## Power System Dynamics and StabilityThis text explores the basic theory and systematic development of dynamic models and their use in multi-machine simulation. Using standard notation and a logical organization, it explains the fundamental laws for basic devices and systems in a mathematical modelling context, presents systematic derivations of standard synchronous machine models with their fundamental controls, and interconnects the individual models for system analysis and simulation. |

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### Contents

ELECTROMAGNETIC TRANSIENTS | 7 |

SYNCHRONOUS MACHINE MODELING | 23 |

SYNCHRONOUS MACHINE CONTROL MODELS | 65 |

Copyright | |

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### Common terms and phrases

admittance matrix analysis approximation assume buses classical model complex compute constant impedance damper-winding damping define differential equations dynamic circuit dynamic model E'di E'qi eigenvalues electrical eliminated energy function equilibrium point exciter faulted fc=i flux linkages flux-decay model frequency given Hopf bifurcation infinite bus initial conditions input integral manifold Jacobian linear load load-flow low-frequency oscillations Lyapunov function multimachine network equations nonlinear obtain off-manifold dynamics parameters participation factors PEBS method postfault system Psvi reactances reactive power reduced-order model resulting root locus rotor angles saturation functions scaled shaft shown in Figure single-machine solution solved speed stability stator algebraic equations steady-state step substituting synchronous machine synchronously rotating system dynamics terminal constraints torque transformation transient trapezoidal rule turbine two-axis model unstable VbdQ X'di Xep)Id