连续潮流(continuous power flow,CPF)是电力系统电压稳定分析的有效工具,也是解决常规潮流中病态潮流问题的方法之一。针对无平衡节点孤岛运行微电网系统的无平衡节点、且有下垂控制分布式电源装置的特性,提出一种无平衡节点孤岛运行...连续潮流(continuous power flow,CPF)是电力系统电压稳定分析的有效工具,也是解决常规潮流中病态潮流问题的方法之一。针对无平衡节点孤岛运行微电网系统的无平衡节点、且有下垂控制分布式电源装置的特性,提出一种无平衡节点孤岛运行微电网CPF计算方法。采用不要求雅可比矩阵非奇异,且具有全局收敛性的LM-TR方法求解初始点。预测环节采用结合局部参数化方法的切线法。校正环节提出新型的超球面参数化方法,并采用结合传统牛顿法和带Armijo型线性搜索牛顿法的组合牛顿法进行校正,以保证CPF校正计算成功,及实现整个CPF过程中在较高计算精度下一直采用较大定步长预测。对改造后的37节点和17节点无平衡节点孤岛运行微电网系统采用所提方法进行CPF计算,验证了其正确性和有效性。展开更多
This paper is concerned with the algorithm of the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model with elastic demands. Both models are further written as...This paper is concerned with the algorithm of the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model with elastic demands. Both models are further written as nonlinear complementarity problems. Semismooth least squares reformulations of the complementarity problems are presented and their convergence properties are investigated. Considering the drawbacks of Quasi-Newton method (using the Fischer-Burmeister function), a semi-smooth Levenberg-Marquardt-type method is proposed to solve the problems. Numerical examples show that the Levenberg-Marquardt-type method can solve the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model significantly, and is more efficient than the Quasi Newton method and the modified projection method. Furthermore, the Levenberg-Marquardt-type method with the equivalent supernetwork based complementarity formulation can be implemented faster than with the supply chain network equilibrium complementarity formulation.展开更多
Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lips...Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2 provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.展开更多
文摘连续潮流(continuous power flow,CPF)是电力系统电压稳定分析的有效工具,也是解决常规潮流中病态潮流问题的方法之一。针对无平衡节点孤岛运行微电网系统的无平衡节点、且有下垂控制分布式电源装置的特性,提出一种无平衡节点孤岛运行微电网CPF计算方法。采用不要求雅可比矩阵非奇异,且具有全局收敛性的LM-TR方法求解初始点。预测环节采用结合局部参数化方法的切线法。校正环节提出新型的超球面参数化方法,并采用结合传统牛顿法和带Armijo型线性搜索牛顿法的组合牛顿法进行校正,以保证CPF校正计算成功,及实现整个CPF过程中在较高计算精度下一直采用较大定步长预测。对改造后的37节点和17节点无平衡节点孤岛运行微电网系统采用所提方法进行CPF计算,验证了其正确性和有效性。
基金supported by the National Basic Research Program of China("973" Program) (Grant No. 2006CB705503)the National Natural ScienceFoundation of China (Grant Nos. 70771005, 71071014, 70631001)the Fundamental Research Funds for Central Universities (Grant No.2009JBM044)
文摘This paper is concerned with the algorithm of the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model with elastic demands. Both models are further written as nonlinear complementarity problems. Semismooth least squares reformulations of the complementarity problems are presented and their convergence properties are investigated. Considering the drawbacks of Quasi-Newton method (using the Fischer-Burmeister function), a semi-smooth Levenberg-Marquardt-type method is proposed to solve the problems. Numerical examples show that the Levenberg-Marquardt-type method can solve the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model significantly, and is more efficient than the Quasi Newton method and the modified projection method. Furthermore, the Levenberg-Marquardt-type method with the equivalent supernetwork based complementarity formulation can be implemented faster than with the supply chain network equilibrium complementarity formulation.
文摘Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2 provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.
