The Interconnection of Quadratic Droop Voltage Controllers Is a Lotka-Volterra System: Implications for Stability Analysis
The Interconnection of Quadratic Droop Voltage Controllers Is a Lotka-Volterra System: Implications for Stability Analysis
复制标题
二次降压控制器的互连是一个 Lotka-Volterra 系统：对稳定性分析的影响
DOI：
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发表时间：
2017
影响因子：
3
通讯作者：
K. Johansson
中科院分区：
文献类型：
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作者：
Matin Jafarian;H. Sandberg;K. Johansson
这封信研究了电力网络的电压动态稳定性，其中节点电压通过二次下垂控制器以非线性交流无功功率作为输入进行控制。我们证明电压动力学是一个 Lotka-Volterra 系统，它是一类非线性正系统。我们通过证明一致的最终有界结果并研究网络协作的条件来研究闭环系统的稳定性。然后，我们限制研究去耦假设（即零相对角度）下电压动态的稳定性。我们分析了系统正象内部平衡点的存在性和唯一性，并证明了渐进稳定性结果。
This letter studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs. We show that the voltage dynamics is a Lotka-Volterra system, which is a class of nonlinear positive systems. We study the stability of the closed-loop system by proving a uniform ultimate boundedness result and investigating conditions under which the network is cooperative. We then restrict to study the stability of voltage dynamics under a decoupling assumption (i.e., zero relative angles). We analyze the existence and uniqueness of the equilibrium in the interior of the positive orthant for the system and prove an asymptotic stability result.