Open-circuit fault diagnosis and voltage sensor fault tolerant control of a single phase pulsed width modulated rectifier

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Open-circuit fault diagnosis and voltage sensor fault tolerant control of a single phase pulsed width modulated rectifier Ahlem Ben Youssef ∗ , Sejir Khojet El Khil, Ilhem Slama Belkhodja Universit´e de Tunis El Manar, ENIT-L.S.E, BP 37-1002, Tunis le Belv´ed`ere, Tunis, Tunisie Received 23 October 2014; received in revised form 8 October 2015; accepted 8 October 2015

Highlights • IGBT open circuit fault and grid voltage sensor fault are considered. • A new open circuit fault detection and isolation approach is proposed, it is based on residual generation with an adaptive threshold. • Grid voltage sensor fault detection and isolation algorithm is considered thanks to the use of parity space equations approach. • A grid virtual flux estimator is used to achieve the grid voltage sensor Fault Tolerance Control. Abstract Recently, single phase pulsed width modulated (PWM) rectifiers become very attractive in different industrial applications that need connection to single phase grid. Like any other PWM converter, the single phase PWM rectifier may be subject to different failures like power switch failures or sensor faults. Hence, fault diagnosis and monitoring are essential to optimize the maintenance costs and increase the reliability levels of the system. This paper discusses the fault detection and isolation (FDI) of both failures. A new open circuit fault detection and isolation approach is proposed. The fault detection method is based on residual generation between measured and observed current form factors (CFFs) with an adaptive threshold in order to avoid the false alarm and increase the reliability of the diagnosis algorithm. Also, the grid voltage sensor FDI is considered in this contribution thanks to the use of parity space equations approach. Moreover, after sensor fault detection and isolation, a grid virtual flux estimator is used to achieve the grid voltage sensor fault tolerance (FTC). Each failure may be detected in few hundred of microseconds. Theoretical analysis, simulations and experimental results are presented to validate the effectiveness of the proposed method. c 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights ⃝ reserved. Keywords: IGBT fault; Sensor fault; Diagnosis

∗ Corresponding author.

E-mail addresses: [email protected] (A. Ben Youssef), [email protected] (S. Khojet El Khil), [email protected] (I. Slama Belkhodja). http://dx.doi.org/10.1016/j.matcom.2015.10.005 c 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights 0378-4754/⃝ reserved.

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1. Introduction Single phase PWM rectifiers are often used in different industrial applications such as: grid connected PV converters, electric railway traction, single phase UPS, etc. [17,7,2,12]. This converter offers the possibility to control the DC-link voltage and the grid side power factor with less grid current harmonics. To achieve this, closed loop control system and the use of bidirectional power switches (IGBTs, MOSFTs) are mandatory [22]. So, rectifier’s performances depend particularly on the reliability and availability of power semiconductors and sensors. Power semiconductor faults are one of the most common faults in the voltage source inverters. The literature review shows that about 38% of faults in AC drives are related to power devices [1]. Power semiconductor faults are broadly classified as short-circuit and open-circuit failures [18]. They are generally caused by electrical or thermal stress or gate driver fault. Short circuit fault is considered as the most dangerous and requires very fast actions to protect the system and to insure its safe shutdown. Consequently, power converters are equipped today with the appropriate hardware circuits and appropriate protections in order to achieve very fast fault detection and the short circuit fault becomes a standard feature of power converters. Open-circuit faults generally do not cause the system shutdown but affect its performances. For grid-connected PWM converter applications, open-circuit faults lead to non-sinusoidal grid current waveforms and decrease the grid power factor. Also the thermal overstress introduced by such fault on the semiconductor may lead to a short-circuit fault. Even if, sensor faults are not often as power semiconductor faults, any erroneous measurement may cause the instability of the closed loop control and even the system’s shutdown. Hence, a reliable diagnosis algorithm should be integrated into the converter controller to achieve fast fault detection and isolation and then to allow continuous work of the rectifier. Recently, different studies have been conducted for power semiconductors failures diagnosis [6,11,16,4,20,15,14] or sensor fault tolerant control [9,3,8,21,10,4,13,23]. In [11], a voltage observer-based technique, avoiding the use of extra sensors, is employed for open-circuit fault diagnosis in closed loop PWM AC regenerative drives. An FPGA based algorithm applied to back-to-back converter for WECS application is presented in [16]. Single and multiple open-circuit fault diagnosis using observer-based approach was addressed in [4,5,20]. In [15], the MRAS approach is employed for open-circuit fault detection in PMSM drives. Current form factors used for single and multiple power semiconductor open-circuit faults in back-to-back converters of PMSG drives for wind turbine systems were addressed in [14]. Speed sensor, DC link sensor and current sensor fault detection of PMSM drive are discussed in [9]. The FDI and FTC approaches are based on Extended Kalman Filter. Once the faulty sensor is isolated a sensorless control allows the continuous work of the drive. A similar approach is proposed in [3] where a high frequency signal injection is used for speed sensor FDI. In [8], an observer based method is used for rotor position sensor fault detection of a PMSM drive. In order to improve the FDI method against motor parameters variations an adaptive threshold is employed. Current sensor fault detection in wind electric conversion systems was discussed in [21] for the doubly fed induction generator and in [10] for the permanent magnet synchronous generator respectively. An easy and fast sensor fault detection and isolation for AC drives using parity space equations is presented in [4]. The main advantage of this method is that it does not need any knowledge of the system model and may be used specially for voltage sensors for example. The MRAS-Luenberger estimator was successfully applied in order to achieve a position sensor fault tolerant control of a PMSM drive in [13]. A state observer based sensor FDI and FTC of a single phase PWM rectifier for electric railway application is presented in [23]. Grid current and DC link voltage sensor fault were considered. The control reconfiguration was achieved by removing the erroneous measurement introducing the estimated quantity in the rectifier’s control loop. The state of the art review shows that observer based methods those traditionally used for sensor FDI and FTC are recently more and more used to detect power switch open-faults. Nevertheless, these methods require the knowledge of the system model. Also, usually they employ fixed thresholds for fault detection which need adjustments relative to system parameters and operating point variations. Hence, false alarms may be avoided by the use of adaptive thresholds [8].

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Regarding sensor FDI, parity space equations are suitable especially when the concerned sensor is measuring a quantity which is an input of the system’s model like voltage sensors for example. This paper proposes robust and fast algorithms that may detect an open-circuit fault and a grid voltage sensor fault in a single phase PWM rectifier. Moreover, grid voltage sensor fault tolerant control using estimated grid virtual flux is also presented in this contribution. The rest of the paper is organized as follows: Section 2 presents the description system, grid side converter, and its control strategy. Section 3 is devoted to analyze the design of the Luenberger-observer of the line current. Section 4 presents the IGBT open-circuit fault diagnosis. Grid voltage sensor fault detection and isolation method is depicted in Section 5. Simulation results are presented in Section 6. Section 7, illustrates the experimental results presenting the performances of the studied approaches. The paper is summed up in a conclusion in Section 8. 2. Control strategy system Fig. 1 illustrates the single phase PWM rectifier structure with its closed loop control. The converter is modeled using the following state equations: di Conv − ri conv + Vin dt d Vdc iC f = C f dt i dc = i C f + i ld Vg = −L

(1)

Vin = (2S − 1) Vdc i dc = − (2S − 1) i conv i conv = −i c where, Vg is the grid voltage, i conv is the inverse grid current i c , Vdc is the DC link voltage, Vin is the rectifier’s input voltage and i dc and i ld are the converter’s output current and the load current respectively. The impedance line is represented by its inductance L and its resistance r , C f is the DC link capacitance and S is the IGBT’s switching control signal. As the aim of the system control strategy is to insure unity grid power factor operation and DC link voltage regulation, an external Vdc control loop, using a proportional integrator (PI) controller maintains the DC link voltage ∗ , when current load or voltage grid varies. An inner loop controls the input current rectifier equal to its reference Vdc using a proportional-resonant controller (PR) in order to ensure unity power factor operation and sinusoidal current absorption with zero phase and zero steady-state errors. Finally, grid synchronization is performed using a Second Order Generalized Integrator (SOGI)-Frequency Look-up Loop (FLL). In order to increase robustness against grid faults, voltage grids are shared in positive and negative sequences using a quadrature-signals generation (QSG). 3. Desıgn of the Luenberger state observer The Luenberger state observer is used here to estimate the states of the PWM rectifier defined in (1) which are grid current i C and DC link voltage Vdc . The particularity of this observer is that it takes into account the rectifier model. 3.1. PWM rectifier state space model According to Eq. (1), the state space model of the converter is given by:  x˙ = Ax + Bu + Dv y = Cx where the matrix system A is:   r 2S − 1 −  L L  , A=  −2S + 1  0 Cf

 1 C= 0

 0 . 1

(2)

(3)

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Fig. 1. Control strategy of single phase PWM rectifier.

Note, S is the IGBT’s switching control signal. It can take two possible values 1 or 0. The input matrixes B and D are:     1 0 − (4) D =  −1  . B =  L, 0 Cf The state vector is defined by the i conv current and the DC bus voltage Vdc , Grid voltage Vg and load current i ld are considered respectively as no controllable and controllable inputs.   x = i conv Vdc u = Vg and v = i ld . As shown in (3), the system matrix A depends on IGBT’s switching control signal S. So in one switching period, matrix A takes two different expressions as given below:     r −1 1 r − −  L  L L L  , . As=0 =  As=1 =  (5)  1   −1  0 0 Cf Cf 3.2. Design of the observer The Luenberger state-observer dynamic equations are expressed by:  xˆ˙ = A xˆ + Bu + Dv + L ob (y − yˆ ) yˆ = C x. ˆ

(6)

State correction vector L ob (y − yˆ ) is defined through feeding back the value of the difference between the measurement and observer quantities, where, matrix gain L is chosen to define the observer dynamics. The observer error dynamics are defined by placing the eigenvalues of the matrix (A − L ob C). Also these desired eigenvalues should be chosen to ensure an observer dynamic faster than the system dynamic one. Observer poles have to be proportional to system poles. The proportionality coefficient is K obs . Note, the system poles are αi and the observer poles are λi , then λi = K obs αi . This is achieved by defining the matrix gain L ob defined by   L1 L3 L ob = . (7) L4 L2

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(a) Vg > 0, i c > 0.

(c) Vg < 0, i c < 0.

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(b) Vg > 0, i c > 0.

(d) Vg < 0, i c < 0.

Fig. 2. Conduction path of the single-phase PWM rectifier in case of a single open circuit fault of IGBT1 .

In order to simplify calculation, gains L 3 and L 4 may be chosen equal to zero. In fact they have no effect on the dynamic observer which depends only on the eigenvalues real part. The latter depend only on L 1 and L 2 gains [23]. 4. Open-circuit fault detection and isolation algorithm Before presenting the power semiconductor open-circuit FDI algorithm, it is important to show the impact of that fault on the studied system operation. Here two failures are considered: single switch and multiple switches opencircuit faults. Power semiconductor open-circuit fault is usually due to driver fault (loss of bonding wires of the control signal) or to a short-circuit fault causing the IGBT rupture. Only simple and multiple open-circuit faults caused by gates misfiring are considered in this work. Fig. 2 presents the conduction path of the rectifier in case of open-circuit fault in IGBT1 . The line current i c paths are changed compared to healthy mode. As mentioned in Fig. 2, conduction path is analyzed through grid voltage and grid current sign (Vg and i c values are positive or negative) and via different case of switching control, (S1 = S4 = 0; S3 = S2 = 1) or (S1 = S4 = 1; S3 = S2 = 0). For the positive half wave of Vg and i c , the possible conduction path is: – In case of switching control S1 = S4 = 1 and S3 = S2 = 0, parallel diodes in IGBT1 and in IGBT4 are turned on and the IGBT2 and IGBT3 are turned off, see Fig. 2(a). – In case of switching control S1 = S4 = 0 and S3 = S2 = 1, IGBT3 and IGBT2 are turned on and the IGBT1 and IGBT4 are turned off, see Fig. 2(b). For the negative half wave of Vg and i c , the possible conduction path is: – In case of switching control S1 = S4 = 1 and S3 = S2 = 0, parallel diodes in IGBT3 and the IGBT4 are turned on and the IGBT1 and IGBT2 are turned off, see Fig. 2(c). – In case of switching control S1 = S4 = 0 and S3 = S2 = 1, the IGBT3 and IGBT2 are turned on and the IGBT1 and IGBT4 are turned off, see Fig. 2(d). The impact of this fault is presented in Fig. 3. The fault does not lead to a degradation of the rectifier’s performances; since the grid power factor (PF) remains constant near one, the grid current i c waveform is quasi-sinusoidal

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Fig. 3. Impact of IGBT1 fault in the rectifier.

(a) Vg > 0, i c > 0.

(c) Vg < 0, i c < 0.

(b) Vg > 0, i c > 0.

(d) Vg < 0, i c < 0.

Fig. 4. Conduction path of the single-phase PWM rectifier in case of a single open circuit fault of IGBT1 and IGBT4 .

and the DC link voltage Vdc is maintained constant and is equal to its reference. Nevertheless, the bidirectionality of the energy exchange between the input and the output sides of the converter is no longer possible because of the diode D1 (anti-parallel diode with IGBT1 ). Multiple switch open-circuit fault (IGBT1 and IGBT4 for example), presents other consequences on the performances of the rectifier, which are more serious. In this case, the conduction path of the single-phase PWM rectifier is illustrated in Fig. 4. In this case, the rectifier topology is changed compared to healthy mode, where the IGBT1 and IGBT4 become two diodes. For the positive half wave of Vg and i C , the possible conduction path is the same in healthy mode, so this fault is masked because the IGBT1 and IGBT2 are blocked in the state: – In case of switching control S1 = S4 = 1 and S3 = S2 = 0, parallel diodes in IGBT1 and in IGBT4 are turned on and the IGBT2 and IGBT3 are turned off, see Fig. 4(a). – In case of switching control S1 = S4 = 0 and S3 = S2 = 1, IGBT3 and IGBT2 are turned on and the IGBT1 and IGBT4 are turned off, see Fig. 4(b). For the negative half wave of Vg and i C , any conduction path is ensured. In this phase, the output current of the rectifier is null and only the capacity becomes the principal power supply to feed the load, see Fig. 4(c) and (d).

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Fig. 5. Impact of the failure in the IGBT1 and IGBT4 in the rectifier.

The impact of this fault on rectifier’s performances is illustrated in Fig. 5. It causes the loss of the positive half cycle of the grid current, i c , and an increase of its amplitude with high ripple of the DC link voltage. Also, this fault causes the appearance of a DC current component and the second rank harmonic equal to 100 Hz. So the power factor (PF) does not maintain its high value and decreases notably. The analysis of the different IGBTs fault scenarios, demonstrates that: – Power semiconductor open-circuit faults degrade seriously the performances of the rectifier. – The grid current is the most sensitive quantity to such failures. For this reason the proposed diagnosis method is based on the analysis of the grid current waveform. 4.1. Design of the fault detection algorithm The proposed fault diagnosis algorithm is based on a comparison between measured and estimated grid current, i c , form factor (CFFs). The current form (or shape) factor is defined as the ratio of the RMS value to the average value of the absolute value of the current i c . Two CCFs are computed, one from measured current (F) and the second from ˆ estimated current ( F). |i c |rms |i c |avg   ˆ  i c  ˆ F =  rms . ˆ  i c  F=

(8)

avg

In healthy operating mode, both F and Fˆ values are equal to 1.11 as mentioned in (9). |i c |rms π = √ = 1.11 |i c |avg 2 2   ˆ  i c  π Fˆ =  rms = √ = 1.11. ˆ  2 2 i c 

F=

(9)

avg

A residual, RIBGT , is then generated and is expressed as follows: RIGBT = Fˆ − F.

(10)

In healthy operation, residual RIBGT should be equal to zero. But, in the real condition, and due to operating point variation, system’s parameter variation or measurement noises the residual value will be different from zero. Hence, a threshold has to be established.

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Table 1 Localization open circuit IGBTs fault. Faulty switches

Direction variables RIGBT

Localization variables AVG(i c )

IGBT1 , IGBT3 or both IGBT1 and IGBT4 IGBT2 and IGBT3 IGBT2 , IGBT4 or both

>TIGBT >TIGBT >TIGBT >TIGBT

[0, e1 ] >e1 < − e1 [−e1 , 0]

4.2. Adaptive threshold establishment In order to increase the robustness of the diagnosis method and to avoid false alarms, an adaptive threshold is developed. Starting from Eqs. (9) and (10), the residual RIGBT can be expressed by the inequality (11).   ˆ  i c  |i c |rms |i c + εic |rms |i c |rms = − RIGBT =  rms − ˆ  |i c |avg |i c + εic |avg |i c |avg i c  avg

RIGBT RIGBT RIGBT

|εic |rms |i c |rms |i c |rms ≤ + − |i c + εic |avg |i c + εic |avg |i c |avg |i c |rms |i c |rms |εic |rms + − ≤ |i c + εic |avg |i c |avg |i c |avg |εic |rms |εic |rms ≤ ≈ |i c + εic |avg |i c |avg + |εic |avg

(11)

where εic is the current estimation error εic = iˆc − i c . Neglecting the value of the |εic |avg compared to the value of the |i c |avg , the inequality (11) can be expressed in (12). So, the inequality below illustrates the expression of adaptive threshold, TIGBT . TIGBT =

|εic |rms . |i c |avg + |εic |avg

(12)

4.3. Fault detection and localization The residual RIGBT signature indicates that a power semiconductor failure is detected but it alone is not enough to isolate the faulty IGBTs or the faulty leg. In this case, the average value of the grid current, AVG(i c ), is used to isolate the faulty leg or the faulty IGBTs. So, a fixed threshold value e1 is defined in order to detect the faulty leg or the faulty IGBTs. The value of e1 is chosen by analyzing the grid current average values under different faults and particularly in case of diagonal IGBTs fault (see Appendix). Table 1 summarize the different case of occurrences IGBT fault, single or multiple fault with e1 = 0.1 p.u. The final structure of the proposed open-circuit fault diagnosis is illustrated in Fig. 6. 5. Grid voltage sensor fault detection and isolation approach The SOGI-PLL block is used to compute the grid angle θg [23]. Any erroneous measurement in the grid voltage will keep mistakes on θg estimation. The gain fault does not perturb the computing of the grid electrical frequency. Nevertheless it should be detected to be computed into the system’s maintenance process. However, when a dc component is present in Vg measurement the SOGI-PLL process is affected by a sinusoidal component at the electrical frequency ωg . As ωg is used to define the grid current reference, the offset fault will distort the grid current waveforms.

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Fig. 6. Open circuit fault diagnosis algorithm.

Grid power factor 1.2 1 POWER FACTOR

Ic/Icn

Grid current FFT 1.2 1 0.8 0.6 0.4 0.2 0

0.8 0.6 0.4 0.2

1 Healthy mode

3 2 Harmonic rank

4

Grid voltage sensor fault

0 1

2

1 - Healthy mode 2 - Grid voltage sensor fault

Fig. 7. Grid side performances in healthy and faulty cases.

As shown in Fig. 7 the offset fault (50%) causes the appearance of new harmonics ranks and decreases the grid power factor. To detect the Vg sensor fault it is not suitable to estimate its value. In fact, according to (1), to estimate Vg value it is necessary to calculate the derivate of the grid current i c which will keep the algorithm more complex and hard to implement. Moreover, Vg is considered as an input for rectifier state model (1) and does not depend on model parameters uncertainties. Hence, it will be nice to use simple algorithm FDI like parity space equations for such sensor fault. The proposed parity space method was firstly introduced in [4], where its efficiency in fault detection and isolation of faulty AC sensor in electrical drives (FDI) was proven. Its principle consists of the calculation of the difference between two consecutive measurements of the sinus signal Vg . The residual expression is given by (13) Rgk = r K + r K −1 + r K −2   r K = VgK − 2VgK −1 + VgK −2 

(13)

where Vgk , Vgk−1 and Vgk−2 are the measured signal Vg at the consecutive times kTs , (k − 1)Ts and (k − 2)Ts respectively and Ts is the sample time. The residual algorithm implementation is depicted in Fig. 8. In healthy mode, with the sinus waveform case, the maximum theoretical value of the residual Rgk is established and defined as the threshold λg . Calculations using trigonometric relationships lead to the expression of the threshold given in (13). More analytical development is performed in [4]. λg = 2Vgm ωg2 Ts2

(14)

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Fig. 8. Residual generation implementation algorithm.

Fig. 9. Residual Rg evolution with fault occurrence at [k, k + 4] interval time.

where Vgm and ωg are respectively the maximum value and the angular frequency of the grid voltage Vg . Variations of residual Rg in case of Vg sensor fault are depicted in Fig. 9. The maximum value of the residual is reached for Rgk+2 so two sample times (2Ts ) after fault apparition. In all cases, an over estimation of this maximum is given by (15). Rgkmax = 2d

(15)

where d is the value of the measurement error (in per unit). Note that, because the grid voltage sensor fault detection algorithm is based on consecutive measurements of the measured signal Vg , grid side faults may cause wrong detection results. Additional detection methods for grid faults should be preceded, and a system-level fault diagnosis is necessary. 6. Simulation results System modeling and simulation as well as of the proposed method of fault diagnostic were performed using the PSIM software environment. The same conditions are made for simulations and the experimental setup. They are summarized in Table 2. 6.1. Open-circuit fault detection and localization The IGBT open-circuit fault is introduced through removing its gate command signal. Fig. 10 illustrates the simulation result of the evolution of the residual RIGBT and its threshold TIGBT in case of healthy operating mode, for different operating point conditions: variation of ±50% of nominal load at 0.8 s and 1.2 s respectively is presented in Fig. 10(a) and line impedance parameters variation of 40% line impedance variation at t = 1.5 s, is presented in Fig. 10(b). In all cases the residual RIGBT is still under the threshold TIGBT . These results show the robustness of the proposed diagnosis method.

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Fig. 10. Evolution of the residual and its threshold in case of healthy operating mode.

Table 2 Experimental setup parameters. Parameter

Value

RMS voltage supply Vg Line resistance r Line inductance L DC link voltage Vdc DC link capacitor C f Maximal variable resistance Rld Sample time (i c , Vdc , i ld ) = 2Ts Sample time (Vg ) = Ts

220 V 0.3  40 mH 400 V 1100 µf 200  100 µs 50 µs

In case of open circuit IGBT fault, we considered the single and multiple IGBT(s) faults. Different simulation tests have been carried out for different instants, such as t = 2 s and t = 2.01 s. Fig. 11 demonstrates the evolution of the signals RIGBT and TIGBT , in this case of open circuit fault in IGBT1 at t = 2 s, see Fig. 11(a) and at t = 2.01 s, see Fig. 11(b). In case of healthy mode, the residual is lower than TIGBT . When a fault appears the TIGBT evaluates and exceeds its residual after a fault detection time, 1t, so in this case a signal alarm is set to one. As shown in Fig. 11(a) and (b), 1t takes different values; it depends on the fault occurrence instant. In fact, the wave form of the current i C is changed which results in the evolution of RIGBT and TIGBT and the fault is detected in 1t = 350 µs (Fig. 11(a)). For Fig. 11(b) the detection time is 1t = 10.350 ms. In Fig. 12(a) and (b), the multiple fault (failure in both IGBT1 and IGBT4 ) is considered at t = 2 s and t = 2.01 s respectively. For single or multiple IGBT(s) open-circuit fault, the detection time 1t may change depending on the time of the fault occurrence (positive or negative half cycle of the current i c ). Consider, as example, the case of IGBT1 and IGBT4 open-circuit fault. These switches operate only in the negative half cycle of the current i c . If the open-circuit fault appears in the negative half cycle of the current i c , the detection time is 1t = 350 µs. If the failure has occurred just in the end of the negative half cycle or in the positive half cycle, as presented in Fig. 12(b), IGBT1 and IGBT4 are not solicited. So, it will be possible to detect this fault only in the next negative half cycle. The fault, in this case, is masked during (T /2). So, the Maximum detection time is: 1T =

T + δt = 10 ms + δt. 2

So, the time fault detection is not fixed; depends on the IGBT fault and its turned on or turned off during each positive or negative half wave of i C and Vg . Fig. 13 presents the faulty switch(es) localization using the average value of the grid current.

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Fig. 11. Evolution of RIGBT and TIGBT in case of failure in IGBT1 for different instants of occurrence fault: (a) at t = 2 s, (b) at t = 2.01 s.

Fig. 12. Evolution of RIGBT and TIGBT in case of failure in IGBT1 and IGBT4 for different instant of occurrence fault: (a) at t = 2 s, (b) at t = 2.01 s.

6.2. Grid voltage sensor FTC Grid voltage Vg senor faults have been applied at t = 2.5 s for two sensor fault types: gain and offset. The offset sensor fault applied is a 50% one (Fig. 14) whereas the gain fault applied is also a 50% one. All the simulation results are given in per unit system. In Fig. 14(a), a 50% gain fault was applied to the grid voltage sensor. The residual Rg and the Vg waveforms are depicted.

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Fig. 13. Faulty switch(es) localization: (a) IGBT1 , IGBT3 or both, (b) IGBT2 , IGBT4 or both, (c) IGBT1 and IGBT4 , (d) IGBT2 and IGBT3 .

Fig. 14. Grid voltage sensor FDI: (a) 50% gain sensor fault, (b) 50% offset sensor fault.

At the instance of the sensor fault occurrence, t f = 2.5 s; the residual Rg exceeds immediately its fixed threshold λg . According to (14), the threshold λg is computed and it is equal to 0.2. Fig. 14(a), shows a spike that reaches the value of 1 which corresponds to twice the gain fault value, and this after two sample times 2Ts from the instant of fault. Hence, the fault is detected and isolated after 100 µs since Ts is chosen equal to 50 µs. The offset sensor fault detection and isolation is reported in Fig. 14(b) where the same performances are obtained with the proposed FDI approach and the sensor fault is also well detected and isolated after two sample times.

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Fig. 15. High pass filter bode diagram.

Once the sensor FDI has been done, the fault tolerance is needed for continuous work of the rectifier. As mentioned previously, it will be difficult to estimate the grid voltage Vg , so in case of Vg sensor fault a grid virtual flux is used to estimate the grid angular frequency. In the literature different methods are presented to estimate the grid virtual flux [19]. As the sensorless control is not the aim of this contribution, a simple method is used. The virtual flux Φgo of the grid voltage, can be expressed by    φgo = Vg (t)dt = −r i c (t)dt + C0 − Li c (t) + C1 + Vin (t)dt + C2 (16) where, the coefficients C0 , C1 and C2 are the constants of integration. Before introducing the virtual flux into the SOGI block (see Fig. 1), the offset values represented by C0 , C1 and C2 have to be removed. Thus, a high band pass filter is used and the virtual flux Φg is used to compute ωg as expressed in (17)   s2 φg = H ( p)φgo = K f φgo (17) s 2 + 2ξ f ω f c s + ω2f c where, K f is the filter gain, ξ f is the damping factor and ω f c is the cut off frequency of the filter. The bode diagram of the filter is presented in Fig. 15. The Vg sensor fault reconfiguration control is depicted in Fig. 16. When the sensor fault is detected and isolated the input of the SOGI block changes from Vg to Φg . After fault reconfiguration the i c current waveform is still sinusoidal, with a unity grid power factor, and the grid angle θg is well computed. 7. Experimental results In order to improve the efficiency of the proposed fault tolerant control algorithm, experimental tests under a laboratory prototype have been performed. The experimental setup (Fig. 17) comprises a single phase autotransformer, a (r, L) impedance line with a Semikron power converter and a 1 kW resistive load. The target for the digital implementation of the rectifier control loop and the FTC algorithm is a microchip dsPIC33FJ256MC710A. Two Hall-effect current sensors (LEM LT25NP) are used to measure the i c , Ild currents and two Hall-effect voltage sensors (LEM LV25) to measure the Vdc , Vg voltages. The analog to digital conversion module of dsPIC33FJ256MC710A is based on 11-bits A/D converters, the conversion time is 5 µs to convert four signals. An interface circuit board allows the voltage level adaptation between the PWM rectifier drivers and the target implementation. The laboratory prototype parameters are shown in Table 2. The experimental results presented in this section demonstrate the performances of the proposed FDI algorithms in case of power semiconductor failure and grid voltage sensor fault respectively.

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Fig. 16. Grid voltage sensor fault control reconfiguration.

Fig. 17. Experimental setup.

a

b

Fig. 18. Measured and estimated quantities: (a) grid current i c , (b) DC link voltage Vdc .

First, system performances in healthy operating mode are carried out in Fig. 18. Measured and estimated values of i c and Vdc are presented in Fig. 18(a) and (b).

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Fig. 19. Evolution of the residual RIGBT and adaptive threshold after and before IGBT open circuit fault: failure in the both IGBT1 and IGBT4 .

Fig. 20. Evolution of the residual RIGBT and adaptive threshold after and before IGBT open circuit fault: failure in the both IGBT1 and IGBT4 .

In order to improve the efficiency of the proposed IGBT fault detection and isolation based on adaptive threshold, which is detailed in paragraph 4, an experimental test has been developed. So, a multiple open circuit fault is considered for IGBT1 and IGBT2 . Fig. 19 shows the evolution of the residual RIGBT and adaptive threshold TIGBT after and before healthy mode. When a fault appearance, the RIGBT increases and exceeds its TIGBT , as result, a signal alarm is set to one. The average value of the grid current, avg(i C ), is used to locate the faulty IGBT, see Table 1. So, in case of multiple open circuit fault of IGBT1 and IGBT4 , avg(i C ) exceeds the fixed threshold, e2 , and the corresponding faulty IGBT is located. Fig. 20 illustrates the evolution of the avg(i C ) and e1 . Note that e1 is defined in healthy mode and taking into account the experimental condition such as the noise, operation point variation. e1 in p.u. is equal to 0.1. The impact of a Vg sensor fault is shown in Fig. 21. After offset fault occurrence (Fig. 21(a)), a sinusoidal component on the grid angle frequency ωg appears which causes the distortion of the grid current and decreases the grid power factor value. However, the gain sensor fault (Fig. 21(b)) does not affect the ωg estimation. Experimental results regarding grid voltage sensor fault detection and isolation are presented in Fig. 22. A 50% offset sensor fault and 100% gain sensor fault are considered. First, an offset fault is applied to the grid voltage sensor. The offset corresponds to 0.5 p.u. The experiment is the same as carried out in simulation (Fig. 14) and the waveforms are shown in Fig. 22(a). It can be observed that the residual generation presents an evident spike at the instant of fault and demonstrates the occurrence of a sensor fault. Then, a sensor gain fault is applied to the output of the voltage sensor Vg which is set to zero. When the fault occurs, the residual Rg changes and becomes higher than its corresponding threshold λg . It is proved in the details of the waveform depicted in Fig. 22(b). For each fault, the duration of the residual waveform is 200 µs which corresponds to 4Ts . The sensor fault detection flag FDVg is set to 1 after 100 µs of fault apparition.

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Fig. 21. Experimental results for grid voltage sensor (a) offset fault impact (b) gain fault impact, on ωg estimation.

Fig. 22. Experimental results for grid voltage sensor FDI: (a) 50% offset sensor fault, (b) 100% gain sensor fault.

Fig. 23. Grid sensor fault tolerant control: (a) control reconfiguration, (b) post-fault operation.

Once the fault is detected, control reconfiguration algorithm is carried out. The estimated grid virtual flux replaces the grid voltage erroneous measurement as an input of the SOGI-PLL block. Fig. 23(a) shows the SOGI-PLL block input and the grid current waveforms before and after fault apparition with control reconfiguration. After control reconfiguration, the grid current i c is still sinusoidal and it is in phase quadrature with the virtual grid flux Φg . Hence the grid power factor is equal to 1. Fig. 23(b), illustrates the good performances of the rectifier after control reconfiguration where the grid angle θg is well computed. 8. Conclusion This paper presents robust and fast algorithms for power semiconductor and grid voltage sensor fault diagnosis. Both algorithms are based on residual generation. For the power semiconductor failure diagnosis, the residual is based on the difference between the form factor of the measured and observer grid current. The adaptive threshold is defined through the evolution of grid current observation error. Regarding the grid voltage sensor FDI approach is based on parity space equations. Than, a sensor fault tolerance is established using the estimated grid virtual flux.

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Several simulation and experimental results are presented to illustrate the effectiveness of the proposed approaches. Acknowledgment “This work was supported by the Tunisian Ministry of Higher Education and Research under Grant LSE-ENIT-LR 11ES15”. Appendix In this paper, mathematical derivations for the resulting line current are obtained. Multiple fault conditions in Single phase rectifier (failure in both IGBT1 and IBGT4 and failure in both IGBT2 and IBGT3 ) are analyzed. For these faulty conditions, the two profiles, described in the following equations are resulting under a steady-state scenario and focusing on the fundamental frequency component.  T   ICM sin(ωt) 0 ≤ t ≤ 2 Failure in IGBT1 and IBGT4 : i C (t) = T  0 ≤t ≤T 2  T  0 0≤t ≤ 2 Failure in IGBT2 and IBGT3 : i C (t) = T   ICM sin(ωt) ≤ t ≤ T. 2 Considering the Fourier series of the faulty current i C (t), the mathematical expressions for fault conditions are obtained by the following expression i C (t) = a0 +

∞ 

ak cos(kωt) + bk sin(kωt)

K =1

where:  1 t a0 = i C (t)dt T 0  t 2 i C (t) cos(kωt)dt k > 1 ak = T 0  2 t bk = i C (t) sin(kωt)dt. T 0 As a result, by a direct substitution of two current profiles into i C Fourier series, the following expressions are obtained i C (t) = i CM sin(ωt) − i DC + 1i C Failure in IGBT1 and IGBT4 . i C (t) = i CM sin(ωt) + i DC − 1i C Failure in IGBT2 and IGBT3 where i CM = 0.3183i CM π ∞  2i CM 1i C = cos(2nωt). 2 − 1) π(4n n=1

i DC =

In this work, the signal i DC can be used to localize the fault IGBT. So, e1 ≤ i DC . References [1] Q.T. An, L. Sun, L.Z. Sun, Current residual vector-based open-switch fault diagnosis of inverters in PMSM drive systems, IEEE Trans. Power Electron. 30 (2014) 2814–2827. [2] B. Bahrani, A. Rufer, Optimization-based voltage support in traction networks using active line-side converters, IEEE Trans. Power Electron. 28 (2012) 673–685.

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