One-step decomposition method for numerical integration of short- and long-term dynamics

A mathematical model is derived and disdussed that represents the structural properties of the alternative linearity and of the triangular block structural connectivity of the sets of differential equations, associated with the machines in the numerical integration of short- and long-term dynamics. In order to take into consideration the structural properties of the model, a one-step decomposition method for the numerical integration of short- and long-term dynamics is proposed. The method can be applied not only to the numerical integration of short- and long-term dynamics but also to all other cases when the model of the dynamic system is alternative-linear and triangular block connected. Numerical stability, accuracy and computation speed are the major advantages of this method, making it suitable for many applications, including the dynamic security analysis of power systems.     

电力系统3阶解析解的推导及验证

推出基于模态级数法的电力系统动态方程3阶解析解，提出求解电力系统动态方程3阶偏导数的数值微分算法。分别在单机无穷大系统及4机2区域系统，应用2个指标定量对比1阶解析解、2阶解析解及3阶解析解在分析遭受大扰动电力系统动态特性的精确性；并应用prony算法检测数值积分曲线中3阶复合模式的存在。从而，验证采用该文推出的3阶解析解分析遭受大扰动时电力系统动态特性的有效性。     

A two-time scale simulation for dynamic analysis of power systems

This paper proposes a two-time scale simulation approach of both short-term and long-term dynamics in power systems. The short-term transient period is analyzed by a full-time scale simulation while a quasi-steady state model of the power system is used to simulate long-term dynamics. The proposed method is inspired of Singular Perturbation theory to model the interaction between the short-term and long-term dynamics. Based on this interaction, a suitable criterion to determine when the quasi-steady state model of a power system can be considered as a uniform approximation of the full-time scale model is proposed, which also determines the appropriate switching time between models. The proposed method is demonstrated on the 10-machine, 39-bus New England system and a 46-machine, 190-bus equivalent Mexican system.     

A decomposition method for the solution of the network equations of short-term dynamics of connected power systems,taking into consideration the axial asymmetry of the machines

In the numerical simulation of the short-term dynamics of power systems, mutual angles of machine rotors and other relevant state variables are observed for a period up to a few seconds after sudden and forced switching on and tripping of the machines, transmission lines, transformers and consumer buses. On the one hand the set of differential equations, which are associated with the machines, is numerically integrated, and on the other the set of algebraic equations, which are associated with the network, is solved. This paper presents a decomposition method for solving the network equations of short-term dynamics of connected power systems, taking into consideration the axial asymmetry of the machines.     

Fast algorithm for multiple time-scale simulation of power system using parallel processing

Power system analysis is the basis of operation and planning. Since power systems are very large and complex, however, long computation time is required for the analysis. Development of a fast calculation method for stability analysis is desirable. Recently, the method using multiple time-scale numerical integration algorithm was developed for analyzing long-term dynamics. This method has the problem of calculation time since the coefficient matrix is very large. It is expected that calculation time can be shortened using parallel processing. In order to increase the efficiency of parallel processing, the coefficient matrix must be divided since solution of a set of linear equations is the main part of stability analysis. In this paper, coefficient matrix is converted into BBDF matrix for effective calculation of parallel processing. Each subnetwork block can be divided again since it is sparse. The algorithm discussed in this paper was implemented on the nCUBE2S parallel processing computer system. The computing time is measured so that it can be compared to the computer time of a single-processor system. © 1997 Scripta Technica, Inc. Electr Eng Jpn, 120(4): 14–22, 1997     

A numerical integration method for long-term power system dynamic simulation

Large power system frequency/voltage fluctuations due to severe faults in trunk transmission lines or major generating units may trip-off other facilities and result in large-scale power system blackout. To prevent such blackout, development of an accurate and fast long-term power system dynamic simulation tool is required. With respect to the development stage, selection of a numerical integration method available for step-size adjustment, and the development of a scheme for the adjustment are principal subjects. The trapezoidal and the second-order Gear methods were selected as possible candidates for the step-size adjustment from the viewpoint of numerical stability. The trapezoidal method is selected from the viewpoint of accuracy and applicability to power system dynamic simulations. A new scheme for the automatic step-size adjustment is proposed for the trapezoidal method to achieve fast simulation of the long-term power system dynamics. The validity of the proposed scheme is verified through simulation studies on a single-machine-to-infinite bus system.     

电力系统全过程动态仿真的数值方法——电力系统全过程动态仿真软件开发之一

电力系统全过程动态仿真是把电力系统的机电暂态过程，中期过程和长期过程有机地统一起来进行仿真。其特点是实现快速的暂态过程和慢速的中长期动态过程的统一仿真。这是典型的刚性系统，需要采用具有自动变阶变步长技术的刚性数值积分方法。在分析了刚性系统求解实质的基础上，采用适用于求解刚性微分方程的数值积分方法－Gear法作电力系统全过程仿真软件的基本算法，并研究根据积分的截断误差控制进行自动变阶变步长技术，构造了基于Gear法的电力系统全过程仿真程序的总体结构。     

基于微分代数神经网络的含新能源区域电网端口动态特性学习方法

高比例新能源渗透背景下,建立能够准确描述复杂环境因素影响下含新能源的区域电网端口特性动态模型,对于新型电力系统动态分析至关重要。为此,提出了一种基于微分代数神经网络的含新能源区域电网端口动态特性学习方法。该方法利用微分代数神经网络,基于区域电网接入点的时序量测以及光照强度、温度等环境量测数据,学习以神经网络表达的端口特性模型。所得模型由初始状态提取模块、微分神经网络模块、代数神经网络模块组成,可直接接入电力系统暂态仿真器中,用于分析电力系统整体动态特性。在IEEE-39节点系统中对该方法进行仿真验证,测试结果表明：所得模型能够适应不同环境场景,准确率高,验证了方法的有效性。该建模方法仅依赖端口时序量测,在新型电力系统动态分析中具有较大的应用潜力。     

采用周期轨Poincaré映射的非线性电力电子系统小干扰稳定性分析

拓扑结构切换、占空比控制方法和非线性元件均可使电力电子系统具有非线性特性,因此其小干扰稳定问题属于微分方程周期轨的稳定问题。由于状态空间平均法误差较大、难以预测分叉,而数值仿真法物理概念不清晰,因此,提出了基于梯形积分法的非线性电力电子系统周期轨稳定性分析方法。利用梯形积分法描述系统占空比方程和每阶段的非线性状态方程,由隐函数求导法和链式求导法计算周期轨Poincaré映射的雅可比(Jacobian)矩阵,提出了系统稳定裕度指标,建立了基于周期轨Poincaré映射的非线性电力电子系统小干扰稳定性分析方法。该方法能够克服小干扰稳定传统分析方法的困难,揭示非线性电力电子系统失稳的动力系统机制。仿真分析验证了算法的有效性。     

电力系统全过程动态仿真技术的现状与展望

随着我国全国性交直流混联电力系统的形成,电力系统的动态特性变得更加复杂。全过程动态仿真能够将电力系统电磁暂态、机电暂态和中长期动态统一起来进行计算,是研究和分析这种非线性超大规模电力系统动态特性机理、事故特征及其安全稳定措施的重要技术手段。分析了电力系统全过程动态仿真技术的研发与应用现状、存在的技术难点,并对技术发展进行了预测,主要包括电磁暂态-机电暂态-中长期动态统一仿真的数值计算方法和建模技术。该文指出新型数值积分算法、适于多时间尺度仿真的直流输电建模方法、具有智能化和开放式与交互式的并行仿真软件开发方法等关键技术,可为大规模交直流互联电网的安全稳定、经济运行及新技术和新设备的应用研究等提供强有力的仿真工具。     

An approach to the evaluation of electromechanical transient processes in power systems

The paper presents an approach to the evaluation of electromechanical transient processes in power systems. On the basis of identification of the physical properties of the system considered, for an adequately chosen time interval, quasilinearization and decomposition of the original system of nonlinear differential equations into subsystems is performed. A linear transformation is introduced which transforms the state matrix of the sub-systems into diagonal form. These simplifications enable the use of numerical integration schemes based on difference state equations, which have an elementary form. As a result, a model is formed which is very suitable for numerical treatment. The integration is performed without numerical instability, quickly and effectively, with the desired simulation accuracy, and with low memory requirements.     

Fast solution method for evaluation of long-term dynamic processes in power systems with provision for island operation

A fast, simple and efficient solution method for evaluation of long-term dynamic processes in power systems with provision for island operation is proposed. The original systems of nonlinear differential equations that describe the dynamics of hydro and steam power plants, for a relatively large time step (1–2 s), are transformed into very simple decoupled difference (algebraic) equations, using linearization, decomposition, diagonalization and Cauchy's formula. This secures a fast, efficient and stable numerical integration process with low memory requirements. The differential equation, used for the evaluation of the dynamics of the uniform frequency change, is also transformed in an appropriate manner, while the resultant difference equation is further incorporated into the model of the electrical network. The full model formed in this way is simultaneously solved iteratively, using a specially developed fast decoupled procedure, which has very good and reliable convergence characteristics. The validity of the procedure developed is tested on analyses of the dynamic behavior of the Yugoslav power system, for the case of large multiple disturbances which lead to the interruption of the parallel operation with UCPTE.     

基于广义向后差分方法的电力系统暂态稳定性快速数值计算方法

为满足电力系统暂态稳定性实时分析计算的需求,将边界值类方法中的广义向后差分方法应用于暂态稳定性数值计算,提出了一种新的暂态稳定性快速数值计算方法。该方法利用广义向后差分方法对微分方程进行连续的时间差分离散,然后对离散后的非线性方程组采用牛顿法进行整体求解。利用雅克比矩阵所具有的带状结构特征,采用矩阵方程分裂—组合技巧,避免了对整体雅可比矩阵或多个分块子矩阵进行三角分解,从而提高了暂态稳定性数值计算的效率。对两个算例系统的测试结果表明:相对于经典的隐式梯形积分方法,所提出的算法在计算效率上具有明显的优势。     

复杂市场环境下区域电网安全校核机制架构设计

安全校核是保障区域电网安全运行和区域内电力市场正常运营的重要技术环节。当前区域电网范围内已呈现电力现货试点省与非试点省并存、省间交易电量与计划电量交织的复杂形态,倒逼电网运行组织者必须创新提出与之相适应的安全校核机制。首先总结分析国外典型单一市场形态下电力市场出清和跨市场/跨国电力交易的电网安全校核机制架构及其借鉴意义,揭示中国复杂市场环境下区域电网安全校核的现实基础、特殊约束与需求,在此基础上设计了与中国近期电力市场形态、现行电力调度管理体制、区域电网结构等相适应的跨省跨区电力中长期交易、区内各省日前市场预出清发电计划和非现货试点省日前发电计划的安全校核机制架构。对于跨省跨区电力中长期交易,提出了基于跨区交易电力曲线典型场景集的电力校核方法和提高安全校核频次的安全校核机制改进方案;针对构建区内日前发电计划安全校核机制,提出了适应复杂市场环境的3种可选择方案,在对比分析三者特点的基础上,给出了方案实施路径建议。     

基于自组织临界理论的南方电网停电事故宏观规律研究

采用自组织临界理论研究了中国南方电网发生事故的宏观规律,初步证明中国南方电网具有自组织临界性(SOC)的一些重要性质。一方面,利用变尺度(R/S)分析方法对比分析了北美和中国南方电网的事故符合幂次定律及其发展趋势,同时表明Hurst指数代表的事故发展趋势符合2个电网的实际情况;另一方面,以海南电网为研究对象,建立了模拟电力系统连锁故障的最优潮流方法(OPA)模型,并进行了数值模拟研究,揭示了其SOC特征。     

Boost变换器中的斜坡补偿法扩展及其性能评估

DC/DC开关变换器是一类强非线性控制系统,其中的混沌现象及混沌控制的研究是近年来电力电子领域中的一个研究热点.本文针对峰值电流模式控制Boost变换器的动力学模型,详细分析了斜坡补偿法控制混沌的原理,并将其扩展为多个周期信号的补偿方法,同时提出了混沌控制的综合评价标准,以对各种补偿信号的控制结果进行综合评估.评估结果表明:三角波补偿是一种较好的混沌控制手段,且理论分析可以给出有效控制的最优相移和幅度的预计,从而为变换器的稳定设计提供了理论指导,另外相关研究也给出了一般非线性系统中混沌控制的评估方案和思路.     

Block Diagrams: A Tutorial Alternative to Dynamical Analogies

Educational advantages and disadvantages of dynamical analogy and block-diagram models for interdisciplinary systems are discussed. If the system equations are known, a block-diagram is a useful tutorial alternative to the conventional dynamical analogy. It is easily drawn and yields a direct, graphical representation of the system equations with block elements that are not required to be physical elements of a specific discipline. Block diagrams illustrate system equations and processes quite differently from dynamical analogies and thereby provide new insights into system performance. They can also be used as alternative representations for linear circuits so that, in principle, it is possible to convert any dynamical analogy into a block diagram. A practical example is given wherein a combined electrical, mechanical, and acoustical system, normally studied using dynamical analogies, is modeled and analyzed with the aid of block diagrams Several interesting technical aspects of this specific, yet typical, interdisciplinary system are assessed.     

A Unified Approach to the Sizing and Control of Energy Storage Systems

Grid operation and planning challenges arising out of large-scale integration of renewable power can to a large extent be solved by the use of energy storage systems (ESSs). The type and size of storage to be used may be decided by the amount of fluctuating power the storage charges or discharges to attain its objective. Storage systems can be used as single devices or as hybrid systems where two or more devices complement the working of each other. The objective of this paper is to find an accurate power and energy sizing methodology for storage devices working in a single or hybrid arrangement such that the power fed to the grid from a wind turbine generator is regulated to a constant value. A strategy for sizing of a hybrid ESS is proposed by choosing the long-term storage to be a battery energy system and the short-term device to be a flywheel and using frequency analysis techniques. In the case of flywheel energy storage system, the inertia and the gain of an integral controller applied to an induction-machine-based flywheel are obtained. The simulations are done in MATLAB.     

Expansion Planning for Renewable Integration in Power System of Regions with Very High Solar Irradiation

In this paper, we address the long-term generation and transmission expansion planning for power systems of regions with very high solar irradiation. We target the power systems that currently rely mainly on thermal generators and that aim to adopt high shares of renewable sources. We propose a stochastic programming model with expansion alternatives including transmission lines, solar power plants (photovoltaic and concentrated solar), wind farms, energy storage, and flexible combined cycle gas turbines. The model represents the long-term uncertainty to characterize the demand growth, and the short-term uncertainty to characterize daily solar, wind, and demand patterns. We use the Saudi Arabian power system to illustrate the functioning of the proposed model for several cases with different renewable integration targets. The results show that a strong dependence on solar power for high shares of renewable sources requires high generation capacity and storage to meet the night demand.