非黎曼空间测地逼近及其在电力系统非线性自适应控制中应用

Geodesic Approaching in Non-Riemannian Space and Its Application to Adaptive Non-linear Control Design in Power systems

电力系统是由输电线把许多发电机群联接起来的统一体，一般，其表征空间是非黎曼空间，空间的测地离差取决于空间的曲率和挠率。本文提出了测地逼近（轨线逼近）的概念并应用于电力系统非线性自适应励磁控制（ＮＡＥＣ）参数设计。设计过程包括两部分：首先在测地线（轨线）某些离散点上求得最佳励磁控制（ＯＥＣ）参数以保证测地线（轨线）稳定；其次，用非线性回归法求得沿测地线（轨线）的ＮＡＥＣ参数曲线实现测地逼近。数字仿真表明：所设计的ＮＡＥＣ可以大大提高系统的稳定性，所提出的方法是实用而有效的。

A power system is unity with groups of generators connected through transmission lines. Generally,the underlying space of a power system is a non-Riemannian space,in which the geodesic deviation depends on the nature of the space,i. e.the curvature/torsion. In this paper,the concept of geodesic approaching (trajectory approaching) is presented and applied to adaptive parameter design of exciation control in power systems. The design procedure includes two steps;first,to obtain a set of optimal parameters at some points along geodesic (trajectory ) to keep the geodesic stable; then second, using multiple non-inear regression (or surface fitting) method to find adaptive parameter curve for implementing geodesic approaching.Results show that the proposed method is practicable and effective for adaptive parameter design of nonlinear decentrallzed local excitation control (NDLEC) in large power systems.