2022 19th International Multi-Conference on Systems, Signals & Devices (SSD'22)
Diagnosis of Supply Voltage Imbalance Using WPD
Energy Enhanced by Current Space Vector (CSV)
Meriem Behim, Leila Merabet, Salah Saad
Laboratoire des Systèmes Electromécaniques (LSELM)
Badji-Mokhtar University
Annaba, Algeria
2022 19th International Multi-Conference on Systems, Signals & Devices (SSD) | 978-1-6654-7108-4/22/$31.00 ©2022 IEEE | DOI: 10.1109/SSD54932.2022.9955936
meriembehim96@gmail.com
Abstract— The present study focuses on the diagnosis of an
important external defect which is the supply voltage
imbalance due to its primary impact on the motor proper
operation. The wavelet packet decomposition (WPD) energy
method and current space vector (CSV) analysis are used.
These techniques are applied on the stator current signals
obtained from induction motor simulation. The results of tests
in Matlab/Simulink environment are discussed and analyzed.
It can be concluded that the proposed techniques are effective
in induction motor supply voltage imbalance diagnosis and can
be extended to other induction motor external or internal
defects.
Keywords— Induction motors, Supply voltage imbalance,
WPD energy , CSV analysis.
I.
INTRODUCTION
The diagnosis of defects, with their diversity, is an
essential aspect in the industrial world in order to minimize
the rate of machine downtime. Overall defects are due to
intrinsic or extrinsic impacts. This work is focalized on
induction motor supply voltage unbalance because of its
great influence on the various components of the motor [1–
4]. This type of defect is already studied in the previous
literature; as examples, Liang et al.[5] used the traditional
spectrum analysis technique while Samsi et al.[6] applied
Symbolic Dynamic Filtering (SDF) technique on the current
and voltage signals; Ahmed et al.[7] exploited the adaptive
neuro-fuzzy inference system for their study and Lashkari et
al.[8] introduced the feed forward multilayer-perceptron
Neural Network method to diagnose the unbalance supply
voltage defect, where Okelola and Olabode[9] proposed the
artificial neural network to distinguish between balanced and
unbalanced supply voltage.
The present paper is organized as follows: Section 2,
presents the literature of the WPD and section 3 contains the
proposed methodology of this paper. Description of the
simulated signals and presentation of the modeled machine is
given in section 4, whereas section 5 is dedicated to the
results and discussions. Finally, the main conclusion is given
in Section 6.
II.
The wavelet transform (WT) is a signal processing
method with resolution adaptive to the size of the object or
the analyzed detail. This technique decomposes the signal in
base of particular functions called wavelets which have the
property of being able to be well localized in time or
frequency due to its basic elements, generated by translation
b and dilatation a from a function ,mother wavelet, as shown
in (1):
Ψa,b t =
1
a
Ψ
t−b
a
)1(
There three types of wavelet transform: continuous
wavelet transform (CWT), discrete wavelet transform
(DWT) and Wavelet packet decomposition (WPD).
Wavelet Packet Decomposition (WPD), proposed by
Coifman and Wickerhauser, overcomes the disadvantages of
the continuous and discrete wavelet transform by generating
at each layer, approximation coefficients containing low
frequency information and detail coefficients containing high
frequency information of the original signal without loss or
redundancy of data [10, 12].
Fig.1 illustrates the wavelet packet decomposition tree
principle.
This work aims to address the supply voltage imbalance
defect using a simple and efficient method combining CSV
analysis with WPD energy used previously to diagnose load
unbalance defect [10]. As the supply voltage imbalance
defect causes a remarkable imbalance in three phase stator
current and subsequently the CSV analysis technique
prevents the loss of information, whereas, the energy levels
obtained by WPD coefficients make differences between
healthy and faulty states under several severities. Moreover,
with WPD, the time-frequency components of the signal can
be determined, and a good understanding of what is
contained in the signal is given, this technique can also be
used to remove noise from the signal [11].
978-1-6654-7108-4/22/$31.00 ©2022 IEEE
WAVELET PACKET DECOMPOSITION
Fig.1 WPD tree
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The improved signal decomposition capabilities makes
WPT an attractive tool for detecting and distinguishing
transients with high frequency characteristics [11].
The approach adopted here, is based on the mathematical
model. Thus, the blocks of the modeling can be resumed by
the following equation[13, 14]:
𝑉𝑎𝑏𝑐 = 𝑅 𝑖𝑎𝑏𝑐 +
The WPD coefficients dj+1,b , given by (Mallat 1999) [11],
are defined by the following expressions:
dj+1,2n =
dj+1,2n+1 =
j-1
h m − 2k dj,n
m g m − 2k dj,n
m
𝑉𝑑𝑞 = 𝐴 𝑉𝑎𝑏𝑐
)3(
)4(
𝑖𝑑𝑞 = 𝐴 𝑖𝑎𝑏𝑐
With A Park transformation matrix.
PROPOSED METHODOLOGY
A =
In this work, the proposed method to diagnose the supply
voltage imbalance defect is based on two steps: (1)
Calculation of current space vector CSV of the simulated
three phase current signals; (2) Computing the energy of
WPD terminal sub-bands coefficients of the resultant signal
obtained from the CSV analysis technique.
IV.
𝐿 𝑖𝑎𝑏𝑐 + 𝑀 𝑖𝑎𝑏𝑐
The Park transformation is defined as:
)2(
With: n= 0,1, 2..., 2 : the numbered nodes of level j.
III.
𝑑
𝑑𝑡
2
3
cos θ
−sin θ
cos θ −
2π
−sin θ −
3
2π
3
cos θ +
2π
−sin θ +
3
2π
)5(
3
The electromagnetic torque Cem is:
3
Cem = pM Iqs Idr -Ids Iqr
2
)6(
SIMULATED SIGNALS DESCRIPTION
An induction motor powered with three voltage sources
is simulated, and characterized as detailed in TABLE 1. The
supply voltage unbalance is modeled (in case of amplitude
unbalance with 10%, 20%, 30% and 40%) using
Matlab/Simulink. In order to simulate the system operation,
it is important to have the machine model taking in account
its transient behavior during load and voltage variations.
Where: M: mutual stator-rotor inductance; p: pair of pole
number; Iqs, Ids, Iqr, Idr: quadratic and direct currents for the
stator and the rotor respectively.
The block diagram of Simulink model of induction motor
is designed as illustrated in fig.2.
Park transformation
Fig. 2 Simulink model of induction motor
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1
ip (t)
1
in (t) = 3 1
1
i0 (t)
2
TABLE I. Induction motor parameters
Rotor Resistance
6.3 Ω
Stator Resistance
10 Ω
Inertia moment
0.02 Kgm²
Friction coefficient
0.000 Nm
Rotor inductance
0.4642 H
Stator inductance
0.4612 H
Mutual inductance
0.4212 H
V.
a2
a
1
1
2
2
𝑖1 (𝑡)
𝑖2 (𝑡)
𝑖3 (𝑡)
)7(
As long as the system is balanced, only the positive
sequence will be considered, and so:
𝑖 𝑡 =
1
pole pairs
a
a2
1
3
)8(
𝑖1 (𝑡) + 𝑎𝑖2 (𝑡) + 𝑎2 𝑖3 (𝑡)
Where: a=e-j2/3 is the Fortescue operator.
The resultant signal i is represented by Fig. 4 in healthy
and faulty states.
RESULTS AND DISCUSSION
Fig.3 represents three phase currents, in case of: healthy
state and amplitude unbalance of 10% in phase A.
a)
b)
Fig. 4 Stator current space vector trajectory in case of healthy state
and amplitude unbalance of 10% in phase A
The WPD of the CSV signal is carried out with
Daubechies 'db44' mother wavelet , the most suitable for
current signal decomposition, and the decomposition level is
calculated by the relation expressed below [16]:
N=int
Fig.3 Three phase currents in case of: a) Healthy state, b) Amplitude
unbalance of 10% in phase A
It is clear that in case of supply voltage unbalance in
phase A, the disturbance affects the three phase current
signals. In order to avoid any loss of information the current
space vector (CSV) technique is introduced. According to
this approach, the three-phase stator currents can be
decomposed into a sum of three balanced systems: positivesequence component (ip), negative-sequence component (in)
and zero-sequence component (io), as expressed by the
matrix below [15]:
Fig.5 represents the energy values corresponding to the
nodes of the ninth level WPD. Through these results, it is
obvious that the energy concentration is located in the node
(9.7), where the energy increases as defect severity rises
which make easy ,through this method, the distinction
f
log s f
e
log (2)
)9(
+2
With: fs: sampling frequency (fs=10000 Hz), fe: supply
frequency (fe=50Hz), and so N=9.
The energy of the WPD coefficients is calculated as:
Ej =
N
n=1
dj (n)
2
)10(
where: dj(n) are the wavelet packet coefficients.
between the healthy state and different defect severities
contrary to previous cited works[5–9] that distinguish only
between healthy and faulty states without considering defect
severities.
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Fig.5 Energy values at ninth level nodes
VI.
CONCLUSION
This paper is aimed at investigating the WPD energy
method in order to diagnose the supply voltage imbalance
defect, using the simulated three phase stator current signals.
The CSV analysis technique is introduced to enhance the
precision of the proposed methodology. From the obtained
results, it can be concluded that the proposed combined
techniques are effective in diagnosing induction motor
supply voltage imbalance and can be extended to other
induction motor external or internal defects.
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