基于Krawczyk算法的直流潮流区间算法

An Interval Algorithm for DC Power Flow Calculations Based on Krawczyk Algorithm

针对高压输电系统直流潮流计算中的不确定问题,提出一种基于Krawczyk算法的直流潮流区间算法。采用区间高斯消去法求解直流潮流线性方程组得到一个包含解集外壳的区间向量,作为Krawczyk迭代的初始值。利用区间导纳矩阵中值的逆矩阵进行迭代计算,以减少保守性。最后,以区间解向量的无穷范数的减小幅度作为迭代结束条件。所述方法可以得到比区间高斯消去法更接近方程组外壳的解。采用Garver-6算例系统,将该算法的计算结果与蒙特卡洛仿真法和区间高斯消去法计算结果相比较,验证了该算法的有效性和应用价值。

In order to handle the uncertainty problem in high voltage transmission system DC power flow calculations,an interval algorithm of DC power flow calculation using Krawczyk algorithm is proposed.An interval vector containing the hull of the solution set is obtained by interval Gaussian elimination method,and is used as the initial value of Krawczyk iteration.The inverse of center of interval coefficient matrix is used in the iterative calculation to reduce the effect of dependence.The reduction range of the infinite norm of interval solution vector is served as termination criterion.The proposed algorithm can obtain sharper bounds of the hull of the solution set of interval linear equations than interval Gaussian elimination method.The proposed method has been tested on Garver-6 system.The results demonstrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and Gaussian elimination method.