A Fast Diagnosis Method for Both IGBT Faults and Current Sensor Faults in Grid-Tied Three-Phase Inverters With Two Current Sensors

This article considers fault detection in the case of a three-phase three-wire (3P3W) inverter, when only two current sensors are used to save cost or due to a faulty current sensor. With two current sensors, there is no current method addressing the diagnosis of both IGBT open-circuit (OC) faults and current sensor faults. In order to solve this problem, this article proposes a method which innovatively combines two kinds of diagnosis variables, line voltage deviations and phase voltage deviations. The unique faulty characteristics of diagnosis variables for each fault are extracted and utilized to distinguish the fault. Using an average model, the method only needs the signals already available in the controller. Both IGBT OC faults and current sensor faults can be detected quickly in inverter mode and rectifier mode, so that the converter can be protected in a timely way to avoid further damages. In addition, error-adaptive thresholds are adopted to make the method robust. Effects such as system unbalance are analyzed to ensure that the method is robust and feasible. Simulation and experimental results are used to verify and validate the effectiveness of the method.


V NL
Voltage between output neutral point and lower point of DC bus. L x Filter inductance of phase X. R x Equivalent resistance of phase X. γ Actual value of signal γ. γ^Sampled value of signal γ. γ * Estimated value of signal γ. Δγ^Deviation between γ and γ^. Δγ * Deviation between γ and γ * . γ [n] Average value of γ during t[n-1] and t [n]. ΔV th,sub Threshold of deviation ΔV sub . Δ sub Polarity of deviation ΔV sub . σ γ Error of signal or parameter γ. ξ Γ Calculation error of function Γ. ξ ∧

ΔvxN,IB
The upper limit of the error caused by system unbalance calculated with sampled currents. ξ *

ΔvxN,IB
The upper limit of the error caused by system unbalance calculated with estimated voltages.

I. INTRODUCTION
G RID-TIED three-phase voltage-source inverters are widely used in renewable energy systems, electrical traction systems, etc. Inverters play the key roles of interfaces controlling and transferring power. However, inverters are of the parts with highest failure rate [1]. Unexpected inverter failure may cause considerable loss; therefore, methods to improve inverter availability, protect systems, and reduce maintenance time are hot topics [2].
In inverters, power semiconductor switches, particularly IG-BTs, are the most vulnerable devices [3]. IGBTs may suffer from short-circuit (SC) faults and open-circuit (OC) faults. Unlike SC fault protection, OC fault protection is not generally included as a standard feature in inverters. However, OC faults also cause malfunction and could lead to failures on other parts [4]. Therefore, it is useful to consider fast and accurate IGBT OC fault diagnosis methods. Many papers have been published focusing on IGBT OC fault diagnosis. These methods include data-driven methods and circuit-driven methods. The data-driven methods apply artificial intelligence algorithms [5]- [7] or advanced signal processing methods [8]- [10] to extract fault indication characteristics. The data-driven methods do not need circuit analysis or models, which makes them suitable for complicated systems. Nevertheless, they require large amounts of data and computational effort. Thus, for now, they are not good candidates for fast online inverter fault diagnosis. Circuit-driven methods can achieve faster fault identification with less data, but they rely on circuit operation analysis or circuit models, so they are suitable for simpler and well-defined systems. Circuit-driven methods can be categorized as voltage signal-based [11]- [14], current signal-based [15]- [18], and model-based [19]- [22]. With extra sampling and diagnosis circuits, voltage signal-based methods introduced in [11] and [12] can detect the IGBT OC faults within one switching period. Current signal-based methods [15]- [18] and model-based methods [19]- [22] can diagnose IGBT OC faults with existing signals. Due to different features in terms of cost, speed, complexity, etc., these methods are favored in different applications.
As well as IGBT faults, inverters are also sensitive to sensor faults [23]. Sensor faults can be more catastrophic than IGBT OC faults. For example, when a fault occurs with a current sensor in grid-tied inverters, the current will rise quickly due to the actions of the close-loop control, which may cause further damages to IGBTs and sensitive loads. Therefore, it is necessary to diagnose sensor faults in a timely way. There have been some reports on fault diagnosis of sensors in inverters. Most of these methods are based on current analysis [24]- [26] and models [27]- [30]. Methods proposed in [24] and [25] are based on load current average values. They are simple and easy to implement. A fast and general method based on a parity space and temporal redundancies is developed in [26]. It is suitable for various kinds of sensor faults. Methods in [29] and [30] can handle multiple current sensor faults by utilizing current residuals generated by state observers.
Methods mentioned earlier show good performance in diagnosing IGBT OC faults or current sensor faults. However, the methods considering only one kind of fault may diagnose falsely when the other kind of fault occurs. IGBT faults and current sensor faults share faulty characteristics. Both faults can cause distortion in the sampled currents. This is why most diagnosis methods for only one kind of fault cannot work in an independent way, but interfere each other. As a result, the methods for IGBT fault diagnosis utilizing sampled currents may have false alarms when current sensor faults occur. On the other hand, the methods for current sensor faults are also interfered by IGBT faults. Therefore, in order to diagnose both faults accurately, it would be better to include both faults diagnosis in the same method. Besides, addressing two kinds of faults by one approach shows better simplicity in implementation than applying two separate methods, because the analysis, calculation and program codes of these two kinds of faults can be shared in part.
In recent years, some methods have been developed to consider both IGBT faults and sensor faults [31]- [33]. In [31], the current deviations generated by a Luenberger observer are used to diagnose both faults. In order to improve diagnosis speed, Ren et al. [32] proposed a method based on average bridge arm pole-to-pole voltage deviations. The method in [33] can diagnose multiple IGBT faults and current sensor faults through stator current analysis. In all these methods, the sum of three phase currents is used to distinguish IGBT faults from current sensor faults. Therefore, these methods are only suitable for the three-phase three-wire (3P3W) inverters with three current sensors.
The literature review shows the problem of diagnosing both IGBT OC faults and current sensor faults in 3P3W inverters with only two current sensors has not been investigated. In this article, two kinds of diagnosis variables, line voltage deviations and phase voltage deviations, are innovatively combined to handle these two kinds of faults. The unique faulty characteristics of each fault is extracted and utilized to distinguish different faults. Importantly, the proposed method takes system unbalance into consideration. The problem of the system unbalance is new and inevitable when considering these two kinds of faults. It is solved by analyzing and computing the calculation error caused by the unbalance in two ways, so that the method is more robust and feasible.
This article is organized as follows. The IGBT OC fault and current sensor fault analysis is given in Section II. The proposed method is detailed in Section III. Section IV discusses calculation errors analysis and thresholds selection. The simulation and experimental results are shown in Section V. Section VI concludes this article.

II. FAULTY CHARACTERISTICS OF OUTPUT VOLTAGE DEVIATIONS
In this part, the deviation models of output line voltages and phase voltages are derived. The deviations are defined as where, γ is the actual value, γ * and γ ∧ are the estimated and sampled values, respectively. Then, the output voltage deviation characteristics under different IGBT OC faults and current sensor faults are analyzed and summarized. Fig. 1 shows a grid-tied 3P3W inverter with two current sensors. Two phase currents, three phase grid voltages and dc voltage are sampled for control.

A. Output Voltage Deviation Models
Voltage sensors are healthy, so the actual output line voltages v xy (x, y = a, b, c) can be considered the same as the sampled output line voltages v ∧ xy . Besides, according to the loop shown in Fig. 2 and Kirchoff Voltage Law, there is where X,Y = A, B, C. L x is the filter inductance and R x is the equivalent resistance. Base on (2), the line voltage can be estimated as   where i ∧ x is the sampled phase current, and V * XY is the estimated bridge arm pole-to-pole voltage.
Then (2) minus (3) gives the output line voltage deviation as Similarly, according to the loop shown in Fig. 3 Based on (5), there is If the system is unbalanced, (7) is inaccurate. The error caused by system unbalance will be discussed in Section IV.
Similar to (4), the output phase voltage deviations are where

B. Faulty Characteristics Analysis
When no fault occurs, Δv * xy = 0 and Δv * xN = 0. Whereas, when fault occurs, there may be Δv * xy = 0 and Δv * xN = 0. In this article, the focused current sensor faults refer to open-circuit faults or short-circuit faults in sensor devices or conditioning circuits, as well as failures in A/D modules. In such faulty scenario, the output of the faulty sampled current is zero or other constants.
T 1 OC fault and sensor CS a fault are taken as examples to analyze the faulty characteristics of output voltage deviations. It is considered that only one kind of fault occurs at a time.
When device T 1 OC fault occurs, according to the fault analysis in [22], there are ΔV * Then, according to (4) and (8), there are When sensor CS a is faulty, With similar analysis, all faulty characteristics of output voltage deviations for different faults can be extracted and concluded in Table I. In the table, the cases where current sensors are in other phases are also included. For example, (CS a ×, CS c ) indicates the case where current sensors are in phases A and C, and the sensor in phase A CS a is faulty.

A. Basic Principle of the Diagnosis Method
It can be observed from Table I    that two kinds of faulty characteristics are combined for fault identification. In order to utilize only existing signals in the controller, especially for a common circumstance where signals are sampled every switching period, the average model is applied to calculate output voltage deviations. The average model can be defined as where T S is the sampling period. The sampling frequency can be different from the switching frequency. In this article, as in most cases, the sampling frequency equals switching frequency. The diagnosis principle is shown in Fig. 4. The average output line and phase voltage deviations are taken as diagnosis variables. The calculation models of diagnosis variables will be given later. Ideally, the deviations should be zero when no fault occurs. However due to calculation error caused by sampling error, inductance error, system unbalance, etc., the deviations are not always exactly zero under normal operation. Therefore, for robustness purposes, the error-adaptive threshold method proposed in [22] is applied in this method, which will be detailed in Section IV. After obtaining the thresholds, the deviation polarities Δ xy [n] and Δ xN [n] can be determined as Then, according to the faulty characteristics given in Table I, the criteria for diagnosing IGBT OC fault and current sensor fault are given in Table II.
In order to further improve robustness against disturbances, such as noise and unmodeled high harmonics, the minimum time judging rule is implemented. The fault diagnosis result has to remain for the minimum time T min to be considered reliable. The higher T min leads to the better robustness and but longer detection time. In this article, T min is set to 2T S . Besides, the signal filters in the conditioning circuirts and software are also helpful for eliminating the effects of disturbances. In the experiments, the harware filters are applied.

B. Calculation of Average Output Voltage Deviations
According to (3) and (12), the average estimated output line voltages can be calculated as where V * Similarly, the average estimated and actual output phase volt- where V * More detailed derivation of the calculation model can be found in [22].
Finally, the average output voltage deviations are Δv In implementation, the calculation can be furtherly simplified.

A. Errors Caused by System Unbalance
For an unbalanced system, (7) is not accurate, which results in calculation errors in the output phase voltage deviations. The error caused by system unbalance ξ ΔvxN,IB can be defined as It can be obtained from (6) that Normally, R a , R b , R c are small and similar thus (24) can be simplified as Considering only current sensors CS a and CS b are available, by replacing i c with (-i a -i b ), (25) can be written as (26) Two methods are developed to estimate the upper limit of ξ ΔvxN,IB corresponding to two circumstances: when current sensors are healthy and when current sensors are faulty (IGBTs are healthy).
1) When Current Sensors Are Healthy: Define ΔL as the maximum inductance unbalance, namely Lࢠ[L-ΔL, L+ΔL]. According to (26), there is (27) Then, the upper limit of ξ ΔvxN,IB can be calculated with sampled currents, which is denoted as ξ ∧ 2) When Current Sensors Are Faulty: When current sensors are faulty, ξ ∧ ΔvxN,IB may be lower than the actual error ξ ΔvxN,IB . Therefore, the second method based on estimated voltages rather than sampled currents is developed. The error calculated with estimated voltages is denoted as ξ * ΔvxN,IB . According to Kirchhoff Voltage Law, there is Then, it can be derived from (30) that There are five parts in (31 shown at the bottom of the next page). The maximum values of PART 1, PART 3, and PART 5 can be obtained easily with the nonlinear programming tool in MATLAB. An example is given below. The parameters in the simulation and experiments are applied in this example, which is given in Table III ]. Then, it can be obtained that PART 1 ≤ 0.0747, PART 3 ≤ 0.0683, PART 5 ≤ 1.29V. Thus After averaging In conclusion, when current sensors are healthy, ξ ∧ ΔvxN,IB [n] calculated by (29)

B. Modeling Errors
Beside system unbalance, the calculation errors can be caused by modeling errors from other factors, including sampling error, inductance error, dead time and delay time.
Define function Г as where γ 1 , .. γ k are sampled signals and model parameters.
Define σ γ1,.. σ γk , as the maximum errors of γ 1 , ..γ k . Then the total error of Г, namely ξ ξ , caused by errors σ γ1,.. σ γ can be estimated as In the derived calculation model, sampling errors and parameter errors are the factors causing modeling errors. According to (37), (14)- (22), the total calculation error of diagnosis variables from sampling and parameter errors are where σ Lf is the maximum inductance error, σ V dc , σ vxy , σ vxN , σ ix are the maximum sampling errors of V dc , v xy , v xN , i x . The determination of sampling errors and inductance error is explained in [34]. Besides sampling errors and parameter errors, dead time and delay time can also cause modeling errors. The impacts of the dead time and the delay time are discussed in [22]. In this manuscript the maximum calculation errors from dead time T DD and delay time T DL can be obtained as

C. Thresholds Selection
After obtaining the calculation errors, the thresholds

V. SIMULATION AND EXPERIMENTAL RESULTS
Simulation and experimental results have been obtained to verify the correctness and effectiveness of the proposed method. The specification of the 3P3W inverter for simulations and experiments is given in Table III. Fig. 5 shows the experimental platform. The system control and fault diagnosis methodologies are implemented using TMS320F28335 digital signal processor (DSP). In the experiments, the insulated gate bipolar transistor (IGBT) OC fault is simulated by removing the corresponding driver signal. The current sensor fault is simulated by setting the faulty sampled current to 0 or 5 A. The fault diagnosis indicator signals are given by outputs on the DSP I/O pins.

A. Simulation Verification of System Unbalance Error Analysis
Simulations in this section aim to verify the theoretical correctness of the calculation error caused by system unbalance. In the simulations, the filter inductances (L a , L b , L c ) are (8.5, 9.5, 9.5 mH), with ΔL of 0.5 mH. The grid voltages are unbalanced by 5%. Current waveforms are also unbalanced.
In Fig. 6, power is varied between 1.2 kW in inverter mode (IM) and 1.2 kW in rectifier mode (RM) several times. It can be observed that the calculation error caused by inductance unbalance is high when power changes drastically, namely when di/dt is high. This is in accordance with (26). The result shows both ξ ∧ ΔvxN,IB and ξ * ΔvxN,IB are always higher than the actual error when no fault occurs. Fig. 7 shows the simulation results when T 1 OC fault or CS a fault occurs. At t 1 , the IGBT T 1 fault occurs. Before and after the T 1 fault, ξ ∧ ΔvxN,IB is always higher than the actual error. Whereas, ξ * ΔvxN,IB is lower than the actual error at t 1 . The current sensor CS a fault occurs at t 2 . Before and after CS a fault, ξ * ΔvxN,IB is always higher than the actual error. However, ξ ∧ ΔvxN,IB is lower than the actual error after CS a fault. These observations are the same as the error analysis.
The simulation results show that the analysis of the calculation error caused by system unbalance is correct. Equation (35) can be used to make sure that the estimated calculation error caused by system unbalance is higher than the actual error. Fig. 8 shows the experimental results under normal operation with power changes ranging from 1.2 kW in RM to 1.2 kW in IM. In this experiment, the filter inductances (L a , L b , L c ) are (8.5, 9.5, 9.5 mH), with ΔL of 0.5 mH. The grid voltages are unbalanced by 5% and the current waveforms are also unbalanced. It can be observed that with various power rates and under drastic power changes at t 1 -t 4 , all the diagnosis variables are within thresholds. No false diagnosis is caused. These experimental results prove this method is featured with strong resistance against system unbalance, modeling errors and power changes.

C. Experimental Results of IGBT Fault and Current Sensor
Fault Diagnosis Fig. 9 shows the experimental waveforms of IGBT T 1 OC fault diagnosis. Before the fault occurs, all the diagnosis variables are within the thresholds. After the fault is triggered at t 0 , the voltage deviation polarities (Δ ab , Δ bc , Δ ca , Δ aN , Δ bN , Δ cN ) change to (N, Z, P, N, P, P) soon. According to the criteria in Table II, T 1 OC fault is diagnosed at t 1 . The fault diagnosis time is 0.2 ms (two switching periods). Fig. 10 demonstrates the result of current sensor CS a fault diagnosis. The current sensor fault is triggered at t 0 , then the voltage deviation polarities change to (N, N, P, N, Z, P) soon. According to the criteria in Table II, CS a fault is diagnosed at t 1 . The fault diagnosis time is 0.2 ms (two switching periods).
Similar experiments have been carried out in rectifier mode, as shown in Figs. 11 and 12. It can be seen that the performance in rectifier mode is the same as in inverter mode. Both faults are diagnosed in two switching periods.
These experiments verify the proposed method can diagnose the IGBT OC faults and current sensor faults accurately and quickly in both inverter mode and rectifier mode.

D. Experimental Diagnosis Speed
In order to give an overview of the diagnosis speed, the diagnosis time of IGBT faults and current sensor faults during  It can be seen that, the diagnosis time of IGBT T 1 fault is short in the positive half period, about 0.2 ms (two switching periods, 1% fundamental period). However, if T 1 fault occurs in the negative half period, the fault cannot be detected immediately but until the next positive half period comes. This is because T 1 fault does not affect the operation of inverter in the negative half periods. During the whole fundamental period, the fault diagnosis time of current sensor CS a fault is short. Most diagnosis time is 0.2 ms (two switching periods, 1% fundamental period).
In conclusion, this method shows outstanding performance in terms of diagnosis speed.

VI. CONCLUSION
The contributions of this article can be concluded as follows. 2) The proposed method is the only method so far that can diagnose both IGBT OC fault and current sensor fault in the grid-tied 3P3W inverter with only two current sensors by utilizing signals already existing in the controller. The fault can be detected in 0.2 ms (two switching periods, 1% fundamental period) at the fastest in inverter and rectifier modes, which enables the converter to be protected in a timely way to avoid further damages.
3) The problem of the system unbalance is solved by computing the calculation error caused by the unbalance in two ways, so that the method is more robust and feasible. The idea of tackling nonideal factors to make a proposed method more practically valuable is interesting and helpful to researchers and engineers.
It should be noted that this method may have some limitations. It can only handle single IGBT OC fault or current sensor fault. It is best effective for current sensor faults which cause the sampled current to be zero or other constants. Other kinds of current sensor faults will be covered in the future work.  In 2014, he joined the PEMC group with the University of Nottingham, U.K., as a Lecturer in power electronics. Since 2019, he has been an Associate Professor with the University of Padova. His current research interests include modular multilevel converters for HVdc, high power density converters, control and stability analysis of ac and dc microgrids.
Dr. Costabeber received the IEEE Joseph John Suozzi INTELEC Fellowship Award in Power Electronics in 2011.