A current sensor fault diagnosis method based on phase angle shift technique applying to induction motor drive

International Journal of Power Electronics and Drive Systems (IJPEDS)
Vol. 13, No. 3, September 2022, pp. 1315~1325
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v13.i3.pp1315-1325  1315
Journal homepage: http://ijpeds.iaescore.com
A current sensor fault diagnosis method based on phase angle
shift technique applying to induction motor drive
Quang Sy Vu1
, Cuong Dinh Tran2
, Bach Hoang Dinh2
, Chau Si Thien Dong3
, Hung Tan Huynh3
,
Huy Xuan Phan4
1
Faculty of Automotive Engineering, School of Engineering and Technology, Van Lang University, Ho Chi Minh City, Vietnam
2
Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University,
Ho Chi Minh City, Vietnam
3
Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4
Long An Power Company, Tan An City, Vietnam
Article Info ABSTRACT
Article history:
Received Apr 18, 2022
Revised May 25, 2022
Accepted June 29, 2022
An improved method using the phase angle shift characteristic of the sine
wave is proposed to diagnose the fault states of the current sensors in an
induction motor drive. The induction motor drive (IMD) system applied in
this study uses the field-oriented control (FOC) loop with integrated two
current sensors and a speed encoder to control the rotor speed. The space
vectors created from the phase angle shift technique are compared to the
estimated current for the fault diagnosis algorithm. Various types of current
sensor failures are investigated by MATLAB/Simulink software to check the
effectiveness of the proposed method. The simulation results have proved
the performance of the proposed method in enhancing the reliability and
stability of the IMD system.
Keywords:
Current sensor fault
Diagnosis algorithm
Fault-tolerant control
Phase angle shift
Three-phase current This is an open access article under the CC BY-SA license.
Corresponding Author:
Cuong Dinh Tran
Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering
Ton Duc Thang University
19 Nguyen Huu Tho, District 7, Ho Chi Minh City, Vietnam
Email: trandinhcuong@tdtu.edu.vn
NOMENCLATURE
𝑖𝑖𝑆𝑆
𝑆𝑆
/𝑖𝑖𝑅𝑅
𝑆𝑆
Stator/ Rotor current vector in [αβ]
𝜓𝜓𝑆𝑆
𝑆𝑆
/𝜓𝜓𝑅𝑅
𝑆𝑆
Stator/ Rotor flux vector in [αβ]
𝑢𝑢𝑆𝑆𝑆𝑆, 𝑢𝑢𝑆𝑆𝑆𝑆 Stator voltage components in [αβ]
𝑢𝑢𝑆𝑆𝑆𝑆, 𝑢𝑢𝑆𝑆𝑆𝑆 Stator voltage components in [xy]
𝑖𝑖𝑆𝑆𝑆𝑆/𝑖𝑖𝑆𝑆𝑆𝑆 Flux current/ Torque current
𝜔𝜔𝑚𝑚 Mechanical angular speed
𝜔𝜔𝑟𝑟 Electrical angular speed
𝜓𝜓𝑅𝑅𝑅𝑅, 𝜓𝜓𝑅𝑅𝑅𝑅 Rotor flux components in [x y]
1. INTRODUCTION
The three-phase induction motor with ideal size, low cost, and high durability is one of the most
popular motor types in industrial applications. Robust developments in power electronics and soft computing
have accelerated the penetration of the induction motor into speed control applications [1]. A modern

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 13, No. 3, September 2022: 1315-1325
1316
induction motor drive IMD system has four main parts: a power supply inverter, an induction machine, a soft
computing controller, and feedback sensors. Control requirements such as flux and the motor speed will be
set in the controller as reference signals. Besides, the sensors provide signs showing the instantaneous
operating state of the IMD system to feedback to the controller. Control algorithms will use reference signals,
feedback signals, and motor parameters to generate control commands for the switching process of the
inverter, thereby providing the proper power to the motor.
Many effective methods have been researched and applied for speed control of IMD systems,
divided into two significant families, including scalar control and vector control. Scalar control with the
simple algorithm, the typical hardware configuration is appropriate for applications that do not need high
precision [2]-[4]. In contrast, vector control is suitable for the speed control and torque control of high-
performance applications [5]. One of the typical vector control techniques is the field-oriented control (FOC)
method, which can precisely control flux and moment based on the stator current separation technique [6].
Based on the control method of the separately excited direct current DC motor, the stator current vector is
separated into two perpendicular components in the rotation coordinate system [xy], whose x-axis is the axis
corresponding to the rotor flux [7]-[9]. The current component on the x-axis is used to maintain the rotor flux
as a constant during operation. Otherwise, the current on the y-axis is applied to adjust the electrical torque
for the speed control of IMD [10], [11].
The feedback current and rotor speed from sensors play a core role in the success of the FOC control
method. Inaccuracy of the feedback signals can cause instability in the operation of the drive system, and in
severe cases, it can damage equipment and lead to negative economic impacts. In recent years, sensor fault-
tolerant control (FTC) methods have been focused on improving the reliability and stability of IMD
systems [12]. FTC techniques are usually divided into two groups, Passive FTC and Active FTC [13].
Conventional passive FTC techniques are incorporated in the general function of the controller to handle a
predefined number of sensor failures. Active FTC techniques focus on diagnosing the fault types,
determining the faulty sensor, performing false signal isolation, and reconfiguring the control system. Most
speed sensor fault diagnosis uses the comparison methods of rotor speed signals such as reference speed,
measured speed, and estimated speed to determine the speed sensor fault [14]. Meanwhile, the current
sensor’s fault diagnosis and identification techniques have been studied in various ways and different
approaches. Therefore, this study focuses on researching solutions for diagnosing current sensor faults in
IMD systems controlled by the FOC method.
Current sensor failures occur in a variety and complexity, often divided into soft and hard fault
types [13], [15]. Soft sensor faults can degrade the performance of the IMD system; if these faults occur for a
long time, they can lead to severe impacts on the operation. Soft sensor fault type includes drift, bias, scaling
faults, etc. Hard sensor fault, known as a complete failure, is a type of sensor fault where the signal is
completely lost; this fault is very severe and can immediately negatively impact the system’s operation. Hard
sensor fault needs to be diagnosed and handled as soon as possible to ensure the safety of IMD.
Kirchoff’s current law is often applied to detect and locate the faulty sensor [16]. However, the
principle of Kirchoff’s law is not possible to diagnose the faulty current sensor in an IMD using two current
sensors. Najafabadi et al. [17], the authors use the difference between root mean square values of the phase
currents and the estimated current to create the current indexes for current fault detection. This method
diagnoses the current sensor accurately, but the fault diagnosis time is extended, especially in the low-speed
zone. Chakraborty and Verma [18], the authors proposed an Axes transformation to detect the current sensor
fault. The measured currents are transferred into two coordinate systems [αβ], each with an α-axis
corresponding to each phase current. Besides, two estimators are also used to create the estimated currents
from current components in the rotating frame [xy] of the FOC loop. In the respective coordinate systems,
each pair of current vectors will be compared to determine the state of each current sensor. Yu et al. [19], the
voltage in the system [abc] is transformed into the coordinate systems [αβ] corresponding to the phase
currents. Therefore, the estimated current vectors will have an α-axis corresponding to each measured
current. The signals of the measured current, the estimated current, and the estimated flux are combined into
a function for determining the state of each current sensor. Extended kalman filter (EKF) is applied to
provide the estimated stator current for the diagnosis algorithms in the article [20]. In the healthy condition,
the difference between sensor outputs and outputs of EKF is equal to zero. When the current sensor faults
occur, leading to a higher residual than a predefined threshold, thus the wrong phase current can be detected.
Tran et al. [21] proposed a current sensor fault diagnosis based on a sine waveform and space vector
combination. The comparison between the sine current and its delay signal is applied to detect the hard
sensor fault; besides, the comparison algorithm between the current space vectors is used to diagnose the soft
sensor fault. The advantage of this method is to quickly detect sensor faults to ensure continuous and stable
operation of the system.

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
A current sensor fault diagnosis method based on phase angle shift technique … (Quang Sy Vu)
1317
This paper proposes a new approach for the current sensor fault diagnosis technique in an IMD
system using two current sensors. Each phase current combines two ±120 degree phase shift signals to create
an independent measured current space vector. Besides, the mathematical model of the induction motor is
also applied to estimate a virtual current space vector. The current space vectors will be compared to
diagnose the fault condition and locate the faulty sensor accurately. After identifying the defective sensor, the
FTC function isolates the failure signal from the control system. Virtual current signals that replace false
signals are used in control algorithms to ensure the continuous and stable operation of the IMD [22]-[24].
The performance of the proposed method will be tested with various sensor fault types by
MATLAB/Simulink software. The simulation results have proved the proposed method to accurately
diagnose the fault status of the current sensors for both soft fault and hard fault.
2. DIAGNOSIS METHOD FOR CURRENT SENSOR FAULTS
The content in this section consists of two main parts: the mathematical model of the IMD system
will be described in part one, and the diagnosis algorithm in part two.
2.1. Mathematical model of induction motor
The electromagnetic relationship in the induction motors is a complex nonlinear relationship
described by differential equations in stationary coordinates [αβ] as:
𝑢𝑢𝑆𝑆
𝑆𝑆
= 𝑅𝑅𝑆𝑆𝑖𝑖𝑆𝑆
𝑆𝑆
+
𝑑𝑑𝛹𝛹𝑆𝑆
𝑆𝑆
𝑑𝑑𝑑𝑑
(1)
0 = 𝑅𝑅𝑅𝑅𝑖𝑖𝑅𝑅
𝑆𝑆
+
𝑑𝑑𝛹𝛹𝑅𝑅
𝑆𝑆
𝑑𝑑𝑑𝑑
− 𝑗𝑗𝜔𝜔𝑟𝑟𝛹𝛹𝑅𝑅
𝑆𝑆
(2)
𝛹𝛹𝑆𝑆
𝑆𝑆
= 𝐿𝐿𝑆𝑆𝑖𝑖𝑆𝑆
𝑆𝑆
+ 𝐿𝐿𝑚𝑚𝑖𝑖𝑅𝑅
𝑆𝑆
(3)
𝛹𝛹𝑅𝑅
𝑆𝑆
= 𝐿𝐿𝑚𝑚𝑖𝑖𝑆𝑆
𝑆𝑆
+ 𝐿𝐿𝑅𝑅𝑖𝑖𝑅𝑅
𝑆𝑆
(4)
In this paper, the FOC technique is applied to precisely control the speed and torque for the IMD. The
general block diagram of the IMD system using the FOC method for speed control is shown in Figure 1.
Figure 1. Block diagram of IMD using FOC

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The three-phase current from the sensors will be transformed to a current space vector in a
stationary coordinate system [αβ] and a rotating coordinate system [xy]. Clark’s and Park’s formulas [25] are
used to analyze the current components in reference frame systems, corresponding to block T2/2 and T2/3.
Clark's fomulas: �
𝑖𝑖𝑆𝑆𝑆𝑆
� = �
10
1
√3
2
√3
� �
𝑖𝑖𝑎𝑎
𝑖𝑖𝑏𝑏
� (5)
Park's fomulas: �
� = �
𝑐𝑐𝑐𝑐𝑐𝑐 𝛾𝛾 𝑠𝑠𝑠𝑠𝑠𝑠 𝛾𝛾
− 𝑠𝑠𝑠𝑠𝑛𝑛 𝛾𝛾 𝑐𝑐𝑐𝑐𝑐𝑐 𝛾𝛾
� �
� (6)
Magnetic current “im,” synchronous speed “ωe,” rotor flux angle “γ” are calculated through the IM current
model. The stator current components in stationary coordinate [αβ] are converted into rotating coordinate
[dq] corresponding to the rotor axis, as (7).
�
� = �
𝑐𝑐𝑐𝑐𝑐𝑐 𝜀𝜀 𝑠𝑠𝑠𝑠𝑠𝑠 𝜀𝜀
− 𝑠𝑠𝑠𝑠𝑠𝑠 𝜀𝜀 𝑐𝑐𝑐𝑐𝑐𝑐 𝜀𝜀
� �
�
Where:
𝜀𝜀 = ∫ 𝜔𝜔𝑟𝑟𝑑𝑑𝑑𝑑 ; 𝜔𝜔𝑟𝑟 = 𝑝𝑝𝜔𝜔𝑚𝑚 (7)
The components of “im” in the rotor rotating coordinate [dq] system are calculated as in (8).
�
𝑖𝑖𝑚𝑚𝑚𝑚
� = �
1
𝑇𝑇𝑅𝑅𝑠𝑠+1
0
0
1
𝑇𝑇𝑅𝑅𝑠𝑠+1
� �
� (8)
The “im” current in rotor rotating coordinate [dq] is transformed back to [αβ] system for determining the
synchronous speed and rotor flux angle, as in:
�
� = �
𝑐𝑐𝑐𝑐𝑐𝑐 𝜀𝜀 − 𝑠𝑠𝑠𝑠𝑠𝑠 𝜀𝜀
𝑠𝑠𝑠𝑠𝑠𝑠 𝜀𝜀 𝑐𝑐𝑐𝑐𝑐𝑐 𝜀𝜀
� �
𝑖𝑖𝑚𝑚𝑞𝑞
� (9)
�
𝛾𝛾 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(
)
𝑖𝑖𝑚𝑚 = �(𝑖𝑖𝑚𝑚𝑚𝑚
2 + 𝑖𝑖𝑚𝑚𝑚𝑚
2
)
(10)
The PI controllers are applied in the FOC loop to modulate the deviations to become reference voltage
signals. The PWM technique will modulate the reference voltage signal to create a switching pulse that
drives the inverter for supplying power to the motor.
2.2. Current sensor fault diagnosis algorithm based on phase angle shift technique
Because the control principle is based on current space vector separation, the measured stator
current plays a crucial role in IMD speed control using FOC method. Inaccuracy of the feedback current
signals will seriously affect the control efficiency. An FTC function can be integrated into IMD’s control
system to enhance the reliability and stability of the system. A block diagram of the FOC integrated FTC
function is shown in Figure 2.
The FTC unit receives the measured current and feedback speed signals to determine the state of the
current sensors by the diagnosis algorithms. If the current sensors are healthy, the output current signal
transfers to the FOC loop as the measured current signal. Otherwise, if the current sensors are damaged, the
FTC will indicate the faulty sensor, and the output current will be the estimated current. Figure 3 presents a
block diagram of the FTC unit. In steady-state, the rotor slip can be calculated from measured stator current, rotor
speed, and time constant, as (11).
𝜔𝜔𝑠𝑠𝑠𝑠 =
𝑇𝑇𝑅𝑅𝑖𝑖𝑆𝑆𝑆𝑆
(11)
The electrical synchronous speed can be determined from the rotor speed and rotor slip, as in (12).
𝜔𝜔𝑒𝑒 = 𝜔𝜔𝑟𝑟 + 𝜔𝜔𝑠𝑠𝑠𝑠 (12)

1319
Figure 2. IMD applying FOC integrated FTC function
Figure 3. Block diagram of the FTC controller
In (13) presents the method of determining the current cycle corresponding to the actual operating
speed of the IMD.
𝑇𝑇 =
2𝜋𝜋
𝜔𝜔𝑒𝑒
(13)
Each phase current will be delayed, corresponding to T/3 and 2T/3 to create two delay-currents, as shown in (14).
⎩
⎨
⎧
𝑖𝑖𝑗𝑗(𝑛𝑛) = 𝑖𝑖𝑗𝑗(𝑡𝑡) = 𝐼𝐼𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠( 𝜔𝜔𝑒𝑒𝑡𝑡)
Delay[T/3]: 𝑖𝑖𝑗𝑗(𝑛𝑛 − 1) = 𝑖𝑖𝑗𝑗(𝑡𝑡 −
𝑇𝑇
3
) = 𝐼𝐼𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠( 𝜔𝜔𝑒𝑒(𝑡𝑡 −
𝑇𝑇
3
)) = 𝐼𝐼𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠( 𝜔𝜔𝑒𝑒𝑡𝑡 −
2𝜋𝜋
3
)
Delay[2T/3]: 𝑖𝑖𝑗𝑗(𝑛𝑛 − 2)𝑖𝑖𝑗𝑗(𝑡𝑡 −
2𝑇𝑇
3
) = 𝐼𝐼𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠( 𝜔𝜔𝑒𝑒(𝑡𝑡 −
2𝑇𝑇
3
)) = 𝐼𝐼𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠( 𝜔𝜔𝑒𝑒𝑡𝑡 −
4𝜋𝜋
3
)
(14)
These currents will be combined to generate a current space vector by formulas (15), (16).
�
𝑖𝑖𝑗𝑗𝑗𝑗𝑗𝑗
𝑖𝑖𝑗𝑗𝑗𝑗𝑗𝑗
� = �
2
3
−
1
3
−
1
3
0
1
√3
−
1
√3
� �
𝑖𝑖𝑗𝑗(𝑛𝑛)
𝑖𝑖𝑗𝑗(𝑛𝑛 − 1)
𝑖𝑖𝑗𝑗(𝑛𝑛 − 2)
� (15)

 ISSN: 2088-8694
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𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = �𝑖𝑖𝑗𝑗𝑗𝑗𝑗𝑗
2
+ 𝑖𝑖𝑗𝑗𝑗𝑗𝑗𝑗
2
(16)
The proposed sensor fault diagnosis method is based on an algorithm comparing the magnitudes of the phase
shift current vectors and the estimated current vector. During operation, the motor parameter variations by
the influence of temperature will lead to the inaccuracy of the virtual current in the direct estimation methods.
Therefore, the current estimation algorithm must be selected appropriately to avoid the excessive influence of
the motor parameters. The Luenberger observer [23] using motor parameters and feedback rotor speed to
estimate the virtual current vector could be considered a reasonable selection.
�
𝑑𝑑𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
𝑑𝑑𝑑𝑑
= −𝐴𝐴𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝐵𝐵𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝐶𝐶𝜔𝜔𝑟𝑟𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝐷𝐷𝑢𝑢𝑆𝑆𝑆𝑆 − 𝐻𝐻1𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝐻𝐻2𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
𝑑𝑑𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
𝑑𝑑𝑑𝑑
= −𝐴𝐴𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝐵𝐵𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 − 𝐶𝐶𝜔𝜔𝑟𝑟𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝐷𝐷𝑢𝑢𝑆𝑆𝑆𝑆 − 𝐻𝐻2𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐻𝐻1𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
�
𝑑𝑑𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
𝑑𝑑𝑑𝑑
= 𝐸𝐸𝑖𝑖𝑆𝑆𝛼𝛼𝛼𝛼𝛼𝛼𝛼𝛼 − 𝐹𝐹𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 − 𝜔𝜔𝑟𝑟𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 − 𝐻𝐻3𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝐻𝐻4𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
𝑑𝑑𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
𝑑𝑑𝑑𝑑
= 𝐸𝐸𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐹𝐹𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 − 𝜔𝜔𝑟𝑟𝜓𝜓𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 − 𝐻𝐻4𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐻𝐻3𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = �𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
2
+ 𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
2
(17)
Where:
𝐴𝐴 =
𝑅𝑅𝑆𝑆𝐿𝐿𝑅𝑅
2 +𝑅𝑅𝑅𝑅𝐿𝐿𝑚𝑚
2
𝜎𝜎𝐿𝐿𝑆𝑆𝐿𝐿𝑅𝑅
2 ; 𝐵𝐵 =
𝐿𝐿𝑚𝑚𝑅𝑅𝑅𝑅
𝜎𝜎𝐿𝐿𝑆𝑆𝐿𝐿𝑅𝑅
2 ; 𝐶𝐶 =
𝐿𝐿𝑚𝑚
𝜎𝜎𝐿𝐿𝑆𝑆𝑅𝑅𝑅𝑅
;
𝐷𝐷 =
1
𝜎𝜎𝐿𝐿𝑆𝑆
; 𝐸𝐸 =
𝐿𝐿𝑚𝑚𝑅𝑅𝑅𝑅
𝐿𝐿𝑅𝑅
; 𝐹𝐹 =
𝑅𝑅𝑅𝑅
𝐿𝐿𝑅𝑅
; 𝜎𝜎 =
𝐿𝐿𝑆𝑆𝐿𝐿𝑅𝑅−𝐿𝐿𝑚𝑚
2
𝐿𝐿𝑆𝑆𝐿𝐿𝑅𝑅
;
𝐻𝐻1 = (𝑔𝑔 − 1)(
1
𝜎𝜎𝑇𝑇𝑆𝑆
+
1
𝜎𝜎𝑇𝑇𝑅𝑅
); 𝐻𝐻2 = −(𝑔𝑔 − 1)𝜔𝜔𝑟𝑟; 𝐻𝐻4 = −(𝑔𝑔 − 1)
𝜎𝜎𝐿𝐿𝑆𝑆𝐿𝐿𝑚𝑚
𝐿𝐿𝑅𝑅
𝜔𝜔𝑟𝑟;
𝐻𝐻3 = (𝑔𝑔2
− 1) �(
1
+
1
)
𝐿𝐿𝑅𝑅
−
𝐿𝐿𝑚𝑚
𝑇𝑇𝑅𝑅
� +
𝐿𝐿𝑅𝑅
(
1
+
1
)(𝑔𝑔 − 1);
𝑔𝑔 > 1;
The magnitude of the current space vectors based on the phase angle shift technique will be compared with
the magnitude of the virtual space vectors to determine the current sensor fault of each phase.
𝐼𝐼𝐼𝐼(�𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 − 𝐼𝐼𝑠𝑠𝑝𝑝𝐸𝐸� > 𝑇𝑇ℎ𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑜𝑜𝑜𝑜𝑜𝑜)
{𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 1; }
𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 (18)
{𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 0; }
The “Threshold” value is the maximum difference between the phase shift current space vector and
the estimated current vector in the healthy sensor condition. This value is an essential factor in determining
the success of the diagnosis algorithm. Especially when a load change occurs suddenly, if the selected
“Threshold” value is not suitable, the diagnosis method can confuse the transient operating condition with the
sensor fault state, thus leading to make inappropriate control decisions. Based on many simulations
performed, this study recommends a value of 15% of the rated current value for the Threshold. After
diagnosing the failure current signal, the FTC unit will isolate and replace the fault signal with the estimated
current and indicate the faulty current sensor to be fixed and replaced at an appropriate time.
3. SIMULATION RESULTS
An IMD model corresponding to the embedded FTC function of the FOC method in Figure 2 is
applied to simulate the current sensor fault cases in the Matlab/Simulink environment. The parameter of the
three-phase motor used in the simulations is present in Table 1, and the reference motor speed is depicted in
Figure 4. Four types of current sensor failures will be diagnosed in this study, including total, scaling, bias,
and drift failures.
First, the diagnosis algorithm will be implemented to determine the effectiveness against the total
fault, a typical type of the hard sensor fault group. IMD applies the FOC method to control the rotor speed
according to the reference speed. Assuming that the current of the A-phase sensor is completely damaged at 2
seconds, the value of the feedback current is equivalent to zero, as shown in Figure 5(a). The fault indication

1321
flag of the A-phase is immediately set to a high level, while the flag of the B-phase remains at a low level,
Figure 5(b). The fault diagnosis function immediately isolates the fault signal and replaces it with an
estimated current to feed the FOC loop, as shown in Figure 5(c). Figure 5(d) has proved that the IMD system
still maintains stable operation even in the current sensor fault condition.
Table 1. Parameters of three-phase motor
Description Symbol Unit Value
Rated Torque Tr Nm 14.8
Rated Speed ωr rpm 1420
Rated current I A 4.85
Number of pole pairs p - 2
Stator/Rotor Resistance RS/RR Ω 3.179/2.118
Magnetizing Inductance Lm H 0.192
Stator/Rotor Inductance LS/LR H 0.209/0.209
Figure 4. Reference speed for the simulations
(a)
(b)
(c) (d)
Figure 5. FTC against total fault: (a) measured current, (b) current sensor fault indication,
(c) output current of FTC unit, and (d) rotor speed
Next, some soft sensor faults are investigated to verify the effectiveness of the proposed diagnosis
method. At the 2-second time, scaling fault occurs at the B-phase sensor, and the amplitude of the B-phase
current is amplified three times, as in Figure 6(a). As in the above case, the defective sensor is determined
rapidly and accurately. Figures 6(b)-6(d) show that the IMD system operates stably and reliably. In the three-
study, the diagnosis method is carried out for bias failure of the A-phase current sensor, and a value of

 ISSN: 2088-8694
1322
2 Amps biases the A-phase current at 2 seconds, as in Figure 7(a). The fault diagnosis function worked
correctly, and the wrong signal was replaced by the estimated current corresponding to Figures 7(b), 7(c).
The performance of the IMD system is firmly maintained against current sensor failure, as in Figure 7(d).
The drift fault is examined in case four. At 2s, B-phase current drifts, as shown in Figure 8(a). In the
initial stage of the drift failure, the change of the B-phase current is still small. It has not seriously affected
the operation of the system, so the system still maintains the process with the measured signal. However,
when the deviation of the wrong signal increased to a level that could affect the stability of the IMD system,
the diagnosis function detected and accurately located the fault, as shown in Figure 8(b). The FTC unit has
provided proper output currents to the FOC loop to ensure the reliable stability of the system, as in
Figures 8(c) and 8(d). The proposed algorithm has successfully diagnosed various types of sensor fault,
including hard sensor fault and soft sensor fault. The proposed diagnosis method has proven its effectiveness
in enhancing the reliability of the IMD system against current sensor faults.
(a) (b)
(c) (d)
Figure 6. FTC against scaling fault: (a) measured current, (b) current sensor fault indication, (c) output
current of FTC unit, and (d) rotor speed
(a) (b)
(c) (d)
Figure 7. FTC against bias fault: (a) measured current, (b) current sensor fault indication, (c) output current
of FTC unit, and (d) rotor speed

1323
(a) (b)
(c) (d)
Figure 8. FTC against drift fault: (a) measured current, (b) current sensor fault indication, (c) output current
of FTC unit, and (d) rotor speed
4. CONCLUSION
A fault diagnosis method based on the phase shift technique is proposed to detect the current sensor
faults during the operation of the IMD. Each measured current will be shifted its phase angle corresponding
to T/3 and 2T/3 to create two delay-currents. As a result, the measured space vector is formed from each
phase current and its two delay phases. The magnitude of each measured current vector will be compared
with the estimated current to determine the operation state of the current sensors. The simulation results
proved that the proposed algorithm effectively detects current sensor fault types, including hard and soft
faults. The IMD system still maintains stable operation when the current sensor fault occurs; the indication
flags accurately identify the fault phase. Corresponding faulty current sensors will be fixed or replaced at the
appropriate time.
ACKNOWLEDGEMENTS
The authors would like to thank Ton Duc Thang University and Van Lang University, Vietnam.
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BIOGRAPHIES OF AUTHORS
Quang Sy Vu is a lecturer in Faculty of Automotive Engineering, School of
Engineering and Technology, Van Lang University, Ho Chi Minh City, Vietnam. He received
the B.E., M.S., and Ph.D. degrees in electrical engineering, all from Peter the Great St.
Petersburg State Polytechnical University in 2012, 2014, and 2019 respectively. He can be
contacted at email: sy.vq@vlu.edu.vn.
Cuong Dinh Tran is a lecturer in the Electrical Engineering Department, Faculty
of Electrical-Electronic Engineering at Ton Duc Thang University. He received his B.E., M.E
degrees from Ho Chi Minh City University Of Technology, Vietnam, and Ph.D. degree from
VSB-Technical University of Ostrava, the Czech Republic, in 2005, 2008, and 2020. His
research interests include the field of modern control methods and intelligent algorithms in
motor drives. He can be contacted at email: trandinhcuong@tdtu.edu.vn.

1325
Bach Hoang Dinh is the head of the Electrical Engineering Department, Faculty
of Electrical-Electronic Engineering at Ton Duc Thang University. He received B.E., M.E
degrees from Vietnam National University-Hochi Minh City and Ph.D. degree from Heriot-
Watt University, Edinburgh, the United Kingdom, in 1995, 1998, and 2009. His research
interests are intelligent and optimal control, computer vision, robotics, power electronics,
SCADA, and industrial communication networks. He is a member of the IEEE Industrial
Electronics Society. He can be contacted at email: dinhhoangbach@tdtu.edu.vn.
Chau Si Thien Dong is now a lecturer in the Faculty of Electrical and Electronics
Engineering of Ton Duc Thang University. She received her M.Sc. and Ph.D. degrees from Ho
Chi Minh City University Of Technology, Vietnam, and VSB-Technical University of
Ostrava, the Czech Republic, in 2003 and 2017. Her research interests include nonlinear
control, adaptive control, robust control, neural network, and the application of modern control
methods in the control of electrical drives. She can be contacted at email:
dongsithienchau@tdtu.edu.vn.
Hung Tan Huynh is studying the Master’s program in Electrical Engineering at
Faculty of Electrical-Electronic Engineering, Ton Duc Thang University. He received his B.E
degree from Ton Duc Thang University, Vietnam, in 2013. His research interests include the
field of modern control methods and intelligent algorithms in motor drives. He can be
contacted at email: huynhtanhung@tdtu.edu.vn.
Huy Xuan Phan is working at Long An Power company, Long An province,
Vietnam. He received his B.E., and M.E, degrees from Ho Chi Minh City University Of
Technology in 2002 and 2010. His research interests include modern control methods of
electrical drives, automatic control systems, intelligent control systems, and operation and
control power systems. He can be contacted at email: huypcla@gmail.com.

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