Question

For a balanced three-phase positive-sequence integers ${\mathbf{I}}_{\mathbf{a}}\mathbf{,}\mathbf{}{\mathbf{I}}_{\mathbf{b}}\mathbf{,}\mathbf{}{\mathbf{I}}_{\mathbf{c}}$, does the equation ${\mathbf{I}}_{\mathbf{a}}\mathbf{+}{\mathbf{I}}_{\mathbf{b}}\mathbf{+}{\mathbf{I}}_{\mathbf{c}}\mathbf{=}\mathbf{0}$ hold good?

Short answer

Therefore, the correct answer is yes.

Step-by-step solution

Determine the symmetrical components of three-phase system

For a three-phase system a, b and c, there are three symmetrical components. These are positive sequence, negative sequence and zero sequence. For phase a, b and c, the positive sequence is abc and the negative sequence is acb.

Determine the total inductance

For a balanced three phase-system, the all phases in positive sequence abc will have same magnitude and phase displacement 120 degrees.

Therefore, the summation of phase currents is zero, that is ${\mathrm{I}}_{\mathrm{a}}+{\mathrm{I}}_{\mathrm{b}}+{\mathrm{I}}_{\mathrm{c}}=0$.

Hence, correct answer is yes.