# Accurate and Efficient Torque Control of an Interior Permanent Magnet Synchronous Motor in Electric Vehicles Based on Hall-Effect Sensors

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## Abstract

**:**

## 1. Introduction

## 2. Parameter Estimation

#### 2.1. Analysis of the IPMSM Energy Model

#### 2.2. Rotor Position Estimation

#### 2.2.1. Rotor Position Estimation Based on Average Motor Speed

#### 2.2.2. Rotor Position Estimation Based on the Power Closed-Loop Method

_{out}can be expressed as follows:

#### 2.3. Permanent Magnetic Flux Linkage Estimation

## 3. Torque Control Strategy

#### 3.1. Feedforward Parameter Iteration Method

- (1)
- Obtain the present motor parameters (the d-axis and q-axis inductances, stator resistance, and energy loss) from lookup tables;
- (2)
- Calculate one set of d-axis and q-axis current using control strategies;
- (3)
- Calculate the motor parameters with the current from step 2 using lookup tables;
- (4)
- Calculate another set of d-axis and q-axis current with the new set of motor parameters from step 3 using control strategies.
- (5)
- If the current error is within tolerance between the current and the previous step, the iteration is complete. Otherwise, return to step 2.

#### 3.2. Maximum Torque Per Ampere Control Strategy

_{dn}and i

_{qn}can be obtained from the lookup tables, as shown in Figure 4. One of the current can be obtained from the lookup tables. The other current can be obtained from the lookup tables directly or calculated by the first current.

## 4. Simulation and Experimental Results

#### 4.1. Simulation Results

#### 4.2. Experimental Results

_{4}battery pack (288 V/180 Ah) was used as a power source. The experimental bench is shown in Figure 10.

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## Nomenclature

${E}_{in}$ | Input energy |

${E}_{out}$ | Output energy |

${E}_{loss}$ | Energy loss |

${E}_{Cu}$ | Copper loss |

${E}_{Fe}$ | Iron loss |

${E}_{str}$ | Stray loss |

${E}_{M}$ | Mechanical loss |

${v}_{u},{v}_{v},{v}_{w}$ | Stator three phase voltages |

${v}_{d},{v}_{q}$ | Stator d-axis and q-axis voltages |

${v}_{d}^{*},{v}_{q}^{*}$ | Reference stator d-axis and q-axis voltages |

${i}_{u},{i}_{v},{i}_{w}$ | Stator three phase current |

${i}_{d},{i}_{q}$ | Stator d-axis and q-axis current |

${i}_{d}^{*},{i}_{q}^{*}$ | Reference stator d-axis and q-axis current |

${i}_{cd},{i}_{cq}$ | d-axis and q-axis iron loss current |

${i}_{dn},{i}_{qn}$ | Normalized stator d-axis and q-axis current |

${i}_{s}$ | Stator current |

${i}_{dFW}$ | d-axis field-weakening current |

${\omega}_{e}$ | Rotor electrical angular speed |

${T}_{e}$ | Electromagnetic torque |

${T}_{e}^{*}$ | Reference electromagnetic torque |

${T}_{en}$ | Normalized electromagnetic torque |

$\theta $ | Actual rotor positon |

${\theta}^{*}$ | Estimated rotor positon |

${L}_{d},{L}_{q}$ | d-axis and q-axis inductances |

${\phi}_{d},{\phi}_{q}$ | d-axis and q-axis flux linkages |

${\phi}_{f}$ | Permanent magnetic flux linkage |

${\stackrel{\wedge}{\phi}}_{f}$ | Estimated Permanent magnetic flux linkage |

$dL$ | Difference of d-axis and q-axis inductances |

${R}_{s}$ | Stator resistance |

${R}_{c}$ | Iron loss resistance |

${P}_{in}$ | Input power |

${P}_{out}$ | Output power |

${P}_{out}^{*}$ | Reference output power |

${P}_{loss}$ | Power loss |

${P}_{Cu}$ | Copper power loss |

${V}_{dc}$ | DC linkage voltage |

$T$ | Control period |

$f$ | Control frequency |

$t$ | Time |

$p$ | Number of pole pairs |

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**Figure 7.**

**F**lux linkage estimation and torque control under maximum torque conditions (1000 rpm/540 Nm).

**Figure 9.**Flux linkage estimation and torque control in the flux weakening region (2800 rpm/256 Nm).

Parameter | Symbol | Value |
---|---|---|

Number of pole pairs | p | 6 |

Stator resistance | R_{s} | 4.23 mΩ |

Magnet flux linkage | ϕ_{f} | 0.1039 Wb |

d-axis inductance | L_{d} | 0.171 mH |

q-axis inductance | L_{q} | 0.391 mH |

DC linkage voltage | V_{dc} | 288 V |

Maximum speed | n_{b} | 4000 Rpm |

Peak current | I_{pk} | 570 Apk |

Rated power | P_{r} | 75 kW |

Peak torque | T_{max} | 540 Nm |

Coefficient of R_{Sac} to R_{sDC} | μ | 0.1 |

Hysteresis current coefficient | K_{h} | 0.6637 |

Eddy current coefficient | K_{e} | 0.00084 |

Stray loss coefficient | c_{Str} | 2.56 × 10^{−9} |

Mechanical friction torque | T_{fric} | 5.24 |

Windage torque coefficient | c_{wind} | 3.35 × 10^{−3} |

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**MDPI and ACS Style**

Yu, L.; Zhang, Y.; Huang, W.
Accurate and Efficient Torque Control of an Interior Permanent Magnet Synchronous Motor in Electric Vehicles Based on Hall-Effect Sensors. *Energies* **2017**, *10*, 410.
https://doi.org/10.3390/en10030410

**AMA Style**

Yu L, Zhang Y, Huang W.
Accurate and Efficient Torque Control of an Interior Permanent Magnet Synchronous Motor in Electric Vehicles Based on Hall-Effect Sensors. *Energies*. 2017; 10(3):410.
https://doi.org/10.3390/en10030410

**Chicago/Turabian Style**

Yu, Lei, Youtong Zhang, and Wenqing Huang.
2017. "Accurate and Efficient Torque Control of an Interior Permanent Magnet Synchronous Motor in Electric Vehicles Based on Hall-Effect Sensors" *Energies* 10, no. 3: 410.
https://doi.org/10.3390/en10030410