Synchronous, PMSM, and BLDC Drives

Introduction

Synchronous drives are AC motor-drive systems in which the average mechanical speed is locked to the electrical excitation frequency. They are important in industrial automation, robotics, electric vehicles, compressors, pumps, machine tools, and renewable-energy conversion. Unlike an induction motor, a synchronous motor does not require slip to produce steady-state torque. Its rotor field is produced either by a DC excitation winding, permanent magnets, or salient rotor geometry interacting with stator magnetic fields.

This chapter develops the operating principles of wound-field synchronous motors, permanent-magnet synchronous motors (PMSMs), and brushless DC (BLDC) motors. Particular attention is given to excitation, torque production, rotor-position dependence, inverter commutation, current control, field weakening, and maximum-torque-per-ampere (MTPA) operation.

Learning Objectives

After studying this chapter, the reader should be able to:

• explain synchronous speed, excitation, torque angle, and torque production;
• distinguish wound-field synchronous, PMSM, and BLDC drives;
• formulate the steady-state dq-axis voltage and torque equations;
• explain rotor-position sensing and sensorless estimation;
• design basic six-step commutation and sinusoidal current control;
• determine voltage, current, speed, and thermal operating limits;
• explain field weakening and MTPA control;
• select an appropriate drive topology for an application.

1. Synchronous Operation and Excitation

For a motor with p pole pairs supplied at electrical frequency f_e, synchronous mechanical speed is

where n_s is in revolutions per minute when f_e is in hertz. The corresponding mechanical angular speed is ω_m = 2πn_s/60, in radians per second. Electrical and mechanical angular speeds satisfy

A synchronous rotor must establish a magnetic field. In a wound-field motor, a DC current produces rotor magnetomotive force. In a permanent-magnet motor, rare-earth or ferrite magnets provide approximately constant rotor flux. Reluctance torque can also arise when a salient rotor tends to align its low-reluctance axis with the stator field.

The rotor field must remain in a stable angular relationship with the rotating stator field. This electrical angle is commonly called the torque angle or load angle, δ. If mechanical load increases, δ increases while speed remains synchronous, provided the stability limit is not exceeded. Excessive load angle causes loss of synchronism.

A converter-fed drive normally contains a DC source or rectifier, a voltage-source inverter, a motor, position or speed measurement, and a controller. The inverter synthesizes currents whose frequency, phase, and magnitude are determined by the controller rather than directly by the utility supply.

2. Machine Models in the Rotating dq Frame

For balanced three-phase operation, sinusoidal quantities can be transformed into direct-axis and quadrature-axis components. The d-axis is aligned with the rotor magnetic axis; the q-axis leads it by 90 electrical degrees. Neglecting zero-sequence components, the PMSM voltage equations are

Here, v_d,v_q are dq stator voltages in volts, i_d,i_q are dq currents in amperes, R_s is stator resistance in ohms, L_d,L_q are d- and q-axis inductances in henries, ω_e is electrical angular speed in radians per second, and ψ_f is permanent-magnet flux linkage in webers. The equations assume balanced sinusoidal windings, a conventional Park transformation, constant parameters, and neglected inverter dead time and saturation.

The electromagnetic torque is

The first term is permanent-magnet torque. The second is reluctance torque and exists when the rotor is salient, meaning L_d ≠ L_q. For a surface-mounted PMSM, L_d ≈ L_q, so reluctance torque is small and

The mechanical dynamic equation is

where J is rotor and load inertia in kg·m², T_L is load torque in N·m, and B is viscous-friction coefficient in N·m·s/rad. It assumes a lumped mechanical model.

The electromagnetic power, excluding losses in the ideal model, is

Electrical input power is higher because of copper, iron, inverter, mechanical, and windage losses.

Steady-state phasor interpretation

When currents are constant in the rotor reference frame, derivative terms vanish. The speed-dependent terms then represent back electromotive force (back EMF). At high speed, back EMF may approach the inverter voltage limit, preventing further current control. This is the central reason for field weakening.

3. Wound-Field Synchronous-Motor Drives

A wound-field synchronous motor has a three-phase stator and a rotor field winding supplied with DC through slip rings or a brushless exciter. Its main advantages are adjustable excitation, capability for power-factor control, and suitability for high-power applications. Its disadvantages include excitation hardware, rotor losses, maintenance in slip-ring systems, and more complex starting.

The excitation current controls air-gap flux. Underexcitation may cause the motor to draw lagging reactive power; overexcitation may cause it to supply leading reactive power. Thus, a synchronous motor can be used for power-factor correction while delivering mechanical power.

A line-connected synchronous motor is not inherently self-starting because the rotor cannot instantaneously follow the rapidly rotating stator field. Starting methods include damper windings, a reduced-frequency converter, an auxiliary motor, or an inverter that gradually increases electrical frequency.

4. PMSM Drives

A PMSM uses permanent magnets mounted on the rotor. Two important constructions are:

PMSMs provide high power density and efficiency because rotor copper loss is absent. However, magnets increase cost, may suffer irreversible demagnetization from excessive temperature or opposing current, and produce back EMF whenever the rotor turns.

The controller must know rotor electrical position. An angular error causes current to be applied on the wrong axis, reducing torque and possibly increasing stress. Position may be obtained from an encoder, resolver, Hall sensors, or sensorless estimation based on back EMF, flux linkage, or saliency.

5. BLDC Drives and Electronic Commutation

A BLDC motor usually has trapezoidal back EMF and concentrated stator windings. It is electronically commutated: semiconductor switches replace the mechanical commutator and brushes of a conventional DC motor. A common six-step strategy energizes two phases while the third is floating. Each conduction interval spans 60 electrical degrees, and the energized phase pair changes according to rotor position.

With ideal rectangular phase current and trapezoidal back EMF, torque is approximately constant over a commutation interval. Hall sensors spaced 120 electrical degrees apart commonly provide six position states. The inverter must apply the correct high-side and low-side switches for each state; invalid states must be blocked to prevent shoot-through or uncontrolled current.

BLDC and PMSM terminology is not completely uniform. The distinction usually concerns back-EMF and current-waveform shape: BLDC drives use trapezoidal excitation, whereas PMSM drives use sinusoidal excitation and vector control. A physical machine may operate with either strategy if its winding distribution and controller permit it.

A simplified phase relation is

where e_a,e_b,e_c are phase back EMFs in volts, i_a,i_b,i_c are phase currents in amperes, and ω_m is mechanical angular speed. This relation follows from electromechanical power balance and is applicable when the phase quantities and speed are consistently defined.

6. Commutation and Current Control

Six-step control

Six-step control uses a position state to select the conducting phase pair. A typical sequence is A+ B−, A+ C−, B+ C−, B+ A−, C+ A−, and C+ B−. The actual order depends on phase wiring and sensor orientation. Current regulation is often implemented with hysteresis control or PWM applied to the conducting switches.

Advantages include low computational cost and simple hardware. Disadvantages include torque ripple, acoustic noise, current harmonics, and poorer low-speed smoothness than sinusoidal vector control.

Sinusoidal and field-oriented control

Field-oriented control transforms measured currents into the rotor dq frame. The d-axis current primarily controls flux, while q-axis current primarily controls torque. PI regulators generate voltage commands, and space-vector PWM or sinusoidal PWM applies them through the inverter.

A typical control structure contains:

1. an outer speed loop producing torque or q-axis-current reference;
2. current measurement and Clarke/Park transformations;
3. d- and q-axis current regulators;
4. decoupling feedforward terms such as ω_eL_qi_q and ω_e(L_di_d+ψ_f);
5. inverse transformation and PWM generation;
6. position feedback or a sensorless estimator.

The current-loop bandwidth must be substantially higher than the speed-loop bandwidth. Excessive proportional gain causes noise sensitivity and voltage saturation; excessive integral action causes windup. Anti-windup logic is therefore required when the inverter reaches its voltage limit.

7. Operating Limits

A drive is constrained by several limits:

• Current limit: determined by semiconductor ratings, winding heating, and demagnetization risk.
• Voltage limit: determined by DC-link voltage, modulation method, dead time, and allowable device voltage.
• Thermal limit: determined by copper, iron, magnet, bearing, and inverter temperatures.
• Speed limit: determined by mechanical stress, rotor retention, bearing capability, and back EMF.
• Torque limit: determined by current, magnetic saturation, and load dynamics.

Copper loss is approximately

for a balanced three-phase motor when R_s is the per-phase resistance and I_phase,rms is the RMS phase current. Temperature changes resistance; for copper, a useful engineering approximation is R(T) = R₀[1 + α(T − T₀), where α is approximately 0.0039 per °C near room temperature. This approximation is valid over moderate temperature ranges.

In a voltage-source inverter, the available fundamental voltage is limited by the DC-link voltage and modulation strategy. The exact numerical limit depends on whether phase, line-to-line, peak, or RMS voltage is used and on the PWM method; therefore, voltage-base calculations must define the convention explicitly.

8. Field Weakening

At high speed, the back-EMF term increases approximately in proportion to speed. If the required voltage exceeds the inverter limit, the controller applies negative d-axis current to reduce effective air-gap flux. For an IPMSM, this action reduces the q-axis flux-linkage term L_di_d + ψ_f.

Field weakening is constrained by both voltage and current. A common current constraint is

where I_max is the allowable current magnitude. Negative i_d consumes current capacity, so maximum torque decreases as speed rises. In the constant-power region, approximately constant power is maintained by reducing torque as speed increases:

Field weakening is not free: it increases copper loss, may increase demagnetization risk, and can reduce efficiency. The controller should enter it only when required by the voltage constraint.

9. Maximum-Torque-per-Ampere Control

MTPA selects i_d and i_q to maximize torque for a specified current magnitude. It is especially valuable in an IPMSM because reluctance torque can supplement magnet torque.

Let I_s² = i_d² + i_q². The optimization problem is

subject to

The exact MTPA current angle depends on ψ_f, L_d, L_q, saturation, and the adopted sign convention. For a surface PMSM with negligible saliency, the optimum is approximately i_d = 0 below the voltage limit. For an interior PMSM, a negative d-axis current is commonly selected when L_q > L_d under the stated torque equation convention. Practical controllers use analytical look-up tables, calibrated maps, or online optimization because inductances vary with current and saturation.

10. Worked Example: PMSM Torque and Speed

An IPMSM has p = 4, ψ_f = 0.08 Wb, L_d = 0.8 mH, L_q = 1.6 mH, i_d = −20 A, and i_q = 50 A. Find electromagnetic torque using the dq model.

First, convert inductances to henries: L_d = 0.0008 H and L_q = 0.0016 H. Then

The magnet term is 4.00 N·m-equivalent, and the reluctance term is 0.80 N·m-equivalent. Therefore,

The current magnitude is √(20² + 50²) = 53.9 A. The result assumes the current and flux-linkage definitions match the stated torque equation and that saturation and losses are neglected.

11. Illustrative Application Case: Electric-Vehicle Traction Drive

Background. An electric vehicle requires high starting torque, efficient cruising, regenerative braking, and a wide constant-power speed range.

Problem. A surface PMSM offers high efficiency and power density, but its permanent-magnet flux produces substantial back EMF at high speed. The inverter has a finite DC-link voltage, and battery current must be limited.

Analysis. At low speed, voltage demand is moderate. The controller can operate near i_d = 0 and use q-axis current to produce torque. During acceleration, current is limited by the inverter and motor thermal model. At base speed, the voltage magnitude approaches its limit. Above base speed, negative d-axis current weakens the effective flux. During regenerative braking, the q-axis-current reference changes sign, while the battery-management system limits charging power.

Approach. The drive uses resolver position feedback, inner dq current loops, MTPA below base speed, and a voltage-constrained field-weakening controller above base speed. A supervisory controller coordinates torque commands with battery state of charge, traction limits, and thermal derating. Fault logic disables gate signals if overcurrent, overspeed, position disagreement, or isolation failure is detected.

Outcome. The strategy provides high launch torque, efficient operation over the normal driving range, controlled regeneration, and safe reduction of torque when thermal or voltage limits are reached.

Learning points. Motor selection cannot be separated from inverter voltage, battery energy, cooling, position sensing, safety, and control strategy. MTPA improves low-speed utilization, while field weakening extends speed at the cost of current and efficiency.

12. Comparison of Drive Types

13. Best Practices, Safety, and Contemporary Developments

Commissioning should begin with phase identification, encoder polarity verification, low-voltage current-limited tests, and confirmation of emergency shutdown. Never assume that a stopped PMSM is electrically safe: rotation can generate hazardous voltage. DC-link discharge time, insulation monitoring, gate-driver interlocks, and safe torque off are essential in professional systems.

Control software should include current-sensor plausibility checks, overspeed protection, thermal derating, watchdogs, parameter validation, and fault logging. Functional-safety design may be guided by standards such as IEC 61800-5-2, while machine and EMC requirements depend on jurisdiction and application.

Current research and industrial development include silicon-carbide inverters, concentrated-winding machines, advanced rotor cooling, sensorless control at zero and low speed, online parameter identification, model-predictive control, and reduced-rare-earth or magnet-free synchronous-reluctance alternatives. Artificial intelligence can assist condition monitoring and parameter estimation, but it should not replace deterministic protection functions unless its safety has been rigorously demonstrated.

Chapter Summary

Synchronous drives maintain a fixed relationship between electrical excitation and mechanical speed. Wound-field machines obtain rotor flux from DC excitation, PMSMs obtain it from permanent magnets, and BLDC drives commonly use trapezoidal back EMF with six-step electronic commutation. The dq model separates flux-producing and torque-producing current components and gives the general PMSM torque equation, including magnet and reluctance torque.

Rotor position is essential for correct commutation and vector control. Six-step control is simple but produces torque ripple, whereas sinusoidal field-oriented control provides smoother torque and supports MTPA and field weakening. Current, voltage, thermal, mechanical, and demagnetization limits define the safe operating envelope. MTPA maximizes torque for a given current, while negative d-axis current extends speed beyond the base-speed voltage limit. Practical drive design requires coordinated attention to machine construction, inverter capability, sensing, thermal management, safety, and application requirements.

Key Terms

Synchronous speed: Mechanical speed locked to electrical excitation frequency.

Pole pair: One north–south magnetic pole pair represented in the electrical cycle relationship.

Torque angle: Electrical angular displacement between stator and rotor magnetic fields.

Wound-field synchronous motor: Synchronous motor whose rotor flux is produced by a DC field winding.

Permanent-magnet synchronous motor: Synchronous motor using permanent magnets for rotor excitation.

Interior PMSM: PMSM with magnets embedded inside the rotor.

Surface PMSM: PMSM with magnets mounted near the rotor surface.

BLDC motor: Permanent-magnet motor commonly operated with trapezoidal back EMF and electronic commutation.

Back EMF: Voltage induced by rotor motion in motor windings.

dq reference frame: Rotating coordinate system aligned with rotor magnetic axes.

Saliency: Difference between d-axis and q-axis magnetic reluctance or inductance.

Reluctance torque: Torque caused by the rotor tendency to align with minimum magnetic reluctance.

Commutation: Controlled switching of inverter phases according to rotor position.

Field-oriented control: Control method that regulates rotor-frame flux and torque current components.

MTPA: Maximum-torque-per-ampere operating strategy.

Field weakening: Application of opposing d-axis current to reduce effective flux and extend speed.

Voltage limit: Maximum voltage that the inverter can synthesize.

Torque ripple: Periodic variation of electromagnetic torque.

Regenerative braking: Operation in which mechanical energy is converted into electrical energy.

Safe torque off: Safety function that prevents the motor from producing torque by disabling power switching.

Review Questions

Short Answer Questions

1. Define synchronous speed and explain the role of pole pairs.
2. Why does a PMSM require rotor-position information for high-performance control?
3. Distinguish magnet torque from reluctance torque.
4. What is the purpose of negative d-axis current in field weakening?
5. State one advantage and one limitation of six-step BLDC control.

Long Answer Questions

1. Explain the construction, excitation, operation, and applications of wound-field synchronous motors.
2. Derive and interpret the dq-axis PMSM torque equation, identifying each torque-producing term.
3. Compare PMSM and BLDC drives in terms of back EMF, commutation, torque ripple, sensing, and applications.
4. Describe a complete field-oriented control structure for a PMSM drive.
5. Discuss the current, voltage, thermal, mechanical, and demagnetization limits of a permanent-magnet drive.

Analytical / Application Questions

1. An IPMSM has p = 3, ψ_f = 0.10 Wb, L_d = 1.0 mH, L_q = 2.0 mH, i_d = −15 A, and i_q = 40 A. Calculate electromagnetic torque using the stated dq torque equation.
2. Design a control sequence for a six-step BLDC drive using three Hall sensors. Explain how invalid sensor states and inverter shoot-through are prevented.
3. An electric vehicle reaches its inverter voltage limit at base speed. Explain how MTPA below base speed and field weakening above base speed should be coordinated, including the effects on current, torque, power, and efficiency.

Multiple Choice Questions with Answers

Question 1

For a synchronous motor with electrical frequency f_e and p pole pairs, the mechanical synchronous speed is:

A. 60pf_e

B. 60f_e/p

C. 2πpf_e

D. f_e/(60p)

Correct Answer: B. 60f_e/p

Question 2

In the stated PMSM torque equation, which current component primarily produces magnet torque?

A. i_d

B. i_q

C. Zero-sequence current

D. Field-winding current only

Correct Answer: B. i_q

Question 3

For a surface-mounted PMSM with negligible saliency, the approximate MTPA condition below the voltage limit is:

A. i_d = 0

B. i_q = 0

C. i_d = i_q

D. i_d = −I_max

Correct Answer: A. i_d = 0

Question 4

The principal purpose of field weakening is to:

A. Increase rotor resistance

B. Reduce effective flux so operation can continue above base speed

C. Eliminate all copper loss

D. Make the motor asynchronous

Correct Answer: B. Reduce effective flux so operation can continue above base speed

Question 5

A common six-step BLDC commutation interval spans:

A. 15 electrical degrees

B. 30 electrical degrees

C. 60 electrical degrees

D. 180 electrical degrees

Correct Answer: C. 60 electrical degrees

Question 6

Which feature most directly distinguishes typical BLDC operation from sinusoidal PMSM operation?

A. Use of a DC link

B. Use of permanent magnets

C. Trapezoidal back EMF and electronic six-step commutation

D. Presence of an inverter

Correct Answer: C. Trapezoidal back EMF and electronic six-step commutation

Question 7

For p = 4, ψ_f = 0.05 Wb, and i_q = 20 A in a surface PMSM, neglecting reluctance torque, the torque is:

A. 1.5 N·m

B. 3.0 N·m

C. 6.0 N·m

D. 12.0 N·m

Correct Answer: C. 6.0 N·m

Question 8

Which operating constraint is represented by i_d² + i_q² ≤ I_max²?

A. Mechanical speed limit

B. Current-magnitude limit

C. DC-link voltage limit

D. Rotor position limit

Correct Answer: B. Current-magnitude limit

Question 9

Why is anti-windup needed in a PMSM current controller?

A. To compensate for pole pairs

B. To prevent integral accumulation when the inverter voltage saturates

C. To increase magnet flux permanently

D. To detect Hall sensor spacing

Correct Answer: B. To prevent integral accumulation when the inverter voltage saturates

Question 10

In an IPMSM with L_q > L_d under the stated sign convention, MTPA commonly uses:

A. Positive d-axis current only

B. Negative d-axis current together with q-axis current

C. Zero q-axis current at all loads

D. Only zero-sequence current

Correct Answer: B. Negative d-axis current together with q-axis current