Adaptive optimal control of chaotic oscillation in

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

power system is a typical nonlinear system. When the amplitude of periodic load meets certain conditions under periodic load disturbance, Chaotic oscillation will occur [, and even make the power system lose stability. Therefore, in order to ensure that the power system can still operate stably under the action of periodic load disturbance, chaotic oscillation must be eliminated. Because the nonlinear feedback control method can compensate the nonlinearity of the system model, it can suppress chaos, which has been applied in many control systems At the same time, nonlinear feedback control can also realize the stability control of power system [6, therefore, nonlinear feedback control can be used to eliminate chaos and stabilize the system. However, this method requires that the system must be accurately modeled, otherwise the controller cannot compensate the nonlinearity of the system. In addition, even if the controller compensates the nonlinearity of the system, the system will not have chaotic oscillation under the action of the controller, but because periodic load disturbance still exists, the system cannot return to the initial equilibrium point, but in a certain Run on a stable periodic orbit [9. Variable feedback control method [7 by adjusting the feedback coefficient to reduce the influence of the nonlinear term of the system, suppress chaos, and make the system enter the unstable periodic orbit inherent in the chaotic attractor. Moreover, this method requires to first determine the instability in the chaotic attractor. Chinese plastic machinery enterprises have expanded the periodic orbit of opening up emerging markets for extruders in recent years. For the power system, we hope that it can return to the initial level under the action of the controller after being disturbed Balance point or new equilibrium point, so we need to find a new control method, so that the system can return to the initial or new equilibrium point under the action of the controller no matter how large the amplitude of periodic disturbance is and whether the system model is accurate, which requires the controller to estimate the amplitude of periodic disturbance. In this paper, the nonlinear optimal control method is combined with adaptive control to design an adaptive optimal controller, and the Lyapunov stability theory is used to prove that the controlled closed-loop system can maintain asymptotic stability. At the same time, numerical simulation is used to verify the control effect of the controller and the approximation to the amplitude of periodic load disturbance. Both theory and simulation show the effectiveness of the controller

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

3.2 adaptive optimal controller design

due to the imprecise modeling of the system, it is assumed that the equivalent damping coefficient D, generator mechanical power PM and disturbance in the system