Nonlinear Dynamics Analysis Of Iron Core Reactor Based On Hysteresis Loop

Ferromagnetic resonance is a complex non-linear phenomenon caused by the non-linear characteristics of ferromagnetic inductors element in power systems.When ferroresonance occurs in power system,it is often accompanied by persistence,high amplitude overvoltage and overcurrent,which can lead to burning or even explosion of power equipment.Ferromagnetic chaotic oscillation is a kind of ferromagnetic resonance.When ferromagnetic chaotic oscillation occurs in power system,the chaotic signal has obvious non-periodicity.The amplitude of overvoltage and overcurrent caused by chaotic oscillation is higher than that caused by linear resonance,it is more harmful to the power system.Iron core reactor is a kind of reactive power compensation device,which plays a very important role in reactive power compensation of power system.Its magnetic circuit part is mainly composed of silicon steel sheet.Silicon steel sheet is a typical representative of soft magnetic materials in ferromagnetic materials.It is widely used to manufacture iron core of ferromagnetic elements in various power systems.The hysteresis characteristic is a very important property of ferromagnetic materials,which seriously affects them.Hysteresis loop mathematical model is often used to describe the hysteresis characteristics of ferromagnetic materials in practical research.In the past research on ferromagnetic resonance,because of the low requirement for accuracy in engineering practice,the magnetization curve model is often used instead of the hysteresis loop model to describe the magnetic properties of ferromagnetic materials.The magnetization curve neglects the hysteresis characteristics and can only describe a general trend of the magnetic properties of ferromagnetic materials.The magnetization curve can not reflect the real performance of ferromagnetic components.In this thesis,the mathematical model of hysteresis loop is used to study the effect of hysteresis characteristics of iron core components on ferroresonance in power system.The main work of this thesis is as follows:Firstly,the hysteresis loop model describing the magnetic properties of ferromagnetic materials is studied,including Preisach model,polynomial hysteresis model,Jiles-Atherton(J-A)hysteresis model,and the ferromagnetic hysteresis model proposed by Hodgdon et al.The polynomial hysteresis model proposed by the scholar Liu Zongchuan is improved,and a simple and convenient Current-flux relationship is obtained.Then,the application of chaos theory in ferroresonance is introduced.The conditions of chaos generation and the characteristics of chaotic signals when chaos occurs are summarized.The methods of describing chaotic signals are summarized for the convenience of later chapters.The structure and basic principle of iron core reactor are elaborated.A ferromagnetic chaotic circuit with iron core reactor is constructed.By using polynomial hysteresis loop model and Hodgdon hysteresis loop model respectively,the ferromagnetic chaotic circuit model is established.The third-order non-autonomous circuit is normalized and the third-order non-autonomous differential equation based on the hysteresis loop model is obtained,the model is analyzed by non-linear dynamics.Finally,the two models are simulated by MATLAB,and the phase plane,Poincare section,Lyapunov exponent,bifurcation and spectrum of the system are drawn.Through the analysis of non-linear dynamics and the simulation results of MATLAB,it can be seen that when the hysteresis characteristics of ferromagnetic materials are different,the chaotic situation of the circuit is also different.