4.1 Synchronous machine construction and principles

Synchronous machine components

Stator construction and armature winding

The stator is the stationary part of a synchronous machine. It houses the armature winding, which connects directly to the external power system. Everything about its design aims to maximize magnetic flux linkage while minimizing losses.

The stator core is built from laminated steel sheets stacked together. The laminations reduce eddy current losses (not hysteresis losses, though laminated steel helps with those too). Along the inner surface of the core, slots are cut to hold the three-phase armature winding. These three phases are spatially displaced by 120 electrical degrees, producing a balanced three-phase voltage.

The armature conductors themselves are insulated copper, chosen for low resistivity and good thermal performance.

Rotor types and field winding

The rotor carries the field winding, which is energized by DC current to produce the main magnetic field. There are two distinct rotor designs, and which one you'll see depends on the application:

• Salient-pole rotors have projecting poles with concentrated windings wrapped around each pole. These are used in low-speed machines like hydroelectric generators (typically 4 or more poles). The non-uniform air gap created by the protruding poles is what gives rise to saliency effects in the machine's electrical model.
• Cylindrical (round) rotors have a smooth outer surface with field windings distributed in slots machined into the rotor body. These are used in high-speed machines like steam or gas turbine generators (typically 2 or 4 poles). The uniform air gap means direct-axis and quadrature-axis reactances are nearly equal.

DC current reaches the field winding either through slip rings and brushes or via a brushless excitation system that uses a rotating rectifier mounted on the shaft. The rotor is supported by bearings and coupled to the prime mover (for generators) or the mechanical load (for motors).

Operation of synchronous generators and motors

Synchronous generator operation

A synchronous generator converts mechanical energy into electrical energy through electromagnetic induction (Faraday's law). The prime mover spins the rotor, and the rotating magnetic field from the DC-excited field winding cuts through the stator armature conductors, inducing an alternating voltage.

Two key relationships govern the induced voltage:

• Frequency depends on rotational speed and pole count. Synchronous speed is:

$N_s = \frac{120f}{P}$

where $f$ is the system frequency in Hz and $P$ is the number of poles. A 2-pole machine on a 60 Hz system runs at 3600 rpm; a 4-pole machine runs at 1800 rpm.

• Voltage magnitude depends on the strength of the rotor's magnetic field (controlled by field current) and the speed of rotation. Increasing the field current raises the induced EMF.

Synchronous motor operation

A synchronous motor works in reverse: electrical energy in, mechanical energy out. When three-phase voltage is applied to the stator, it creates a rotating magnetic field in the air gap. The DC-excited rotor locks onto this rotating field and spins at exactly synchronous speed.

The torque developed by the motor depends on:

• The magnitudes of the stator and rotor magnetic fields
• The power angle (also called torque angle or load angle), which is the angular displacement between the rotor field and the stator rotating field

For both generators and motors, the rotor must stay in synchronism with the stator's rotating field. Any disturbance that pushes the power angle too far can threaten stability, which is the central concern of this course.

Factors affecting synchronous machine performance

Excitation current and power factor

The excitation current (DC field current) controls the rotor's magnetic field strength. In a generator, this directly sets the induced EMF. In a motor, it influences the developed torque and reactive power exchange.

The relationship between excitation and power factor is important for reactive power control:

• An overexcited machine (field current above the level needed for unity power factor) operates at a leading power factor, supplying reactive power to the system.
• An underexcited machine operates at a lagging power factor, absorbing reactive power from the system.

Armature reaction is the effect of the magnetic field produced by stator currents on the main rotor field. It can strengthen, weaken, or distort the air-gap flux depending on the power factor. Adjusting the excitation current compensates for armature reaction and maintains the desired terminal voltage or reactive power output.

Machine parameters and losses

Saliency refers to the difference between the direct-axis reactance ($X_d$) and the quadrature-axis reactance ($X_q$). In salient-pole machines, $X_d > X_q$ because the magnetic path through the pole face (d-axis) has a smaller air gap than the path between poles (q-axis). This difference produces an additional reluctance torque component and affects the machine's power-angle characteristic. Cylindrical rotor machines have $X_d \approx X_q$, so saliency effects are negligible.

Other performance factors include:

• Stator winding resistance and leakage reactance cause voltage drops between the internal EMF and the terminal voltage
• Losses fall into several categories: copper losses ($I^2R$) in both windings, core losses (hysteresis and eddy currents) in the stator iron, and mechanical losses (friction and windage)
• Cooling systems (air, hydrogen, or water) determine how much power the machine can deliver continuously. Hydrogen cooling, for example, allows higher power density because hydrogen has better thermal conductivity and lower windage losses than air.

Mechanical vs. electrical aspects of synchronous machines

Power balance and torque

The mechanical side and electrical side of a synchronous machine are linked through the rotor shaft. Understanding this link is essential for stability analysis.

On the mechanical side, the prime mover (generator) or load (motor) exchanges torque with the rotor. Mechanical power is the product of torque and angular speed.

On the electrical side, the three-phase power at the machine terminals is:

$P = \sqrt{3} \, V \, I \, \cos\phi$

where $V$ is the line-to-line terminal voltage, $I$ is the line current, and $\cos\phi$ is the power factor.

In steady state, the power balance must hold:

• Generator: Mechanical power in = Electrical power out + Total losses
• Motor: Electrical power in = Mechanical power out + Total losses

The electromagnetic torque developed inside the machine is proportional to the product of the stator and rotor field magnitudes and the sine of the power angle $\delta$. This $\sin\delta$ relationship is fundamental: it means torque (and power transfer) increases with the power angle up to a maximum at $\delta = 90°$ (for a round-rotor machine), beyond which the machine loses synchronism.

Stability and excitation control

When the mechanical torque and electromagnetic torque are not equal, the rotor accelerates or decelerates. This changes the power angle, which in turn changes the electrical power output. Three machine properties determine how well it rides through disturbances:

1. Inertia (characterized by the inertia constant $H$) resists changes in rotor speed. Higher inertia means slower power angle swings, giving control systems more time to respond.
2. Synchronizing torque is the restoring torque that pulls the rotor back toward its equilibrium power angle. It exists as long as the machine operates on the stable portion of the power-angle curve ($\delta < 90°$ for a round rotor).
3. Damping torque opposes rotor speed deviations and helps oscillations decay. Damper windings (amortisseur windings) on salient-pole machines provide this effect; in cylindrical rotor machines, eddy currents in the solid rotor steel serve a similar role.

The excitation system is the primary control interface between the electrical and mechanical domains. By adjusting the field current, it regulates terminal voltage (in generators) or reactive power (in motors). Fast-acting excitation systems can boost synchronizing and damping torques during disturbances, making them a critical tool for maintaining transient stability.