Power system transient stability simulation under uncertainty based on Taylor model arithmetic

The Taylor model arithmetic is introduced to deal with uncertainty.The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model(TM).Thus,time domain simulation under uncertainty is transformed to the integration of TM-based differential equations.In this paper,the Taylor series method is employed to compute differential equations;moreover,power system time domain simulation under uncertainty based on Taylor model method is presented.This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation.It is computationally fast compared with the Monte Carlo method,which is another technique for uncertainty analysis.The proposed method has been tested on the 39-bus New England system.The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.

Real-time transient stability assessment in power system based on improved SVM

Due to the strict requirements of extremely high accuracy and fast computational speed, real-time transient stability assessment(TSA) has always been a tough problem in power system analysis.Fortunately, the development of artificial intelligence and big data technologies provide the new prospective methods to this issue, and there have been some successful trials on using intelligent method, such as support vector machine(SVM) method.However, the traditional SVM method cannot avoid false classification, and the interpretability of the results needs to be strengthened and clear.This paper proposes a new strategy to solve the shortcomings of traditional SVM,which can improve the interpretability of results, and avoid the problem of false alarms and missed alarms.In this strategy, two improved SVMs, which are called aggressive support vector machine(ASVM) and conservative support vector machine(CSVM), are proposed to improve the accuracy of the classification.And two improved SVMs can ensure the stability or instability of the power system in most cases.For the small amount of cases with undetermined stability, a new concept of grey region(GR) is built to measure the uncertainty of the results, and GR can assessment the instable probability of the power system.Cases studies on IEEE 39-bus system and realistic provincial power grid illustrate the effectiveness and practicability of the proposed strategy.

A transient energy function for power systems including the induction motor model

A construction method for power system transient energy function is studied in the paper, which is simple and universal, and can unify the forms of some current en- ergy functions. A transient energy function including the induction motor model is derived using the method. The unintegrable term is dealt with to get an approxi- mate energy function. Simulations in a 3-bus system and in the WSCC 4-generator system verify the validity of the proposed energy function. The function can be applied to direct transient stability analysis of multi-machine large power systems and provides a tool for analysis of the interaction between the generator angle stability and the load voltage stability.

Solution of Delay Differential Equations Using a Modified Power Series Method

This paper presents a Modified Power Series Method (MPSM) for the solution of delay differential equations. Unlike the traditional power series method which is applied to solve only linear differential equations, this new approach is applicable to both linear and nonlinear problems. The method produces a system of algebraic equations which is solved to determine the coefficients in the trial solution. The method provides the solution in form of a rapid convergent series. The obtained results for numerical examples demonstrate the reliability and efficiency of the method.

基于隐式Taylor级数法的电力系统暂态稳定计算

基于快速高阶Taylor级数法暂态稳定计算,结合隐式积分梯形公式,推导了隐式Taylor级数法。对该方法的数值稳定性进行了分析,得到了一种可调谐的隐式Taylor级数法。该方法保留了显式Taylor级数法准确、快速、递推和编程简单的优点,并明显提高了数值计算稳定性。分析与计算表明,该方法具有隐式积分数值稳定性好、可以采用较大的积分步长、能够适应较长动态过程仿真计算的特点,同时又具有显式积分编程简单可靠、便于扩展的优点。

快速高阶Taylor级数法暂态稳定计算

本文从解析发电机节点入手,分析和研究了发电机与系统网络座标系之间座标变换矩阵的导数规律。并结合因子表技术,得到了在计及发电机暂态凸极效应的情况下,发电机与系统网络接口处各种时变量的各阶导数的递推公式,形成了快速高阶Taylor级数法暂态稳定计算方法。分析和计算结果表明该方法具有准确、快速和递推的优点,在电力系统暂态稳定计算与分析中有很大的实用价值。

基于能量函数高阶Taylor级数展开技术的直接法

本文提出了一种基于能量函数高阶Ｔａｙｌｏｒ级数展开技术的电力系统暂态稳定性直接法。该方法首先推导出动能、势能和总能量的各阶导数，然后形成动能、势能和总能量的高阶Ｔａｙｌｏｒ级数展开式，井在此基础上快速求取临界故障切除时间。实例分析表明，本文方法具有准确度高、速度快的特点，可以用于电力系统暂态稳定性的快速分析。

基于移相器统一特性和高阶Taylor级数展开技术的暂态稳定计算方法

根据移相器的共同性质，对暂态稳定计算中的移相器作了统一处理，得出了移相器支路对网络节点导纳矩阵影响的统一形式。将此形式与高阶Taylor级数展开技术相结合，形成了能灵活统一地处理各种移相器并具有快速计算能力的暂态稳定计算方法。

多步高阶Taylor级数暂态稳定最优积分格式

研究了多步高阶Taylor级数暂态稳定方法。在算法步数、阶数和精度确定的情况下,根据其计算量特点设计部分权系数为零,依据算法的收敛性和稳定性要求求取部分权系数,从而给出多步高阶Taylor级数法最优积分格式准则。应用所提准则设计2步2阶算法最优积分格式。算例结果验证了最优算法相对于普通多步高阶方法及单步高阶方法在稳定性和快速性上的提升。

Taylor级数法暂态稳定计算中阶数的动态控制

在对Taylor级数法暂态稳定计算的计算量进行定量分析的基础上，根据计算精度的要求，提出了Taylor级数法暂态稳定计算中阶数的动态控制。分析与计算结果表明，由于在计算过程中按计算精度的要求动态选取求导阶数，从而在保证计算精度的前提下，有效地提高了Taylor级数法暂态稳定计算的解算效益，具有实用价值。

多群模式Taylor级数法暂态稳定计算

Taylor级数法自引入到电力系统暂态稳定分析领域以来,因其高效的计算效率而倍受青睐,但其求解的是不等值N机系统的微分方程,因此计算效率未发挥到极致。文中从减少微分方程个数角度,借助于同调分群技术得出多群模式等值参数,并推导了多群模式下发电机的电磁功率、功角新的Taylor级数表达式,该方法保留了Taylor级数简洁、循环递推的特点,具有更高的计算效率。新英格兰10机系统算例分析表明:采用等值参数的多群模式Taylor级数法,在保持准确性的同时,减少了模拟的微分方程个数,极大提高了暂态稳定分析效率。

基于Taylor级数轨迹灵敏度的动态安全域求解

动态安全域(DSR)是电力系统稳定分析的重要内容,实用动态安全域(PDSR)由描述各节点注入功率上、下限的垂直于坐标轴的超平面和描述暂态稳定性临界点的超平面围成。结合轨迹灵敏度法和高阶Taylor技术,推导轨迹灵敏度的高阶Taylor级数递推求解形式。基于势能界面(PEBS)法和高阶Taylor级数轨迹灵敏度技术,快速有效地计算能量裕度灵敏度,从而迭代求解临界功率注入点。利用临界功率点的能量裕度灵敏度数值,求解电力系统有功功率注入空间上的PDSR。New England 10机39节点系统的仿真结果验证了所提方法的有效性。

变阶多步Taylor级数法暂态稳定并行计算

多步高阶Taylor级数法是电力系统暂态稳定分析的有效工具,但其尚未实现灵活阶数控制和并行计算技术相结合,因此Taylor级数法有待于进一步改进。基于数值稳定域理论,构造了具有较好稳定域的多步变阶Taylor级数法,并结合电力系统暂态稳定仿真计算特点,根据计算精度要求实现Taylor级数阶数的灵活控制;同时提出了结合并行技术的高阶Taylor级数的空间并行暂态稳定分析方法。New England 10机39节点算例验证了所提方法数值稳定性好,能消除固定阶数多步Taylor级数法计算冗余,和并行计算结合能有效提高暂态稳定分析效率。

基于Taylor级数法动态步长控制的暂态能量函数法

势能边界面PEBS(PotentialEnergyBoundarySurface)法是暂态能量函数法的一种,将Taylor级数法暂态稳定计算的动态步长控制应用到PEBS法中,可以大步长的模拟持续故障轨迹,减小模拟区间数,提高计算效率,同时也可以满足计算精度的要求。计算结果表明,Taylor级数法暂态稳定计算的动态步长控制有效地提高了PEBS法的解算效益。

隐式Taylor级数暂态稳定计算变步长方法初探

隐式调谐Taylor级数暂态稳定算法是一种具有A稳定性的高精度时域仿真算法。为了进一步改善算法的性能,文中在该算法基础上利用其基于预估-校正迭代格式的特点对其暂态稳定计算步长进行动态控制。该方法充分利用其实现过程中迭代格式的特点,在不增加额外计算量的基础上实现了变步长算法。计算与分析结果表明,该步长的动态控制方法很好地利用了原算法具有A稳定性可进行大步长计算的特点,既保持了算法的高精度优点,又显著提高了计算速度,进一步提升了算法的实用价值。

多维导数阶数控制的多步Taylor级数暂态稳定计算方法

为提高电力系统暂态稳定分析效率,本文提出了多维阶数控制的多步Taylor级数暂态稳定快速计算方法。该方法基于多步Taylor级数展开理论,针对不同时间常数的机组及不同积分时刻的机组转角状态量,根据时域仿真计算精度建立了转角状态量的高阶导数阶数差异化控制策略,并从理论上分析了忽略部分高阶导数对转角轨迹的影响。所提方法可实现状态变量时间和空间上的动态多维导数阶数控制,消除常规Taylor级数法暂态稳定分析的计算冗余。New England 10机39节点算例仿真验证了所提方法可灵活方便地实现Taylor级数法的时空多维阶数控制,能有效提高暂态稳定分析效率。

可调谐的隐式Taylor级数暂态稳定算法的变步长研究

可调谐的隐式Taylor级数暂态稳定算法是在隐式Taylor级数法的基础上,通过合理设置参数位置及其大小得到的一种具有A稳定性和高精度特点的优秀暂态稳定分析算法。通过分析故障时发电机功角曲线的变化规律和定义曲线变化因子,并根据曲线变化因子不断调整步长,提出一种新的变步长方法,在满足计算精度的条件下,可进一步提高算法的计算效益。

STABILITY ANALYSIS OF VISCOELASTIC CURVED PIPES CONVEYING FLUID

Based on the Hamilton' s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.

A New One-Twelfth Step Continuous Block Method for the Solution of Modeled Problems of Ordinary Differential Equations

In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.

Alleviating Bottlenecks in Power Interconnectors by Means of FACTS

Power interconnections are becoming increasingly important in various parts of the world, as incentives for power exchange between countries are growing. A current example is that the Baltic Energy Market Interconnection Plan is launched by the European Council. For a variety of reasons, it is desirable to keep transmission corridors as slender as possible, i.e. keeping the number of lines as limited as possible, while still keeping adequate stability and power transmission capacity over the corridor. This is true, no matter whether it concerns a green-field project, or if it is a question of expanding an existing transmission corridor into higher power transmission capability. To achieve this, FACTS （flexible AC transmission systems）, based on state of the art high power electronics, is a highly useful option, from technical, economical and environmental points of view, to increase the utilization and stability of a transmission system or intertie. The paper presents salient design features as well as benefits of recently installed FACTS devices, more specifically SVC （static var compensators） and series capacitors, for enabling or improving cross-border as well as interregional power transfer in a cost-effective and environmentally friendly way.