# Electromagnetic Analysis and Design Methodology for Permanent Magnet Motors Using MotorAnalysis-PM Software

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## Abstract

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## 1. Introduction

## 2. General Characteristics of MotorAnalysis-PM Software

- Based on time-stepping magnetostatic FE simulations assuming ideal sinusoidal or trapezoidal current waveform.
- Calculation of most commonly used motor parameters like voltage, current, power, back-electromotive force (EMF), torque, power factor, efficiency, and power losses.
- Used to analyze cogging torque and torque ripple, back-EMF harmonics, steel core losses, PM losses, and demagnetization effects of PMs.
- Visualization features include time-series waveform plots, air gap distribution and field plots as well as field animations.

- Based on time-stepping transient FE simulations considering induced eddy current effects.
- An electrical circuit solver paired with an electromagnetic solver to couple external electrical circuits with FE PM motor models.
- Arbitrary supply current or voltage waveforms including pulse width modulation (PWM) inverter supply.
- Used to analyze transient motor behavior, cogging torque and torque ripple, back-EMF harmonics, steel core losses including higher harmonics, and demagnetization effects in PMs.
- Visualization features include time-series waveform plots, air gap distribution, and field plots as well as animations.

- Based on a conventional model of the PM motor in d-q reference frame with sinusoidal back-EMF derived from FE solutions.
- Saturation and cross-saturation of magnetic cores as well as steel core losses are considered.
- Calculation of steady-state performance characteristics, efficiency maps and other performance maps considering field-weakening strategy.

- Based on the dynamic model of the motor in d-q reference frame with sinusoidal back-EMF.
- Simulation of the PM motor with PWM supply and current control algorithm including field-oriented control and current hysteresis control.

## 3. Analysis Methods and Models Used in MotorAnalysis-PM

_{dq}and cross saturation magnet flux linkage Ψ

_{mqd}lying in the q-axis are considered. With the cross saturation terms the d-axis and q-axis flux linkages are given as follows [17]:

_{d}, L

_{q}, L

_{dq}, and magnet flux linkage Ψ

_{md}, and Ψ

_{mqd}values depend on current components I

_{d}and I

_{q}to consider magnetic saturation. The steady state equations, used for the d-q analysis, after resolving voltages into d and q components, can be written as:

_{d}and Ψ

_{q}are the d-axis and q-axis flux linkages, I

_{d}and I

_{q}are the d-axis and q-axis current components.

_{s}is the stator winding phase resistance, L

_{sew}is the stator end winding inductance, and ω is the electrical operating speed.

_{d}, L

_{q}, L

_{dq}, Ψ

_{md}and Ψ

_{mqd}in MotorAnalysis-PM is based on the magnetostatic FE analysis for one rotor position with permeance freezing. This allows the use of the superposition method to extract the parameters of the PM motor while considering the magnetic saturation and cross-saturation [17]. This process is referred to as the parameterization of the d-q model. During parameterization, the magnetostatic FE simulation is run for the entire range of advance angle values from 0° to 360° (electrical degrees) and current values from zero to the maximum current defined by the user. This process can also be repeated for several rotor positions to consider variation of the d-q model parameters with rotor position. Finally, the time-stepping magnetostatic FE simulation is performed for several operating points to include information about the steel core losses into the d-q model. Every time the d-q model is utilized, its parameters are interpolated depending on the current and advance angle values, so the non-linear behavior of the motor is included in the d-q model.

## 4. Design Methodology Using MotorAnalysis-PM

#### 4.1. Initial Design Assumptions

#### 4.2. Initial Winding Configuration

#### 4.3. Geometry Design

_{q}/L

_{d}. The saliency ratio, in turn, is affected by the rotor geometry and stator winding configuration [26,27]. Figure 5 shows curves of the saliency ratio versus the advance angle for different stator currents generated using the d-q analysis of MotorAnalysis-PM. It is seen that the saliency ratio changes significantly with a change in current and advance angle. The dependence on the advance angle becomes more evident as the rotor saturates which should be considered while designing the motor. Increasing the saliency ratio with the advance angle is an important factor to consider especially for the field-weakening operation. This means that the reluctance torque component increases during operating conditions when the magnet torque component decreases with the weakened flux of the PMs.

#### 4.4. Number of Turns and Parallel Paths

_{pp}is the number of parallel paths of the winding, W is the number of turns, ${I}_{s}$

_{RMS}(1) and ${V}_{s}$

_{RMS}(1) are the stator RMS phase current and RMS phase voltage with one parallel path and one turn winding corresponding to corner speed and rated current density.

#### 4.5. Demagnetization Analysis

#### 4.6. Field-Weakening Operation

_{ch}= λ

_{pm}/L

_{d}

_{pm}is the magnet flux linkage in the d-axis and L

_{d}is the d-axis inductance. According to (12), the characteristic current of the Prius IPM motor is determined from the MotorAnalysis-PM d-q analysis to be:

_{ch}= 0.1607/0.00226 = 71 A

_{pm}and L

_{d}nonlinearly depend on the advance angle γ, the characteristic current is determined for γ at which the maximum torque occurs (MTPA operation is implied). This is illustrated in Figure 7. On the other hand, since the values of λ

_{pm}and L

_{d}also depend on the stator current, multiple iterations are required and calculation is repeated for different stator currents until I

_{ch}converges.

_{rated}[31,32] (which is not the case for the Prius motor considered). According to (12) an increase in λ

_{pm}and/or a decrease in L

_{d}leads to an increase of the characteristic current. Therefore, any change in PM dimensions, PM residual flux density, slot dimensions, or winding arrangement may be considered by the designer to adjust the characteristic current. It should be noted that, according to (11), changing the number of turns and number of parallel paths does not affect the I

_{ch}/I

_{rated}ratio even if it changes L

_{d}.

#### 4.7. Analysis over Entire Speed and Torque Ranges

## 5. Verification with Experimental Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Torque versus advance angle curves obtained with d-q analysis (blue) and time-stepping magnetostatic finite-element (FE) analysis (red).

**Figure 4.**Flux lines and magnetic flux density distributions (in Wb/m) for: (

**a**) rated current density, (

**b**) quarter of rated current density.

**Figure 5.**Saliency ratio versus advance angle curves obtained with d-q analysis for different RMS stator currents.

**Figure 8.**Output mechanical power versus speed curves for different stator currents in MTPA and field-weakening regimes.

**Figure 9.**Torque versus speed curves for different stator currents in MTPA and field-weakening regimes.

**Figure 10.**Advance angle versus speed curves for different stator currents in MTPA and field-weakening regimes.

**Figure 12.**Simulated and measured peak back-electromotive force (EMF) versus speed; simulated data are presented for 25 °C and 80 °C.

**Figure 14.**Locked rotor experimental results for different rotor positions and peak currents compared with corresponding torque-advance angle curves obtained from the d-q analysis simulation results.

Features | FEMM | SyR-e tool | JMAG-Express Public | Emetor | MotorAnalysis-PM |
---|---|---|---|---|---|

Geometry templates | No | Yes | Yes | Yes | For stator only |

Geometry import from DXF file | Yes | No | No | No | Yes |

Automated winding setup | No | Yes | Yes | Yes | Yes |

Materials library | Yes | Yes | Yes | Yes | Yes |

Magnetostatic FE analysis | Yes | Yes | No | Yes | Yes |

Transient FE analysis | With scripting only | No | No | No | Yes |

Analytical analysis | No | No | Yes | No | Yes |

Motor characteristic graphs | With scripting only | Yes | Yes | No | Yes |

Efficiency map generation | No | No | No | No | Yes |

Parametric analysis | No | Yes | Yes | No | No |

Specification | Value |
---|---|

Rated current density | 27.4 A/mm^{2} |

Rated current | 230 A |

Corner speed | 1200 rpm |

Rated power | 50 kW |

Rated torque | 400 Nm |

Stator outer diameter | 269.2 mm |

Lamination length | 83.6 mm |

Lamination material | M-19 29 Ga |

PM Motor Parameters | Rated Current Density | Quarter of Rated Current Density |
---|---|---|

Current density (A/mm^{2}) | 27.4 | 6.85 |

Speed (rpm) | 1200 | 1200 |

Advance angle (deg.) | 50 | 50 |

Torque (Nm) | 396.8 | 108.9 |

Output power (kW) | 49.9 | 13.7 |

Efficiency (%) | 85.5 | 95.9 |

Root mean square (RMS) phase current for one turn (A) | 2070.3 | 517.6 |

RMS phase voltage for one turn (V) | 17.7 | 10.6 |

Copper losses (W) | 8317.5 | 519.8 |

Iron core losses (W) | 139.5 | 69.4 |

Magnet losses (W) | 4.4 | 0.1 |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kuptsov, V.; Fajri, P.; Trzynadlowski, A.; Zhang, G.; Magdaleno-Adame, S.
Electromagnetic Analysis and Design Methodology for Permanent Magnet Motors Using MotorAnalysis-PM Software. *Machines* **2019**, *7*, 75.
https://doi.org/10.3390/machines7040075

**AMA Style**

Kuptsov V, Fajri P, Trzynadlowski A, Zhang G, Magdaleno-Adame S.
Electromagnetic Analysis and Design Methodology for Permanent Magnet Motors Using MotorAnalysis-PM Software. *Machines*. 2019; 7(4):75.
https://doi.org/10.3390/machines7040075

**Chicago/Turabian Style**

Kuptsov, Vladimir, Poria Fajri, Andrzej Trzynadlowski, Guoliang Zhang, and Salvador Magdaleno-Adame.
2019. "Electromagnetic Analysis and Design Methodology for Permanent Magnet Motors Using MotorAnalysis-PM Software" *Machines* 7, no. 4: 75.
https://doi.org/10.3390/machines7040075