ECE 8830 - Electric Drives Topic 15: Permanent Magnet Synchronous and Variable Reluctance Motors Spring 2004

Introduction Permanent magnet synchronous motors have the rotor winding replaced by permanent magnets. These motors have several advantages over synchronous motors with rotor field windings, including: Elimination of copper loss Higher power density and efficiency Lower rotor inertia Larger airgaps possible because of larger coercive force densities.

Introduction (cont’d) Some disadvantages of the permanent magnet synchronous motor are: Loss of flexibility of field flux control Cost of high flux density permanent magnets is high Magnetic characteristics change with time Loss of magnetization above Curie temperature

Permanent Magnets Advances in permanent magnetic materials over the last several years have had a dramatic impact on electric machines. Permanent magnet materials have special characteristics which must be taken into account in machine design. For example, the highest performance permanent magnets are brittle ceramics, some have chemical sensitivities, all have temperature sensitivity, and most have sensitivity to demagnetizing fields. Proper machine design requires understanding the materials well.

B-H Loop A typical B-H loop for a permanent magnet is shown below. The portion of the curve in which permanent magnets are designed to operate in motors is the top left quadrant. This segment is referred to as the “demagnetizing curve” and is shown on the next slide.

Demagnetizing Curve

Demagnetizing Curve (cont’d) The remnant flux density Br will be available if the magnet is short-circuited. However, with an air gap there will be some demagnetization resulting in the no-load operating point, B’. Slope of no-load line is smaller with a larger air gap. With current flowing in the stator, there is further demagnetization of the permanent magnet causing the operating point to shift to C’ at full load.

Demagnetizing Curve (cont’d) Transients or machine faults can lead to a worst-case demagnetization as shown which results in permanent demagnetization of the permanent magnet. The recoil line following the transient is shown and shows a reduced flux density compared to the original line. It is clearly important to control the operation of the magnets to keep the operating point away from this worst-case demagnetization condition.

Permanent Magnetic Materials Alnico - good properties but too low a coercive force and too square a B-H loop => permanent demagnetization occurs easily Ferrites (Barium and Strontium) - low cost, moderately high service temperature (400C), and straight line demagnetization curve. However, Br is low => machine volume and size needs to be large.

Permanent Magnet Materials (cont’d) Samarium-Cobalt (Sm-Co) - very good properties but very expensive (because Samarium is rare) Neodymium-Iron-Boron (Nd-Fe-B) - very good properties except the Curie temperature is only 150C

Permanent Magnet Materials (cont’d)

PM Motor Construction There are two types of permanent magnet motor structures: 1) Surface PM machines - sinusoidal and trapezoidal 2) Interior PM machines - regular and transverse

Circuit Model of PM Motor (cont’d) Based on the recoil line, we can write: where Prc, the permeance, is the slope of the line. From this equation we can write:

Equivalent Circuit Model of PM Motor Rearranging the slope equation, we get: This equation suggests the following equivalent circuit for a permanent magnet:

Equivalent Circuit Model of PM Motor (cont’d) It can be shown that the mmf, flux and permeance are the mathematical duals of current, voltage, and inductance, respectively. Therefore, the following electrical equivalent circuits can be used to represent the magnetic circuit:

Equivalent Circuit Model of PM Motor (cont’d) We can now use this equivalent circuit of the permanent magnets on the rotor and the previous equivalent equivalent circuits of the synchronous motor to develop a set of qd0 equivalent circuits for the permanent magnet synchronous motor. Assuming the PM synchronous motor has damper cage windings but no g winding, the qd0 equivalent circuits are as shown on the next slide.

Equivalent Circuit Model of PM Motor (cont’d)

Equivalent Circuit Model of PM Motor (cont’d) Here the PM magnet inductance Lrc can be lumped with the common d-axis mutual inductance of the stator and damper windings, and the combined d-axis mutual inductance indicated by Lmd. Also, the current i’m is the equivalent magnetizing current for the permanent magnet referred to the stator side.

qd0 Equations for Permanent Magnet Synchronous Motor The qd0 equations for a permanent magnet motor are given in the table below:

qd0 Equations for Permanent Magnet Synchronous Motor (cont’d)

qd0 Equations for Permanent Magnet Synchronous Motor (cont’d) The developed electromagnetic torque expression has three components: 1) A reluctance component (which is negative for Ld<Lq) 2) An induction component (which is asynchronous torque) 3) An excitation component from the field of the permanent magnet.

qd0 Equations for Permanent Magnet Synchronous Motor (cont’d) The mutual flux linkages in the q- and d-axes may be expressed by: The winding currents can be expressed (as before) as:

qd0 Equations for Permanent Magnet Synchronous Motor (cont’d) Combining these equations gives: where . Similar expressions for mq and LMQ can be written for the q-axis.

qd0 Equations for Permanent Magnet Synchronous Motor (cont’d) Under steady state conditions where =e as in the case of Ef in the wound field synchronous motor, we can express em’ or xmdim’ by Em, the permanent magnet’s excitation voltage on the stator side. If the stator resistance is neglected and the Ef term in the earlier torque expression replaced by Em, the torque of a permanent magnet synchronous motor in terms of the rms phase voltage Va at its terminal can be written as:

Simulation of PM Synchronous Motor A line-start permanent magnet motor has magnets embedded in the rotor to provide synchronous excitation and a rotor cage provides induction motor torque for starting. Thus it is a high efficiency synchronous motor with self-start capability when operated from a fixed frequency voltage source.

Simulation of PM Synchronous Motor (cont’d) The simulation equations for the PM synchronous motor are given below:

Simulation of PM Synchronous Motor (cont’d)

Simulation of PM Synchronous Motor (cont’d) The Simulink file s4 in Ch.7 Ong implements a simulation of a line-start 3 PM synchronous motor connected directly to a 60Hz, 3 supply of rated voltage. The overall block diagram is:

Simulation of PM Synchronous Motor (cont’d) This slide and the next few slides show the internal blocks of the Simulink model.

Simulation of PM Synchronous Motor (cont’d)

Simulation of PM Synchronous Motor (cont’d)

Simulation of PM Synchronous Motor (cont’d)

Simulation of PM Synchronous Motor (cont’d)

Simulation of PM Synchronous Motor (cont’d)

Simulation of PM Synchronous Motor (cont’d)

Trapezoidal Surface Magnet Motor A trapezoidal surface permanent magnet motor is the same as a sinusoidal PM motor except the 3 winding has a concentrated full-pitch distribution instead of a sinusoidal distribution.

Trapezoidal Surface Magnet Motor (cont’d) This 2-pole motor has a gap in the rotor magnets to reduce flux fringing effects and the stator has 4 slots per phase winding per pole. As the machine rotates the flux linkage will vary linearly except when the magnet gap passes through the phase axis. If the machine is driven by a prime mover, the stator phase voltages will have a trapezoidal wave shape as shown on the next slide.

Trapezoidal Surface Magnet Motor (cont’d)

Trapezoidal Surface Magnet Motor (cont’d) An electronic inverter is required to establish a six-step current wave to generate torque. With the help of an inverter and an absolute-position sensor mounted on the shaft, both sinusoidal and trapezoidal SPM motors can serve as brushless dc motors (although the trapezoidal SPM motor gives closer dc machine-like performance).

Synchronous Reluctance Motor A synchronous reluctance motor has the same structure as that of a salient pole synchronous motor except that it does not have a field winding on the rotor.

Synchronous Reluctance Motor (cont’d) The stator has a 3, symmetrical winding which creates a sinusoidal rotating field in the air gap. This causes a reluctance torque to be created on the rotor because the magnetic field induced in the rotor causes it to align with the stator field in a minimum reluctance position. The torque developed in this type of motor can be expressed as:

Synchronous Reluctance Motor (cont’d) The reluctance torque stability limit can be seen to occur at (see figure below).

Synchronous Reluctance Motor (cont’d) Iron laminations separated by non-magnetic materials increases reluctance flux in the qe-axis. With proper design, the reluctance motor performance can approach that of an induction motor, although it is slightly heavier and has a lower power factor. Their low cost and robustness has seen them increasingly used for low power applications, such as in fiber-spinning mills.

Variable Reluctance Motors A variable reluctance motor has double saliency, i.e. both the rotor and stator have saliency. There are two groups of variable reluctance motors: stepper motors and switched reluctance motors. Stepper motors are not suitable for variable speed drives. Ref: A. Hughes, “Electric Motors and Drives”, 2nd. Edn. Newnes

Switched Reluctance Motors The structure of a switched reluctance motor is shown below. This is a 4-phase machine with 4 stator-pole pairs and 3 rotor-pole pairs (8/6 motor). The rotor has neither windings nor permanent magnets.

Switched Reluctance Motors (cont’d) The stator poles have concentrated winding rather than sinusoidal winding. Each stator-pole pair winding is excited by a converter phase, until the corresponding rotor pole-pair is aligned and is then de-energized. The stator-pole pairs are sequentially excited using a rotor position encoder for timing.

Switched Reluctance Motors (cont’d) The inductance of a stator-pole pair and corresponding phase currents as a function of angular position is shown below.

Switched Reluctance Motors (cont’d) Applying the stator pulse when the inductance profile has positive slope induces forward motoring torque. Applying the stator pulse during the time that the inductance profile has negative slope induces regenerative braking torque. A single phase is excited every 60 with four consecutive phases excited at 15 intervals.

Switched Reluctance Motors (cont’d) The torque is given by: where m=inductance slope and i=instantaneous current.

Switched Reluctance Motors (cont’d) Switched reluctance motors are growing in popularity because of their simple design and robustness of construction. They also offer the advantages of only having to provide positive currents, simplifying the inverter design. Also, shoot-through faults are not an issue because each of the main switching devices is connected in series with a motor winding. However, the drawbacks of this type of motor are the pulsating nature of their torque and they can be acoustically noisy (although improved mechanical design has mitigated this problem.)