Back to Home

Symmetric Three-Phase Supply · Three-Phase Voltage Waveforms

Symmetric three-phase sinusoidal voltages: equal amplitude, same frequency, \(120^\circ\) phase difference between phases.
\(v_A(t) = V_m \sin(\omega t), \quad v_B(t) = V_m \sin(\omega t - 120^\circ), \quad v_C(t) = V_m \sin(\omega t + 120^\circ)\)
(Or \(v_C\) lags \(120^\circ\); the diagram uses standard phase sequence A → B → C with \(120^\circ\) lag between successive phases)

Three-Phase Voltage Parameters

Amplitude \(V_m\): 1.0 V (peak)
Frequency \(f\): 50 Hz (angular frequency \(\omega = 2\pi f = 100\pi\) rad/s)
Phase relationship:

\[ \begin{aligned} v_A(t) &= V_m \sin(\omega t) \\[2pt] v_B(t) &= V_m \sin(\omega t - 120^\circ) \\[2pt] v_C(t) &= V_m \sin(\omega t + 120^\circ) \end{aligned} \]

• Phase sequence: A → B → C with successive \(120^\circ\) lag (C phase leads \(120^\circ\), equivalent to lagging \(240^\circ\)).
• Line voltage amplitude is \(\sqrt{3}\) times the phase voltage (if amplitude is 1V, line voltage peak is ~1.732V).
• The sum of instantaneous three-phase voltages is always zero: \(v_A + v_B + v_C = 0\).

📌 Horizontal axis is time \(t\) (seconds), showing two complete periods (0~0.04s). Hover to view instantaneous voltage values and corresponding phase angles.

Key Observations

  • Phase A (blue) starts from 0°, Phase B (orange) lags by 120°, Phase C (green) leads by 120° (or lags by 240°).
  • At any instant, the algebraic sum of three-phase voltages is zero, forming a symmetric system.
  • The phase difference between adjacent phases is 120°, corresponding to a time difference of \(T/3\) (~6.67ms) on the waveform.
  • When hovering, the tooltip displays precise voltage values (V) and phase angles (degrees).

Three-Phase Voltage Waveforms \(v_A(t), v_B(t), v_C(t)\)

Phase Sequence A → B → C | Phase Difference ±120°
Amplitude \(V_m = 1.0\,\text{V}\), frequency \(f = 50\,\text{Hz}\), showing two complete periods. Hover to read voltage values and phase angles.
Phase A: \(v_A = V_m \sin(\omega t)\)
Phase B: \(v_B = V_m \sin(\omega t - 120^\circ)\)
Phase C: \(v_C = V_m \sin(\omega t + 120^\circ)\)