非自治非线性多刚体系统运动稳定性的定量分析——兼论电力系统暂态稳定性(续前)

非自治系统稳定性理论至今几乎仍是空白。虽然数值积分法可以给出精确的受扰轨迹，并按经验判断该轨迹 是否稳定，但是缺乏稳定裕度的概念。李雅普诺夫方法不能提供稳定的必要条件，即使对定常系统也只能为 稳定性提供保守的定性结论。对于一般的非保守力系或时变系统，几乎不可能构造严格的李雅普诺夫函数， 并使其稳定域具有工程意义；而采用不严格的李雅普诺夫函数，则甚至连稳定的充分条件也难以保证。文中 对非自治非线性多刚体系统的运动稳定性给出了严格的充要条件：互补群群际能量壁垒准则 （complementary-cluster energy-barrier criterion,缩写为CCEBC）。该定量化稳定理论清晰地反映了失稳的机理， 发现并解释了非线性系统的许多特有现象；所提出的稳定裕度算法适用于任意多刚体运动系统的大扰动稳定 性评估和任意参变量极限值的求取。已在国内外电力系统暂态稳定分析的控制工程中得到实际应用的扩展等 面积准则（EEAC）就是这样的一个范例。

QUANTITATIVE STUDY OF GENERAL MOTION STABILITY

Numerical integration can show accurate trajectory of the disturbed system, however, no quantitative answer to stability can be given. Lyapunov functions provide sole sufficient but not necessary condition for autonomous systems stability, so that they are not suitable for quantitatively studying motion stability. For non-conservative or nonautonomous systems, it is very difficult to develop Lyapunov functions with meaningful stability domain, and the guarantee on sufficient condition for stability might be lost by using Lyapunov-like functions. The Complementary-Cluster Energy-Barrier Criterion (CCEBC) developed in this paper is a rigorous theory and quantitative method for nonautonomous motion stability. Many relevant problems are studied in the paper. The Extended Equal-Area Criterion (EEAC) for power system transient stability, which has been used in engineering projects, is just such an example.