## Small Signal Analysis of Power SystemsPower system oscillations without a big disturbance occur spontaneously in a power system and if they are not damped out properly may lead to grid failure. In this book we examine the methodology to study this phenomenon from several angles. Modeling the system to investigate these oscillations is given top priority along with physical interpretation of the phenomenon. The book covers low frequency 1-3 Hz as well as sub synchronous oscillations in the 10-50 Hz range. The latter are called torsional oscillations. Design of Power system stabilizers as well as damping techniques for sub synchronous oscillations are discussed. Modeling and design of FACTS devices is included. The small signal analysis of multimachine systems along with the selective computation of Eigen value(s) of interest in a large system is presented. |

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### Contents

INTRODUCTION | 1 |

OVERVIEW OF SYNCHRONOUS MACHINE | 7 |

LOWFREQUENCY OSCILLATIONS IN POWER SYS | 41 |

single machine infinite bus bar model | 62 |

SMALL SIGNAL ANALYSIS | 99 |

MODELLING OF FACTS CONTROLLERS | 149 |

MULTIMACHINE SMALL SIGNAL ANALYSIS | 197 |

Linearization | 212 |

SELECTIVE COMPUTATION OF EIGENVALUES | 255 |

A PHASE AND DQ IMPEDANCES | 267 |

B SYNCHRONOUS MACHINE MODEL | 273 |

### Common terms and phrases

AESOPS amortisseur winding armature block diagram BSVC buses capacitive capacitor coils components computed constant control range corresponding d-axis damper windings damping torque dynamic eigenvalues electrical equivalent circuit FACTS controllers field winding flux linkages function g-axis gain given Heffron-Phillips model Hopf bifurcation HVDC IEEE IEEE Trans impedance induction generator effect infinite bus input interarea mode Jacobian load flow low-frequency oscillations machine model matrix module multimachine negative damping network equations nonlinear parameters Park's phase power balance power flow power system stabilizer reactance reactive power reference frame resonance rotating series capacitors series compensation shown in Figure small oscillations small signal model static var compensators stator steady sub-synchronous frequency SVC bus SVC control synchronizing torque synchronous machine synchronously rotating TCSC thyristor thyristor controlled torsional interaction torsional mode transformation transient transmission line variables vector voltage regulator XTCSC zero