欢迎您！东篱公司
退出
-
申报数据库
-
立项数据库
-
成果数据库
-
项目获奖数据库
中文摘要：
对电力系统中具有重大应用价值的地网腐蚀诊断问题抽象出仿真求解的一种新的数学模型：即求解带约束的非线性隐式方程组模型．但由于问题本身的物理特性决定了所建立的数学模型具有以下特点：一是非线性方程组为欠定方程组，而且非线性程度非常高；二是方程组的所有函数均为隐函数；三是方程组附加若干箱约束条件．这种特性给模型分析与算法设计带来巨大困难．对于欠定方程组的求解，文中根据工程实际背景，尽可能地扩充方程的个数，使之成为超定方程组，然后对欠定方程组和超定方程组分别求解并进行比较．将带约束的非线性隐函数方程组求解问题，转化为无约束非线性最小二乘问题，并采用矩阵求导等技术和各种算法设计技巧克服隐函数的计算困难，最后使用拟牛顿信赖域方法进行计算．大量的计算实例表明，文中所提出的数学模型及求解方法是可行的．与目前广泛采用的工程简化模型相比较，在模型和算法上具有很大优势．
英文摘要：
In this paper, a novel mathematical model is proposed for corrosion diagnosis of grounding grid, which will be of great use value in electric power systems. The new model boils down to solving the constrained nonlinear implicit equations, which has the following characteristics, on the one hand, the number of equations is usually less than that of unknown variables, in particular, all equations are nonlinear intensively ; on the other hand, all equations consist of implicit functions; moreover, on all variables should be imposed box constraints. There are no available and practical algorithms to solve this kind of problems. So it＇s more difficult to reach the true solution in conformity with the actual problem. In the paper, the problem is converted into solving an unconstrained nonlinear least squares problem by transformation, and worked out finally by means of quasi-Newton trust region method. Lots of numerical tests show that the new mathematical model and solving algorithms are feasible.
同期刊论文项目
同项目期刊论文
期刊信息
位置：