# PMSM Calculation Model

**Repository Path**: dejunN/pmsm-calculation-model

## Basic Information

- **Project Name**: PMSM Calculation Model
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: MIT
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 2
- **Created**: 2024-08-08
- **Last Updated**: 2024-08-08

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

[TOC]

# Permanent Magnet Synchronous Motor (PMSM) Model

## Three-Phase Sinusoidal Model Electrical System

dq-轴下电机模型可以表示为：
$$
\frac{d}{dt}i_d=\frac{1}{L_d}v_d-\frac{R}{L_d}i_d+\frac{L_q}{L_d}p\omega_m i_q
$$

$$
\frac{d}{dt}i_q=\frac{1}{L_q}v_q-\frac{R}{L_q}i_q-\frac{L_d}{L_q}p\omega_m i_d-\frac{\lambda p\omega_m}{L_q}
$$

$$
T_e=1.5p\left[\lambda i_q+\left(L_d-L_q\right)i_d i_q\right]
$$

其中，参数的物理含义如下表所示：

| Symbol       | Meaning                                                      |
| ------------ | ------------------------------------------------------------ |
| $L_d$, $L_q$ | d-axis and q-axis inductances                                |
| $R$          | resistance of the stator windings                            |
| $i_d$, $i_q$ | d-axis and q-axis currents                                   |
| $v_d$, $v_q$ | d-axis and q-axis voltages                                   |
| $\omega_m$   | angular velocity of the rotor                                |
| $\lambda$    | amplitude of the flux induced by the permanent magnets of the rotor in the stator phases |
| $p$          | number of pole pairs                                         |
| $T_e$        | electromagnetic torque                                       |

## Mechanical System

电机的机械运动方程为：
$$
\frac{d}{dt}\omega_m = \frac{1}{J}\left(T_e - T_f - F\omega_m - T_m\right)
$$

$$
\frac{d\theta}{dt}=\omega_m
$$

$$
N_r=\frac{30}{\pi}\omega_m
$$



其中，参数的物理含义如下表所示：

| Symbol     | Meaning                                          |
| ---------- | ------------------------------------------------ |
| $J$        | combined inertia of rotor and load               |
| $F$        | combined viscous friction of rotor and load      |
| $\theta$   | rotor angular position                           |
| $T_m$      | shaft mechanical torque                          |
| $T_f$      | shaft friction torque                            |
| $\omega_m$ | angular velocity of the rotor (mechanical speed) |
| $N_r$      | motor rotation speed (unit rpm)                  |

## Park Transform