Synchronous machine equations

(per unit)

 

vs = Rsis + dλs/ω0dt + ωmMλs      (armature)

                                                                                          Space vector     f  = [fd ; fq]     

0 = Rkik + dλk0dt                        (dampers)

                                                              900 rotator    M = [0 -1 ; 1 0]

vf = Rfif + dλf0dt                         (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 = Mλsis

 

 

                          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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