# A Comparative Reliability Study of Three Fundamental Multilevel Inverters Using Two Different Approaches

^{*}

## Abstract

**:**

## 1. Introduction

- diode-clamped or neutral-clamped (NPC)
- capacitor-clamped or flying capacitor (FC)
- cascade H-bridge (CHB)

## 2. Fundamental Principle of Reliability

#### 2.1. Reliability

- Software reliability
- Hardware reliability
- Human reliability

- The early failure or burn-in period, where the hazard function decreases with time.
- The random failure or useful life period, where the hazard function is constant.
- The wear-out period, where the hazard function increases.

#### 2.2. Failure

#### 2.3. Failure rate

#### 2.4. Mean Time to Failure

^{−λt}. Thus, the more simplified form of MTTF is as follows [18,34,35,36]:

#### 2.5. Mean Time to Repair

#### 2.6. Mean Time between Failures

#### 2.7. Availability and Average Availability

_{avg}as (MTBF-MTTR)/MTBF is usually avoided [33]. According to the authors of [51], increasing MTTF does not necessarily increase the value of Availability and Average Availability; also, Availability and Average Availability can be increased without changing MTTF.

## 3. Methodology

#### 3.1. Approximate Method

_{ref (i)}, and N is the number of parts.

#### 3.2. Exact Method

_{T}, T

_{M}, and P are the shape parameters, T is the temperature, ΔT is the difference between maximum allowable temperature with no junction current and the maximum allowable temperature with full rated junction current or power, S is the stress ratio that can be calculated by the ratio of actual stress to rated stress.

_{p}is the predicted failure rate, λ

_{O}is the failure rate from operational stresses, λ

_{e}is the failure rate caused by environmental stresses, λ

_{C}is the failure rate caused by temperature cycling stresses, λ

_{Sj}is the failure rate caused by solder joints, λ

_{i}is the failure rate caused by induced stresses, π

_{O}is the operational factor, π

_{e}is the environmental factor, π

_{C}is the cycling factor, and π

_{Sj}is the solder joints factor.

_{b}is the base failure rate, which is 0.012 and 0.064 for switch and diode, respectively. Equation (20) must be used to calculate λ

_{b}for inductors [47,67]:

_{HS}is the heat sink temperature or the temperature of the inductor hot spot, which is calculated as follows [26,47,67]:

_{A}is the device ambient operating temperature (in degrees Celsius); ∆T is also average temperature rise above ambient. The following equation must be used to calculate λ

_{b}for capacitors [47]:

_{T}is the temperature factor and can be calculated as is shown below [26,47]:

_{j}is the junction temperature and must be obtained by the following equation:

_{C}is the heat sink temperature, θ

_{jc}is the thermal resistance of diode or switch (assumed 0.25 for switch and 1.6 for diode) and P

_{loss}is the power loss of switch or diode; π

_{S}is the stress factor and is calculated as follows [47]:

_{S}is the ratio of operating voltage to nominal voltage.

_{CV}is the capacitor factor which can be obtained by [47]:

_{Q}(quality factor) and π

_{E}(environment factor) have been considered to be equal to 1, and consequently have been ignored [26,66]. To increase the accuracy, the values of quality factor for semiconductor, inductor and capacitor, can be considered 5.5, 10 and 20 respectively. The value of 1 is considered as environment factor π

_{E}for all components. Application factor π

_{A}, and contact construction factor π

_{C}can be obtained from Table 1 and Table 2:

## 4. Results and Discussion

- Diode rectifiers
- DC link capacitors
- IGBT switching devices

_{P}for each component and then multiplying these failure rates by the number of each component to obtain total failure rate. Failure rate of whole system then can be calculated using the following equation [47]:

_{T}, is very important. Matlab Simulink software has been used to accurately calculate the power loss in diodes and switches. A 1-ohm resistor has been used to measure the current.

#### Series Redundancy

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Circuit diagrams of three-level/phase: (

**a**) neutral point clamped (NPC); (

**b**) flying capacitor (FC); and (

**c**) cascade H-bridge (CHB).

Application (P_{r} Rated Output Power) | π
_{A} |
---|---|

Linear Amplification (P_{r} < 2 W) | 1.5 |

Small Signal Switching | 0.7 |

Non-Linear, (P_{r} ≥ 2 W) | |

2 ≤ P_{r} < 5 W | 2.0 |

5 ≤ P_{r} < 50 W | 4.0 |

50 ≤ P_{r} < 250 W | 8.0 |

P_{r} ≥ 250 W | 10 |

Contact Construction | π_{C} |
---|---|

Metallurgically Bonded | 1.0 |

Non-Metallurgically Bonded and Spring Loaded Contacts | 2.0 |

Component/Inverter Type | NPC | FC | CHB |
---|---|---|---|

IGBTs | 12 × 400 | 12 × 400 | 12 × 100 |

Capacitors | 2 × 300 | 5 × 300 | 3 × 400 |

Diodes | 18 × 100 | 12 × 100 | 12 × 100 |

Total FITs | 7200 | 7500 | 3600 |

Failure Rate (failure/10^{6} hours) | 7.2 | 7.5 | 3.6 |

MTTF | 138,888 | 133,333 | 277,777 |

Type | P_{Loss} (S) | T_{C} (°C) | T_{j} (°C) | π_{T} | π_{A} | π_{E} | π_{Q} | λ_{P} |
---|---|---|---|---|---|---|---|---|

NPC | 95.27 W | 45 | 68.817 | 2.288 | 10 | 1 | 5.5 | 1.511 |

FC | 130.5 W | 45 | 77.625 | 2.636 | 10 | 1 | 5.5 | 1.740 |

CHB | 18.46 W | 45 | 49.615 | 1.637 | 10 | 1 | 5.5 | 1.080 |

Type | P_{Loss} (D) | T_{C} (°C) | T_{j} (°C) | π_{T} | π_{C} | π_{S} | π_{E} | π_{Q} | λ_{P} |
---|---|---|---|---|---|---|---|---|---|

NPC | 11.144 W | 35 | 52.830 | 1.938 | 1 | 0.0518 | 1 | 5.5 | 0.0353 |

FC | 0.088 W | 35 | 35.140 | 1.381 | 1 | 0.0016 | 1 | 5.5 | 0.0007 |

CHB | 1.118 W | 35 | 36.789 | 1.427 | 1 | 0.0128 | 1 | 5.5 | 0.0064 |

Type | Capacitor | T_{A} (°C) | λ_{b} | π_{CV} | π_{E} | π_{Q} | λ_{P} |
---|---|---|---|---|---|---|---|

NPC | 200 mF | 22.7 | 0.045 | 1.471 | 1 | 10 | 0.6619 |

FC | 2200 µF | 22.7 | 0.065 | 0.856 | 1 | 10 | 0.5565 |

CHB | 660 µF | 22.7 | 0.102 | 0.733 | 1 | 10 | 0.7472 |

Parameter/Type | NPC | FC | CHB |
---|---|---|---|

Failure Rate (Failure/10^{6} hours) | 19.9853 | 23.6709 | 15.2784 |

MTTF (hour) | 50,036 | 42,245 | 65,451 |

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**MDPI and ACS Style**

Alavi, O.; Hooshmand Viki, A.; Shamlou, S.
A Comparative Reliability Study of Three Fundamental Multilevel Inverters Using Two Different Approaches. *Electronics* **2016**, *5*, 18.
https://doi.org/10.3390/electronics5020018

**AMA Style**

Alavi O, Hooshmand Viki A, Shamlou S.
A Comparative Reliability Study of Three Fundamental Multilevel Inverters Using Two Different Approaches. *Electronics*. 2016; 5(2):18.
https://doi.org/10.3390/electronics5020018

**Chicago/Turabian Style**

Alavi, Omid, Abbas Hooshmand Viki, and Sadegh Shamlou.
2016. "A Comparative Reliability Study of Three Fundamental Multilevel Inverters Using Two Different Approaches" *Electronics* 5, no. 2: 18.
https://doi.org/10.3390/electronics5020018