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...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。展开更多
A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special tec...A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special technique of only storing non-zero elements is carried out. The incomplete LU factorization without fill-ins is adopted to reduce the condition number of the coefficient matrix. The BiCGSTAB algorithm is extended from the real system to the complex system and it is used to solve the preconditioned complex linear equations. The locked-rotor state of a single-sided linear induction machine is simulated by the software programmed with the finite element method and the PBiCGSTAB algorithm. Then the results are compared with those from the commercial software ANSYS, showing the validation of the proposed software. The iterative steps required for the proposed algorithm are reduced to about one-third, when compared to the BiCG method, therefore the algorithm is fast.展开更多
The reliability of BiCGStab and IDR solvers for the exponential scheme discretization of the advection-diffusion-reaction equation is investigated.The resulting discretization matrices have real eigenvalues.We conside...The reliability of BiCGStab and IDR solvers for the exponential scheme discretization of the advection-diffusion-reaction equation is investigated.The resulting discretization matrices have real eigenvalues.We consider BiCGStab,IDR(S),BiCGStab(L)and various modifications of BiCGStab,where S denotes the dimension of the shadow space and L the degree of the polynomial used in the polynomial part.Several implementations of BiCGStab exist which are equivalent in exact arithmetic,however,not in finite precision arithmetic.The modifications of BiCGStab we consider are;choosing a random shadow vector,a reliable updating scheme,and storing the best intermediate solution.It is shown that the Local Minimal Residual algorithm,a method similar to the“minimize residual”step of BiCGStab,can be interpreted in terms of a time-dependent advection-diffusion-reaction equation with homogeneous Dirichlet boundary conditions for the residual,which plays a key role in the convergence analysis.Due to the real eigenvalues,the benefit of BiCGStab(L)compared to BiCGStab is shown to be modest in numerical experiments.Non-sparse(e.g.uniform random)shadow residual turns out to be essential for the reliability of BiCGStab.The reliable updating scheme ensures the required tolerance is truly achieved.Keeping the best intermediate solution has no significant effect.Recommendation is to modify BiCGStab with a random shadow residual and the reliable updating scheme,especially in the regime of large P´eclet and small Damk¨ohler numbers.An alternative option is IDR(S),which outperforms BiCGStab for problems with strong advection in terms of the number of matrix-vector products.The MATLAB code used in the numerical experiments is available on GitLab:https://gitlab.com/ChrisSchoutrop/krylov-adr,a C++implementation of IDR(S)is available in the Eigen linear algebra library:http://eigen.tuxfamily.org.展开更多
复合材料的高电阻率会影响飞机原有的导电路径,为保障飞机电气系统的正常运行,需要构建复合材料飞机电气结构网络系统模型来探究其电气特性。首先,针对电磁场下电气结构网络电气特性的计算问题,采用有限元法与稳定双共轭梯度法共同构建...复合材料的高电阻率会影响飞机原有的导电路径,为保障飞机电气系统的正常运行,需要构建复合材料飞机电气结构网络系统模型来探究其电气特性。首先,针对电磁场下电气结构网络电气特性的计算问题,采用有限元法与稳定双共轭梯度法共同构建了电气结构网络系统模型,计算空间消耗量比部分元等效电路(Partial Element Equivalent Circuit,PEEC)法节省了63.92%。其次,通过对多类型激励源/多区域接入点组合的探究,分析了区域阻抗特性、电势分布图谱、电流密度矢量等多维度电学结果及性能影响。通过构建与测量实物模型,对实测结果与仿真结果进行了差异化分析,并验证了实测结果符合适航规章HB 6129。最后,基于实际工况角度与适航规章,对系统模型进行了接触因素系统误差分析、精细化理想模型分析和部件应力因素分析。所获结果及分析对复合材料飞机/电动飞机的电气结构网络的构建具有重要意义。展开更多
文摘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。
文摘A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special technique of only storing non-zero elements is carried out. The incomplete LU factorization without fill-ins is adopted to reduce the condition number of the coefficient matrix. The BiCGSTAB algorithm is extended from the real system to the complex system and it is used to solve the preconditioned complex linear equations. The locked-rotor state of a single-sided linear induction machine is simulated by the software programmed with the finite element method and the PBiCGSTAB algorithm. Then the results are compared with those from the commercial software ANSYS, showing the validation of the proposed software. The iterative steps required for the proposed algorithm are reduced to about one-third, when compared to the BiCG method, therefore the algorithm is fast.
文摘The reliability of BiCGStab and IDR solvers for the exponential scheme discretization of the advection-diffusion-reaction equation is investigated.The resulting discretization matrices have real eigenvalues.We consider BiCGStab,IDR(S),BiCGStab(L)and various modifications of BiCGStab,where S denotes the dimension of the shadow space and L the degree of the polynomial used in the polynomial part.Several implementations of BiCGStab exist which are equivalent in exact arithmetic,however,not in finite precision arithmetic.The modifications of BiCGStab we consider are;choosing a random shadow vector,a reliable updating scheme,and storing the best intermediate solution.It is shown that the Local Minimal Residual algorithm,a method similar to the“minimize residual”step of BiCGStab,can be interpreted in terms of a time-dependent advection-diffusion-reaction equation with homogeneous Dirichlet boundary conditions for the residual,which plays a key role in the convergence analysis.Due to the real eigenvalues,the benefit of BiCGStab(L)compared to BiCGStab is shown to be modest in numerical experiments.Non-sparse(e.g.uniform random)shadow residual turns out to be essential for the reliability of BiCGStab.The reliable updating scheme ensures the required tolerance is truly achieved.Keeping the best intermediate solution has no significant effect.Recommendation is to modify BiCGStab with a random shadow residual and the reliable updating scheme,especially in the regime of large P´eclet and small Damk¨ohler numbers.An alternative option is IDR(S),which outperforms BiCGStab for problems with strong advection in terms of the number of matrix-vector products.The MATLAB code used in the numerical experiments is available on GitLab:https://gitlab.com/ChrisSchoutrop/krylov-adr,a C++implementation of IDR(S)is available in the Eigen linear algebra library:http://eigen.tuxfamily.org.
文摘复合材料的高电阻率会影响飞机原有的导电路径,为保障飞机电气系统的正常运行,需要构建复合材料飞机电气结构网络系统模型来探究其电气特性。首先,针对电磁场下电气结构网络电气特性的计算问题,采用有限元法与稳定双共轭梯度法共同构建了电气结构网络系统模型,计算空间消耗量比部分元等效电路(Partial Element Equivalent Circuit,PEEC)法节省了63.92%。其次,通过对多类型激励源/多区域接入点组合的探究,分析了区域阻抗特性、电势分布图谱、电流密度矢量等多维度电学结果及性能影响。通过构建与测量实物模型,对实测结果与仿真结果进行了差异化分析,并验证了实测结果符合适航规章HB 6129。最后,基于实际工况角度与适航规章,对系统模型进行了接触因素系统误差分析、精细化理想模型分析和部件应力因素分析。所获结果及分析对复合材料飞机/电动飞机的电气结构网络的构建具有重要意义。
