a

beautiful current curve form at approximately 3 kHz switching frequency, and thus the topmost curve can be followed.

The switching frequency of the old SAMI STAR is so low that the motor current has necessarily to be limited. At

speeds above rated speed, the torque is no longer restricted by cooling, but the lack of voltage. Since at the rated speed,

all the DC link voltage is already required, it is not possible to maintain the flux of the machine at speeds higher than

the rated speed, which leads to field weakening. Since the torque is produced based on the cross product of the flux and

the current, and the magnitude of the flux is now reduced, also the torque decreases.

Figure 11.24 depicts an estimate of the load capacity of a totally enclosed fan-cooled induction

motor in the corresponding circumstances.

T/Tn

0

0.5

1.0

0 1 2f/fn

ACS 350,fsw > 5 kHz DTC

SAMI STAR

ACS 400fsw= 3 kHz

Figure 11.24 Load capacity of a totally enclosed fan-cooled inverter-driven induction motor (ABB 2000). Now, the

exterior cooling of the motor functions well, but the rotor heat exchange is weakened, since the integral blower is

dependent on the rotation speed of the machine. The effect of the switching frequency is clearly detectable. The old

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SAMI STAR inverters typically applied a switching frequency below 1 kHz, and therefore the motor current deviates

already clearly from the sinusoidal.

11.9 Control Methods of an Induction Motor

The control methods of an induction motor in chronological order are the scalar control, the vectorcontrol, and the direct torque control. The first inverters were based on the scalar control principle.

Blaschke (1971) introduced the idea of vector control for rotating field machines in the early 1970s,

and the vector control was taken into wider use in the 1980s. In 1986, the direct flux linkage control

was introduced, and it was followed by the direct torque control, when ABB introduced its DTC

inverter in 1994.

11.9.1 Scalar Control

Scalar control is based chiefly on the information on the steady state of the motor. The scalar

control is a frequency control by nature. The control parameters are the motor frequency, voltage

and their corrections (adjustments) by current measurements. Figure 11.25 illustrates the schematicof the scalar control of an inverter.

Torque-

control

M3 ph

ImaxIeff

pulse encoder

n

nref

Tref

frefcontrol method

PI

uf

uref

modulator

+

-

+

-+

-

f 'ref

fref

frefuref

iact

Figure 11.25 Schematic of the control system of a scalar-controlled inverter.

The external reference of a scalar-controlled inverter is either a frequency, torque, or a speed

reference. The frequency reference is fed directly through the voltage reference block to the

modulator. The torque reference instead is fed to the torque controller, usually a PI controller. The

inverters usually include a digital PI controller also for the speed control. The implementation of the

frequency reference fref

might cause an overcurrent of the inverter, and therefore the frequency

reference is limited by a block monitoring the current and limiting it to the maximum allowed

value.

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The voltage reference block includes either the generation of the constant u/fratio obtained straight

from the induction law, a root-mean-square voltage curve, or an IR-compensated voltage reference

curve. In a drive requiring high torque at low speeds, IR-compensation is applied to; the method

takes into account the resistive voltage losses of the inverter and the motor, and increases the

terminal voltage of the machine at low speeds in order to keep the flux linkage at its rated value.

For drives slightly lighter than this, a constant ratio for the voltage and frequency can be applied to.

In blower drives, for energy saving purposes, it is possible to reduce the motor voltage at lowfrequencies and to employ a quadratic voltage curve.

The modulator of an inverter is often a unit that digitally implements sine-triangle comparison, and

generates the references for the inverter change-over switches. As its references, the modulator

requires a frequency and amplitude modulation stage that corresponds to the desired voltage. The

modulators of the modern scalar inverters implement asynchronous pulse width modulation. The

conventional thyristor inverters used a synchronous modulation technique. In certain cases, third

harmonic is added to the voltage reference to increase the rms value of the voltage.

Scalar control is capable of implementing the torque control by estimating the active current of the

motor. When the modulator produces voltage vectors, a kind of an instantaneous average can be

computed for the vectors, and thus to estimate the exact position of the voltage vector. With the

measured phase currents, it is easy to generate a current vector. Now we can calculate the angle

between the current and voltage. The active current of the inverter is proportional to the torque

produced by the motor, and thus, by the active current, it is possible to obtain an estimate for the

actual value of the torque. The scalar control can thus estimate the torque of the motor; however, it

does not contain an actual motor model. Scalar control is not capable of reacting exactly to fast

torque steps, but the drive switches gradually to a new operating state. The settling time can

typically be hundreds of milliseconds.

Scalar-controlled inverters often include a so-called slip compensation, in which the frequencyreference is increased proportional to the active current of the motor. This way, a scalar-controlled

drive is made to rotate almost at a constant speed irrespective of the load. The control electronics

require an information of the nameplate values of the motor and the calculated rated slip, by which

the slip compensation can be performed.

The simplest U/fspeed control method does not include a feedback. Particularly when operating in

the field weakening region, the stepped increase of the frequency reference may lead to a situation

in which the slip exceeds the value corresponding to the breakdown torque, and the motor is driven

to an unstable area. A similar unstable situation may arise when the reference value decreases

stepwise. Therefore it is important that the reference value of the angular speed during both

acceleration and deceleration follows the mechanical speed, in which case the slip will not exceedthe breakdown torque. Figure 11.26 illustrates the stable acceleration of the rotation speed in scalar

control. When the control system obtains the stepped change in the rotation speed reference and

raises the frequency reference, the slip will increase until the stator current reaches the set limit.

The situation is illustrated by the range 12 in the torqueangular-speed graph. Next, the frequencyis increased under current limitation in the constant torque range (23). After this, the stator currentdecreases until a new point 4 of a continuous state is reached.

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2

1 4

3

TT

Figure 11.26 Stable increase in rotation speed in scalar control from operating point one to operating point four. Thefigure depicts the static torque curves of an asynchronous machine at different supply frequencies.

If the U/fratio cannot be kept constant, the created air gap flux linkage may be saturated or it amy

remain below the desired value. The fluctuation of the parameters of the stator circuit resulting from

the temperature and saturation may cause fluctuations in the air gap flux linkage. When the air gap

flux linkage of the machine decreases, the slip has to increase (an increase in the stator current) in

order to reach the same torque; as a result, the transient stability of the motor will be reduced.

11.9.2 Field Weakening

Field weakening is required in a situation where the target is to make the motor rotate at a speed

higher than its rated speed. Now the voltage of the motor cannot be increased together with the

rotation speed, since all the voltage reserve is already in use, that is, the voltage has reached its

rated value. If the voltage is kept at its rated value and the frequency is increased, the U/f ratio

decreases, and simultaneously, also the flux linkage diminishes. The breakdown torque of an

asynchronous machine is reached when the angle between the stator and rotor flux linkage is

about 45 degrees. When the angle increases, the magnitude of the air gap flux linkage reduces as an

effect of the stator and rotor leakage inductances. When operating at a high torque in the deep field

weakening region, the magnitudes of the stator current and rotor current increase and the angle

between them increases, Therefore the magnetising current imdecreases and the air gap flux linkage

mproduced by it decreases. The excitation current imrequired by the asynchronous machine is acomponent of the stator current is, as shown in Figure 11.27.

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im

Lsis

us= 1.0

m

r

ir

Lrir

s= 0.5

is = 1.5

2Lsis

sm

r

im

Lsis

us= 1.0

m

r

ir

Lrir

s

= 0.5is

= 1.5

Figure 11.27 Vector diagrams of an induction machine in the deep field weakening region. The left-hand illustration

depicts the machine operating above its breakdown torque, the right-hand illustration shows the machine operating

approximately at the breakdown point. The speed is about double, since the magnitude of the flux linkage is about 0.5.

The relative values of the stator and rotor leakage inductances are about 0.15 (these are disproportionately large owing

to the limitations in the graphics technique). The magnitude of the rotor flux linkage is 0.16 and the magnitude of the

rotor current producing torque is about 1.48, and thus the relative torque in this left-hand illustration is about 0.24.

Correspondingly, the torque at right is about 0.44. At the breakdown point, the vector diagram is approximately equal

to the simplified small illustration below.

The simplified vector diagram (the small illustration below in Figure 11.27) shows clearly that the

approximate breakdown torque is reached in a situation similar to the one illustrated in Figure 11.27

when the stator and rotor flux linkage are in an angle of about 45. Assuming the stator and rotorleakage inductance equal, an approximately right-angled flux linkage triangle of Figure 11.27 is

obtained. Since the torque of the asynchronous machine is proportional to the cross product

s r , as was previously shown, we can easily see that with the set boundary conditions, thehighest torque would in theory be reached, when these flux linkages were perpendicular to each

other. This, however, is not possible, as can be seen from Figure 11.27. If the power factor angle

increases excessively, the air gap flux linkage and the rotor flux linkage start to decrease, and

consequently, the torque starts to decrease.

From the point of view of an asynchronous machine, field weakening is an interesting operating

region, since as far as the mechanical structure of the machine is concerned, the machine is adapted

to the normal operation at least at double its rated speed. However, the torque production capacity

of the machine has to be considered carefully in the field weakening, as was already shown in the

previous discussion. Figures 11.28 and 11.29 show the behaviour of an asynchronous machine at

different speeds. The operating ranges can be divided into constant torque, constant power and

high- speed ranges. In the constant torque range, the air gap flux linkage is kept constant, and the

machine is capable of producing a constant torque at the constant slip frequency fslip. The relative

slip decreases as the speed increases. In the field weakening, the ratioUs/of the terminal voltageand the angular frequency decreases, and thus the flux has also to decrease. In the constant power

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range, the torque of the machine is thus reduced inversely proportional to the frequency, since the

air gap flux linkage has to be reduced approximately inversely proportional to the frequency.

Let us next consider the high-speed range. The torque of the machine can be expressed by the rotor

current and the air gap flux linkage, which are already perpendicular to each other

T ie m r m r 3

2p i . (11.8)

The electromotive force induced to the rotor is

E k fEr m slip . (11.9)

In the rotor, this emf generates a current

IE

R L

k f

R fE

r

r

r slip r

m slip

r

m slipj

. (11.10)

By combining Eq. (11.8) and Eq. (11.9) we obtain

T fe m slip 2 . (11.11)

Assuming that Us m , we obtain from Eq. (11.11)

T

U

fes

2 slip

2

. (11.12)

In the field weakening, in the constant power range, the rotor current has to be of the rated value, as

shown in the figure; this corresponds to a relative constant slip, which can be shown by Eq. (11.10),

the information ms

U, and the definition of the slip frequency f sfslip

constantsr sUI . (11.13)

Since the supply frequency is constant, also the relative slip is constant in the constant power range.

Thus, the actual slip frequency increases as the supply frequency f increases f sfslip . When Us

and fslip/f remain constant in the constant power range, and the magnitude of the flux linkage

decreases inversely proportional to the frequency, we can easily determine the maximum torque in

the constant power range

Tf

fTe max

nim

nim . (11.14)

In practice, in the constant power range, the motor can produce a power higher than its rated power,

since as the excitation current and the air gap flux are reduced, an increased proportion of the

current can be used in torque production. The reduction of the air gap flux linkage decreases iron

losses, and furthermore, the improved cooling resulting from the high speed also assists thesituation.

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When the terminal voltage is constant in the field weakening, the air gap flux linkage of the

machine decreases constantly as the speed of the machine increases. Depending on the structure of

the machine typically at the relative speeds of 1.52 the air gap flux linkage has reduced to such

an extent that the motor approaches its breakdown torque, as shown in Figure 11.29. Should the

speed be raised from this, some margin has to be left with respect to the breakdown situation and

the torque has to be decreased again we have now shifted to the high-speed range. In this range,

the slip frequency of the rotor cannot be increased, and the maximum torque behaves inverselyproportional to the square of supply frequency.

Tfe max

1

2 . (11.15)

Both the motor current and the torque decrease when proceeding to the high-speed range, since it is

not the thermal load capacity of the motor, but the breakdown torque that limits the drive.

Te/Tnom

1

00 1 2 nom

prop. 1/f

prop. 1/f 2

const. torque, const. power, high speed Figure 11.28 Torque as a function of the rotor rotation speed.

The rapid reduction of the breakdown torque of an asynchronous machine results from the increase

in the slip frequency, and from the fact that the rotor becomes more and more inductive in the field

weakening. Figure 11.29 illustrates the voltage Us, the stator current Is, the rotor current Ir, the

excitation currentIm, and the torque Teof an asynchronous machine as a function of rotor speed

in normal duty, in the field weakening in the constant power range and in the high-speed range.

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const. torque, const. power, high speed

Te

Te

TeIr

Ir

Us

Us

ImIm

sfslip

0 1 2 f/fnom

0 1 2 f/fnom

Figure 11.29 The performance of an asynchronous machine in normal duty, i.e., in the constant torque range; in the

field weakening, i.e., in the constant power range and high-speed range. The topmost illustration depicts the voltageUs,the stator currentIs, the rotor currentIr, and the torqueTe; the illustration below shows the slip s and the slip frequency

fslipas a function of the rotor angular speed.

Sometimes the insulation level of the voltage of motors is such that the rated voltage given for the

motor can be exceeded when increasing the frequency. This enables running an inverter-driven

motor at values above the rated voltage and angular speed. If the machine is wound for 230/400 V,

50 Hz with D/Y connections, it can be operated in delta connection at 87 Hz frequency at 400 V

voltage at the rated air gap flux linkage, and thus the power increases in the ratio 3 1: . This

arrangement, however, normally requires a consent of the manufacturer. Figure 11.30 illustrates the

operating point A of the motor at the rated values: the rated voltage is 230 V, the frequency is 50

Hz, and the rotation speed is 1400 rpm. At the operating point B, the motor is run at the 1.74-fold

voltage 400 V and the frequency 87 Hz. By changing the values of the voltage and frequency larger

in the range 5087 Hz (operating point B), the constant torque range can be expanded from the

original. The torque production capacity remains stable up to the rotating speed 2436 rpm [3].

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f/Hz

0

50 87

Us/V

400

230

1400 2436

ABTeB

UsB

TeB

TeA

TeA

UsA

UsAUsB

rpm

T,

TeB

Figure 11.30 The voltage and frequency of an induction motor at rated values (operating point A) and at 1.74-fold

values (operating point B). By using the voltage and frequency values at point B, the constant torque range of the motor

can be expanded from the original. Naturally, a higher current is required of the inverter than in the original 50 Hz 400

V drive.

11.9.3 Vector Control

Vector control is a magnetic-field-oriented control method for an induction motor. Vector control is

by nature a torque control, for which the rotation speed control gives a reference value. In the

computation, a two-axis model of the asynchronous machine is employed in such a way that the

measured current is divided into direct-axis and quadrature-axis components. The direct-axis

current component idproduces the excitation state of the machine, and it gives the actual value for

the flux linkage. The other current component, that is, the quadrature-axis component iqproduces

the torque of the machine, and it gives the actual value for the torque. Figure 11.31 depicts the

schematic diagram for the conventional vector control.

M

3 ph

pulse encoder

n

nref

Tref

ref

PI

uref

modulator

+

- i1

i2

iq

id

iq,ref

idref

torque-

control

flux control

motor modelidentification

circuit

+

+k

fref

+

r

L1, L2, L3

Figure 11.31 Schematic diagram for the conventional vector control [2].

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Figure 11.32 shows that the vector control also includes a motor model. The motor model is based

on the equivalent circuit of the two-axis motor model, which may be fixed for instance to the rotor

flux linkage reference frame. The required control parameters are calculated with this motor model

and feedbacks. In the identification block, the rotor time constant ris computed; this time constant

is important for controlling the dynamic state of the motor. The vector control keeps the dynamic

state of the motor notably better under control than the scalar control.

Good alternatives for the implementation of the vector control of an asynchronous machine are the

stator reference frame (g= 0), the rotor reference frame (g=p), or some flux linkage reference

frame. The flux linkage equations based on the space vector theory are next recapitulated in brief

s s s m r s s m L L Li i i . (11.16)

r r r m s r r m L L Li i i . (11.17)

m m s r m m L Li i i . (11.18)

All the flux linkages depend on both the stator current and the rotor current. The rotor current

causes a problem in an induction machine, since its measurement is impossible in practice. For the

implementation of the vector control, one of the flux linkages has to be estimated by measurable

parameters. Let us next consider a method conventionally applied in the vector control. The

asynchronous machine is presented in the rotor reference frame, Figure 11.32.

Lm

Ls LrRs Rr

jps

us

is

ir

ims

m r

Figure 11.32. The equivalent circuit of an induction motor based on the space vector theory, presented in a rotor

reference frame.

Equation (5.7) ( u ir r r r g rd

dj R

tp

) can be presented in the rotor reference frame in

the form

Rt

r r

rd

di

. (11.19)

We solve the rotor current from Eq. (11.17)

ii

r

r m s

r

L

L. (11.20)

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We obtain by substitution

d

d

r r

r

r

r

r

m s

t

R

L

R

LL i . (11.21)

next, we adopt the no-load time constant of the rotor

r

r

r

L

R; (11.22)

this term is often referred simply as the rotor time constant. Now Eq. (11.21) can be rewritten as

r

r

r m s

d

dtL i . (11.23)

Transformation to the Laplace domain

r r r m ss s s L i , (11.24)

from which we solve the rotor flux linkage

r

m s

r

sL

s

i

1, (11.25)

The above corresponds to the first-order low-pass filter, and thus the rotor flux linkage can be

determined by filtering the stator current multiplied by the magnetizing inductance. Estimation isperformed in practice by transforming the measured stator current vector to the rotor reference

frame, by multiplying by the magnetizing inductance, and by filtering the result with a low-pass

filter based on the rotor time constant, Figure 11.33

3 2iaibic

r

isd

isqLm r

rq

rd

Figure 11.33 Estimation of the rotor flux linkage in the rotor reference frame.

Since the rotor is magnetically symmetric, no absolute rotor angle information is required, but the

relative information suffices; therefore, a pulse encoder is well adapted for the purpose.

The presented method is somewhat problematic, since none of the above mentioned machine

parameters remains constant: the rotor resistance changes as a function of skin effect and

temperature, and magnetic saturation has an effect on the magnetizing inductance. Consequently, asaturation model and a rotor temperature estimator should be constructed for the machine. Torque

can be calculated by substituting Eq. (11.20) for rotor current to Eq. (11.16) for flux linkage

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T i i i i i e s s s sm

r

r m s s

m

r

r s

3 3 3

2 2 2p p L

L

LL p

L

L

(11.26)

T pLL

i iem

r

rd sq rq sd=3

2 (11.27)

Thus, when the machine parameters are known, the actual values of the control can be estimated.

Since the machine is usually voltage-fed, it is necessary to determine next how the voltage control

is constructed in order to implement the rotor-flux-oriented current vector control. In a system

based on the rotor flux linkage, the machine equations can conveniently be transformed into the

rotor flux linkage reference frame r,T. In the transformation from the rotor reference frame to therotor flux linkage frame, the required trigonometric functions are obtained from the known

parameters

sin , cos

d

rq

rd rq

rq

rd

rd

r

2 2

. (11.28)

Further, the torque can be expressed based on the cross field principle

T iem

r

r s

e

m

r

r sT rT s

m

r

r sT

3

3 3

2

2 2

pL

L

T pL

Li i p

L

Li

,

. (11.29)

The simple result is explained by the fact that the rotor flux does not have a quadrature componentin the rotor flux linkage reference frame. Torque control is performed by the component isT

perpendicular to the rotor flux linkage. Its reference value is obtained directly from Eq. (11.25). The

control of flux linkage is not quite as simple as the torque control. The rotor voltage equation (7.2)

is written in the rotor flux linkage reference frame by components

u R it

p

u R it

p

r r r

r

r rT

rT r rT

rT

r r

d

d

d

d

0

0

. (11.30)

In the rotor flux linkage reference frame, the result is simplified somewhat further

0

0

R it

R i p

r r

r

r rT r r

d

d

. (11.31)

Equation (11.31) yields, similarly as Eq. (11.23),

r

r

r m s

d

d

t L i . (11.32)

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The magnitude of the rotor flux linkage follows the stator current component is aligned with the

rotor linkage flux at the rotor no-load time constant, which, depending on the machine size, varies

typically between 0.151.5 s. The flux linkage remains constant by keeping the stator current

component isconstant. When operating in the field weakening region, we have to take into account

the differential term of Eq. (11.32, when the speed changes rapidly. When the rotor flux linkage is

kept constant while the torque changes, we obtain according to Eq. (11.31) ir= 0. Now the flux

linkages behave as shown in Figure 11.34

Lsisus s

m

r

ir

Lrir

is

r

T

is

isT

Lsis

us

s

m

r

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