Electrical Fundamentals
Everything else in the ETO syllabus is this, applied. Ohm's law, the three-phase relationships and the power triangle carry more marks than any single machine.
What the paper asks
Series and parallel circuits; Kirchhoff's laws; AC waveforms, RMS and peak; inductance, capacitance and reactance; three-phase star and delta relationships; power factor and the power triangle; and per-unit and cable calculations.
The concepts, in order
The power triangle explains the whole ship's electrical system. Real power in kW does the work, reactive power in kVAr magnetises the motors and transformers, and apparent power in kVA is what the cables and generators must carry. Power factor is the ratio of the first to the last.
Star and delta are not interchangeable. In star the line voltage is √3 times the phase voltage and the currents are equal; in delta the voltages are equal and the line current is √3 times the phase current. Every three-phase calculation starts by establishing which connection is in use.
Reactance is frequency dependent. Inductive reactance rises with frequency, capacitive reactance falls. That is why a motor drawing acceptable current at 60 Hz behaves differently on a 50 Hz supply, and why harmonics from converters overheat equipment that is not overloaded.
Poor power factor costs current. The same useful kilowatts at a lower power factor mean more amps in the cables, more copper loss, and generators that reach their current limit before their power limit.
Where marks are lost
- Using peak voltage where RMS is meant. Ratings are RMS; peak is √2 times larger.
- Applying the √3 factor twice. It belongs either to the voltage or to the current, depending on the connection.
- Confusing kW and kVA. Generator ratings are usually in kVA at a stated power factor.
- Forgetting that cable resistance changes with temperature. A hot cable drops more volts.
- P = √3·V_L·I_L·cos φ.
- Star: V_L = √3·V_ph. Delta: I_L = √3·I_ph.
- RMS = peak/√2.
- Low power factor means more current for the same kW.
- X_L rises with frequency, X_C falls.