229 Nonlinear Excitation Control in Electrical Power Systems Xin Zhang and Jin Jiang Department of Electrical and Computer Engineering University of Western Ontario London Ontario,N6A 5B9 Canada Abstract-Based on differential geometric theory,a feedback linearization was addressed in detail in [2-4]. systematic design of a nonlinear excitation controller is However,only recently,feedback linearization developed for a third order single machine infinite bus techniques have been used to design the nonlinear (SMIB)power system.The design approach is to controller for electrical power systems.The first transform the original nonlinear system into an application of nonlinear control in power systems was equivalent linear system.Furthermore,this approach reported in [5].Nonlinear controller design were has been extended to the design of a nonlinear considered in [6-7]for SMIB,[8-9]for multi-machine systems. controller for multimachine power systems.One of the advantages of the nonlinear controller for multimachine power system lies in the fact that the MIMO nonlinear In this paper,a nonlinear controller is first developed system is decoupled under the proper state for a SMIB,and then extended to multi-machine power transformation.Also,the obtained nonlinear controller systems.The formula for the nonlinear control law are can be implemented via local measurements.Finally presented explicitly.Finally,the performance of the the performance of the nonlinear controller is examined nonlinear controller is evaluated by simulation. by simulation when it is used with high order power II.Controller design for SMIB Power System systems. In the paper,the nonlinear controller is first designed I.Introduction for a SMIB system represented by a third order equation (1),which is derived from the sixth order by using an Electric power systems are highly nonlinear in nature integral manifold approach [10]. due to nonlinear synchronous generators and loads.The interconnected large electric power systems are being do expanded for more reliable and economic generation dt =0-06 and transmission of power energy.Also,the rapid growth in the load demand reduced the system stability = margin.As a consequence,the nonlinear characteristics d 2H of the system dominate more and more heavily on the system behavior.Even though the well developed linear control theory has a long history of many successful applications in industry,it is very difficult to deal with such nonlinearities in electric power systems.The xa-xa) general practice is to linearize the power system at a dt Tao v,cos6] x specific operating point,and then design a linear controller for the linearized system.Of course,such a For simplicity,let's define linear controller is unable to compensate for large variations in the system operating conditions.On the x1=δ，x2=0-06,x3=eg other hand,nonlinear controllers can handle nonlinearities in the large range operation directly,if Po= @b Vr (2) properly designed. 器BR= 2Hx Twenty years ago,the feedback linearization technique P2= was successfully applied to flight control systems[1]. The differential geometric theory associated with the 0-7803-4314-X/98/$10.00©1998IEEE229 Nonlinear Excitation Control in Electrical Power Systems Xin Zhang and Jin Jiang Department of Electrical and Computer Engineering University of Westem Ontario London Ontario, N6A 5B9 Canada Abstract - Based on differential geometric theory, a systematic design of a nonlinear excitation controller is developed for a third order single machine infinite bus (SMIB) power system. The design approach is to transform the original nonlinear system into an equivalent linear system. Furthermore, this approach has been extended to the design of a nonlinear controller for multimachine power systems. One of the advantages of the nonlinear controller for multimachine power system lies in the fact that the MIMO nonlinear system is decoupled under the proper state transformation. Also, the obtained nonlinear controller can be implemented via local measurements. Finally, the performance of the nonlinear controller is examined by simulation when it is used with high order power systems. I. Introduction Electric power systems are highly nonlinear in nature due to nonlinear synchronous generators and loads. The interconnected large electric power systems are being expanded for more reliable and economic generation and transmission of power energy. Also, the rapid growth in the load demand reduced the system stability margin. As a consequence, the nonlinear characteristics of the system dominate more and more heavily on the system behavior. Even though the well developed linear control theory has a long history of many successful applications in industry, it is very difficult to deal with such nonlinearities in electric power systems. The general practice is to linearize the power system at a specific operating point, and then design a linear controller for the linearized system. Of course, such a linear controller is unable to compensate for large variations in the system operating conditions. On the other hand, nonlinear controllers can handle nonlinearities in the large range operation directly, if properly designed. Twenty years ago, the feedback linearization technique was successfully applied to flight control systems[ 11. The differential geometric theory associated with the feedback linearization was addressed in detail in [2-41. However, only recently, feedback linearization techniques have been used to design the nonlinear controller for electrical power systems. The first application of nonlinear control in power systems was reported in [5]. Nonlinear controller design were considered in [6-71 for SMIB, [8-91 for multi-machine systems. In this paper, a nonlinear controller is first developed for a SMIB, and then extended to multi-machine power systems. The formula for the nonlinear control law are presented explicitly. Finally, the performance of the nonlinear controller is evaluated by simulation. 11. Controller design for SMIB Power System In the paper, the nonlinear controller is first designed for a SMIB system represented by a third order equation (I), which is derived from the sixth order by using an integral manifold approach [lo]. =W-Wb d6 dt - For simplicity, let’s define x, = 6, x2 = o -ob, x3 = el 0-7803-4314-X/98/$10.00 0 1998 IEEE