Swing equations

(per unit)

 

                              dδ/dt = ωo (ωm – 1)

 

                            m/dt = (Pm – P)/2H

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

       ω0 = 2πf0                                f0 = frequency (Hz)            

                                                       δ = angle (rad) 

         P = EVsinδ/X                    ωm = speed

                                                    H   = inertia constant (s)

    E = internal voltage               Pm = mechanical power

    V = terminal voltage              P   = electrical power

                                                     Xbefore   (before fault)

    Transfer reactance X  >>>    Xduring   (during fault)          

                                                     Xafter      (after fault)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

IC:

           ωm(0) = 1.0

              δ(0) = sin-1(PmX0/EV)