Three-Phase Systems: Necessity

Three-Phase Systems: Necessity

1. What Three-Phase Is

Three-phase system = three sinusoidal voltages of same magnitude and frequency but 120° apart in phase, generated by three windings spaced 120° on same rotor, carried by 3 wires (or 4 with neutral).

Expressions (balanced, positive sequence):

Sum

at any $t$ (if balanced) ⇒ neutral current zero in balanced load.

2. Why Three-Phase Is Necessary (vs Single-Phase) — Exam List (5 reasons)

Reason	Explanation
1. Constant instantaneous power	In balanced 3-phase, total $p(t)=3·V_{ph}I_{ph}cosφ$ constant (not pulsating at $2ω$ like single-phase $p(t)=VI cosφ(1-cos2ωt)$) ⇒ smooth torque for motors, less vibration
2. Higher power with same copper	For same amount of conductor, 3-phase transmits ~1.5× more power (or needs less copper for same power)
3. Smaller, self-starting motors	Rotating magnetic field naturally produced by 3-phase currents in 3 windings ⇒ induction motor self-starts (single-phase needs capacitor)
4. Efficient transmission	For same $P$, 3-phase needs smaller current per wire and no neutral current when balanced ⇒ less $I²R$ loss, smaller transformers/generators
5. Flexibility	Can add single-phase loads between one phase and neutral (230V) while three-phase loads use line-to-line (400V); two voltage levels from same system

3. Worked Illustration

Single-phase pulsating: p(t)= V_m I_m sinωt sin(ωt-φ) ⇒ average P=VI cosφ, but instant dips to zero twice per cycle ⇒ motor torque pulsates.

Three-phase: p_total = p_a+p_b+p_c = 3VI cosφ constant ⇒ motor smooth.

4. Exam Points

• Define three-phase as three $120°$ apart sinusoids — 3-5 marks, frequent.
• List 4–5 reasons/needs for three-phase vs single-phase — 5-7 marks, very frequent (the most common necessity question).
• Show constant power and rotating field as advantages — 5 marks, frequent.
• Mention $v_a+v_b+v_c=0$ — 3 marks.