Existence and Stability of Equilibrium of DC Micro-Grid Under Master-Slave Control
Existence and Stability of Equilibrium of DC Micro-Grid Under Master-Slave Control
复制标题
主从控制下直流微电网平衡的存在性及稳定性
DOI：
10.1109/tpwrs.2021.3085872
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发表时间：
2021-06
影响因子：
6.6
通讯作者：
Jinghang Lu
中科院分区：
文献类型：
--
作者：
Zhangjie Liu;Ruisong Liu;Ziqing Xia;Mei Su;Xiaofei Deng;Xin Zhang;Jinghang Lu
本文分析了主从控制下直流微电网平衡的存在性和稳定性，其中一些分布式代（dg）采用双环下垂控制（drop - dg），一些dg采用MPPT控制（MPPT- dg）。首先，得到了带CPLs的主从控制下直流微电网的功率流方程。然后，将功率流方程的可解性转化为一个收缩映射的不动点的存在性。基于Banach不动点定理，导出了直流微电网潮流解存在的充分条件。该条件不仅适用于主从控制，而且适用于下垂控制。此外，为了计算潮流解，提出了一种指数收敛的迭代算法。其次，我们使用奇异摄动模型来预测系统在平衡点附近的定性行为。通过分析边界层系统的特征值和降阶系统雅可比矩阵，得到了系统的鲁棒稳定解析条件。分析了采样延迟对系统稳定性的影响，利用线性矩阵不等式得到了系统的鲁棒稳定性条件。仿真结果验证了所提条件的正确性。所得条件为建立可靠的直流微电网提供了参考。
In this paper, we analyze the existence and stability of equilibrium of dc micro-grids under the master-slave control (where some distributed generations (DGs) are under droop control with dual-loop (Droop-DGs) and some DGs are under MPPT control (MPPT-DGs)). Firstly, the power-flow equation of the dc micro-grids under master-slave control with CPLs is obtained. Then, we transform the solvability of the power-flow equation into the existence of a fixed point for a contraction mapping. Based on Banach's fixed point theorem, a sufficient condition to guarantee the existence of the power-flow solution in dc micro-grids is derived. The condition derived in this paper is not only useful for master-slave control but also for droop control. Besides, to calculate the power-flow solution, an iterative algorithm with exponential convergence rate is proposed. Secondly, we use a singular perturbation model to predict the qualitative behavior of the system near the equilibrium point. By analyzing eigenvalues of the boundary layer system and reduced-order system Jacobian matrix, the robust stable analytic conditions of the system are obtained. The effect of the sampling delay on the system stability is analyzed, the robust stability condition is obtained by using linear matrix inequality. The simulation results verify the correctness of the proposed conditions. The obtained conditions provide a reference for establishing a reliable dc micro-grid.