# Optimal Dynamic Analysis of Electrical/Electronic Components in Wind Turbines

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## Abstract

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## 1. Introduction

- Type A: Constant speed.
- -
- A0: WTs use passive stall control;
- -
- A1: WTs employ active stall control;
- -
- A2: WTs use a pitch control system, the most advanced technology used in larger WTs;

- Type B: Limited variable speed;
- Type C: Variable speed with partial-scale frequency converter. With DFIG (doubly fed induction generator);
- Type D: Variable speed with full-scale frequency converter:
- -
- DD: Direct-drive: Gearless and variable speed with full-scale frequency converter:
`o`- DDE: This type uses an electrically excited synchronous generator.
`o`- DDP: This group uses a permanent magnet synchronous generator, PMSG;

- -
- DI: Indirect-drive: Variable speed indirect drive with a full-scale power converter:
`o`- DI1P: It is the only configuration with a single-stage gearbox with PMSG;
`o`- DI3W: Three stages gearbox with a wound rotor synchronous generator;
`o`- DI3P: Three stages gearbox with PMSG;
`o`- DI3S: Three stages gearbox with squirrel-cage induction generator.

- Statistical methods.
- Trend analysis.
- Filtering methods.
- Time-domain analysis.
- Cepstrum analysis.
- Time synchronous averaging
- Fast-Fourier transform.
- Amplitude demodulation.
- Order analysis.
- Wavelet transforms.
- Hidden Markov models.
- Novel approaches.

## 2. Electrical/Electronic Failures Analysis

- Calibration error
- Connection failure
- Electrical overload
- Electrical short
- Insulation failure
- Lightning strike
- Loss of power input
- Conducting debris
- Software design fault

- Electrical insulation
- Electrical failure
- Output inaccuracy
- Software fault
- Intermittent output

## 3. Reliability Analysis

_{i}) and 10 non-basic events (g

_{i}). An event is called a “basic event” if it cannot be broken down into simpler components. They are connected by logical gates. The example shown in Figure 7 has seven “OR” gates and four “AND” gates. Top event is an undesirable event and it is unique in the FT. Non-basic events can be repeated in the FT, but their branch must be the same. FTs provide the information required to carry out a qualitative analysis. BDDs have been successfully found in the constant search for an efficient way to simulate FTs. BDD is a direct graph representation of a Boolean function where equivalent Boolean sub-expressions are uniquely represented [52].

_{sys}= P(CS

_{1}) + P(CS

_{2}) + P(CS

_{3}) + P(CS

_{4}) + … = P(e

_{5})·P(e

_{1}) + P(e

_{6})·(1 − P(e

_{5}))·P(e

_{1}) + P(e

_{10})·(1 − P(e

_{6}))·(1 − P(e

_{5}))·P(e

_{1}) + P(e

_{8})·P(e

_{7})·(1 − P(e

_{10}))·(1 − P(e

_{6}))·(1 − P(e

_{5}))·P(e

_{1}) + …

## 4. FT Dynamic Analysis for Converter, Generator, Electrical and Electronic Components

_{sys}(t) over time. This probability has been obtained for 20 months. It does not continue rise because there are events (periodic functions) that undergo preventive maintenance.

_{sys}to be obtained over time using different time increments to evaluate the system. This is a novelty regarding the state of the art that has resulted in increasing the accuracy of the quantitative analysis. Figure 11 shows the Q

_{sys}obtained by using a variable time increment from 3 to 9 (blue line). The time increment is five times smaller than the increment used from 9 to 20 (green line). This is an important advantage because the critical zone (marked as dashed square) can be analysed in further detail. A threshold has been arbitrarily established with probability of 0.00125 (horizontal red dashed line).

_{sys}, followed by e0015 and e014 and, finally, by e016 and e017 (see Figure 13). The criticality enables the real risk of each failure to be evaluated considering not only the contribution of the event to the global system but also the probability of the event. From Figure 13 it can be gathered that, among the most critical failures, the short circuit is the most probable event. However, the open circuit does not represent an imminent risk in spite of being a very critical failure according to Birnbaum importance.

_{sys}, followed by the events e013, e014, e015, e016 and e017. Only the Birnbaum method demonstrates that the main events are e012, e013 and e014. Therefore, the event ‘short circuit’ should be studied in detail because all the methods provide a high IM value.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

BDD | Binary decision diagram |

BFS | Breadth-first search |

CMS | Condition monitoring system |

CS | Cut-set |

DFIG | Doubly fed induction generator |

DFS | Depth-first search |

FT | Fault tree |

GWEC | Global wind energy council |

IGBT | Insulated gate bipolar transistor |

IM | Importance measure |

O&M | Operation and maintenance |

PFE | power feed equipment |

PMSG | permanent magnet synchronous generator |

PWM | pulse width modulation |

SCADA | Supervisory control and data acquisition system |

TDLR | Top-Down-Left-Right |

WT | Wind turbine |

3L-NPC-BTB | Three-Level Neutral-Point Diode Clamped Back-To-Back |

2L-BTB | Two-level back-to-back voltage source converter |

Formula Expressions | |

CS | Cut-set |

Q_{sys} | Unavailability of the system |

$\left(\mathit{P}\left({\mathit{e}}_{\mathit{i}}\right),\mathit{t}\right)$ | Probability of the event ‘ i’ over time |

$\mathit{\lambda}$ | probability rising velocity |

$\mathit{\alpha}$ | period size |

$\mathit{K}$ | Constant |

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**Figure 1.**Distribution of failure frequencies between different turbine types, sorted by turbine size (Adapted from [5]).

**Figure 2.**Main components of the most installed WT where: 1—pitch system; 2—hub; 3—main bearing; 4—low speed shaft; 5—gearbox; 6—high speed shaft; 7—brake system; 8—generator; 9—yaw system; 10—bedplate; 11—converter; 12—tower; 13—meteorological unit. (Adapted from [10]).

**Figure 3.**Distribution of the component costs for a typical 2 MW wind turbines (adapted from [15]).

**Figure 4.**Annual failure probability for subcomponents (adapted from [29]).

**Figure 5.**Failure root cause distribution (adapted from [37]).

**Figure 6.**The current sensors for the brake hydraulic system inside the main control panel of the WT Reproduced with permission from [42]. Elsevier, 2012.

Ranking Method | TLDR | DFS | BFS | Level | AND |
---|---|---|---|---|---|

Number of CS | 46 | 31 | 36 | 46 | 35 |

Non-Basic Events | Basic Events | ||
---|---|---|---|

Critical Generator Failure | g001 | Abnormal Vibration G | e001 |

Power electronics and electric controls failure | g002 | Cracks | e002 |

Mechanical failure (generator) | g003 | Imbalance | e003 |

Electrical failure (generator) | g004 | Asymmetry | e004 |

Bearing generator failure | g005 | Air-Gap eccentricities | e005 |

Rotor and stator failure | g006 | Broken bars | e006 |

Bearing generator fault | g007 | Dynamic eccentricity | e007 |

Rotor and stator fault | g008 | Sensor Tª error | e008 |

Abnormal signals A | g009 | Temperature above limit | e009 |

Overheating generator | g010 | Short circuit (generator) | e010 |

Electrical fault (PE) | g011 | Open circuit (generator) | e011 |

Mechanical fault (PE) | g012 | Short circuit (electronics) | e012 |

Open circuit (electronics) | e013 | ||

Gate drive circuit | e014 | ||

Corrosion | e015 | ||

Dirt | e016 | ||

Terminals damage | e017 |

Ranking Method | Number of CSs |
---|---|

TDLR | 99 |

DFS | 171 |

BFS | 171 |

Level | 99 |

AND | 99 |

Event | Probability Model | Parameters |
---|---|---|

e001 | Exponential increasing | 𝜆 = 0.0030 months^{−1} |

e002 | Constant | K = 0.0010 |

e003 | Exponential increasing | 𝜆 = 0.0025 months^{−1} |

e004 | Exponential increasing | 𝜆 = 0.0045 months^{−1} |

e005 | Linear increasing | m = 0.0015 months^{−1} |

e006 | Linear increasing | m = 0.0009 months^{−1} |

e007 | Linear increasing | m = 0.0007 months^{−1} |

e008 | Constant | K = 0.0040 |

e009 | Periodic | 𝜆 = 0.0025 months^{−1}, $\alpha $ = 5 months |

e010 | Constant | K = 0.0012 |

e011 | Constant | K = 0.0013 |

e012 | Constant | K = 0.0020 |

e013 | Constant | K = 0.0021 |

e014 | Linear increasing | m = 0.0010 months^{−1} |

e015 | Periodic | 𝜆 = 0.0035 months^{−1}, $\alpha $ = 7 months |

e016 | Periodic | 𝜆 = 0.0015 months^{−1}, $\alpha $ = 10 months |

e017 | Linear increasing | m = 0.0010 months^{−1} |

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**MDPI and ACS Style**

García Márquez, F.P.; Pliego Marugán, A.; Pinar Pérez, J.M.; Hillmansen, S.; Papaelias, M.
Optimal Dynamic Analysis of Electrical/Electronic Components in Wind Turbines. *Energies* **2017**, *10*, 1111.
https://doi.org/10.3390/en10081111

**AMA Style**

García Márquez FP, Pliego Marugán A, Pinar Pérez JM, Hillmansen S, Papaelias M.
Optimal Dynamic Analysis of Electrical/Electronic Components in Wind Turbines. *Energies*. 2017; 10(8):1111.
https://doi.org/10.3390/en10081111

**Chicago/Turabian Style**

García Márquez, Fausto Pedro, Alberto Pliego Marugán, Jesús María Pinar Pérez, Stuart Hillmansen, and Mayorkinos Papaelias.
2017. "Optimal Dynamic Analysis of Electrical/Electronic Components in Wind Turbines" *Energies* 10, no. 8: 1111.
https://doi.org/10.3390/en10081111