On the application of the complex torque coefficients method to the analysis of torsional dynamics

The complex torque coefficients method has been widely accepted for the analysis of the phenomenon of torsional interaction of turbine-generator units in power systems. This paper shows that, depending on the system parameters and the operating point, the complex torque coefficients method may exhibit limitations and not accurately and fully predict the system behavior in the frequency range of interest. These shortcomings consist of inability to i) predict monotonic instability due to real poles, ii) identify all electromechanical oscillatory modes, and iii)accurately predict damping (and consequently stability) of the oscillatory modes. This paper develops mathematical expressions to highlight the limitations of the complex torque coefficients method. Quantitative results based on three case studies, including a study on the first IEEE Benchmark System, are reported and results from eigenvalue analysis method, complex torque coefficients method, and time-domain simulation are presented and compared. This paper concludes that the complex torque coefficients method can be used only as a preliminary method for the investigation of torsional interactions and the results must be verified by other methods.     

Analysis of torsional oscillations using an artificial neuralnetwork

A novel approach using an artificial neural network (ANN) is proposed for the analysis of torsional oscillations in a power system. In the ANN those system variables, such as generator loadings and the capacitor compensation ratio, which have major impact on the damping characteristics of torsional oscillation modes were used as the inputs. The outputs of the neural net provided the desired eigenvalues for torsional modes. Once the connection weights of the neural network have been learned using a set of training data derived offline, the neural network can be applied to torsional analysis in real-time situations. To demonstrate the effectiveness of the proposed neural net, torsional analysis was performed on the IEEE First Benchmark Model. It is concluded from the test results that accurate assessment of the torsional mode eigenvalues can be achieved by the neural network in a very efficient manner     

蒸汽轴向流动对汽轮发电机组轴系扭振响应的影响

对在汽轮机高压和中压调节阀快关动作后蒸汽沿轴向流动过程对轴系扭振响应的影响进行了研究。轴系的计算模型采用连续质量模型。外激励模型是考虑了汽轮机ＤＥＨ系统、热力系统以及单机对无穷大电网的机电耦合数学模型。对３００ＭＷ汽轮发电机组的仿真计算表明,考虑蒸汽流动导致的激励扭矩沿汽轮机轴向瞬时变化时,对轴系的扰动和轴系扭振的激励加强,蒸汽载荷变化对汽轮发电机组轴系扭振的影响是较大的,在轴系安全评价中必须加以考虑。图４参３     

Impact of renewable generation unit on stability of power systems

Nowadays, the development of the electric power system is associated with the penetration of power generation units based on renewable energy sources and operated with energy storage systems. However, the operation of such generation units changes and complicates the processes in the electric power system, which determines the need for a number of studies and analyses. This paper presents the results of assessing the impact of the operation of photovoltaic plants on the static stability of the electric power system. To achieve the goal, the EUROSTAG software was used. The results of studies of normal and post-emergency modes of electric power system with the different penetration level of generation units are presented, power system stability coefficients of active power and voltage are determined, damping properties of electric power system based on the calculation of the transient damping coefficient of the damping process are estimated.     

Stabilizing torsional oscillations using a hunt reactor controller

Results of a study on the application of shunt reactors for the damping of torsional oscillations that occur in a power system containing series-capacitor compensation are presented. The IEEE Second Benchmark Model, system-1 is used to investigate the benefits of the utilization of modulated reactive power in suppressing unstable subsynchronous resonance (SSR) modal interactions. A set of shunt reactors is connected to the generator bus of the affected synchronous machine whose shaft is directly coupled to the turbine system of the benchmark model. In order to stabilize all the torsional modes, a unified approach based on modal control theory is proposed for the design of a shunt reactor controller, which is essentially a dynamic output compensator. To demonstrate the effectiveness of the damping enhanced by the proposed scheme, eigenvalue analysis for different loading conditions and sensitivity analysis for controller parameters are performed     

Coherency-based low order models for shaft systems ofturbine-generator sets

Accurate low order lumped models that represent the low frequency torsional motion of turbine-generator sets are needed for determining shaft torsional responses resulting from subsynchronous resonance conditions, electric power system faults and planned/unplanned switching actions in the electric network. This paper presents a coherency-based method that resolves a high order inertia-spring lumped model into a low order inertia-spring lumped model, while preserving the selected group of natural torsional frequencies and their associated mode shapes. Forced eigen-frequency matching and conservation of angular momentum form the basis of the iterative procedure developed in the paper. Numerical examples are included to illustrate the capabilities of the proposed method in determining accurate low order dynamic equivalents     

Application of STATCOM for damping torsional oscillations in seriescompensated AC systems

This paper presents the results of a study on the application of the recently developed FACTS device, the static compensator (STATCOM), for the damping of torsional oscillations that occur in a series compensated AC system. The IEEE first benchmark system is considered for this study. In order to suppress unstable torsional mode oscillations, a STATCOM with a PI controller to regulate the bus voltage, and with an auxiliary signal derived from the generator speed deviations is employed at the generator terminal. The eigenvalue analysis technique is used for small signal analysis and optimization of the control system parameters is done through step response studies. In addition, dynamic performance of the nonlinear system with optimized STATCOM controller is evaluated under a three-phase fault. Results from the analytical and digital simulation studies reveal the technical feasibility of using STATCOM for damping of turbine-generator torsional oscillations in series compensated AC systems     

Torsional system parameter identification of turbine-generator sets

Accurate low order linear models that represent the torsional motion of turbine-generator sets are needed for determining shaft torsional responses resulting from subsynchronous resonance conditions, electric system faults and planned/unplanned switching actions in the electric network. This paper outlines the theoretical background and the methodology used for identification of linear state-space models of turbine-generator systems. These analytic mass-spring-damper models are lumped-parameter approximations, which in reality represent a continuous nonlinear system. For transient torque studies these models are adequate representations of the torsional dynamics of interest. Reduced analytic models of any particular turbine-generator unit, however, usually do not match precisely the behavior of the real machine. The paper describes an optimization method that can give a more precise representation of a particular turbine-generator based on actual plant tests and an assumed model of that unit. The parameter identification process is illustrated using plant test data from a 618 MVA turbine-generator unit     

基于有向图和序贯蒙特卡洛法的含电动汽车配电网可靠性评估

大规模电动汽车接入后将对配电网可靠性带来极大影响,快速有效的可靠性评估方法是亟待解决的关键问题之一。针对含电动汽车的配电网,提出了一种基于有向图和序贯蒙特卡洛算法的可靠性评估方法。首先基于有向图矩阵,利用前推和回推搜索辨识系统故障后的局部网络,并构建系统故障模式影响分析表;分析提出了考虑电动汽车接入后故障模式影响分析表的修正方法,并基于序贯蒙特卡洛算法定量分析了电动汽车接入后对配电网可靠性带来的影响,并从电动汽车接入位置和接入时段等角度对电动汽车接入电网提出了相应的建议。算例分析的结果表明所提方法能够快速修正电动汽车接入后的系统故障模式影响分析表,并能够适应不同场景下的含电动汽车配电网可靠性评估,为电动汽车合理接入电网提供理论依据。     

The influence of shaft spring constant uncertainty on torsionalmodes of turbogenerator

The paper explores the dependence of torsional modes of turbogenerator on the uncertainty in the shaft spring constant (stiffness). The analysis is performed on a typical single machine infinite bus system. Small-signal stability analysis as well as large-disturbance analysis are performed on a five rotational mass mechanical system. Different operating conditions of the generator are examined. It is shown that the spring constant (stiffness) of the shaft can significantly influence damping and frequency of torsional modes. Effects on maximum torsional torques developed in the shaft following large disturbance in the electrical system are also analysed. The paper underlines the importance of accurate modelling of the turbine-generator shaft for studies of torsional oscillations and subsynchronous resonance     

Dynamic response analysis on torsional vibrations of wind turbine geared transmission system with uncertainty

Gearbox transmission system is the major part of the wind turbine drive train. Due to the manufacturing and assembling errors, lubrication condition, wear and uncertainties in material and geometric properties, the system parameters, including mesh stiffness, transmission error and damping of the meshing gears are always uncertain. For a more reasonable evaluation of dynamic characteristics of the gearbox transmission system, the influence of the uncertain parameters should be taken into consideration. Based on the Chebyshev interval method (CIM), the dynamic responses of a geared transmission system with uncertain parameters are thus investigated in this paper. A torsional vibration model is derived for a geared system, in which some parameters including the mesh stiffness, the transmission error, the mesh damping, the shaft damping, the moment of inertia of the input blades and the torsional stiffness of the driving coupling shaft are considered as uncertain but bounded parameters. Interval dynamic equations of the geared system are solved by use of the CIM in combination with the variable-step Runge-Kutta numerical integration method. The accuracy of the CIM is demonstrated in comparison with the Monte Carlo (MC) simulation. Variations of the upper and lower bounds of the dynamic mesh force with input speed are obtained. The effects of those uncertain parameters on the frequency response of the dynamic mesh force are discussed in detail. It is shown that small parameter uncertainties might be propagated in the vibration system and lead to relatively large uncertainties of the dynamic response of system. The result is of significance for the design and condition monitoring of wind turbine drive trains.     

汽轮发电机组轴系扭振模型——四端网络模型的完善

四端网络模型是一种精确的低阶分布质量模型，在理想化扭振模型基础上，从满足现场生产实际角度出发，考虑了汽轮发电机组轴系扭振的阻尼和附加惯量的影响，对该模型作了进一步完善。详细推导了两种情况下轴系扭振特性传递方程式，虽然它们具有相似的方程形式，但方程式中的轴系扭振特性参数却是不同的，结合具体算例，比较了在不同阻尼系数比情况下，机组轴系各阶固有频率的变化。     

Damping and synchronizing torques of salient-pole generators withaccurate representation of saturation

The paper presents an accurate evaluation to the damping and synchronizing torques of a saturated salient pole generator. This objective is achieved by improving the accuracy of saturation representation and the method of computing damping and synchronizing torques. The alternator is represented by using a detailed circuit model which incorporates, properly, the saturation effects under steady-state and dynamic conditions. Based on this detailed model, the damping and synchronizing torque coefficients have been calculated by a least square algorithm which is unrestricted to the degree of complexity of the system. To generalize the conclusion, the damping and synchronizing torque coefficients have been calculated over a wide range of operating conditions. Furthermore, the effect of saturation on the operating boundaries is also exhibited     

关于发动机轴系振动与噪声的研究——正弦波扫描激振与应力电测的应用

摘要本文介绍了应用正弦波扫描激振、应力电测对静态、动态的发动机轴系进行了测试与研究,阐明了发动机某些零部件的固有频率特性、阻尼特性、扭振特性对轴系振动噪声的影响以及轴系共振区域的划分,对发动机系统降噪的研究进行了有益的探索.     

基于灵敏度分析的内燃机曲轴扭振系统结构动力学修改

应用系统矩阵法利用系统矩阵法,分析了内燃机曲轴扭振系统无阻尼自由振动固有频率和振型对转动惯量及刚度的灵敏度。基于固有特性灵敏度分析,给出了扭振系统结构动力学修改的计算方法。以某内燃机曲轴扭振系统为例计算分析了固有频率和振型的灵敏度问题,在此基础上进行了动力学修改,提出了改进方案。     

单位气缸阻尼系数问题的研究（一）：阻尼系数随曲柄转角变化的规律

摘要本文探讨了解决发动机阻尼系数问题的途径;分析了曲柄连杆机构在轴系扭转振动中的几何运动关系及各部件阻尼系数随曲柄转角的变化规律.最后通过能量法给出了转化到曲轴中心处的单位气缸当量阻尼系数.     

有阻尼柴油机轴系扭转自由振动计算方法研究

为使轴系自由振动计算得到的固有频率更加接近实际情况,提出了一种有阻尼柴油机轴系扭转自由振动计算方法,将柴油机轴系中大阻尼部件的阻尼参数纳入到轴系扭转振动自由振动计算的考量范围。将该方法应用到某PC2-6柴油机试验台架扭振计算,计算结果与实测结果吻合较好,验证了该方法的可靠性和实用价值。     

单位气缸阻尼系数问题的研究（二）：阻尼系数变化的实验分析

作为前文的继续，作者利用带有十字头结构的单缸模型机，通过回转与“非回转”实验，对发动机动力轴系扭转振动中的单位气缸阻尼系数问题进行了系统的研究，揭示了单位气缸扭振阻尼系数随曲柄转角变化的规律，并指出了形成这种变化的主要原因。     

Heat propagation on a shaft due to transient torsional vibration

During transient torsional vibration of rotating shafts heat is generated due to material damping, which results in substantial temperatures. The problem of a cylinder of infinite length heated by way of a transient torsional vibration of variable amplitude is investigated and an expression of the maximum surface temperature is obtained. Diagrams with the appropriate dimensionless parameters are presented together with a numerical example. It is shown that substantial temperatures can be developed as a result of this mechanism of heat generation. This quantities the belief that this phenomenon was the reason for a major generator failure in a power system.     

曲轴减振器特性参数检测系统开发研究

本文开发出一套曲轴减振器特性参数的计算机检测分析系统。该系统通过激振器激励减振器扭振并自动采集成振器的响应，根据频响曲线计算得出减振器的特性参数。对比试验结果表明，该系统能准确测定减振器的振动特性参数。并对测试系统的杭干扰进行了详细分析。