# A Review of the Advancements in the Design of Brushless Doubly Fed Machines

^{*}

## Abstract

**:**

## 1. Introduction

- The evolution of cascaded IMs to contemporary BDFM topologies. In this section, significant contributions to the present day BDFM topologies are highlighted, with the underlying reasons for these design developments.
- Discussions on the aspects of BDFM design. A comprehensive run-down of recent developments and approaches employed in the design of BDFMs, are presented in this section.

## 2. Development of BDFMs from Cascade Induction Motors

#### 2.1. The Thompson Motor

#### 2.2. The Lydall Motor

#### 2.3. The Hunt Motor

#### 2.4. The Broadway & Burbridge Motor

#### 2.5. Cascade Systems to Brushless Doubly Fed Operations

## 3. Recent BDFM Design Development

#### 3.1. Stator Winding Development

#### 3.1.1. Relative Winding Pole Size

#### 3.1.2. Unbalanced Magnetic Pull and Magnetic Coupling

#### 3.1.3. Commonly Used Pole Pair Combinations

#### 3.2. Rotor Winding Development

#### 3.3. BDFM Sizing and Power Ratings

#### 3.4. Vibrations and Harmonics Mitigation

#### 3.5. BDFM Design and Optimization Procedures

## 4. Conclusions and Future Research

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

BDFM | Brushless doubly fed machine |

CC | Coupled circuit |

CW | Control winding |

DFIG | Doubly fed induction generator |

EEC | Electric equivalent circuit |

FEA | Finite element analysis |

IL | Isolated loops |

IM | Induction machine |

LVRT | Low voltage ride through |

MEC | Magnetic equivalent circuit |

NL | Nested loops |

NSGA-II | Non dominated sorting genetic algorithm |

O&M | Operational and maintenance |

${p}_{1}$ | PW pole pairs |

${p}_{2}$ | CW pole pairs |

PW | Power winding |

RSA | Response surface approximation |

SCIM | Squirrel cage induction motor |

SW | Series wound |

UMP | Unbalanced magnetic pull |

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**Figure 1.**Steinmetz cascade system examples: (

**a**) two motors with rotor of primary motor connected to secondary stator, (

**b**) two motors with both rotors connected to each other, and (

**c**) four motors [16].

**Figure 2.**Thompson motor winding illustration [14].

**Figure 3.**Schematic representation of the Lydall motor [13].

**Figure 5.**Broadway & Burbridge rotor winding arrangements: (

**a**) Graded winding rotor and (

**b**) multicircuit winding rotor [18].

**Figure 6.**Broadway & Burbridge rotor prototypes: (

**a**) Graded winding rotor for (6 + 2) poles machine, and (

**b**) multicircuit rotor for (18 + 12) poles machine [18].

**Figure 9.**Widely used BDFM rotors: (

**a**) NL rotor winding arrangement for ${p}_{1}+{p}_{2}=5$, (

**b**) NL rotor prototype [42], and (

**c**) Cage + NL rotor prototype.

**Figure 10.**Double layer bar rotor: (

**a**) Winding arrangement for ${p}_{1}/{p}_{2}=2/4$, and (

**b**) prototype [30].

**Figure 12.**Proposed design procedure for a 6-MW BDFM [4].

**Figure 13.**Design process and thermal model in [61]: (

**a**) Design flow chart, and (

**b**) Radial equivalent thermal network of a BDFM.

**Figure 15.**Design process proposed by authors: (

**a**) Geometric and winding design process and (

**b**) optimization process.

Parameters | Pole Pair Combinations $({\mathit{p}}_{1}/{\mathit{p}}_{2})$ | ||
---|---|---|---|

2/3 | 2/4 | 4/6 | |

Power density [29,38,39] | High | Medium | Low |

Efficiency [29,38,39] | High | Medium | Low |

Torque ripple [38] | Low | High | Low |

Harmonic distortion [40,41] | Low | High | Low |

UMP [35,36] | Present | - | - |

**Table 2.**Resistance descriptions in thermal model [61].

Component | Description |
---|---|

R_{s0} | Thermal resistance between external frame and environment with thermal resistance of external frame |

R_{s1} | Thermal resistance of stator core |

R_{s2} | Thermal resistance of coil insulator |

R_{s3}/R_{s5}R _{s7}/R_{s9} | Thermal resistance of PW & CW end-winding to middle of slot at drive end/non-drive end sections |

R_{s4}/R_{s6}R _{s8}/R_{s10} | Thermal resistance between PW & CW end-winding and environment at drive end/non-drive end sections |

R_{ag} | Thermal resistance between rotor and stator |

R_{r1} | Thermal resistance of rotor slot insulator |

R_{r2}/R_{r4} | Thermal resistance of rotor end-winding to middle of slot at drive end/non-drive end sections |

R_{r3}/R_{r5} | Thermal resistance between rotor end-winding and environment at drive end/non-drive end sections |

R_{r6} | Thermal resistance of rotor core |

R_{r7} | Thermal resistance between shaft and environment |

P_{fe,(s/r)}, P_{fric} | Stator/rotor iron, frictional losses |

P_{cu,ew}, P_{cu,slot} | End-winding, slot copper losses |

Description | Relevant References | Models/Analytical Methods | Applications/Advantages | Limitations |
---|---|---|---|---|

6 MW BDFM design | [4,23,58] | Equivalent circuit models, CC models, FEA | Comprehensive MW rated BDFM design | Impractical for smaller designs |

BDFM design with EEC and MEC models | [59,60] | EEC and MEC models | Computationally cheap | Limited functionality |

Electromagnetic and thermal design of BDFMs | [61,62] | EEC, MEC & thermal models, vibration analysis, 2D FEA, imperialist competitive algorithm | Robust design procedure; broad functionality | Complex implementation |

BDFM rotor design and power density optimization | [49,66,67] | CC model, Transient FEA, NSGA-II, Response surface approximations | Rotor type selection; Systematic power output evaluation; computationally cheap optimization | No thermal considerations; slightly complex implementation |

Electric and magnetic loading optimization | [63,64] | Equivalent circuit model, Tabu search method | Maximizing power output, easy implementation | Power factor constraint too low |

Multi-objective optimizations | [39,40,65] | Magnetostatic FEA, NSGA-II | Computationally cheap optimizations; material cost, efficiency & torque optimizations | No power factor consideration |

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**MDPI and ACS Style**

Olubamiwa, O.I.; Gule, N.
A Review of the Advancements in the Design of Brushless Doubly Fed Machines. *Energies* **2022**, *15*, 725.
https://doi.org/10.3390/en15030725

**AMA Style**

Olubamiwa OI, Gule N.
A Review of the Advancements in the Design of Brushless Doubly Fed Machines. *Energies*. 2022; 15(3):725.
https://doi.org/10.3390/en15030725

**Chicago/Turabian Style**

Olubamiwa, Oreoluwa I., and Nkosinathi Gule.
2022. "A Review of the Advancements in the Design of Brushless Doubly Fed Machines" *Energies* 15, no. 3: 725.
https://doi.org/10.3390/en15030725