一类非线性动力网络方程组的性质与解法及其应用

PROPERTIES AND SOLUTIONS OF A CLASS OF NONLINEAR POWER NETWORK EQUATIONS AND THEIR APPLICATIONS

对于一般的非线性动力网络,在某些参数值已知的条件下,本文讨论了网络方程组解的存在唯一性问题,在不要求支路特性曲线可微的条件下,给出了一个求解唯一解问题的总体收敛算法。同时指出了这些理论在某些具体网络分析与设计中的应用,这些网络包括矿井通风网络、煤气供给网络、城市给水网络、线性和非线性电阻网络。

In this paper, for general nonlinear power network, author discusses the existence and uniqueness of the Solution of the network equations. Under the condition that the differentiability of branch characteristic curve is not required, author gives a global convergent algorithm to find unique solution. Meanwhile, the applications in some concrete networks are given. These networks include mine ventilation network, coal gas pipeline network, urban water supply network and nonlinear resistance network.