# 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.

January 31, 2017

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).

## 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.

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.

## SPM versus IPM

A PM motor can be separated into two main categories: surface permanent magnet motors (SPM) and interior permanent magnet motors (IPM) (see Figure 3). Neither motor design type contains rotor bars. Both types generate magnetic flux by the permanent magnets affixed to or inside of the rotor.

SPM motors have the magnets affixed to the exterior of the rotor surface. Because of this mechanical mounting, their mechanical strength is weaker than that of IPM motors. The weakened mechanical strength limits the motor’s maximum safe mechanical speed. In addition, these motors exhibit very limited magnetic saliency (Ld ≈ Lq). Inductance values measured at the rotor terminals are consistent regardless of the rotor position. Because of the near unity saliency ratio, SPM motor designs rely significantly, if not completely, on the magnetic torque component to produce torque.

IPM motors have the permanent magnet imbedded into the rotor itself. Unlike their SPM counterparts, the location of the permanent magnets make IPM motors very mechanically sound, and suitable for operating at very high speeds. These motors also are defined by their relative high magnetic saliency ratio (Lq > Ld). Due to their magnetic saliency, an IPM motor has the ability to generate torque by taking advantage of both the magnetic and reluctance torque components of the motor (see Figure 4).

## PM motor structures

PM motor structures can be separated into two categories: interior and surface. Each category has its subset of categories. A surface PM motor can have its magnets on or inset into the surface of the rotor, to increase the robustness of the design. An interior permanent magnet motor positioning and design can vary widely. The IPM motor’s magnets can be inset as a large block or staggered as they come closer to the core. Another method is to have them imbedded in a spoke pattern.

## PM motor inductance variation with load

Only so much flux can be linked to a piece of iron to generate torque. Eventually, the iron will saturate and no longer allow flux to link. The result is a reduction to the inductance of the path taken by a flux field. In a PM machine, the d-axis and q-axis inductance values will reduce with increases to the load current.

The d and q axis inductances of an SPM motor are nearly identical. Because the magnet is outside of the rotor, the inductance of the q axis will drop at the same rate as the d axis inductance. However, the inductance of an IPM motor will reduce differently. Again, the d-axis inductance is naturally lower because the magnet is in the flux path and does not generate an inductive property. Therefore, there is less iron to saturate in the d axis, which results in a significantly lower reduction in flux with respect to the q axis.

## Flux weakening/intensifying of PM motors

Flux in a permanent magnet motor is generated by the magnets. The flux field follows a certain path, which can be boosted or opposed. Boosting or intensifying the flux field will allow the motor to temporarily increase torque production. Opposing the flux field will negate the existing magnet field of the motor. The reduced magnet field will limit torque production, but reduce the back-emf voltage. The reduced back-emf voltage frees up voltage to push the motor to operate at higher output speeds. Both types of operation require additional motor current. The direction of the motor current across the d axis, provided by the motor controller, determines the desired effect.

## Angle of excitation

The angle of excitation is the angle at which the vector sum of the d-axis and q-axis waveforms are excited to the motor with respect to the d axis. The d axis is always viewed to be where the magnet exists. Maximum magnetic flux is achieved at the q axis, which is 90 electrical deg from the d axis. Therefore, most references of the angle of excitation already take into account the 90-deg difference from the d axis to the q axis.

## Phase angle and torque

Magnetic torque is maximized when the stator field excites the motor rotor 90 electrical deg from the d axis (motor magnet position). Reluctance torque follows a different path and is maximized 45 electrical deg past the q axis. The maximum magnetic torque takes advantage of both the motor’s reluctance and magnetic torques. Shifting further away from the q axis reduces magnetic toque, but is far outweighed by the gain in reluctance torque. The maximum combined magnetic and reluctance torque occurs near 45 electrical deg from the q axis, but the exact angle will vary based on the characteristics of the PM motor.

## IPM motor power density

A PM motor’s power generation depends on the configuration of the motor magnets and the resulting motor saliency. Motors with a high saliency ratio (Lq > Ld) can increase motor efficiency and torque production by incorporating the motor’s reluctance torque. An inverter can be used to change the angle of excitation with respect to the d axis to maximize both the reluctance torque and magnetic torque of the motor.

## PM motor magnet types

There are few types of permanent magnet materials currently used for electric motors. Each type of metal has its advantages and disadvantages.

## Permanent magnet demagnetization

Permanent magnets are hardly permanent and do have limited capabilities. Certain forces can be exerted onto these materials to demagnetize them. In other words, it is possible to remove the magnetic properties of the permanent magnet material. A permanent magnetic substance can become demagnetized if the material is significantly strained, allowed to reach significant temperatures, or is impacted by a large electrical disturbance.

First, straining a permanent magnet is typically done by physical means. A magnetic material can become demagnetized, if not weakened, if it was to experience violent impacts/falls. A ferromagnetic material has inherent magnetic property. However, these magnetic properties can emit in any multitude of directions. One way ferromagnetic materials are magnetized is by applying a strong magnetic field to the material to align its magnetic dipoles. Aligning these dipoles forces the magnetic field of the material into a specific bath. A violent impact can remove the atomic alignment of the material’s magnetic domains, which weakens the strength of the intended magnetic field.

Secondly, temperatures also can affect a permanent magnet. Temperatures force the magnetic particles in a permanent magnet to become agitated. The magnetic dipoles have the ability to withstand some amount of thermal agitation. However, long periods of agitation can weaken a magnet’s strength, even if stored at room temperature. In addition, all magnetic materials have a threshold known as the “Curie temperature,” which is a threshold that defines the temperature at which the thermal agitation causes the material to completely demagnetize. Terms such as coercivity and retentivity are used to define magnetic material strength retention capability.

Finally, large electrical disturbances can cause a permanent magnet to demagnetize. These electrical disturbances can be from the material interacting with a large magnetic field or if a large current is passed through the material. Much in the same way a strong magnetic field or current can be used to align a material’s magnetic dipoles, another strong magnetic field or current applied to the field generated by the permanent magnet can result in demagnetization.

## Self-sensing versus closed-loop operation

Recent advances in drive technology allow standard ac drives to “self-detect” and track the motor magnet position. A closed-loop system typically uses the z-pulse channel to optimize performance. Through certain routines, the drive knows the exact position of the motor magnet by tracking the A/B channels and correcting for error with the z-channel. Knowing the exact position of the magnet allows for optimum torque production resulting in optimum efficiency.

## Servomotors

Servomotors are permanent magnet motors used for motion control applications. Typically, in an interior/internal permanent-magnet motor design, these motors are paired with a specific amplifier as part of a matched set to maximize performance. The amplifier has been fine tuned to the PM motor to reach optimum performance by its manufacturer. The motion amplifier/servo configuration typically uses motor feedback, which also provides a magnetic pole position and speed feedback.

Christopher Jaszczolt is a drives product management specialist at Yaskawa America Inc. He has more than nine years of experience in motion control. In addition to his current title, Jaszczolt has worked as a technical support engineer and an application engineer. He has a BSEE from Northern Illinois University, DeKalb, Ill.