Understanding permanent magnet motors

A permanent magnet (PM) motor is an ac motor that uses magnets imbedded into or attached to the surface of the motor’s rotor. This article provides an elementary understanding behind the terminology, concepts, theory, and physics behind PM motors.

01/31/2017


Figure 1: Magnetic saliency is the inductance variation at the motor terminals according to the rotor position. Courtesy: Yaskawa America Inc.Controlling the speed of ac motors is accomplished using a variable frequency drive (VFD) in most cases. While many scenarios involve using VFDs with induction motors with stator windings to generate a rotating magnetic field, they also can achieve precise speed control using speed or position feedback sensors as a reference to the VFD.

In some situations, it is possible to obtain comparably precise speed control without the need for feedback sensors. This is made possible using a permanent magnet (PM) motor and a process called the "high-frequency signal injection method." 

Induction machines

An ac induction machine (IM) also is commonly referred to as an ac motor. A rotating field is generated by the stator winding. The rotating field induces a current in the rotor bars. The current generation requires a speed difference between the rotor and the magnetic field. The interaction between the field and the current produces the driving force. Therefore, ac induction machines are the predominant motor operated by adjustable speed drives. 

PM motors

A PM motor is an ac motor that uses magnets imbedded into or attached to the surface of the motor's rotor. The magnets are used to generate a constant motor flux instead of requiring the stator field to generate one by linking to the rotor, as is the case with an induction motor. A fourth motor known as a line-start PM (LSPM) motor incorporates characteristics of both motors. An LSPM motor incorporates a PM motor's magnets within the rotor and a squirrel cage motor's rotor bars to maximize torque and efficiency (see Table 1). 

Courtesy: Yaskawa America Inc.

Flux, flux linkage, and magnetic flux

To understand the operation of PM motors, it is important to first understand the concepts of magnetic flux, flux linkage, and magnetic flux. 

Flux: The flow of current through a conductor creates a magnetic field. Flux defines the rate of flow of a property per unit area. Flux current is the rate of current flow through a given conductor cross-sectional area. 

Flux linkage: Flux linkage occurs when a magnetic field interacts with a material such as what would happen when a magnetic field goes through a coil of wire. Flux linkage is determined by the number of windings and flux, where ϕ is used to indicate the instantaneous value of a time-varying flux. Flux linkage is defined by the following equation: 

Magnetic flux: Magnetic flux is defined as the rate of a magnetic field flowing through a given conductor's cross-sectional area. Magnetic flux field is generated by a permanent magnet within or on the surface of a permanent magnet motor. 

Inductor: An inductor is a circuit element that consists of a conducting wire usually in the form of a coil. A conductor carrying a constant current will generate a constant magnetic field. It can be demonstrated that a magnetic field and the current that produced it are linearly related. Changing the magnetic field will induce a voltage in a nearby conductor proportional to the rate of change of the current that produced the magnetic field. The voltage in the conductor is determined by the following equation:


Inductance: Inductance (L) is the constant of proportionality that defines the relationship between the voltages induced by a time rate of change in current that produced a magnetic field. In simpler terms, inductance is the flux linkage per unit current. It must be made clear that inductance is a passive element and is purely a geometric property. Inductance is measured in Henrys (H) or weber-turns per ampere. 

The d axis and q axis: In geometric terms, the "d" and "q" axes are the single-phase representations of the flux contributed by the three separate sinusoidal phase quantities at the same angular velocity. The d axis, also known as the direct axis, is the axis by which flux is produced by the field winding. The q axis, or the quadrature axis is the axis on which torque is produced. By convention, the quadrature axis always will lead the direct axis electrically by 90 deg. In simplistic terms, the d axis is the main flux direction, while the q axis is the main torque producing direction. 

Magnetic permeability: In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field.

PM motor equivalent circuit: A permanent magnet motor can be represented in a few different motor models. One of the most common methods is the d-q motor model. 

PM motor d-axis and q-axis inductance: The d axis and q axis inductances are the inductances measured as the flux path passes through the rotor in relation to the magnetic pole. The d-axis inductance is the inductance measured when flux passes through the magnetic poles. The q-axis inductance is the inductance measure when flux passes between the magnetic poles.

In an induction machine, the rotor flux linkage will be the same between the d axis and the q axis. However, in a permanent magnet machine, the magnet reduces the available iron for flux linkage. A magnet's permeability is near that of air. Therefore, the magnet can be viewed as an air gap. The magnet is in the flux path as it travels through the d axis. The flux path traveling through the q axis does not cross a magnet. Therefore, more iron can be linked with the q-axis flux path, which results in a larger inductance. A motor with an imbedded magnet will have a larger q-axis inductance than the d-axis inductance. A motor with surface-mount magnets will have nearly identical q-axis and d-axis inductances because the magnets are outside the rotor and do not limit the amount of iron linked by the stator field. 

Magnetic saliency: Salience or saliency is the state or quality by which something stands out relative to its neighbors. Magnetic saliency describes the relationship between the rotor's main flux (d axis) inductance and the main torque-producing (q axis) inductance. The magnetic saliency varies depending on the position of the rotor to the stator field, where maximum saliency occurs at 90 electrical deg from the main flux axis (d axis) (see Figure 1). 

Excitation current: Excitation current is "the current in the stator windings required to generate magnetic flux in the rotor core." Permanent magnet machines do not require excitation current in the stator winding because a PM motor's magnets already generate a standing magnetic field. 

Secondary current: Secondary current, otherwise known as "the torque-producing current," is the current required to generate motor torque. In a permanent magnet machine, torque-producing currents make up the majority of the current draw. 

Pull-in current: Unlike an amplifier and servo matched set intended for motion control, a conventional VFD does not have information about the position of the motor's rotor magnetic pole. Without knowledge of the magnetic pole position, a field cannot be generated in the stator to maximize torque production. Therefore, a VFD has the ability to provide dc voltage to lock the magnetic field into a known position. The current draw required to pull in the rotor is called the "pull-in current."

High-frequency injection: High frequency injection is an inverter methodology used to detect a PM motor's magnetic pole position. The method begins by the inverter injecting a high-frequency, low-voltage signal into the motor at an arbitrary axis. The inverter then swings the angle of excitation and monitors the current.

Figure 2: The drawing on the left shows that when high-frequency voltage is injected, motor impedance changes. The graph on the right shows IPM motor impedance variation according to injection angle. Courtesy: Yaskawa America Inc. Figure 2: The drawing on the left shows that when high-frequency voltage is injected, motor impedance changes. The graph on the right shows IPM motor impedance variation according to injection angle. Courtesy: Yaskawa America Inc.

According to the injection angle, rotor impedance varies. Interior permanent magnet (IPM) motor terminal impedance decreases when the high-frequency signal injecting axis and the magnetic pole axis (d-axis) are aligned, i.e. at 0 deg. The impedance is maximum at ±90 deg. Using this characteristic, the drive can detect the rotor position without pulse encoders by injecting high frequency ac voltage/current to the IPM motor. Moreover, the high-frequency signal injection method can be used for speed detection in the low-speed region where typically full-load torque control is very difficult because the motor's back-emf voltage level is too low.

Back-emf waveform

Back emf is short for back electromotive force, but also known as the counter-electromotive force. The back electromotive force is the voltage that occurs in electric motors when there is a relative motion between the stator windings and the rotor's magnetic field. The geometric properties of the rotor will determine the shape of the back-emf waveform. These waveforms can be sinusoidal, trapezoidal, triangular, or something in between.

Both induction and PM machines generate back-emf waveforms. In an induction machine, the back-emf waveform will decay as the residual rotor field slowly decays because of the lack of a stator field. However, with a PM machine, the rotor generates its own magnetic field. Therefore, a voltage can be induced in the stator windings whenever the rotor is in motion. Back-emf voltage will rise linearly with speed and is a crucial factor in determining maximum operating speed. 

Understanding PM machine torque

An electric machine's torque can be broken down into two components: magnetic torque and reluctance torque. Reluctance torque is the "force acting on the magnetic material that tends to align with the main flux to minimize reluctance." In other words, reluctance torque is the torque generated by the alignment of the rotor shaft to the stator flux field. Magnetic torque is the "torque generated by the interaction between the magnet's flux field and the current in the stator winding."

Reluctance torque: Reluctance torque pertains to the torque generated through the alignment of the rotor that occurs when the magnetic field forces a desired direct flow from the north stator pole to the south stator pole. 

Magnetic torque: Permanent magnets generate a flux field in the rotor. The stator generates a field that interacts with the rotor's magnetic field. Changing the position of the stator field with respect to the rotor field causes the rotor to shift. The shift due to this interaction is the magnetic torque. 


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