Z+zz. +ZZ Z Zb +zz +z (96) Zaz+ziz + zza Z Equations(9.)and (9.6)are general relationships and apply to any set of impedances connected in a wye or delta configuration. For the balanced case where Z,=Zb=Z, and Z,=Z2=Z3, the equations above reduce to Z=-Z Z、=3Z (98) Defining Ter Balanced voltages of the three-Phase connection: The three voltages satisfy 0 where T network: The equations of the T network are V1=(Z1+Z3)I1+Z3l v2=ZI1+(Z2+Z3)I2 I,=(Y, YbV-Y,v2 =-Y VI+(Yb+Yv T and li can be transferred to each other Related T 3.5 Three-Phase Circuits e 2000 by CRC Press LLC© 2000 by CRC Press LLC Similary, if we solve Eq. (9.4) for Z1, Z2, and Z3, we obtain (9.6) Equations (9.5) and (9.6) are general relationships and apply to any set of impedances connected in a wye or delta configuration. For the balanced case where Za = Zb = Zc and Z1 = Z2 = Z3, the equations above reduce to (9.7) and ZD = 3ZY (9.8) Defining Terms Balanced voltages of the three-phase connection: The three voltages satisfy Van + Vbn + Vcn = 0 where Van = Vp –0° Vbn = Vp ––120° Vcn = Vp –+120° T network: The equations of the T network are V1 = (Z1 + Z3)I1 + Z3I2 V2 = Z3I1 + (Z2 + Z3)I2 P network: The equations of P network are I1 = (Ya + Yb )V1 – YbV2 I2 = –YbV1 + (Yb + Yc)V2 T and P can be transferred to each other. Related Topic 3.5 Three-Phase Circuits Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z 1 2 3 = + + = + + = + + a b b c c a c a b b c c a b a b b c c a a Z Z Y = 1 3