Open-Switch Fault Diagnosis for Three-Phase AC-DC Power Converter with Park's Vector Method Considering Modulation Schemes

Open-switch fault accounts for large proportions among failures in power conversion system. Previously, fault defection methods are carried out by researches from transient period or circuit configuration with complicated algorithms. This paper reveals characteristics of single IGBT open-switch fault in rectifier from perspective of modulation scheme It presents that with a suitable modulation index and modulation scheme, current park's vector diagnosis method can become simple and effective for two-level three-phase AC-DC power converter. In that way, park's vector can be generalized for localizing faults in both inverter and rectifier.


I. INTRODUCTION
wo-level three-phase AC-DC power converter is widely used among different industrial areas, such as wind power generation, electric vehicle and the like. It is estimated that roughly 38% of unhealthy condition in power converter is due to semiconductor's failure and almost 70% of these faults was related to open circuit faults, short-circuit faults and gate-misfiring faults [1]. Short-circuit fault often happens during bond-wire rupture, gate-circuit degradation and over-current. The fault causes the whole system shutdown, even can destroy other peripheral devices. Basically, short-circuit can be detected through gate driver. Authors in [2] propose a method to locate short-circuit fault within one carrier period. In contrast, the system can still run under open-switch fault and can remain working for a period of time. At last, unhealthy working condition can cause overstress on IGBT, DC-link ripple and eventually lead to secondary fault after a period of abnormal operation, which also lead to secondary fault in power conversion system. Several diagnosis methods for open-switch fault in voltage source inverter (VSI) have been investigated and developed during the last decade [3]- [7]. However, less research work pays much attention to rectifier. Since phase current mainly flows through IGBT as an inverter while the main flowing path is freewheeling diode when it is used for rectifying. As a result, current park's vector patterns make inverter's diagnosis methods hard to be applied in AC-DC power converter. In [8], the method not only can locate single openswitch fault, but also can diagnose multiple open-switch fault. Actually, threshold value of inductance energy storage is not easy to choose. In [9], diagnosis method strictly depends on symmetrical circuit. Moreover, the diagnosis algorithm is complex, which imposes extra calculation burden on DSP, especially in high frequency power conversion applications. In [10], a modified current park's vector method needs at least two fundamental periods to detect fault. Besides, normalized DC current method is also sensitive to output power, which needs half cycle to detect fault. In [11], current angle detection method was presented. But, effectiveness of diagnosis is highly dependent on system parameter and output power. Authors in [12] proposed a method based on three-variable detection in PMSG drive system. More specifically, two different types of fault localization method are respectively used in grid-side and generator-side converter. It should be noted that low-pass filter is needed to be implemented, and also the experimental result is easily influenced by high-frequency noise. Modelbased method proposed by authors in [13] can achieve multiple open-switch diagnosis.
Although these diagnosis methods are proposed for rectifier, few researchers take modulation schemes into consideration in open-switch fault condition. Hence, how modulation schemes impact faulty characteristics, and in turn whether it expands application scenarios of park's vector during the fault, comprehensive studies should to be carried out further.
The configuration of this paper is as follows. In Section II, the faulty characteristics under open-switch condition. In Section III, commutation periods during open-switch fault are analyzed. In Section IV, the influence of modulation schemes in open-switch fault is deeply investigated and generalized current park's vector method is proposed. The simulation results are shown in Section V. Conclusions are drawn in Section VI.

II. THE FAULTY CHARACTERISTICS UNDER OPEN-SWITCH CONDITION
Without loss of generality, VT1 is in open-switch fault in Fig.1, and unity power factor condition is considered for discussion. For inverter system, it can be showed in Fig.2(a) that pole voltage of faulty phase is positive while current is in its negative period. In that case, when VT1 fault occurs, freewheeling diode D2 cannot be conducted in a half-period. Unlike VSI, reference voltage and current vector have the same space position showed in Fig.2(b). In [11], the authors point out when composing Vref in S2-2 and S5-2, phase-A current has a short zero-crossing period because D2 does not meet the conduction requirement. The characteristics of unhealthy phase current have been showed in [10]. More importantly, the authors present that specific interval is attributed to lower pole voltage compared with other poles, and negative current conducted by freewheeling diode is also influenced by output power and inductor value.
Additionally, only half-period phase current conduction during the fault can be observed in [14]. However, no more explanations in this paper. This is the basic phenomenon of single open-switch fault in two-level AC-DC power converter system discussed and studied by researchers for many years.
However, the fundamental mechanism of circulating current in freewheeling diode during open-switch fault is still unknown. Briefly, the pole voltage VUN can determine conductivity of D2. Nevertheless, VUN is a series of voltage pulse waveform, it is difficult to analyze its impact on freewheeling diode during a fundamental cycle. One of the applicable methods is the concept of modulation waveform which is the essence of SVPWM as well.

III. COMMUTATION PERIOD DURING OPEN-SWITCH FAULT
Since commutation period influences the faulty phasecurrent characteristics during open-switch fault, it is essential to analyze it with reference space voltage vector composing. Generally, PMSG-PWM rectifier system is showed in Fig.3.
Ia>0  When Vref is needed to be synthesized in left half plane of hexagon (shadow area) in Fig.4., switching state of phase-A is always zero. The conduction of D2 can guarantee zerostate meanwhile phase-current is in its negative direction at that time. However, it must meet diode conduction requirement. Red and blue solid-line showed in Fig.3. correspond to phase-current in diode and IGBT, respectively. While red dash-line denotes possible faulty phase current direction.  Through the analysis above, it can be seen that switching states impact current flowing direction in unhealthy condition. Since the modulation schemes are made up of different switching sequences. Hence, it is possible to be considered from modulation perspective.

A. Schematics of continuous SVPWM
Continuous SVPWM consists of two traditional modulation schemes: CSVPWM0 and CSVPWM1. The former switching sequence begins and ends up with switching state 000 and put 111 switching state in the middle, the latter begins and ends up with switching state 111 and put 000 switching state in the middle. The switching sequence with dwell time of CVPWM0 and CVSPWM1 can be showed in Fig.5.
In essence, SVPWM can be easily achieved when zerosequence voltage component is injected into three-phase sinusoidal modulation signal. Therefore, modulation functions can be used to estimate the pole voltage among the three arms. VUO can be defined as voltage between phase-A and neural-point of DC-link. Its mathematical function is expressed in (1).
Where M is modulation index, VVO and VWO can be attained by shifting VUO with 120° and 240°, respectively. From (1), it can be seen that maximum and minimum value of VUO both are ±MVdc/2 for CSVPWM0-1 scheme. Thus, Min(VUN) can be calculated to define the minimum pole voltage of phase-U .
can be easily completed through freewheeling diode D2. However, for CSVPWM0, CSVPWM1 and DPWMMAX, VUN is related to modulation index (MI) and reference DClink voltage (Vdc). Because according to the definition of MI defined by (8). DC-link voltage is also one part of it. When MI is not high enough, D2 is reverse truncation. In this circumstance, current park's vector method can be used to diagnose under CSVPWM0, CSVPWM1 and DPWMMAX scheme.
The space vector diagram with unity power factor can be depicted in Fig.6., voltage drop on resistance is neglected due to small value. From this diagram, it can be found that MI is also associated with the inductor value. Through the analysis above, it may explain the reason that system parameters can influence faulty phenomena described in [5].
Modulation waveform can be observed from pole voltage by adding a low-pass filter in Fig.7 where Vdc is set to 500V and MI is 0. Similarly, for the rest of modulation schemes, unhealthy phase current can be obtained in Fig.9. under the same conditions. From the analysis and current waveform showed above, it can be concluded that the phase-A current cannot be blocked in its negative period within all range of MI.

B. Generalized current park's vector trajectories based on different modulation schemes
The current-park's vector diagram under single openswitch fault of VT1, VT3 and VT5 in each arm can be showed in Fig.10, respectively. Current park's vector diagram is a half-circle with CSVPWM, CSVPWM1 and DPWMMAX schemes in which MI is not high enough to guarantee conductivity of freewheeling diode. The edge angle of halfcircle can be used to locate the fault. For example, 90°, 210°a nd 330°are the edge angle of park's vector trajectory for faulty VT1, VT3 and VT5, respectively. It can be seen that one fundamental period fundamental period is needed to detect the fault. By contrast, current patterns of other modulation schemes are ineffective and independent with MI. The trajectory of the park's vector become irregular shape and is totally degraded. An example by using DPWM3 scheme with faulty VT1 is illustrated in Fig.11. The simulation results show the consistency of mathematical analysis discussed in Section-IV. Park's vector is still exceptionally applicable for diagnosis of open-switch fault in relatively low modulation applications with special modulation schemes.

VI. CONCLUSION
From perspective of modulation scheme, single openswitch fault in two-level power converter is investigated and analyzed. The effectiveness of the diagnosis method is well studied with a suitable modulation index and CSVPWM0, CSVPWM1 or DPWMMAX modulation scheme. It can be found that modulation scheme has a tight relationship with