Sections: Power | Impedance | Students Challenge

Power

Definition.

S = P + jQ = V_aI*_a + V_bI*_b + V_cI*_c

Where:
V_a V_b V_c are the voltages to neutral, and I*_a I*_b I*_c are the currents.

Thus,

Or: S = [AV]^T [AI]^*

But: [AV]^T = A^T V^T, and [AI]^* = A^* I^*. Thus, S = A^T V^T A^* I^*. We also know:

A^T = A because a and a² are conjugates, thus the equation becomes:

Thus, S= 3V₀I₀^* + 3V₁I₁^* + 3V₂I₂^*