2021 17-th International Conference on Electrical Machines, Drives and Power Systems (ELMA), 1-4 July 2021, Sofia, Bulgaria
Fault Diagnosis Modeling of Induction Machine
Nikolay Djagarov
Electrical Department
Nikola Vaptsarov
Naval Academy
Varna, Bulgaria
jagarov@ieee.bg
Georgi Enchev
Electrical Department
Nikola Vaptsarov
Naval Academy
Varna, Bulgaria
georgi.encheff@gmail.com
Abstract — The issues of developing a ship's wireless centralized control system are considered. An induction motor universal
mathematical model is presented, with the help of which all types
of faults of an induction motor are simulated. Some of the obtained experimental results received by simulating the faults of the
stator, rotor and bearings are shown.
Keywords—induction motor, fault diagnosis, mathematic model,
transient modeling
I. INTRODUCTION
Ship power systems are complex multi-connected systems
that include a large number of electrical machines - generators
and motors. Their autonomous operation requires greater reliability and stable operation. For these purposes, modern data acquisition control systems are used. Senseless control systems
are being developed [1-5], which allow monitoring the state of
electrical equipment and electrical machines.
Due to its advantages, induction electric drives have found
the greatest distribution. The main task of the ship's service personnel (crew) is to maintenance and diagnosis electrical equipment and electric drives.
Statistical diagnostic studies show the following damage
data: in the stator - 38%; in the rotor - 10%; in bearings - 40%;
others - 12%.
A large number of methods for fault diagnosing based on
models, based on knowledge methods and based on signal processing methods are used [7-10]. However, all known models
of induction motor defect simulation allow simulating one or
two defects.
The article proposes aх universal complete mathematical
model of an induction electric drive, with the help of which it
is possible to simulate all types of fault of induction motors.
Simulations are carried out and experimental results are presented, the analysis of which allows diagnosing the motors.
II. REVIEW OF THE USED MATHEMATICAL MODELS OF
INDUCTION MOTORS FOR DIAGNOSTICS
There are many methods for monitoring and diagnosing induction motor: motor current signature analysis, electromagnetic torque analysis, noise and vibration monitoring, acoustic
noise measurements, and partial discharge [3,5,6]. Mathematical models are used to study the performance and diagnostics
of motors. The models used can be divided into three groups:
electric and magnetic circuit models, state space d-q models,
finite-element models.
With the method of equivalent magnetic circuit, equivalent
circuits are drawn up for all parts of the motor, with the help of
which the magnetic potential and magnetic flux are analyzed in
the presence of fault. Using the finite difference method, the
magnetic field distribution is calculated using difference equations. The winding function method uses the magnetic coupling
of the motor fluxes to calculate mutual inductances, which
978-1-6654-3582-6/21/$31.00 ©2021 IEEE
Sergey Kokin
Julia Djagarova
Ural Power Engendering Institute
Ural Federal University
Yekaterinburg, Russia
Electrical Department
Nikola Vaptsarov
Naval Academy
Varna, Bulgaria
julija_d@abv.bg
kokinser@list.ru
takes into account time and spatial harmonics. The finite element method evaluates the distribution of magnetic flux taking
into account the size and parameters of the magnetic circuits.
The used mathematical models of induction motors are developed under certain assumptions and describe them as a symmetrical electric machine. The appearance of various types of
faults (defects) leads to the appearance of various types of
asymmetries, which cause changes in electromechanical parameters and processes in an induction motor.
There are two types of models: 1. Quantitative models (differential equations, state-space methods, transfer functions,
etc.) that estimate parameters, states, areas. That is, faults
change the physical parameters, which leads to a change in the
parameters of the model. 2. They use methods of artificial intelligence, that is, they use high-quality modeling, with the help
of which processes in operating and emergency modes are predicted. Fault detection is performed by comparing the forecast
and observation of the processes. Another area of diagnostics
of artificial intelligence fault for dynamic systems is also used:
neural networks, fuzzy logic and neuro-fuzzy methods. These
methods do not use explicit mathematical models. Neural network training and data-driven fuzzy rule development provide
implicit models of the object being monitored (data-driven
models).
Faults of an induction motor can occur in: stator, rotor,
bearings, and other types of malfunctions can also occur.
Stator faults are usually associated with damage to the insulation, beginning with an inter-turn short circuit, which
causes heating and imbalance of the magnetic field. These
faults can be divided into two groups: 1. Core (overheating, demagnetization) and housing (vibration, circulating currents, deterioration of cooling, ground faults); 2. Malfunctions of the
stator windings: most often associated either with the end part
of the winding, or with the groove part.
Rotor faults - most often there are several reasons for the
breakdown of the rotor rod and end ring, and they are mainly
caused by: thermal stresses and imbalance; magnetic voltages;
residual stresses; dynamic stresses; the impact of the environment; mechanical stress.
Breakage of rotor rods is the main consequence of the listed
voltages, which causes speed fluctuations, torque ripple, supply
current change, temperature rise, arcing and vibration. Therefore, early detection of rotor asymmetry is important not only
to protect the rotor, but also to reduce some other types of motor
failures.
Ball bearing faults can be classified according to the damaged element as ball defect, inner raceway defect and outer
raceway defect.
Other types of faults are air gap eccentricity (static, dynamic).
2021 17-th International Conference on Electrical Machines, Drives and Power Systems (ELMA), 1-4 July 2021, Sofia, Bulgaria
To detect faults of induction motors, signature analysis of
currents, the spectrum of the stator current using the fast Fourier transform, the stator current vector hodograph, the positive,
negative and zero sequence current, and instantaneous power
are used.
Single phase stator short circuit model
With an asymmetric short circuit (change in the active and
reactive resistance of one stator phase), the stator resistance and
mutual inductance between the stator and the rotor will change.
For example, with a short circuit of stator phase a, the modified
rotor resistance in the reference system a,b,c is set as follows:
Model of induction machine with broken rotor bars
Broken rotor rods cause asymmetry in phase resistances and
inductances, which changes the electromagnetic field of the
motor. This causes harmonics in the stator currents. This
emergency mode can be modeled through a change in rotor
resistance, neglecting changes in inductances due to their
smallness.
Different faults affect in different ways the parameters of
the operating modes of an induction motor, therefore it is very
difficult to create a universal mathematical model with the help
of which to study all emergency operating modes. The choice
of the type of mathematical model depends to a large extent on
the purpose of the study and the field of application.
For diagnostics, models are needed, with the help of which
it is possible to analyze electromechanical processes in static
and transient modes in the event of defects.
The article develops a universal mathematical model of an
induction motor in d-q state space, with the help of which it is
possible to simulate all types of faults. Some of the experimental results for faults of the stator, rotor and bearings of the
induction motor are given.
The article developed models of the above malfunctions of
induction motors. With the models shown, faults were simulated. Some of the experimental results obtained are presented.
The information obtained was used to select various methods
for identifying faults.
III. INDUCTION MOTOR DRIVE MODEL
Mathematical model of an induction motor in a,b,c axes:
for the stator winding:
ψ a 0 0 
 u a   r a 0 0  i a 
d 

  = 0



r b 0  . i b  +  0 ψ b 0  =
u b  
dt
 0 0 ψ c 
 u c   0 0 r c  i c 
d
= U abc = Rabc .I abc + Ψ abc
dt
(1)
ψ a   l s m s m s  i a 
 =
  
ψ b   m s l s m s  .  i b  +
ψ c   m s m s l s  i c 

cos θr
cos ( θr + 120° ) cos ( θr − 120° ) 


+ m.  cos ( θr − 120° )
cos θr
cos ( θr + 120° )  ×
cos ( θr + 120° ) cos ( θr − 120° )

cos θr
i ra 
× i rb  == M ss .I abc + M sr .I r.abc = Ψ abc
( 4)
i rc 
cos θr
cos ( θr + 120° ) cos ( θr − 120° ) 

ψ ra 

  = m. cos θ − 120°
cos θr
cos ( θr + 120° )  ×
)
 ( r
ψ rb 
cos ( θr + 120° ) cos ( θr − 120° )

ψ rc 
cos θr
i a   l r m r m r  i ra 
× i b  +  m r l r m r  i rb  = M rs .I abc + M rr .I r.abc = Ψ r.abc ( 5 )
i c   m r m r l r  i rc 
After transformation the equation of an induction motor to
rotating coordinate axes d,q, we obtain:
d
ψ − ω k .ψ q
dt d
d
u q = r s .i q + ψ q + ω k .ψ d
dt
u d = r s .i d +
(6)
d
ψ − ( ω k − ω r ) .ψ rq
dt rd
d
0 = r r .i rq + ψ rq + ( ω k − ω r ) .ψ rd
dt
d
1
1
ωr = ( M e − M m) = ψrd.i q −ψrq.i d − M m =
dt
τm
τm
1
= xad ( i rd.i q − irq.i d ) − M m
0 = r r .i rd +
(
(7)
)
(8)
τm
ψ d = l s .i d + m ad .i rd
ψ q = l s.i q + m ad .i rq
ψ rd = m ad .i d + l r .i rd
(9)
ψ rq = m ad .i q + l r .i rq
0 
ψ ra 0
0   r ra 0 0  i ra 
d 

0  =  0



r rb 0  i rb  +  0 ψ rb 0  =
  
dt
 0
0   0
0 r rc  i rc 
0 ψ rc 
(2)
d r
r
r
= 0 = R abc
I abc + Ψ abc
dt
978-1-6654-3582-6/21/$31.00 ©2021 IEEE
θ r =  ω rdt ;
where:
for the rotor winding:
for angular speed of rotation:
d
1
(T e − T m )
ωr =
dt
τm
where: Tе = k.ψr.Ir.cosϕ2 – motor electromagnetic torque; τm mechanical time constant of the motor and the load; Tm – braking mechanical torque;
(3)
The mathematical model after replacing the flux linkages
with currents, in the Cauchy form, in the system of p.u. MF [6]:
2021 17-th International Conference on Electrical Machines, Drives and Power Systems (ELMA), 1-4 July 2021, Sofia, Bulgaria
d
i d = −a11.i d + ( ω k + a12.ω r ) .i q − a13.i rd + a14.ω r .i rq + b11.u d ;
dt
d
i q = − ( ω k + a12.ω r ) .i d − a11.i q − a14.ω r .i rd + a13.i rq + b11.u q ;
dt
d
i rd = a 31.i d − a 32.ω r .i q − a 33.i rd + ( ω k − a 34.ω r ) .i rq − b13.u d ;
dt
d
i rq = a 32.ω r .i d + a 31.i q − ( ω k − a 34.ω r ) .i rd − a 33.i rq − b13.u q ;
dt
1
d
(10 )
ω r =  x ad ( i rd .i q − i rq .i d ) − T m 
dt
τm
where: parameters aij and bij are functions of motor parameters
and angular velocities of the coordinate system ωk and rotor ωr:
2
xad
'=
−
;
xd xs
xr
1
x ad
;
;
b11 =
b13 =
'
xd
x r .x d '
a12 = x ad .b13 ;
a13 = r r .b13 ;
a14 = x ad .b11 ;
a32 = x s .b13 ; a33 = r r .b33 ; a34 = x s .b11 .
IV.
a11 = r s .b11 ;
a31 = r s .b13 ;
Rdq 0
 r11 r12
= TP .Rabc .T =  r21 r22
 r31 r32
−1
P
r13 
r23 
r33 
(14)
2
2
2
2
(
r a cos θk ) + ( r c cos [θk + 120°]) + ( r b cos [θk + 240°])
3
1
r21 = − ( r a sin 2θ k ) + ( r b.sin 2 [θ k + 240°]) + ( r c.sin 2 [θ k + 120°])
3
{
r11 =
}
{
r31 =
1
( r a cos θk ) + ( r b cos [θk + 240°]) + ( r c cos [θk + 120°])
3
{
r12 = −
r22 =
FAULT DIAGNOSIS INDUCTION MOTOR MODELS
}
1
( r a sin 2θ k ) + ( r b sin 2 [θ k + 240°]) + ( r c sin 2 [θ k + 120°])
3
{
}
1
( 2r a sin 2 θk ) + ( 2r c sin 2 [θk + 120°]) + ( 2r b sin 2 [θk + 240°])
3
{
r32 = −
r13 =
}
2
3
}
1
( r a sin θk ) + ( r b sin [θk + 240°]) + ( r c sin [θk + 120°])
3
{
{( r
}
a
}
cos θ k ) + ( r b cos [θ k + 240°]) + ( r c cos [θ k + 120°])
sr
sr
sr
r
ψ as   l sa m sab m sac  i sa  
m aa.cos θr
m ab.cos ( θr + 120° ) m ac.cos ( θr − 120° )  i a 
 s  s






r
s
s
s
sr
sr
sr
m bb.cos θr
m bc.cos ( θr + 120° )  .  i b  =
ψ b  =  m ba l b m bc  .  i b  +  m ba.cos ( θr − 120° )
sr
r
s
s
s
s
sr
sr
ψ cs   m ca
m cb l c   i c   m ca.cos ( θr + 120° ) m cb.cos ( θr − 120° )
m cc.cos θr
  i c 
 
(16 )
r
s
s
= M ss .I abc
+ M sr .I abc
= Ψ abc
rs
rs
rs
s
r
r
r
r
ψ ra  
m aa.cos θr
m ab.cos ( θr + 120° ) m ac.cos ( θr − 120° )  i a   l a m ab m ac  i a 
 r   rs
  s  r
rs
rs
r
r   r
m bb.cos θr
m bc.cos ( θr + 120° )  . i b  + .  m ba l b m bc  . i b  =
ψ b  =  m ba.cos ( θr − 120° )
r
rs
rs
rs
r
r
r
ψ c   m ca
  i cs   m rca m cb
.cos ( θr + 120° ) m cb
.cos ( θr − 120° )
m cc.cos θr
l c  i c 
 
(17 )
r
r
s
= M rs .I abc
+ M rr .I abc
= Ψ abc
Any fault in an induction motor causes a certain asymmetry.
The mathematical model of the motor in the d,q axes is obtained for an induction motor that is symmetrical in magnetic
and electrical terms. Fault simulation is performed by changing
the phase parameters of the motor model. Therefore, to create
a universal model of an induction motor to simulate different
types of faults, it is necessary to create a new model in which
you can change the phase parameters of the model and go back
to the model in the d,q axes for further simulation.
Transformation of stator equations of an induction motor
to the axes d,q, using the system of equations:
d
(T −P1.TP .Ψ abc ) =
dt
d
d
= Rdq 0 .I dq 0 + Ψ dq 0 + TP . (T −P1) .Ψ dq 0
(11)
dt
dt
TP .U abc = TP .Rabc .T −P1.TP .I abc + TP .
= U dq 0
where: TP, T −P1 - direct and inverse Park transformation matrix:
 cos θ k
2
TP =  - sin θ k
3
 1 / 2
cos ( θ k − 120° ) cos ( θ k + 120° ) 

− sin ( θ k − 120° ) - sin ( θ k + 120° )  (12)

1/ 2
1/ 2

cos θ k
- sin θ k
1


-1
T P =  cos ( θ k − 120° ) - sin ( θ k − 120° ) 1
 cos ( θ k + 120° ) - sin ( θ k + 120° ) 1


978-1-6654-3582-6/21/$31.00 ©2021 IEEE
(13)
r23 = −
r33 =
2
3
{( r
a
}
sin θ k ) + ( r b sin [θ k + 240°]) + ( r c sin [θ k + 120°])
1
{r a + r b + r c}
3
(15)

sin θ k
cos θ k
0
d -1


T P = −  sin ( θ k − 120° ) cos ( θ k − 120° ) 0  .ω k ; (18)
dt
 sin ( θ k + 120 ° ) cos ( θ k + 120° ) 0 
 0 −ωk 0
d −1 
TP . (T P ) = ωk
0 0 ;
dt
 0
0 0
I dq 0 = TP .I abc
Ψ dq 0 = TP .Ψ abc ;
(19)
(20)
Transformation of rotor equations of an induction motor to
the axes d,q, using the system of equations:
−1
0 = T Pr .R rabc .T Pr
.T Pr .I rabc + T Pr .
= R rdq0.I rdq0 +
d
r
−1
(
T Pr .T Pr .Ψ abc ) =
dt
d r
d
−1
) .Ψ rdq0
Ψ dq0 + T Pr . ( T Pr
dt
dt
( 21)
where: TP, T −P1 - rotor direct and inverse Park transformation
matrix:
2021 17-th International Conference on Electrical Machines, Drives and Power Systems (ELMA), 1-4 July 2021, Sofia, Bulgaria
TPr
 cos ( θ k − θ r ) cos ( θ k −θ r − 120° ) cos ( θ k −θ r + 120° ) 
2

=  - sin ( θ k − θ r ) - sin ( θ k −θ r − 120° ) - sin ( θ k −θ r + 120° ) 
3


1/ 2
1/ 2
1/ 2
(22)
T
-1
Pr
R
 cos ( θ k − θ r )
- sin ( θ k − θ r )
1


=  cos ( θ k − θ r − 120° ) - sin ( θ k − θ r − 120° ) 1
 cos ( θ k − θ r + 120° ) - sin ( θ k − θ r + 120° ) 1
(23)
r
dq0
r
abc
= T Pr.R .T
−1
Pr
r
r
r
 r 11
r 12 r 13 
 r
r
r 
=  r 21 r 22 r 23 
r
r
r
 r 31
r 32 r 33 
(24)
The elements of the matrix R rdq0 are calculated by formulas
(15) by replacing the argument of the trigonometric functions
θk by θk -θи.
V.
FAULT DIAGNOSIS MODELS SIMULATION
Simulation of various types of faults can be performed in
two ways: by changing the parameters (r, l, m) of the mathematical model of the motor; by changing the motor model state
variables (u, i, ψ, ωr) [11,12,13].
Motor stator fault
The most common faults in induction motors are insulation
failure of the stator winding. Most often, due to mechanical
stress and vibrations, the fastener can deteriorate or the phase
conductor can break.
Turn-to-turn short-circuit. The main electrical damage to
the stator is an adjacent coil short circuit caused by insulation
damage. Basically, a short circuit that occurs in one phase of
the stator is investigated. This mode is simulated by replacing
the stator phase resistances with a short-circuit resistance.
Coil-to-coil short-circuit. two-phase short-circuit. phase-toground short-circuit. These types of short circuit are simulated
by changing the corresponding reactance of the stator windings
of the motor.
Open-circuit of stator windings. This fault can be simulated
by two methods - either by introducing a resistor of large parameters, or by zeroing the current of the corresponding phase.
In the first case, the real process of attenuation of the inductive
current is taken into account, and in the second, it is not taken
into account and large overvoltage are obtained.
Insulation fault. The most common defects in induction motors are insulation failure of the stator winding. Most often, due
to mechanical stress and vibrations, the fastener can deteriorate
or the phase conductor can break. Active resistances, self-inductances and mutual inductances of the motor change depending on the degree of change in the insulation resistance.
Motor rotor fault
Thermal stress. Thermal overload of the motor occurs during starting, running or stopping. The reasons for this are: frequent start-up; uneven heat exchange; rotor bending, circulating currents. These modes are simulated by changing the active
resistances of individual phases.
Electrical, magnetic, dynamic, mechanical and residual
stresses ultimately, they cause changes in the active and reactive parameters of the induction motor. For individual types of
978-1-6654-3582-6/21/$31.00 ©2021 IEEE
impacts, the changes in parameters are different both in magnitude and in the type of parameters.
Broken end ring. The causes for the failure of the rod and
the end ring of the rotor are dynamic, external, mechanical
stresses, thermal, electromagnetic forces, noise and vibration,
and fatigue of parts. All these faults lead to a change in the active and reactive resistances of the rotor winding.
Mechanical fault
Ball-bearing faults. Damage to ball bearings results in sudden loss and increased contact, resulting in a large number of
intermittent impulse forces. This fault is simulated by introducing periodic changes in the braking torque on the motor shaft
Tm.
Eccentricity (static, dynamic, mixed) of rotor and stator.
With static eccentricity, the air gap is fixed, however, the rotor
magnetic field causes a change in the current in the stator and
side frequency bands appear:


1− s 
 ± nws 
f ec = f g (r ± nd ).
(25)
 p 


where: fec – eccentricity frequency; fg – grid frequency; s – slip;
p – pole pair; r – rotor bars numbers; nd = ± 1; nws – 1,3,5,7, …
Central frequency: fc = r.fg.
VI.
THE INVESTIGATED SHIP POWER SYSTEM
GOVERNIOR
DIESEL ENGINE
GENERATOR
M
LOAD
EXCITATION
AVR
Fig.1. Block- scheme of investigated ship power system
Figure 1 shows a block diagram of the investigated ship
electric power system, consisting of a synchronous generator
driven by a diesel engine with appropriate speed and excitation
controllers. An induction motor is powered by a generator and
his shaft is connected with load, which creates a braking torque.
The general model of the system is created using a non-iterative algorithm proposed in [6]. The model of a synchronous
generator in the d,q,0 axes in the Cauchy form with respect to
currents is written similarly to the model of an induction motor
(10):
 I Gs   AGss AGsr   I Gs   B Gss B Gsr  U Gs 
.
.
+
(26)

 r  =  rs
rr   r   rs
rr  
 I G   AG AG   I G   B G B G   u f 
where: index G means generator; indices s and r - mean stator
and rotor, respectively; uf - excitation voltage; U Gs - vector stator voltage; elements of matrices aij and bij are functions of active and reactive resistances of the generator and angular velocity of rotation of the coordinate system d,q,0 - ωk.
Generator equation of rotation:
d
dt
d
1
ωk =
(TPM − TG )
dt
τm
(27)
2021 17-th International Conference on Electrical Machines, Drives and Power Systems (ELMA), 1-4 July 2021, Sofia, Bulgaria
where: TPM - prime mover torque (diesel); TG=ψd.iq-ψq.id - generator
electromagnetic
torque;
ψd=ld.iq+mad.if+mad.ig;
ψq=lq.iq+maq.ih.
The voltage at the generator/motor terminals is calculated
using the differential form of first Kirchhoff's law :
mG .
d s
d s
I G + mM . I M = 0
dt
dt
(28)
I [A]
2
0
SG
S
= 1 , mM = M - scaling factors for different
SG
SG
generator and motor power.
After replacing the values of the derivatives of the stator
currents of the generator and the motor with the right sides of
the differential equations (10) and (26), we obtain the algebraic
system of equations:
where: mG =
ss
ss
sr
mG .AG .I Gs + mG .AGsr.I Gr + mG .B G .U Gs + mG .B G .u f +
ss
M
s
M
sr
M
ss
M
r
M
s
M
(29)
+ mM .A .I + mM .A .I + mM .B .U = 0
and after conversion to an unknown voltage it will turn out
(U
s
G
= U sM ) :
ss
On Figure 3. and Figure 4. we see what is happening with
the current in phase A (Ia) as in Figure 3 we see how after starting the engine the current gradually normalizes and reaches its
nominal value. As at point 2 the current suddenly becomes 6
times larger than the nominal.
0
ss
+ mM .A M .I sM + mM .A srM .I rM
ss
G
mG .B + mM .B
ss
M
1
(30)
2
EXPERIMENTAL RESULTS
0
Several experiments / simulations were performed in
MatLab SIMULINK. They are the most common IM defects
we can see. They are:
- Blocked rotor, where at moment 2500 rad / s the rotor
stops rotating / blocking
- Lack of phase - at time 2500 rad /s from start of the simulation the current of phase C becomes equal to 0, or in other
words one of the phases disconnects.
- Phase to housing - the phase touches the housing and the voltage becomes equal to 0 at the moment of 2500 rad/s.
Fig. 4. Detailed view of current of phase A
t [rad/s]
Lack of Phase
rpm
Blocked rotor
Figure 2 shows how the engine speed changes. In point 1,
rpm
they are already established and permanent. At point 2, the rotor blocks and rpm instantly become 0.
1
0
0
1
t [rad/s]
Fig. 3. Current of Phase A
I [A]
sr
mG .A G .I Gs + mG .A Gsr.I Gr + mG .B G .u f +
s
s
UG =UM =
1
0
2
2
Fig. 5. Speed of rotation of IM
t [rad/s]
0
Fig. 2. Rotation speed of IM
978-1-6654-3582-6/21/$31.00 ©2021 IEEE
t [rad/s]
Figures 5. and Figure 6. show how IM rotates and what happens when one of the phases fails. At point 0 is the starting moment. At point 1, the revolutions begin to establish. In point 2,
one of the phases is omitted. Figure 6 shows in detail what happens at the time when phase C dropout.
2021 17-th International Conference on Electrical Machines, Drives and Power Systems (ELMA), 1-4 July 2021, Sofia, Bulgaria
I [A]
rpm
2
0
0
1
2
Fig. 6. Detailed view of rpm
t [rad/s]
As respectively in Figure 7, Figure 8 and Figure 9 it is
shown what happens in the three phases. Figure 7 and Figure 8
are phases A and B and in Figure 9 - phase C. Index 2 shows
the time of current on phase C dropout as we see in the graph.
Fig. 9. Detailed view of current of phase C
t [rad/s]
Phase to housing
rpm
I [A]
0
2
0
Fig. 10. RPM of IM during phase to housing
2
Fig. 7. Detailed view of current of phase A
t [rad/s]
I [A]
t [rad/s]
In the Figure 10 we see what is happening with the speed of
IM when one of the phases fails. As in the Figure 11 is shown
in more detailed/close view.
rpm
0
0
2
2
Fig. 8. Detailed view of current of phase B
t [rad/s]
t [rad/s]
Fig. 11. Detailed view of RPM of IM during phase to housing
978-1-6654-3582-6/21/$31.00 ©2021 IEEE
2021 17-th International Conference on Electrical Machines, Drives and Power Systems (ELMA), 1-4 July 2021, Sofia, Bulgaria
U [V]
REFERENCES
[1]
0
[2]
[3]
2
[4]
Fig. 12. Detailed view of voltage of phase A
t [rad/s]
[5]
Figure 12 shows what happens to the voltage in phase A. It
is identical to that in phase B, observing a peak of nearly 100
times the nominal voltage. This occurs when the phase C connect with the housing. This is indicated in the graph by index
2.
[7]
U [V]
[8]
[6]
[9]
[10]
[11]
0
2
[12]
[13]
Fig. 13. Detailed view of voltage of phase C
t [rad/s]
On Figure 13 we can easily see how at point 2 the voltage
in phase C becomes equal to 0. Which is caused by phase to
housing connection.
CONCLUSION
The development of modern wireless ship control systems
is especially urgent. Induction electric drives are the main electrical equipment of most ships. The main problem is on-line
and off-line diagnostics of electric drives. For the purposes of
diagnostics, a mathematical model has been developed, with
the help of which it is possible to investigate the faults of induction motors and select the appropriate diagnostic methods.
The article developed a universal model in d-q state space, with
the help of which it is possible to simulate all types of faults.
Any damage to the induction motor leads to the need to simulate faults by changing the phase parameters and phase model
variables. This turns the mathematical model of the motor into
an asymmetric one with a large number of periodic (trigonometric) coefficients. Part of the experimental results obtained
in the simulation of certain defects of induction electric drives
are presented.
978-1-6654-3582-6/21/$31.00 ©2021 IEEE
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