Elsevier

Automatica

Volume 39, Issue 1, January 2003, Pages 81-89
Automatica

Brief Paper
Adaptive nonlinear excitation control with L2 disturbance attenuation for power systems

https://doi.org/10.1016/S0005-1098(02)00175-9Get rights and content

Abstract

This paper presents a design approach to nonlinear feedback excitation control of power systems with unknown disturbance and unknown parameters. It is shown that the stabilizing control law with desired L2 gain from the disturbance to a penalty signal can be designed by a recursive way without linearization. A state feedback law is presented for the case of the system with known parameters, and then the control law is extended to adaptive controller for the case when the parameters of the electrical dynamics of the power system are unknown. Simulation results demonstrate that the proposed controllers guarantee transient stability of the system regardless of the system parameters and faults.

Introduction

Recently, advanced nonlinear control techniques have been used in the excitation control of power systems (Lu & Sun, 1989; Wang, Guo, & Hill, 1997; Chapman, Ilic, King, Eng, & Kaufman, 1993; Ortega, Stankovic, & Stefanov, 1998). The most successful nonlinear excitation scheme is based on the exact feedback linearization (Lu & Sun, 1989; Gao, Chen, Fan, & Ma, 1992). It was shown in the literatures that the dynamics of the power system can be exactly linearized by employing nonlinear pre-compensation. Then one can use conventional linear control theory to provide good performance (see Gao et al., 1992; Hill, Hiskens, & Wang, 1993 and the references quoted therein). However, we are often faced with uncertainty in practical power systems (Hill et al., 1993). In this case, it is difficult to exactly linearize the system with nominal parameters. There is thus a need for controllers which are insensitive to the uncertainty. Several robust excitation control schemes have been proposed by using linear robust control theory such as H design (Ahmed, Chen, & Petroianu, 1996; Taranto, Chow, & Othman, 1993) and L-stability theory (Vittal, Khammash, & Pawloski, 1993). However, these control schemes are essentially based on the linearized model so that it only deals with small disturbances and modeling uncertainty about an operating point.

To deal with unknown disturbance, the stabilization approach with disturbance attenuation has been proposed by van der Schaft (1996) and Isidori and Astofi (1992). As is well known, the disturbance attenuation approach is basically established from dissipative systems theory, and the design problem is usually solved by a solution of Hamilton–Jacobi–Issacas (HJI) inequalities (van der Schaft, 1996; Isidori and Astofi, 1992; Shen and Tamura, 1995) which imposes a formidable difficulty. Very recently, several approaches have been presented to solve this problem without the solution of HJI inequalities. It has been shown by Isidori (1996) and Marino, Respondek, & Van der Schaft (1989) that under appropriate geometric condition, we can use the recursive method to construct a storage function and feedback law that renders the closed-loop system dissipative. Indeed, it is an extension of the recursive design approach for constructing a Lyapunov function in the stabilization problem (Byrnes, Isidori, & Willems, 1991; Lin & Shen, 1999).

Adaptive stabilization for the nonlinear systems with unknown parameters has been investigated using the recursive design method based on passive systems theory (Krstic, Kanellakopoulos, & Kokotovic, 1995). Since the passivity is a special case of dissipativity, this shows that one can introduce the parameter adaptation function into the stabilizing controller with disturbance attenuation. Indeed, this natural extension problem has been addressed by Shen (1997). However, it should be noted that most recursive design schemes mentioned above require the nonlinear system to be of strict-feedback form and the unknown parameters to be of the parametric pure-feedback form (Krstic et al., 1995).

In this paper, we focus our attention on the power systems with unknown disturbance and unknown parameters. Our aim is to design a nonlinear excitation controller ensuring asymptotical stability and the L2 disturbance attenuation performance. It should be noted that the structure of power system under consideration is not of the strict-feedback form mentioned above, so it is not able to use the existing design method. We will show that if we choose the penalty signal as a linear function of the rotor angle and the relative speed of the generator, then we can find a desired feedback law by recursively constructing the storage function. The design approach will be extended to an adaptive version for the case where the system parameters are unknown and also to the multimachine systems. Finally, simulation results will be given to support the theoretical claims.

Section snippets

Plant model and problem description

Consider a single-machine infinite-bus power system as shown in Fig. 1. The dynamics of the system are presented by the following model (Lu & Sun, 1989; Wang et al., 1997).δ̇=ω(t)−ω0,ω̇=ω0MpmDM{ω(t)−ω0}−ω0E′q(t)VsMxΣsinδ+s1d1(t),Ėq=−1T′dE′q(t)+1T′d0xd−x′dxΣVscosδ(t)+1Td0Vf(t)+s2d2(t).The notation for the model is given in (Lu, Sun, & Mei, 2000). The first two equations represent the mechanical dynamics of the generator and the third equation gives the electrical dynamics of the power system,

Controller design

First, we suppose the parameters in system (2) are exactly known, and consider the state feedback law Vf=α(x1,x2,x3) and the following coordinate transformation:ξ1=x1,ξ2=kx1+x2,ξ3=φ(x1,x2,x3),where k>0 is any given number and φ(φ(0,0,0)=0) is a smooth function to be designed.

Our goal is to find α(x1,x2,x3) and φ(x1,x2,x3) such that the closed-loop system is asymptotically stable at the operating point x=0 and (4) holds with S(x0,θ̂0)=S(x0) where S(x0)>0,∀x0≠0.

From dissipative systems theory,

Extension to multimachine systems

Consider a large-scale power system consisting of n generators interconnected through a transmission network. As is well known (see Lu, Sun, Xu, & Mochizuki, 1996), the ith machine can be presented byδ̇ii(t)−ωi0ω̇i=ωi0Mi[pmi−pei(t)]−DiMii(t)−ωi0}+si1di1(t)(i=1,2,…,n),Ėqi=−1T′di[E′qi(t)+Idi(t)(xdi−x′di)]+1T0iVfi+si2di2(t)wherepei(t)=GiiE′qi2+E′qij=1,j≠inE′qj{Gijcosi−δj)+Bijsini−δj)},Idi(t)=−BiiE′qi+j=1,j≠inE′qj{Gijsini−δj)−Bijcosi−δj)}.

The notation for this model is the same as

Simulation results

The simulations were implemented in the PSASP package, which is a professional testing system for power systems. In order to compare the performance with conventional control, a proportion-based controller provided by standard module of the PSASP package is simulated.

Conclusions

In this paper, the idea of transient stability enhancement via L2 disturbance attenuation was proposed for the power system with uncertainty. Generally, the solution of HJI inequality is required for L2-gain synthesis, and structure of the system under consideration should be of the strict-feedback form for the recursive design. It was pointed out that the power system is not of the strict-feedback form, and the proposed design method does not require solution of the HJI inequality. Also, the

Acknowledgements

The research was supported by Joint Project under Japan Society for the Promotion Science and National Science Foundation of China, and by Chinese National Natural Science Foundation (No. 59837270) and Chinese National Key Basic Research Special Fund (No. 59837270).

Tielong Shen was born in Heilongjiang, China in 1957. He received the B. Eng and M. Sc. degree in Automatic Control from Northeast Heavy Machinery Institute, China in 1982 and 1986, respectively, and the Ph.D. degree in Mechanical Engineering from Sophia University, Tokyo, Japan in 1992. Since then he has been a faculty member as an Assistant Professor of the Department of Mechanical Engineering at Sophia University. He is the author/coauthor of four textbooks. His current research interests

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Tielong Shen was born in Heilongjiang, China in 1957. He received the B. Eng and M. Sc. degree in Automatic Control from Northeast Heavy Machinery Institute, China in 1982 and 1986, respectively, and the Ph.D. degree in Mechanical Engineering from Sophia University, Tokyo, Japan in 1992. Since then he has been a faculty member as an Assistant Professor of the Department of Mechanical Engineering at Sophia University. He is the author/coauthor of four textbooks. His current research interests include H_infinity control theory, robust control of linear and nonlinear systems and its applications.

Shengwei Mei received his B.S. degree in Mathematics from Xinjiang University, M. S. Degree in operations research from Tsinghua University, and Ph.D. degree in automatic control from Chinese Academy of Sciences, Beijing, in 1984, 1989, and 1996 respectively. He is now an associate professor of Tsinghua University. His research interest is in control theory applications in power systems.

Qiang Lu graduated from the Graduate School of Tsinghua University, China, in 1963 and joined the faculty of the same University. He was a visiting scholar and a visiting professor in Washington University, St. Louis and Colorado State University, Ft. Collins, respectively in 1984–1986 and a visiting Professor of Kyushu Institute of Technology (KIT), Japan in 1993–1995. He is now a professor in Tsinghua University, and an academician of Chinese Academy of Science (since 1991). His research interest is in nonlinear control theory applications in power system.

Wei Hu is a Ph. D. candidate in Tsinghua University. His research interest is in nonlinear control theory applications in power systems.

Katsutoshi Tamura was born in Morioka, Japan, in 1940. After receiving Master degree from Nagoya University, Japan, he was appointed to a research associate there, and began his Ph.D. research on optimal control theory and algorithm to obtain optimal control input to linear and nonlinear systems. After this he moved to Sophia University as a lecture and got promotion to an Associate Professor and to Professor. Now, he is working on adaptive control and nonlinear control.

This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate editor Michael Johnson under the direction of Editor Mituhiko Araki.

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