## Nonlinear Control Synthesis for Electrical Power Systems Using Controllable Series CapacitorsIn this work we derive asymptotically stabilizing control laws for To start with, the CSC is modeled by the injection model which is Next, we consider a different control methodology, immersion and invariance (I\&I), to synthesize an asymptotically stabilizing control law for the SMIB system with a CSC. The CSC is described by a first order system. As a generalization of I\&I, we incorporate the power balance algebraic constraints in the load bus to the |

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### Contents

1 Introduction | 1 |

2 Modeling of Power Systems | 7 |

Part I Interconnection and Damping AssignmentBased Control Synthesis | 14 |

3 Stabilization via Interconnection and Damping Assignment Injection Model for the CSCs | 17 |

4 Stabilization Via Interconnection and Damping Assignment First Order Model of the CSC | 31 |

Part II Immersion and InvarianceBased Control Synthesis | 44 |

5 Stabilization via Immersion and Invariance with the First Order Model of the CSC | 47 |

6 An Application of Immersion and Invariance to a Class of Differential Algebraic Systems | 61 |

7 Conclusions and Scope for Future Work | 89 |