AC Theory and Alternating Current Machines Study Guide

Working Principles of the Alternator and AC Voltage

The alternator is a generator specifically designed to produce alternating current (AC). Its fundamental operation involves the interaction of magnetic fields and armature windings through mechanical rotation.

Core Components:

Stator (Stationary): Contains the armature windings where the AC voltage is induced. It is constructed from a magnetic steel core made of laminated silicon iron sheets.
Rotor (Rotating): Carries the field windings supplied with DC excitation current via a single pair of slip rings. As the rotor turns, its magnetic field cuts the stationary stator conductors.
Excitation System: A DC supply input, often controlled by an exciter field rheostat, provides the necessary magnetism to the rotor.
Slip Rings and Brushes: In a rotating field alternator, these carry only the relatively low excitation current, facilitating electrical contact between the stationary DC supply and the moving rotor.

Working Principle: The rotor's magnetic field rotates at a constant speed, cutting the stator conductors. According to the laws of electromagnetic induction, this relative motion induces an electromotive force (EMF) in the stator windings. The magnitude and direction of this EMF vary with the rotor's position, resulting in an AC voltage output.

Advantages of Alternating Current (AC) over Direct Current (DC)

AC power systems offer several practical advantages that make them the standard for electrical distribution:

Transformation: AC voltage can be easily stepped up for long-distance transmission (to reduce line losses) and stepped down for local distribution using simple transformers. DC power cannot be transformed this way.
Commutator Limits: DC generators require commutators, which are limited to low voltages because higher voltages cause destructive arcing across the segments. AC generators avoid this by using slip rings or having stationary armature windings.
Distribution Efficiency: AC can be generated at high voltages, distributed efficiently, and reduced to safe levels at the user’s location.

AC Generation: Cycles, Frequency, and Electrical Degrees

The generation of AC follows a periodic waveform, typically a sine wave, corresponding to the physical rotation of the generator.

Electrical Degrees and Mechanical Rotation: The relationship between mechanical rotation ( $\theta_m$ ) and electrical degrees ( $\theta_e$ ) depends on the number of poles ( $P$ ):

$1^\circ \text{ Mechanical} = \frac{P}{2} \text{ electrical degrees}$

$360^\circ \text{ mechanical} = 360 \times \frac{P}{2} \text{ electrical degrees}$

Cycle and Frequency:

Cycle: One complete sequence of the sine wave (from zero to positive maximum, to negative maximum, and back to zero). This is produced when a conductor passes across two poles ( $1$ North and $1$ South).
Frequency ( $f$ ): Measured in Hertz ( $Hz$ ) or cycles per second.
Relationship Example: For a two-pole machine, one revolution ( $360^\circ$ mechanical) equals one electrical cycle. To produce $60\,Hz$ power, the rotor must spin at $60$ revolutions per second ( $3600\,r/min$ ).
Multi-pole Machines: A four-pole alternator produces two complete cycles per revolution. Therefore, to achieve $60\,Hz$ , it only needs to rotate at $1800\,r/min$ .

Phase Relationships in AC Circuits

The relationship between voltage ( $V$ ) and current ( $I$ ) depends on the circuit's load characteristics:

Purely Resistive Circuit: Voltage and current reach their maximum values simultaneously; they are "in phase."
Purely Inductive Circuit: Current reaches its maximum Value later than voltage; the current is "lagging" by $90^\circ$ .
Purely Capacitive Circuit: Current reaches its maximum value earlier than voltage; the current is "leading" by $90^\circ$ .

Three-Phase Alternating Power

In a three-phase alternator, the stator contains three separate sets of windings ( $E_1, E_2, E_3$ ) physically displaced by $120^\circ$ .

Operation: The induced voltages in these phases are separated by $120$ electrical degrees.
Advantages vs. Single-Phase:

Constant Power: While single-phase power pulsates (dropping to zero twice per cycle), the total power in a three-phase system remains constant.
Efficiency: Three-phase machines are smaller, lighter, and more efficient than single-phase machines of the same capacity.
Industrial Application: Three-phase power is superior for high-power motors (like welding or industrial drives) because it provides a more even power output without the zero-crossings of single-phase supply.

Reactance, Impedance, and Power Factor

Inductance and Inductive Reactance ( $X_L$ ): According to Lenz's Law, the direction of an induced EMF opposes the applied voltage. This counter EMF creates a resistance to current flow known as Inductive Reactance ( $X_L$ ), measured in Ohms ( $\Omega$ ).

Capacitance and Capacitive Reactance ( $X_C$ ): Capacitance is the ability to store electrical energy in a dielectric material between two conductors. Capacitive Reactance ( $X_C$ ) is the opposition to current flow in a capacitive circuit. Current in these circuits is directly proportional to the capacitance ( $Farads$ ) and the frequency.

Reactance ( $X$ ): The combined effect when both are present in series:

$X = X_L - X_C$

Impedance ( $Z$ ): The total opposition to current flow in an AC circuit, combining resistance ( $R$ ) and reactance ( $X$ ). This relationship is often visualized using an impedance triangle.

Power Factor (PF):

Real Power ( $P$ ): The actual power consumed, measured in Watts ( $W$ ). $P = E \times I \times \cos(\theta)$ .
Apparent Power ( $S$ ): The product of effective voltage and current, measured in Volt-Amperes ( $VA$ ) or $kVA$ . $S = E \times I$ .
Reactive Power ( $Q$ ): Power consumed by the reactance, measured in $VAR$ (Volt-Ampere Reactive). $Q = E \times I \times \sin(\theta)$ .
PF Equation: $\text{Power Factor} = \cos(\theta)$ . It ranges from $0$ to $1$ .
Typical PF Values:
Small Induction Motors: $0.6$ to $0.8$
Large Induction Motors: $0.8$ to $0.9$
Incandescent Lighting: $0.95$ to $1.0$

Low power factor (especially from inductive loads) results in higher line losses and voltage drops. PF can be improved by connecting corrective static capacitors in parallel with the power line.

Alternator Rotor Designs

The physical construction of the rotor depends on the speed of the prime mover:

Cylindrical Rotors: Used for high-speed applications (exceeding $1800\,r/min$ ), such as those driven by steam or gas turbines. They are typically two-pole designs, being more compact and less expensive for high-speed operation.
Salient Pole Rotors: Feature projecting field poles and are used for slow-speed machines ( $1200\,r/min$ or less), such as those driven by diesel engines or water turbines. A typical multi-pole engine-type generator might have $28$ field poles and rotate at $257\,r/min$ to produce $60\,Hz$ power.
Structural Components: Rotors use non-magnetic steel retaining rings (end bells) to secure windings against centrifugal force. Windings are usually copper strips insulated with micanite and secured by steel wedges.

Cooling Systems for Large Alternators

Cooling is the primary limit on an alternator's output. Various methods are employed to dissipate heat from the rotor and stator.

Air Cooling:

Direct Air: Uses shaft-mounted fans. It carries risks of dust accumulation (choking ducts) and fire hazards.
Enclosed Air: Recirculates air through water-cooled heat exchangers. It is cleaner and quieter, though water leaks pose a short-circuit risk.

Liquid Cooling: Uses hollow copper conductors through which high-purity distilled water circulates. Distilled water is required to ensure low electrical conductivity and minimize leakage current.

Hydrogen Cooling ( $H_2$ ): Used in large turbo-alternators due to hydrogen's superior properties:

Advantages: Heat transfer coefficient is higher than air; density is $1/14$ th that of air (reducing windage/braking losses); high specific heat ( $14\,times$ air).
Performance: Increasing hydrogen pressure improves cooling. Raising pressure by $7\,kPa$ above atmosphere yields roughly a $1\%\,gain$ in output.
Safety: Hydrogen is explosive between $4\%$ and $74\%$ concentration in air. To prevent this, $CO_2$ is used as a buffer gas during charging ( $CO_2 \rightarrow \text{Air} \rightarrow H_2$ ) and purging ( $CO_2 \rightarrow H_2 \rightarrow \text{Air}$ ). Special shaft seals are required to prevent gas escape.

Synchronization and Parallel Operation

Before connecting an incoming alternator to a live system (bus bars), four conditions must be met:

Terminal Voltage: Must match the system voltage (adjusted via the field rheostat).
Frequency: Must match the system frequency (adjusted via prime mover speed).
Phase Sequence: Must have the same rotation as the system.
Phase Alignment: The phase voltage must reach maximum at the same time as the system (monitored via synchroscope).

Synchronization Methods:

Lamp Method (One Dark, Two Bright): The switch is closed when the specific lamp is dark and the others are equally bright.
Synchroscope: The preferred method for large machines. The pointer must be vertical and pointing upward.
Automatic Synchronization: Uses speed-matching, voltage-matching, and synchronizing relays as part of the startup sequence.

AC Motors: Induction and Synchronous

Three-Phase Induction Motors:

Principle: Stator AC creates a Rotating Magnetic Field (RMF). This field induces current in rotor bars (squirrel cage), creating a secondary magnetic field that produces torque.
Slip: The rotor always spins slower than the RMF. This difference is called "slip."
Wound-Rotor (Slip-Ring) Motor: Uses coils on the rotor connected to slip rings. This allows for external resistance to be added during starting to achieve high torque with low current. It also allows for limited speed control.

Synchronous Motors:

Operation: The rotor field (DC excited) "locks in" with the stator's RMF. The motor runs at a constant synchronous speed regardless of load.
Leading Power Factor: A unique benefit is that they can be run at a leading power factor to help correct the overall plant power factor.
Starting: They are not self-starting. They require a separate starting motor or damper windings (special squirrel cage windings in the pole faces) to reach synchronous speed before DC excitation is applied.

Induction Motor Starting and Speed Control

Large induction motors can draw $6\,times$ their full-load current during startup, causing voltage dips. Reduced voltage starting is common.

Starting Methods:

Variable Frequency Drives (VFDs): Convert AC to DC, then invert back to AC at a variable frequency to control speed ( $f \propto \text{speed}$ ).
Line Impedance Starters: Use resistors or inductors in series to limit current.
Star-Delta Starters: Start in "Star" configuration (reducing current to $1/3$ ) and switch to "Delta" for running.
Auto-transformer Starters: Use voltage taps to provide excellent starting torque per kVA.

Transformers

Operation: Based on mutual inductance. A change in magnetic flux in the primary winding induces a voltage in the secondary winding.

Voltage Relationship: $\frac{N_p}{N_s} = \frac{E_p}{E_s}$ Where $N$ is the number of turns and $E$ is the voltage.

Types:

Instrument Transformers: Includes Current Transformers (CTs). Warning: The secondary winding of a CT must never be opened while the circuit is active, as it can induce dangerously high voltages.
Auto-Transformers: Share part of the winding for both primary and secondary. Efficient for small transformation ratios.
Core and Shell Types: Core type windings wrap around both legs; shell type windings are wrapped around a center leg and encased in iron.
Cooling: Units may use Oil Natural Air Forced (ONAF) or radiators with fans.