高压SF_6断路器动态电弧混沌现象研究
摘要
有触点开关电器作为发、输、配、用电力系统中主要的控制与保护电器，其开断与介质恢复特性是影响系统安全可靠、稳定、高效运行的重要因素之一。高压断路器是发电厂、变电所及电力系统中重要的控制和保护设备，SF6断路器在高压、超高压电力系统中占据着主导地位。随着SF6断路器电压等级的不断提高，短路开断能力是衡量高压SF6断路器产品性能的最基本和最重要的技术指标。
作为有触点开关电器，开断过程中不可避免产生电弧，在开断过程中，电弧的发生与发展决定了能量、密度、压力和温度在灭弧室内空间和时间的分布，从而成为决定短路开断成功与否的重要因素之一，且电弧演变行为的时空演变具有混沌特征。本文从混沌角度出发，以高压SF6断路器大电流开断中吹弧气流动力学行为与动态电弧演变历程为主要研究对象，对非定常、非线性电弧分岔、激波及湍动气流动力学行为展开具体研究，以探讨复杂灭弧系统气流参数演变内在物理本质和运动规律。主要研究内容如下：
1．灭弧系统内动态电弧混沌现象物理数学表征。基于SF6断路器开断过程中灭弧系统内非定常、非线性方程组（N-S方程）描述，采用Fourier级数展开式逼近原函数的性质，推演并表征灭弧系统动态电弧混沌特性，定量分析灭弧系统非线性复杂系统失稳后所产生分岔行为，找到灭弧系统通向混沌的两种典型途径，即：倍周期分岔和概周期过程。
2．动态电弧混沌行为主要影响因素的确定与描述。计及洛仑兹力、SF6灭弧与绝缘介质物性参数对电弧等离子体影响，基于动量守恒方程、能量守恒方程、Maxwell方程及电流密度方程，采用ACS理论将非线性电弧模型线性化表征，定量描述SF6电弧不稳定性，建立混沌电弧数学模型，发现激波是导致灭弧室出现混沌行为的根源之一。调整混沌电弧数学模型的SF6电弧物性参数值，得到状态变量随时间变化的时间历程图、Lyapunov指数图，高压SF6断路器在开断过程电弧出现了更为复杂、多样化的非线性现象，最终体现出SF6断路器电弧混沌特征。采用对照分析手段，对电弧等离子体进行变物性参数数值实验，找寻电弧混沌特征。研究相空间下混沌动态电弧行为特征、分岔、运动域及变轨迹，描述起弧、燃弧至熄弧遍历态行为。
3．激波与混沌动力学行为相关性研究。采用分离变量法求解灭弧系统内吹弧气体流动方程基本解，基于有限体积法求解不同喷口流路下气流场马赫数分布，得到典型行程下激波处密度、压力、速度及温度场空间分布，研究激波不稳定性所致灭弧系统混沌态、概周期态及周期态演变过程，得到激波混沌态对介质恢复特性影响。基于机构与灭弧系统联合仿真，研究开断进程中激波处时间序列带宽变化对混沌动力学行为影响，提出混沌特性调控方向。
4．开关电弧混沌特性实验研究。基于可拆卸灭弧系统搭建混沌特性实验平台，在线采集燃弧过程中电参数，利用相空间理论进行数据分析，将仿真模拟与实验研究相结合，研究灭弧系统内在混沌态行为与特征。开断电流越大，电弧温度上升越快，最大lyapunov指数越大，混沌特征越强；断路器灭弧室内的吹弧气流速度越大，最大lyapunov指数越大，混沌特征就越强；断路器喷口上下游的压力差越大，灭弧室内吹弧气流的速度越大，混沌特征越明显。
通过以上几方面深入研究，从理论上分析了高压SF6电弧的不稳定性及其非线性系统中的混沌现象，揭示了高压SF6断路器激波处的分岔路径和混沌运动形成机制，对高压SF6断路器合理设计具有重要的探索意义。
Switch is an important and protective electrical device in the generation, transmission,distribution and utilization power systems, its interruption performance and dielectricrecovery property are crucial to the effective operation, safety and stability of the system.SF6circuit breaker (CB) is an important control and protective device in the electricalpower systems, and its interruption performance is the key consideration for the reliableoperation of the system.
During the interruption, the spacial and time distribution of energy, density, pressureand temperature in arc quenching chamber were determined by the formation anddevelopment of arc, which was the key factor to determine the successful interruption ofthe breaker.Arc is inevitably generated during interruption and its developing behaviorexists chaotic characteristics. In this thesis, taking the dynamic behavior of gas flow andevolvement of dynamic arc during large current interruption in SF6CB as investigationsubject, unsteady and nonlinear arc bifurcation, shock wave and dynamic behavior ofturbulent gas flow in the system were studied to discuss the physical essence andmovement law of gas flow in the complex arc extinguish system. The main contentscovers:
1．Physical and mathematical description of the dynamic arc chaotic behavior in arcextinguish system. Based on the unsteady and nonlinear N-S equations in arc extinguishchamber during the interruption of SF6CB, the chaotic characteristics of dynamic arc in arcextinguish system was deduced and described using the convergence of Fourier series. Thearc bifurcation happened after the instability of the complex nonlinear system in SF6arcextinguish chamber were quantitatively analyzed and two typical ways to chaos in arcextinguish system were found, that is, period-doubling bifurcation and almostperiodic.
2．Determination of the factors influencing the chaotic behavior of dynamic arc. Byintroducing Maxwell and current density equations in the conservation of momentum andenergy equations and considering the effect of Lorentz force, SF6arc extinguishment andphysical parameters of insulation dielectrics on arc plasma, the nonlinear equations in arc model were linearized using ACS theory to analyze the instability of SF6arc and themathematical arc model based was derived to describe the chaotic behavior. By adjustingthe physical parameter of arc plasma, the dynamic arc behavior was simulated andcompared to obtain the arc chaotic characteristics. The chaotic behaviors of dynamic arc inphase space, bifurcation and existence domain of arc movement track were investigated todescribe process of the arc starting, erosion and extinguishment.
3． Correlation analysis of shock wave and chaotic dynamic behaviors. Thefundamental solution of the equations describing the gas flow in arc extinguish chamberwas resolved using separation of variables method. The distribution of Mach number in gasflow field under different nozzle circuit were simulated using finite volume method (FVM),the pressure, density, velocity and temperature distribution of gas flow under differentopen strokes were obtained. The periodic, quasi-periodic and chaotic arc evolvement in arcextinguish chamber due to the instability of shock wave were investigated, which provedthat the shock wave is one of the origin leading to the chaotic dynamic behaviors. Theeffect of chaotic shock wave on the dielectric recovery property and the effect of timeseries variation at shock wave during interruption on the chaotic dynamic behavior wereobtained. Based the joint simulation for hydraulic actuator and arc quenching chamber, thecontrolling strategies of the chaotic characteristics were proposed to improve theinterruption performance of SF6CB.
4．Experimental study on the chaotic characteristics of switching arc. An experimentalplatform was established based on a demountable arc quenching chamber to investigate thechaotic behavior in the system. The electrical data of arc during arcing process werecollected and analyzed using the phase space theory. By combining the simulation andexperimental study, the arc chaotic behavior and characteristics in arc extinguish systemwere researched. The results showed that with increase of current and gas flow velocityin the system, the arc temperature and pressure ratio in the SF6CB nozzle increased andthe chaotic behavior became more evident accordingly. Above results suggested that moreevident chaotic behavior in SF6CB will contribute to the better interruption of SF6CB.
In a word, the physical essence of SF6arc was discussed and the arc instability andthe chaotic behavior in nonlinear system for SF6CB were theoretically studied in this work. The bifurcation at shock wave and formation mechanism of chaos in SF6wereexplained. All these results provide important guidance for the proper design of SF6CB.
作为有触点开关电器，开断过程中不可避免产生电弧，在开断过程中，电弧的发生与发展决定了能量、密度、压力和温度在灭弧室内空间和时间的分布，从而成为决定短路开断成功与否的重要因素之一，且电弧演变行为的时空演变具有混沌特征。本文从混沌角度出发，以高压SF6断路器大电流开断中吹弧气流动力学行为与动态电弧演变历程为主要研究对象，对非定常、非线性电弧分岔、激波及湍动气流动力学行为展开具体研究，以探讨复杂灭弧系统气流参数演变内在物理本质和运动规律。主要研究内容如下：
1．灭弧系统内动态电弧混沌现象物理数学表征。基于SF6断路器开断过程中灭弧系统内非定常、非线性方程组（N-S方程）描述，采用Fourier级数展开式逼近原函数的性质，推演并表征灭弧系统动态电弧混沌特性，定量分析灭弧系统非线性复杂系统失稳后所产生分岔行为，找到灭弧系统通向混沌的两种典型途径，即：倍周期分岔和概周期过程。
2．动态电弧混沌行为主要影响因素的确定与描述。计及洛仑兹力、SF6灭弧与绝缘介质物性参数对电弧等离子体影响，基于动量守恒方程、能量守恒方程、Maxwell方程及电流密度方程，采用ACS理论将非线性电弧模型线性化表征，定量描述SF6电弧不稳定性，建立混沌电弧数学模型，发现激波是导致灭弧室出现混沌行为的根源之一。调整混沌电弧数学模型的SF6电弧物性参数值，得到状态变量随时间变化的时间历程图、Lyapunov指数图，高压SF6断路器在开断过程电弧出现了更为复杂、多样化的非线性现象，最终体现出SF6断路器电弧混沌特征。采用对照分析手段，对电弧等离子体进行变物性参数数值实验，找寻电弧混沌特征。研究相空间下混沌动态电弧行为特征、分岔、运动域及变轨迹，描述起弧、燃弧至熄弧遍历态行为。
3．激波与混沌动力学行为相关性研究。采用分离变量法求解灭弧系统内吹弧气体流动方程基本解，基于有限体积法求解不同喷口流路下气流场马赫数分布，得到典型行程下激波处密度、压力、速度及温度场空间分布，研究激波不稳定性所致灭弧系统混沌态、概周期态及周期态演变过程，得到激波混沌态对介质恢复特性影响。基于机构与灭弧系统联合仿真，研究开断进程中激波处时间序列带宽变化对混沌动力学行为影响，提出混沌特性调控方向。
4．开关电弧混沌特性实验研究。基于可拆卸灭弧系统搭建混沌特性实验平台，在线采集燃弧过程中电参数，利用相空间理论进行数据分析，将仿真模拟与实验研究相结合，研究灭弧系统内在混沌态行为与特征。开断电流越大，电弧温度上升越快，最大lyapunov指数越大，混沌特征越强；断路器灭弧室内的吹弧气流速度越大，最大lyapunov指数越大，混沌特征就越强；断路器喷口上下游的压力差越大，灭弧室内吹弧气流的速度越大，混沌特征越明显。
通过以上几方面深入研究，从理论上分析了高压SF6电弧的不稳定性及其非线性系统中的混沌现象，揭示了高压SF6断路器激波处的分岔路径和混沌运动形成机制，对高压SF6断路器合理设计具有重要的探索意义。
Switch is an important and protective electrical device in the generation, transmission,distribution and utilization power systems, its interruption performance and dielectricrecovery property are crucial to the effective operation, safety and stability of the system.SF6circuit breaker (CB) is an important control and protective device in the electricalpower systems, and its interruption performance is the key consideration for the reliableoperation of the system.
During the interruption, the spacial and time distribution of energy, density, pressureand temperature in arc quenching chamber were determined by the formation anddevelopment of arc, which was the key factor to determine the successful interruption ofthe breaker.Arc is inevitably generated during interruption and its developing behaviorexists chaotic characteristics. In this thesis, taking the dynamic behavior of gas flow andevolvement of dynamic arc during large current interruption in SF6CB as investigationsubject, unsteady and nonlinear arc bifurcation, shock wave and dynamic behavior ofturbulent gas flow in the system were studied to discuss the physical essence andmovement law of gas flow in the complex arc extinguish system. The main contentscovers:
1．Physical and mathematical description of the dynamic arc chaotic behavior in arcextinguish system. Based on the unsteady and nonlinear N-S equations in arc extinguishchamber during the interruption of SF6CB, the chaotic characteristics of dynamic arc in arcextinguish system was deduced and described using the convergence of Fourier series. Thearc bifurcation happened after the instability of the complex nonlinear system in SF6arcextinguish chamber were quantitatively analyzed and two typical ways to chaos in arcextinguish system were found, that is, period-doubling bifurcation and almostperiodic.
2．Determination of the factors influencing the chaotic behavior of dynamic arc. Byintroducing Maxwell and current density equations in the conservation of momentum andenergy equations and considering the effect of Lorentz force, SF6arc extinguishment andphysical parameters of insulation dielectrics on arc plasma, the nonlinear equations in arc model were linearized using ACS theory to analyze the instability of SF6arc and themathematical arc model based was derived to describe the chaotic behavior. By adjustingthe physical parameter of arc plasma, the dynamic arc behavior was simulated andcompared to obtain the arc chaotic characteristics. The chaotic behaviors of dynamic arc inphase space, bifurcation and existence domain of arc movement track were investigated todescribe process of the arc starting, erosion and extinguishment.
3． Correlation analysis of shock wave and chaotic dynamic behaviors. Thefundamental solution of the equations describing the gas flow in arc extinguish chamberwas resolved using separation of variables method. The distribution of Mach number in gasflow field under different nozzle circuit were simulated using finite volume method (FVM),the pressure, density, velocity and temperature distribution of gas flow under differentopen strokes were obtained. The periodic, quasi-periodic and chaotic arc evolvement in arcextinguish chamber due to the instability of shock wave were investigated, which provedthat the shock wave is one of the origin leading to the chaotic dynamic behaviors. Theeffect of chaotic shock wave on the dielectric recovery property and the effect of timeseries variation at shock wave during interruption on the chaotic dynamic behavior wereobtained. Based the joint simulation for hydraulic actuator and arc quenching chamber, thecontrolling strategies of the chaotic characteristics were proposed to improve theinterruption performance of SF6CB.
4．Experimental study on the chaotic characteristics of switching arc. An experimentalplatform was established based on a demountable arc quenching chamber to investigate thechaotic behavior in the system. The electrical data of arc during arcing process werecollected and analyzed using the phase space theory. By combining the simulation andexperimental study, the arc chaotic behavior and characteristics in arc extinguish systemwere researched. The results showed that with increase of current and gas flow velocityin the system, the arc temperature and pressure ratio in the SF6CB nozzle increased andthe chaotic behavior became more evident accordingly. Above results suggested that moreevident chaotic behavior in SF6CB will contribute to the better interruption of SF6CB.
In a word, the physical essence of SF6arc was discussed and the arc instability andthe chaotic behavior in nonlinear system for SF6CB were theoretically studied in this work. The bifurcation at shock wave and formation mechanism of chaos in SF6wereexplained. All these results provide important guidance for the proper design of SF6CB.
引文
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