论文标题
使用单片中的功率流程方程中利用对称性
Exploiting Symmetry in the Power Flow Equations Using Monodromy
论文作者
论文摘要
我们提出使用单片求解功率流程方程。我们证明所考虑的多样性分解为微不足道和非平凡的亚变化，而非平凡的亚变量是不可估的。我们还在解决方案中显示了各种对称性。我们通过给出数值结果，将单轨道与多面体和总级同义方法进行比较，并给出一个网络的示例，在该方法中，我们可以使用其他同型技术失败的单构型来找到所有功率流程方程的解决方案。这项工作使人们希望找到实现现实规模网络的电源流程方程的所有解决方案。
We propose solving the power flow equations using monodromy. We prove the variety under consideration decomposes into trivial and nontrivial subvarieties and that the nontrivial subvariety is irreducible. We also show various symmetries in the solutions. We finish by giving numerical results comparing monodromy against polyhedral and total degree homotopy methods and giving an example of a network where we can find all solutions to the power flow equation using monodromy where other homotopy techniques fail. This work gives hope that finding all solutions to the power flow equations for networks of realistic size is possible.
