# Nonlinear Control Synthesis for Electrical Power Systems Using Controllable Series Capacitors

Springer Science & Business Media, Feb 10, 2012 - Technology & Engineering - 90 pages

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.

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### 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 Copyright