# Redundancy Determination of HVDC MMC Modules

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Reliability Prediction Metrics

#### 2.1. Reliability

#### 2.2. Failure Rate

#### 2.3. Mean Time to Failure

#### 2.4. Mean Time to Repair

#### 2.5. Availability and Average Availability

## 3. Reliability Assessment of Power Electronic Systems

#### 3.1. Component-Level Reliability Models

#### 3.2. System or Subsystem-Level Reliability Models

**(1) Part-Count Models**: The main advantage of part-count method lies in its simplicity. A part-count model can provide adequate reliability estimation for small systems. It is also an effective approach to reliability comparison among different power electronic system architectures at the beginning of design stage. However, for the systems that can tolerate some failures or that can be repaired, the approach leads to over conservative results [3].

**(2) Combinatorial Models**: Combinatorial models are extensions to part-count models and include fault trees, success trees, and reliability blocks diagrams. These methods can be used to analyze reliability of simple redundant systems with Journal of Power Electronics perfect coverage. Fault tree has been used to analyze reliability of electric drive systems. Unfortunately, combinatorial models cannot reflect the details of fault-tolerant systems, such as repair process, imperfect coverage, state rates, order of component failures, and reconfiguration [3].

**(3) Markov Model**: The Markov model is based on graphical representation of system states that correspond to system configurations, which are reached after a unique sequence of component failures and transitions among these states [3]. The system is said in failure-free state when all components are nonfaulted. The system can evolve from the failure other states when faults occur to the components. Markov chain is a very effective approach to quantify the reliability of fault-tolerant systems. This approach can cover many features of fault-tolerant systems, such as sequence of failures, failure coverage, and state-dependent failure rates. There are some limitations associated with Markov model. One important property of Markov process is that the transition probability from one state to another does not depend on the previous states but only on the present state. Hence, the Markov model cannot be used to evaluate the system reliability when components have time-varying failure rates. Another shortcoming is that state space grows exponentially with the number of components. For large system, it is difficult to generate the Markov model from the system functional description and components failure analysis. The challenge of applying Markov models to increasingly complicated systems can be clearly appreciated in a high-power multilevel converter that may have hundreds of components and subsequent failure mode transitions.

**(4) Binomial Distribution Model**: The binomial failure model is an important probability model that is used when there are two possible outcomes (hence “binomial”). In a binomial experiment there are two mutually exclusive outcomes, often referred to as “success” and “failure”. Probability of success is p, the probability such an experiment whose outcome is random and can be either of two possibilities, “success” or “failure”, is called a Bernoulli trial. Binomial Distribution Model is defined as [1,4,5]:

## 4. Module Reliability of VSC Multilevel Converter

Module Voltage | Number of Submodule |
---|---|

1.6 kV | 375 |

1.8 kV | 334 |

2.0 kV | 300 |

^{−9}failures/hour).

Component | No. | Failure Rate (FIT) | Total Failure Rate | Comments |
---|---|---|---|---|

- IGBT and gate drive | 2 | 40 | 80 | Power Circuit |

- Thyristor and gate drive | 1 | 47 | 47 | |

- Bypass Switch | 1 | 1000 | 1000 | |

- Power Capacitor | 1 | 10 | 10 | |

- Power Resistor | 1 | 265 | 265 | |

- Custom IC | 1 | 150 | 150 | Control |

- Optical Rx/Tx | 2 | 100 | 200 | |

- IC Circuit | 1 | 13 | 13 | |

- Ferrite Core | 2 | 22 | 44 | Power Supply |

- Switching Power Supply | 1 | 1000 | 1000 |

_{0}to 𝛾

_{11}represent the values from the “Total Failure Rate” column as elements in a vector the expression becomes:

^{3}[FIT]

**Figure 4.**Unavailability function for the target system with 334 modules according to redundant modules increment.

- Maintenance periods are 1 year, 2 years and 3 years
- IGBT devices used are 1.6 kV, 1.8 kV and 2 kV
- FIT of DC/DC converter changed 1000 to 500

- •
- seven modules for a 1.6 kV IGBT device,
- •
- six modules for a 1.8 kV IGBT device,
- •
- five modules for a 2 kV IGBT device

- •
- 22 modules for a 1.6 kV IGBT device,
- •
- 20 modules for a 1.8 kV IGBT device5,
- •
- 17 modules for a 2 kV IGBT device

- •
- 28 modules for a 1.6 kV IGBT device,
- •
- 25 modules for a 1.8 kV IGBT device5,
- •
- 20 modules for a 2 kV IGBT device

- •
- 7 modules for a 1-year maintenance interval,
- •
- 12 modules for a 2-year maintenance interval,
- •
- 15 modules for a 3-year maintenance interval.

Module Voltage | No. of Module | Additional Cells Against Maintenance Period | ||
---|---|---|---|---|

1 Year | 2 Years | 3 Years | ||

1.6 kV | 375 | 7 | 22 | 28 |

1.8 kV | 334 | 6 | 20 | 25 |

2.0 kV | 300 | 5 | 17 | 20 |

## 5. Conclusions and Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Department of Defense. Military Handbook: Electronic Reliability Design Handbook; MIL-HDBK-338B1; Department of Defense: Washington, DC, USA, 1998.
- Department of Defense. Military Handbook: Reliability Prediction of Electronic Equipment; MIL-HDBK-217F; Department of Defense: Washington, DC, USA, 1991.
- Song, Y.; Wang, B. Survey on Reliability of Power Electronic Systems. IEEE Trans. Power Electron.
**2013**, 28, 591–604. [Google Scholar] [CrossRef] - Høyland, A.; Rausand, M. System Reliability Theory: Models and statistical methods; Wiley: New York, NY, USA, 1994. [Google Scholar]
- Dummer, G.W.A. Electronics Reliability—Calculation and Design: Electrical Engineering Division; Pergamon: Oxford, UK, 1966. [Google Scholar]
- Voltage Source Converter Development Engineering Report; AREVA: Paris, France, 2008.
- Boas, M.L. Mathematical Methods in the Physical Sciences, 3rd ed.; Wiley: New York, NY, USA, 2005. [Google Scholar]

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**MDPI and ACS Style**

Kim, C.; Lee, S.
Redundancy Determination of HVDC MMC Modules. *Electronics* **2015**, *4*, 526-537.
https://doi.org/10.3390/electronics4030526

**AMA Style**

Kim C, Lee S.
Redundancy Determination of HVDC MMC Modules. *Electronics*. 2015; 4(3):526-537.
https://doi.org/10.3390/electronics4030526

**Chicago/Turabian Style**

Kim, Chanki, and Seongdoo Lee.
2015. "Redundancy Determination of HVDC MMC Modules" *Electronics* 4, no. 3: 526-537.
https://doi.org/10.3390/electronics4030526