Energy Resources

Contains only sections 4 & 5, as these are the ones coming up on the exam

Three-phase generators

When three separate supply lines, from three-phase generators, are used to deliver power to “components”

Line voltage (V_L)

The potential difference between any two supply lines

Phase Voltage (V_P)

The potential difference across the load on any single supply line

Line Current (I_L)

The current through any single supply line

Phase Current (I_P)

The current through the load of any single supply line

Three-phase system in a Star Config

• Line Voltage (V_L) ≠ Phase Voltage (V_P)

• Line current (I_L) = Phase Current (I_P)

• Neutral may be required

Three - Phase system in Delta config

• Line Voltage (V_L) = Phase Voltage (V_P)

• Line current (I_L) ≠ Phase current (I_P)

• Neutral NOT possible

Synchronous machines

• Rotor usually powered by a three-phase AC supply

• Constant phase difference between Rotor magnet and Stator magnet

• Run at a constant speed (revs / s)

• Locked to a constant supply frequency

Induction machines

• Rotor is a set of short circuited coils

• Rotates at a higher frequency than that of the stator, and induces a current due to change in flux.

• Running speed is less than synchronous speed (fractional slip)

• Speed of rotation varies as load increases.

Synchronous motors

f = np

• Supply frequency (f) ∝ revolution speed (n)

• Supply frequency (f) ∝ number of poles on rotor (p)

Properties of an Ideal Transformer

1. Zero winding impedance

2. Perfect soft-iron core

   • No fluyx leakage

   • No losses

   • Zero magnetising currents (No eddy currents)

transformer equivalent circut for a synchronous motor

The impedances highlighted in blue represent the internal impedances of the primary and secondary coils of the ideal transformer.

R_e = core eddy current and hysterisis losses

jX_N = magnetising flux

Losses in a Transformer

Iron loss

• Losses due to Eddy current and hysterisis in the core.

• Approximately constant with the load. {R_e ∝ R_L}

Copper loss

• Due to I²R in the Transformer windings

• Varies to the square of the load current.

Maximum efficiency of a transformer

A transformer achieves max efficiency when copper Losses = Iron Losses