NRMRL-RTP-P-185
EPA/600/A-97/022
LOSS MODELING OF CONVERTER INDUCTION MACHINE SYSTEM
FOR VARIABLE SPEED DRIVE"
Gilberto C. D, Sousa", Bimal K. Bosc
Department of Electrical Engineering
The University of Tennessee
Knoxvilie, TN 37996
John Cleland
Research Triangle Institute
Research Triangle Parte, NC 27709
Ronald J. Spiegel and P. Jeffrey Chappell
US Environmental Protection Agency
Air & Energy Engineering Research Laboratory
Research Triangle Parte, NC 27711
ABSTRACT
A reliable and reasonably accurate loss model of a converter induction
machine system is extremely important for performance prediction of
variable speed drive. The paper describes a unified loss model
development of converter machine system such that steady state loss
characteristics as well as the dynamic behavior of both machine and
converter are accurately represented in the model. The machine electrical
losses, such as stator and rotor copper loss, core loss, and stray loss are
considered for both fundamental and harmonic frequencies. Also
considered are the skin effect on rotor resistance, temperature effect on
both stator and rotor resistances, magnetizing inductance saturation, and
friction and windage loss. All the above features are incorporated in a
synchronously rotating frame dynamic D'-Q' equivalent circuits. A
converter system that includes a diode rectifier and PWM transistor
inverter has been modeled accurately for conduction and switching losses.
The machine and converter models have been simulated for a vector
controlled drive system and validity in both steady state and transient
condition has been verified. The models are valid for any type of control
strategy with an arbitrary PWM algorithm, and can be used for purposes,
such as loss-optimized design of converter machine system, efficiency
evaluation, cooling system design and general dynamic studies.
1. INTRODUCTION
Precise and reliable loss models for induction motor and converter
systems are very important for performance prediction of variable speed
drives. The machine electrical losses, such as copper loss, core loss and
stray load loss have been traditionally studied by using per-phase
equivalent circuit because the losses become primarily important in steady
state condition. However, the same equivalent circuit can not be used in
transient condition. On the other hand, for dynamic study, the
synchronously rotating D'-Q' model is normally used, but in this case the
losses are not properly represented. With sinusoidal power supply, precise
evaluation of machine losses is not straightforward. With inverter-fed
power supply that generates harmonic-rich non-sinusoidal waveforms, the
machine loss model becomes much more complex. Loss modeling of
induction motor has received wide attention in the literature over a
number of years. Neglecting the effects of space harmonics, the machine
parameters become dependent of time harmonic frequencies impressed by
* The project was funded in part by the US Environmental Protection
Agency under the subcontract from Research Triangle Institute.
** Mr. Sousa is a member of faculty in the Federal University of Espirito
Santo, Brazil, and is currently pursuing doctoral study in the University
of Tennessee.
0-7803-0582-5 /92S3.00©1992 IEEE
the inverter. Klingshim and Jordan [6] applied superposition principle to
calculate harmonic currents and the corresponding losses with pcr-phase
equivalent circuit, where the rotor resistance and leakage inductance for
each harmonic were corrected for deep bar (skin) effect. Kawagishi et al.
[7] were able to verify experimentally the frequency dependency of
parameter by using a high frequency power supply and validate some of
the theoretical predictions. Honsinger [1] systematically studied the losses
for a six-step inverter-fed machine and propose harmonic per-phase
equivalent circuit. Since both core loss and stray load loss arc basically
due to hysteresis and eddy current effects, he proposed representation of
stray loss by frequency dependent resistance in parallel with leakage
inductance in the equivalent circuit. More recently, Udayagiri and Lipo
[3] proposed a new simulation model that incorporates core loss but
neglects the skin effect and leakage flux induced core loss, thereby
underestimating the total loss.
In high frequency PWM inverter system, both conduction loss and
switching loss arc important in the loss model. The switching loss has
been discussed analytically by McMurray [8] where the effect of both
tum-on and turn-off snubbers was considered. Jovanovich ct al. [9] made
experimental evaluation of switching characteristics and losses for a
number of power devices with different base drives and load conditions.
Ikeda et al. (10] have proposed loss modeling of PWM voltage-fed
inverter and discussed the effect of carrier frequency on inverter losses.
Circuit simulation programs, such as PSPICE that embed the detailed
model of devices can give realistic lossy converter simulation. However,
the drawbacks arc that the losses remain somewhat transparent and can
not be easily partitioned between the conduction and switching losses.
Besides, such programs arc not convenient for drive system simulation.
In this paper, both induction motor and PWM converter system lossy
models have been derived in detail for variable frequency drive system
shown in Fig. 1, and then validated by extensive simulation study. The
unified system loss model can be used for both transient and steady state
performance evaluation. The motivation for the project is to predict losses
in a vector-controlled motor drive that uses fuzzy logic based efficiency
optimization control.
i i i
230 V
H
60 Hi
11 2 \ 2 £
XJ1
-fo
INDUCTION
MOTOR
RECTIFIER
INVERTER
fig. 1. Converter-machine system for variable speed drive.
114
-------
2. LOSS MODELING OF INDUCTION MACHINE
Stray Losses
2.1. Eleeu ical and Mechanical Losses
Copper Loss
Proper evaluation of copper loss requires the consideration of
temperature ( discussed in the next subsection) and skin effect on winding
resistance. The skin effect in stator winding in lower end of power rating
can be ignored, but the effect is very dominant in rotor bars of squirrel
cage machine. The skin effect has been widely discussed in the literature.
In inverter-fed machine, the skin effect due to fundamental slip frequency
can be ignored, but for the harmonic frequencies the rotor appears almost
stationary, and therefore, practically all the stator harmonic currents flow
in the rotor creating dominant skin effect. The rotor resistance at
harmonic frequency f is given approximately by [5)
*/r>
(i)
where Rrf. = dc resistance, d = bar depth, and c, is a constant that takes
into account the bar material and shape. With a number of harmonic
frequencies, the superposition principle can be applied approximately by
assuming that machine parameters for all harmonic frequencies are
identical to those computed at carrier frequency. For a PWM inverter
with sinusoidal PWM or hysteresis-band current control, the carrier
frequency and the near sidebands are most dominant
Core Losses
A precise prediction of core losses associated with high frequency
harmonic fluxes is a very difficult task [4], Here, it is assumed that the
core losses due to mutual harmonic flux are governed by the same
principle that controls the losses by fundamental mutual flux. The stator
core loss Pa due to fundamental frequency mutual flux can be given as
P--K
(2)
Kf
where f is the fundamental frequency, and k,, and k. arc the hysteresis and
eddy current coefficients, respectively. The corresponding rotor core loss
is given as
pct'kh sftf * K (Sff 4>2
(3)
here f is substituted by s f (s = per unit slip). These equations can be
added and rearranged as follows:
/
(4)
As the mutual or air-gap flux is related to air-gap voltage Va by
The stray losses actually represent a group of losses, as indicated by
Alger et al. til]. They used empirical equations to evaluate each
individual loss component that requires the knowledge of machine
dimensions, type of core material, lamination thickness, winding
geometry, etc. In this work, however, instead of evaluating stray loss
individually, wc treat them as a whole. The fundamental idea is that the
stray loss is essentially due to eddy current and hysteresis losses induced
by various types of leakage fluxes in the laminations and other structural
parts of the machine. Therefore, the stray loss can be modeled in a way
similar to that used for core loss modeling. The stator per phase stray loss
at harmonic frequency f can be given as
(9)
where V,)n = voltage across the stator leakage inductance and k,ln = stray
loss constant. The loss can be represented by an equivalent resistance
in parallel with the leakage inductance as
R
1
(10)
/,
A similar expression can be derived for rotor harmonic stray loss. The
stray loss due to fundamental current is essentially concentrated in the
stator and an equation similar to eqn. 10 can also be used. However, this
resistance will be represented in series with the stator leakage reactance
Xh for reasons that will be clear later. The fundamental voltage drop V,
across the leakage reactance Xb is 2k f L,, 1, where I is the
fundamental stator current. It can be substituted in eqn. 9 to derive
fundamental per-phase stray loss P, as
'jit =k*i
(id
where Ru, = equivalent series resistance (see Fig. 2(c)). From this
expression, R, is given as
(12)
Friction and windage losses
The friction and windage loss is essentially a function of motor speed
w, and does not depend on the type of power supply. It can be expressed
(13)
4>=vC
(5)
2.2. Temperature and Saturation Effects
eqn. 4 can be rewritten as
The equivalent core loss resistance R can then be derived as
1
*_ = -
(6)
(7)
Assuming that the coefficients k,, and k, remain the same at harmonic
frequency, and since harmonic slip s=l the equivalent core loss
resistance R, at frequency f can be obtained from eqn. 7 as
Temperature Effects
Both stator and rotor resistances increase with temperature. The stator
temperature can be monitored and approximate correction factor can be
applied, but there is no easy way to measure or estimate the rotor
temperature. Precise prediction of temperature in each part of the machine
requires detailed dynamic thermal model that depends on machine
geometry, material characteristics, cooling effects, etc, and is extremely
difficult to estimate. The machine transient thermal response can be given
approximately by a first order model where the temperature rise AT can
be given as
R.
0.5
(8)
AT = -
i (14)
6(1 *tj)
where P = total machine loss, 0 = steady state thermal resistance and t
= thermal time constant. The 8 and x parameters can be estimated
approximately by experimentation. Both rotor and stator resistances can
be corrected for temperature effects by using the well known formula:
(IS)
115
-------
where a,, = temperature coefficient (usually at T,=25 °C), and AT = (T2
- T,). The temperature corrected resistances arc then used to calculate
fundamental and Harmonic copper losses. For harmonic rotor losses, the
skin effect is superimposed on the temperature effect.
Saturation effects
Although saturation is strictly present in both leakage and magnetizing
inductances, we will ignore saturation in the former and represent
magnetizing inductance Lm saturation by a piece-wise linear function of
magnetizing current I:
is obtained;
(16)
where L0 = unsaturated inductance and Im = magnetizing current at the
Start of saturation. The saturation coefficient m is selected to best fit the
actual saturation curve of the machine.
K,
Rf 2 «¦ X2
**¦ * Aj_
where R,|5 = Rn + (R - R,). Solving for Rn
xl±
rL
2 2
f \ A
() - 4 X,^
rU
(21)
(22)
For most practical drives, R, > Xtal and therefore, the plus sign is
coasidcred in the above equation. With a similar procedure, the
expression of Ri can be derived. In practice, the value of R, is very
small compared to R,tl). Therefore, R^, can be taken equal to R, Note
that R^ represents not only the rotor harmonic stray loss, but also the
additional harmonic copper loss due to skin effect.
2.3. Per-Phase Harmonic Equivalent Circuit
The effects of time harmonics have been traditionally investigated by
solving the pcr-phase equivalent circuit [ I ] shown in Fig. 2(a), where the
harmonic stray losses are represented by shunt resistances (R and R,).
For each harmonic component, the circuit is solved and superposition
principle is applied to get the overall harmonic effect [1). In this way,
the frequency dependence of machine parameters can be taken into
account precisely. The following simplifying assumptions can be made
at this point:
. For sinusoidal PWM or hysteresis-band current-controlled inverter,
only the carrier frequency can be considered for computation of frequency
dependent parameters, and the resulting circuit can be used to compute
the effect of all the harmonics with little loss of precision.
. The harmonic frequencies arc sufficiently high such that the harmonic
slip s is essentially one.
With these assumptions. Fig 2(a) can be converted to series equivalent
form of Fig. 2(b). The barred parameters are simply the series equivalents
of the corresponding original parameters. For example, the series
equivalent stator stray loss resistance can be expressed as
*«, = -
*L+xL
(17)
since the secondary leakage reactance X. is very small. The harmonic
rotor resistance R is shown split into fundamental rotor resistance R, and
(Rj.-R,) Similarly, Rn is shown as the sum of the fundamental frequency
stray loss resistance R,n and (R,-R,u) The harmonic core loss resistance
R^ is substituted in Fig. 2(b) by a series combination of the fundamental
core loss resistance R and a modified secondary magnetizing reactance
Xfcn', so as to ensure constancy of harmonic core loss Pen- From Fig.
2(a), the harmonic core loss Pcl (neglecting small X^, is given as
3VL
(18)
where Vm is the rms harmonic airgap voltage. From Fig. 2(b), is
given by
svL R.
(19)
K + x
lout
In order to keep the harmonic core loss invariant, the two equations must
yield the same result. By equating the two expressions, the modified
secondary magnetizing reactance is derived as follows:
(20)
The circuit of Fig. 2(b) is next transformed into the modified "shunt"
form of Fig. 2(c). The final values of the harmonic stray loss resistances
R4, and R4, are obtained by equating the corresponding resistive terms
in Figs. 2(b) and 2(c). Neglecting the small X4, the following expression
a)
Rsl! xl" Rren(R,_R,)
I*
ssn Rssn
C)
Fig. 2, Per phase harmonic equivalent circuit of induction motor.
Ca) Generic circuit for harmonic of order n.
(b) "Series" equivalent form of circuit (a),
(c) Modified "shunt" equivalent form of circuit (b).
2.4. Equivalent Circuit Derivation in Synchronously Rotating Frame
The pcr-phase equivalent circuit derived in Fig. 2(c) is only valid for
steady state operation, and can not be used for dynamic performance
study. Usually, synchronously rotating frame D'-Qe equivalent circuits
[12] are used for dynamic study. The standard D'-Qc equivalent circuits
can not be represented with core loss resistor in parallel with magnetizing
inductance because dc current (equivalent fundamental frequency current)
will not flow through it. In this section, these circuits will be modified to
incorporate core loss resistor, and then the harmonic equivalent circuits
will be superimposed to derive the unified lossy equivalent circuits.
D'-O' Equivalent Circuits with Core Loss Resistor
The stationary frame D'-Q* equivalent circuits [12] can easily
incorporate core loss resistor in parallel with magnetizing inductance.
With this modifications the following equations can be written easily
R.
<
<.t\
r *
+ L
*R.
4rm
'il
lvi
(23)
116
-------
/ _ V
/
qm
fa,
(V
* I <
V*J ^
V U 4"
vW *
-------
Fig. A. Diode rectifier equivalent circuit.
Conduction Loss
The conduction loss in the inverter is distributed between transistors and
feedback diodes. Fig. 5(a) shows an inverter phase leg with feedback
diodes and snubbers, and Fig. 5(b) shows its conduction loss equivalent
circuit. Again, from the transistor saturation characteristics, the following
linear voltage drop equation can be derived with the help of
TABLE-CURVE:
v^ = va+R,'c (31)
For the feedback diodes, the voltage drop eqn. 29 is valid for the
particular devices.
Fig. 5. (a) Transistor inverter phase teg.
(b> Conduction loss equivalent circuit of inverter phase leg.
Switching Loss
Fig. 6 shows the typical tum-on and turn-off switching waves for
transistor Q, of Fig. 5. Evidently, the snubber power loss of the inverter
is given as
. (32)
P, = ( 3/2)//,C,^/
where N, = the number of switchings (ON-OFF or OFF-ON) in a phase
leg, per cycle of fundamental frequency f, Vd= dc link voltage arid C, =
snubber capacitance. The snubber loss can be represented by an
equivalent shunt resistance R, across the dc bus as follows:
Turn-off Switching Loss
Tum-off and turn-on switching losses have been discussed and
mathematically analyzed in detail by Mc Murray [8] for a dc chopper.
The same mathematical analysis can be easily extended to inverter design.
It can be shown [8] [14] that for optimum total loss ( snubber loss +
tum-loss) , usually the value of C, is small such that the
collector-emitter voltage v rise time is smaller than the colector
current ic fall time t(. In this condition, it can be shown that
2C,Vdtf
(34)
where Vd = dc link voltage, and I = half-cycle average of absolute value
of load current. Therefore, the average transistor turn-off power loss Pt0(,
can be derived as
toff
(35)
where N/2 = number of lossy tum-offs per converter leg in one cycle of
fundamental frequency f, and the turn-off constant K, is given by:
K = J-
°S i
3 '/ 2 '/
(36)
The eqns. 35 and 36 indicate that the tum-off loss decreases as the
snubber capacitance is increased. The transistor tum-off loss of eqn. 36
can be represented by an equivalent dc link shunt resistance as
Vt (37)
R.
toff
Tum-on Switching Loss
For a transistor inverter, no snubber inductance L as indicated in Fig.
5 is normally used. The stray inductance due to the wiring between the
dc link capacitor and the transistor will act as a parasitic inductance for
tum-on snubber. Using a procedure similar to that used for tum-off loss
computation, the transistor tum-on power loss can be given as (8)
*
(38)
where the tum-on constant is defined as
3 fN.C,
k C$< charging.
D
-------
4. SIMULATION STUDY
Boili the convener and machine models, as discussed above, were
simulated in detail (using PC-SIMNON language) for a 10 HP drive with
indirect vector control. The inverter uses hysteresis-band cuiTcnt control
where the number of switchings per cycle N, and the carrier frequency fc
are counted. These variables are then used in the computation of
converter and machine frequency dependent parameters. The equivalent
circuits of Fig. 3 are used in the derivation of machine state equations.
Both steady state and transient conditions of the system were considered
in the validation process of the models. Table 1 shows the complete
power circuit parameters of the drive. The steady state system
performance was initially investigated, for various load torque and speed
conditions. Fig. 7 shows the machine loss at various load torque and
speed. For a given speed, the total loss increases with torque, primarily
due to increased fundamental copper and stray load losses. For a constant
load torque, the losses increase with speed mainly because of additional
core loss and friction and windage losses. Fig. 8 shows the corresponding
total converter loss for the same load torque and speed conditions. It can
be seen that the converter loss is more affected by an increase in load
torque at constant speed, rather than by increase of machine speed at
constant load torque. This can be explained as follows:
With rated flux, the machine current is essentially a'function of load
torque and is practically independent of speed. Therefore, the inverter
losses that basically depend on machine current, is dominantly influenced
by load torque. Again, the diode rectifier loss is a function of dc link
current that increases with converter output power Therefore, the rectifier
loss is influenced by both speed and torque of the machine. Fig. 9 shows
the total system efficiency at various torque and speed conditions.
gain tuning, and Fig. 10(d) is for the same model except the slip gain is
tuned for actual machine parameters at the operating condition. It appears
that the response for all the three conditions are practically identical.
iqs*
T- (N. H)
v-
. «. i a. tm a. li
«> t(s)
,'~nWiWYiW~"WM
b)
. In o?ii
t(s)
Te (N.M)
-"W-
-yj
c)
I7TS3 S7n
t(fl)
Te (N.M)
*fr
d)
t<8)
KADIINE LOSS (W)
LOAD TORQUE (N M|
Fig. 7. Machine loss at various torque and speed
Fig. 10. Torque response of the drive at rated flux (speed=900 rpm)
(a) Command current step.
(b) Ideal and lossless converter-machine model (slip gain
parameters are nominal machine parameters).
(c) lossy converter-machine model (slip gain parameters are
nominal machine parameters).
(d) lossy converter-machine model (slip gain parameters track
with machine parameters)
5. CONCLUSION
CONVERTER LOSS M
0Jr-135ORPVU
CJr-900RPM
CJr» 450 RPM
LOAD TORQUE (N.M)
fig. 8. Converter loss at various torque and speed.
EFFICIENCY!*)
LOAD TORQUE (N.M)
fig. 9. System efficiency at various torque and speed.
In this paper, a unified loss model of converter induction machine
system has been developed such that it truly represents the physical
system. Therefore, the model can be used for precise performance
investigation under both static and dynamic conditions. The model
incorporates all the relevant losses, and takes into account the effects of
temperature and saturation on the induction machine performance The
simulation study confirmed the validity of the model for both steady state
and dynamic conditions. Although the basic motivation for the project
was to predict the losses in a vector-controlled induction motor drive that
uses fuzzy logic based efficiency optimization control, it can also be used
for other purposes, such as loss-optimized design of converter machine
system, loss evaluation of a PWM algorithm, cooling system design, and
general dynamic performance studies.
6. ACKNOWLEDGMENT
The authors wish to acknowledge the help of Marcelo G. Simoes and
Sunil M. Chhaya in this project.
Finally, the transient torque response of the vector-controlled drive is
investigated at constant speed, as indicated in Fig. 10, to study possible
effect for Dc-Qe equivalent circuits modification. Fig. 10(a) shows the
step in the torque component of current (i^*) at the rated flux condition.
Fig. 10(b) shows the corresponding torque response for lossless converter
and ideal Dc-Qe machine model with slip gain parameter tuned with the
nominal machine parameters. The observed rise time is essentially due to
intrinsic delay of hysteresis-band current controller. Fig. 10(c) shows the
response for lossy converter-machine model with nominal parameter slip
7. REFERENCES
[1] V. B. Honsinger, "Induction motors operating from inverters", IEEE
IAS Annual Meeting Conf. Rec., pp. 1276-1285, 1980.
[2] B. J. Chalmers and B. R. Sarkar, "Induction motor losses due to
nonsinusoidal supply waveforms", Proc. IEEE vol. 115, pp.1777-1782,
Dec. 1968.
119
-------
[3] M. R. Udayagiri and T. A. Lipo, "Simulation of inverter fed induction
motors including core losses", IEEE IECON'89 Conf. Rcc., pp.
232-237, 1989.
[4] D. W. Novotny et al., "Frequency dependency of time harmonic
losses in induction machines", Int'l Conf. on Elec. Machines Conf.
Rec pp. 233-238, 1990.
[5] F. G. de Buck et al., "A simple but reliable loss model for inverter
supplied induction motors", IEEE Trans. Ind. Appl., vol. 20, pp.
1190-1202, Jan./Feb. 1984.
[6] E. A. Klingshim and H. E. Jordan, "Polyphase induction motor
performance and losses on nonsinusoidal voltage sources", IEEE
Summer Power Meeting Conf. Rcc., Portland, Oregon, pp. 624-631,
1967.
[7] K. Kawagishi et al., "Frequency dependency of induction motor
parameters and their measuring method", Int'l. Pow. Elec. Conf. Rec.,
Tokyo, pp. 202-213, 1983.
[8] W. McMurray, "Selection of snubbcrs and clamps to optimize the
design of transistor switching converters", IEEE Trans Ind. Appl., vol.
16, pp. 5 i 3-523, July/Aug. 1980.
[9] M. M. Jovanovic et al., "Characterization of high power BJT's for
motor drive applications", IEEE IAS Annul Meet. Conf. Rec., pp.
440-447, 1986.
[ 10] Y. Ikeda et al., "The power loss of a PWM voltage-fed inverter",
PESC Conf. Rec., pp. 277-283, 1988.
[11] P. L. Alger et al., "Stray load losses in polyphase induction
machines", AIEE Trans, on Pow. App. and Syst., vol. 78, pp.
349-357, 1959.
[12] B. K. Bose, Power Electronics and AC Drives, Prentice Hall, NJ,
1986.
[13] TableCurve 3.0 User's Manual, Jandel Scientific, CA, 1991.
[14] B. W. Williams, Power Electronics, John Wiley, NY, 1987.
[15] J. J. Cathey , and P. Famouri, "Loss minimization control of an
induction motor drive", IEEE Ind. Appl. Soc. Trans., Jan-Fcb, 1991,
Vol. 27, no. 1, pp 32-37.
120
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tuotv/tdt DTD 13 iqc TECHNICAL REPORT DATA
1\ Jtrt ivirt J_i~ Jtt X r~ Jr~ io 0 (Please read Instructions on the reverse before completing)
t. REPORT NO. 2,
EPA/600/A-97/022
3. RECI
4. TITLE AND SUBTITLE
Loss Modeling of Converter Induction Machine
System for Variable Speed Drive
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7. authoris) q_ c. D. Sousa and B. K. Bose (Univ. of Tenn.)
J. Cleland (RTI), and R. Spiegel and J. Chappell (EPA)
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME ANO ADORESS
Dept. of Electrical Engrg. Research Triangle Inst.
The Univ. of Tennessee PO Box 12194
Knoxville, TN 37996 Rsrch Tri. Pk, NC 27709
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
CR 818282 (RTI)
12. SPONSORING AGENCY NAME ANO ADDRESS
EPA, Office of Research and Development
Air Pollution Prevention and Control Division
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Published paper; 9/91-4/96
14. SPONSORING AGENCY COOE
EPA/600/13
16.supplementary notes APPCD project officer is Ronald J. Spiegel, Mail Drop 63, 919/
541-7542. Presented at IEEE Int. Conf. on Industrial Electronics, Control, Instru-
mentation and Automation, San Diego, CA, 11/9-13/92.
16. abstract paper describes a unified loss model development of a converter mac-
hine system such that steady state loss characteristics and the dynamic behavior of
both machine and converter are accurately represented in the model. (NOTE: A
reliable and reasonably accurate loss model of a converter induction machine sys-
tem is extremely important for performance prediction of variable speed drive.)
Machine electrical losses (e. g., stator and rotor copper loss, core loss, and stray
loss) are considered for both fundamental and harmonic frequencies. Also consider-
ed are the skin effect on rotor resistance, temperature effect on both stator and ro-
tor resistances, magnetizing inductance saturation, and friction and windage loss.
All the above features are incorporated in synchronously totating frame dynamic
D-Q equivalent circuits. A converter system that includes a diode rectifier and
pulse width modulated (PWM) transistor inverter has been modeled accurately for
conduction and switching losses. The machine and converter models have been simu-
lated for a vector controlled drive system, and validity in both steady state and
transient conditions has been verified. The models are valid for any type of control
strategy with an arbitrary PWM algorithm.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. cosati Field/Group
Pollution
Variable Speed Drives
Induction Motors
Electric Converters
Pollution Prevention
Stationary Sources
Loss Modeling
Electrical Losses
13 B
131
09 C
09E
18. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 <9-73)
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