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What is Three-phase AC?

A system that transmits three sinusoidal AC voltages shifted in phase by 120° from one another. It carries the same power with fewer wires than single-phase AC and can create a rotating magnetic field, so it is used for power transmission and distribution and for factory motors. In a Y connection the line voltage is √3 ≈ 1.73 times the phase voltage (a 200 V line voltage means a phase voltage of about 115 V), and in a Δ connection the line current is √3 times the phase current. The power of a balanced load is P = √3 × line voltage × line current × power factor.

Read the beginner explainer: What Is an Inverter? DC to AC for Air Conditioners and EVs

Japanese name: 三相交流

Three-phase AC appears in 9 practice questions across 4 topics, including Circuit Analysis: AC, Linear Circuits and Transients, Power Electronics Circuits, Circuit and electromagnetism basics.

Y (star) and Δ (delta) connections of a three-phase load (a) Y a Z b Z c Z N Ia Vp = VL/√3 (b) Δ a b c Z Z Z Ia Iab IL = √3 × Ip
Y (star) and Δ (delta) connections of a three-phase load · View in diagrams

Field: Circuit Analysis: AC, Linear Circuits and Transients

Try it: questions about Three-phase AC

In a balanced three-phase system with a Y (star) connection, the phase voltage (between each phase and the neutral) is 100 V RMS. Which is closest to the line-to-line voltage (RMS)?

  1. AAbout 141 V
  2. B200 V
  3. CAbout 173 V
Show answer and explanation

Answer: C. About 173 V

In a balanced three-phase system the phase voltages are 120° apart, and a line-to-line voltage is the (vector) difference of two phase voltages. Its magnitude is √3 times the phase voltage: 100 V × √3 ≈ 173 V. Conversely, a Y connection with 400 V line-to-line has a phase voltage of 400/√3 ≈ 231 V. In a delta connection the line and phase voltages are equal, and the line current is √3 times the phase current.

For a balanced three-phase load with a line voltage of 200 V, a line current of 10 A and a power factor of 0.8, which is closest to the load's active power (total of all three phases)?

  1. AAbout 1.6 kW
  2. BAbout 4.8 kW
  3. CAbout 2.8 kW
Show answer and explanation

Answer: C. About 2.8 kW

The active power of a balanced three-phase load is P = √3 × VL × IL × cos φ, whether it is Y- or delta-connected: √3 × 200 V × 10 A × 0.8 ≈ 2771 W ≈ 2.8 kW. Viewed as a Y connection, the phase voltage is 200/√3 ≈ 115.5 V and the phase current is 10 A, so each phase takes 115.5 × 10 × 0.8 ≈ 924 W, and three times that is the total.

Three-phase AC in the explanations

Questions that mention Three-phase AC (9)

  1. In a balanced three-phase system with a Y (star) connection, the phase voltage (between each phase and the neutral) is 100 V RMS. Which is closest to the line-to-line voltage (RMS)?
  2. For a balanced three-phase load with a line voltage of 200 V, a line current of 10 A and a power factor of 0.8, which is closest to the load's active power (total of all three phases)?
  3. As in figure (b), a balanced three-phase load is Δ-connected with an impedance of Z = 30 Ω per phase. If it is replaced by an equivalent Y connection as in figure (a) that draws the same line currents, which of the following is the impedance per phase?
  4. A Δ-connected load with a 20 Ω resistor in each phase, as in figure (b), is connected to a balanced three-phase source with a line voltage of 200 V RMS. Which of the following is closest to the RMS line current?
  5. A Y-connected load with an impedance of Z = 8 + j6 Ω per phase, as in figure (a), is connected to a balanced three-phase source with a line voltage of 200 V RMS. Which of the following is closest to the total three-phase active power?
  6. How many switching devices does a typical three-phase inverter for driving a three-phase motor use?
  7. Which of the following correctly describes the output of a three-phase full-wave rectifier that rectifies three-phase AC with a bridge of six diodes?
  8. A three-phase inverter on a 400 V DC supply is operated with sinusoidal PWM at a modulation index of 1. Which of the following is closest to the RMS value of the fundamental of the output line-to-line voltage?
  9. Which of the following is the synchronous speed of a four-pole induction motor operated from three-phase AC at 50 Hz?

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Related terms

Power factor Impedance Inverter Phasor Pulse-width modulation (PWM) Rectifier circuit Smoothing capacitor Sinusoidal PWM RMS value Induction motor

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