6.6 Synchronous Motors

6.6 Synchronous Motors

Introduction to Synchronous Motors

A synchronous motor is an AC motor that operates at a constant speed fixed by the supply frequency, irrespective of load, as long as the load torque does not exceed the motor's pull-out torque. Its rotor rotates in perfect synchronism with the rotating magnetic field of the stator, i.e., at synchronous speed ($N_s = 120f/P$). While not as common as induction motors for general-purpose drives due to its non-self-starting nature and higher cost, the synchronous motor excels in applications requiring constant speed and, crucially, its unique ability to operate at leading power factor. This latter property makes it invaluable for power factor correction in large industrial plants. This section covers its operation, starting techniques, V-curves, and its role as a synchronous condenser.

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1. Operation Principle and Torque-Angle Characteristics

1.1 Principle of Operation

1. Rotating Magnetic Field (RMF): When a three-phase supply energizes the stator windings, it produces an RMF that rotates at synchronous speed $N_s$.

2. Rotor Excitation: The rotor carries field windings supplied with DC current (via slip rings and brushes) to create fixed North and South poles. In permanent magnet synchronous motors (PMSM), this field is provided by permanent magnets.

3. Magnetic Locking (Synchronism): The rotor's DC poles attempt to align themselves with the opposite poles of the rotating stator field. This magnetic attraction creates a torque that pulls the rotor into synchronism with the RMF. Once synchronized, the rotor "locks" magnetically to the RMF and rotates at exactly $N_s$.

1.2 Torque Production and Load Angle ($\delta$)

1. Load (Torque) Angle: In motor operation, the rotor magnetic axis lags behind the stator RMF axis by an angle $\delta$. This angle is not a physical displacement but an electrical phase difference between the rotor mmf and the resultant air-gap mmf (or between the internal generated voltage $E_f$ and the terminal voltage $V$).

2. Torque Equation: The electromagnetic torque developed is proportional to the sine of the load angle. $T = \frac{3 V_{ph} E_f}{\omega_s X_s} \sin \delta$ Where:

   • $T$ = Developed torque (Nm)

   • $V_{ph}$ = Terminal voltage per phase (V)

   • $E_f$ = Internal voltage per phase induced by rotor field (back EMF) (V)

   • $\omega_s$ = Synchronous speed (rad/s)

   • $X_s$ = Synchronous reactance per phase (Ω)

   • $\delta$ = Load (torque) angle (electrical radians/degrees)

3. Power-Angle Curve: The plot of $P$ (or $T$) vs $\delta$ is a sine wave, identical in shape to that of a synchronous generator but interpreted differently.

   • Stable Operation: Occurs for $-90^\circ < \delta < +90^\circ$, but motoring operation typically lies in the range $0^\circ < \delta < 90^\circ$.

   • Maximum (Pull-Out) Torque: Occurs at $\delta = 90^\circ$. $T_{max} = \frac{3 V_{ph} E_f}{\omega_s X_s}$

   • Stability: If the load torque exceeds $T_{max}$, the rotor pulls out of synchronism, $\delta$ increases beyond 90°, the motor stalls, and draws excessive current.

1.3 Operation at Constant Speed

The defining characteristic: $N_r = N_s = \text{constant}$, provided $T_{load} < T_{max}$. The motor adjusts to increased mechanical load by increasing its torque angle $\delta$, thereby drawing more electrical current and power from the supply, all while maintaining constant speed.

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2. Starting Methods

A fundamental drawback: A synchronous motor produces zero average starting torque when connected directly to AC supply with the DC field excited. This is because the RMF rotates too fast for the rotor's inertia to follow and lock onto it instantly.

2.1 Methods to Start a Synchronous Motor

1. Using an External Prime Mover:

   • Procedure: An auxiliary motor (pony motor) is used to bring the synchronous motor up to synchronous speed. It is then synchronized to the AC supply as if it were a generator, and the load is applied.

   • Application: Rare, used only for very large motors in special situations.

2. Damper Winding (Amortisseur Winding) Start - The Most Common Method:

   • Construction: Most synchronous motors have damper windings—copper or aluminum bars embedded in the pole faces and short-circuited by end rings, similar to a squirrel cage.

   • Principle:

     • Start: The DC field winding is short-circuited through a discharge resistor (to protect it from high induced voltages) or left open.

     • The stator is energized with AC. The damper winding acts as the rotor of a squirrel-cage induction motor, producing induction motor torque to accelerate the rotor.

     • Pull-in: As the rotor speed approaches synchronous speed (slip ≈ 2-5%), DC excitation is applied to the field winding. The rotor poles magnetically lock with the stator RMF, pulling the rotor into exact synchronism.

   • Characteristics: Provides simple, robust, and effective starting. The motor starts as an induction motor and runs as a synchronous motor.

3. Variable Frequency Start (VFD Start):

   • Principle: A Variable Frequency Drive (VFD) supplies the stator at a very low frequency (e.g., 2-3 Hz). This creates a slow-moving RMF that the rotor's DC poles can easily lock onto.

   • Procedure: The frequency is then gradually increased, pulling the rotor speed up in synchronism. The DC field is applied from the beginning.

   • Advantages: Smooth, controlled acceleration with full torque control. No damper windings needed. Common for large modern drives and PMSMs.

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3. Counter Electromotive Force (CEMF) and Armature Reaction

3.1 Counter EMF ($E_f$ or $E_r$)

1. Generation: When the rotor rotates at synchronous speed within the stator's magnetic field, an EMF is induced in the stator (armature) windings, just as in a generator.

2. Effect: This induced voltage, called Counter EMF (CEMF) or back EMF, opposes the applied terminal voltage ($V$). It is the motor's internal voltage source due to rotor excitation.

   • Armature circuit equation (neglecting $R_a$): $V_{ph} = E_f + j I_a X_s$

   • The net voltage driving current through the synchronous reactance is $(V_{ph} - E_f)$.

3.2 Armature Reaction

1. Definition: The effect of the stator (armature) current on the main magnetic field produced by the rotor's DC excitation.

2. Nature: Depends entirely on the power factor of the armature current.

   • Unity PF Load ($I_a$ in phase with $V$): Armature mmf is cross-magnetizing. It distorts the main field, strengthening one pole tip and weakening the other.

   • Lagging PF Load ($I_a$ lags $V$): Armature mmf is demagnetizing. It directly opposes the main rotor field, weakening the net air-gap flux. Requires increased DC excitation to compensate.

   • Leading PF Load ($I_a$ leads $V$): Armature mmf is magnetizing. It aids the main rotor field, strengthening the net air-gap flux. Allows reduced DC excitation to maintain voltage.

3. Modeling: The effect of armature reaction is included in the synchronous reactance ($X_s$) parameter of the equivalent circuit. $X_s = X_l + X_{ar}$, where $X_{ar}$ represents the reactance equivalent of the armature reaction effect.

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4. Effect of Excitation: Leading/Lagging Power Factor Operation

The most significant and useful feature of a synchronous motor is that its power factor can be controlled by varying its DC field excitation, independent of the load. This is visualized using V-curves and inverted V-curves.

4.1 Phasor Diagram Analysis

From the approximate phasor equation (neglecting $R_a$): $V_{ph} = E_f + j I_a X_s$

For a constant mechanical load (constant output power $P_{out} \approx 3V_{ph}I_a\cos\phi$), the component of current in phase with $V_{ph}$ ($I_a \cos\phi$) is constant.

1. Normal Excitation (Unity PF):

   • Field current is adjusted such that $E_f \cos\delta = V_{ph}$.

   • Armature current $I_a$ is minimum and in phase with $V_{ph}$.

2. Under-Excitation (Lagging PF):

   • Field current is reduced. Magnitude of $E_f$ decreases.

   • To satisfy the phasor equation, $I_a$ must increase and lag $V_{ph}$.

   • The motor draws lagging current from the supply, acting like an inductive load.

3. Over-Excitation (Leading PF):

   • Field current is increased. Magnitude of $E_f$ increases.

   • To satisfy the phasor equation, $I_a$ must increase and lead }.

   • The motor draws leading current from the supply, acting like a capacitive load.

4.2 V-Curves and Inverted V-Curves

1. V-Curves:

   • Plot of Armature Current ($I_a$) vs Field Current ($I_f$) for constant load.

   • Shape: A family of "V" shaped curves, one for each load (no-load, half-load, full-load).

   • The bottom of each "V" corresponds to minimum $I_a$ and unity PF.

   • Left limb of the V = Under-excited (lagging PF) operation.

   • Right limb of the V = Over-excited (leading PF) operation.

2. Inverted V-Curves (Power Factor Curves):

   • Plot of Power Factor ($\cos\phi$) vs Field Current ($I_f$) for constant load.

   • Shape: An inverted "V". Power factor is 1.0 at normal excitation, decreases to lagging on the left (under-excited), and decreases to leading on the right (over-excited).

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5. Application in Power Factor Improvement (Synchronous Condenser)

This is the most important industrial application of over-excited synchronous motors.

5.1 Principle

• A synchronous motor, running at no mechanical load (or very light load) and over-excited, draws a leading current from the AC supply.

• This leading current supplies the reactive power (kVAR) required by other lagging power factor loads (induction motors, transformers) in the plant.

5.2 Operation as a Synchronous Condenser

• Definition: A synchronous motor operated specifically for power factor correction, without a mechanical load, is called a synchronous condenser or synchronous capacitor.

• Control: Its field current is adjusted to generate the exact amount of leading reactive power needed to bring the overall plant power factor close to unity.

• Equivalent: It behaves like a variable capacitor whose capacitive reactance can be adjusted by changing $I_f$.

5.3 Advantages Over Capacitor Banks

1. Smooth and Continuous Control: Reactive power output can be varied smoothly from lagging to leading by simply adjusting the DC field current. Capacitor banks provide only stepwise control.

2. No Harmonics: Does not introduce harmonics into the system, unlike capacitor banks which can resonate with system inductance.

3. Inertia for Stability: Provides rotational inertia to the power system, which can help dampen transient swings and improve system stability.

4. Ability to Absorb Reactive Power: If under-excited, it can also absorb lagging VARs, providing bidirectional reactive power control.

5.4 Disadvantages

1. Higher Losses: Has rotational losses (friction, windage, core loss) in addition to copper losses.

2. Higher Initial Cost and Maintenance: More expensive and requires more maintenance than static capacitor banks due to its rotating parts and brush gear.

3. Application: Justified for large-scale power factor correction in substations and heavy industries where fine, continuous control is needed.

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6. Speed Control Characteristics (Constant Speed Operation)

6.1 Inherent Constant Speed Operation

1. Fundamental Characteristic: The speed of a synchronous motor is locked to the supply frequency. $N_r = N_s = \frac{120 f}{P}$

2. Consequence: Under steady load (within pull-out limit), the speed is absolutely constant and independent of load torque. This is a unique advantage over induction motors where speed drops with load.

3. Load Change Response: For a step increase in load torque, the rotor momentarily slows down, increasing the load angle $\delta$. This increases the developed torque until it matches the load torque, all while the average speed remains precisely $N_s$.

6.2 Methods to Change Speed (Limited)

Since speed is tied to $f$ and $P$, control is possible but less flexible than with DC or induction motors.

1. Change Supply Frequency ($f$):

   • Requirement: A Variable Frequency Drive (VFD).

   • Operation: Similar to starting with a VFD. The frequency is varied, and the motor's speed follows synchronously.

   • Constraint: The VFD must also control the magnitude of the supply voltage (maintaining a constant V/f ratio to avoid magnetic saturation) and properly control the field excitation (for wound-field motors).

   • Application: Used in high-performance servo drives (PMSM) and large compressor drives.

2. Change Number of Poles ($P$):

   • Method: The stator winding is constructed to allow reconnection for different pole numbers (e.g., 4/6/8 poles).

   • Result: Provides two or three discrete synchronous speeds (e.g., 1500, 1000, 750 RPM for 50 Hz).

   • Application: Used in some special multi-speed drives (e.g., large fans, pumps).

6.3 Comparison of Speed Characteristics

Motor Type	Speed Regulation	Speed Control Methods
Synchronous	Zero regulation (perfectly constant speed up to pull-out)	Change frequency (requires VFD) or change poles (discrete steps)
Induction	Good (2-5% slip at full load)	Change frequency (VFD), change poles, change voltage, change rotor resistance (WRIM)
DC Shunt	Good (slight droop)	Change armature voltage, change field flux

Conclusion: The synchronous motor's value lies not in versatility but in precision and specialized capability. Its absolute constant-speed characteristic is unmatched for certain processes like paper mills and record players (historically). However, its crowning application is as a synchronous condenser, where it acts as a dynamic, adjustable reactive power source, playing a vital role in voltage regulation and improving the efficiency of entire power systems. Understanding its operation from the torque-angle relationship to the powerful effect of excitation on power factor is key to leveraging its unique strengths in electrical engineering.