# 6.5 Synchronous Generators (Alternators)

## 6.5 Synchronous Generators (Alternators)

#### **Introduction to Synchronous Generators**

A synchronous generator, commonly called an alternator, is the primary machine for generating electrical power worldwide. It converts mechanical energy from a prime mover (turbine, diesel engine) into alternating current (AC) electrical energy. Its defining characteristic is that the rotational speed of the rotor is **synchronized** with the frequency of the generated voltage, as given by the fundamental relationship $$N\_s = 120f/P$$. Unlike induction generators, synchronous generators can supply both active and reactive power independently, making them essential for grid voltage control and stability. This section covers their construction, operating principles, performance characteristics, and the critical process of connecting them to an existing power grid.

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### 1. Construction (Stator and Rotor)

The construction is characterized by a **rotating magnetic field** system, which is the opposite of most DC and induction machines. This design places the high-power, high-voltage armature windings on the stationary stator, simplifying insulation and allowing for higher power ratings.

#### 1.1 Stator (Armature)

1. **Frame**: Outer cylindrical structure, provides mechanical support and often acts as part of the cooling circuit.
2. **Stator Core**: Built up from thin, laminated silicon steel sheets to minimize eddy current losses. The inner periphery contains slots.
3. **Stator (Armature) Winding**:
   * A **three-phase, double-layer, distributed winding** placed in the stator slots.
   * Windings are connected in star (Y) configuration, with the neutral point often brought out for grounding.
   * The winding design (pitch and distribution factors) is optimized to produce a near-sinusoidal output voltage.
4. **Function**: The stationary armature winding is where the three-phase AC power is generated and collected.

#### 1.2 Rotor (Field System)

The rotor carries the field winding and is rotated by the prime mover. There are two main types, distinguished by their shape and application.

**A. Salient Pole Rotor**

1. **Structure**: Has **projecting poles** (salient poles) bolted onto a spider or wheel. Poles are made of laminated steel.
2. **Field Winding**: Concentrated coils are wound around the pole cores.
3. **Damper Windings (Amortisseur Windings)**:
   * Copper or aluminum bars embedded in the pole faces, short-circuited by end rings.
   * **Functions**: Suppress hunting (rotor oscillations), provide starting torque for synchronous motors, and help during transients.
4. **Characteristics**:
   * Large diameter, short axial length.
   * Mechanically less robust, suited for **lower speeds** (typically 100 to 1500 RPM).
   * **Applications**: Hydroelectric turbines, diesel engine generators (low-speed prime movers).

**B. Cylindrical (Non-Salient / Round) Rotor**

1. **Structure**: A smooth, solid steel cylinder made from a single forging, with slots machined along its length.
2. **Field Winding**: Distributed winding placed in the rotor slots.
3. **Characteristics**:
   * Small diameter, long axial length.
   * Mechanically robust, can withstand high centrifugal forces at **very high speeds**.
   * Uniform air gap results in better voltage waveform and less noise.
   * **Applications**: Steam turbine-driven generators (turbo-alternators), gas turbines (high-speed prime movers, typically 1500 or 3000/3600 RPM).

#### 1.3 Winding Diagrams (Stator)

1. **Double-Layer Winding**: Standard for alternators. Each stator slot contains two coil sides (one from the top layer of one coil, one from the bottom layer of another).
2. **Pitch Factor (**$$K\_p$$**)**: Accounts for the effect of using **short-pitched** or **chorded** coils (coil span < 180° electrical). It reduces harmonics and saves copper. $$K\_p = \cos\left(\frac{\alpha}{2}\right)$$ where $$\alpha$$ is the angle of chording in electrical degrees.
3. **Distribution Factor (**$$K\_d$$**)**: Accounts for the voltage induced in distributed coils (spread over several slots per pole per phase) being less than that in a concentrated coil. $$K\_d = \frac{\sin\left(\frac{m\gamma}{2}\right)}{m \sin\left(\frac{\gamma}{2}\right)}$$ where $$m$$ = slots per pole per phase, $$\gamma$$ = slot angle in electrical degrees.

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### 2. Relationship Between Speed, Frequency, and Poles

This is the **fundamental synchronous relationship** that defines the machine. $$N\_s = \frac{120 f}{P}$$ $$f = \frac{P N\_s}{120}$$

**Where**:

* $$N\_s$$ = Synchronous speed of the rotor (RPM)
* $$f$$ = Frequency of the generated EMF (Hz)
* $$P$$ = Number of poles

**Derivation**: One complete cycle of AC is generated when a pair of poles (N and S) passes a stator conductor. In one revolution, $$P/2$$ cycles are generated. Therefore, frequency = (Cycles per revolution) × (Revolutions per second).

**Implications**:

* For a constant grid frequency (e.g., 50 Hz or 60 Hz), the prime mover must rotate at a **fixed, synchronous speed**.
* **Examples**:
  * 2-pole generator at 50 Hz: $$N\_s = (120 × 50)/2 = 3000 \text{ RPM}$$.
  * 4-pole generator at 60 Hz: $$N\_s = (120 × 60)/4 = 1800 \text{ RPM}$$.

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### 3. EMF Equation and Voltage Regulation

#### 3.1 EMF Equation per Phase

The RMS value of the generated EMF in each phase of a synchronous generator is: $$E\_{ph} = 4.44 \ K\_p \ K\_d \ f \ \phi \ T\_{ph}$$

**Where**:

* $$E\_{ph}$$ = RMS induced EMF per phase (V)
* $$K\_p$$ = Pitch (Chording) Factor
* $$K\_d$$ = Distribution (Breadth) Factor
* $$K\_f = K\_p K\_d$$ = Winding Factor (typically 0.85 - 0.95)
* $$f$$ = Frequency (Hz)
* $$\phi$$ = Flux per pole (Webers)
* $$T\_{ph}$$ = Number of turns per phase in series

#### 3.2 Voltage Regulation

1. **Definition**: The change in terminal voltage from full-load to no-load, expressed as a percentage of the rated terminal voltage, when the field current and speed are kept constant. $$% \text{Voltage Regulation} = \frac{E\_0 - V\_{FL}}{V\_{FL}} \times 100$$ where:
   * $$E\_0$$ = No-load terminal voltage (phase value).
   * $$V\_{FL}$$ = Full-load rated terminal voltage (phase value).
2. **Significance**: It indicates the inherent ability of the generator to maintain constant voltage under varying load conditions. **Lower regulation is desired**.
3. **Factors Affecting Regulation**: Armature resistance ($$R\_a$$), synchronous reactance ($$X\_s$$), and the load power factor.
   * **Leading PF Loads**: Can produce **zero or negative regulation** ($$E\_0 < V\_{FL}$$ due to magnetizing effect of leading current).
   * **Lagging PF Loads**: Always produce **positive regulation** ($$E\_0 > V\_{FL}$$ due to demagnetizing armature reaction).

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### 4. Equivalent Circuit and Power/Torque Angle Characteristics

#### 4.1 Per-Phase Equivalent Circuit

The steady-state model of a cylindrical rotor synchronous generator (neglecting saliency) is simple due to the constant air gap.

1. **Model**:
   * An internal generated EMF source ($$E\_f$$) per phase, proportional to field current and speed.
   * In series with the **synchronous impedance (**$$Z\_s$$**)**. $$Z\_s = R\_a + jX\_s$$
   * **Synchronous Reactance (**$$X\_s$$**)**: The most important parameter. It is the sum of:
     * **Armature Leakage Reactance (**$$X\_l$$**)**: Due to leakage flux.
     * **Armature Reaction Reactance (**$$X\_{ar}$$**)**: Reactance representing the effect of the stator MMF on the main field flux. $$X\_s = X\_l + X\_{ar}$$
   * **Terminal Voltage**: $$V\_{ph}$$ appears across the load.
2. **Phasor Diagram**: Essential for analysis. For a lagging power factor load:
   * $$E\_f$$ leads $$V\_{ph}$$ by an angle $$\delta$$, known as the **load angle** or **torque angle**.
   * The phasor $$I\_a R\_a$$ is in phase with $$I\_a$$, and $$j I\_a X\_s$$ leads $$I\_a$$ by 90°.
   * The relationship is: $$\vec{E\_f} = \vec{V\_{ph}} + I\_a (R\_a + jX\_s)$$.
   * For large machines, $$R\_a$$ is often neglected, simplifying to $$E\_f \angle \delta = V\_{ph} \angle 0 + j I\_a X\_s$$.

#### 4.2 Power and Torque Angle Characteristic

1. **Output Power Equation (Per Phase)**: Derived from the phasor diagram (neglecting $$R\_a$$): $$P\_{ph} = \frac{E\_f V\_{ph}}{X\_s} \sin \delta$$ For a three-phase generator: $$P = 3 \frac{E\_f V\_{ph}}{X\_s} \sin \delta$$
2. **Electromagnetic Torque Equation**: $$T = \frac{P}{\omega\_s} = \frac{3 E\_f V\_{ph}}{\omega\_s X\_s} \sin \delta$$ where $$\omega\_s$$ is the synchronous speed in rad/s.
3. **The Significance of** $$\delta$$:
   * $$\delta$$ is the angle by which the rotor field ($$E\_f$$) leads the resultant air-gap field (or terminal voltage $$V\_{ph}$$).
   * It is a measure of the **load on the generator**. As mechanical input power increases, the rotor momentarily accelerates, increasing $$\delta$$, which in turn increases the electrical output power until a new equilibrium is reached.
4. **Power-Angle Curve**: A sine curve plotting $$P$$ vs $$\delta$$.
   * **Stable Operation**: Occurs for $$0 < \delta < 90^\circ$$ (for a cylindrical rotor).
   * **Maximum Power (Pull-out Power)**: Occurs at $$\delta = 90^\circ$$. $$P\_{max} = \frac{3 E\_f V\_{ph}}{X\_s}$$
   * **Stability Limit**: If the prime mover tries to deliver more power than $$P\_{max}$$, $$\delta$$ exceeds 90°, the generator loses synchronism (**pulls out of step**), causing severe damage and tripping.

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### 5. Synchronization (Parallel Operation) Process

Synchronization is the process of connecting an incoming alternator to an already energized AC busbar (the grid) without causing large disturbances. This is essential for adding generators to a network and for maintenance.

#### 5.1 Necessary Conditions for Synchronization

The following conditions must be met **precisely** at the moment of closing the circuit breaker:

1. **Equal Voltage Magnitude**: The RMS terminal voltage of the incoming generator must be equal to the busbar voltage.
2. **Equal Frequency**: The frequency of the incoming generator must be exactly equal to the busbar frequency.
3. **Same Phase Sequence**: The phase sequence (RYB) of the generator must be identical to the busbar phase sequence.
4. **Same Phase Angle**: The phase angle between the corresponding phases of the generator and busbar must be zero (i.e., they must be "in phase").

#### 5.2 Synchronization Procedure (Using Synchroscope/Lamps)

1. **Pre-checks**: Verify correct phase sequence using a **phase sequence indicator** or three-lamp method (dark lamp method).
2. **Adjustments**:
   * Use the prime mover governor to adjust the **speed/frequency** of the incoming generator.
   * Use the generator field rheostat to adjust its **terminal voltage**.
3. **Observing Synchronization**:
   * **Synchroscope Method (Most Common)**: A synchroscope indicates the phase difference and relative speed. The pointer should rotate **very slowly in the "Fast" direction** (indicating incoming generator is slightly faster, so it will take on load when connected) and the breaker is closed when the pointer is at the 12 o'clock (zero phase difference) position.
   * **Three Dark Lamps Method**: Three lamps connected across the three phases will glow and darken sequentially. The frequency of flickering indicates the frequency difference. The breaker is closed when the lamps are at their **maximum darkness** (zero voltage difference across them).
4. **Closing the Breaker**: Once all conditions are satisfied, the main circuit breaker is closed, connecting the generator to the busbar.
5. **Loading the Generator**: After synchronization, the governor of the incoming machine is adjusted to increase its mechanical input, causing it to share the active power (kW) load. Its field current is adjusted to share the reactive power (kVAR) load.

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### 6. Applications of Permanent Magnet Synchronous Generators (PMSG)

PMSGs replace the conventional rotor field winding with **permanent magnets** (e.g., Neodymium-Iron-Boron, Samarium-Cobalt). This eliminates the need for a DC exciter, slip rings, and brushes, leading to a simpler, more robust design.

#### 6.1 Key Features and Advantages

1. **High Efficiency**: No field copper losses ($$I\_f^2R\_f$$), leading to higher efficiency, especially at partial loads.
2. **High Power Density**: Permanent magnets provide strong flux, allowing for a more compact and lighter machine for a given output.
3. **Simplified Construction and Maintenance**: No brushes, slip rings, or field windings. More reliable and suitable for harsh environments.
4. **Fast Dynamic Response**: The rotor has low inertia (especially in surface-mounted PM designs), enabling rapid changes in power output.
5. **Improved Voltage Regulation**: With power electronic converters, excellent voltage and frequency control is possible in standalone systems.

#### 6.2 Major Applications

1. **Wind Energy Conversion Systems (WECS)**:
   * A dominant application, especially in **direct-drive** configurations.
   * The turbine is coupled directly to the low-speed, multi-pole PMSG, eliminating the gearbox. This increases reliability and reduces maintenance.
   * The variable-frequency AC output is converted to DC by a rectifier, then inverted to grid-frequency AC via a full-power converter, providing maximum control over power delivery.
2. **Small/Micro Hydroelectric Generators**:
   * Used in low-head, low-power installations where simplicity and low maintenance are critical.
3. **Marine and Shipboard Power**:
   * Used as shaft generators driven by the main propulsion engine, providing auxiliary power with high efficiency.
4. **Auxiliary Power Units (APUs) and Mobile Generators**:
   * In vehicles, aircraft, and portable generators where weight, size, and reliability are paramount.
5. **High-Speed Microturbines**:
   * Coupled directly to high-speed gas turbines for distributed generation and combined heat and power (CHP) systems.

#### 6.3 Challenges and Considerations

1. **High Cost of Magnets**: Rare-earth magnets are expensive and subject to price volatility.
2. **Demagnetization Risk**: Magnets can be demagnetized by excessive temperature (Curie point) or very high fault currents.
3. **Controlled Output**: Since the field flux is fixed, the terminal voltage varies directly with speed. For connection to a constant-voltage grid or load, a **full-power electronic converter interface is mandatory**, which adds cost and complexity but provides ultimate control flexibility.

**Conclusion**: The synchronous generator is the backbone of the electrical power system. Its ability to precisely control both frequency (via prime mover speed) and terminal voltage (via field excitation) makes it uniquely suited for grid formation and stabilization. From the fundamental speed-frequency relationship and the pivotal concept of the torque angle to the meticulous process of synchronization, understanding alternator operation is essential for power engineers. The evolution towards PMSG technology highlights the ongoing drive for higher efficiency and reliability, particularly in renewable energy integration.
