数据视角下的电力系统暂态稳定边界分析

随着泛在电力物联网的提出,基于数据挖掘的电力系统分析将在能源互联网的建设中发挥越来越重要的作用。同时临界暂态稳定的边界问题是评价电力系统暂态稳定性的核心问题之一,当前在暂态稳定评估时,常常由于无法对电网临界状态给出准确判断,使安全评估存在模糊区域。为此从数据分析的角度,展开电力系统临界暂态稳定边界特征提取的相关研究。首先基于暂态稳定单机模型及能量函数,刻画分析电力系统临界暂态稳定的边界现象;然后基于BPA自动仿真程序解决了暂态稳定数据样本生成问题;最后完成了"源-网"输入特征的选择及输入特征相关性分析,并利用IEEE-39母线系统完成验证。     

Fast transient control of power systems using a partial energy function

Abstract

The partial energy function is applied to assess the transient stability for a power system subjected to a large disturbance. Following this assessment, an energy‐based analytical sensitivity method for fast transient control to prevent loss of synchronism of generators is presented. The sensitivity of the partial energy margin at any instant to the change of generation level has been analytically derived in a closed form. The proposed sensitivity technique offers a systematic calculation for quantitative estimation of generation that must be adjusted to maintain system stability. Furthermore, this paper proposes two local control strategies using the energy‐based sensitivity method with the superconducting magnetic energy storage (SMES) unit as an adaptive transient controller to enhance the power system transient performance. The accuracy test of the partial energy function and the effectiveness of both control schemes are illustrated with the Taipower system. The results are found to be encouraging.     

Power system energy analysis incorporating comprehensive load characteristics

The energy function method developed so far assumes that the active load is constant. However, most of the actual load is voltage dependent, which hinders the application of the energy analysis method to the actual power system. On the other hand, the fast development of measurement techniques, especially the wide area measurement systems (WAMS) applied widely in worldwide power system nowadays, presses for the on-line transient stability analysis tools based on the system measurements. The voltage-dependent load into the energy analysis of power system transient stability is discussed. The effect of the comprehensive load characteristics on the system energy is discussed and a WAMS-based energy indicator on the system stability status is proposed. The indicator is easy to be calculated and thus real-time in the operation centre is monitored. The proposed method does not rely on any specific load model, and various load characteristics on different buses can be considered. Simulations on two test systems verify the effectiveness of the proposed method.     

Singular perturbations for sensitivity analysis in symmetric bifurcation buckling

A direct procedure for the evaluation of imperfection‐sensitivity in bifurcation problems is presented. The problems arise in the context of the general theory of elastic stability (Koiter's theory) for discrete structural systems, in which the total potential energy is employed together with a stability criterion based on energy derivatives. The imperfection sensitivity of critical states, such as bifurcations and trifurcations, is usually represented as a plot of the critical load versus the amplitude ε of the imperfection considered. However, such plots have a singularity at the point with ε=0, so that a regular perturbation expansion of the solution is not possible. In this work, we describe a direct procedure to obtain the sensitivity of the critical load (eigenvalue of the bifurcation problem) and the sensitivity of the critical direction (eigenvector of the bifurcation problem) using singular perturbation analysis. The perturbation expansions are constructed as a power series in terms of the imperfection amplitude, in which the exponents and the coefficients are the unknowns of the problem. The solution of the exponents is obtained by means of trial and error using a least degenerate criterion, or by geometrical considerations. To compute the coefficients a detailed formulation is presented, which employs the conditions of equilibrium and stability at the critical state and their contracted forms. The formulation is applied to symmetric bifurcations, and the coefficients are solved up to third‐order terms in the expansion. The algorithmis illustrated by means of a simple example (a beam on an elastic foundation under axial load) for which the coefficients are computed and the imperfection‐sensitivity is plotted. Copyright © 2001 John Wiley & Sons, Ltd.     

呼吸性裂纹转子的瞬态振动特性分析

旋转机械转子轴萌生裂纹后,瞬态加速过程中转涡差角时变使裂纹周期性开合,系统发生不同于稳态情况的振动。本文基于中性轴法确定裂纹开合,数值计算了呼吸裂纹引起刚度时变的转子过临界转速的瞬态振动,分析了裂纹大小、方向角和重力对线性加速转子瞬态振动的影响,以及定功率加速瞬态过程中系统振动响应及稳定性。结果发现,瞬态条件下带呼吸裂纹转子系统亚谐波共振并不明显;裂纹越大,过临界转速时瞬态振幅越大;在临界转速附近裂纹瞬时张开会激起很大的振动;定功率加速过程下,若功率不足够提供转子顺利穿过临界转速,则会出现外界扭矩与瞬态振动的能量耦合,大裂纹还可能造成瞬态振动发展成混沌。     

Transient stability assessment using projection formulations

Definitions of angle radius and coordinates axis are presented to propose a new transient stability method that is simple and reliable for transient stability assessment. The concept of angle radius is further developed to introduce the novel concept of projection energy function (PEF), which in turn allow to the assessment of critical clearing time and generation limit of system in a new way. The advantage of the new method is that no concept of advanced generator group is required in the assessment contingency stability index. Case studies on the ten-generator New England test power system are reported to verify the validity of the PEF method.     

基于广域测量信息的电力系统暂态稳定控制技术研究

基于响应的电力系统暂态稳定控制是广域测量系统（wide-area measurement system,WAMS）重要的应用领域之一。广域测量系统可以实时获取全网的动态响应数据,为基于响应的电力系统暂态稳定控制技术提供有力的技术支撑。该文对基于响应信息的暂态稳定控制的关键技术进行了综述,主要包括：暂态稳定功角受扰轨迹预测,暂态稳定判别以及暂态稳定紧急控制3个方面。指出现有方法的不足,并总结了基于响应的暂态稳定控制的特点,在此基础上提出未来亟待解决的关键问题。     

Comparative Study of Resistive and Inductive Superconducting Fault Current Limiters SFCL for Power System Transient Stability Improvement

This paper presents a comparative study of resistive and inductive superconducting fault current limiter (SFCL) for power systems transient stability improvement. Two applications of transient stability assessment are presented in this paper: The first shows the efficiency of the resistive and inductive SFCL in series with a generator, the second uses SFCL installed in series with a transmission line. SFCL can just be operated during the period from the fault occurrence to the fault clearing; the modeling and the effect of SFCL has been investigated to have higher benefits for the power system. In the present work, modification of the admittance matrix method is used for modeling of SFCL; Critical Clearing Time (CCT) has been used as an index for evaluated transient stability. The transient stability is assessed by the criterion of relative rotor angles, using the Runge–Kutta method. The effectiveness of the proposed method is tested on the WSCC3 nine-bus system applied to the case of three-phase short circuit fault in one transmission line. A simulation and comparison are presented in this document.     

A frequency-domain approach for modelling transient elastodynamics using scaled boundary finite element method

This study develops a frequency-domain method for modelling general transient linear-elastic dynamic problems using the semi-analytical scaled boundary finite element method (SBFEM). This approach first uses the newly-developed analytical Frobenius solution to the governing equilibrium equation system in the frequency domain to calculate complex frequency-response functions (CFRFs). This is followed by a fast Fourier transform (FFT) of the transient load and a subsequent inverse FFT of the CFRFs to obtain time histories of structural responses. A set of wave propagation and structural dynamics problems, subjected to various load forms such as Heaviside step load, triangular blast load and ramped wind load, are modelled using the new approach. Due to the semi-analytical nature of the SBFEM, each problem is successfully modelled using a very small number of degrees of freedom. The numerical results agree very well with the analytical solutions and the results from detailed finite element analyses.     

顶部自由、底部嵌固桩的稳定性分析

用能量法对顶部自由、底部嵌固桩在顶部集中荷载和桩侧摩阻力作用下的竖向稳定性问题进行了研究。对于部分埋置于Winkler地基中的桩,首先建立了桩的受力模型,根据边界条件给出了桩的挠曲函数,导出了系统总势能的表达式;然后根据最小势能原理推导了求解失稳问题的计算公式,用数值方法求得了桩的临界长细比()的数值解,通过对数值解的分析,最后得到了简捷易用的近似计算公式;最后给出了算例,计算表明：地基的抗力对有重要影响,当地基的抗力较大时,桩侧摩阻力对影响甚小。     

Slow dynamics simulation of power systems

This paper investigates the simulation of slow dynamics in two-time-scale power systems. A new approach is proposed to obtain the slow dynamics by projecting the trajectory of the post-fault system onto its slow manifold. This is achieved by a nonlinear projection of the full order system initial condition onto the slow manifold, such that the fast intraarea dynamics are not excited. A projection scheme is developed and applied to two-test power systems.     

Corrected transient energy function-based strategy for stability probability assessment of power systems

A new model describing the uncertainty of fault clearing time for probabilistic transient stability assessment of power systems is proposed. In this, a corrected transient energy function-based strategy is developed to evaluate the probabilistic instability index of systems. The advantage of this approach is that evaluations of critical clearing time in the system stability probability assessment are only conducted for very severe contingencies, an extremely small fraction of all considered contingencies. Hence, the computation efficiency has been remarkably enhanced. Case studies on a representation of the North China power system are reported to show that the proposed assessment strategy is effective and practical.     

On the preconditioners for fast multipole boundary element methods for 2D multi-domain elastostatics

Fast multipole method (FMM) has been successfully applied to accelerate the numerical solvers of boundary element method (BEM). However, the coefficient matrix implicitly formed by using FMM is sometimes ill-conditioned in cases when mixed boundary conditions exist, resulting in poor rate of convergence for iteration. So preconditioning is a critical part in the development of efficient FMM solver for BEM. In this paper, preconditioners based on sparse approximate inverse type are used for fast multipole BEM to deal with 2D elastostatics. Several sparsity patterns of the preconditioner are considered for single- and multi-domain problems, especially for 2D elastic body with large number of inclusions or cracks. Algorithms and cost analysis of preconditioning under different prescribed sparsity patterns are discussed. GMRES is used as the iterative solver. Numerical results show this type of preconditioner achieves satisfactory rate of convergence for fast multipole BEM and performs well for problems of fairly large sizes.     

Modeling, identification and control of air-conditioning systems

In this paper, feedback controller design for the air-conditioning system is addressed through systematic modeling and identification. Particularly, the physical model of the system reveals the key parameter that dictates energy efficiency, and the identification procedure produces a low-order, linear model suitable for controller design. The feedback controller employed is multi-input–multi-output-based and possesses a cascade structure for dealing with the fast and slow dynamics in the system. To determine appropriate control parameters, conditions that establish performance and stability of the cascade design are given. Experiments show that the controller can simultaneously achieve satisfactory transient response in the indoor temperature, and improve energy efficiency at steady state.     

A meshfree method for incompressible fluid dynamics problems

We show that meshfree variational methods may be used for the solution of incompressible fluid dynamics problems using the R‐function method (RFM). The proposed approach constructs an approximate solution that satisfies all prescribed boundary conditions exactly using approximate distance fields for portions of the boundary, transfinite interpolation, and computations on a non‐conforming spatial grid. We give detailed implementation of the method for two common formulations of the incompressible fluid dynamics problem: first using scalar stream function formulation and then using vector formulation of the Navier–Stokes problem with artificial compressibility approach. Extensive numerical comparisons with commercial solvers and experimental data for the benchmark back‐facing step channel problem reveal strengths and weaknesses of the proposed meshfree method. Copyright © 2003 John Wiley & Sons, Ltd.     

Stable Boundary and Internal Data Reconstruction in Two-Dimensional Anisotropic Heat Conduction Cauchy Problems Using Relaxation Procedures for an Iterative MFS Algorithm

We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. The iterative MFS algorithms with relaxation are tested for over-, equally and under-determined Cauchy problems associated with the steady-state anisotropic heat conduction in various two-dimensional geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the method.     

Failure prediction of a plate weakened by an elliptic hole under thermal or mechanical load

The failure initiation and crack trajectory are predicted for a plate weakened by an elliptic hole under thermal or mechanical load. The closed form solutions are obtained by using the complex variable theory and the fracture behavior is predicted by applying the strain energy density criterion. The results lead to a number of important conclusions. A general trend is that failure initiation always occurs at the site near the interface with material inhomogeneity while the fracture trajectory tends to spread away from the boundary of an elliptic hole whether thermal or mechanical loads are imposed in the given problem. Fracture initiation is most likely to take place at the site with relatively low temperature accompanied by the presence of tensile stress. Depending on material geometry, kinking phenomena are observed at the boundary layer adjacent to the interface. In general, the critical load in compression is larger than that in tension.     

脆性材料复合型裂纹的断裂准则

实际工程中,脆性材料中的裂纹多处于复合型受力状态,因此,确定脆性材料中的复合型裂纹起裂角和临界荷载有着重要的理论意义和实用价值。以复合型裂纹为研究对象,将裂纹尖端的最小无量纲塑性区尺度ρmin和广义合成偏应力强度理论相结合,建立脆性材料复合型裂纹的断裂准则,预测裂纹起裂角及临界荷载,将其结果与最大周向应力准则和应变能密度因子准则相比较发现,基于该文方法得到的临界荷载曲线大于最大周向应力准则得到的临界荷载曲线,与应变能密度因子准则得到的临界荷载曲线比较接近。因而,表明了用该文的方法来预测脆性材料复合型裂纹起裂角和临界荷载是行之有效的。