Distributed Transient Stability Simulation of Power Systems Based on a Jacobian-Free Newton-GMRES Method

As power systems becoming more closely interconnected and are being deregulated in energy markets, distributed simulations among different dispatch centers are highly required for online full system analysis and control applications. In this paper a new algorithm for distributed transient stability simulation of interconnected power systems is presented. Based on a Jacobian-free Newton-GMRES(m) method, this algorithm requires only exchanges of states of boundary buses among different regions. Therefore, it has strong scalability in distributed computing environments built on heterogeneous computing resources. Moreover, several accelerating methods are developed to enhance its efficiency, including continuous preconditioning with adaptive preconditioners, predicting boundary conditions and multistep coordination. The standard IEEE 39-bus system and a real power system with 1165 buses were used as test systems. The test results show that these accelerating methods greatly enhance the convergence rate of the proposed algorithm and reduce communication costs remarkably, which proves the novel algorithm is feasible and can be adopted in wide area networks with high-latency.      

基于Jacobian-Free Newton-GMRES(m)方法的电力系统分布式暂态仿真算法

分布式暂态仿真是实现市场环境下互联电力系统在线一体化仿真分析的有效途径.文中研究了电力系统分布式暂态仿真计算模型,提出了基于Jacobian-Free Newton-GMRES(m)方法的协调求解算法.该算法只需要交换边界母线状态信息,接口简单,实用性强.为了提高算法收敛速度,减少协调求解所需通信次数,提出了自适应预处理和连续修正预处理矩阵、预估边界条件初值及多时步同时协调等改进方法并将其应用于新算法中.测试结果表明,新的暂态仿真分解协调算法收敛快,通信次数少,非常适合在基于广域网络的分布式环境中实现.     

Solving the nonlinear power flow equations with an inexact Newtonmethod using GMRES

This paper presents a detailed investigation into the effectiveness of iterative methods in solving the linear system subproblem of a Newton power flow solution process. An exact Newton method employing an LU factorization has been one of the most widely used power flow solution algorithms, due to the efficient minimum degree ordering techniques that attempt to minimize fill-in. However, the LU factorization remains a computationally expensive task that can be avoided by the use of an iterative method in solving the linear subproblem. An inexact Newton method with a preconditioned Generalized Minimal Residual (GMRES) linear solver is presented as a promising alternative for solving the power flow equations. When combined with a good quality preconditioner, the Newton-GMRES method achieves a better than 50% reduction in computation, compared to Newton-LU, for two large-scale power systems: one with 3493 buses and 6689 branches, another with 8027 buses and 13765 branches     

基于局部几何参数化和JFNG算法的微电网群分布式连续潮流计算

由于分布式电源、电动汽车等新型电气化负荷内存在无功限幅约束,传统连续潮流在分析微电网的带负荷能力和微电网之间的联络能力时存在因错误识别节点类型而导致计算失败的现象,并且其不适配于微电网群的分布式管理模式。提出一种局部几何参数化连续潮流算法,相较于弧长参数化,该算法具有参数化方程易于解耦、分岔点计算精度较高等优点;采用费舍尔伯明斯特互补函数来处理非光滑无功限幅特性,避免节点类型频繁切换的问题。基于连续潮流模型,结合非精确牛顿-广义最小残差(JFNG)算法分布式框架,提出仅交换边界信息就可收敛的微电网群分布式连续潮流算法。算例结果验证了所提算法的有效性。     

基于子空间迭代法的快速N-1潮流计算方法研究

为提高N-1潮流计算的求解速度,提出基于子空间迭代法的快速N-1潮流计算方法。对初始潮流的雅克比矩阵进行不完全LU分解,得到固定的预条件子,应用结合了自适应GMRES(m)法的牛顿法求解N-1潮流。自适应GMRES(m)算法是GMRES算法的改进,能自动调节重启参数值,进一步提高算法收敛速度。对IEEE118、IEEE300、2383wp电力系统的仿真证明了基于子空间迭代法的快速N-1潮流计算方法的有效性。算例结果表明,自适应GMRES(m)算法能快速求解大规模线性方程组,适用于大规模系统的N-1潮流问题。     

基于改进Jacobian-Free Newton-GMRES(m)的电力系统分布式潮流计算

为了提高互联电网分布式潮流算法的实用性,应尽可能减少协调计算中的交换信息.文中采用隐函数方式表示分布式潮流的边界协调方程,并采用具有自适应预处理能力的Newton-GMRES(m)方法构建分解协调算法.该方法具有Jacobian-Free特性,协调计算中只需要交换边界节点状态信息.以IEEE标准系统和大规模实际系统为算例的测试结果表明,新的分布式潮流算法具有较高的收敛性,数据交换接口简单,实用性强,适合于求解连续变化的分布式潮流问题.     

Optimization of distributed generation systems using a new discrete PSO and OPF

Many methods have been applied to achieve optimal site and size of distributed generation systems. This paper introduces a new hybrid method, which employs discrete particle swarm optimization and optimal power flow to overcome this shortcoming. The main technical constraints are imposed for utilities, which could apply this approach to search the best sites to connect distributed generation systems in a distribution network choosing among a large number of potential combinations. A fair comparison between the proposed algorithm and other methods is performed. For such goal, convergence curves of objective function versus number of iterations are computed. The proposed algorithm reaches a better solution than Genetic Algorithms considering similar number of evaluations.     

基于分解协调的分布式动态潮流计算方法研究

考虑负荷和发电机调节特性的动态潮流是EMS和DTS系统的基础功能之一.采用分解协调方式的多调度中心间分布式动态潮流计算是全网在线一体化潮流分析的一种新的途径.本文以隐函数形式的边界协调方程对全网动态潮流方程协调求解问题建模.该模型可统一考虑边界节点功率平衡和不平衡功率在分区电网间的合理分配问题.进一步,本文采用Jacobian Free NewtonGMRES方法实现协调求解过程.广域网络通信环境中的测试结果表明所提算法通信接口简单、通信次数较少,能够满足在线应用的需求.     

配电网区间线性三相潮流的非迭代仿射求逆计算方法

现有配电网区间潮流计算大多是以迭代法为基础扩展得到的,需要进行多次区间迭代以获取收敛的潮流解,因而存在收敛性和计算效率低下问题。为此,文中将线性三相潮流算法与仿射求逆方法相结合,提出了一种配电网区间线性三相潮流的非迭代仿射求逆计算方法。所提方法采用仿射数描述区间变量间的相关性,将潮流方程转化为仿射线性潮流方程,并引入仿射矩阵求逆方法对其进行求解。该方法无须迭代,不存在收敛性问题。最后采用多个三相不平衡系统作为算例,通过与其他3种方法的分析比较,验证了所提算法的性能。结果表明,所提算法兼具高效性和低保守性优点,且性能稳定。     

对分布式潮流协调计算收敛机理的一种新分析

异步迭代模式下的分布式潮流分解协调计算外层迭代格式的构造取决于对分解协调计算收敛机理的分析和认识。将基于同心松弛概念的池塘理论加以扩展,用来分析边界等值注入误差在潮流计算中对各节点产生的影响。在此思路下提出了4个铺垫引论,据其对分解协调算法的收敛机理从同心松弛概念这一新角度做出了理论分析,并在此基础上提出了确定协调计算合并参数的新方法——直接选取法,再将其和原有方法进行了比较讨论,给出了已有的对收敛机理理论解释之间的联系。IEEE9、39、118节点系统上进行的数值仿真实验验证了本文的分析以及直接选取法的优点。     

基于改进多中心校正解耦内点法的动态最优潮流并行算法

基于改进的多中心校正(MCC)和解耦技术,提出一种求解动态最优潮流(DOPF)的并行算法。结合内点算法(IPM)框架与DOPF修正方程的分块箭形结构,给出修正方程的并行解耦-分解-回代解法。并结合这一解法特点,提出动态步长拉大技术及自适应最大校正次数技术,以单次迭代计算量小幅增加为代价,换取迭代步长的增大,迭代点中心性的提高,总迭代次数和计算时间的显著减少。解耦技术的使用,使得所提算法的核心计算都可并行完成。6～118节点系统的串行仿真结果表明,算法具有很好的鲁棒性和收敛速度,在多核集群系统上的并行仿真表明,算法具有理想的加速比和可扩放性,适合求解大规模的DOPF问题。     

基于改进多目标粒子群算法的有源配电网储能优化配置

储能系统可解决分布式电源加入配电网所产生的不良影响,而储能系统的合理配置是其有效应用的前提。以电网脆弱性衡量指标、有功网损、储能额定容量三个方面,考虑规划与运行之间的耦合性建立储能系统在有源配电网中的多目标选址定容模型。提出改进的多目标粒子群算法用于求解。该算法在种群更新过程中引入准对立学习策略以增强解的覆盖范围和收敛速度,并根据迭代次数采用自适应分裂策略分离过早聚集的粒子,从而增强粒子多样性,保证了算法跳出局部最优的能力。通过在IEEE33节点配电系统上进行分析,验证了所提模型及算法在优化分布式储能选址定容及运行策略中的合理性,并能有效改善电网的运行经济性与脆弱性,具有更强的全局寻优能力。     

Decomposition-coordination interior point method and its application to multi-area optimal reactive power flow

A decomposition-coordination interior point method (DIPM) is presented and applied to the multi-area optimal reactive power flow (ORPF) problem in this paper. In the method, the area distributed ORPF problem is first formed by introducing duplicated border variables. Then the nonlinear primal dual interior point method (IPM) is directly applied to the distributed ORPF problem in which a Newton system with border-matrix-blocks is formulated. Finally the overall ORPF problem is solved in decomposition iterations with the Newton system being decoupled. The proposed DIPM inherits the good performance of the traditional IPM with a feature appropriate for distributed calculations among multiple areas. It can be easily extended to other distributed optimization problems of power systems. Numeric results of five IEEE Test Systems are demonstrated and comparisons are made with those obtained using the traditional auxiliary problem principle (APP) method. The results show that the DIPM for the multi-area OPRF problem requires less iterations and CPU time, has better stability in convergence, and reaches better optimality compared to the traditional auxiliary problem principle method.     

基于预处理BICGSTAB法的电力系统潮流并行计算方法

为实现大规模电力系统潮流的准确、快速求解,以非精确牛顿法为基础,提出一种基于CPU-GPU异构平台的电力系统潮流并行计算方法。修正方程组的求解是牛拉法潮流计算中最为耗时的部分,提升修正方程组的求解效率可有效提升潮流计算效率。为此,根据雅可比矩阵的不对称不定性,采用稳定双正交共轭梯度(bi-conjugate gradient stabilized, BICGSTAB)法进行修正方程组的求解。进一步,为改善BICGSTAB法的收敛性,根据雅可比矩阵的稀疏性和类对角占优性,提出一种改进PPAT(Preconditioner with sparsity Pattern of AT, PPAT)预处理器和改进Jacobi预处理器相结合的两阶段预处理方法,并对雅可比矩阵进行预处理,提升BICGSTAB法的收敛性能。然后,将上述潮流算法移植到CPU-GPU异构平台,实现电力系统潮流的并行求解。最后,通过不同测试系统算例对所提方法进行验证、分析。结果表明,所提潮流并行计算方法可实现电力系统潮流的准确、快速求解。     

Critical investigation of preconditioned GMRES via incomplete LU factorization applied to power flow simulation

For solving the power flow sublinear problem efficiently by the GMRES preconditioned via incomplete LU factorization (ILU), this paper investigates causes associated to the preconditioner low quality and proposes a method to improve it and the GMRES convergence rate as well. The goal is provide a well-organized ILU-GMRES for solving linear systems of difficult solution comprising ill-conditioned coefficient matrices, normally associated to heavy load power systems. The investigations reveal that a dropping rule for nonzero elements (fill-ins) based on a relative tolerance may introduce large errors during the preconditioner construction, lowering its quality and the GMRES performance. Based on that, it is proposed a fill-in dropping rule making use of two criteria; one based on the resulting error and the other based on a relative tolerance, applied to the preconditioner lower (L) and upper (U) triangular matrices, respectively. Ordering schemes are also considered. Numerical experiments taking into account different power system configurations operating under heavy load conditions corroborate the efficiency of such strategies.     

基于网络分割的电力系统潮流分解协调计算

因现有计算模式的速度已无法满足现代大规模电力系统实时计算的要求,故引入对等计算(P2P)模式以提供低廉而充足的计算力。为此研究了网络计算环境下的电力系统潮流计算模型,结合基于支路切割的网络分割方法和基于注入电流的潮流模型,提出了基于网络分割的电力系统潮流分解协调算法,将大规模互联电力系统分解成若干子网络,子网络间只需交换边界母线的电压状态就可完成分布式潮流计算,保证各个子网络潮流计算模型的独立性。对IEEE标准系统进行潮流计算的结果表明该法具有较高的收敛速度和计算精度,适合网络计算环境。     

Assessment of branch outage contingencies using the continuation method

This paper provides a contribution to the contingency analysis of electric power systems under steady state conditions. An alternative methodology is presented for static contingency analyses that only use continuation methods and thus provides an accurate determination of the loading margin. Rather than starting from the base case operating point, the proposed continuation power flow obtains the post-contingency loading margins starting from the maximum loading and using a bus voltage magnitude as a parameter. The branch selected for the contingency evaluation is parameterised using a scaling factor, which allows its gradual removal and assures the continuation power flow convergence for the cases where the method would diverge for the complete transmission line or transformer removal. The applicability and effectiveness of the proposed methodology have been investigated on IEEE test systems (14, 57 and 118 buses) and compared with the continuation power flow, which obtains the post-contingency loading margin starting from the base case solution. In general, for most of the analysed contingencies, few iterations are necessary to determine the post-contingency maximum loading point. Thus, a significant reduction in the global number of iterations is achieved. Therefore, the proposed methodology can be used as an alternative technique to verify and even to obtain the list of critical contingencies supplied by the electric power systems security analysis function.     

Fault Current Limiter Placement Using Multi-Objective Firework Algorithm

This paper presents a method for determining the optimum number, impedance, and locations of fault current limiter (FCL) to reduce the negative impact of distributed generations presence in the power systems such as increasing the short circuit current levels and improve the system reliability. In the considered method, we have modeled the FCL placement as an optimization problem while the objectives are; bus fault current difference, reliability, the number and impedance of FCLs. Moreover, to solve the proposed problem, a new multi-objective optimization algorithm based on firework algorithm namely multi-objective firework algorithm has been implemented. In the new algorithm, several iterations have been considered, and the non-dominated solutions are extracted and stored in an external repository in the iterations. Finally, a fuzzy clustering technique is used to control the size of the repository during the algorithm evolution. The proposed approach is tested on two different systems, namely, Roy Billinton Test System (RBTS) 2 and RBTS 4 test system. The obtained results demonstrate the effectiveness and feasibility of the new method.     

考虑自适应虚拟阻抗的微电网分布式功率控制策略

针对低压微电网中,采用传统有功功率—电压幅值下垂控制的分布式电源在阻抗不匹配时难以按照下垂系数合理分配负荷有功功率的问题,提出了一种基于自适应虚拟阻抗的分布式功率控制策略,有效补偿了不匹配的馈线阻抗引起的电压降差异,实现了负荷功率的合理分配。所提策略基于多智能体一致性理论,构建了分布式的控制结构,各分布式电源仅需使用本地和相邻电源的功率信息对虚拟阻抗的模进行自适应调节,避免了对全局信息的依赖。通信网络拓扑中包含生成树的系统需求易于通过稀疏网络实现。同时,根据输出功率因数调节虚拟阻抗的阻抗角,增强了系统的鲁棒性。仿真结果证明了所提策略的有效性和可行性。     

预条件处理CG法大规模电力系统潮流计算

研究了预条件处理的CG(ConjugateGradient)法求解大规模电力系统潮流方程的问题。采用预处理CG法代替传统的LU直接法对高维稀疏潮流方程进行求解,详细比较各种预条件处理技术对CG法潮流方程求解的效果,提出一种新的节点优化排序的IncompleteCholesky预处理方法,实验分析证明它是CG法快速求解潮流的一种十分有效的预处理方法。对IEEE-30、IEEE-118和多个合成的大规模电力系统进行潮流计算,结果表明:这种预处理方法比其它预处理方法需要更少的迭代次数和浮点运算次数,对超大规模电力系统潮流问题也比传统LU直接法更具速度和存储优势。在电力系统互联程度不断增加使其潮流计算面临大规模甚至超大规模计算压力时,该方法能够成为传统方法的一个替代。