| 混流式水轮机调节系统非线性建模与分叉分析 |
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| 引用本文： | 张记坤,曾 云,王芳芳,杨光波,张振凯,钱 晶.混流式水轮机调节系统非线性建模与分叉分析[J].教育技术导刊,2019,18(12):102-107. |
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| 作者姓名： | 张记坤 曾 云 王芳芳 杨光波 张振凯 钱 晶 |
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| 作者单位： | 昆明理工大学 冶金与能源工程学院，云南 昆明 650093 |
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| 基金项目： | 国家自然科学基金项目（51579124）；昆明理工大学分析测试基金项目（2017M20162202073） |
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| 摘 要： | 基于Matlab仿真软件，考虑弹性水击对水轮机调节系统的影响，建立弹性水击水轮机微分代数模型，并与调速器和发电机共同构成水轮机调节系统非线性模型。在此基础上运用非线性动力学分叉理论对PID调速器参数进行Hopf分叉行为研究，得出PID参数三维分叉曲面、二维分叉曲线及稳定域，并通过对时域图、相轨迹图等的综合分析，得到取不同调速器参数时系统的非线性动力学特性，为机组PID参数选择提供理论依据。最后通过系统仿真得出，在小扰动下线性模型和非线性模型均能适用，在大扰动下非线性模型能更真实地反映机组动态特性。
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| 关 键 词： | 弹性水击 非线性模型 Hopf分叉 分叉曲面 动力学特性 |
| 收稿时间： | 2019-03-15 |
Nonlinear Modeling and Bifurcation Analysis of Francis Hydraulic Turbine Regulation System |
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| ZHANG Ji-kun,ZENG Yun,WANG Fang-fang,YANG Guang-bo,ZHANG Zhen-kai,QIAN Jing.Nonlinear Modeling and Bifurcation Analysis of Francis Hydraulic Turbine Regulation System[J].Introduction of Educational Technology,2019,18(12):102-107. |
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| Authors: | ZHANG Ji-kun ZENG Yun WANG Fang-fang YANG Guang-bo ZHANG Zhen-kai QIAN Jing |
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| Institution: | Faculty of Metallurgical and Energy Engineering， Kunming University of Science and Technology， Kunming 650093， China |
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| Abstract: | Considering the influence of elastic water hammer in the turbine regulation system， a differential algebraic model of the elastic water hammer turbine is established， and together with the governor and the generator， a nonlinear model of the turbine governing system is constructed under the Matlab simulation software. Based on this， the nonlinear dynamic bifurcation theory is used to study the Hopf bifurcation behavior of PID governor parameters， then the three-dimensional bifurcation surface and two-dimensional bifurcation curve and stability domain of PID parameters are obtained， and meanwhile the nonlinear dynamics of the system with different governor parameters are analyzed through the time domain diagram and the phase trajectory diagram， providing a theoretical basis for the selection of unit PID parameters. Finally， the simulation shows that both the linear model and the nonlinear model are applicable under small disturbances. The nonlinear model under large disturbance can reflect the dynamic characteristics of the unit more accurately. |
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| Keywords: | elastic water hammer nonlinear model Hopf bifurcation bifurcation surface dynamic characteristic |
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