A Fuzzy Logic Based Approach for the monitoring of Open Switch Fault in a SVM Voltage Source
Inverter fed Induction Motor Drive H. Merabet 1, T. Bahi 2, K. Bedoud1,2, D. Drici1
1 Research Center in Industrial Technologies (CRTI) P.O. Box 64 Cheraga, Algeria.
2 Automatic Laboratory and Signals (LASA) Badji Mokhtar University, Annaba, Algeria.
The reliability of power electronics system such as three phase inverter is important in many industrial processes. The monitoring in industrial systems represents an important economic objective. To guarantee the safety and the continuity in production, exploitation and to record the useful events with the feedback experience for the curative maintenance. One of the possible faults that occur in inverter is the open switch fault. The cost of this schedule can be high, and this justifies the development of fault diagnostic methods.
In this work we present a reliable strategy for monitoring and detection of open switch in Space Vector Modulation of voltage source inverter (SVM-VSI) faults using the fuzzy logic approach. The principle of the suggested approach strategy is based on the acquisition of stator currents, to calculate the average absolute values of currents (AAVC), which allows the real-time detection and localization of inverter IGBT open-circuit faults using just the motor phase currents. A model of the system is built using MATLAB/SIMULINK. Simulation results are presented showing the monitoring approach performance under distinct operating conditions.
Keywords: Monitoring, Detection, Fault inverter, SVM, VSI, AAVC, Fuzzy logic
1. INTRODUCTION
The SVM voltage source inverter (SVM-VSI) has become the standard in industrial applications for variable speed operation systems such as energy conversion system, electrical motor drives, active power filters, and even traction of hybrid electric vehicle.
These inverters mostly use power electronics switches based on the insulated-gate bipolar transistor(IGBT),due to its advantages features which include sinusoidal input current with unity power factor and high-quality of output voltage [1,2] The reliability of the power conversion systems have been always important issue. So, fault diagnosis methods of the system are required to improve reliability and guarantee scheduled maintenance [3]. In literature the several statistical researches are introduced to prove the components the most susceptible to failures. These researches show that about 38% of the failures in variable speed AC/DC/AC drives systems in industry are mostly found in power electronics equipment and 53% in the control circuits [4-6].
During the operating of component of the electronics power system in the industrial processes, the IGBT can be presents various natures of failures (open-circuit or short-circuit faults) emanating from an early mature, while revealing breakdowns in the total system [7].These failures cause considerable economic losses, it is thus of primary importance to implement monitoring systems in order to avoid the unexpected shutdown. Thus, in this work will particularly focus on of open switches faults of SVM voltage source inverter [8].
The open switch faults can be generally caused either by device driver failure, the rupture of the connections induced by overheating, or the lift of bonding wire resulting from thermal cycling [9-12]. Open switch faults of the system do not cause system shutdown contrary to short circuit faults, but degrades its performance. Such degradations in return represent the source of secondary faults. If such state of abnormal operation lasts for extended period of time, accumulated fatigue under unstable operation may generate malfunctions in several devices of the system. Accordingly, there is high probability of secondary faults occurrence in the load, grid, and converter system. Therefore, diagnosis techniques of power conversion systems are required for monitoring and detecting of open switch faults [13-15].
The progresses of diagnosis system reveal additional expensive solution in the industrial investment, but it deadens during the production phase. During the execution of the diagnosis strategy, the measurable signals can provide significant information on the faults appearance to facilitate the determination of the supervision parameters, representing the faults signatures, their degree and persistence from these parameters, the decisional system can conceive powerful monitoring approach [16, 17].
The new monitoring approaches of industrials system have widely used the condition-based maintenance strategies to reduce unexpected failures and downtimes. These approaches have progressed from known approaches to artificial intelligence based on Artificial Neural Network (ANN), Fuzzy logic Inference System (FIS), or combined structure techniques of Adaptive Neuro-Fuzzy Inference System (ANFIS). These techniques have many advantages compared to conventional fault diagnosis approaches [18- 20].
Therefore, the suggested approach in this paper is based on the fuzzy logic technique, last that used as input to fuzzy system the average absolute values of currents (AAVC), in the aim to increase the efficiency and the reliability of the monitoring of detection and localization IGBT open circuit fault of the SVM voltage source inverter (SVM-VSI). The models based on artificial intelligence approach as well as the overall model are implemented by using MATLAB®/SIMULINK software.
2. SVM-VSIINDUCTION MACHINE MODELLING
The three-phase SVM inverter induction machine drive system is shown in figure 1[21].
Figure 1SVM Voltage Source Inverter (SVM-VSI) fed Induction Machine
UB UC
2.1 SVM-Voltage Source Inverter Modelling
The phase voltage of an inverter fed induction machine (shown in Figure 1) can be expressed by Fourier series as [22]:
= 1
sin = 1
sin Where:
U dc: dc supply voltage,
= : peak value of the n harmonic
= 1 + 6 = 0, ±1, ±2, … … …
The switching states for the voltage source inverter which will be discussed in figure 3
From the equation (1) the fundamental peak value is given as:
=" # (2) This value will be used to define the modulation index M used in pulse width modulation (PWM) methods. For the sake of the inverter structure, each inverter-leg can be represented as an ideal switch described as U0 to U7. The equivalent inverter states are shown in Figure 2. There are eight possible positions of the switches in the inverter. These states correspond to voltage vectors. Six of them (Fig. 3a-f) are active vectors (U1,..., U6) and the last two (Figure g-h) are zero vectors(U0 and U7). The output voltage represented by space vectors defined as [23]:
$
%&'() % ⁄ + = 1 … … . .6 0 + = 0,7
(3) (1)
Figure 3 Switching states for the voltage source inverter
The vectors divide the α-ß plane in six sectors specified by an angle α, as in Figure 3 and Table I
Sector number Area of the αααα-ß plans defined by ɣ [rad]
1 .0,
%/
2 .
%,
%/
3 .
%, 0/
4 .0,
1%/
5 .
1%,
2%/
6 .
2%,
3/
Table I. definition of the sectors
In accordance with the modulation technique, the average voltage vectors Us over the time period Ts can be obtained by applying the adjoining U1, U2 vectors (as in the situation of Figure.3), for the intervals t1 and t2and the zero vectors are used for a total duration t0or t7[24]. The t1, t2, t0and t7values (which constitute Ts) depend on the assumed control method, called space vector modulation (SVM).
2.2 Modelling of the induction machine
The stator and rotor equations which are defined as [25, 26]:
$+456 = 768456+9:456
0 = 7;845;+9 :45; (4) U1
U2
U3
U4
U5 U6
1 3
4
5 6
Uref
U0
U7 αααα
β β β β
Figure 3 Interpretation of the voltage space vectors for the Inverter Ɣ
The stator and rotor flux equations are given by:
<:456 = =456. 8456+ =456;. 845;
:45; = =45;6.8456+ =45;. 845; (5) The inductances matrices are obtained by:
=66 =
>?
??
@=A6B=6 −=6 −=6
−=6 =A6B=6 −=6
−=6 −=6 =A6B=6DEEEF
(6)
=6;=
>?
??
@ =sin G; =sin HG;+%I =sin HG;−%I
=sin HG;−%I =sin G; =sin HG;+%I
=sin HG;+%I =sin HG;−%I =sin G; DEEEF
(7)
=;6=
>?
??
@ =sin G; =sin HG;−%I =sin HG;+%I
=sin HG;+%I =sin G; =sin HG;−%I
=sin HG;−%I =sin HG;+%I =sin G; DEEEF
(8)
=;; =
>?
??
@=A;B=; −=; −=;
−=; =A6;B=; −=;
−=; −=; =A;B=;DEEEF
(9)
With;
The mutual inductance of the stator ⁄ rotor tow-phase winding can be formulated according to the following expressions:
=J= KLM;AHNPOI (10) x: indicate the stator phase s or the rotor phase r
The self-mutual inductance of the stator and rotor is given by:
==KLM;AHNPQI HNPRI (11) Where;
Lls, Llr: respectively the stator and the rotor leakage inductances;
Ns, Nr: respectively number of the stator and the rotor turns;
g, P: respectively thickness of the air-gap and poles number;
l, r: respectively length and means radius of stator/rotor;
µ0:air permeability.
The electromagnetic Torque is described by the following law:
ST =. UXVQW V
XY.Z [=RW 66\ [=6;\ [=66\] [=;;\^ . _VQ
X
VR
X` (12)
3. PROPOSED OF INVERTER FAULT MONITORING APPROACH 3.1 Fuzzy monitoring systems
The fuzzy logic is used for the monitoring and detection of open-circuit switches faults in SVM source voltage inverter (SVM-VSI) induction machine.
The diagram of the suggested approach is shown in figure 4.
The measured motor phase currents are normalized using the modulus of the Park’s Vector defined as [27]:
a8 = b%84−√d 85 −√d 8
8 = √ 85−√ 8
(13)
Where;
ia, ib and ic: the stator phase current of the induction motor;
id and iq: the components of the Park’ Vectors.
The Park’s Vector modulus |fg|6 (PVM) is can be expressed by:
|fg| = b86 + 8h (14) Figure 4 Diagram of proposed monitoring system
Sn En
The normalized stator phase currents of induction motor are given by [28]:
8N =|kij
g|Q (15) Where;
= , lm
Therefore, haughty that the induction motor is fed by a healthy inverter generating a perfectly balanced three phase sinusoidal current system, that can be given by:
8 = no
p 84 = qsin6 + : 85 = qsin H6 −% + :I 8 = qsin H6 +% + :I
(16)
Where;
Im: currents maximum amplitude;
6 : motor currents frequency;
: : initial phase angle.
Then the new expression of the Park’s Vector modulus can be defined by
|fg| = q6 b% (17) The normalized stator currents will always get values within the range of±r2 3⁄ , independent of the measured motor phase current amplitude, as [29] :
8N = no
p 84N = sin6 85N = sin H6 −%I 8N = sin H6 +%I
(18)
The average absolute values of the three normalized motor phase currents .|8N|/ are be given by:
6t |83vQu N| =bw% (19) In the lastly, the three input monitoring variables in fuzzy system inference& &4, &5, &, are obtained from the errors of the normalized currents average absolute values as:
& = x − .|8N|/ (20) Where x is a constant value equivalent to the average absolute value of the normalized motor phase currents under normal operating conditions presented by equation (19), that given as:
x = bw%≈ 0.5198 (21)
The values taken by En and Sn allow generating a distinct fault signature which corresponds to a specific faulty operation condition, to achieve this, fault symptom variables can be formulated according to the following expressions [30]:
} = ~ 7 & < 0
7 & < 0 (22)
= ~ 7 .8N/ < 0
7 .8N/ > 0 (23) 3.2 Fuzzy System Input and Output Variables
The values of En(Ea, Eb and Ec) and Sn(Sa, Sb and Sc) are selected as input variables of the fuzzy system.
The monitoring inverter state (CMI), are selected as output variables of the fuzzy system.
All these variables are defined by using the fuzzy set theory. Figure 5, shows that CMI interprets the state of the inverter as a linguistic variable, which could be T (CM) = {O_TR1, O_TR2, O_TR3, O_TR4, O_TR5, O_TR6, HI}.
Each limit in T (CMI) is characterized by a fuzzy subset. The dialog system CMI:
{Open_TR1 (O_TR1)}: interpret that the open TR1;
{Open_TR2 (O_TR2)}: interpret that the open TR2;
{Open_TR3 (O_TR3)}: interpret that the open TR3;
{Open_TR4 (O_TR4)}: interpret that the open TR4;
{Open_TR5 (O_TR5)}: interpret that the open TR5;
{Open_TR6 (O_TR6)}: interpret that the open TR6;
{Healthy inverter (HI)}: interpret that Healthy inverter.
The input variables (Ea, Eb and Ec) and (Sa, Sb and Sc)are also interpreted as linguistic variables, with: t (Q) = { Positive (P), Negative (N), as it is showing in figure 6.
Figure 5 Membership functions for output variables
Figure 6 Membership functions for input variables
The fuzzy rules membership functions for the input and the output. These rules are then defined, as follows :
Rules If Ea
and Eb
and Ec
If Sa and Sb and Sc
T h en C M I
is
Rule (01) P N N N P P
OpenT
R1Rule (02) P N N P N N
OpenT
R2Rule (03) N P N P N P
OpenT
R3Rule (04) N P N N P N
OpenT
R4Rule (05) N N P P P N
OpenT
R5Rule (06) N N P N N P
OpenT
R6Rule (07) P P P P P P Healthy
Inverter
Table 2 Fuzzy rules member ship function 4. SIMULATION AND DISCUSSION
The three phase stator current ‘Isa, Isb and Isc’ in the faulty case of open switch fault in TR1
are presented in Figure 7.a, in this case of fault, it is noted that the stator phases currents are unbalanced at the moment of failure (t = 0.4s), and the cancellation of the positive sequence of the phase current "a".
(a) Three stator phases currents
In the figure 7.b, we note that the three diagnostic variables are taking the position (Ea = Positive, Eb = Negative, Ec = Negative).
The figure 7.c shows the stator currents average absolute values are taking the position (Sa = Negative, Sb = Positive, Sc = Positive).
These positions of the input variables of En and Sn presented in the two preceding figures (figure 7.b and figure 7.c) are corresponding to the rule number 1 of table 2, based on these position states, the fuzzy inference system made the decision that the TR1 is faulty as shown in Figure 7.d.
(c) Input currents average values of fuzzy system
(d) Output fuzzy values (case of fault in switch TR1) Figure 7 case of open switch fault in TR1
The figure 8.a present the three phase stator current ‘Isa, Isb and Isc’ in the faulty case of open switch fault in TR2,
In this case of fault, it is noted that the stator phases currents are unbalanced at the moment of failure (t = 0.4s) as case of fault in TR1, but in this case we notice that the cancellation of the negative sequence of the phase current "a".
(b) Input diagnosis variables of fuzzy system (a) Three stator phases currents
In the figure 8.b, we note that the three diagnostic variables are taking the position (Ea = Positive, Eb = Negative, Ec = Negative).
The figure 8.c present the stator currents average absolute values are taking the position (Sa = Positive, Sb = Negative, Sc = Negative).
The positions of the input variables of En and Sn shown in figure 8.b and figure 8.c respectively are corresponding to the rule number 2 of table 2, so decision of the fuzzy inference system shown in Figure 8.d is open switch fault in the TR2.
(c) Input currents average values of fuzzy
(d) Output fuzzy values (case of fault in switch TR2) Figure 8 case of open switch fault in TR2
At the moment (t = 0.4s) the three stator currents ‘Isa, Isb and Isc’ are unbalanced with the cancellation of the negative magnitude of phase “b” which shows the presence of a fault of the inverter at this moment, In the figure 9.b, we reminder that the three diagnostic variables are taking the position (Ea = Negative, Eb = Positive, Ec = Negative).
(b) Input diagnosis variables of fuzzy system (a) Three stator phases currents
The figure 9.c illustrated the stator currents average absolute values, that are taking the following position (Sa = Negative, Sb = Positive, Sc = Negative) at time of presence of faulty in the inverter. .
The condition positions of the input variables of En and Sn shown in figure 9.b and figure 9.c respectively are equivalent to the rule number 4 of table 2, thus decision of the fuzzy inference system revealed in Figure 9.d is open switch fault in the TR4.
(c) Input currents average values of fuzzy
Figure 9 case of open switch fault in TR4 (d) Output fuzzy values (case of fault in switch TR4)
The figure 10.a present the curve of the three phase stator current ‘Isa, Isb and Isc’ with case of open switch fault in TR5 at the moment of failure (t = 0.4s), in this case we notice that the phases currents are unbalanced with cancellation of the negative sequence of the phase current "c".
In the figure 10.b, we note that the input values of the three diagnostic variables are taking the position (Ea = Negative, Eb = Negative, Ec = Positive).
(a) Three stator phases currents
(b) Input diagnosis variables of fuzzy system
The figure 10.c present the stator currents average absolute values are taking the position (Sa = Positive, Sb = Positive, Sc = Negative).
The positions of the input variables of En and Sn shown in figure 10.b and figure 10.c respectively are corresponding to the rule number 5 of table 2, so in figure 10.d the fuzzy inference system made decision, is open switch fault in the TR5.
In this study we present only five tests cases of healthy and open transistor faults (TR1 TR4 TR2 TR5) in arm 1 and 2, but those tests case can be shown the validation of that the approach is reliable and exploitable.
(c) Input currents average values of fuzzy system
Figure 10 case of open switch fault in TR5 (d) Output fuzzy values (case of fault in switch TR5)
5. CONCLUSIONS
The safe function of electrical drives can profit facilities. It is therefore important to develop monitoring tools to detect early faults may appear on both the inverter on the machine. The rapid and accurate diagnosis of any system employing electrical drive systems remains one of the current problems. Comparing with conventional fault diagnosis methods of inverter fed induction machine, in our work we are presented a reliable strategy for monitoring, detection and localization of open switch in Space Vector Modulation of voltage source inverter (SVM-VSI) induction machine faults using the fuzzy logic approach by supervising the stator currents phase.
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