PMSM Basic Structure and Working Principle

The working principle of the permanent magnet synchronous motor (PMSM) is that the stator generates a rotating magnetic field when alternating current is passed through it, and the rotor is a permanent magnet. The magnetic field generated by the stator drives the permanent magnet to rotate at the synchronous speed.

The biggest advantage of PMSM is that AC power energy is provided by DC, which can accurately control the motor and solve the life problem caused by brushes.

1. Basic structure of PMSM

1.1 Classification of Motors

• DC Motor
• AC asynchronous motor
  • AC induction motors: single-phase asynchronous motor, three-phase asynchronous motor, shaded-pole asynchronous motor.
  • AC commutation motor: single-phase series-excited motor, AC/DC dual-purpose motor, and repulsion motor.
• AC synchronous motor
  • Permanent magnet synchronous motor: uses permanent magnets to provide excitation.
  • Reluctance synchronous motor: It works by using the unequal reluctance in the direct and quadrature axis directions of the rotor to generate reluctance torque.
  • Hysteresis synchronous motor: It operates by the hysteresis torque generated by the action of the hysteresis material rotor and the rotating magnetic field of the stator.

1.2 Structure of Permanent Magnet Synchronous Motor (PMSM)

A permanent magnet synchronous motor consists of two key components, a multi-polar permanent magnet rotor and a stator with appropriately designed windings.

• The stator adopts a laminated structure and is equipped with a three-phase AC winding.
• The rotor can be made solid or laminated, and permanent magnet material is mounted on the rotor.

Depending on the location of the permanent magnet material on the motor rotor, permanent magnet synchronous motors can be divided into two structural types: surface mounted and built-in.

• The surface-mounted rotor has a simple magnetic circuit structure and low manufacturing cost, but since the starting winding cannot be installed on its surface, asynchronous starting cannot be achieved.
• The permanent magnets of the built-in rotor are placed inside the rotor, and the magnetic circuit structures mainly include radial, tangential and hybrid types.

The typical permanent magnet synchronous motor structure consists of a stator (Figure 1) that supports three windings/coils connected in a star or delta configuration, which are powered by an AC power supply. These windings/coils are placed around magnetic pole shoes, which force the magnetic flux generated by the AC current passing through the coils to flow along a specific path to maximize the motor efficiency.

The rotor of a permanent magnet synchronous motor (Figure 2) typically consists of permanent magnets mounted on the surface (SPM) or inside the rotor (IPM) and a steel shaft that transmits torque to various devices.

The key to rotating the rotor of an electric machine is to be able to generate a rotating magnetic field in the stator as shown in Figure 3. The most common way to generate a rotating magnetic field is to energize a coil with an AC current. If a three-phase balanced current system is passed through a system consisting of three windings/coils that are spatially spaced 120 degrees apart, the resulting magnetic field will rotate at the same frequency as the three-phase AC current.

If we simplify the physics happening inside the stator coils and yoke, and instead of a continuous AC current waveform, we select just 6 points of interest, then it is easy to see how the resulting magnetic flux vector changes direction in sync with the AC current system.

1.3 Principle of Permanent Magnet Synchronous Motor (PMSM)

The working principle of permanent magnet synchronous motor is based on the interaction between electromagnetic induction and permanent magnet magnetic field. Specifically, when three-phase current is passed through the three-phase symmetrical winding of the stator, a rotating magnetic motive force with constant amplitude is generated, which interacts with the magnetic field of the permanent magnet on the rotor, generating electromagnetic torque that drives the motor to rotate and drives the permanent magnet to rotate.

When three-phase current is passed through the three-phase symmetrical winding of the permanent magnet synchronous motor stator, the magnetic motive force generated by the current synthesizes a rotating magnetic motive force with a constant amplitude. Since its amplitude is constant, the trajectory of this rotating magnetic motive force forms a circle, which is called circular rotating magnetic motive force F.

$$F=\genfrac{}{}{0ex}{}{3}{2}{F}^{\varphi l}=\genfrac{}{}{0ex}{}{3}{2}\ast 0.9k\ast \genfrac{}{}{0ex}{}{NI}{P}$$

Where, F is the circular rotating magnetomotive force, (T・m); Fφl is the maximum amplitude of the single-phase magnetomotive force, (T・m); k is the fundamental winding coefficient; p is the number of motor pole pairs; N is the number of series turns of each coil; I is the effective value of the current flowing through the coil.

Since the speed of the permanent magnet synchronous motor is always the synchronous speed, the rotating magnetic field generated by the rotor main magnetic field and the stator circular rotating magnetic motive force remains relatively static. The two magnetic fields interact with each other to form a synthetic magnetic field in the air gap between the stator and the rotor, which interacts with the rotor main magnetic field to generate an electromagnetic torque Te that drives or hinders the rotation of the motor, that is:

$$Te=k\ast B^R\ast B^{net}\ast sin\theta$$

Where Te is the electromagnetic torque, (N・m);$\theta$is the power angle, rad;$B^R$is the rotor main magnetic field, T;$B^{net}$is the composite magnetic field of the air gap, T. The power angle refers to the angle between the rotor main magnetic field and the composite magnetic field of the air gap.

Due to the different positional relationships between the air gap composite magnetic field and the rotor main magnetic field, the permanent magnet synchronous motor can operate in both the motor state and the generator state. When the air gap composite magnetic field lags behind the rotor main magnetic field, the electromagnetic torque generated is opposite to the direction of rotor rotation, and the motor is in the generating state; when the air gap composite magnetic field leads the rotor main magnetic field, the electromagnetic torque generated is in the same direction as the rotor rotation, and the motor is in the motoring state.

2. Comparison between PMSM and BLDC

Permanent magnet synchronous motor (PMSM) and brushless direct current motor (BLDC) are both permanent magnet motors: the rotor is composed of permanent magnets as the basic structure, and the stator has multi-phase AC windings. The magnetic field generated by the permanent magnet rotor and the AC current of the stator interact to generate the motor torque, and the stator current in the winding must be synchronized with the rotor position feedback.

The difference between PMSM and BLDC lies in the back EMF. The BLDC back EMF is a trapezoidal wave, while the PMSM back EMF is a sine wave.

• The operating current is different: to generate constant electromagnetic torque, PMSM uses a sinusoidal stator current, while BLDC uses a rectangular wave current.
• The stator winding distribution is different. PMSM uses short-pitch distributed winding, and sometimes fractional slot or sinusoidal winding to further reduce ripple torque; BLDC uses full-pitch concentrated winding.
• The shapes of permanent magnets are different. The PMSM permanent magnet is parabolic in shape, and the magnetic flux density generated in the air gap is distributed as sinusoidally as possible; the BLDC permanent magnet is tile-shaped, and the magnetic flux density generated in the air gap is distributed in a trapezoidal wave.
• The operation modes are different. PMSM uses three phases to work simultaneously, and the current of each phase differs by 120° electrical angle, requiring a position sensor. BLDC uses windings that are turned on in pairs, with each phase turned on for 120° electrical angle, and phase switching every 60° electrical angle, requiring only phase switching point position detection.

The advantage of BLDC is that it is easy to control. The sinusoidal controller of PMSM is more complex and more expensive than the trapezoidal controller of BLDC. The advantage of PMSM is that it reduces noise and harmonics in the current waveform.

Note: Back EMF refers to the electromotive force that opposes the tendency of current to pass through, and is essentially an induced electromotive force. When the motor rotates, an induced electromotive force will be generated in the coil, which has the effect of weakening the electromotive force of the power supply, that is, the back EMF, which hinders the rotation of the coil.
The back EMF reflects the parameters of the entire motor magnetic field distribution, which is determined by the electromagnetic design in the motor design, that is, the design of the stator coil winding (generating the stator magnetic field) and the rotor magnetic steel distribution design (generating the rotor magnetic field) determine the back EMF, especially the stator winding design.

The differences between PMSM and BLDC in design and control are as follows:

• Torque ripple
  Torque ripple is the biggest problem of electromechanical servo systems. It directly affects the difficulty of accurate position control and high-performance speed control. In low-speed and direct drive applications, torque ripple will seriously affect system performance and deteriorate the accuracy and repeatability of the system.
  Both PMSM and BLDC have torque ripple problems. Torque ripple is mainly caused by the following reasons: cogging effect and flux distortion, torque caused by current commutation, and torque caused by machining.
• Power density
  Power density is limited by the heat dissipation capacity of the motor, that is, the surface area of ​​the motor stator. For permanent magnet motors, most of the power losses occur in the stator, including copper loss, eddy current loss and hysteresis loss, while rotor loss is often ignored. So for a given structural size, the smaller the motor loss, the higher the allowable power density.
  At the same size, BLDC can provide 15% more power output than PMSM. If the iron loss is also the same, the power density of BLDC can be increased by 15% compared to PMSM.
• Torque-to-
  inertia ratio The torque-to-inertia ratio refers to the maximum acceleration that the motor can provide. BLDC can provide 15% more output power than PMSM, and can obtain 15% more electromagnetic torque than PMSM. If the speed is the same, the torque-to-inertia ratio of BLDC is 15% larger than that of PMSM.
• In position detection
  BLDC, only two phases of windings are turned on at any one time, and each phase is turned on for 120° electrical angle. As long as these commutation points are detected correctly, the normal operation of the motor can be guaranteed. Usually three Hall sensors are used.
  PMSM requires sinusoidal current. When the motor is working, all three phases of windings are turned on at the same time. Continuous position sensors are required, and the most common ones are high-precision encoders.
• Current detection:
  For three-phase motors, two current sensors are usually used. For simple brushless DC motors, only one current sensor can be used to detect the bus current to reduce costs.

3. Torque control of PMSM

There are three control objectives for motor control: position control, speed control, and torque control.
Regardless of the control objective, torque control must be used as the innermost control loop; for speed control and position control, corresponding outer control loops are also required.

To control a motor, it is necessary to first understand the controlled object. After the alternating voltage with a difference of 120 degrees passes through the three phases of the stator, a rotating magnetic field can be seen on the stator core. Under the action of this rotating magnetic field, a force is generated with the rotor magnetic field, driving the rotor to rotate.

How is the motor torque generated? The torque is proportional to the armature (stator) current.

How is the current generated? We can imagine each winding of the motor as a resistor + inductor rotating in a magnetic field, as shown in the following equivalent circuit:

Assuming the motor is running in open loop, when a voltage with a difference of 120 degrees is given to the three phases of the motor stator to establish a rotating magnetic field, if there is no load at this time, the motor will rotate rapidly (no load) until the back electromotive force is completely equal to the given voltage; at this time, the current in the stator winding is still 0, and the rotating magnetic field of the stator can be imagined (virtual/equivalent) as a magnet rotating around the axis of the motor, and the south pole of this imaginary magnet coincides with the north pole axis of the rotor magnet.

When there is a load on the rotor, according to Newton’s law of motion, the motor speed will inevitably slow down, which means that the back electromotive force in the above equivalent circuit decreases, and when the given voltage remains unchanged, the remaining voltage will generate current in the resistor. What else happened during this deceleration process? Because it is dragged by the load, the axis of the rotor magnet lags behind the virtual axis of the stator magnet by an angle, which is what we call the “power angle”.

The torque control of the motor is to find some combinations of switch tubes to synthesize a given voltage for the motor stator through a certain control algorithm . The torque corresponding to the current generated by this voltage after offsetting the back electromotive force is just balanced with the external load. Various diagrams of the motor vector model can be found on the Internet.

There are currently two main schools of thought for motor torque control: field-oriented control (FOC) and direct torque control (DTC). Of course, in principle, these two control algorithms are applicable to all AC motors. This article only talks about their similarities and differences in permanent magnet synchronous motor control.

3.1 Field Oriented Control (FOC)

Field Oriented Control (FOC) is often used to maximize the efficiency of PMSM three-phase motors.

The FOC control theory was first proposed by Siemens engineers in the 1970s. As mentioned above, the magnetic field generated by the stator can be virtualized as a magnet rotating at high speed around the rotor.

The stator magnetic potential can be decomposed into the d-axis magnetic potential and the q-axis magnetic potential. The d-axis magnetic potential is coaxial with the rotor magnetic potential and cannot generate a tangential torque, but it will affect the magnetic field generated by the permanent magnet of the permanent magnet synchronous motor rotor; the q-axis is 90 degrees out of phase with the rotor magnetic potential, thus generating a tangential torque (similar to the interaction force generated by two vertical bar magnets).

The basic idea of ​​FOC control is to convert the relevant variables in the three-phase static ABC coordinate system to the rotating coordinate system (d, q) for mathematical operations, and control the change of the voltage of the d-axis and q-axis to achieve the purpose of controlling the d-axis and q-axis current. However, the voltage of the three-phase motor can only be the voltage in the static coordinate system, so in the control algorithm, the voltage of the dq axis needs to be converted into the ABC three-phase voltage again for the drive bridge. That is, there is a process from physical model -> mathematical model -> control algorithm -> physical model.

The essence of field-oriented control is to align the stator current vector (is), which produces the rotating magnetic field (the red dashed arrow in the figure), with the rotor torque axis. In order for the motor to achieve its peak efficiency, the magnetic flux produced by the stator winding must be at an electrical angle of 90 degrees to the magnetic flux produced by the rotor.

Input of FOC:

• The three -phase current of the motor
  can be restored by using two current sensors or a low-side or high-side bus current sensor, using the time-sharing sampling current reconstruction method.
• Motor position signal

FOC includes the following control modules:

• Clark-Park Transform
• PI regulation of d-axis and q-axis
• Inverse Clark-Park transform
• SVPWM

Specific control process:
(1) Measure the three-phase stator current. These measurements can obtain the values ​​of ia and ib, and ic can be calculated by the following formula: ia+ib+ic=0
(2) Transform the three-phase current to a two-axis system. This transformation will obtain variables iα and iβ, which are transformed from the measured ia and ib and the calculated ic value. From the stator point of view, iα and iβ are mutually orthogonal time-varying current values.
(3) According to the transformation angle calculated in the previous iteration of the control loop, the two-axis system is rotated to align with the rotor flux. The iα and iβ variables can be transformed to obtain Id and Iq. Id and Iq are orthogonal currents transformed to the rotating coordinate system. Under steady-state conditions, Id and Iq are constants.
(4) The error signal is obtained by comparing the actual values ​​of Id and Iq with their respective reference values.
· The reference value of Id controls the rotor flux
· The reference value of Iq controls the torque output of the motor
· The error signal is the input to the PI controller
· The outputs of the controller are Vd and Vq, which are the voltage vectors to be applied to the motor
(5) The new transformation angle is estimated, where Vα, Vβ, iα and iβ are the input parameters. The new angle tells the FOC algorithm where the next voltage vector is.
(6) Using the new angle, the Vd and Vq output values ​​of the PI controller can be inverted to the stationary reference coordinate system. This calculation will produce the next orthogonal voltage values ​​Vα and Vβ.
(7) The Vα and Vβ values ​​are inverted to obtain the 3-phase values ​​Va, Vb and Vc. The 3-phase voltage values ​​can be used to calculate the new PWM duty cycle values ​​to generate the desired voltage vector.

3.2 Direct Torque Control (DTC)

Direct torque control (DTC)

DTC was proposed by German scholar Professor Depenbrock in the mid-1980s. Its basic idea is to no longer convert the relevant variables on the stator side to the rotating coordinate system of the rotor, abandon the control idea of ​​current decoupling in vector control, remove the PI adjustment module, inverse Clark-Park transformation and SVPWM module, and instead directly calculate the motor flux and torque by detecting the bus voltage and stator current, and use two hysteresis comparators to directly realize the decoupling control of the stator flux and torque.

The stator winding itself is a sensor that directly measures the induced voltage. The direct integral of the stator voltage is the magnetic flux, and the voltage is the differential of the magnetic field. The position and direction of the magnetic field can be determined. This method is called direct torque control (DTC).