King Saud University
From the SelectedWorks of Hadeed Sher
2011
Effect of DC Link Capacitor Failure on Free
Wheeling Diodes of Inverter Feeding an
Induction Motor
Hadeed A Sher, King Saud University
Available at: http://works.bepress.com/hadeed-sher/10/
Effect of DC Link Capacitor Failure on Free
Wheeling Diodes of Inverter Feeding an Induction
Motor
Hadeed Ahmed Sher
Khaled E. Addoweesh
Yasin Khan
Department of Electrical Engineering
King saud University
Riyadh,Saudi Arabia
Email: hsher@ksu.edu.sa
Department of Electrical Engineering
King Saud University,
Riyadh, Saudi Arabia
Email: khaled@ksu.edu.sa
Department of Electrical Engineering
King Saud University,
Riyadh, Saudi Arabia
Email: yasink@ksu.edu.sa
Abstract—Modern industrial progress is very much dependent
on the ruggedly constructed induction motors. Almost every
sophisticated process of industry is based on induction motors.
Mostly these motors are controlled by means of varying the
frequency. Inverter fed induction motors are thus a vital part
of such industrial systems. For such reasons it is important to
understand the fault behavior of different components of drive
system. This research work is a continuation of our fault analysis
of an inverter fed induction motor drive. We represent here the
effect of capacitor short circuit on free wheeling diodes that
are connected in anti parallel direction to the power switches
of inverter. This research investigates the after shocks of one
of the faults that may occur on DC link of an inverter fed
induction motor. DC link capacitors are well designed and even
the probability of capacitor failure is high, it is always a rare case
if they puncture, however this analysis will add to the reliability
of the induction machine under variable operating condition.
Index Terms—DC Link Capacitor, Free-Wheeling Diodes, Back
EMF.
I. I NTRODUCTION
Reliability analysis of induction motor is an important issue
in the research community and fault analysis of induction
machine is an area that is directly related to the reliability of
electric drive system. In industry induction motors are usually
fed via an inverter to produce the mechanical characteristics of
user own choice. Industrial plants that utilize the inverter fed
induction motors need a very accurate fault tolerant system
for smooth operation of industrial work. In literature, a lot
of work has been done on the fault analysis, monitoring and
diagnosis of inverter fed induction motor [1]- [2]. These faults
includes the following
• Transistor failure
• Gate drive pulse failure
• Inverter leg open
• DC link capacitor faults
Some researchers [2], [3] have studied the probability of
different faults in inverter fed induction motor drives. According to them, in the past the failure probability for semiconductor components was high due to the non availability
of sophisticated and reliable Pulse Width Modulation (PWM)
chips. However, this high failure rate is now considerably
reduced after the availability of microcontroller and FPGA
based control systems. Since, capacitors are used in a lot
of power electronics applications including the inverters and
Switch Mode Power Supply (SMPS), Fuchs [3] work showed
that the probability of capacitor failure is 60 %. Lahyani also
studied the capacitor failure symmetrically in fault analysis
and concluded that more than half of the faults in SMPS
are related to capacitor failure [2]. It is pertinent to mention
that the Equivalent Series Resistance (ESR) of the capacitor
increases with the passage of time. In ordinary circuits it
may not be a problem but when the capacitor is used in a
switching circuit the ESR can combine with the switching
frequency and causes self heating and indirectly leads towards
the failure of capacitor. Many researchers have mentioned a
DC link short circuit while formulating the possible faults in an
inverter operation [4]–[8]. However, they did not investigated
the said problem very deeply. Some researchers declared that
the said problem may not be a serious issue since almost every
commercially available electric drive is well equipped with the
protection schemes [4], [8]. A. Ebrahim,et.al. [5] discussed
the voltage drop in DC link but did not considered a very
low voltage for sustained period. B.Biswas et.al [6] presented
a fault analysis and deduced results in term of the current
harmonics. But it aims to focus on semiconductor based faults
and did not cater for the effect of DC link voltage drop on
current harmonics. Peuget et.al. [7], [9] classified the DC link
capacitor failure under the umbrella of DC bus faults but they
stated that they are interested in semiconductor components
failure. As a conclusion most of the work done in this regard is
related to fault analysis at semiconductor based components.
Keeping in view the need of analysis for the said problem
this paper analyzes the effect of capacitor short circuit on
DC-AC inverter. In this paper, an inverter feeding a three
phase induction motor is considered. The effect of DC link
capacitor short circuit is studied thoroughly and its effect on
free wheeling diode in particular is considered. The results can
be incorporated in the designing of a fault tolerant system and
the optimal protection system design.
II. P ROBLEM D ESCRIPTION
For a three phase inverter feeding an inductive load it is an
essential practice to counter the stress on power transistor. Free
wheeling diodes are connected in antiparallel direction that
provides a path for current to flow in the same direction during
the time motor inductance changes its polarity. In normal
condition the current drawn by the motor is controlled by the
state of switches and the generation of back e.m.f. In any
case if the back e.m.f exceeds the applied voltage then the
motor starts behaving like a generator. If the terminal voltages
becomes zero while the motor is running then the back e.m.f
becomes greater than the applied voltage. There may be serval
reasons for terminal voltages to be zero e.g
• Inverter output terminal open circuit
• Shut down of input supply
• DC Link capacitor short circuit
The problem for inverter output terminal open circuit may
occur due to loose connection but this will only hamper the
normal operation of motor and will shut down the motor
making its speed zero. The shut down of input supply will
off course make the output voltage zero and for a small time
the free wheeling diode will conduct and motor will stop
depending upon the inertia of load. The last case is very
interesting that is a short circuit across a DC link capacitor. In
this case the output of inverter will go to zero thus making the
back e.m.f greater than the applied voltage. So the induction
motor start behaving like an induction generator. The point of
interest is the short circuit that will appear at the terminals
of the motor via faulty DC link capacitor. This short circuit
will draw currents from the motor. The short circuit current
will pass through the switch or freewheeling diode depending
upon the direction of flow of current. However, in this paper
the analysis of capacitor short circuit on the free wheeling
diodes is presented.
Fig. 1.
qs
Vdss
Voss
2
=
3
sinΘ
0.5
sin(Θ − 120◦ )
0.5
sin(Θ + 120◦ )
0.5
Vbs
Vcs
(1)
where, Voss is a zero sequence component that may be
present. Solving eq.(1) gives
1
1
2
Vas − Vbs − Vcs
3
3
3
1
1
= − √ Vbs + √ Vcs
3
3
Vqss =
(2)
Vdss
(3)
This stationary frame of reference is then converted to rotating
two phase frame of reference. This rotating reference frame
rotates at a synchronous speed ωe w.r.t. ds -q s and the angle
Θe = ωe t. The realization of this synchronously rotating reference frame is given below [11]
III. M ATHEMATICAL M ODELING OF I NDUCTION M OTOR
Induction motor is represented by the equivalent models
as shown in fig. 1 [10], [11]. The conventional per phase
equivalent circuit is sustainable only in the analysis of induction motor in steady state. The mathematical model of
induction motor is presented here since the motor used in
our simulation setup is tested for a d-q modeling scenario.
For analysis in transient state the three phase induction motor
stationary reference frame (As -B s and C s ) is converted into
two phase stationary reference frame (ds -q s ) which is then
transformed into the rotating two phase frame of reference
(de -q e ). Here the superscripts ’s’ refers to stationary reference
frame and ’e’ for rotating reference frame. Axis transformation
from the three phase stationary axis As -B s -C s to q s -ds is
given below [11]:
h cosΘ cos(Θ − 120◦ ) cos(Θ + 120◦ ) i h Vas i
h V s i
DQ equivalent model of Induction Motor. [10]
Vqs = Vqss cosθe − Vdss sinθe
(4)
Vds = Vqss sinθe + Vdss cosθe
(5)
The flux linkage equations on the basis of DQ transformations
are given below as described in Krause model [10]. Based on
fig. 1, the transient model of electric machine in terms of
voltage and current can be written as below [10], [11].
" V #
qs
Vds
Vqr
Vdr
Rs + SLs
−ωe Ls
−(ωe − ωr )Lm
ωe Ls
Rs + SLs
SLm
=
SLm
−ωe Lm
−(ωe − ωr )Lr
(6)
ωe Lm )
SLm
Rr + SLr
"
iqs
ids
iqr
idr
where, S is a Laplace operator and as in our case for a squirrel
cage induction motor the two values i.e. Vqr and Vdr will be
zero [10], [11].
From eq. 6 above, the speed ωr is related to the torque and
cannot be considered as a fixed entity. The torque is given as
[11]
2 dωr
dωm
= TL + J
(7)
Te = TL + J
dt
p dt
#
Fig. 2.
AC-DC-AC Inverter.
where,
• TL represents the load torque
• ωm the mechanical speed
• and J is the rotor inertia
After keeping in mind the interaction of air flux gap and the
rotor m.m.f. relating the d-q components of variables the value
of torque derived can be expressed as following [11].
3 p
Te =
ψm Ir
(8)
2 2
In terms of de -qe components, the eq.(8) can be expressed as
3 p
(ψdm Iqr − ψqm Idr )
(9)
Te =
2 2
The developed torque in terms of inductance and the current
values with d-q phases can be rewritten as
3 p
Te =
Lm (Iqs Idr − Ids Idr )
(10)
2 2
Eqs. (6), (7) and (10) above represents as a whole the complete
dynamic behavior of induction motor which is obviously a non
linear model [11].
IV. M ATHEMATICAL A NALYSIS
Figure 2 shows the diagram of the AC-DC-AC inverter
feeding a three phase induction motor. The input three phase
voltages are converted into DC by using an uncontrolled three
phase bridge rectifier. The DC obtained is supplied to the DC
bus and is smoothed using DC link capacitor C as shown in fig.
2 and its equivalent circuit in fig. 3. The inverters are switched
in regular intervals using PWM technique. The voltage at
the output of inverter is a stepped waveform and the current
drawn by the motor is usually sinusoidal in nature. Here the
back e.m.f. is represented as a source of sinusoidally varying
voltage and the windings parameters are represented as series
resistance R and inductance L per phase. The transistors work
as a switch so they either make or break the connection of DC
link with the motor. In fig. 3 the MOSFETS Q1, Q2 and Q6
are responsible for conduction at that time and are represented
as a short circuit and Q3, Q4 and Q5 are not conducting at
that instant so are represented as an open circuit. All diodes
are represented as it is, without any change. For an instance
lets consider a scenario where the current is such that phase
Fig. 3.
Equivalent circuit of a motor as a load
A contains the current equal to the sum of phase B and phase
C as given in eq.(11).
Ia = Ib + Ic
(11)
Since the current is going from phase A that is connected to
the positive side of DC bus therefore according to KVL the
equation for phase A is given in eq.(12)
Vao = Vz + Eba
(12)
where
• Vao = Phase A voltage with respect to ground
• Vz = Voltage drop across the line impedance
• Eba = Back E.M.F of motor for phase A
Therefore eq.( 12) becomes
di
Vao = iR + L + Eba
(13)
dt
After the short circuit at DC bus the voltage at the inverter
output will become zero as shown in [12]. Therefore the
eq.(12)becomes
di
−Eba = iR + L
(14)
dt
here the (-) sign shows that the current flow convention is from
negative polarity to the positive polarity. The simplified circuit
of the said problem is depicted in fig. 3. Before the time t=
(0-) the expression for current is given by
Eba − Vdc
(15)
ir (0−) = il (0−) =
R
At time t=0 the switch S1 is turned ON, thus creating a short
circuit along Vdc . Therefore Vdc becomes zero. So eq.(15)
becomes
Eba
ir (0+) = il (0+) =
(16)
R
Since there is inductance L in the loop so it will oppose
sudden change in current, therefore the current can not change
instantaneously. However,the current will follow the particular
solution as given below in eq. (17) [13]
−t
Eba
i=
(1 − e τ )
(17)
R
L
where τ = ( R
) of the equivalent circuit
Fig. 4.
Simulation setup
V. S IMULATION S ETUP
The simulation setup for the said problem is shown in fig.
4. The simulation is performed in MATLAB/ SIMULINK.
Switch S1 is used to simulate the failure of capacitor. Since
the failure of capacitor is mostly due to main insulation
breakdown, it is actually an internal short circuit [14]. To
carry out the failure of capacitor, switch S1 is turned ON at
time t=1.5sec. The motor model used has the following rated
parameters
• Power = 5hp
• Rated voltage = 460 V
• Rated frequency = 60 Hz
• Rated speed =1750 RPM
The inverter consists of MOSFET switches. They are controlled using the most widely used sinusoidal PWM. The
carrier frequency used for PWM is 2kHz and the frequency
of sine wave is 50 Hz. System is simulated with a load of 5
N-m torque.
Fig. 5.
Motor electrical parameters before fault
VI. R ESULTS
The induction motor is connected with three phase where
the input line voltage is 381 Vp (for 220 V) with 50Hz
frequency. The generated ripple frequency will be 300Hz
which is 6 times the input frequency. For a three phase rectifier
the average output voltage is given as
Vdc = 1.635 × Vm
Fig. 6.
RPM and Torque before fault
(18)
For the circuit diagram (fig. 4) two comprehensive analysis
studies of induction motor behavior are carried out
• Without creating a fault
• By creating a fault at DC link capacitor
The motor runs very smooth in the steady state condition
before the fault is created as observed by the waveforms shown
in fig. 5 and fig. 6. The motor attains its speed as well, in
a very short time (0.4sec) as depicted in fig. 6. After testing
the system in healthy condition, the system is also tested for
a fault in DC link capacitor C. The possibilities of capacitor
failure is very high in case of inverters and SMPS. The time
instant t=1.5 sec is selected so that motor comes to steady state
condition and to prevent the fault in transient condition when
motor draws heavy current. When the switch S1 is turned on
at t=1.5 sec the dc link gets short circuited and the terminal
voltages of the motor goes to zero, since the motor is running
at a speed of 1500 RPM it can not stop immediately rather it
Fig. 7.
Equivalent circuit after the fault
Fig. 10.
Fig. 8.
Stator currents after the fault
Current and voltage of DC link
a serious issue if motor is running at high speed and inertia.
Larger the inertia longer will be the generation of back emf. So
in case of the said problem the free wheeling diodes will bear
the current for longer time. The reverse current depends on
the speed of motor therefore it can damage the free wheeling
diode in the inverter. While troubleshooting if only a capacitor
is replaced without verifying the inverter then the high reverse
current can cause damage to the switch as well. The nature of
change in various parameters of drive system provides basis
for the diagnosis and designing of fault tolerant system. Proper
monitoring of inverter semiconductors can make the basis of
fault tolerant system.
ACKNOWLEDGMENT
Authors like to thank Dr.Ali M Eltamaly and Deanship
of Scientific Research, King Saud University, for support in
carrying out this research work.
R EFERENCES
Fig. 9.
Electrical parameters observed at free wheeling diode
will work like a generator with the output short circuited as
shown in fig. 7. Simulation results shown in fig. 8 depicts the
unusual hike of current right after the fault. This fault current
is approximately 8 times more than the steady state current
that is almost equal to the max current drawn by motor in
transient condition. Figure 9 shows the current through the
freewheeling diode. At the time of fault this current goes high
enough and rises up to 40A and then decays very swiftly as
the motor tends to decelerate with the passage of time. Figure
10 shows the current through the DC link and voltage across
the DC link capacitor at the time of fault. This negative current
spike through the DC link is due to the reverse flow of current
from the motor to DC link capacitor during fault.
VII. C ONCLUSION
This paper mainly highlights the effect of capacitor short
circuit on free wheeling diode as well as the after shocks of
one of the fault that may occur on DC link of inverter fed
induction motor. The failure of DC link capacitor could be
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