次同步扭振动态特性研究
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摘要
随着“西电东送、南北互供、全国联网”发展战略实施,大型煤电基地相继投运,普遍采用单机容量为600 MW-1000 MW的大型汽轮发电机组,并且大量应用加装串补电容的输电线路来提高传输能力。大容量机组与大电网相互作用,特别是与串补线路相互作用,极易引起汽轮发电机组轴系次同步扭振问题。因此,次同步扭振问题是我国顺利实现“西电东送、南北互供、全国联网”发展战略、协调大电网大机组安全稳定运行所急需解决的重要问题。本文开展次同步扭振动态建模与分析方法研究,主要工作如下：
现存的电机参数与等值电路参数关系主要包括经典参数关系、近似精确参数关系以及迭代参数关系。本文分析了这3种参数关系存在的问题,分别建立了基于“静止频率响应”和“空载三相突然短路”试验的严格参数关系,分析了各种参数关系的区别与联系。并且分别应用同步电机运算电抗频率响应特性和特征值分析,研究了各种近似参数关系对次同步扭振分析结果的影响。研究结果显示了应用严格参数关系的必要性。
推导了在同步电机dq坐标系下的5阶感应电动机动态方程,此方程能够与包含电网电磁暂态的动态方程接口。进而建立了包含恒阻抗、恒电流、恒功率及动态负荷的次同步扭振分析线性化方程,分析了不同类型负荷对次同步扭振模态阻尼的影响。分析结果显示,只有当系统等值阻抗特别小的情况下,才可以忽略负荷对扭振模态阻尼的影响；在通常系统等值阻抗情况下,仅考虑RLC谐振电路影响而忽略负荷与扭振模态之间互作用,结果可能过于乐观。
应用机电耦合模型推导了扭矩线性解,定义了扭矩模态型及扭矩贡献因子,把小扰动扭振动态与机电系统模态联系起来,建立了小扰动扭振动态解析方法。另外,定义了“转子角全模态型”、“扭振模态型”等物理概念,推导了受迫振动模型的解。并应用上述分析回答了3个问题：“机电耦合模型”、“自由振动模型”和“受迫轴系模型”等3种模型的轴系扭振动态是否等价；为何模态型和自然扭振频率的计算值和测量值有很大偏差；怎样直接分析小扰动扭振动态特性。
针对大扰动扭振动态问题,推导了扭矩2阶解,定义了模态非线性指标及非线性贡献因子,把大扰动扭振动态特性分析与非线性模态分析联系起来,建立了分析大扰动扭振动态特性解析方法。提出了模态叠加原理,并将该原理应用于2阶解,提出了一种预测暂态扭矩放大的方法。
最后,应用上述建模及分析方法研究了某实际6机串补系统汽轮发电机组轴系扭振动态特性。分析结果表明,同步电机参数转化对实际多机系统扭振模态阻尼的计算结果有重要影响,各种近似参数转化方法都无法保证其自身计算结果的保守性。在实际多机系统中振荡模态繁多,应用本文所提出的大(小)扰动扭振动态特性研究方法,能够将这些模态与大(小)扰动扭振动态直接联系起来,也能够深入理解扭振动态的内部机制,提供描述大(小)扰动扭振动态特性的定量信息。这些定量信息指导机电系统安全运行,为研究汽轮发电机轴系次同步扭振抑制措施奠定了基础,进一步显示了本文所提出的建模及分析方法的优势。
With the implementation of the strategic plan of "transmission of electricity from the west to the east, exchange electricity between the south and the north, and the interconnection of power grids", the coal power bases have been commissioned one after another. They have commonly employed the turbine-generators with the unit capacity from 600 MW to 1000 MW. Series capacitive compensation measure has been widely used for enhancing the transmission capability of the corridors. The interactions of the high-capacity generator units and the large-scale grid, especially the series capacitive compensation transmission lines, readily lead to turbine-generator shaft torsional fatigue. Thus, subsynchronous torsional dynamics is an imperative problem for the implementation of the strategic plan and the security operation of large-scale interconnected power system and high-capacity units. In this dissertation, the modelling and analysis methodologies of subsynchronous torsional dynamics are studied, which is mainly composed of following parts.
The three categories of parameter translations between measured parameters and equivalent circuit parameters for synchronous machines, including the classic parameter, the approximate accurate parameter and the iterative parameter translations, are given, and their drawbacks are revealed. The accurate translations are respectively established based on standstill-frequency-response tests and sudden short-circuit tests. The relations and differences between all kinds of the above mentioned parameter translations are clarified. The effect of parameter translations on torsional dynamics are analyzed by using the frequency-response characteristics for operational reactance and the eigenvalues method. The analysis results show that it is necessary to adopt the accurate translations for subsynchronous torsional dynamics analysis.
The fifth-order dynamic equation for induction motors is derived in the dq-coordinates of synchronous machines. This equation can interface with the dynamic equations including the electromagnetic transients of electrical networks. Furthermore, the linear equations including fifth-order induction motors and constant impedance (Z), constant current (I), constant power (P) load models, are established for investigating subsynchronous torsional dynamics. Effects of different loads on the damping torsional modes are analyzed. The results show that the effect of loads on the damping of torsional modes can be neglected under the system with the very small equivalent impedance; the loads have the important effect on the damping of torsional modes under the system with the average equivalent impedance. The calculated damping of torsional modes can be overly optimistic without the consideration of load models under the average equivalent impedance.
The linear solutions of torsional torques are derived based on the electromechanical coupling model, and then they are used to define mode shapes and mode contribution factors of torques, which directly relate the electromechanical system modes to shaft torsional dynamics. Thus, the analytical method is established for analyzing small-signal torsional dynamics. Additionally, all-mode shapes and torsional mode shapes are defined. The solutions of forced vibration model are developed under the same electrical torque for the electromechanical coupling model. By using the above analyses, the three questions are answered:whether the three models of "electromechanical coupling model", "free vibration model" and "forced vibration model" are equivalent or not, why there is large deviation between the calculated and measured values for mode shapes and natural torsional frequencies, how shaft torsional dynamics can be directly represented.
Based on the modal series method, the second-order solutions of torsional torques are derived, and the nonlinearity modal indices and contributor factors of torques are defined to quantify the effects of nonlinear modal interactions on torsional dynamics. The analytical method is established for investigating nonlinear torsional dynamics directly from the physical concepts. Moreover, the principle of modal superposition is developed and it is used to establish a methodology for predicting transient torque amplification based on the second-order solutions of torques.
Finally, the proposed modelling and analysis methodologies are used to investigate the torsional dynamics for an actual series compensation system with six turbine-generators from the China Grid. The numerical results shows that the parameter translations have the significant effect on the damping for the calculated torsional modes for the actual system; all kinds of parameter translations can not make sure that they are conservative for the calculated torsional modes. Additionally, there exist a lot of oscillation modes. The proposed analysis method for investigating the large (small) disturbance torsional dynamics can establish the direct relationships of the fundamental modes of the electromechanical system and the large (small) disturbance torsional dynamics, and it can provide the quantitative analysis for the large (small) disturbance torsional dynamics. These quantitative analyses can provide recommendations for the actual operation and lay the foundation for developing the measures for suppressing the subsynchronous shaft torsional dynamics problems. The advantages for employing the proposed modelling and analysis methodologies are shown in the actual systems.
现存的电机参数与等值电路参数关系主要包括经典参数关系、近似精确参数关系以及迭代参数关系。本文分析了这3种参数关系存在的问题,分别建立了基于“静止频率响应”和“空载三相突然短路”试验的严格参数关系,分析了各种参数关系的区别与联系。并且分别应用同步电机运算电抗频率响应特性和特征值分析,研究了各种近似参数关系对次同步扭振分析结果的影响。研究结果显示了应用严格参数关系的必要性。
推导了在同步电机dq坐标系下的5阶感应电动机动态方程,此方程能够与包含电网电磁暂态的动态方程接口。进而建立了包含恒阻抗、恒电流、恒功率及动态负荷的次同步扭振分析线性化方程,分析了不同类型负荷对次同步扭振模态阻尼的影响。分析结果显示,只有当系统等值阻抗特别小的情况下,才可以忽略负荷对扭振模态阻尼的影响；在通常系统等值阻抗情况下,仅考虑RLC谐振电路影响而忽略负荷与扭振模态之间互作用,结果可能过于乐观。
应用机电耦合模型推导了扭矩线性解,定义了扭矩模态型及扭矩贡献因子,把小扰动扭振动态与机电系统模态联系起来,建立了小扰动扭振动态解析方法。另外,定义了“转子角全模态型”、“扭振模态型”等物理概念,推导了受迫振动模型的解。并应用上述分析回答了3个问题：“机电耦合模型”、“自由振动模型”和“受迫轴系模型”等3种模型的轴系扭振动态是否等价；为何模态型和自然扭振频率的计算值和测量值有很大偏差；怎样直接分析小扰动扭振动态特性。
针对大扰动扭振动态问题,推导了扭矩2阶解,定义了模态非线性指标及非线性贡献因子,把大扰动扭振动态特性分析与非线性模态分析联系起来,建立了分析大扰动扭振动态特性解析方法。提出了模态叠加原理,并将该原理应用于2阶解,提出了一种预测暂态扭矩放大的方法。
最后,应用上述建模及分析方法研究了某实际6机串补系统汽轮发电机组轴系扭振动态特性。分析结果表明,同步电机参数转化对实际多机系统扭振模态阻尼的计算结果有重要影响,各种近似参数转化方法都无法保证其自身计算结果的保守性。在实际多机系统中振荡模态繁多,应用本文所提出的大(小)扰动扭振动态特性研究方法,能够将这些模态与大(小)扰动扭振动态直接联系起来,也能够深入理解扭振动态的内部机制,提供描述大(小)扰动扭振动态特性的定量信息。这些定量信息指导机电系统安全运行,为研究汽轮发电机轴系次同步扭振抑制措施奠定了基础,进一步显示了本文所提出的建模及分析方法的优势。
With the implementation of the strategic plan of "transmission of electricity from the west to the east, exchange electricity between the south and the north, and the interconnection of power grids", the coal power bases have been commissioned one after another. They have commonly employed the turbine-generators with the unit capacity from 600 MW to 1000 MW. Series capacitive compensation measure has been widely used for enhancing the transmission capability of the corridors. The interactions of the high-capacity generator units and the large-scale grid, especially the series capacitive compensation transmission lines, readily lead to turbine-generator shaft torsional fatigue. Thus, subsynchronous torsional dynamics is an imperative problem for the implementation of the strategic plan and the security operation of large-scale interconnected power system and high-capacity units. In this dissertation, the modelling and analysis methodologies of subsynchronous torsional dynamics are studied, which is mainly composed of following parts.
The three categories of parameter translations between measured parameters and equivalent circuit parameters for synchronous machines, including the classic parameter, the approximate accurate parameter and the iterative parameter translations, are given, and their drawbacks are revealed. The accurate translations are respectively established based on standstill-frequency-response tests and sudden short-circuit tests. The relations and differences between all kinds of the above mentioned parameter translations are clarified. The effect of parameter translations on torsional dynamics are analyzed by using the frequency-response characteristics for operational reactance and the eigenvalues method. The analysis results show that it is necessary to adopt the accurate translations for subsynchronous torsional dynamics analysis.
The fifth-order dynamic equation for induction motors is derived in the dq-coordinates of synchronous machines. This equation can interface with the dynamic equations including the electromagnetic transients of electrical networks. Furthermore, the linear equations including fifth-order induction motors and constant impedance (Z), constant current (I), constant power (P) load models, are established for investigating subsynchronous torsional dynamics. Effects of different loads on the damping torsional modes are analyzed. The results show that the effect of loads on the damping of torsional modes can be neglected under the system with the very small equivalent impedance; the loads have the important effect on the damping of torsional modes under the system with the average equivalent impedance. The calculated damping of torsional modes can be overly optimistic without the consideration of load models under the average equivalent impedance.
The linear solutions of torsional torques are derived based on the electromechanical coupling model, and then they are used to define mode shapes and mode contribution factors of torques, which directly relate the electromechanical system modes to shaft torsional dynamics. Thus, the analytical method is established for analyzing small-signal torsional dynamics. Additionally, all-mode shapes and torsional mode shapes are defined. The solutions of forced vibration model are developed under the same electrical torque for the electromechanical coupling model. By using the above analyses, the three questions are answered:whether the three models of "electromechanical coupling model", "free vibration model" and "forced vibration model" are equivalent or not, why there is large deviation between the calculated and measured values for mode shapes and natural torsional frequencies, how shaft torsional dynamics can be directly represented.
Based on the modal series method, the second-order solutions of torsional torques are derived, and the nonlinearity modal indices and contributor factors of torques are defined to quantify the effects of nonlinear modal interactions on torsional dynamics. The analytical method is established for investigating nonlinear torsional dynamics directly from the physical concepts. Moreover, the principle of modal superposition is developed and it is used to establish a methodology for predicting transient torque amplification based on the second-order solutions of torques.
Finally, the proposed modelling and analysis methodologies are used to investigate the torsional dynamics for an actual series compensation system with six turbine-generators from the China Grid. The numerical results shows that the parameter translations have the significant effect on the damping for the calculated torsional modes for the actual system; all kinds of parameter translations can not make sure that they are conservative for the calculated torsional modes. Additionally, there exist a lot of oscillation modes. The proposed analysis method for investigating the large (small) disturbance torsional dynamics can establish the direct relationships of the fundamental modes of the electromechanical system and the large (small) disturbance torsional dynamics, and it can provide the quantitative analysis for the large (small) disturbance torsional dynamics. These quantitative analyses can provide recommendations for the actual operation and lay the foundation for developing the measures for suppressing the subsynchronous shaft torsional dynamics problems. The advantages for employing the proposed modelling and analysis methodologies are shown in the actual systems.
引文
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