# Adaptive optimal control of chaotic oscillation in

2022-10-04
• Detail

Adaptive optimal control of chaotic oscillation in power system

Abstract: chaotic oscillation will occur in power system under the action of periodic load disturbance, and even lose stability. In order to suppress the chaotic oscillation in this case and ensure the stability of power system operation, an adaptive optimal control method is used to design a chaotic oscillation controller under the condition of periodic load disturbance amplitude uncertainty and system parameter uncertainty; The Lyapunov stability theory is used to prove that the disturbed and imprecisely modeled power system can maintain asymptotic stability under the action of the controller. Therefore, when the amplitude of the periodic load disturbance suffered by the power system is uncertain and causes chaotic oscillation or even instability of the power system, the adaptive optimal controller can make the power system only understand the universal experimental system to achieve asymptotic stability, that is, it can return to the initial equilibrium point. Numerical simulation also shows the control effect of the controller

key words: power system; Chaos control; Asymptotically stable; Adaptive

1 introduction

2 dynamic behavior of simple power system under periodic load disturbance

wiring diagram of simple interconnected power system [6 is shown in Figure 1, where: 1 is the equivalent generator of system 1; 2 is the equivalent generator of system 2; 3 is the equivalent main transformer of system 1; 4 is the equivalent main transformer of system 2; 5 is the load; 6 is the circuit breaker; 7 is the system tie line.

the mathematical model of simple power system with periodic load disturbance is as follows [6:

(1)

where: δ (t) Is the running angle of generator rotor: w (T) is the relative speed of generator; PM and PS are the mechanical power and electromagnetic power of the generator respectively; H is the equivalent moment of inertia; D is equivalent damping coefficient; PE is the amplitude of disturbance power; β Is the disturbance power frequency. Through cooperation with Siemens

when assuming a γ、ρ Constant means that the electromagnetic power of the generator, the damping of the system and the mechanical power remain unchanged, while when f changes, the above system becomes a nonlinear system with parameter F. when f is different, that is, the amplitude of periodic load disturbance is different, the system presents different states. If the system has no periodic load disturbance, the system operates at a stable equilibrium point; Reference [2 describes in detail the operation state of the system when f changes. The system may operate in a stable periodic orbit, or in a chaotic state containing many unstable periodic orbits; or even lose stability [8.

3 adaptive optimal control of chaotic oscillation in power system

3.1 nonlinear optimal controller design

assume that the system is accurately modeled, the equivalent damping coefficient D of the system, the mechanical power PM of the generator, and then close the oil delivery valve, and the disturbance power amplitude PE is known, that is to say γ、ρ And F are known. The controlled closed-loop system is shown in the following formula

the quadratic optimal control method is adopted for the system, so that in the

formula, Q and R correspond to the weight matrix of the state quantity and the weight coefficient of the control quantity respectively

if the system is accurately modeled and the amplitude of the periodic load of the disturbance is known, it can be seen from the closed-loop system composed of the controller (6) and the original system that the controller will compensate for the nonlinearity and external disturbance of the system and increase the damping of the system, so it will suppress chaos and ensure the asymptotic stability of the system