改进的潮流方程解的个数估计及方程的吴消元解法

Improved Estimate of the Number of Solutions of Power Flow Equations and Wu Method Solving for All Solutions

主要是对电力系统潮流方程解的个数上限的进一步讨论。利用相似多项式性质以及同伦算法,分别讨论了网络中不同类型节点间的线路断开后,潮流方程解减少的个数,由此得到对于稀疏网络,其潮流方程解个数的上限必定小于现有结果NNC2。最后,对于一般的N节点网络,给出了改进的潮流方程解个数上限的通用公式,与NNC2相比范围大大缩小,更为精确。同时还应用吴消元法求解算例电力系统模型潮流方程的全部解,验证了以上结论。

With the aid of polynomial character and topology, the paper discusses how many equilibrium solutions will be lost when lines between nodes are disconnected, and makes further discussion and improvement to the upper boundary number of equilibrium solutions of power flow equation. Generally for an N-node power system grid not fully connected, a formula is worked out to calculate the upper boundary number of equilibrium solutions, which is more accurate than the previous NNC2. To validate the conclusion, all the solutions of example network equations have been calculated with the aid of Wu Method, which strikes forward a trial step to the application of Wu method in power system calculation. The results match the conclusion well.