考虑同步机制的双馈风电系统小扰动建模与稳定性分析

对比分析了锁相环同步机制和虚拟同步发电机同步机制下的双馈风电系统小扰动稳定性及动态特性。针对2种同步机制下的双馈风电系统,基于数学方程分别得出相应的小扰动模型,进而利用特征值分析法对系统小扰动稳定性进行研究。在StarSim硬件在环(StarSim-HIL)半实物仿真平台上搭建相关模型,通过仿真对2种同步机制下的双馈风电系统有功支撑等动态特性及小扰动稳定性进行了分析与验证。对2种同步机制的适用性进行总结,指出锁相环型控制虽然动态特性好、响应速度快,但是在弱电网下的小扰动稳定性及有功支撑等方面,虚拟同步发电机控制更有优势。     

虚拟同步直驱风电场经MMC-HVDC并网的低频振荡特性分析

虚拟同步直驱风电场经功率同步环与模块化多电平换流器柔性直流(MMC-HVDC)输电互联,将存在低频振荡风险。考虑MMC-HVDC和直驱风机网侧换流器以及转子侧换流器内部的动态过程,首先建立虚拟同步直驱风电场经MMC-HVDC并网的小信号模型,并通过精细化电磁暂态仿真验证其准确性。随后,利用根轨迹方法,分析风电功率波动和交流系统强度变化对互联系统稳定性的影响,设计功率变化时虚拟同步直驱风电场的参数整定方法。结果表明,由于功率外环和MMC-HVDC送端整流站电压环作用,在风电场输出功率增大和交流系统强度降低的过程中,互联系统存在低频振荡现象。通过合理调整锁相环、虚拟同步机(VSG)有功环和MMC-HVDC送端整流站电压环的控制器参数、改变VSG阻尼项形式,可以抑制振荡并实现稳定运行。     

计及多模态分量的新能源电力系统节点频率分析方法

“双碳”背景下,大规模新能源接入电力系统,频率响应空间分布差异扩大,此时各节点频率响应中的非全局分量可能主导频率稳定问题,而对于此类问题的研究目前尚不充分。为此,基于频率响应模态分解思路,提出新能源电力系统节点频率响应量化分析方法。首先,用惯量-阻尼-调频系统统一结构近似各类型设备频率-有功传递函数。然后,基于二次特征值分析方法将各节点频率响应进行分解,获得共模频率与若干差模频率的表达式。进一步地,解析了各频率分量的最大偏移量、变化率等关键特征量,并类比总惯量与全局频率变化率间的对应关系,针对各节点各模态频率分量定义了节点模态惯量指标。所提频率分解方法与指标直观地展示了电力系统中各差模频率的节点分布差异。最后,仿真验证了所提频率分解方法和指标的有效性。     

含光伏电站的电力系统低频振荡广域阻尼协同控制方法

大规模新能源接入电网增加了弱阻尼振荡模式被激发的风险。首先,考虑同步发电机和光伏的动态特性,建立了详细的小信号模型,分析了光伏对低频振荡模式的影响,提出了含光伏电站的电力系统低频振荡广域阻尼控制架构,实现光伏-同步机协调阻尼控制;然后,以特征值分析结果为依据,提出了广域阻尼控制参数的优化模型,并对控制参数进行优化整定;最后,在PSCAD/EMTDC平台中搭建了含光伏电站的四机两区域系统电磁暂态仿真模型,验证了所提广域阻尼控制方法的有效性。     

Error estimation for the automated multi‐level substructuring method

In this study, we propose an effective method to estimate the reliability of finite element models reduced by the automated multi‐level substructuring (AMLS) method. The proposed error estimation method can accurately predict relative eigenvalue errors in reduced finite element models. A new, enhanced transformation matrix for the AMLS method is derived from the original transformation matrix by properly considering the contribution of residual substructural modes. The enhanced transformation matrix is an important prerequisite to develop the error estimation method. Adopting the basic concept of the error estimation method recently developed for the Craig–Bampton method, an error estimation method is developed for the AMLS method. Through various numerical examples, we demonstrate the accuracy of the proposed error estimation method and explore its computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

In this study, the effect of the centrifugal forces on the eigenvalue solution obtained using two different nonlinear finite element formulations is examined. Both formulations can correctly describe arbitrary rigid body displacements and can be used in the large deformation analysis. The first formulation is based on the geometrically exact beam theory, which assumes that the cross section does not deform in its own plane and remains plane after deformation. The second formulation, the absolute nodal coordinate formulation (ANCF), relaxes this assumption and introduces modes that couple the deformation of the cross section and the axial and bending deformations. In the absolute nodal coordinate formulation, four different models are developed; a beam model based on a general continuum mechanics approach, a beam model based on an elastic line approach, a beam model based on an elastic line approach combined with the Hellinger–Reissner principle, and a plate model based on a general continuum mechanics approach. The use of the general continuum mechanics approach leads to a model that includes the ANCF coupled deformation modes. Because of these modes, the continuum mechanics model differs from the models based on the elastic line approach. In both the geometrically exact beam and the absolute nodal coordinate formulations, the centrifugal forces are formulated in terms of the element nodal coordinates. The effect of the centrifugal forces on the flap and lag modes of the rotating beam is examined, and the results obtained using the two formulations are compared for different values of the beam angular velocity. The numerical comparative study presented in this investigation shows that when the effect of some ANCF coupled deformation modes is neglected, the eigenvalue solutions obtained using the geometrically exact beam and the absolute nodal coordinate formulations are in a good agreement. The results also show that as the effect of the centrifugal forces, which tend to increase the beam stiffness, increases, the effect of the ANCF coupled deformation modes on the computed eigenvalues becomes less significant. It is shown in this paper that when the effect of the Poisson ration is neglected, the eigenvalue solution obtained using the absolute nodal coordinate formulation based on a general continuum mechanics approach is in a good agreement with the solution obtained using the geometrically exact beam model.     

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions.     

New hybrid Monte Carlo methods and computing the dominant generalized eigenvalue

In this paper, the computation of dominant generalized eigenvalue problem using the new Monte Carlo method are presented. We also compare the numerical results and the CPU-time of two different methods for evaluating dominant generalized eigenvalue. The first method is the QR method. The second method is the extended Monte Carlo method which is called the resolvent Monte Carlo algorithm. Finally, using these methods the numerical results for the general symmetric dense/sparse matrices are performed.     

A symmetric positive definite preconditioner for saddle-point problems

For the classical saddle-point problem, we present precisely two intervals containing the positive and the negative eigenvalues of the preconditioned matrix, respectively, when the inexact version of the symmetric positive definite preconditioner introduced in Section 2.1 of Gill et al. [Preconditioners for indefinite systems arising in optimization, SIAM J. Matrix Anal. Appl. 13 (1992), pp. 292–311] is employed. The model of Stokes problem is used to test the effectiveness of the presented bounds as well as the quality of the symmetric positive definite preconditioner.