3상 교류회로의 Y-𝚫 변환

1. $Y$ → $\Delta$ 변환

• $\Delta$ 변환 임피던스
  

  $\displaystyle \dot{Z}_{ab}=\frac{\dot Z_a\dot Z_b + \dot Z_b\dot Z_c + \dot Z_c\dot Z_a}{\dot Z_c}[\Omega]$

  $\displaystyle \dot{Z}_{bc}=\frac{\dot Z_a\dot Z_b + \dot Z_b\dot Z_c + \dot Z_c\dot Z_a}{\dot Z_a}[\Omega]$

  $\displaystyle \dot{Z}_{ca}=\frac{\dot Z_a\dot Z_b + \dot Z_b\dot Z_c + \dot Z_c\dot Z_a}{\dot Z_b}[\Omega]$

• 각 상의 임피던스 동일($\displaystyle Z_a=Z_b=Z_c$)할 때
  
  $\displaystyle Z_\Delta=3Z$
  
  

2. $\Delta$ → $Y$ 변환

• Y 변환 임피던스
  

  $\displaystyle \dot{Z}_a=\frac{\dot Z_{ab}\dot Z{ca}}{\dot Z_{ab}+\dot Z_{bc}+\dot Z_{ca}}[\Omega]$

  $\displaystyle \dot{Z}_b=\frac{\dot Z_{bc}\dot Z{ab}}{\dot Z_{ab}+\dot Z_{bc}+\dot Z_{ca}}[\Omega]$

  $\displaystyle \dot{Z}_c=\frac{\dot Z_{ca}\dot Z{bc}}{\dot Z_{ab}+\dot Z_{bc}+\dot Z_{ca}}[\Omega]$

• 각 상의 임피던스가 동일($Z_{ab}=Z_{bc}=Z_{ca}$)할 때
  
  $\displaystyle Z_Y=\frac{1}{3}Z_\Delta$