Electrical Machines · Chapter 91

Switched Reluctance Motors

Part 6 · Single-Phase and Special Machines — the most rugged rotor ever built, driven entirely by reluctance torque.

Prof. Mithun Mondal Engineering Devotion Digital Textbook
i Learning Objectives

By the end of this chapter you should be able to:

  1. Describe the doubly salient construction of the switched reluctance motor (SRM).

  2. Derive the torque from the co-energy and the inductance profile \(L(\theta)\).

  3. Compute stroke angle, strokes per revolution and switching frequencies.

  4. Explain the asymmetric half-bridge converter and the motoring and generating regions.

  5. List the merits, problems and applications of the SRM.

Section 91-1

Construction

Both stator and rotor have salient poles — the machine is doubly salient. Only the stator carries windings: concentrated coils on diametrically opposite poles are connected in series to form a phase. The rotor is simply a stack of shaped laminations, with no windings, no magnets and no cage.

  • Common configurations: 6/4 (three-phase), 8/6 (four-phase), 12/8 (three-phase).

  • \(N_s \ne N_r\) so that some rotor pole is always approaching alignment with an excitable stator pole.

Same principle, different purpose. The SRM works on the same alignment principle as the variable-reluctance stepper of Chapter 88, but it is controlled with rotor-position feedback and designed for continuous rotation and power, not for discrete positioning.
Section 91-2

Torque Production

Exciting a phase pulls the nearest rotor poles towards alignment, where the reluctance is minimum and the inductance maximum. From the co-energy method of Part 1, with a linear magnetic circuit,

∠
SRM torque
Torque depends on the slope of inductance, not on current direction
\[T = \frac{\partial W'_\text{co}}{\partial\theta}\bigg|_{i} = \frac12\,i^2\,\frac{dL}{d\theta}\]

  • \(dL/d\theta > 0\) (poles approaching): motoring torque.

  • \(dL/d\theta < 0\) (poles separating): generating/braking torque.

  • Since torque ∝ \(i^2\), current is unidirectional.

Each phase must be switched on as its inductance starts to rise and off before it starts to fall — hence a rotor-position sensor (or a sensorless estimator) is essential.

Idealised inductance profile and motoring current pulse phase current Lu (unaligned) La (aligned) dL/dθ > 0: motoring dL/dθ < 0: generating Rotor angle θ
Figure 91.1 — Current is applied while the phase inductance rises; applied while it falls, the same current would brake the machine.
Section 91-3

Stroke Angle and Frequencies

One stroke is the rotation produced by one phase excitation. With \(m\) phases and \(N_r\) rotor poles:

\[\varepsilon = \frac{360^\circ}{mN_r}, \qquad \text{strokes per revolution} = mN_r\]
\[f_\text{phase} = \frac{N_rN}{60}, \qquad f_\text{stroke} = \frac{mN_rN}{60}\]
1 Worked Example 91.1 — A 6/4 SRM

Problem. A three-phase 6/4 SRM has aligned and unaligned inductances of 60 mH and 8 mH; the inductance rises linearly over 30° of rotation. Find (a) the stroke angle, (b) the average torque during the rising region at a constant 10 A, and (c) the phase-current and stroke frequencies at 3000 rev/min.

\[\text{(a)}\quad \varepsilon = \frac{360^\circ}{3 \times 4} = 30^\circ\]
\[\text{(b)}\quad \frac{dL}{d\theta} = \frac{0.060 - 0.008}{\pi/6} = 0.0993~\text{H/rad}, \qquad T = \tfrac12(10)^2(0.0993) = 4.97~\text{N·m}\]
\[\text{(c)}\quad f_\text{phase} = \frac{4 \times 3000}{60} = 200~\text{Hz}, \qquad f_\text{stroke} = 3 \times 200 = 600~\text{strokes/s}\]

The linear-inductance result is optimistic: real SRMs operate deep in saturation, where the co-energy, not \(\tfrac12 i^2 dL/d\theta\), must be used.

Section 91-4

The Asymmetric Half-Bridge Converter

Each phase is fed by two switches and two diodes. Turning both switches on applies \(+V_\text{dc}\) to build up current; turning one off lets current freewheel at zero volts; turning both off forces the current through the diodes against \(-V_\text{dc}\), returning the stored magnetic energy to the DC link and collapsing the current quickly before \(dL/d\theta\) turns negative.

  • Phases are electrically independent: a fault in one leaves the others working — valuable in aerospace and safety-critical drives.

  • There is no shoot-through risk, since each switch is in series with a phase winding.

  • At low speed the current is regulated by chopping (hysteresis or PWM); at high speed the back-EMF limits current, and control is by advancing the turn-on and turn-off angles (single-pulse mode).

Section 91-5

Merits, Problems and Applications

Merits

Simplest, cheapest and most rugged rotor; very high speed capability; no magnets (no rare-earth cost, works at high temperature); losses mainly in the stator; fault tolerant; high starting torque.

Problems

High torque ripple; acoustic noise and vibration from radial forces; needs position sensing; non-linear magnetics make control harder; requires a special converter.

Applications: washing machines and vacuum cleaners, high-speed compressors and fans, mining and textile drives, aerospace starter-generators, and research prototypes for magnet-free EV traction.

Section 91-6

Summary and Common Mistakes

Key Points

  • Doubly salient; windings only on the stator; rotor is plain iron.

  • \(T = \tfrac12 i^2\,dL/d\theta\): sign set by the slope of \(L\), not by current direction.

  • Stroke angle \(\varepsilon = 360^\circ/(mN_r)\).

  • Asymmetric half-bridge: independent phases, energy return through the diodes.

Common Mistakes

  • Using the number of stator poles instead of rotor poles in the stroke-angle formula.

  • Leaving a phase energised into the falling-inductance region — it produces braking torque.

  • Using degrees instead of radians in \(dL/d\theta\).

Section 91-7

Chapter Review

Practice Problems

  1. P91.1 Find the stroke angle and strokes per revolution of a four-phase 8/6 SRM.

    Show answer
    \(\varepsilon = 360/(4 \times 6) = 15^\circ\); 24 strokes/rev.

  2. P91.2 In Example 91.1, what current gives 10 N·m in the rising region?

    Show answer
    \(i = \sqrt{2T/(dL/d\theta)} = \sqrt{20/0.0993} = 14.2\) A.
Multiple-Choice Questions

  1. MCQ 1. The rotor of an SRM carries:
    (a) a cage   (b) magnets   (c) a field winding   (d) none of these

    Show answer
    (d)

  2. MCQ 2. Reversing the current in an SRM phase:
    (a) reverses torque   (b) does not change torque   (c) doubles torque   (d) gives zero torque

    Show answer
    (b) — torque depends on \(i^2\).
Conceptual Questions

  1. Why must \(N_s \ne N_r\) in an SRM?

  2. Why is the SRM considered fault tolerant?

  3. What causes the acoustic noise of an SRM?

Looking Ahead

The final chapter covers two machines built for specialised duties: the servo motor, designed for fast, accurate response inside a feedback loop, and the linear induction motor, which unrolls the induction motor to produce straight-line thrust.