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Inverter-Fed Asynchronous Motors for Traction Systems
INVERTER-FED ASYNCHRONOUS MOTORS FOR TRACTION SYSTEMS
c. Rossi*, G. Stopiglia**
and E. Tortello***
*Divisione Transporti, Ansaldo S.p.A. **Dire%ione Ricerca e Sviluppo, Ansaldo S. p.A. "*Divisione GrandiMacchine, Ansaldo, S.p.A.
INTRODUCTION Variable-frequency 1nverter-fed asynchronous motor constitutes, in the field of electric t~tkm, an effective option to traditional d.c. motor. The success of this equipment is connected to the advantages the squirrel cage asynchron·jus motor may provide o.ower weight and small dimensions, higher power at high speed, less maintencnce requirements, higher mechanical rotor strength, lower cost, greater travelling comfort) and is a direct consequence of the enormous progress obtained by power electronics during recent years, both as concerns costs and reliability. During the latest few years our Company too has been devoting itself to develop this for employ in electrical Traction. An equipment with continuative power of 120kW and maximum power of 180kW was built and tested for an experimental trolley-bus; a motor with continuative power of 280kW is now being built for an E 323 electric shunting locomotive of Italian Railways. At the same time many higher-rating motor designs have been completed (also exceding 1000 kW) that have confirmed even more the advantages of a motor of this kind, specially as concerns weight and dimensions. The aim of this paper is to report the results of a complete tests series performed on the prototype trolley-drive. TEST EQUIPMENT The system and instrumentation employed for performing tests are indicated in diagrams shown in possibilities and analysis and also any kind fig. 1 and 2. They allow great testing of behaviour simulation: a) Inverter feeding, as well as recovery of power delivered by the load d.c. generator, are obtained by two controlled rectifiers with an adeguate power and voltage (275 kW to 1000 V). b) By acting on the two converters resulation it has been possible to reproduce transients both in the inverter feeding voltage and in the motor load. c) The instruments chosen for measurements of electric feeding of the motor have optimum frequency response, and consent to consider correctly all the harmonics actually important for the motor. d) Also the torque measure is obtained by an instrument with a very ~ood dynamic performance. Its rotating part consists of an oscillator and a strain-gages bridge bonded on the load coupling/shaft. The torsional strain determinffi the bridge unbalance and consequently a frequency modulation of the oscillator. Such frequency is transmitted, without any contact, to a frequencyvoltage transducer, and its exit may be measured, recorded or acquired on a minicomputer. e) Rotor temperature measurement is possible in different positions. Thermoresismrs employed and the. signal is transferred from the rotating part by a collector.
are
f) The voltages,currents and ~ouples waveforms may be acqUired both under steady and transient state conditions, on a minicomputer which may be connected contemporaneously with a maximum of 8 analogic and 4(16 bit)digital channels. It is thn~ possible to obtain experimentally both instant values and harmonic analysis first dise storing and them printing or plotting.
797
798
c.
Rossi, G. Stopiglia and E. Tortello
ANALYSIS OF TEST RESULTS Before analysing asynchronous motor tests,we report in Tab. I and fig. 3 its mrin characherist::iai compared to the d.c. motor it replaces [1,2 J The mechanical characteristic of the asyncronous motor (fig. 3) was obtained with a linear increase of voltage and frequency in the range 0~75 Hz, and a constant voltage in the range 75~190 Hz. Considering efficiencies and power factors constant, current absorbed is also constant in the whole working range. The motor design is related to the limit between the two feeding laws as flux, torque and voltage qttain in it simultaneously the respective maximum values. Fig. 4 shows asynchronous motor efficiency versus speed with inverter and sinusoidal feeding. On the same diagram the d.c. motor efficiency is reported. In the higher frequency range the two motors efficiencies are similar, being the asynchronous one higher. The analysis of the asynchronous motor behaviour in both cases, of sinusoidal and inverter supply is very effective. In the constant power range, in which the inverter feeds the motor with a square wave the efficiency decrease is less than 1.5% In the low frequency range we must keep in mind that this relates to starting and so it is not too significant from the efficiency point of view. In this range too, however, the a~hronous motor behaviour is considerably better than the d.c. motor one. The difference with the sinusoidal supply efficiency is on the contrary greater, as the haDno~ content of the supply is higher and the motor filtering is less effective. The phenomenon is emphasized by the reduced value of the rotor leakage inductance, and Us effect evident in the stator winding heating diagrams (fig. 5) and in the data reported in table 11, relative to an 80 Hz test with both inverter and sinusoidal supply. Separation of iron losses from additional ones was not carried out as a sufficiently satisUc~y method does not exist in every situation. The motor thermal behaviour is described in full taking ventilation diagram into account (~6). The measured overtemperatures are under the insulation class limits in the whole working range. Harmonics, which we saw cause a loss increment, have an effect as well on the magnetizing characteristic. No load tests (fig. 7), in fact, indicate that the fundamental component of current is higher with inverter supply, that is the magnetizing inductance decreases. When the motor runs near the saturation, the presence of time harmonics determines an in~ in the maximum induction value, and consequently an increase in the current. An even greater effect is due to the saturation of those parts of the magnetic circuit in which harmonic fluxes close. A complete calculation of this additional saturation effect is very complex and it isprefexable to adopt the semi-empirical method suggested by Klingshirn,Jordan[4] , based on the assumption that such additional saturation is proportional to the instantaneous sum_of the current haDnonks and particularly to its maximum. The adoption of this method in our case has given good r~l~
3].
REJ.ATlON BETWEEN SUPPLY WAVEFORM AND JOULE LOSSES
f4
I
5
I
6
I
7]
Traction asynchronous motors, owing to required performances, must be dimensioned in terms of torque and for this reason are particularly affected by the flux weakening working range amplitude. The low inductance values of such motors favour harmonic currents circulation and this makes the importance to improve the supply waveform at low frequencies evident. The inverter chops the d.c. voltage according to the following diagram: Frequency range
Chopping type
0+ 42 Hz 42.;. 60 Hz 60 -:-75 Hz 75 -:-190 Hz
5 pulses PWM 3 pulses PWM
sub-harmonic PWM
square wave
Inverter-fed asynchronous motors for traction systems
Joule losses measured for the stator and semi~erimentally deduced for the rotor, are diagrammed in fig. 8 and 9, fig. 10 and 11 report the r.m.s. current values for the entire frequency range and, for some frequency values, the harmonic .analysis of both tension and current. In the analysis of such values rotoric parameters variation related to frequency was taken into account (fig. 12). The correlation between Joule losses and supply waveforms was clarified by the analysis carried out on every chopping condition used in the 0.;-75 Hz frequency range. The results of such analysis are given in diagrams shown in fig. 13 and 14. The sub-harmonic PWM chopping is preferable up to frequencies of 20~30 Hz, beyond which the square wave is better. With PWM chopping the higher the impulses number and the frequency, the better are the results obtained. The curves may be of help in the choice of the frequency range for every type of supply modulation.
I
TABLE
D.C.MOTOR
INDUCTION MOTOR
CV 1227
M-6-120
Rated voltage
550
V
430 V (line to line)
Rated current
190
A
215
A/Phase
Cont I nuous rat Ing
105
kW
120
kW
One-hour
120
kW
150
kW
1950
rpm
1500
rpm
Maximum speed
3600
rpm
3800
rpm
Number of pOles
6
Supply frequency
-
TYPE
Rated
rating
speed
6
660
Weight One-hour rating /welght
0.182
0~190
Hz
kg
600
kg
kW/kg
0.25
kW/kg
TAB.l -
TABLE
2
f = 80 Hz
SINUSOIDAL WAVE
LOSSES
V = 430 V SQUARE WAVE
2.2
kW
2.3
kW
IRClHSTRAY
1.3
kW
1.9
kW
MECHANICAL
0.8
kW
0.8
kW
12 R
1.2
kW
2.1
kW
6.1
kW
7.6
kW
STATOR
TOTAL
C.OPl'ER
ROTOR
TAB. 2 - Motor losses (full load) 80 Hz/430 V.
799
c.
800
Rossi, G. Stopiglia and E. Tortello
INVER:r-ERt--..
FIG. 1 - Test equipment.
DISPLAY
I ~~~OMPUTER L'O'TA'
PAINTER
PDP ,,'. .
~
III
a: U
Cl
C
III
J
~
0
0
0
..... >
If ~
0 III III
COUNTEI\
lL
l/I
MULTIMETEI\ VOLTAGE TRANSDUCE"
THERMOMETE" TRANSOUCE!\8
FIG. 2-Instrumentation •
Inverter-fed asynchronous motors for traction systems
!\
150
•
A
;'~
"
A
801
j.
I'
I \
I, 1\
,\ :' :" J\ , ,, , IJ'\ I, \\ , , ': \ 1\: ,"
,
,
100
"':
"'I
I
",,
"I
~ '( '.
,.
I
.1
I
.,. \, ,
I I
r~ I I
,, ,
50
\
.
.J
,
..........
"" ... d ...........
-----
o FIG. 3 -
1500
3000
S~pmJ
Torque VS.' speed characteristics of M/6/120 and CV 1227 motors a) M/6/120 maximum rating b) M/6/120 continuous rating c) CV 1227 weak field d) CV 1227 full field
1•
.9
.8
.7
.6
.5t----------=.-::---------....---------...,....--=~_;__
o
50
100
1000
2000
FIG. 4 - Efficiency vs. speed and frequency. A) Sinusoidal - M-6-120 B) Inverter - M-6-120 C) Weak field CV 1227 D) Full field CV 1227
150 F~z]
3000
S(rpn]
C. Rossi, G. Stopig lia and E. Tortel lo
802
2
6T
[CO]
10
-
o
100
50
-
_A B
150 F[HZ]
fIG. 5 - Stator copper overhe ating vs. frequen cy a) invert er b) sinuso idal
F
[nTfs] .5
.4
,3
,2
,1
o
1500
ed. FIG. 6 - Ventil ation curve. Open circui t, self-v entilat
3000
sfrpm]
Inverter-fed asynchronous motors for traction systems
~
803 A
F
9
[\fHz 6
5
4
3
2
1
o
50
100
150 F[Hz]
FIG. 7 - Magnetization curve, a)sinusoidal- b) square wave
4
3
2
o
- - - - - - - - -....____=::
A
-==============9
50
FIG. 8 - Copper stator losses vs. frequency a) inverter b) sinusoidal
100
~ull-load)
150 F[Hz]
c.
804
Rossi, G. StopigJia and E. TorteJ.J.o
4
3
2
------
A
---------------
o
50
-e
100
150
F[HZ]
FIG. 9 - 1 2 R rotor losses vs. frequency (full-load) a) inverter b) sinusoidal
I
[A] 300
----
200
-------------------~:-:--:_: __:_::_:_:_:_:_~-----
A
B
100
50
75
FIG. 10 - Current (r.m.s. value) vs. frequency a) inverter b) sinusoidal
100
150
F[HZ]
s Inverte r·-fed asynchr onous motors for tractio n system
V,
1,
P.u.
Ru.
1
1
50Hz
.5
I
I
5 7
13 17 19
11
57
23 25
11 13
I
J
1719 :?3 25
• 11 P.u. 1
61Hz
.5
.5
, I 5 7
11
13
I
I.
1719
2325
5 7
"
V, Ru. 1
11 13
n19
~325
P.u.
1
80Hz
.5
.5
57
11 13 1719
2325
5 7
FIG. 11 - Voltag e and curren t harmon ic spectra .
1113
1719 2325
805
c.
806
Rossi, G. StopigJ.ia and E. TorteJ.Jo
2 R2 [p.u.]
L
1
10
o
500
1000
1500
2000
2500
3000F~~
FIG. 12 - Rotor parameter vs. rotor frequency.
A
5
10
FIG. 13 - Copper stator losses frequency a) PWM - 3 pulses b) PWM - 5 pulses c) PWM - 7 pulses d) Square wave e) Subharmonic PWM
50
75 F[H~
Inverter-fed asynchronous motors for traction systems
807
5
50
10 FIG. 14 :. 1 2 R
rotor losses versus a) PWM - 3 pulses b) PWM - 5 pulses c) rwM - 7 pulses d) Square wave e) subharmonic P'wm
75 F[Hz]
frE~u~ncy
BIBLIOGRAPHY 1
G. Giovanardi - "L'impiego del motore asincrono alimentato a tensione e a frequenza vari.!! bili quale motore di trazione per locomotive ed automotrici ferroviarie" LXXVII Riunione annuale A.E.I. di Sorrento 1976.
2
G. Stopiglia E. Tortello
3
F. Ghislanzoni- "Filobus sperimentale a frequenza variabile" LXXVII Riunione annuale A.E.I. S. Gho di Sorrento 1976.
4
E.A.Klingshirn- "Poliphase Induction Motor Performance and losses on Sinusoidal Voltage H.E. Jordan sources". IEEE P.A.S. vol. 87.
5
H. Largiader -
6
Svante Von Zweygbergk "Verlustermittlung im stromrichtergespeisten asynchron motor" E. Sokolov ETZ -A - Bd. 90 H 23
7
A. Bellini A. De Carli M. La Cava
"La macchina asincrona a gabbia come motore di trazione" LXXVII Riunione annuale A.E.I. di Sorrento 1976.
"Quelques aspects du 'dimensionnement des moteurs asynchrones alimentes par convertisseurs statiques de frequence pour la traction electrique". Rev. Brown Boveri - 4-70.
"Parameter Identification for Induction Motor Simulation" IFAC Symposium on Control in Power Electronic and Electrical Drives. Duesserldorf, October - 7-9, 1974.
c. Rossi*, G. Stopiglia**
and E. Tortello***
*Divisione Transporti, Ansaldo S.p.A. **Dire%ione Ricerca e Sviluppo, Ansaldo S. p.A. "*Divisione GrandiMacchine, Ansaldo, S.p.A.
INTRODUCTION Variable-frequency 1nverter-fed asynchronous motor constitutes, in the field of electric t~tkm, an effective option to traditional d.c. motor. The success of this equipment is connected to the advantages the squirrel cage asynchron·jus motor may provide o.ower weight and small dimensions, higher power at high speed, less maintencnce requirements, higher mechanical rotor strength, lower cost, greater travelling comfort) and is a direct consequence of the enormous progress obtained by power electronics during recent years, both as concerns costs and reliability. During the latest few years our Company too has been devoting itself to develop this for employ in electrical Traction. An equipment with continuative power of 120kW and maximum power of 180kW was built and tested for an experimental trolley-bus; a motor with continuative power of 280kW is now being built for an E 323 electric shunting locomotive of Italian Railways. At the same time many higher-rating motor designs have been completed (also exceding 1000 kW) that have confirmed even more the advantages of a motor of this kind, specially as concerns weight and dimensions. The aim of this paper is to report the results of a complete tests series performed on the prototype trolley-drive. TEST EQUIPMENT The system and instrumentation employed for performing tests are indicated in diagrams shown in possibilities and analysis and also any kind fig. 1 and 2. They allow great testing of behaviour simulation: a) Inverter feeding, as well as recovery of power delivered by the load d.c. generator, are obtained by two controlled rectifiers with an adeguate power and voltage (275 kW to 1000 V). b) By acting on the two converters resulation it has been possible to reproduce transients both in the inverter feeding voltage and in the motor load. c) The instruments chosen for measurements of electric feeding of the motor have optimum frequency response, and consent to consider correctly all the harmonics actually important for the motor. d) Also the torque measure is obtained by an instrument with a very ~ood dynamic performance. Its rotating part consists of an oscillator and a strain-gages bridge bonded on the load coupling/shaft. The torsional strain determinffi the bridge unbalance and consequently a frequency modulation of the oscillator. Such frequency is transmitted, without any contact, to a frequencyvoltage transducer, and its exit may be measured, recorded or acquired on a minicomputer. e) Rotor temperature measurement is possible in different positions. Thermoresismrs employed and the. signal is transferred from the rotating part by a collector.
are
f) The voltages,currents and ~ouples waveforms may be acqUired both under steady and transient state conditions, on a minicomputer which may be connected contemporaneously with a maximum of 8 analogic and 4(16 bit)digital channels. It is thn~ possible to obtain experimentally both instant values and harmonic analysis first dise storing and them printing or plotting.
797
798
c.
Rossi, G. Stopiglia and E. Tortello
ANALYSIS OF TEST RESULTS Before analysing asynchronous motor tests,we report in Tab. I and fig. 3 its mrin characherist::iai compared to the d.c. motor it replaces [1,2 J The mechanical characteristic of the asyncronous motor (fig. 3) was obtained with a linear increase of voltage and frequency in the range 0~75 Hz, and a constant voltage in the range 75~190 Hz. Considering efficiencies and power factors constant, current absorbed is also constant in the whole working range. The motor design is related to the limit between the two feeding laws as flux, torque and voltage qttain in it simultaneously the respective maximum values. Fig. 4 shows asynchronous motor efficiency versus speed with inverter and sinusoidal feeding. On the same diagram the d.c. motor efficiency is reported. In the higher frequency range the two motors efficiencies are similar, being the asynchronous one higher. The analysis of the asynchronous motor behaviour in both cases, of sinusoidal and inverter supply is very effective. In the constant power range, in which the inverter feeds the motor with a square wave the efficiency decrease is less than 1.5% In the low frequency range we must keep in mind that this relates to starting and so it is not too significant from the efficiency point of view. In this range too, however, the a~hronous motor behaviour is considerably better than the d.c. motor one. The difference with the sinusoidal supply efficiency is on the contrary greater, as the haDno~ content of the supply is higher and the motor filtering is less effective. The phenomenon is emphasized by the reduced value of the rotor leakage inductance, and Us effect evident in the stator winding heating diagrams (fig. 5) and in the data reported in table 11, relative to an 80 Hz test with both inverter and sinusoidal supply. Separation of iron losses from additional ones was not carried out as a sufficiently satisUc~y method does not exist in every situation. The motor thermal behaviour is described in full taking ventilation diagram into account (~6). The measured overtemperatures are under the insulation class limits in the whole working range. Harmonics, which we saw cause a loss increment, have an effect as well on the magnetizing characteristic. No load tests (fig. 7), in fact, indicate that the fundamental component of current is higher with inverter supply, that is the magnetizing inductance decreases. When the motor runs near the saturation, the presence of time harmonics determines an in~ in the maximum induction value, and consequently an increase in the current. An even greater effect is due to the saturation of those parts of the magnetic circuit in which harmonic fluxes close. A complete calculation of this additional saturation effect is very complex and it isprefexable to adopt the semi-empirical method suggested by Klingshirn,Jordan[4] , based on the assumption that such additional saturation is proportional to the instantaneous sum_of the current haDnonks and particularly to its maximum. The adoption of this method in our case has given good r~l~
3].
REJ.ATlON BETWEEN SUPPLY WAVEFORM AND JOULE LOSSES
f4
I
5
I
6
I
7]
Traction asynchronous motors, owing to required performances, must be dimensioned in terms of torque and for this reason are particularly affected by the flux weakening working range amplitude. The low inductance values of such motors favour harmonic currents circulation and this makes the importance to improve the supply waveform at low frequencies evident. The inverter chops the d.c. voltage according to the following diagram: Frequency range
Chopping type
0+ 42 Hz 42.;. 60 Hz 60 -:-75 Hz 75 -:-190 Hz
5 pulses PWM 3 pulses PWM
sub-harmonic PWM
square wave
Inverter-fed asynchronous motors for traction systems
Joule losses measured for the stator and semi~erimentally deduced for the rotor, are diagrammed in fig. 8 and 9, fig. 10 and 11 report the r.m.s. current values for the entire frequency range and, for some frequency values, the harmonic .analysis of both tension and current. In the analysis of such values rotoric parameters variation related to frequency was taken into account (fig. 12). The correlation between Joule losses and supply waveforms was clarified by the analysis carried out on every chopping condition used in the 0.;-75 Hz frequency range. The results of such analysis are given in diagrams shown in fig. 13 and 14. The sub-harmonic PWM chopping is preferable up to frequencies of 20~30 Hz, beyond which the square wave is better. With PWM chopping the higher the impulses number and the frequency, the better are the results obtained. The curves may be of help in the choice of the frequency range for every type of supply modulation.
I
TABLE
D.C.MOTOR
INDUCTION MOTOR
CV 1227
M-6-120
Rated voltage
550
V
430 V (line to line)
Rated current
190
A
215
A/Phase
Cont I nuous rat Ing
105
kW
120
kW
One-hour
120
kW
150
kW
1950
rpm
1500
rpm
Maximum speed
3600
rpm
3800
rpm
Number of pOles
6
Supply frequency
-
TYPE
Rated
rating
speed
6
660
Weight One-hour rating /welght
0.182
0~190
Hz
kg
600
kg
kW/kg
0.25
kW/kg
TAB.l -
TABLE
2
f = 80 Hz
SINUSOIDAL WAVE
LOSSES
V = 430 V SQUARE WAVE
2.2
kW
2.3
kW
IRClHSTRAY
1.3
kW
1.9
kW
MECHANICAL
0.8
kW
0.8
kW
12 R
1.2
kW
2.1
kW
6.1
kW
7.6
kW
STATOR
TOTAL
C.OPl'ER
ROTOR
TAB. 2 - Motor losses (full load) 80 Hz/430 V.
799
c.
800
Rossi, G. Stopiglia and E. Tortello
INVER:r-ERt--..
FIG. 1 - Test equipment.
DISPLAY
I ~~~OMPUTER L'O'TA'
PAINTER
PDP ,,'. .
~
III
a: U
Cl
C
III
J
~
0
0
0
..... >
If ~
0 III III
COUNTEI\
lL
l/I
MULTIMETEI\ VOLTAGE TRANSDUCE"
THERMOMETE" TRANSOUCE!\8
FIG. 2-Instrumentation •
Inverter-fed asynchronous motors for traction systems
!\
150
•
A
;'~
"
A
801
j.
I'
I \
I, 1\
,\ :' :" J\ , ,, , IJ'\ I, \\ , , ': \ 1\: ,"
,
,
100
"':
"'I
I
",,
"I
~ '( '.
,.
I
.1
I
.,. \, ,
I I
r~ I I
,, ,
50
\
.
.J
,
..........
"" ... d ...........
-----
o FIG. 3 -
1500
3000
S~pmJ
Torque VS.' speed characteristics of M/6/120 and CV 1227 motors a) M/6/120 maximum rating b) M/6/120 continuous rating c) CV 1227 weak field d) CV 1227 full field
1•
.9
.8
.7
.6
.5t----------=.-::---------....---------...,....--=~_;__
o
50
100
1000
2000
FIG. 4 - Efficiency vs. speed and frequency. A) Sinusoidal - M-6-120 B) Inverter - M-6-120 C) Weak field CV 1227 D) Full field CV 1227
150 F~z]
3000
S(rpn]
C. Rossi, G. Stopig lia and E. Tortel lo
802
2
6T
[CO]
10
-
o
100
50
-
_A B
150 F[HZ]
fIG. 5 - Stator copper overhe ating vs. frequen cy a) invert er b) sinuso idal
F
[nTfs] .5
.4
,3
,2
,1
o
1500
ed. FIG. 6 - Ventil ation curve. Open circui t, self-v entilat
3000
sfrpm]
Inverter-fed asynchronous motors for traction systems
~
803 A
F
9
[\fHz 6
5
4
3
2
1
o
50
100
150 F[Hz]
FIG. 7 - Magnetization curve, a)sinusoidal- b) square wave
4
3
2
o
- - - - - - - - -....____=::
A
-==============9
50
FIG. 8 - Copper stator losses vs. frequency a) inverter b) sinusoidal
100
~ull-load)
150 F[Hz]
c.
804
Rossi, G. StopigJia and E. TorteJ.J.o
4
3
2
------
A
---------------
o
50
-e
100
150
F[HZ]
FIG. 9 - 1 2 R rotor losses vs. frequency (full-load) a) inverter b) sinusoidal
I
[A] 300
----
200
-------------------~:-:--:_: __:_::_:_:_:_:_~-----
A
B
100
50
75
FIG. 10 - Current (r.m.s. value) vs. frequency a) inverter b) sinusoidal
100
150
F[HZ]
s Inverte r·-fed asynchr onous motors for tractio n system
V,
1,
P.u.
Ru.
1
1
50Hz
.5
I
I
5 7
13 17 19
11
57
23 25
11 13
I
J
1719 :?3 25
• 11 P.u. 1
61Hz
.5
.5
, I 5 7
11
13
I
I.
1719
2325
5 7
"
V, Ru. 1
11 13
n19
~325
P.u.
1
80Hz
.5
.5
57
11 13 1719
2325
5 7
FIG. 11 - Voltag e and curren t harmon ic spectra .
1113
1719 2325
805
c.
806
Rossi, G. StopigJ.ia and E. TorteJ.Jo
2 R2 [p.u.]
L
1
10
o
500
1000
1500
2000
2500
3000F~~
FIG. 12 - Rotor parameter vs. rotor frequency.
A
5
10
FIG. 13 - Copper stator losses frequency a) PWM - 3 pulses b) PWM - 5 pulses c) PWM - 7 pulses d) Square wave e) Subharmonic PWM
50
75 F[H~
Inverter-fed asynchronous motors for traction systems
807
5
50
10 FIG. 14 :. 1 2 R
rotor losses versus a) PWM - 3 pulses b) PWM - 5 pulses c) rwM - 7 pulses d) Square wave e) subharmonic P'wm
75 F[Hz]
frE~u~ncy
BIBLIOGRAPHY 1
G. Giovanardi - "L'impiego del motore asincrono alimentato a tensione e a frequenza vari.!! bili quale motore di trazione per locomotive ed automotrici ferroviarie" LXXVII Riunione annuale A.E.I. di Sorrento 1976.
2
G. Stopiglia E. Tortello
3
F. Ghislanzoni- "Filobus sperimentale a frequenza variabile" LXXVII Riunione annuale A.E.I. S. Gho di Sorrento 1976.
4
E.A.Klingshirn- "Poliphase Induction Motor Performance and losses on Sinusoidal Voltage H.E. Jordan sources". IEEE P.A.S. vol. 87.
5
H. Largiader -
6
Svante Von Zweygbergk "Verlustermittlung im stromrichtergespeisten asynchron motor" E. Sokolov ETZ -A - Bd. 90 H 23
7
A. Bellini A. De Carli M. La Cava
"La macchina asincrona a gabbia come motore di trazione" LXXVII Riunione annuale A.E.I. di Sorrento 1976.
"Quelques aspects du 'dimensionnement des moteurs asynchrones alimentes par convertisseurs statiques de frequence pour la traction electrique". Rev. Brown Boveri - 4-70.
"Parameter Identification for Induction Motor Simulation" IFAC Symposium on Control in Power Electronic and Electrical Drives. Duesserldorf, October - 7-9, 1974.