适用于次同步振荡分析的直驱风电场平衡降阶方法

直驱风电场(direct-drive wind farm,DDWF)并入弱交流系统存在发生次同步振荡(sub-synchronous oscilla￣tion,SSO)的风险。由于DDWF模型阶数较高,实际分析时须降阶处理。现有平衡降阶方法在分析SSO问题时,无法在降阶过程中精确保留系统SSO模式。针对此问题,文中提出一种适用于SSO分析的平衡降阶方法。该方法基于参与因子分析,保留与SSO模式强相关的状态变量,并结合Hankel奇异值确定降阶阶数,建立与全阶系统模型SSO特性和动态特性都一致的降阶系统模型。首先,对DDWF并入弱交流系统的全阶小信号模型进行平衡变换,建立平衡系统模型。然后,对平衡系统模型进行参与因子分析,结合Hankel奇异值确定保留状态变量集合,再利用残差降阶法建立降阶系统模型。最后,对全阶系统模型和降阶系统模型进行对比验证,结果表明所提降阶方法适用于DDWF并入弱交流系统SSO问题的研究。     

基于平衡理论的双端柔性直流输电系统降阶小信号建模

为了提高直流输电系统小扰动稳定性分析计算效率,建立了直流输电系统小信号降阶模型。文章以双端直流输电系统为研究对象,首先建立了双端柔性直流输电系统小信号模型,然后基于平衡理论将系统状态量按Hankel奇异值数目排序进行阶数选择,经过矩阵变换实现小信号模型的降阶。通过计算全阶系统和降阶系统的主导特征根变化轨迹,验证了降阶系统与全阶系统具有一致的小扰动稳定性。仿真结果表明,降阶前后具有相似的动态响应,验证了降阶模型的准确性。在复杂网络环境下,基于平衡理论的降阶方法不仅减小模型复杂度、提高了计算效率,还可对系统的稳定性进行预判。     

Hybrid system reduction method using a reduced system regulator

In order to analyze the transient stability of large‐scale power systems, it is advantageous to apply the system reduction method to external systems. The short‐circuit current method is a typical engineering reduction technique. However, the dominant eigenvalues are not necessarily conserved in the reduced system. Therefore, the hybrid reduction method, in which controller parameters are adjusted to conserve the dominant eigenvalues, was proposed. Automatic voltage regulators (AVR) and power system stabilizers (PSS) have been used for parameter adjustment so far. However, since there are many parameters in AVR and PSS, complicated procedures are required to adjust them. Therefore, in this paper, the reduced system regulator (RSR) is proposed for the hybrid system reduction method. The RSR has only two parameters for adjustment. It is easier to adjust the RSR than AVR/PSS. In addition, the initial gains of the RSR are set to zero so that the dynamic behavior of the system is not influenced before adjustment. The effect and accuracy of the hybrid system reduction method with RSR are examined using a typical longitudinal power system, the IEEJ WEST 10‐machine system model. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 179(4): 33–40, 2012; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21258     

Order Reduction of Power Systems by Modal Truncated Balanced Realization

In this paper, a general approach for constructing reduced-order models of power system models based on a truncated balanced realization (TBR) linear reduction procedure is described. The method enables efficient computation of Gramian covariance matrices in terms of the system frequency response, and it can be used for control design and sensitivity analysis. The method guarantees convergence of the controllability and observability Gramians and avoids the need for frequency sweep of the transfer function matrix. A key innovation for the TBR-based reduced-order models introduced in this paper is the use of modal information to approximate the controllability and observability Gramians. With this approach, the connection between the linear system modes and the Gramians is clarified, and the contribution of critical system motion modes to the collective dynamics is readily determined. Conditions for convergence of the model and approximation methods are then investigated, and the issues of accuracy, applicability, and computational effort are discussed. The technique is tested on two real-world test power systems.     

Robust model order reduction technique for MIMO systems via ANN‐LMI‐based state residualization

Even though model order reduction (MOR) techniques for linear dynamical systems are developed rather properly, there are still quite a lot of issues to be considered. This paper addresses a novel MOR technique for multi‐input multi‐output system with dominant eigenvalue preservation, which leads to controller cost minimization. The new technique is formulated based on an artificial neural network (ANN) prediction of an upper triangular form of the system state matrix A. Using the new system state matrix along with the linear matrix inequality (LMI) optimization method, a permutation matrix is obtained which leads to the new formulation of the complete system considered for MOR. Utilizing the non‐projection state residualization technique, a reduced model order is obtained. The proposed ANN‐LMI‐based MOR method is compared with well‐known reduction techniques such as the balanced Schur decomposition, proper orthogonal decomposition (POD), and state elimination through balanced realization. Copyright © 2010 John Wiley & Sons, Ltd.     

并网逆变器小信号建模方法对比及其适用性分析

小信号建模是当前微电网稳定性分析和逆变器控制器设计的重要手段。依据是否考虑滤波器和线路的动态特性,小信号模型可以分为高阶模型和降阶模型,因此产生两种模型的对比问题。文中在考虑功率环、LC滤波器与线路阻抗等各环节小信号建模的基础上,针对单逆变器并网系统建立了高阶小信号模型。进而采用稳态方程描述滤波器和线路的动态特性,得到系统的降阶模型与误差表达式。然后针对单逆变器并网工况,利用MATLAB/Simulink软件,仿真验证了两种模型的正确性。随后,通过对特征根、主要相关状态变量与误差表达式进行分析,均表明降阶模型能够高精度地获取低频特征根。此外,通过对两种小信号模型获取的参数灵敏度和根轨迹进行分析,发现降阶模型应用到低频振荡、阻尼分析和控制器设计等场合的效果与高阶模型一致。但因无法获得中高频特征根,在低阻抗比或感性网络中存在稳定性判断错误的可能性。最后,通过根轨迹及功率响应波形,验证了这些结论的正确性。     

Reduced-order model of Type-C wind turbine generators

This paper presents a wind turbine generator (WTG) reduced-order model for time domain simulations. Selective modal analysis is used to reduce the model order by focusing on the most relevant modes and variables. In most cases, a single relevant mode is found; thus, a first-order model that captures the relevant mode is derived. Depending on the WTG dynamics, in some cases, reduced-order models of higher order are required. The proposed model is applied to both 4-bus and 39-bus test systems. The results show that the proposed reduced-order model closely resembles the impact of WTGs in a power system, even when large perturbations occur. Line and synchronous generator (SG) outages are taken into account. The proposed model reduces the simulation time and the power system model complexity.     

基于奇异摄动法的降阶模型对系统稳定性的影响

电力系统含有大量非线性高阶的数学模型,电力系统稳定性分析时,不可避免地要采用简化的系统模型,文章首先对电力系统动态负荷模型和发电机模型进行了研究并进一步推导变形,然后采用奇异摄动法中多重时间尺度的思想将非线性的电力系统负荷模型分解成不同时间尺度下的几个子系统,并将高阶模型降阶为低阶模型,最后通过仿真得到一系列数据验证了奇异摄动法降阶后的模型更接近完整模型,所得结果偏差更小。摄动法使模型降阶有了依据,避免了经验降阶带来的较大误差。     

基于Arnoldi算法的金属导体PEEC模型缩减方法

详细分析了渐近波形估算(AWE)方法的固有数值病态问题,提出使用基于Krylov子空间的Arnoldi算法对系统高阶模型进行缩减,将直接矩量显式计算转化为间接矩量隐式计算,将主导极点的抽取转化为主导特征值的抽取.然后给出了独立于频率之外的简化等效电路解耦模型,得到了解耦电阻电感参数,并通过计算实例验证了该方法的正确性.该研究成果克服了AWE等直接矩量显式计算方法只能提取有限几条缩减支路的不足,建立了模型缩减方法广泛使用的基础,具有重要的理论和工程应用价值.     

A Green's function‐based method for the transient analysis of plane waves obliquely incident on lossy and dispersive planar layers

This paper presents a new methodology for the transient analysis of plane waves obliquely incident on a planar lossy and dispersive layer. The proposed model is based on the Sturm–Liouville problem associated with the propagation equations. Green's function is calculated in a series form and the open‐end impedance matrix is obtained as the sum of infinite rational functions. This form permits an easy identification of poles and residues. Furthermore, the knowledge of poles leads to the development of a model order reduction technique by selecting only the dominant poles of the system. The pole–residue representation is converted into a state‐space model that can be easily interfaced with ordinary differential equation solvers. The numerical results confirm the effectiveness of the proposed modeling technique. Copyright © 2008 John Wiley & Sons, Ltd.     

直驱永磁同步风力发电系统的降阶模型研究

研究了适用于小干扰稳定分析的直驱永磁同步风力发电系统降阶模型.建立了直驱永磁同步风力发电系统的13阶详细模型;对于通过传输线接入无穷大母线系统的单个直驱永磁同步风力发电系统,应用特征值分析方法,保留其与主导特征值相关的状态变量,消去其它状态变量,将系统状态方程阶数降为4阶;再用时域仿真法,对降阶模型与详细模型的动态特性进行了比较.结果表明,提出的降阶模型与详细模型具有较好的一致性,也具有较高的精度.     

中压直流配电系统等效降阶建模及控制参数设计

合适的等效降阶模型能够为中压直流(MVDC)配电系统的稳定性分析及控制参数设计提供便利.首先,基于所提出的开闭环逐步等效降阶建模方法,建立了MVDC配电系统的等效降阶电路模型,并据此建立了计及换流器间动态交互的开环等效降阶模型.在不增加开环等效降阶模型阶数的前提下,基于泰勒展开的状态反馈控制方法为系统振荡频率及阻尼比的精准设计创造了有利条件.然后,基于所建立的计及换流器间动态交互的闭环等效降阶模型,并结合所提出的MVDC配电系统控制参数设计方法,实现了系统振荡频率及阻尼比的精准设计.最后,硬件在环实验结果验证了理论分析的合理性.     

模拟训练机模型简化算法的研究

在模拟训练机数学模型的仿真计算时,为了提高过程模拟的反应速度,增强人体感官的模拟效果,需要在实际的模型解算过程中,缩短计算模型所耗费的机时.针对模型解算的简化问题,提出一种设计思想,即在过程动态时采用通用滤波器的快速仿真算法,在稳态时采用模型降阶和时矩输出拟合相结合的算法.由六阶系统模型降为四阶模型的仿真结果表明,采用时矩输出拟合的降阶系统在其单位阶跃响应中,输出拟合的精确度范围可达输入幅值的0.05％ ～5.8％.采用所提出的设计思想,在动态时可以保证仿真的实时性,缩短模型的解算时间,在稳态时又可以提高简化模型的输出拟合精确度.     

并网逆变器降阶模型及其构建方法的分析与对比

并网逆变器的小信号模型是判断系统稳定性和参数设计的重要工具。并网逆变器的完整状态方程描述会附带较多冗余信息,采用适当的降阶模型能够方便系统参数整定与调试。然而现有的一些典型降阶模型适用面较窄,在特定工况下精度较低或随着参数的变化而失去通用性。首先,通过等效惯性常数与等效阻尼系数的概念建立了通用的功率环模型;通过单边傅里叶分析指出传统的三阶模型仅适用于分析大惯性、高阻尼系统;通过输出阻抗分析指出电磁五阶模型精度对于控制参数较为敏感。为了解决降阶模型精度的问题,利用逆变器时间尺度自然分离的特性,提出了一种基于时间常数的模型降阶方法,所提方法简单、有效,并导出了可靠、简洁的高带宽降阶模型,所得模型精度高、适用面广。最后,通过对比实验验证了理论分析的正确性和所提降阶方法与降阶模型的有效性。     

Fixed-speed wind-generator and wind-park modeling for transient stability studies

Increasing levels of wind-turbine generation in modern power systems is initiating a need for accurate wind-generation transient stability models. Because many wind generators are often grouped together in wind parks, equivalence modeling of several wind generators is especially critical. In this paper, a reduced-order dynamic fixed-speed wind-generator model appropriate for transient stability simulation is presented. The model is derived using a model reduction technique of a high-order finite-element model. Then, an equivalencing approach is presented that demonstrates how several wind generators in a wind park can be combined into a single reduced-order model. Simulation cases are presented to demonstrate several unique properties of a power system containing wind generators. The results in this paper focus on horizontal-axis turbines using an induction machine directly connected to the grid as the generator.     

An optimal modal approximation method for model reduction of linear power system models

A number of recent studies have examined the problem of modal reduction of large-scale power system linear models. In this paper, an optimal model reduction strategy for the analysis and control of inter-area oscillations in power systems that uses concepts from proper orthogonal decomposition and modal analysis and preserves exactly the input–output properties of the original system is presented. The technique uses a new projection matrix that minimizes the error between the states of the original system and the states of its reduced-order model, and is suitable for analyzing large power system models described by differential–algebraic equation (DAE) systems.Based on this theoretical framework, an efficient algorithm for model reduction is proposed which combines the ease of use of linear modal analysis, with the flexibility of extracting relevant behavior that statistical multivariate methods can offer. Methods for analysis of reduced system representations using linear approximations are critically reviewed and compared. The proposed technique is tested on a 50-machine, 145-bus, and 453-line test system. The effects of system dimension, accuracy of the approximations to capture inter-system oscillations, and the generality of the techniques are discussed in detail in the parametric study. Accuracy of the solution and weaknesses of the model reduction are also investigated. Direct numerical simulation of the power system dynamic model is performed to investigate the accuracy and robustness of the method.     

小干扰稳定性分析中一种关键特征值计算的稀疏实现

该文提出了一种大规模电力系统小干扰稳定性分析中基于稀疏技术的关键特征值求解方法。该方法借助于Cayley变换，将关键特征值计算变为主特征值的计算，导出了基于稀疏增广状态矩阵的幂法迭代公式，并利用稀疏2×2分块矩阵及稀疏三角分解技术实现了该方法。2个示例系统的计算结果验证了算法的正确性和有效性。该方法不但可用于低频振荡抑制中控制器参数的协调优化，而且其中使用的多种基本技术也可以推广到基于子空间法求取部分关键特征值的各种迭代计算中。     

Reducing the order of very large power system models

Results are presented for reduced-order models of power systems as large as 254 generators and 2500 buses, using the modal-coherency method of model reduction. Extension of order estimation, based on balanced realizations, to larger systems is discussed. An alternative order-estimation approach based on the intergenerator coherency ranking table is introduced and compared to the balanced realization approach. The alternative approach is consistent with the balancing results and more than an order of magnitude faster     

利用有限时间扰动后的响应辨识电力系统的主导特征值

研究电网在运行点处线性化系统的特征值分布是分析小干扰稳定的重要手段。文章分析了零输入响应下线性系统特征值辨识的特点，给出了可辨识性条件，提出了一种新的获得电力系统主导特征值分布的方法，即运用改进Prony算法，在线辨识电力系统在有限时间扰动后不同测点多路零输入响应的信号模型参数，从而得出电力系统主导特征值的分布，辨识过程与系统激励无关。该方法克服了传统离线分析方法中由于运行方式、模型参数不确定而导致结果可信度低等诸多缺点。文章给出了基于WAMS实时数据平台实现电网特征值在线监视的流程和框架。36节点多机仿真系统和实际电网现场测量的分析结果验证了方法的有效性。     

基于阻抗法的大规模风电场等值方法研究

大规模风电场的馈入会导致电力系统出现新的振荡稳定性问题。目前,大多数研究都将风电场等效为单个风机进行振荡稳定性分析。然而,该方法忽略了风电场内部的动态交互作用,可能会造成不准确的分析结果。通过矩阵变换,将一个具有M台永磁同步发电机(PMSG)的风电场分解为一个对角矩阵,每个对角矩阵表示等效的PMSG子系统。在此基础上,利用矩阵摄动理论,建立了基于阻抗法的风电场降阶模型,充分考虑了风电场的拓扑结构和内部动态特性。所提出的风场等值方法能够在保证精度的同时很大程度降低解析建模的复杂程度,适用于大规模风电场并网的振荡稳定性分析。通过仿真验证了所提方法的有效性。