# Comparative Analysis of Parallel Hybrid Magnet Memory Machines with Different PM Arrangements

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- High torque density and power density; high torque for starting, at low speeds and hill climbing, and high power for high-speed cruising;
- (2)
- wide speed range, with a constant power operating range of around 3~4 times the base speed being a good compromise between the peak torque requirement of the machine and the volt-ampere rating of the inverter;
- (3)
- high efficiency over wide speeds and torque ranges, including low torque operation;
- (4)
- intermittent overload capability, typically twice the rated torque for short durations;
- (5)
- high reliability and robustness appropriate to the vehicle environment;
- (6)
- acceptable cost;
- (7)
- low acoustic noise and low torque ripple.

## 2. Configurations and Operating Principle

#### 2.1. Machine Configurations

#### 2.2. Operating Principle

_{c}

_{2}, but the values of remanence B

_{r}

_{1k}are different. The set of recoil lines can be expressed as [14,15]:

_{0}and μ

_{r}are the vacuum permeability and the relative permeability of LCF PMs, respectively; H

_{m}is the remagnetizing field intensity, while B

_{r}

_{1k}represents the remanence corresponding to the kth sets of hysteresis loops.

_{mr}of the LCF PM can be defined as a ratio of B

_{r}

_{1k}to the remanence B

_{r}

_{1}, i.e.,

_{mr}ranges from −1 to 1, which means that the flux linkage can be flexibly adjusted as the operating point of LCF PM moves along the different recoil lines. The value of k

_{mr}is “1” when the LCF PMs are magnetized with HCF PMs in the same direction, while changes to “−1” with two opposite magnetized directions in turn. Figure 4 shows the open-circuit field distributions of the HLH and LHL structure under the flux-enhanced (K

_{mr}= 1) and flux-weakened (K

_{mr}= −1) states. It is clear to see that the magnetic flux paths and flux density distributions of the two structures are basically the same under the flux-enhanced state. On the other hand, the HCF PM fields are short-circuited by the LCF PM fields at the flux-weakened state, leading to a flux loop formed within the rotor core.

## 3. Analytical Analyses of PHMMM

_{m}

_{1}and F

_{m}

_{2}represent the equivalent MMFs of HCF and LCF PMs, respectively. Besides, R

_{m}

_{1}and R

_{m}

_{2}are the magnetic reluctances of HCF and LCF PMs, respectively, while R

_{g}is the air-gap magnetic reluctance.

_{m}can be expressed as:

_{δ+}and Φ

_{δ-}into (5), the flux adjusting ratio of the proposed HPMMM can be rewritten as:

_{c}

_{1}and H

_{c}

_{2}are the coercive forces of LCF and HCF PMs, respectively; μ

_{r}

_{1}and μ

_{r}

_{2}are the relative permeability of LCF and HCF PMs, respectively; moreover, A

_{m}

_{1}and A

_{m}

_{2}represent the cross-sectional, respectively.

_{m}of the PHMMM is associated with the ratio of A

_{m}

_{1}to A

_{m}

_{2}. Since the level of the coercive force and remanence of the two types of PMs are different, even if the usage of two kinds of PMs in different structures is the same, the thickness of the two types of PMs is still different due to the geometric limitation of the U-shaped structure, so that the magnetic resistances of the two types of PMs in HLH and LHL structures are unequal. As a result, the peak air-gap fluxes of the HLH and LHL structures are different.

_{m}

_{1}to A

_{m}

_{2}, which can be also evidenced by the open-circuit field distributions in Figure 5. Moreover, the fundamental back EMFs, as functions of the magnetization ratio of LCF PMs, are shown in Figure 6. It can be observed that the HLH structure shows a slightly wider flux regulation range due to the larger ratio of A

_{m}

_{1}to A

_{m}

_{2}, as presented in (7). In addition, the HLH structure shows quite a low fundamental back EMF at the flux-weakened state, resulting in low torque and efficiency. In this case, according to the required flux adjusting range of three times, the MSs “K

_{mr}= 1” and “K

_{mr}= −0.5” are chosen for further analysis.

## 4. Electromagnetic Performance Comparison

#### 4.1. Open-Circuit Performance

_{mr}= −0.5 state, while the flux density of the LHL structure under K

_{mr}= 1 state is basically the same as the HLH structure.

#### 4.2. Magnetization Performance

#### 4.3. Torque Characteristics

_{0}and the armature current I

_{a}, that is to say, q axis refers to the current angle of 0 current degrees, and d axis corresponds to the current angle of −90 current degrees. It is obvious that the d-axis inductance experiences a more significant fluctuation than the q-axis inductance for the two structures due to the design of the q-axis barriers. For the HLH structure, the flux-intensifying characteristics with “L

_{d}> L

_{q}” can be achieved when the current angle is between “−15” and “35” degrees. For the LHL structure, the range will be slightly reduced, between“−5” and “35” degrees.

_{mr}= 1” state are basically the same. However, the LHL structure torque amplitude is relatively higher under the “K

_{mr}= −0.5” state. This is mainly resulted from larger fifth-order harmonics in the back EMFs, as reflected in Figure 7b.

_{mr}= −0.5” state is illustrated in Figure 15. It can be observed that the maximum torques all occur at a positive current angle of 15 and 25 elec. deg. in the two cases, respectively. Due to the low MS of the LCF PMs, the magnet torque decreases significantly compared with that at the flux-enhanced state.

#### 4.4. Demagnetization Withstand Capability

_{1}and E

_{2}are the fundamental back EMFs before and after applying rated current. The demagnetization ratio DR of the two structures under different loads is calculated, as shown in Figure 17.

_{mr}= 1 are higher than those of the HLH structure. Moreover, the unintentional demagnetization will aggravate with larger current amplitude. In addition, both two structures show a small cross-coupling demagnetization ratio under the “K

_{mr}= −0.5” state. This is because the HCF PMs are short-circuited by LCF PMs, leading to a flux loop formed within the rotor core. In this case, the HCF PMs can stabilize the working points of the LCF PMs in turn. It can be summarized that the LHL structure turns out to be more susceptible to the armature reaction, which shows a lower undesired demagnetization withstand capability.

#### 4.5. Efficiency Performance

_{mr}= ±1, ±0.5, 0) of the two motors are simulated, and the comprehensive efficiency map is obtained as shown in Figure 18. It can be seen that both motors have relatively high comprehensive efficiency.

## 5. Experimental Verification

_{mr}= 1 and the low magnetization state K

_{mr}= −0.5. The torque-speed curves obtained are shown in Figure 23, and the experimental results can be seen to have high consistency with the simulation.

_{mr}= 1 and K

_{mr}= −0.5 states. It can be seen that it is similar to the simulation situation. The pulse current demagnetization can be applied to the motor at point A to effectively broaden the motor operating area. The turning speed is about 3200 rpm.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**Open-circuit field distributions of proposed PHMMMs under different magnetization. (

**a**) HLH structure. (

**b**) LHL structure.

**Figure 8.**Open-circuit air gap flux density waveforms under different MSs. (

**a**) Waveforms. (

**b**) Harmonic spectra.

**Figure 9.**Variations of LCF PM working point of HLH and LHL structures subject to a d-axis demagnetizing current pulse of 2A.

**Figure 10.**Open-circuit back-EMF fundamental magnitudes of two structures as functions of demagnetizing current pulse @ 1500 r/min.

**Figure 11.**Open-circuit back-EMF fundamental magnitudes of two structures as functions of remagnetizing current pulse @ 1500 r/min.

**Figure 12.**Comparison of d/q-axis inductance in two structures under various current angles. (

**a**) Kmr = 1. (

**b**) Kmr = −0.5.

**Figure 13.**Cogging torque of HLH and LHL structures under different MSs. (

**a**) K

_{mr}= 1. (

**b**) K

_{mr}= −0.5.

**Figure 14.**Torque against current angle characteristics (rated current = 6.35 Arms) when K

_{mr}= 1. (

**a**) HLH structure. (

**b**) LHL structure.

**Figure 15.**Torque against current angle characteristics (rated current = 6.35 Arms) when K

_{mr}= −0.5. (

**a**) HLH structure. (

**b**) LHL structure.

**Figure 16.**Steady torque waveforms (rated current = 6.35 Arms). (

**a**) HLH structure. (

**b**) LHL structure.

**Figure 22.**Comparison of the back-EMF fundamental magnitudes as functions of (

**a**) demagnetizing and (

**b**) remagnetizing current pulse.

**Figure 23.**The T-N curve of PHMMM under the control of i

_{d}constant 0. (

**a**) K

_{mr}= 1 (

**b**) K

_{mr}= −0.5.

Items | HLH | LHL |
---|---|---|

Rated power (kW) | 1.2 | |

Rated speed (r/min) | 1500 | |

Outer diameter of stator (mm) | 122 | |

Inner diameter of stator (mm) | 63.5 | |

Back-iron thickness (mm) | 8.25 | |

Stator tooth width (mm) | 4.8 | |

Air-gap length (mm) | 0.35 | |

Active stack length (mm) | 55 | |

HCF PM grade | NdFeB | N35SH |

LCF PM grade | AlNiCo 9 | |

HCF/LCF PM coercivity (kA/m) | 915/112 | |

HCF/LCF PM remanence (T) | 1.2/1.0 | |

Steel grade | 35CS440 | |

HCF PM thickness × length (mm × mm) | 3.5 × 6 | 3 × 7 |

LCF PM thickness × length (mm × mm) | 3 × 7 | 3.5 × 6 |

Armature winding turns per phase | 210 | |

Rated current (Arms) | 6.35 | |

Current density (A/mm2) | 6.5 | |

DC-link voltage U_{dc} (V) | 200 |

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**MDPI and ACS Style**

Wang, Y.; Yang, H.; Zheng, H.; Lin, H.; Lyu, S.
Comparative Analysis of Parallel Hybrid Magnet Memory Machines with Different PM Arrangements. *World Electr. Veh. J.* **2021**, *12*, 177.
https://doi.org/10.3390/wevj12040177

**AMA Style**

Wang Y, Yang H, Zheng H, Lin H, Lyu S.
Comparative Analysis of Parallel Hybrid Magnet Memory Machines with Different PM Arrangements. *World Electric Vehicle Journal*. 2021; 12(4):177.
https://doi.org/10.3390/wevj12040177

**Chicago/Turabian Style**

Wang, Yixian, Hui Yang, Hao Zheng, Heyun Lin, and Shukang Lyu.
2021. "Comparative Analysis of Parallel Hybrid Magnet Memory Machines with Different PM Arrangements" *World Electric Vehicle Journal* 12, no. 4: 177.
https://doi.org/10.3390/wevj12040177