# Design Analysis of a Novel Synchronous Generator for Wind Power Generation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Principle of Half-Wave Rectified Excitation

#### 2.1. Generator Model

#### 2.2. Voltage Equation

_{ed}= r

_{e}i

_{ed}+ dλ

_{ed}/ dt − ωλ

_{eq}

e

_{eq}= r

_{e}i

_{eq}+ dλ

_{eq}/ dt + ωλ

_{ed}

e

_{fd}= r

_{fd}i

_{fd}+ dλ

_{fd}/ dt

_{e}stands for the resistance of the stator excitation winding and r

_{fd}, that of the rotor field winding.

_{ed}= L

_{ed}i

_{ed}+ M

_{fd}i

_{fd}

λ

_{eq}= L

_{eq}i

_{eq}

λ

_{fd}= M

_{fd}i

_{ed}+ L

_{fd}i

_{fd}

_{fd}is the mutual inductance between the direct axis winding and the field winding.

#### 2.3. Principle of Brushless Excitation

_{ea}= A

_{f}(t) sin θ

i

_{eb}= A

_{f}(t) sin (θ − 2π / 3)

i

_{ec}= A

_{f}(t) sin (θ − 4π / 3)

_{f}(t). From Equation (3), the dq-axis currents are described by:

_{f}(t) of Equation (3) is a triangular wave in this figure. Since i

_{eq}equals zero, λ

_{eq}becomes zero. When the flux linkage through the field winding λ

_{fd}increases, the negatively-biased diode turns off in the field circuit. When the flux linkage decreases, the diode turns on, and the field current i

_{fd}flows to compensate for the decrease of the flux linkage. The field flux linkage λ

_{fd}becomes the sum of the flux linkage M

_{fd}i

_{ed}produced by the d-axis excitation current i

_{ed}and the flux linkage L

_{fd}i

_{fd}produced by the above field current i

_{fd}. If the time constant related with the decreasing flux is large enough, the flux is almost kept constant.

## 3. Fundamental Performances of a Half-Wave Rectified Brushless Synchronous Generator

#### 3.1. Under DC Excitation

**Figure 6.**Flux linkage and induced voltage under DC current excitation. (

**a**) Flux linkage; (

**b**) induced voltage.

#### 3.2. Under Half-Wave Rectified Excitation

#### 3.2.1. No-Load Condition

_{f}(t) is controlled to a triangular wave with an effective value of 1.1 A and a frequency of 250 Hz. The induced voltage of Phase-a is shown in Figure 9b. It is shown that the flux linkage is almost constant, but the induced voltage includes many harmonics. Figure 9c shows the induced voltage for the 10-degree skewed rotor. The small pulsations or harmonic components are reduced; however, high-level pulses are not reduced. The high-level pulses are generated at every turn-on time of the diode connected with the rotor field windings, and they are not able to be reduced by the rotor skew.

**Figure 9.**No-load induced voltage under half-wave rectified excitation with triangular wave modulation. (

**a**) Flux linkage; (

**b**) induced voltage; (

**c**) induced voltage for skewed rotor.

_{f}(t) of Equation (3). Figure 10a shows the flux linkage when A

_{f}(t) is a sinusoidal wave whose peak value and bias frequency are the same as the triangular wave, shown in Figure 11. Figure 10b,c shows the induced voltages for without and with the rotor skew, respectively. In both induced voltages, the harmonic components exist. However, the high-level pulses generated by the switching of the diode are reduced in comparison with that of the triangular wave in Figure 9b,c.

**Figure 10.**No-load induced voltage under half-wave rectified excitation with sinusoidal wave modulation. (

**a**) Flux linkage; (

**b**) induced voltage; (

**c**) induced voltage for skewed rotor.

#### 3.2.2. Load Condition

_{f}(t) of Equation (3), two functions are selected. One is the triangular wave function with an effective value of 12.9 A and a frequency of 250 Hz. Another is the sinusoidal wave function with the same peak value and frequency as the triangular function.

_{o}is output active power at the load circuit of Figure 12, P

_{i}is iron loss and P

_{c}is the sum of copper loss of the excitation winding and the armature winding. Mechanical loss is ignored.

Load Resistance (Ω) | Induced Voltage (Vrms) | Load Current (Arms) | Output Power (W) | Iron Loss (W) | Copper Loss (W) | Efficiency (%) |
---|---|---|---|---|---|---|

10 | 70.1 | 6.4 | 1069.9 | 77.8 | 126.4 | 86.6 |

20 | 103.0 | 4.9 | 1215.5 | 122.3 | 121.5 | 86.9 |

30 | 114.9 | 3.7 | 1024.2 | 125.3 | 119.2 | 84.9 |

40 | 120.3 | 2.9 | 847.2 | 132.7 | 119.1 | 82.1 |

50 | 123.4 | 2.4 | 715.7 | 137.3 | 120.3 | 79.1 |

Load Resistance (Ω) | Induced Voltage (Vrms) | Load Current (Arms) | Output Power (W) | Iron Loss (W) | Copper Loss (W) | Efficiency (%) |
---|---|---|---|---|---|---|

10 | 79.9 | 7.0 | 1348.8 | 87.4 | 168.3 | 86.4 |

20 | 111.7 | 5.3 | 1432.1 | 127.8 | 164.6 | 86.2 |

30 | 121.7 | 3.9 | 1149.3 | 137.8 | 161.3 | 83.3 |

40 | 126.0 | 3.1 | 930.6 | 143.7 | 161.7 | 79.5 |

50 | 127.8 | 2.5 | 768.3 | 144.5 | 160.1 | 76.8 |

**Figure 14.**Flux linkage and torque wave form at 1800 rpm. (

**a**) Triangular wave modulation (R = 20 Ω); (

**b**) triangular wave modulation (R = 40 Ω); (

**c**) sinusoidal wave modulation (R = 20 Ω); (

**d**) sinusoidal wave modulation (R = 40 Ω).

**Figure 15.**Flux linkage and torque wave form at 600 rpm. (

**a**) Triangular wave modulation (R = 20 Ω); (

**b**) triangular wave modulation (R = 40 Ω); (

**c**) sinusoidal wave modulation (R = 20 Ω); (

**d**) sinusoidal wave modulation (R = 40 Ω).

## 4. Design Analysis for Improving Performance

#### 4.1. Rotor Diameter

_{f}(t) of Equation (3) is the triangular wave with the effective value of 12.9 A. The rotational speed is 1800 rpm. The resistance R of the load circuit is 20 Ω.

Design Model (Rotor Radius (mm)) | Induced Voltage (V) | Output Power (W) | Efficiency (%) |
---|---|---|---|

Design 1 (74.4) | 103.01 | 1215 | 86.9 |

Design 2 (69.4) | 116.01 | 1530 | 87.4 |

Design 3 (64.4) | 115.14 | 1471 | 82.2 |

#### 4.2. Rotor Configuration

Design Model (Rotor Radius (mm)) | Induced Voltage (V) | Output Power (W) | Efficiency (%) |
---|---|---|---|

Design 4 (74.4) | 115.10 | 1,523 | 88.1 |

Design 5 (69.4) | 134.26 | 2,064 | 89.7 |

Design 6 (64.4) | 138.17 | 2,156 | 87.4 |

#### 4.3. Air Gap Length

Design model (Rotor Radius (mm)) | Induced Voltage (V) | Output Power (W) | Efficiency (%) |
---|---|---|---|

Design 7 (74.4) | 139.11 | 2285 | 90.7 |

Design 8 (69.4) | 149.33 | 2640 | 91.7 |

Design 9 (64.4) | 149.67 | 2646 | 91.9 |

## 5. Speed Characteristics

_{f}(t) of Equation (3) is the triangular wave. A solid line shows the characteristics when the amplitude of A

_{f}(t) is kept constant at 12.9 A. The induced voltage and output power increases with increasing the rotational speed. A dotted line shows the characteristics when the amplitude of A

_{f}(t) is decreased to 9.9 A at 3200 rpm. The flux linkage is decreased to 0.5 Wb, and the induced voltage is controlled with 140 V constant.

**Figure 21.**Speed characteristics of Design 8. (

**a**) Flux linkage; (

**b**) induced voltage; (

**c**) torque; (

**d**) output power; (

**e**) efficiency.

## 6. Conclusions

## Conflicts of Interest

## References

- Oyama, J.; Toba, S.; Higuchi, T.; Yamada, E. The characteristics of half-wave rectified brushless synchronous motor. In Proceedings of the Beijing International Conference on Electrical Machines, Beijing, China, 10–14 August 1987; pp. 654–657.
- Oyama, J.; Toba, S.; Higuchi, T.; Yamada, E. The principle and fundamental characteristics of half-wave rectified brushless synchronous motor. Electr. Eng. Jpn.
**1987**, 107, 98–106. [Google Scholar] - Nonaka, S.; Kesamaru, K. Brushless self-excited type single-phase synchronous generator using wound-rotor type three-phase induction machine. Trans. IEEE Jpn
**1981**, 101, 743–750. [Google Scholar] - Sakimura, K.; Higuchi, T.; Yuichi, Y.; Abe, T. Principle and characteristic analysis of a half-wave rectified brushless synchronous generator. In Proceedings of the International Conference on Electrical Machines and Systems, Busan, Korea, 26–29 October 2013; pp. 708–711.

© 2014 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Higuchi, T.; Yokoi, Y.; Abe, T.; Sakimura, K.
Design Analysis of a Novel Synchronous Generator for Wind Power Generation. *Machines* **2014**, *2*, 202-218.
https://doi.org/10.3390/machines2030202

**AMA Style**

Higuchi T, Yokoi Y, Abe T, Sakimura K.
Design Analysis of a Novel Synchronous Generator for Wind Power Generation. *Machines*. 2014; 2(3):202-218.
https://doi.org/10.3390/machines2030202

**Chicago/Turabian Style**

Higuchi, Tsuyoshi, Yuichi Yokoi, Takashi Abe, and Kazuki Sakimura.
2014. "Design Analysis of a Novel Synchronous Generator for Wind Power Generation" *Machines* 2, no. 3: 202-218.
https://doi.org/10.3390/machines2030202