Damping Effect In Classical Power System

Power system is the system of power generation and consumption and it is composed of generate electricity,transmission,substation,power distribution and electricity consumption et al.It is one of the most important and the largest engineering systems in our modern society.In order to more efficiently use earth resources,protect environment and improve economic efficiency,power system began to develop to be more intelligent at home and abroad.Meanwhile,some of the world’s large power grids have been reported to collapse,which resulting in a lot of economic losses.Due to the power system is a complex network,so the power system is high dimensional nonlinear systems.This paper studies the dynamic behavior,stability basins and bifurcation analysis of a fundamental three-order power system model,which mainly takeing into account the model of three-order synchronous generator.Synchronous generator model uses third-order single infinite bus models including angle dynamics(swing equation)and voltage dynamics(flux decay equation).The nonlinear dynamic behavior of the third-order model of synchronous generator is analyzed by using the nonlinear dynamics theory,and compared with that of the second-order model of the synchronous generator(swing equation).In the study,the article mainly considers the variation of mechanical power Pn,inertia M and damping coefficient Y three parameters.Y is considered to be either positive to negative.Firstly,when the damping coefficient Y is positive,the third-order model and the second-order model of synchronous generator have the similar dynamic behavior,showing stable fixed point,stable limit cycle and their coexistence.Secondly,when the damping coefficient y is negative,the dynamics behavior of the third order model and the second order model of synchronous generator is completely different.The second order model of synchronous generator shows collapse only,but the third order model of synchronous generator exhibits a variety of attractors including fixed point,stable limit cycle,period-doubling orbits,quasi-periodic orbits and strange attractors.The chaos phenomenon occurs in the third order synchronous generator model,while the second order synchronous generator model does not show chaos.Finally,the third order model of synchronous generator exhibits chaotic and quasi-periodic orbits that lead to the emergence of system collapse.Similarly,when the damping coefficient y are positive and negative,the system appears a similar dynamic behavior with the change of inertia M.These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics,but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.According to the theoretical analysis and using the bifurcation analysis software MATCONT,the static bifurcation curve and the two-parameter bifurcation curve are analyzed and simulated,and the results of theoretical analysis and software simulation are completely consistent.In the static bifurcation curve,the system only appears the saddle node bifurcation.In the two-parameter bifurcation curves,a Hopf bifurcation occurs,and the Hopf bifurcation is so-called supercritical Hopf bifurcation.Due to the Hopf bifurcation,the system will oscillates and even leads to the emergence of chaos or collapse.To summarize the whole thesis,the first chapter is the introduction part,mainly introducing the development of power systems and the application of the basic theory of nonlinear dynamics.In the second chapter,the third-order model of synchronous generator is derivated in detail.In the third chapter,the stability region,the dynamic behavior,the parameter space and the collapse of the system are numerically simulated under the condition of either positive or negative damping coefficient.In the fourth chapter,the bifurcation analysis and simulation of the system are carried out based on the theoretical derivation and using the standard bifurcation analysis software MATCONT.The last chapter,a summary of the work mentioned is given,and a discussion of possible follow-up work of the study is given.