High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms
High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms
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DOI：
10.1109/lcsys.2017.2717578
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发表时间：
2017-06
影响因子：
3
通讯作者：
Krishnamurthy Dvijotham;Enrique Mallada;J. Simpson-Porco
中科院分区：
文献类型：
--
作者：
Krishnamurthy Dvijotham;Enrique Mallada;J. Simpson-Porco
交流潮流方程描述了电网的稳态行为。虽然已经开发了许多算法来计算潮流方程的解，但很少有理论结果可用于表征何时存在此类解，或者何时可以保证这些算法收敛。在这封信中，我们得到的必要条件和充分条件的存在性和唯一性的平衡径向配电网均匀（均匀R/X比）传输线的潮流。我们研究了三种不同的解决方案的方法：1）不动点迭代; 2）凸松弛;和3）能量函数，我们表明，这三种算法成功地找到一个解决方案，当且仅当一个解决方案存在。此外，所有三种算法总是找到唯一的高压解决方案的潮流方程，我们正式建立的存在性。在这个解决方案中，我们证明：1）电压幅值是无功功率注入的递增函数; 2）解决方案是注入的连续函数; 3）解决方案是最后一个消失，因为系统负载超过可行性边界。
The ac power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such solutions exist, or when these algorithms can be guaranteed to converge. In this letter, we derive necessary and sufficient conditions for the existence and uniqueness of a power flow solution in balanced radial distribution networks with homogeneous (uniform R/X ratio) transmission lines. We study three distinct solution methods: 1) fixed point iterations; 2) convex relaxations; and 3) energy functions—we show that the three algorithms successfully find a solution if and only if a solution exists. Moreover, all three algorithms always find the unique high-voltage solution to the power flow equations, the existence of which we formally establish. At this solution, we prove that: 1) voltage magnitudes are increasing functions of the reactive power injections; 2) the solution is a continuous function of the injections; and 3) the solution is the last one to vanish as the system is loaded past the feasibility boundary.