3-phase motors have significantly higher efficiency at converting electrical to mechanical energy, and therefore lower operating costs.

• are inherently self-starting, and because of their higher torque, especially during starting, they are ideal for heavy industrial applications
• Three phases is the minimum number you can have without having "dead" spots in the [cycle](https://electronics.stackexchange.com/questions/185308/why-three-phase-power-why-not-a-higher-number-of-phases?answertab=createdasc#tab-top:~:text=Using a 9 phase grid for example would require running 9 wires for the entire distribution grid%2C not cost effective.)
• FAQ: What are the Benefits of 4-Phase Linear Motors?
  • higher resolution & control
  • as you go up you do need more material, coils, and it gets more expensive

3-phase: how it’s made

• Consists of 3 single-phase lines, each 1/3 of a cycle out of phase from the previous one, producing a more consistent power level.
  • sin(x)
  • sin(x + 𝝿/3)
  • sin(x -𝝿/3)
• power is supplied through three active wires and a single ground wire.
• It has 2x the single-phase power voltage, which means that the wires do not need to be as thick for same power requirements.

[Source](https://www.emotorsdirect.ca/knowledge-center/article/singlephase-vs-3phase-which-is-better#:~:text=Because of this design%2C 3,ideal for heavy industrial applications.)

3 phase wiring has 3 sets of wires going into the motor

• useful for high power, high voltage applications

• useful in rotational machines for lower vibrations— produces constant power, is the lowest number of windings that can do so

• 3 phases are split equally throughout the unit circle equaling to 120 deg or pi/3 equivalent phase sections

• labelled phase a, b, and c

• notation for phase is phi, φ

What is 3 phase from Math & Science

Voltage of phases a, b, and c

• a: $V_a$ = $V_m$ * Cos(ωt + 0°) ⇒ $V_a$ = $V_m$ ∠ 0°
  • the reference
• b: $V_b$ = $V_m$ * Cos(ωt - 120°) ⇒ $V_b$ = $V_m$ ∠ -120°
  • typically b will always be a negative phase angle relative to phase a
• c: $V_c$ = $V_c$ * Cos(ωt + 120°) ⇒ V_c = $V_m$ ∠ 120°
  • typically phase c will be a positive angle relative to a