中文摘要：

为满足日益扩大的复杂互联电网的暂态仿真需求,讨论一种基于自适应修正牛顿（Shamanskii）算法和非诚实牛顿法（very dishonest Newton method,VDHN）的可变步长暂态稳定仿真组合算法。本算法在微分代数方程组联立求解框架下,首先根据隐式梯形积分局部截断误差理论,对步长进行控制,在保证精度的条件下,减少了积分步数;其次,在每时步非线性方程组迭代求解中,考虑牛顿类算法的收敛性,引入Shamanskii算法,自适应控制雅可比矩阵的更新,并进一步应用VDHN法对迭代过程中电压向量的计算进行简化。针对多组算例进行测试,讨论该算法的有效性及局限性。计算结果表明：该算法可适应不同规模算例,在故障较严重情况下,仍可较好地提升仿真效率。

英文摘要：

In order to satisfy the strong desire for fast transient stability simulation,a novel mixed algorithm was introduced to power system transient stability simulation,in which Shamanskii method and very dishonest Newton algorithm（VDHN） combined with variable step size technique.In the framework of simultaneous solution method of differential-algebra equations,this proposed algorithm utilized the step-size control strategy on the basis of the local truncation error theory firstly.In addition,according to a class of Newton methods＇convergence index,Shamanskii method was employed,which can control the update of Jacobian matrix adaptively.Furthermore,VDHN method applied to simplify the computation of voltage vector.Several test cases testify the validity and practicability of the proposed algorithm,which is especially efficient to improve the simulation when the fault of the network is serious.Some comments on its limitations are also provided.