Concurrent Detection and Classification of Faults in Matrix Converter using Trans-Conductance

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 5, No. 1, July 2014, pp. 93~100
ISSN: 2088-8694  93
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
Concurrent Detection and Classification of Faults in Matrix
Converter using Trans-Conductance
Sarah Azimi*, Mehdi VejdaniAmiri**
* Departement of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran
** Departement of Electrical Engineering, University of Calgary, Alberta, Canada
Article Info ABSTRACT
Article history:
Received Apr 6, 2014
Revised May 22, 2014
Accepted Jun 2, 2014
This paper presents a fault diagnostic algorithm for detecting and locating
open-circuit and short-circiut faults in switching components of matrix
converters (MCs) which can be effectively used to drive a permanent magnet
synchronous motor for research in critical applications. The proposed method
is based on monitoring the voltages and currents of the switches. These
measurements are used to evaluate the forward trans-conductance of each
transistor for different values of switch voltages. These trans-conductance
values are then compared to the nominal values. Under healthy conditions,
the values obtained for the fault signal is less than the tolerable value. Under
the open/short-circuit conditions, the fault signal exceeds the threshold,
hence enables the matrix converter drive to detect and exactly identify the
location of the faulty IGBT. The main advantages of this diagnostic method
include fast detection and locating of the faulty IGBT, easiness of
implementation and independency of the modulation strategy of the
converter.
Keyword:
Fault detection
Matrix converter
Open-circuit fault
Short-circuit fault
Trans-conductance
Copyright © 2014 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Sarah Azimi,
Departement of Electrical and Computer Engineering,
Isfahan University of technology,
Isfahan, Iran.
Email: Sarah.Azimi88@gmail.com
1. INTRODUCTION
Matrix converters have received considerable attention due to the recent uses in automotive,
aerospace and military applications [1]-[2]. The commercialization, modulation technique and commutation
issue of the matrix converter have been thoroughly investigated and have reached their maturity.
Matrix converter placed the traditional voltage source inventers and current source inverters by their
effective advantages such asunity power factor, the lack of bulky capacitors, high number of voltage vectors
available for modulation and sinusoidal input current [3], [5]. It has minimal energy storage requirement,
which allows to get rid of bulky and lifetime, limited energy, storing capacitors frequency converters.
The matrix converter belongs to the direct conversion family since it directly connects the input ac
lines to the output ac lines through bidirectional switches without the need for energy storage devices such as
capacitors or inductors. As a consequence, their strengths are important weight/volume reduction and
inherent four-quadrant operation, which are desirable features for transportation systems. The lack of energy
storage devices does favor the possibility to arrange semiconductors in such a way that higher voltages and
more voltage levels can be reached [4].
However, system reliability remains an open issue and has not received much attention. As a three
phase matrix converter is an array of nine bidirectional power switches, if each switch is made of an anti-
series connection of two standard IGBT's, there will be eighteen IGBTs per converter. The high number of

 ISSN: 2088-8694
IJPEDS Vol. 5, No. 1, July 2014 : 93 – 100
94
components increases the probability of occurrence of faults, giving additional importance to the diagnosis of
faults in these systems.
There have been several methods investigating the detection and locating of switch faults in matrix
converters. The first method of detecting open-circuit fault in switches of MC was proposed in [6] and
developed in [7]-[9]. This method compares the measured value of the MC output voltage and the reference
value acquired from the modulation algorithm. The proposed method in [12], uses the measured output
currents, the reference angles of the input and output voltage vectors and the values of the duty-cycle of the
switching state for detecting open-circuit faults when the optimum Alesina-Venturini modulation method is
used. It is important to focus on the possibility of occurring faults in one or both transistors of bidirectional
switches. The method proposed in [11] is based on discrete wavelet transform analysis of the measured
output current waveform. This work has focused on the detecting of faults in only one or both transistors of a
bidirectional switche. However, the existing studies have been mainly concerned with the detection of open-
circuit fault, but the topic of short-circuit detection is relatively new and has received more isolated attention.
This paper presents a new method to detect and locate open-circuit and short-circuit faults in one or
more transistors of matrix converters (MCs). In section II the possible faults that may occur in the MCs are
presented. The proposed diagnosis method for these faults is then described in section III. Simulation results
and the validation of the proposed method are presented in section IV.
2. FAULTS IN MATRIX CONVERTERS
A three phase matrix converter consists of an array of three by three bidirectional switches. Usually
constructed by two power transistors (IGBT) and two anti-parallel diodes, each bi-directional switch may
have the common emitter or the common collector topology. When the gate is fired then depending on the
switch voltage polarity, it will conduct in one of the two directions. Two major types of faults can appear in
these IGBTs. These faults consist of open-circuit faults and short-circuit faults of one or more transistors.
Possible causes of open-circuit faults include driver fault, a power transistor rupture caused by short-circuit
or a soldering fault caused by high currents. The short-circuit fault of a power transistor may caused by an
over-voltage, a temperature overshoot or a wrong voltage at the gate due to a driver fault, a DC supply fault
or / disturbance.
An open-circuit fault results in a power failure at the motor drive. Short-circuit fault on the other
hand may cause uncontrollable damage to the system due to the resulting high currents. Therefore, it is
important to be able to timely detect the occurrence of faults.
3. MC FAULT DIAGNOSIS BASED ON TRANS-CONDUCTANCE ESTIMATION
As explained before, open and short-circuit faults may cause considerable damages to the system.
Hence fault diagnosis of MCs seems to be a necessary part of the system. In this section a novel technique to
detect and locate a fault in these converters is explained.
The main idea of the proposed technique is to estimate the trans-conductance of the IGBTs at proper
time i.e. when the IGBT is in its ON state. Using the estimated values of the trans-conductance during a gate
pulse one can compare it to the nominal value to build a fault signal. A new fault signal is proposed in this
paper to indicate healthy or faulty conditions.
To estimate the trans-conductance, it is necessary to measure the currents and the voltages of the
switches and then deduce the IGBT voltages. In each switching period i.e. during a gate pulse, only three
switches (six IGBTs) are selected by the control unit. Therefore, it is necessary to measure the currents and
the voltages of these six IGBTs. The currents of theIGBTs are the same as the phase output currents which
are measured during the velocity control process of the system. Hence, no additional measurements are made
by considering these variables. To obtain the collector-emitter voltages of the IGBTs, one can read the
measured values of the input and output phase voltages. The difference between these values can be
considered as the collector emitter voltages of the active IGBTs. As a matter of fact, the voltage and the
current of an IGBT are not constant during a gatepulse. As are shown in Figures 1 and 2 the measured
voltage and current across an IGBT shows fluctuations. Accordingly, the trans-conductance of the IGBT can
be estimated as the derivative of current with respect to the voltage:

IJPEDS ISSN: 2088-8694 
Concurrent Detection and Classification of Faults in Matrix Converter using… (Sarah Azimi)
95
Figure 1. The behavior of the fault signal versus trans-conductance
(1)
In which the first order derivative is implemented by finite differences. Depending on the sampling
rate, the number of samples along a gate pulse is limited. To build a sensitive fault function, it may be
necessary to interpolate the voltage-trans-conductance pairs to increase the number of samples. In this paper,
using the linear interpolation, the number of points was increased to 50. Assuming that the tans-conductance
in healthy conditions is denoted by then the fault signal was defined as below:
(2)

In which . denotes the expectation operator and represents the sample number. This fault
signal has the property that for the open-circuit case i.e. 0 will be 1 and in the case of short-circuit
i.e. ∞
Figure 2. The measured current across an IGBT
Will take the 1 value and in the healthy condition i.e will be zero.
The next step is to find a threshold to compare the fault signal with respect to it. To obtain a
threshold, the sources of error in the system should be recognized first. There are two main types of error in
the system. The first one is the sensor uncertainty or noise level which is represented by . The other source
of error may come from the tolerance of the trans-conductance which is called . To set the threshold it is
necessary to estimate the fault signal in the presence of these non-idealities. Assuming that the measured
trans-conductance can be written as:
1.46 1.48 1.5 1.52
x 10
-3
0.5
1
1.5
2
Time (seconds)
Current
Time Series Plot:

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96
(3)
Then, the fault signal will take the following form:
(4)
This in turn can be written as follows:
(5)
Figure 2 depicts the behavior of fault signal versus different values of trans-conductance. As can be
seen from this equation, if the number of samples during a gate pulse is high enough, then the measurement
error effect will be negligible i.e. 0. But in practice this depends on the sampling frequency. For
higher sampling rates this error will have less effect on the estimation. However, due to the limited number of
samples in the simulations performed in this paper, it is necessary to include the effect of this average. It is
well-known [12] that the variance of the sample mean, for as the number of samples used to estimate the
sample mean of a white noise with standard deviation of , will be . Therefore, the standard deviation of
sample mean will be
√
. Accordingly, the fault signal at multiple of the standard deviation will be:
(6)
Which in turn can be used as the threshold to maintain constant false alarm. This threshold is obtained at
standard deviation of the noise. One can trade off this value to reduce the false alarms. Accordingly, the
probability of detection will degrade.
4. PROBABILITY OF INCORRECT DETECTION
Since the voltage and current uncertainty or noise influence on the estimated trans-conductance,the
effect of noise on the proposed detection method is investigated. is the sample mean, for which is the
number of samples used to estimate. The variance of is
√
.
(7)
According to Equations (3) and (4), the fault signal will be:
(8)
To obtain the probability of incorrect alarm when the IGBT is healthy, the distribution function of
the fault signal should be considered.Since has Gaussian distribution and fault signal is dependent of

97
then, as it is well-known [10] for the probability density function (PDF) of a function of a random variable
with known PDF, the PDF of the fault signal can be obtained:
(9)
In which is the probability distribution function of . The derivative can be written as:
(10)
Knowing that:
(11)
Then, the distribution of can be obtained as follows:
(12)
Considering as:
(13)
Where is the signal to noise ratio for the transconductance signal. The the variance of noise will then be:
(14)
Consequently, the probability distribution function (PDF) can obtained as:
(15)
Having PDF, Prabability of the incorrect alarm can be determined.
According to the Equation (6) the threshold is defined as:
(16)
Then the probability of incorrect alarm for this threshold will be:
(17)
If the following deffinitions are applied to the integral:

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98
(18)
Then the parobabilityof incorrect alarm can be obtained by:
(19)
In which, erf(.) denotes the error function. This equation, generally, shows that by using the
threshold in (16), the probability of incorrect alarm will be independent of the noise statistics, sample size,
SNR and will be constant.
5. RESULT AND DISCUSSION
5.1. Simulation Model
Simulations of the proposed diagnostic approach have been carried out using a developed
Matlab/Simulink model of an MC. The motor parameters are shown in table I. A direct torque control (DTC)
is used to drive permanent magnet synchronous motor. DTC directly controls both the torque and flux of an
electrical machine. The main advantages of this control strategy are its structure simplicity and robustness,
since it does not depend on the motor parameters. The switching frequency of the DTC drive is a variable
quantity that depends not only on the controller hysteresis bands but also on the slope of the developed
torque.
Table 1. PMSM parameters
2ARated current200wOutput power
8.3 mH
s
dl per phase100vVoltage
6mH
s
ql per phase4Pole pairs
3000rpmRated speed0.64NmTorque
4500rpmMaximum speed2.5ΩStator resistance
5.2. Simulation Results
Using the simulation model described before, the matrix converter the fault signal of the specific
IGBT in healthy condition is shown in Figure 4.
Figure 4. The fault signalunder healthy condistion
At t=1.3 ms, an open-circuit fault is introduced in IGBT number three, which connects the input
phase C to the output phase A. This fault is simulatedas an increase in the resistance of the IGBT.
0 1 2 3 4 5 6 7 8
x 10
-3
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
time(second)
TheFaultSignal
R Signal
th1
th2

99
Figure 5 depicts the results obtained when open-circuit fault occurs. If the outputs phasevoltage
changes, the collector-emitter voltage will increase. Therefore, the trans-conductance decreases from its
nominal value and causes the fault signal exceed the threshold.
Figure 5. The fault signal under open-circuit condition
Figure 6 illustrates the fault signal in the case of a short-circuit fault occurring in to the IGBT
number three. The collector current increase dramatically and accordingly, the trans-conductance increase
from its nominal value and allows detecting the faulty IGBsT by exceeding the faulty signal from the
threshold.
Using this diagnostic method, it is possible to detect faults in any transistor independently of the
existence of faults in other IGBTs. Hence, allowing a fast and concurrent detection and identification of the
faulty components. These results demonstrate the effectiveness of the proposed technique for detection of
open-circuit and short-circuit faults in MC.
Figure 6. The fault signal under short-circuit condition
6. CONCLUSION
This paper present a new method for detecting and locating the faulty IGBT in bidirectional
switches of matrix converter. The proposed method is based on monitoring the voltages and currents of
IGBTs for appraising trans-conductance of each transistor. When any of the IGBTs causes open/short-circuit
fault, the dedicated value of trans-conductance makes the fault signal of the faulty IGBT exceed from the
threshold, which help the system identify a faulty IGBT and also the type of fault that happened. It’s worth to
say that the algorithm is based on divisions, sums and derivatives. Therefore, it is not computationally
intensive. Using this algorithm, it is possible to detect the existence of more than one faulty transistor at the
same time. Therefore, allows a fast and concurrent detection and identification of the faulty components.
0 0.01 0.02 0.03 0.04 0.05
-1.5
-1
-0.5
0
0.5
1
1.5
Time (seconds)
SignalValue
Time Series Plot:
R Signal
fault time
th1
th2
0 0.002 0.004 0.006 0.008 0.01
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Time (seconds)
SignalValue
Time Series Plot:
R signal
fault time
th1
th2

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