Time-varying instantaneous voltages for L1 (Three-phase electric application)


In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time by one-third of the period. A three-phase system may be arranged in delta (∆) or star (Y) (also denoted as wye in some areas). A wye system allows the use of two different voltages from all three phases, such as a 230/400 V system which provides 230 V between the neutral (centre hub) and any one of the phases, and 400 V across any two phases. A delta system arrangement only provides one voltage magnitude, however it has a greater redundancy as it may continue to operate normally with one of the three supply windings offline, albeit at 57.7% of total capacity. Harmonic current in the neutral may become very large if non-linear loads are connected.

In a star (wye) connected topology, with rotation sequence L1 – L2 – L3, the time-varying instantaneous voltages for the first rotation sequence (L1) can be calculated as shown here.

Related formulas


VL1time varying voltage (V*rad)
VPpeak voltage (V)
θphase angle (rad)