## Nonlinear Control Synthesis for Electrical Power Systems Using Controllable Series Capacitors (Google eBook)In this work we derive asymptotically stabilizing control laws for electrical power systems using two nonlinear control synthesis techniques. For this transient stabilization problem the actuator considered is a power electronic device, a controllable series capacitor (CSC). The power system is described using two different nonlinear models - the second order swing equation and the third order flux-decay model. To start with, the CSC is modeled by the injection model which is based on the assumption that the CSC dynamics is very fast as compared to the dynamics of the power system and hence can be approximated by an algebraic equation. Here, by neglecting the CSC dynamics, the input vector $g(x)$ in the open loop system takes a complex form - the injection model. Using this model, interconnection and damping assignment passivity-based control (IDA-PBC) methodology is demonstrated on two power systems: a single machine infinite bus (SMIB) system and a two machine system. Further, IDA-PBC is used to derive stabilizing controllers for power systems, where the CSC dynamics are included as a first order system. 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 SMIB swing equation, and extend the design philosophy to a class of differential algebraic systems. The proposed result is then demonstrated on another example: a two-machine system with two load buses and a CSC. The controller performances are validated through simulations for all cases. |

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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 |

### Common terms and phrases

actuator dynamics additional damping algebraic constraints Assumption asymptotically stable boundedness closed-loop system control law 6.60 control objective Controllable Series Capacitors Damping Assignment dash-dot line closed-loop deﬁned denote described differential algebraic equations domain of attraction Dotted line open dynamical system electrical power systems energy function excitation control flux-decay model I&I control law IDA-PBC control law Immersion and Invariance injection model input Interconnection and Damping line closed-loop response line open loop Lyapunov function machine system manifold N. S. Manjarekar Nonlinear Control Synthesis off-the-manifold coordinate open loop response open loop system operating equilibrium order model Ortega oscillations Phase plots power system stabilization proposed control law R. N. Banavar reactance reactive power rotor satisﬁed shown in Fig Simulation Results SMIB system solid line closed-loop stabilizing control law stable equilibrium sublevel sets swing equation model synchronous synchronously rotating synthesize a stabilizing target dynamics Tcsc trajectories transient stabilization tuning parameters voltage