Synchronous machine equations
(per unit)
vs = Rsis + dλs/ω0dt + ωmMλs (armature)
Space vector
f = [fd
; fq]
0 = Rkik
+ dλk/ω0dt (dampers)
900 rotator M = [0 -1 ; 1 0]
vf = Rfif
+ dλf/ω0dt (field)
λ = [λs ;
λ k; λf] i
= [is ; ik
; if] λ = L i
i = L -1
λ
Inductance
matrix
L= [Lal+Lmd 0
Lmd 0 Lmd
0
Lal+Lmq 0
Lmq 0
Lmd 0
Lmd+Lkdl 0 Lmd
0
Lmq 0
Lmq+Lkql 0
Lmd 0 Lmd 0
Lmd+Lfl]
Torque
Te
= Mλs • is
Machine parameters (pu)
:
ω0 = 2πfo = Base frequency (rad/s)
f0 = Frequency (Hz)
ωm = Speed
Ra
= Stator resistance
Lmd
= Direct-axis magnetizing inductance
Lmq
= Quadrature-axis magnetizing inductance
Lal = Armature leakage inductance
Rf = Field resistance
Lfl = Field leakage inductance
Rkd =
Direct-axis damper resistance
Lkdl
= Direct-axis damper leakage inductance
Rkq = Quadrature-axis damper resistance
Lkql
= Quadrature-axis damper leakage inductance
H
= Inertia constant [s]
Bm = Damping coefficient
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