Description of inverter faults.

## Abstract

The growing importance of power conversion systems and their dependency on the performance and reliability of static converters has motivated extensive research efforts in this field. A variety of different techniques have been applied to detect open-circuit faults in power converters. The present chapter is focusing on the techniques of detection and localization of open-circuit faults in a three phase voltage source inverter fed induction motor. A comparative study is carried out between different detection techniques: the Park current vectors and its enhancement by using the polar coordinates, the mean value of the currents, the stator current spectrum analysis and the measurement of the current drop. The aim of this comparison is to investigate the relative strengths and weaknesses of the different techniques and evaluate the performance of each detection technique studied. The comparison study focuses on the time detection, the localization ability and the hardware aspect. To validate these techniques, an experimental setup is developed in our diagnostic group laboratory which consists of a two-level voltage source inverter controlled by a DSPACE-1104, Card to generate the PWM vector control of the induction motor. The obtained simulation and experimental results illustrate well the detection feasibility of each technique as well as the benefits and merits of the performed comparative study.

### Keywords

- induction motor
- inverter
- open-circuit fault
- detection
- localization
- Park’s vectors
- polar coordinates
- mean value
- frequency spectrum
- current drop

## 1. Introduction

The applications of electronics were for a long time limited to the technique of high frequencies. The possibilities of application were limited by the unreliability of the electronic elements available at that time. This reliability was insufficient to meet the high demands of new applications in the industrial field. It was only after the development of special electronic power components of higher reliability and more limited tolerance that new techniques could be envisaged, thus creating a new branch of electronics called power electronics.

One area where power electronics is widely used today is the industrial applications related to machine-static power converter associations, particularly the industrial variable speed AC drives. These drives are mainly used in which the machines are connected through a static power electronic converter usually a three-phase inverter. It is estimated that about 38% of the faults in these industrial drives are due to failures of the supply system. Some uses of the machine-static power converter sets do not tolerate untimely failures, mechanical or electrical failures at the machine or related to static power converter failure. An industrial survey [1] conducted in 2011, comes to the conclusion that 93% of respondents stated that reliability is a paramount issue in the field of static power electronic converters. The faults of the static power converters have various causes; they can be related to the open-circuit faults of the IGBT switches for example. This type of malfunction induces damage constraints for the production system if the personnel are not notified and a nuisance shutdown can eventually result.

The growing interest of manufacturers in the maintenance of electrical drives justifies the emphasis placed on research into the diagnosis of machine-static power converter associations. The complexity of the systems involved and the necessary approach from the new angle of diagnosis today require a preliminary work of detection/diagnosis of the faults of the machine-converter association.

Several researchers have studied the behavior of static power converters with internal failure, focusing particularly on the open-circuit fault of an IGBT switch. Such a fault can lead to secondary faults in other converter components that can result in high repair costs [2].

Authors [3, 4] propose the Park vector technique, the principle of this technique is based on the tracking of the current trajectory of Park (*id, iq*). In the healthy case, the trajectory takes a circle shape and in the case of an IGBT switch open-circuit fault, the circle becomes a semicircle.

The position of this trajectory in the *(d-q)* frame makes it possible to calculate the intervals of the angles of the fault to localize the faulty IGBT. Other researchers [5, 6, 7, 8] have proposed the Park.

Average current (*i*_{dmean}, *i*_{qmean}) technique to calculate the exact open-circuit fault angle in order to identify the faulty IGBT switch. Authors [9, 10, 11] have proposed the technique based on the spectral analysis of the stator currents. This technique is based on the study of the harmonic analysis of each phase current. The amplitude and argument of each harmonic can be used in detecting and localizing the faults. The analysis of the first harmonics shows that the difference between the healthy state and the open-circuit fault case resides in the zero-order harmonics which signifies the presence of the DC component in the signal. The argument of the harmonic zero with respect to the fundamental makes it possible to know the type of fault; on the other hand, the argument of this harmonic also makes it possible to know the faulty IGBT switch either the high or the lower one. The authors [12] combined normalized standard currents with additional diagnostic variables for one or more IGBT switch open-circuit faults. The diagnostic alarms were performed by the Boolean output signals. In the paper presented by [13], the same authors proposed another extension based on the use of fuzzy logic symptoms. The author [14] proposes the Clarke technique followed by the polarity of the trajectory slope in the complex *α-β* frame identify the faulty IGBT switch.

The present chapter is focusing on techniques of detection and localization of IGBT switch open-circuit faults in a three phase voltage source inverter fed induction motor. A comparative study is carried out between different detection techniques: the Park current vectors and its enhancement by using the polar coordinates, the mean value of the currents, the stator current spectrum analysis and the measurement of the current drop. The comparison study aims at exhibiting the relative strengths and weaknesses of the different techniques and at assessing each detection technique in terms of its performance; that is the time detection and the localization ability; as well as in terms of hardware; that is the number of current sensors required for IGBT switch open-circuit fault detection. To validate these techniques, an experimental setup is developed in our diagnostic group laboratory which consists of a two-level voltage source inverter controlled by a *DSPACE-1104* Card to generate the *PWM* vector control of the induction motor. The obtained simulation and experimental results illustrate well the detection feasibility of each technique as well as the benefits and merits of the performed comparative study.

## 2. Space voltage vector and switching states for the case of both healthy and faulty inverter

Figure 1 shows the general structure of a three phase two-level voltage source inverter feeding an induction motor.

This inverter is controlled by the *PWM* vector control strategy. For each leg of the inverter, there are two possible states:

**State 1:** The higher switch *Kx* (*x = 1, 2 or 3*) is closed, while the lower switch *K2x* (*x = 1, 2 or 3*) is open. The output voltage relative to the neutral of the dc source is *Vdc.*

**State 0:** The lower switch *Kx* (*x = 1, 2 or 3*) is closed, while the higher switch *K1x* (*x = 1, 2 or 3*) is open. The output voltage relative to the neutral of the dc source is *0v*.

It is to note that the faulty inverter used in this chapter is defined as an inverter with one of its IGBT switch exhibiting an open-circuit fault.

The experimental setup used in this chapter is depicted in the photo of Figure 2. It includes a three-phase squirrel-cage induction motor fed by a three-phase two-level voltage source inverter. The detailed characteristics of the motor are given in the appendix. Furthermore, the motor is mechanically coupled to a DC generator supplying a bank of resistors which allows varying the load torque. Moreover, the measuring system includes three current Hall Effect sensors and three voltage sensors and a DSPACE 1104 acquisition card to generate pulses for triggering the IGBT’s gates in the inverter. The whole set is connected to a computer for visualizing and analyzing the processed sensed signal [14].

Because of the randomness of the measured signals and for a reliable analysis, 05 acquisitions are performed for each case. The acquisition time used is T_{acq} = 20s. To study the effect of the load on the induction motor signals, the following mode of operation is considered; the rated load operation with a rated current of 7A and an estimated torque of 20 Nm and a frequency of sampling Fe = 1.5kHz.

## 3. Fault detection techniques for a faulty inverter

During its operation, the inverter is subjected to various internal and external constraints resulting in its failure; especially those failures related to the IGBT semiconductor switches because of their fragility. Two types of faults are usually linked with the inverter and can be reported in Table 1 as follows:

In this chapter section, different techniques for fault detection and localization of the inverter IGBT switches open-circuit fault are presented in the summarized Table 2 and thoroughly discussed.

### 3.1. Technique based on the Park vectors

The Park vectors technique is based on the tracking of the trajectory of the current vector. Indeed, in normal conditions (without fault), the trajectory of the current vector in the *d-q* frame is a circle. The circle becomes a semicircle when an IGBT open-circuit fault of an inverter leg occurs. The position of this semicircle in the *d-q* frame allows identifying the faulty switch as developed by [10]. Applying the Park transformation on the three phase currents *(ia, ib, ic)* results in two currents *(id, iq)* in the *d-q* frame. The current is expressed by the following mathematical system:

Its slope is used to identify the faulty leg. As mentioned above, the extraction of information of any faulty leg can be obtained from the angle between the current vector and the *d-q* frame using the following equation:

where

Figure 3 depicts the angle of the faulty leg when applying an open-circuit fault at *t = 1.5 s*.

In reference to Figure 3, the leg fault angle **θ**_{l} is used to identify the faulty leg of the inverter. For the case of a healthy inverter, the angle values are always π or -π. Any angle values different from π or -π are therefore considered as an indication confirming faulty legs presence. The various faulty inverter legs corresponding to the various fault angle values are expressed in Table 3.

Faults | Description |
---|---|

Short-circuit | Short-circuit faults affecting the IGBT switches are the most serious faults. In the presence of such a fault, the current reaches limits which can cause the fusion of its chip or its connection. If the detection of this type of fault does not occur rapidly (less than 10 μs), then the IGBT switch which is still active on the same leg undergoes the same phenomenon and so the whole inverter leg is shorted. |

Open-circuit | Open-circuit faults affecting the IGBT switches may occur when, for any reason, the IGBT is disconnected, is damaged, or had a problem in its grid control signal. This type of fault is very difficult to perceive directly because the motor can continue to operate but with a degradation of its performance due to the occurrence of fluctuations in the mechanical parameters (speed and torque) as well as an imbalance of the currents where the currents of the other two healthy legs take high values to maintain the average torque and the speed. The starting of the motor in the presence of this type of fault cannot always be ensured. |

Number | Methods for open-circuit IGBT switch faults |
---|---|

1 | Technique based on the Park vectors and enhanced Park vectors with polar coordinates |

2 | Technique based on the mean value of the currents |

3 | Technique based on the stator current spectrum analysis |

4 | Technique based on the measure of the current drop |

Faulty leg | IGBT switches | Leg fault angle θl |
---|---|---|

leg A | K1, K2 | π/2 or –π/2 |

leg B | K3, K4 | 5π/6 or –π/6 |

leg C | K5, K6 | 5π/6 or –π/6 |

The Park trajectory slope is used to identify the faulty switch. As mentioned above, the extraction of information of any faulty switch can be obtained from the angle between the mean current vector and the *d-q* frame using the following equation:

where **θ**_{K} is the inverter switch fault angle.

Figure 4 depicts the angle of the faulty switch when applying an open-circuit fault at *t* = 1.5 s.

Figure 4 shows the fault angles switch **θ**_{K}. The various faulty inverter switches corresponding to the various fault angle values are expressed in Table 4.

IGBT | Fault angles of inverter switch θK |
---|---|

K1 open | [0, π/2] or [3π/2, 2π] |

K2 open | [π/2, 3π/2] |

K3 open | [π/6, 7π/6] |

K4 open | [0, π/6] or [7π/6, 2π] |

K5 open | [5π/6, 11π/6] |

K6 open | [0, 5π/6] or [11π/6, 2π] |

For example for the case of a faulty inverter switch *K1* corresponds the angle intervals *[0, π/2]* or *[3π/2, 2π]*.

Figure 5 depicts the trajectories of the currents for both healthy and faulty inverters.

#### 3.1.1. Enhanced Park vectors with polar coordinates

A polar coordinates calculation is proposed associated with the technique of Park vectors in order to enhance the inverter IGBT switch fault localization. This section focuses on the localization of each faulty IGBT switch by calculating the borders of each trajectory as well as the fault current vector. This calculation is carried out by proposing the use of the polar coordinates diagram as shown by Figure 6.

The mathematical model based on the polar coordinates is related to the trajectory and the angle **θ**_{icf} of the specified faulty IGBT. Consequently, a change in the shape of the trajectory and the angle indicates the occurrence of a fault condition. This represents an indicator for the localization of the faulty IGBT switch. The angle is calculated from Eqs. 4–6 as follows:

The radius of this trajectory can be calculated from the following equation:

The *d-q* currents at the center of the trajectory *i*_{dc} and *iqc* can be computed using the maximum and minimum of the currents vectors as follows:

For the case of a faulty IGBT switch, the current vector is given by the following equation:

From this calculation, the open-circuit fault of each IGBT switch can be localized and Table 5 summarizes the computation of the fault angle values and the fault current vectors for the case of each faulty IGBT switch.

A significant advantage of the polar coordinates calculation is that it enables to yield the exact value of the angle for inverter faults detection while other existing techniques gives rather an interval of angles.

Figure 7 shows the fault current vector **i**_{cf} when the inverter is operating under both healthy and faulty conditions. For the case of a healthy inverter, the average amplitude of the fault current vector is zero. If a failure occurs, the magnitude of the fault current vector becomes non-zero. The faulty IGBT is identified by the phase angle and the fault current vector magnitude.

## 4. Technique based on the mean value of the currents

This technique uses the mean phase current value for fault detection. A fault in a semiconductor switch can produce offsets in the currents of the electrical machine phases. This diagnostic technique is to calculate the mean values of these currents from which the fault can be detected. A current threshold is defined in order to distinguish between the open-circuit faults in a semiconductor switch.

The mathematical model of this technique is illustrated by the following steps:

*1st step:* Extraction of the three currents of the stator (*ias, ibs, ics*) as follows:

*2nd step*: Calculation of the mean value of the three stator currents:

where length (Ia,b,c): number of point the three current signals *Ia, Ib, Ic.*

After the introduction of a fault in the IGBT of the inverter, one can easily observe the change in the form of the stator currents and also their mean values. This technique allows us therefore to easily identify and localize the faults which are expressed by the following equation:

The open-circuit fault detection algorithm that will be applied in this technique is based on the calculated mean value of the currents and can be described by the following algorithm as shown in Figure 11 (Table 6).

IGBT | Fault current vector icf |
---|---|

K1 open | icf = 6.5∟π |

K2 open | icf = 6.5∟2π |

K3 open | icf = 4.95∟5π/3 |

K4 open | icf = 4.95∟2π/3 |

K5 open | icf = 5.3∟π/3 |

K6 open | icf = 5.3∟4π/3 |

State | Phase A | Phase B | Phase C |
---|---|---|---|

Healthy | , (0) | , (0) | , (0) |

K1 open | −IThresh < Iamean < 0, (Iamean = −1.5) | Ibmean ≥ 0, (Ibmean = 0) | Icmean ≥ 0, (Icmean = 0) |

K3 open | Iamean ≥ 0, (Iamean = 0) | −IThresh < Ibmean < 0, (Ibmean = −1.5) | Icmean ≥ 0, (Icmean = 0) |

K5 open | Iamean ≥ 0, (Iamean = 0) | Ibmean ≥ 0, (Ibmean = 0) | −IThresh < Icmean < 0, (Icmean = −1.5) |

K2 open | 0 < Iamean ≤ IThresh, (Iamean = 1.5) | Ibmean ≤ 0, (Ibmean = 0) | Icmean ≤ 0, (Icmean = 0) |

K4 open | Iamean ≤ 0, (Iamean = 0) | 0 < Ibmean ≤ IThresh, (Ibmean = 1.5) | Icmean ≤ 0, (Icmean = 0) |

K6 open | Iamean ≤ 0, (Iamean = 0) | Ibmean ≤ 0, (Ibmean = 0) | 0 < Icmean ≤ IThresh, (Icmean = 1.5) |

### 4.1. Simulation results for healthy and faulty inverter using the technique of the mean value of the currents

See Figures 12 and 13.

### 4.2. Experimental results for healthy and faulty inverter using the technique of the mean value of the currents

See Figures 14 and 15.

## 5. Technique based on the stator current spectrum analysis

This technique is based on the study of the harmonic analysis of each phase current. The amplitude and the argument of each harmonic may be used in the detection and location of the faults [15].

### 5.1. Simulation results for healthy and faulty inverter using the stator current spectrum analysis

In what follows we will present the simulation for both the healthy state and the inverter with open-circuit switch fault state. Figure 16 shows the harmonic spectrum of the current for the healthy state.

For an open-circuit *K1* IGBT fault, the harmonic spectrum for each phase is shown as in Figure 17. Note that the occurrence of the zero harmonic (i.e., the presence of the DC component) indicates the presence of a fault in *K1*.

The analysis of the first eight harmonics shows that the difference between the healthy state and the case of open-circuit fault state lies at the zero-order harmonics which means the presence of the DC component in the signal. The argument of zero harmonic relative to the fundamental enables us to know the type of fault. On the other hand, the argument of this harmonic enables us also to know the faulty switch either the upper one or the lower one.

From the result of Table 7, we note that the phase which contains the open-circuit fault has its dc component equals to the sum of the dc component of the two other phases and is expressed by the following relations as:

If the fault is at phase A, then: h

_{0A}= h_{0B}+ h_{0C}If the fault is at phase B, then: h

_{0B}= h_{0A}+ h_{0C}If the fault is at phase C, then: h

_{0C}= h_{0A}+ h_{0B}

Zero-order harmonic of the three phases | |||
---|---|---|---|

Faults types | Phase A | Phase B | Phase C |

Healthy case | |||

open | |||

open | |||

open | |||

open | |||

open | |||

open |

Where h_{0A} is the zero-order harmonic of phase A, h_{0B} the zero-order harmonic of phase B and h_{0C} the zero-order harmonic of phase C.

### 5.2. Experimental results for healthy and faulty inverter using the stator current spectrum analysis

In what follows we will present the experimental results for the healthy and open-circuit faulty inverter. Figure 18 shows the harmonic spectrum of the current for the healthy state, while Figure 19 depicts the experimental results for open-circuit fault state.

## 6. Technique based on the measure of the current drop

This technique requires the use of two current sensors by inverter leg. The current measurement may be performed using Hall Effect sensors. Hence the two current sensors for each leg give the measurements of currents **i**_{K1} and **i**_{K2}. If the current of phase A is positive, the *K1* switch is under open-circuit fault if it is ordered to close **C**_{K1} **= 1** but the current **i**_{K2} remains negative. For the *K2* switch and when ik1 is negative, the open-circuit fault is detected if **C**_{K2} **= 1** and **i**_{K1}, remain negative. We therefore obtain the following equations as given in [16]:

where **C**_{K1} **= 1** is the Control of *K1* IGBT and **C**_{K2} **= 1** is the Control of *K2* IGBT (Table 8).

C_{K1} | C_{K2} | i_{K1} < −i_{0} | i_{K2} < −i_{0} | Conclusion |
---|---|---|---|---|

1 | 0 | 0 | 1 | K1 open |

0 | 1 | 1 | 0 | K2 open |

The algorithm of the open-circuit detection applied in this technique; as shown in Figure 20; is based on the measurement of the current drop and can be described by the following steps:

*1st step:*Measure the current*Ij*.*2nd step:*Search the current error*ej*by comparing the current*Ij*to the threshold current*I0*.*3th step:*Identify whether any of the six errors exceed the threshold*I0*.*4th step:*If so, identify the faulty leg of the inverter that should be immediately isolated.

In what follows, the experimental results for the case of a healthy inverter state and an open-circuit fault of the *K1* switch state, of an inverter are represented as shown in Figure 21, using the technique based on the measurement of the switch current drop.

## 7. Comparative study between the different techniques

The comparative study is carried out between different detection techniques. The aim of this comparison is to investigate and evaluate the performance of each detection technique studied. The comparison study focuses on the time detection, the localization ability, the hardware aspect and also the error between the threshold set to zero and the fault value. From this comparison study as illustrated both in Figure 22 and Table 9, we come up with the following deductions: the fastest technique in terms of open-circuit fault time detection (*1.5 ms*) is the measurement of the switch current drop technique. Unfortunately this technique presents also two disadvantages: the first one is related to its inability for localization and is used only for detection purpose. The second drawback of this technique is concerned with the hardware and implementation aspect as it utilizes six current sensors (one for each gate of the six IGBT gates of the three phase two-level voltage source inverter).

Techniques | Hardware | Detection time (ms) | Detection | Localization | Error | Quality and performance |
---|---|---|---|---|---|---|

Park stator current Vectors | Three current sensors | 5 | Yes | Yes | 7.62 | Good |

Average value of stator currents | Three current sensors | 3 | Yes | Yes | 1.5 | Good |

Stator current spectrum analysis | Three current sensors | 2.5 | Yes | Yes | 5.37 | Very good |

Measure of the stator current drop | Six current sensors | 1.5 | Yes | No | 3 | Average |

The three other techniques: the one based on the Park vectors witch polar coordinate, the one based on the average value of the currents and the one based on the current spectral analysis are all used for the detection and localization of open-circuit switch faults in inverters. It should be noted that the three techniques require only three sensors, hence presenting an advantage over the measurement of the current drop technique in terms of cost and implementation. The current spectral analysis has an additional advantage in terms of detection time rapidity (*2.5 ms*) compared to the two other ones (*3* and *5 ms*) respectively. This comparative study is summarized in Table 9. For all detection techniques presented in this chapter study, the calculated error in Table 9, is that between the normal value corresponding to the threshold for the healthy state case (note that the healthy state is taken as a reference corresponding to zero value of the threshold) relative to the fault value corresponding to the IGBT switch open-circuit fault state.

In what follows, Figure 22. illustrates the detection time of the four techniques used for open-circuit fault occurrence at *t = 1.5 ms*.

## 8. Conclusion

In this chapter work, the main purpose is to present a very detailed study of some detection techniques using both simulation and experimental work. The study is followed by a performance comparison between the various techniques to illustrate the feasibility and merits of each one of them and shows the suitability of each technique for a diagnostic situation. The study focuses mainly on the detection time as a key parameter in the detection procedure, the ability of the technique to localize in an exact manner the inverter IGBT switch open-circuit fault and also to assess the hardware aspect in terms of number of sensors required. The experimental work is conducted to validate the simulation results obtained.

The Technique based on the measure of the current drop is found to be superior in terms of fault time detection rapidity but unfortunately cannot be used for fault localization which is a drawback with respect to the three other presented techniques. Another disadvantage of this technique is the high number of required current sensors which has doubled in comparison to the three other studied techniques.

The three other techniques based on the Park vectors associated with polar coordinates, the average value of the currents and the current spectral analysis can be all used for detection and localization of inverter IGBT open-circuit faults and they require only three sensors, hence presenting an advantage over the measure of the current drop technique in terms of cost and implementation. The current spectrum analysis has an additional advantage in terms of detection time rapidity (*2.5 ms*) compared to the two other ones (*3 ms* and *5 ms*).

The chapter also proposes polar coordinates calculation to enhance the Park current vectors technic by developing a simple graphical representation which enables the exact computation of both the magnitude and the phase angle of the fault current vector related to the faulty inverter IGBT switch.