Sequence Impedances of Transmission Lines

jXm jXm jXs Ia Va jXm Va’ Vb jXs Ib Vb’ Vc Vc’ jXs Ic Ia+Ib+Ic Ground Va = jXsIa + jXmIb + jXmIc + Va’ Vb = jXsIb + jXmIa + jXmIc + Vb’ Vc = jXsIc + jXmIa + jXmIb + Vc’ Put into Matrix Notation: Va Va’ Xs Xm Xm Ia Vb - Vb’ = j Xm Xs Xm Ib Vc Vc’ Xm Xm Xs Ic

Zph

Recall that: Z012 = A-1

Zabc A

Z0=zs+2zm

Z1=zs-zm

Z2=zs-zm

4

Symmetrical components of generator

Symmetrical components of generator

• Z1 = synchronous reactance (Xd)

transient reactance (Xd’)

subtransient reactance (Xd’’)• Depends on the analysis required

(breaker setting, fault analysis, transient stability studies, steady state analysis)

Z2 = Xd’’

Z0 = leakage reactance (Xl)

Symmetrical components of transformer

• Although Z0 slightly differ from other two, it is

customary to takeZ1 = Z2 = Z0 = Xl

7

Symmetrical components of transformer (zero)

•