BCIT Logo

Module 8: Poly-phase systems

Useful Equations

Y-Y Y-Δ Δ-Y Δ-Δ
$$ E_\Phi = \frac{V_L}{ \sqrt{3} } = V_\Phi $$ $$ E_\Phi = \frac{V_L}{ \sqrt{3} } = \frac{V_\Phi}{ \sqrt{3} } $$ $$ E_\Phi = V_L = \sqrt{3} V_\Phi $$ $$ E_\Phi = V_L = V_\Phi $$
$$ I_{\Phi g} = I_L = I_{\Phi L} $$ $$ I_{\Phi g} = I_L = \sqrt{3} I_{\Phi L} $$ $$ I_{\Phi g} = \frac{I_L}{ \sqrt{3} } = \frac{I_{\Phi L}}{ \sqrt{3} }$$ $$ I_{\Phi g} = \frac{I_L}{ \sqrt{3} } = I_{\Phi L} $$
Y-Y Y-Delta Delta-Y Delta-Delta

Active Power: $$ P_\Phi = V_\Phi I_\Phi cos\theta_{I_\Phi}^{V_\Phi} = I_\Phi^2 R_\Phi = \frac{V_R^2}{R_\Phi} $$ $$ P_T = 3P_\Phi $$

Reactive Power: $$ Q_\Phi = V_\Phi I_\Phi sin\theta_{I_\Phi}^{V_\Phi} = I_\Phi^2 X_\Phi = \frac{V_X^2}{X_\Phi} $$ $$ Q_T = 3Q_\Phi $$

Apparent Power: $$ S_\Phi = V_\Phi I_\Phi $$ $$ S_T = 3S_\Phi = \sqrt{3}E_L I_L $$

Power Factor: $$ F_P = \frac{P_T}{S_T} $$