The zero sequence component of the unbalanced system of vectors VA, VB, and VC is 1/3rd of their vector sum.

In a three-phase power system, the zero sequence component refers to the component of current or voltage that is equal and in phase with all three phases. It is also called the homopolar component.

The vector sum of the three-phase currents or voltages can be represented as:

Isum = IA + IB + IC

The zero sequence component of the system is equal to the sum of the three individual zero sequence components, which can be represented as:

I0 = (IA₀ + IB₀ + IC₀)

It can be shown mathematically that the zero sequence component of the three-phase system is equal to one-third of the vector sum of the three-phase currents or voltages:

I0 = (IA₀ + IB₀ + IC₀) = (IA + IB + IC)/3