Fault Tolerant Control of DC-Link Voltage Sensor for Three-Phase AC/DC/AC PWM Converters

Abstract

In this paper, a fault detection scheme for DC-link voltage sensor and its fault tolerant control strategy for three-phase AC/DC/AC PWM converters are proposed, where the Luenberger observer is applied to estimate the DC-link voltage. The Luenberger observer is based on a converter model, which is derived from the voltage equations of a grid-side converter and the power balance on a DC link. A fault of the voltage sensor is detected by comparing the measured value of the DC-link voltage with the estimated one. When a sensor fault is detected, a fault tolerant control strategy is performed, where the estimated DC-link 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 grid-connected 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 short-circuits of switching devices and DC-link 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 DC-link 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 PWM-VSC (voltage-source converter) requires information on the DC-link 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 DC-link voltage cannot be controlled at a desired value, which may damage or trip the system. In addition, if the measured value of the DC-link voltage contains a ripple component, the input current of the PWM converter is also distorted by the action of the DC-link voltage controller [14].

Recently, several studies have been presented to estimate DC-link voltage. At first, DC-link voltage monitoring was studied for grid-connected wind turbine converters [14], where a combination of the PI (proportional-integral) control and the predictive algorithm is employed to compensate for measurement errors of the DC-link 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 DC-link 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 start-up, the wrong estimation may cause an overcurrent. In another method, the DC-link 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 DC-link voltage sensor and its tolerant control scheme are proposed for three-phase AC/DC/AC PWM converters, where the Luenberger observer is employed to estimate the DC-link 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 DC-link 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 DC-link 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 three-phase AC/DC/AC PWM converters for the AC motor drives.

Fig. 1.Three-phase AC/DC/AC PWM converter.

A. Voltage Equations

The voltage equations in a three-phase AC/DC PWM converter are expressed as:

where ea, eb and ec are the input phase voltages, ia, ib and ic are the input currents, and va, vb and vc are the input voltages of the converter. In addition, Rs and Ls are the resistances and inductances in the AC side, respectively.

The source voltage can be rewritten in the d-q 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, vdqe, can be expressed as:

where vdc is the DC-link voltage, and are the duty ratios transformed into the d-q frame from the a-b-c frame [17], [18].

B. Power Balance in the DC-Link

The power flow at the DC-link side of the back-to-back converter is shown in Fig. 1, and is expressed as:

where pcap is the capacitor power, pin is the input power flowing into the DC-link from the AC source with the converter loss neglected, and pout is the output power delivered from the DC-link 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 idc2 is the output current of the DC-link side.

The capacitor power is expressed as [1]:

where Cdc is the DC-link capacitance, and Vdc0 is the DC-link voltage at the operating point. In order to keep the DC-link 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 three-phase AC/DC PWM converter is described as [20]:

where:

 

III. ESTIMATION OF DC-LINK 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 left-half 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].

Fig. 2.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 upper-case variables () refer to the operating points in the steady state, whereas the lower-case 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 DC-link voltage and the variations of the system parameters (Ls , Cdc ), 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 λLO 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 ± j3,000. Then, from (17) and (19)-(21), the gain matrix L is calculated as:

 

IV. FAULT DETECTION OF THE DC-LINK VOLTAGE SENSOR AND TOLERANT CONTROL

A. Fault Detection of the DC-Link Voltage Sensor

With the estimation of the DC-link 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 low-pass 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 DC-link voltage sensors and tolerant control by a sensorless control algorithm when the failure of a sensor occurs.

The faults of DC-link voltage sensors are detected by a comparison of the measured DC-link 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, Ff, is set to 1, while it is zero under normal conditions.

The voltage estimation error, r(t) , is calculated as:

Then:

where Vth is a threshold value. In this study, Vth is chosen as 10%.

B. Control of AC/DC PWM Converters

For three-phase AC/DC/AC PWM converters, the DC-link voltage is controlled by the source-side converter, where the control structure is cascaded by an outer voltage control loop and inner d-q current control loops as shown in Fig. 3 [1]. For DC-link voltage control without any overshoot in the transient states, an IP (integral-proportional) regulator is preferred, where the anti-windup technique is also employed [26], [27]. The dq-axis components of the source currents are regulated by PI (proportional-integral) controllers, where the crosscoupling terms and the source voltage as a disturbance are compensated in a feed-forward type, as shown in Fig. 3.

Fig. 3.Control block diagram of the AC/DC PWM converter.

Fig. 4.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 DC-link 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 source-side 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.

TABLE IPARAMETERS OF SOURCE-SIDE 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 d-axis 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 q-axis current and the DC-link voltage are shown in Fig. 5(b) and (c), respectively. Fig. 5(d) shows the estimation error of the DC-link voltage, which is about 3 V.

Fig. 5.Estimation performance using sliding mode observer in the case of abrupt load changes. (a) d-axis currents. (b) q-axis currents. (c) DC-link voltages. (d) DC-link voltage estimation error.

Fig. 6.Estimation performance of Luenberger observer in the case of abrupt load changes. (a) d-axis currents. (b) q-axis currents. (c) DC-link voltages. (d) DC-link voltage estimation error.

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 DC-link 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.

Fig. 7.Estimation performance of Luenberger observer in the case of parameter variations. (a) d-axis currents. (b) q-axis currents. (c) DC-link voltages. (d) DC-link voltage estimation error. (e) Variation of input filter inductance and DC-link 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 DC-link 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 DC-link 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 DC-link voltage sensor is shown in Fig. 8, were the estimated value of the DC-link 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 DC-link 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.

Fig. 8.Performance of DC-link voltage control without DC-link voltage sensor in the case of abrupt load changes. (a) d-axis currents. (b) q-axis currents. (c) DC-link voltages. (d) DC-link voltage estimation error.

Fig. 9.Control performance of the fault tolerant control under the sensor failure of the DC-link voltage. (a) d-axis currents. (b) q-axis currents. (c) DC-link 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 DC-link 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 DC-link voltage is reduced to zero at the fault. However, with the fault tolerant control, the DC-link 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 three-phase AC/DC/AC PWM converter, which feeds an induction motor drive.

Fig. 10 shows the layout of the experimental setup. The parameters of the source-side 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.

Fig. 10.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 DC-link capacitance. It can be seen in Fig. 11(c) that the DC-link 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 DC-link voltage. The fault flag shown in Fig. 12(a) illustrates that the DC-link voltage sensor fault occurred at 4 s, while the sensed DC-link voltage is zero during the fault, as shown in Fig. 12(b). However, the DC-link 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.

Fig. 11.Estimation performance of Luenberger observer in the case of parameter variations. (a) Variation of input filter inductance. (b) Variation of DC-link capacitance. (c) DC-link voltages. (d) d-axis currents. (e) q-axis currents.

Fig. 12.Control performance of the fault tolerant control under the sensor failure of the DC-link voltage (exp.). (a) Fault flag. (b) DC-link voltages. (c) d-axis currents. (d) q-axis currents. (e) Output power.

 

VII. CONCLUSIONS

In this paper, a fault detection and tolerant control scheme for the DC-link voltage sensors in three-phase AC/DC/AC PWM converters has been proposed, where the Luenberger observer is used to estimate the DC-link 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 DC-link capacitance.