In this paper, a fault detection scheme for DClink voltage sensor and its fault tolerant control strategy for threephase AC/DC/AC PWM converters are proposed, where the Luenberger observer is applied to estimate the DClink voltage. The Luenberger observer is based on a converter model, which is derived from the voltage equations of a gridside converter and the power balance on a DC link. A fault of the voltage sensor is detected by comparing the measured value of the DClink voltage with the estimated one. When a sensor fault is detected, a fault tolerant control strategy is performed, where the estimated DClink voltage is used for the feedback control. The estimation error from the observer is about 1.5 V, which is sufficiently accurate for feedback control. In addition, it is shown that the observer performance is robust to parameter variations of the converter. The validity of the proposed method has been verified by simulation and experimental results.
I. INTRODUCTION
AC/DC/AC PWM converters are widely used in various industrial areas such as electric machine drives, UPSs (uninterruptible power supply), UPQCs (unified power quality conditioner) and gridconnected renewable energy systems
[1]

[3]
. A research survey has reported that the failure rates of these converter are 30%, 26%, 21% and 13% due to their capacitors, printed circuit boards, semiconductors, and soldering, respectively
[4]
,
[5]
. Therefore, the reliability and performance of PWM converters has been paid a great deal of attention. Recently, fault detection and tolerant control techniques for power converters have attracted a lot of interest due to their higher reliability and lower maintenance.
Therefore, some studies on the fault detection and tolerant control of the PWM converters, which are mainly on the openor shortcircuits of switching devices and DClink capacitors, have been introduced
[6]

[12]
. However, the fault detection of the sensor and its tolerant control scheme have not been studied very much. A study on DClink voltage sensorless control has been reported
[13]
, which focuses on cost reduction rather than preparation for failures. Therefore, research on the fault diagnosis and tolerant control of DC voltage sensor is needed.
The control of a PWMVSC (voltagesource converter) requires information on the DClink voltage, and the grid voltages and currents, where the control performance depends a great deal on accurate measurements by voltage and current sensors. In the case of a malfunction of a DC voltage sensor, the DClink voltage cannot be controlled at a desired value, which may damage or trip the system. In addition, if the measured value of the DClink voltage contains a ripple component, the input current of the PWM converter is also distorted by the action of the DClink voltage controller
[14]
.
Recently, several studies have been presented to estimate DClink voltage. At first, DClink voltage monitoring was studied for gridconnected wind turbine converters
[14]
, where a combination of the PI (proportionalintegral) control and the predictive algorithm is employed to compensate for measurement errors of the DClink voltage. This method requires a high sampling frequency (equal to four times the switching frequency) with a complicated timing synchronization for the sampling and prediction of currents and voltages. Another method has been introduced, which estimates the DClink and source voltages simultaneously using a switching table and a derivative of the boost inductor current
[15]
. In this scheme, the estimation performance is sensitive to measurement noise. Furthermore, if the switching time is not chosen appropriately for the initial estimation at startup, the wrong estimation may cause an overcurrent. In another method, the DClink voltage and grid currents are estimated by a sliding mode observer
[16]
. A disadvantage of this method is that an undesirable chattering phenomenon is inevitable on the estimation variables. In addition, experimental verification of the actual system has not been provided.
In this paper, fault detection for the DClink voltage sensor and its tolerant control scheme are proposed for threephase AC/DC/AC PWM converters, where the Luenberger observer is employed to estimate the DClink voltage. For this estimation scheme, the PWM converter is modeled as a nonlinear system which results from including the power balance between the input and the output. At first, the nonlinearity of the PWM converter model is linearized by using a small signal analysis
[17]

[19]
. Then, the Luenberger observer is applied to estimate the DClink voltage, since it is known to give good performance with a fast responses and high reliability. The estimation error is less than 3% in the transient states of the load change or variations of the system parameters. The fault condition of the DC voltage sensor is discerned by comparing the measured value with the estimated one. Then, the DClink voltage is still controlled well during the sensor fault by feeding the estimated one back. The validity of the proposed estimation and control method is verified by simulation and experimental results.
II. NONLINEAR MODELING OF AC/DC PWM CONVERTERS
Fig. 1
shows the threephase AC/DC/AC PWM converters for the AC motor drives.
Threephase AC/DC/AC PWM converter.
 A. Voltage Equations
The voltage equations in a threephase AC/DC PWM converter are expressed as:
where
e_{a}
,
e_{b}
and
e_{c}
are the input phase voltages,
i_{a}
,
i_{b}
and
i_{c}
are the input currents, and
v_{a}
,
v_{b}
and
v_{c}
are the input voltages of the converter. In addition,
R_{s}
and
L_{s}
are the resistances and inductances in the AC side, respectively.
The source voltage can be rewritten in the
dq
synchronous reference frame as
[1]
:
where the superscript ‘
e
’ represents a quantity in the synchronous reference frame and ‘
p
’ denotes a differential operator.
In (4) and (5), the converter input voltages,
v_{dq}^{e}
, can be expressed as:
where
v_{dc}
is the DClink voltage, and
are the duty ratios transformed into the dq frame from the abc frame
[17]
,
[18]
.
 B. Power Balance in the DCLink
The power flow at the DClink side of the backtoback converter is shown in
Fig. 1
, and is expressed as:
where
p_{cap}
is the capacitor power,
p_{in}
is the input power flowing into the DClink from the AC source with the converter loss neglected, and
p_{out}
is the output power delivered from the DClink to the load. The input power can be expressed with the source voltage and current in the synchronous reference frame as:
The output power is given by:
where
i_{dc2}
is the output current of the DClink side.
The capacitor power is expressed as
[1]
:
where
C_{dc}
is the DClink capacitance, and
V_{dc0}
is the DClink voltage at the operating point. In order to keep the DClink voltage constant, the variation of the capacitor power is required to be zero.
 C. Nonlinear Modeling of the AC/DC PWM Converter
By rearranging equations (4) to (11), the nonlinear model of the threephase AC/DC PWM converter is described as
[20]
:
where:
III. ESTIMATION OF DCLINK VOLTAGE BY THE LUENBERGER OBSERVER
 A. Luenberger Observer
The Luenberger observer is a kind of state observer which estimates the internal state of linear systems. The state equations for the Luenberger observer are expressed as
[20]

[24]
:
where “^” indicates the estimated values, x(t) is the state vector, u(t) is the input vector, y(t) is the output vector,
A
,
B
and
C
are the system parameter matrices, and
L
is the observer gain matrix. The observer error dynamic is expressed as:
where:
.
Fig. 2
shows a block diagram of the Luenberger observer. In order to ensure that the estimation error approaches zero asymptotically from any of the initial states, the observer poles should be placed on the lefthalf plane, which is set by the gain matrix
L
. In this study, the observer poles are placed in order to have one real and two complex roots, as
p
and
α
±
jβ
, respectively
[25]
.
Block diagram of Luenberger observer.
 B. Linearization of the Nonlinear System of an AC/DC PWM Converter
First, the nonlinear system in (12) is linearized by smallsignal analysis. Then, the linear system is obtained as
[18]
,
[19]
:
where:
In (15) and (16), the uppercase variables (
) refer to the operating points in the steady state, whereas the lowercase variables (
) represent the perturbations around their operating points.
 C. Determination of the Luenberger Observer Gains
In order to obtain stable estimation for all of the ranges of the DClink voltage and the variations of the system parameters (
L_{s}
,
C_{dc}
), the observer gain matrix should be selected so that the real parts of all eigenvalues of (
A

LC
) are negative. In this case the observer gain matrix
L
is expressed as:
To determine the eigenvalues of matrix (
A

LC
), the characteristic is expressed as:
where
λ_{LO}
is the observer pole matrix as:
In this study, the observer pole locations are selected by trial and error as 15,000 and 5,000 ±
j
3,000. Then, from (17) and (19)(21), the gain matrix
L
is calculated as:
IV. FAULT DETECTION OF THE DCLINK VOLTAGE SENSOR AND TOLERANT CONTROL
 A. Fault Detection of the DCLink Voltage Sensor
With the estimation of the DClink voltage, the PWM converter can be controlled with a sensorless control algorithm, which reduces the whole system cost. Regardless of the cost reduction, the degree of redundancy for reliable operation of the system cannot be secured with only the sensorless control algorithm. For this degree of redundancy, the voltages and currents need to be both measured and estimated. Then, the converter can continue operating when a sensor fault occurs.
The sensor fails when it sends out a wrong signal with a significant error. The voltage is normally measured through hall sensors, analog scaling circuits consisting of an amplifier and a lowpass filter, and A/D (analog to digital) converters. Sensor failures sometimes occur due to a malfunction of the power supply of the sensors, and circuit board faults due to humidity, high temperature, etc
[12]
,
[14]
. This study focuses on the fault detection of DClink voltage sensors and tolerant control by a sensorless control algorithm when the failure of a sensor occurs.
The faults of DClink voltage sensors are detected by a comparison of the measured DClink voltage and the estimated one. If there is a significant difference between the two values, it is discerned that the sensor is faulty. When a sensor fault is detected, the fault flag,
F_{f}
, is set to 1, while it is zero under normal conditions.
The voltage estimation error,
r(t)
, is calculated as:
Then:
where
V_{th}
is a threshold value. In this study,
V_{th}
is chosen as 10%.
 B. Control of AC/DC PWM Converters
For threephase AC/DC/AC PWM converters, the DClink voltage is controlled by the sourceside converter, where the control structure is cascaded by an outer voltage control loop and inner dq current control loops as shown in
Fig. 3
[1]
. For DClink voltage control without any overshoot in the transient states, an IP (integralproportional) regulator is preferred, where the antiwindup technique is also employed
[26]
,
[27]
. The
dq
axis components of the source currents are regulated by PI (proportionalintegral) controllers, where the crosscoupling terms and the source voltage as a disturbance are compensated in a feedforward type, as shown in
Fig. 3
.
Control block diagram of the AC/DC PWM converter.
Flow chart of fault tolerant control of voltage sensor.
When a sensor fault is detected, a fault tolerant control scheme is activated. In this case, the measured DClink voltage is replaced by the estimated one for the feedback control, as shown in
Fig. 3
.
Fig. 4
shows a flowchart of the sensor fault detection and tolerant control algorithm.
V. SIMULATION RESULTS
Simulations using PSIM were carried out to verify the validity of the proposed method, where an induction machine drive is used as a load for the AC/DC/AC PWM converter. The system parameters for the sourceside converter are listed in
Table I
. The switching frequency of the converters is 5 kHz. The sampling time is 100 μs. In the simulation, the controller gains were chosen so that the bandwidths of the current and voltage controllers are 398 Hz and 32 Hz, respectively.
PARAMETERS OF SOURCESIDE CONVERTER
PARAMETERS OF SOURCESIDE CONVERTER
First, the estimation performance with the sliding mode observer
[16]
, for the AC/DC/AC PWM converter under stepwise load variations was investigated, as shown in
Fig. 5
. The load profile applied to the AC/DC PWM converter is no load → 3 kW →  2 kW → no load.
Fig. 5
(a) shows the daxis currents, where the estimated current converges to the actual one. However, the ripple component of the estimated current is high. The same phenomena for the qaxis current and the DClink voltage are shown in
Fig. 5
(b) and (c), respectively.
Fig. 5
(d) shows the estimation error of the DClink voltage, which is about 3 V.
Estimation performance using sliding mode observer in the case of abrupt load changes. (a) daxis currents. (b) qaxis currents. (c) DClink voltages. (d) DClink voltage estimation error.
Estimation performance of Luenberger observer in the case of abrupt load changes. (a) daxis currents. (b) qaxis currents. (c) DClink voltages. (d) DClink voltage estimationerror.
Next, the performance of the Luenberger observer, under the same conditions as those used in the case of
Fig. 5
, is illustrated in
Fig. 6
, where the observer gains designed in section III are used.
Fig. 6
(a) shows the
d
axis current, where the estimated current is nearly the same as the measured one. In addition, the
q
axis current is estimated well, even under transient conditions, as shown in
Fig. 6
(b).
Fig. 6
(c) shows the estimated and measured DClink voltages, which are very close. The estimation error is about 1.5 V, which is shown in
Fig. 6
(d). These results show that the estimation performance is excellent even when the load is changed.
Estimation performance of Luenberger observer in the case of parameter variations. (a) daxis currents. (b) qaxis currents. (c) DClink voltages. (d) DClink voltage estimation error. (e) Variation of input filter inductance and DClink capacitance.
Fig. 7
shows the estimation performance of the Luenberger observer under parameter variations, where the parameter values are assumed to be changed in the controller rather than in the actual system. An increase of 40% in the input inductance or an increase of 20% in the DClink capacitance have been considered, and are shown in
Fig. 7
(e) and (f), respectively.
Fig. 7
(a) and (b) show the
d
 and
q
axis components of the source currents, respectively. It can be seen that the estimated currents follow the measured currents well. The measured and estimated DClink voltages are shown in
Fig. 7
(c), and the estimation error is shown in
Fig. 7
(d). These results illustrate that the estimation error is less than 2 V even under parameter variations.
The control performance of the converter without the DClink voltage sensor is shown in
Fig. 8
, were the estimated value of the DClink voltage is used as the feedback control. The
d
 and
q
axis source currents follow their references well, and are shown in
Fig. 8
(a) and (b), respectively.
Fig. 8
(c) shows the DClink voltage, which is well kept at its reference of 360 V. The estimation error is shown in
Fig. 8
(d), where the maximum error in the transient state is less than 1.5 V.
Performance of DClink voltage control without DClink voltage sensor in the case of abrupt load changes. (a) daxis currents. (b) qaxis currents. (c) DClink voltages. (d) DClink voltage estimation error.
Control performance of the fault tolerant control under the sensor failure of the DClink voltage. (a) daxis currents. (b) qaxis currents. (c) DClink voltages. (d) Output power. (e) Fault flag.
Fig. 9
shows the performance of the fault tolerant control under load variations when a fault of the DClink voltage sensor occurs. For this investigation, it is assumed that the sensor fault occurs for an interval of 200 ms, which is shown in
Fig. 9
(e). It can be seen in
Fig. 9
(c) that the sensed DClink voltage is reduced to zero at the fault. However, with the fault tolerant control, the DClink voltage is controlled well at its reference, as shown in
Fig. 9
(c).
Fig. 9
(a) and (b) show the
d
 and
q
axis current components, where the control performances are good even under sensor fault and load variation conditions.
Fig. 9
(d) shows the output power of the converter.
VI. EXPERIMENTAL RESULTS
To verify the feasibility of the proposed method in practical applications, experimental tests were carried out in the laboratory for a threephase AC/DC/AC PWM converter, which feeds an induction motor drive.
Fig. 10
shows the layout of the experimental setup. The parameters of the sourceside converter are the same as those of the simulation as shown in
Table 1
. A DSP chip (TMS320VC33) is used as the main processor, and the switching frequency of the converters is 5 kHz. The experimental conditions are the same as those of the simulation.
Experimental setup.
Fig. 11
shows the estimation performance of the Luenberger observer when changing the converter parameters in the controller.
Fig. 11
(a) and (b) show an increase of 40% in both the input inductance and the DClink capacitance. It can be seen in
Fig. 11
(c) that the DClink voltage is estimated well, since the estimation error is about 7 V even in the case of parameter variations.
Fig. 11
(d) and (e) show the estimated and measured values of the
d
 and
q
axis components of the source currents, respectively.
Fig. 12
shows the control performance of the fault tolerant control for the PWM converter under a sensor failure of the DClink voltage. The fault flag shown in
Fig. 12
(a) illustrates that the DClink voltage sensor fault occurred at 4 s, while the sensed DClink voltage is zero during the fault, as shown in
Fig. 12
(b). However, the DClink voltage is well kept at its reference of 360 V with the fault tolerant control.
Fig. 12
(c) and (d) show the
d
 and
q
axis current components, where the control performances are good even under sensor fault and load variation conditions.
Fig. 12
(e) shows the output power of the converter.
Estimation performance of Luenberger observer in the case of parameter variations. (a) Variation of input filter inductance. (b) Variation of DClink capacitance. (c) DClink voltages. (d) daxis currents. (e) qaxis currents.
Control performance of the fault tolerant control under the sensor failure of the DClink voltage (exp.). (a) Fault flag. (b) DClink voltages. (c) daxis currents. (d) qaxis currents. (e) Output power.
VII. CONCLUSIONS
In this paper, a fault detection and tolerant control scheme for the DClink voltage sensors in threephase AC/DC/AC PWM converters has been proposed, where the Luenberger observer is used to estimate the DClink voltage. The linear Luenberger observer system has been built from a nonlinear model of the PWM converter, where the estimation error is about 1.5 V in the transient condition. With the proposed algorithm, the system reliability is improved, which can avoid tripping the system when sensor faults occur. The effectiveness of the proposed method has been verified by simulation and experimental results. They show that the estimation scheme works well under variations of the parameters in the PWM converter such as the input inductance and the DClink capacitance.
Acknowledgements
This work has been supported by KESRI (Korea Electrical Engineering and Science Research Institute) (2009T100100651), which was funded by MKE (Ministry of Knowledge Economy).
BIO
SooCheol Kim was born in 1985. He received his B.S. and M.S. degrees in Electrical Engineering from Yeungnam University, Gyeongsan, Korea, in 2011 and 2013, respectively. He is presently with Daewoo Shipbuilding and Marine Engineering Co., Ltd., Seoul, Korea. His current research interests include AC machine drives, the control of power converters, and electric propulsion systems.
Thanh Hai Nguyen was born in Dong Thap, Vietnam. He received his B.S. degree in Engineering from the Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam, in 2003, and his M.S. and Ph.D. degrees in Electrical Engineering from Yeungnam University, Gyeongbuk, Korea, in 2010 and 2013, respectively. He is presently working as a Research Professor at Yeungnam University. He was an Assistant Lecturer in the College of Technology, Can Tho University, Can Tho, Vietnam, from May 2003 to February 2008. His current research interests include power converters, machine drives, HVDC transmission systems, and wind power generation.
DongChoon Lee received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Seoul National University, Seoul, Korea, in 1985, 1987, and 1993, respectively. He was a Research Engineer with Daewoo Heavy Industry, Korea, from 1987 to 1988. Since 1994, he has been a faculty member in the Department of Electrical Engineering, Yeungnam University, Gyeongbuk, Korea. As a Visiting Scholar, he joined the Power Quality Laboratory, Texas A&M University, College Station, TX, USA, in 1998, the Electrical Drive Center, University of Nottingham, Nottingham, U.K., in 2001, the Wisconsin Electric Machines and Power Electronic Consortium, University of Wisconsin, Madison, Wisconsin, USA, in 2004, and the FREEDM Systems Center, North Carolina State University, Raleigh, North Carolina, USA, from September 2011 to August 2012. His current research interests include ac machine drives, the control of power converters, wind power generation, and power quality. Professor Lee is currently a Publication Editor for the Journal of Power Electronics of the Korean Institute of Power Electronics.
KyoBeum Lee received the B.S. and M.S. degrees in electrical and electronic engineering from the Ajou University, Korea, in 1997 and 1999, respectively. He received the Ph.D. degree in electrical engineering from the Korea University, Korea in 2003. From 2003 to 2006, he was with the Institute of Energy Technology, Aalborg University, Aalborg, Denmark. From 2006 to 2007, he was with the Division of Electronics and Information Engineering, Chonbuk National University, Jeonju, Korea. In 2007 he joined the School of Electrical and Computer Engineering, Ajou University, Suwon, Korea. He is an associated editor of the IEEE Transactions on Power Electronics and the Journal of Power Electronics. His research interests include electric machine drives, electric vehicles, and renewable power generations.
JangMok Kim was born in Busan, Korea, in August 1961. He received his B.S. degree from Pusan National University (PNU), Pusan, Korea, in 1988, and his M.S. and Ph.D. degrees from the Department of Electrical Engineering, Seoul National University, Seoul, Korea, in 1991 and 1996, respectively. From 1997 to 2000, he was a Senior Research Engineer with the Korea Electrical Power Research Institute (KEPRI). Since 2001, he has been with the School of Electrical Engineering, Pusan National University (PNU), where he is presently a Faculty Member. In addition, he is a Research Member of the Research Institute of Computer Information and Communication at PNU. His current research interests include the control of electric machines, electric vehicle propulsion, and power quality.
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