#
Mathematical Model Derivation and Experimental Verification of Novel Consequent-Pole Adjustable Speed PM Motor^{ †}

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Overview of Novel Consequent-Pole PM Motor

#### 2.1. Motor Structure and Driving Principle

#### 2.2. Effect of Adjustable Speed

_{d}= −30 A) and the FFT analysis results. From Figure 5, it can be seen that the U-phase flux linkage can be varied by field weakening (I

_{d}= −30 A) because the primary component of the flux linkage at field weakening is 12% of the primary component of the flux linkage at no load. Figure 6 shows the N-T characteristics of the proposed motor at I

_{d}= 0 control and I

_{d}= −30 A. It can be seen from Figure 6 that the rotational speed at low load is increased by lowering the back e.m.f. due to field weakening.

#### 2.3. Mathematical Model Derivation

#### 2.3.1. Magnetic Circuit of the Novel Consequent-Pole PM Motor

_{s}is the reluctance of the stator back yoke, R

_{t}is the reluctance of the stator teeth, R

_{g}is the reluctance of the air gap between stator and rotor, R

_{r}is the reluctance of the rotor, and R

_{pu}, R

_{pv}, R

_{pw}, R′

_{pu}, R′

_{pv}, and R′

_{pw}are the reluctances of the rotor core surface. N is the number of coil turns in each phase. R

_{pu}, R

_{pv}, R

_{pw}, R′

_{pu}, R′

_{pv}, and R′

_{pw}are variable depending on the rotation position because the reluctance of the magnetic pole part and the image pole part have a different value. Since the reluctance of the rotor core surface in each phase is a square wave with respect to rotor rotation, it is expressed by Equations (1)–(6) using the Fourier series. When the U-phase axis coincides with the d-axis, θ = 0 (electric angle) and R

_{ac}is the square wave amplitude. The reason why Equations (4)–(6) have the opposite sign of Equations (1)–(3) is that Equations (4)–(6) have the opposite phase of Equations (1)–(3). However, the model is expressed using the Fourier series to make the model similar to the real reluctance. In this way, the validity of the mathematical model can be judged by comparing it with the analysis results for each detailed part.

#### 2.3.2. Six-Phase Hexagon-Star Transformation

_{1}–R

_{6}, r

_{1}–r

_{6}) are equivalent (R, r), and the magnetomotive force is a symmetric six-phase alternating current with an amplitude value of E. In each magnetic circuit, the currents (i, i′) flowing in one phase are calculated using the superposition theorem. Then, the equivalent conversion of the reluctance is considered from its current value. Figure 10 shows each magnetic circuit when only E

_{1}is supplied and E

_{2}to E

_{6}are shorted.

_{2}is supplied, and E

_{1}and E

_{3}to E

_{6}are shorted, the current ${i}_{E2}$ is as follows:

_{1}is expressed by:

_{6}is as follows:

_{2}is supplied, and E

_{1}and E

_{3}to E

_{6}are shorted, the current $i{\prime}_{E2}$ is as follows:

#### 2.3.3. Derivation of the Theoretical Equation for the Armature Flux

_{d}′ is the DC component term, and R

_{ac}is the amplitude of the AC component. The Fourier series is simply expressed as Σ

_{u}, Σ

_{v}, and Σ

_{w}for each phase.

_{uu}

_{1}) flowing from the U1-phase is generated by the magnetomotive force of the U1-phase, and the armature fluxes (Φ

_{uv}

_{1}, Φ

_{uv}

_{1}, Φ

_{uu}

_{2}, Φ

_{uv}

_{2}, Φ

_{uw}

_{2}) flowing into the U1-phase are generated by the magnetomotive force of the V1, W1, U2, V2, and W2-phases. Therefore, the armature magnetic flux (Φ

_{U}

_{1}) flowing in the U1-phase can be expressed by:

_{u}

_{1}, the mutual inductance between the U-phase and V-phase is M

_{uv}

_{1}, and the mutual inductance between the U-phase and W-phase is M

_{uw}

_{1}.

_{V}

_{1}, Φ

_{W}

_{1}, Φ

_{U}

_{2}, Φ

_{V}

_{2}, Φ

_{W}

_{2}) flowing in the V1, W1, U2, V2, and W2-phases can be derived in a similar way to the derivation of the armature magnetic flux (Φ

_{U}

_{1}) flowing in the U1-phase. The winding connection of the novel consequence-pole motor is a three-phase configuration connecting in-phase windings in series. Therefore, the theoretical value of the armature flux flowing in the U-phase is the sum of the armature flux flowing in the U1 and U2 phases. Here, only the theoretical equation of the armature flux linkage Φ

_{U}flowing in the U-phase is shown as:

_{u}of the U-phase, the coefficient of the V-phase current is the mutual inductance M

_{uv}between the U-phase and the V-phase, and the coefficient of the W-phase current is the mutual inductance M

_{uw}between the U-phase and the W-phase.

#### 2.3.4. Derivation of the Voltage Equation of the Novel Consequent-Pole PM Motor

_{u−mag}, Ψ

_{v−mag}, Ψ

_{w−mag}) and the flux linkage of the three-phases (Ψ

_{u}, Ψ

_{v}, Ψ

_{w}) can be expressed by:

_{f}is the amplitude value of the magnetic flux linkage to each phase, L

_{u}, L

_{v}, and L

_{w}are the self-inductance of each phase coil, and M

_{uv}, M

_{uv}, and M

_{uw}are the mutual inductances.

^{T}is a transposed matrix of C, and C

^{T}C is a unit matrix, and absolute transformation in which the instantaneous power is invariant before and after the coordinate transformation was used. The transformation equation and transformation matrix are shown as:

^{T}is the transposed matrix of D, and D

^{T}D is the unit matrix. However, the transformation equation, transformation matrix, and the voltage equation of the dq coordinate system can be shown as:

_{dc}/2, which is a DC component only. Therefore, the voltage equation of the novel consequent-pole PM motor is the same as that of the general SPM motor.

#### 2.3.5. Mathematical Model Validation by Analysis

_{u}

_{1}, M

_{uv}

_{1}, M

_{vw}

_{1}) of the analytical results and that of Equation (21) and their FFT results. However, the reluctance of the mathematical model has been calculated from the dimensions of the verification motor model. The relative permeability of the stator and rotor core of the analytical and mathematical model is 5000 to exclude the effect of magnetic saturation.

_{u}, M

_{uv}, M

_{vw}) of the analytical results and that of Equation (22) and their FFT results. Figure 15 shows the armature flux linkage waveform (Φ

_{U}, Φ

_{U}

_{1}, and Φ

_{U}

_{2}) when a DC 1 A is applied in the analysis and FFT results. Φ

_{U}is the sum of Φ

_{U}

_{1}and Φ

_{U}

_{2}. From Figure 14, it can be confirmed that the DC component of the mathematical inductance in the U-phase was in good agreement with that of the analytical inductance. Moreover, it can be confirmed in Figure 14 that the inductance of the analytical results has only a few even-order harmonic components. This is because in the analysis, as shown in Figure 15, the change of the armature flux linkage when the reluctance of the rotor surface increases with rotor rotation, that is, when the rotor rotation position changes from the image-pole to the magnet pole, and the change of the armature flux linkage when the reluctance of the rotor surface decreases with rotor rotation, that is, when the rotor rotation position changes from the magnet pole to the image-pole, are not symmetrical. In Figure 15, it can be confirmed that the waveform of Φ

_{U}, which is the sum of Φ

_{U}

_{1}and Φ

_{U}

_{2}, has not only a DC component but also an even-order harmonic component.

#### 2.3.6. Induced Voltage Cancellation Verification by Analysis

_{d}= −36.74 A) is supplied. However, the theoretical value is the sum of the d-axis magnetic flux calculated from Equation (21) and the magnetic flux linkage at no-load derived in the previous section. Figure 17 shows a discrepancy between the analytical and theoretical flux linkage at the pole switching section. It is considered that the factor is magnetic leakage flux at the end of the magnet. Therefore, it was confirmed that the analytical and theoretical values were almost identical. Furthermore, it was confirmed that the flux linkage of the winding facing the magnet pole and that facing the image pole were in opposite phases, and thus the induced voltage was canceled.

## 3. Mathematical Model Validation by Prototype Motor Drive

#### 3.1. Prototype Motor

#### 3.2. Validation of Effect of Adjustable Speed by Prototype Motor

_{d}= 0 A) and when the d-axis current is supplied (I

_{d}= −30 A). Although the q-axis current is applied to drive the motor, it is the minimum value to counter the windage loss, mechanical loss of the bearing, and core iron loss at each current condition. From Figure 21, it can be seen that the fundamental wave component of the estimated U-phase flux linkage at I

_{d}= −30 A is about 3% of the fundamental wave component of the flux linkage at I

_{d}= 0 A. Similar to the analysis results shown in Section 2.2, it was found that a wide range of magnetic flux variation was possible in the prototype motor. If the flux linkage is infinitely close to zero, the rotating speed should theoretically approach infinity. However, the reason why the rotating speed does not reach infinity when the flux linkage is close to zero is that only the fundamental wave component is used for the back-calculation and that the harmonic component is included in the magnetic flux and the inductance in the prototype motor.

#### 3.3. Back e.m.f. Characteristics

#### 3.4. N-T Characteristics

_{d}= 0 A and I

_{d}= 30 A. However, the results were measured by driving an ordinary three-phase inverter using the voltage equation derived in Section 2 as the motor control theory. It can be seen from Figure 23 that the rotating speed is increased in the low load region by applying field weakening. When no d-axis current is supplied (0 A), the experimental value is almost the same as the analysis value, but when a d-axis current of −30 A is provided, the rotating speed of the experimental value is smaller than that of the analysis value at low load. It is considered that the required supply voltage of the prototype motor was higher than that of the analysis motor due to the magnet sticking error and assembling error at the time of manufacturing and due to the harmonic component included in the magnetic flux and the inductance in the prototype motor. However, since the N-T characteristics of the analytical and experimental value were almost the same, it was confirmed that the driving control principle based on the derived voltage equation was established in the prototype motor.

#### 3.5. Demagnetizing Characteristics

## 4. Comparison of Characteristics of Novel Consequent-Pole PM Motor

#### 4.1. Motor Specifications

#### 4.2. Comparison of No-Load Electromotive Force

#### 4.3. Comparison of Inductance

#### 4.4. Comparison of N-T Characteristics

## 5. Conclusions

- The derived voltage equation is equivalent to that of the general SPM type.
- The derived voltage equation was shown to be valid, with the same trend as the analytical results.
- The control theory for the motor drive based on the derived mathematical model worked on the prototype motor and was shown to be valid by measurement.
- The proposed motor can vary the fundamental component of the number of the flux linkage in the range of 3–100% by field weakening in the experiment.
- The demagnetization resistance of the proposed motor was high. There was virtually no significant degradation of motor characteristics due to irreversible demagnetization in analysis and measurement.
- Analysis clarified that the harmonic component of the proposed motor was less than that of the conventional consequent-pole type.
- The proposed motor has the most extensive high-speed operation range with the least negative d-axis current; thus, the field weakening operation can be achieved efficiently through the three motors.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Kato, T.; Minowa, M.; Hijikata, H.; Akatsu, K.; Lorenz, D.R. Design Methodology for Variable Leakage Flux IPM for Automobile Traction Drives. IEEE Trans. Ind. Appl.
**2015**, 51, 3811–3821. [Google Scholar] [CrossRef] - Wang, J.; Yuan, X.; Atallah, K. Design Optimization of a Surface-Mounted Permanent Magnet Motor with Concentrated Windings for Electric Vehicle Applications. IEEE Trans. Veh. Technol.
**2013**, 62, 1053–1064. [Google Scholar] [CrossRef] - Kuwahara, Y.; Kosaka, T.; Kamada, Y.; Kajiura, H.; Matsui, N. Experimental Verification of High-Power Production Mechanism by Increasing Field Winding Current in Wound Field Flux Switching Motor for HEV Traction Drive. IEEJ Trans. Ind. Appl.
**2015**, 135, 939–947. [Google Scholar] [CrossRef] - Kato, T.; Limsuwan, N.; Yu, C.; Akatsu, K.; Lorenz, D.R. Rare Earth Reduction Using a Novel Variable Magnetomotive Force Flux-Intensified IPM Machine. IEEE Trans. Ind. Appl.
**2014**, 50, 1748–1756. [Google Scholar] [CrossRef] - Motoki, K.; Fukami, T.; Koyama, M.; Mori, T.; Yamada, M.; Nakano, M. Driving Characteristics of an Electromagnet-Assisted Magnet Motor. IEEJ Trans. Ind. Appl.
**2018**, 138, 546–552. [Google Scholar] [CrossRef] - Namba, M.; Hiramoto, K.; Nakai, H. Novel Variable-Field Motor with a Three-Dimensional Magnetic Circuit. IEEJ Trans. Ind. Appl.
**2015**, 135, 1085–1090. [Google Scholar] [CrossRef] - Kalluf, H.J.F.; Tutelea, L.; Boldea, I.; Espindola, A. 2/4-Pole Split-Phase Capacitor Motor for Small Compressors: A Comprehensive Motor Characterization. IEEE Trans. Ind. Appl.
**2014**, 50, 356–363. [Google Scholar] [CrossRef] - Tanaka, A.; Nakada, T.; Hoshika, S.; Takahashi, N.; Koike, Y.; Yamazaki, K. Development of traction motor for 100% electric drive hybrid vehicle. In Proceedings of the IEEJ Industrial Applications Society Conference, Nagaoka, Japan, 25–27 August 2021; pp. 245–248. [Google Scholar]
- Shimizu, R.; Sakai, K. Basic Study on Variable Flux Hybrid Reluctance Motor for Electric Vehicles. In Proceedings of the IEEJ Annual Meeting, Okayama, Japan, 21–23 March 2022; pp. 104–105. [Google Scholar]
- Iwama, K.; Noguchi, T. Operation Characteristics of Adjustable Field IPMSM Utilizing Magnetic Saturation. Energies
**2022**, 15, 52. [Google Scholar] [CrossRef] - Lee, D.; Ro, J. Analysis and Design of a High-Performance Traction Motor for Heavy-Duty Vehicles. Energies
**2020**, 13, 3150. [Google Scholar] [CrossRef] - Yamazaki, N.; Ogata, S.; Ishikawa, T. Analysis of Slotless PM Synchronous Motor for EPS. In Proceedings of the IEEJ Annual Meeting, Oosaka, Japan, 9–11 March 2021; p. 48. [Google Scholar]
- Swamy, M.; Kume, J.T.; Maemura, A.; Morimoto, S. Extended High Speed Operation via Electronic Winding Change Method for AC Motors. IEEE Trans. Ind. Appl.
**2006**, 42, 742–752. [Google Scholar] [CrossRef] - Kume, T.; Iwakane, T.; Sawa, T.; Yoshida, T.; Nagai, I. A Wide Constant Power Range Vector Controlled AC Motor Drive Using Winding Changeover Technique. IEEE Trans. Ind. Appl.
**2006**, 27, 934–939. [Google Scholar] [CrossRef] - Ostovi, V. Pole Pole-Changing Permanent Permanent-Magnet Machines. IEEE Trans. Ind. Appl.
**2002**, 38, 1493–1499. [Google Scholar] [CrossRef] - Sridharbabu, M.; Kosaka, T.; Matsui, N. Design Reconsiderations of High Speed Permanent Magnet Hybrid Excitation Motor for Main Spindle Drive in Machine Tools Based on Experimental Results of Prototype Machine. IEEE Trans. Magn.
**2011**, 47, 4469–4472. [Google Scholar] [CrossRef] - Song, C.; Song, I.; Shin, H.; Lee, C.; Kim, K. A Design of IPMSM for High-Power Electric Vehicles With Wide-Field-Weakening Control Region. IEEE Trans. Magn.
**2022**, 58, 8700305. [Google Scholar] [CrossRef] - Ngo, D.; Hsieh, M.; Le, T. Analysis on Field Weakening of Flux Intensifying Synchronous Motor Considering PM Dimension and Armature Current. IEEE Trans. Magn.
**2022**, 57, 8202305. [Google Scholar] [CrossRef] - Isam, M.; Mikail, R.; Husain, I. Field Weakening Operation of Slotless Permanent Magnet Machines Using Stator Embedded Inductor. IEEE Trans. Ind. Appl.
**2021**, 57, 2387–2397. [Google Scholar] [CrossRef] - Morimoto, S.; Takeda, Y.; Hirasa, T.; Taniguchi, K. Expansion of Operating Limits for Permanent Magnet Motor by Current Vector Control Considering Inverter Capacity. IEEE Trans. Ind. Appl.
**1990**, 5, 866–871. [Google Scholar] [CrossRef] - Morimoto, S.; Hatanaka, K.; Tong, Y.; Takeda, Y.; Hirasa, T. Variable Speed Drive System of Permanent Magnet Synchronous Motors with Flux-weakening Control. IEEJ Trans. Ind. Appl.
**1992**, 112, 292–298. [Google Scholar] [CrossRef] - Jahns, M.T. Flux-weakening Regime Operation of an Interior Permanent magnet Synchronous Motor Drive. IEEE Trans. Ind. Appl.
**1987**, 4, 681–689. [Google Scholar] [CrossRef] - Donald, E.B.; Novotny, W.D.; Lipo, A.T. Field weakening in Buried Permanent magnet AC Motor Drive. IEEE Trans. Ind. Appl.
**1987**, 2, 398–407. [Google Scholar] - Morimoto, S.; Sanada, M.; Takeda, Y.; Takeda, Y. Wide Speed Operation of Interior Permanent Magnet Synchronous Motors with High Performance Current Regulator. IEEE Trans. Ind. Appl.
**1994**, 4, 920–926. [Google Scholar] [CrossRef] - Noguchi, T.; Murakami, K.; Hattori, A.; Kaneko, Y. Torque Boost Operation of New Consequent-Pole Permanent Magnet Motor Using Zero-Phase Circuit. In Proceedings of the 2019 IEEE 12th International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 11–14 August 2019. [Google Scholar]
- Murakami, K.; Noguchi, T.; Hattori, A.; Kaneko, Y. Investigation on Torque Boost Operation of Novel Consequent-Pole Motor Using Zero-Phase Circuit. In Proceedings of the IEEJ Technical Meeting on Semiconductor Power Converter and Motor Drive, Iwate, Japan, 12–13 September 2019; pp. 91–96. [Google Scholar]
- Wu, Z.; Fan, Y.; Chen, H.; Wang, X.; Lee, T.C. Electromagnetic Force and Vibration Study of Dual-Stator Consequent-Pole Hybrid Excitation Motor for Electric Vehicles. IEEE Trans. Veh. Technol.
**2021**, 70, 8700205. [Google Scholar] [CrossRef] - Jiang, J.; Niu, S.; Zhao, X.; Fu, N.W. A Novel Winding Switching Control Strategy of a Consequent-Pole Ferrite-PM Hybrid-Excited Machine for Electric Vehicle Application. IEEE Trans. Magn.
**2022**, 58, 742–752. [Google Scholar] [CrossRef] - Nara, G.; Shiomura, S. Torque Ripple Reduction Method by Injecting Harmonic Current in PMSM. In Proceedings of the IEEJ Industrial Applications Society Conference, Nagaoka, Japan, 25–27 August 2021; pp. 371–372. [Google Scholar]
- Zhang, Z.; Zhang, M.; Yin, J.; Wu, J.; Yang, C. An Analytical Method for Calculating the Cogging Torque of a Consequent Pole Hybrid Excitation Synchronous Machine Based on Spatial 3D Field Simplification. Energies
**2022**, 15, 878. [Google Scholar] [CrossRef] - Morimoto, S.; Sanada, M. Principle and Design Method of Energy-Saving Motor; Kagakujyoho Shuppan Co., Ltd.: Ibaraki, Japan, 2013; pp. 9–13. [Google Scholar]
- Takeda, Y.; Matsui, N.; Morimoto, S.; Honda, Y. Design and Control of Interior Permanent Magnet Synchronous Motor; Ohmusha Co., Ltd.: Tokyo, Japan, 2001; pp. 35–54. [Google Scholar]
- Akatsu, K.; Wakui, S. A Design Method of Fractional-Slot Concentrated Winding SPMSM Using Winding Factor and Inductance Factor. IEEJ Trans. Ind. Appl.
**2007**, 127, 1171–1179. [Google Scholar] [CrossRef][Green Version] - Huang, W.; Wang, J.; Zhao, J.; Zhou, L.; Zhang, Z. Demagnetization Analysis and Magnet Design of Permanent Magnet Synchronous Motor for Electric Power Steering Applications. In Proceedings of the 2020 IEEE 1st China International Youth Conference on Electrical Engineering (CIYCEE), Wuhan, China, 1–4 November 2020. [Google Scholar]

**Figure 2.**Motor cross-section and the reluctance on the rotor surface viewed from each phase: (

**a**) conventional consequent-pole-type PM motors; (

**b**) novel consequent-pole-type PM motor.

**Figure 4.**Outline of flux cancellation at field weakening: (

**a**) Motor cross-section; (

**b**) Flux linkage at no load; (

**c**) Flux linkage at field weakening.

**Figure 5.**Outline of adjustable flux linkage at field weakening: (

**a**) flux linkage waveform; (

**b**) FFT analysis result.

**Figure 9.**Six-phase magnetic circuit: (

**a**) the load side connection is a hexagon configuration; (

**b**) the load side connection is a star configuration.

**Figure 10.**Load side magnetic circuit when only E

_{1}is supplied: (

**a**) hexagon configuration; (

**b**) star configuration.

**Figure 11.**Six-phase star configuration magnetic equivalent circuit of the novel consequent-pole PM motor.

**Figure 12.**Cross-section of the verification motor structure of the novel consequence-pole PM motor.

**Figure 13.**Comparison of inductance between analytical and theoretical value in U1-phase: (

**a**) L

_{u}

_{1}; (

**b**) M

_{uv}

_{1}; (

**c**) M

_{uw}

_{1}.

**Figure 14.**Comparison of inductance between analytical and theoretical value in U-phase: (

**a**) L

_{u}; (

**b**) M

_{uv}; (

**c**) M

_{uw}.

**Figure 15.**Analytical armature flux linkage waveform (Φ

_{U}, Φ

_{U}

_{1}, and Φ

_{U}

_{2}) at 1 A (DC) and FFT results.

**Figure 16.**Theoretical and analytical magnetic flux linkage at no load: (

**a**) flux linkage waveform of the U-phase, U1-phase, and the U2-phase; (

**b**) FFT analysis result of the U-phase.

**Figure 18.**Configuration of prototype motor: (

**a**) Cross-section of the prototype motor from the axial direction; (

**b**) Cross-section of the prototype motor from the radial direction; (

**c**) Winding diagram.

**Figure 19.**Configuration of prototype motor: (

**a**) Photograph of the motor; (

**b**) Photograph of the rotor.

**Figure 21.**Adjustable flux by d-axis current: (

**a**) Relationship between the rotating speed with respect to the d-axis current; (

**b**) Estimated U-phase flux linkage in the prototype motor at no load and I

_{d}= −30 A.

**Figure 24.**Contour diagram of the demagnetizing factor: (

**a**) maximum range is 40%; (

**b**) maximum range is 1%.

**Figure 25.**Analytical U-phase back e.m.f. before and after irreversible demagnetization at 1000 r/min: (

**a**) waveforms; (

**b**) FFT results.

**Figure 26.**U-phase back e.m.f. of the prototype motor before and after the experiment at 1000 r/min: (

**a**) waveforms; (

**b**) FFT results.

**Figure 27.**Cross-section of motor model: (

**a**) proposed motor; (

**b**) consequent pole motor; (

**c**) SPM motor.

Items | Value | |
---|---|---|

number of poles and slots | 4 poles, 6 slots | |

stack length | 37 mm | |

stator | stator outer diameter | 90 mm |

stator inner diameter | 45 mm | |

width of tooth | 9 mm | |

width of backyoke | 9 mm | |

relative permeability of core | 5000 | |

winding method | Concentrated windings | |

winding connection method | Star configuration | |

rotor | rotor outer diameter | 42.85 mm |

thickness of magnets | 3.425 mm | |

coercive force of PM | 985 kA/m | |

remanent flux density of PM | 1.29 T | |

maximum energy product of PM | 322 kJ/m^{3} |

Items | Value | |
---|---|---|

number of poles and slots | 8 poles, 12 slots | |

stack length | 37 mm | |

stator | stator outer diameter | 81 mm |

stator inner diameter | 76.2 mm | |

material of core | 50 JNE300 | |

winding method | Concentrated windings | |

winding connection method | Star configuration | |

rotor | rotor outer diameter | 42.8 mm |

material of magnets | NMX-43SH | |

magnet arrangement | SPM type | |

thickness of magnets | 5.7 mm |

Items | Proposed PM Motor | Consequent Pole PM Motor | SPM Motor |
---|---|---|---|

Stator diameter | 80 mm | 80mm | 80mm |

Rotor diameter | 42.85 mm | 42.85 mm | 42.85 mm |

Stack length | 37 mm | 37 mm | 37 mm |

Air gap length | 1.045 mm | 1.045 mm | 1.045 mm |

Number of poles | 8 (PM:4, Image pole:4) | 8 (PM:4, Image pole:4) | 8 |

Number of slots | 12 | 12 | 12 |

Number of turns | 16 | 16 | 16 |

PM volume | 7.672 cc | 7.672 cc | 15.344 cc |

Armature winding connection | 4-series star connection | 4-series star connection | 4-series star connection |

PM type | NMX-43SH | NMX-43SH | NMX-43SH |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hattori, A.; Noguchi, T.; Murakami, K. Mathematical Model Derivation and Experimental Verification of Novel Consequent-Pole Adjustable Speed PM Motor. *Energies* **2022**, *15*, 6147.
https://doi.org/10.3390/en15176147

**AMA Style**

Hattori A, Noguchi T, Murakami K. Mathematical Model Derivation and Experimental Verification of Novel Consequent-Pole Adjustable Speed PM Motor. *Energies*. 2022; 15(17):6147.
https://doi.org/10.3390/en15176147

**Chicago/Turabian Style**

Hattori, Akihisa, Toshihiko Noguchi, and Kazuhiro Murakami. 2022. "Mathematical Model Derivation and Experimental Verification of Novel Consequent-Pole Adjustable Speed PM Motor" *Energies* 15, no. 17: 6147.
https://doi.org/10.3390/en15176147