03/04/2022
Using Trigonometry to Analyze the Waveform in the Neutral of a Balanced Three-Phase
Power System.
In the USA, our power grid transported energy around the country via alternating
voltages that are sine waves. 480V three-phase sinewaves are commonly used in
commercial and industrial power systems where higher energy is needed. The
equations of the three sine waves are:
𝑉𝐴 = 679 sin(377𝑡) 𝑉𝐵 = 679 sin(377𝑡 + 120°) 𝑉𝐶 = 679 sin(377𝑡 − 120°)
The sketch of the three waveforms are below:
In a balanced three-phase Wye configuration, the waveforms meet at the Neutral wire.
See schematic below.
The voltage on the Neutral is given by 𝑽𝑵 = 𝑽𝑨 + 𝑽𝑩 + 𝑽𝑪
Now it’s time to use the Trigonometric Identities in Chapter 4 to solve for VN. Simply the
VN equation. You will be surprised the answer…I was. The beauty of sinusoidal
waveforms. Please do not google or search the web for the answer.
You must show your work and label any identities you use like you are doing a proof.
This is worth 20 points.