Nonlinear adaptive decentralized stabilizing control of multimachine systems

https://doi.org/10.1016/S0096-3003(01)00254-5Get rights and content

Abstract

This work develops a design approach to a nonlinear adaptive control system with unknown parameters and applies it to the excitation control of power systems. The adaptive control strategy is formed by an adaptive backstepping way without involving transformation of linearization. The characteristic of the controller is that which involves a dynamic estimator of parameters. A general expression of nonlinear adaptive decentralized excitation control strategy for multimachine systems is acquired, in which all of the feedback variables are local measurements. Simulation results on a 6-machine, 22-bus system manifest the validity of the nonlinear adaptive controllers.

Introduction

Suffering repeatedly from power system collapse in the world, the problem of improving the stability of power systems is being paid more and more attention. Over the past decade, advanced nonlinear control approaches have been developed and applied to power systems to improve small disturbance and especially large disturbance stability. Significant contributions have been made by a series of literature [1], [2], [3], [4], [11], which successfully wield the approach of feedback linearization (FBL). The precondition of utilization of the FBL approach is twofold: firstly, the model of the objective affine nonlinear system is satisfied by necessary and sufficient conditions for exact linearization via feedback and secondly, the parameters in the model of the system are known and fixed. However, as is usually the case, the designers have to face the knotty problem of disturbance dissatisfaction over either the first or the second prerequisite above mentioned.

Some other literature have developed a nonlinear adaptive control framework by mainly the wielding recursive method [5], [6], [7], [8], in the light of which a stabilizing control strategy could be acquired without involving the transformation of linearization and with unknown parameters in the model.

In this paper, drawing inspiration from the above-mentioned theoretical framework of nonlinear adaptive control, we focus our attention to meet the challenge of nonlinear adaptive decentralized stabilizing control of multimachine systems with unknown parameters. The adaptive backstepping [10] is used to construct the Lyapunov function, so a nonlinear adaptive controller can be obtained. The characteristics of the controller proposed in this paper are those, where all of the feedback variables in the derived control strategy are local measurements, and the controller is accompanied by a dynamic estimator of parameters. The developed approach in this paper of nonlinear adaptive stability control could be generally applied to other nonlinear control systems.

Simulation results on a 6-machine, 22-bus system manifest the effectiveness of the controllers for improving transient stability and dynamic performances of the multimachine system.

Section snippets

A brief review of adaptive backstepping technique

The section provided the basic approach of adaptive backstepping for constructing the Lyapunov function in control design [10].

Consider the following system:ẋ=u+θ·ϕ(x),where x∈R is the state, u∈R is the control input, and θ∈R is an unknown constant parameter.

We use system (1) to introduce the basic approach for adaptive backstepping.
Step 1. LetV1(x)=12x2andu=−θ̂·ϕ(x)−c1x,where θ̂ is the estimate of θ, c1>0.

Substituting (3) to (1), we obtainẋ=−c1x+θ̃·ϕ(x),where θ̃ is the parameter errorθ̃=θ−θ̂.

Simulation results

The system under study is shown in Fig. 2 and the data of the system are included in Appendix A. In order to investigate the effectiveness of the different types of excitation controllers, we will make comparisons among the following control configurations.

First, Nos. 2–5 generators are the PSS-equipped machines (the structure of a PSS is given in Appendix B.1); secondly, the above-mentioned generators are equipped with linear optimal controllers designed by applying the LQR approach (the

Conclusions

This paper is concerned with the multimachine excitation system with unknown parameters. Based on adaptive backstepping, a novel recursive design approach is proposed for constructing the Lyapunov function of a power system. Furthermore, the nonlinear adaptive decentralized controller is designed, which can make the resulting adaptive system asymptotically stable. Simulations performed on 6-machine system prove that the proposed controller can guarantee the stability of a multimachine power

Acknowledgements

This work was supported partly by Chinese National Natural Science Foundation (No. 59837270), by Chinese National Key Basic Research Fund (No. G1998020309) and by the NSFC–JSPS Scientific Cooperation Program, as well as supported in part by National Important Scientific Technology Projects (No. 97-312-01-11-1a).

References (11)

  • L. Gao et al.

    A nonlinear control design for power systems

    Automatica

    (1992)
  • Q. Lu et al.

    Decentralized nonlinear optimal excitation control

    IEEE Trans. Power Systems

    (1996)
  • Y. Wang et al.

    Transient stability enhancement and voltage regulation of power systems

    IEEE Trans. Power Systems

    (1993)
  • C. Sun et al.

    Design of nonlinear robust excitation control for multimachine power systems

    IEE Proc. Gener. Distrib.

    (1996)
  • D. Seto et al.

    Adaptive control of nonlinear systems with triangular structure

    IEEE Trans. AC

    (1994)
There are more references available in the full text version of this article.

Cited by (13)

View all citing articles on Scopus
View full text
Copyright © 2002 Elsevier Science Inc. All rights reserved.