Switched reluctance motor: how a doubly salient motor with no magnets works

Doubly salient structure

In an SRM the stator has concentrated coils on salient poles and the rotor is a stack of steel laminations with salient teeth: no magnets, no cage, no windings. Opposite stator coils are connected into one phase. The most common arrangements are

• 6/4: 6 stator poles, 4 rotor poles, 3 phases
• 8/6: 8 stator poles, 6 rotor poles, 4 phases

The number of rotor poles is different from that of stator poles on purpose, so that when one phase is aligned the other phases are partly offset and a torque can always be started in a chosen direction. The step angle between phase strokes is 360° / (m × N_r): 30° for a 6/4 and 15° for an 8/6.

Minimum reluctance and the torque equation

When a stator phase is energised, a rotor pole nearby is pulled into alignment with it, because the flux wants the path of lowest reluctance. In the aligned position the inductance is maximum (L_a), and when the rotor pole is between the stator poles it is minimum (L_u). The torque is the change in stored magnetic energy with angle; for a phase without saturation:

T = ½ × i² × dL/dθ

Two consequences. First, the torque has the sign of dL/dθ, not the sign of the current, so a unidirectional current is enough and the converter does not need to reverse it. Second, the phase can only produce positive torque while the inductance is rising, as the rotor pole approaches alignment. If current is still flowing when the pole passes alignment, the inductance is falling and the torque becomes negative, which brakes the rotor.

Worked example for an 8/6 machine with L_u = 5 mH, L_a = 30 mH (a ratio of 6), a rising region of 20° mechanical (0.349 rad) and a current of 20 A, without saturation:

dL/dθ = 0.025 / 0.349 ≈ 0.072 H/rad T = ½ × 20² × 0.072 ≈ 14.3 N·m for the phase

The torque follows the square of the current, and saturation of the iron makes it a little smaller in a real machine.

Phase sequencing and the converter

To keep the rotor turning, the phases are energised in turn, each one just before its rotor pole reaches alignment. Reversing the sequence reverses the direction. The control needs the rotor position from a sensor or an estimate, and the switching angles are defined as turn-on and turn-off angles:

• Turn-on angle: set early enough that the current has risen before the inductance begins to increase. Earlier turn-on gives more torque but also more current.
• Turn-off angle: set early enough that the current has fallen to zero before alignment so there is no negative torque.

The usual converter is the asymmetric half bridge: for each phase, two switches and two diodes. With both switches on, the phase gets +V_dc. At turn-off both open and the diodes return the stored energy to the DC link with −V_dc. The phase winding is always between a switch and a diode, so the two switches of a leg can never short the DC link, which makes the converter robust. At low speed the current is held by chopping at a set limit; at high speed the back-EMF and the short stroke prevent the current from reaching the limit and the phase fires as a single pulse.

Torque ripple and acoustic noise

Each phase gives its torque in a pulse, and the total torque is the sum of the pulses. The torque therefore dips between strokes. The ripple is greater with fewer strokes per revolution (the 6/4 has 12 and the 8/6 has 24), and with a narrow conduction window. The stroke frequency is m × N_r × n / 60, which for an 8/6 at 3000 rpm is 4 × 6 × 3000 / 60 = 1200 Hz.

The same radial pulling that creates torque also deforms the stator. Each time the phase turns off the stator rings like a bell, and this is the main source of audible noise and vibration, which gets worse around the mechanical resonance of the stator. Remedies are more phases, shaped current waveforms, adjusted turn-off angles, and a stiffer stator. Ripple and noise are the reason SRMs are less common where quiet running is the first need.

Strengths and uses

• Simple and cheap rotor: only steel, so it is strong at very high speed (above 20 000 rpm) and tolerates high temperature.
• No magnets and no rotor currents: no rare earth, cold rotor, and no uncontrolled generation when the drive stops.
• Fault tolerance: phases are electrically and magnetically independent, so the motor can keep running on the remaining phases, and a converter leg cannot short-circuit.
• Wide constant-power speed range and good efficiency over a large speed and load range.

Common uses are vacuum cleaners and appliances, fans and pumps, electric vehicle prototypes, aerospace starter generators and mining or textile drives. The negatives are the torque ripple, noise, the need for a rotor position sensor or an estimator, and a converter designed for the machine.

How the simulator models the SRM

The simulator treats a phase over one electrical cycle at constant speed. The inductance is a trapezoid versus rotor angle: L_u when the poles do not overlap, a linear rise over 120° electrical, L_a when fully overlapped, and a linear fall. L_a / L_u = 6. The flux linkage saturates as ψ = ψ_sat × tanh(L × i / ψ_sat), and torque is the derivative of the co-energy, which reduces to ½ × i² × dL/dθ without saturation.

The converter integrates dψ/dt = v − R × i with +V_dc between turn-on and turn-off, current chopping modelled as an ideal hysteresis, and −V_dc after turn-off until the flux reaches zero. The other phases are shifted copies of the first. The model finds the speed where average torque equals load plus friction and iron loss. The machine is derived from the nameplate: rated power, rated speed and rated DC-link voltage.

Limits: no PWM ripple, dead time, mutual inductance or in-cycle speed ripple; the pole arcs and L_a / L_u are fixed. It is a teaching model.

Try it in the switched reluctance motor simulator

The switched reluctance motor simulator starts as an 8/6, four-phase machine of 1.5 kW, 3000 rpm and 300 V.

• Compare One electrical cycle of a phase: the Inductance, the Phase currents with turn-on and turn-off marks, and the Total torque with its average.
• Change the Turn-off angle (in electrical degrees, 0° = aligned; the default is −65°) towards 0° and beyond. The current continues into the falling inductance, a Negative torque share appears, and a warning shows when the turn-off is too late. Moving the Turn-on angle (default −125°) earlier or later changes the torque and peak current.
• Switch Stator/rotor poles between 6/4 and 8/6 and compare the Torque ripple readout; the 6/4 gives larger ripple. The Commutation frequency changes as well.
• Use the Current reference (chopping limit). The Current control mode shows Current chopping at low speed and Single pulse at high speed, and the Torque against speed chart labels the Chopping and Single pulse regions and the Speed cap.
• Change the Mechanical load and watch the Average torque, the speed and the DC-link current. Above what the drive can hold, the motor stalls.
• In the 3D view, the coils of the conducting phase glow orange while magnetising and blue while the energy is returned to the DC link.

The key habit: set the angles so the current flows only while the inductance is rising.

Try it in the simulator