# Parameter Identification of Doubly-Fed Induction Wind Turbine Based on the ISIAGWO Algorithm

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Mathematical Model of DFIG

- (1)
- Voltage equation:

- (2)
- Magnetic chain equation:

- (3)
- Electromagnetic torque, power equation

## 3. Algorithm Introduction

#### 3.1. Grey Wolf Algorithm

#### 3.2. Adaptive Grey Wolf Algorithm Based on Information-Sharing Search Strategy (ISIAGWO)

#### 3.3. Algorithm Performance Test

## 4. DFIG Parameter Identification

#### 4.1. Identifiability of the Parameters

#### 4.2. The DFIG Identification Model

#### 4.3. Principle and Steps of the ISIAGWO Algorithm for Identification

## 5. Simulation and Analysis

#### 5.1. Parameter Settings

#### 5.2. Results and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Trajectory sensitivity of ${\mathit{R}}_{\mathit{s}}$, ${\mathit{R}}_{\mathit{r}}$, and ${\mathit{L}}_{\mathit{m}}$.

**Figure 18.**(

**a**) Actual and identification model Ids output; (

**b**) Actual and identification model Idr output; (

**c**) Actual and identification model Iqs output; (

**d**) Actual and identification model Iqr output.

Name of Function | Functions | Value Range | Optimum |
---|---|---|---|

Sphere Function | ${f}_{1}(x)={\displaystyle \sum _{i=1}^{n}{x}_{i}^{2}}$ | [−100, 100] | 0 |

Schwefel’s Problem 2.22 | ${f}_{2}(x)={\displaystyle \sum _{i=1}^{30}\left|xi\right|+{\displaystyle \prod _{i=1}^{30}\left|xi\right|}}$ | [−10, 10] | 0 |

Generalized Rastrigin’s Function | ${f}_{3}(x)={\displaystyle \sum _{i=1}^{30}[{x}_{i}^{2}-10\mathrm{cos}(2\pi {x}_{i})+10]}$ | [−5.12, 5.12] | 0 |

Generalized Griewank’s Function | $\begin{array}{c}{f}_{4}(x)=-20\mathrm{exp}(-0.2\sqrt{\frac{1}{30}{\displaystyle \sum _{i=1}^{30}{x}_{i}^{2}}})-\\ \mathrm{exp}(\frac{1}{30}{\displaystyle \sum _{i=1}^{30}\mathrm{cos}2\pi xi})+20+e\end{array}$ | [−32, 32] | 0 |

Functions | GWO | IGWO | ISIAGWO | ||||||
---|---|---|---|---|---|---|---|---|---|

Optimum | Mean | Variance | Optimum | Mean | Variance | Optimum | Mean | Variance | |

${f}_{1}$ | 2.286 × 10^{−21} | 6.680 × 10^{1} | 4.357 × 10^{2} | 7.842 × 10^{−24} | 6.775 × 10^{1} | 4.494 × 10^{2} | 6.679 × 10^{−42} | 2.654 × 10^{1} | 1.639 × 10^{2} |

${f}_{2}$ | 2.580 × 10^{−13} | 4.817 × 10^{−1} | 2.082 | 2.681 × 10^{−15} | 4.532 × 10^{−1} | 3.107 | 4.228 × 10^{−22} | 3.406 × 10^{−1} | 1.886 |

${f}_{3}$ | 4.979 | 9.456 | 6.765 | 9.950× 10^{−1} | 3.987 | 6.235 | 0.000 | 1.531 | 6.168 |

${f}_{4}$ | 1.737× 10^{−11} | 7.779× 10^{−1} | 2.888 | 4.232× 10^{−13} | 7.137× 10^{−1} | 2.801 | 3.997× 10^{−15} | 6.900× 10^{−1} | 2.697 |

Components | Parameters | Values |
---|---|---|

Doubly-fed generator | Stator resistance ${R}_{s}$ (p.u.) | 0.023 |

Stator inductors ${L}_{r}$ (p.u.) | 0.180 | |

Rotor resistance ${R}_{r}$ (p.u.) | 0.016 | |

Rotor inductors ${L}_{r}$ (p.u.) | 0.160 | |

Stator-rotor mutual inductance ${L}_{m}$ (p.u.) | 2.900 | |

Wind Turbine | Rotor inertia time constant ${H}_{g}$ (s) | 0.685 |

Wind turbine inertia time constants ${H}_{w}$ (s) | 4.320 | |

Damping factor of the shaft system ${D}_{sh}$ (p.u.) | 1.110 | |

Shaft system stiffness factor ${K}_{sh}$ (p.u.) | 1.500 | |

polar logarithms $P$ | 3.000 | |

Grid | Grid voltage $U$ (kV) | 120.000 |

Grid capacity $S$ (MVA) | 2500.000 |

Parameters | Initialization Range | True Value |
---|---|---|

Stator resistance ${R}_{s}(p.u.)$ | 0.01500~0.03200 | 0.02300 |

Rotor resistance ${R}_{r}(p.u.)$ | 0.01000~0.02200 | 0.01600 |

Stator inductors ${L}_{s}(p.u.)$ | 0.10000~0.22000 | 0.1800 |

Rotor inductors ${L}_{r}(p.u.)$ | 0.10000~0.22000 | 0.1600 |

Stator-rotor mutual inductance ${L}_{m}(p.u.)$ | 1.50000~5.00000 | 2.900 |

Algorithms | Minimum | Average | Variance |
---|---|---|---|

GWO | 3.2388 | 9.0968 | 10.0749 |

IGWO | 2.3159 | 4.3267 | 3.5354 |

ISIAGWO | 0.6576 | 1.01616 | 2.26446 |

**Table 6.**Comparison of the results of three algorithms for the identification of generator parameters.

Algorithms | $\mathit{R}\mathit{s}$ | $\mathit{R}\mathit{r}$ | $\mathit{L}\mathit{s}$ | $\mathit{L}\mathit{r}$ | $\mathit{L}\mathit{m}$ | |
---|---|---|---|---|---|---|

GWO | True value | 0.02300 | 0.01600 | 0.18000 | 0.16000 | 2.90000 |

Identifying value | 0.02331 | 0.01671 | 0.16764 | 0.16921 | 2.83616 | |

Relative error% | −1.34% | −4.44% | 6.87% | −5.75% | 2.20% | |

IGWO | True value | 0.02300 | 0.01600 | 0.18000 | 0.16000 | 2.90000 |

Identifying value | 0.02260 | 0.01582 | 0.17441 | 0.16671 | 2.85539 | |

Relative error% | 1.75% | 1.10% | 3.11% | −4.19% | 1.54% | |

ISIAGWO | True value | 0.02300 | 0.01600 | 0.18000 | 0.16000 | 2.90000 |

Identifying value | 0.02314 | 0.01614 | 0.18137 | 0.16269 | 2.93127 | |

Relative error% | −0.63% | −0.85% | −0.76% | −1.68% | −1.08% |

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**MDPI and ACS Style**

Yang, F.; Zeng, Y.; Qian, J.; Li, Y.; Xie, S. Parameter Identification of Doubly-Fed Induction Wind Turbine Based on the ISIAGWO Algorithm. *Energies* **2023**, *16*, 1355.
https://doi.org/10.3390/en16031355

**AMA Style**

Yang F, Zeng Y, Qian J, Li Y, Xie S. Parameter Identification of Doubly-Fed Induction Wind Turbine Based on the ISIAGWO Algorithm. *Energies*. 2023; 16(3):1355.
https://doi.org/10.3390/en16031355

**Chicago/Turabian Style**

Yang, Fanjie, Yun Zeng, Jing Qian, Youtao Li, and Shihao Xie. 2023. "Parameter Identification of Doubly-Fed Induction Wind Turbine Based on the ISIAGWO Algorithm" *Energies* 16, no. 3: 1355.
https://doi.org/10.3390/en16031355