7
Sequence Impedances of Transmission Lines
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)
•
