This paper deals with the problem of power sharing in DC micro-grids in mesh topology with multiple active buses. We formally analyze the feedback loop composed by the micro-grid as a multi-agents process, the DC generation units as actuators, the distributed arbitrary loads as disturbances, and a linear consensus based control strategy, in order to characterize its performance in terms of secondary level control objectives as power sharing and mean voltage regulation. Based on existing consensus control strategies, the novelty of this approach relays on the possibility of comparing the performance of different controllers through numeric indicators. Furthermore, the chosen control strategy is not necessarily derived as the Laplacian matrix of an undirected graph. In this way, the proposed strategy can be tuned to achieve optimal behavior in terms of convergence speed, disturbances rejection, or communication links requirements. Furthermore, by doing this we are able to prove that the traditional droop control strategy does not necessarily achieve the desired objectives in mesh topology. Therefore, we focus on the consensus dynamics of the closed loop system, deriving simple test to conclude on its behavior, and to propose a Linear Matrix Inequality (LMI) based procedure to verify the region of voltage deviations at which the control objective can be achieved. Finally, the results of the paper are illustrated through a simulation example.

本文涉及具有多条有源母线的网状拓扑结构中直流微电网的功率共享问题。我们正式分析了由微电网组成的反馈回路作为多代理过程，直流发电机组作为执行器，分布式任意负载作为扰动，以及基于线性一致性的控制策略，以表征其性能二级控制目标为功率共享和平均电压调节。基于现有的共识控制策略，这种方法的新颖性在于可以通过数字指标比较不同控制器的性能。此外，所选择的控制策略不一定是作为无向图的拉普拉斯矩阵导出的。这样，可以调整所提出的策略以在收敛速度、干扰抑制或通信链路要求方面实现最佳行为。此外，通过这样做，我们能够证明传统的下垂控制策略不一定能实现网格拓扑中的预期目标。因此，我们专注于闭环系统的一致性动力学，推导出简单的测试以得出其行为的结论，并提出基于线性矩阵不等式 (LMI) 的程序来验证可以实现控制目标的电压偏差区域. 最后，通过一个仿真实例说明了论文的结果。通过这样做，我们能够证明传统的下垂控制策略不一定能实现网格拓扑中的预期目标。因此，我们专注于闭环系统的一致性动力学，推导出简单的测试以得出其行为的结论，并提出基于线性矩阵不等式 (LMI) 的程序来验证可以实现控制目标的电压偏差区域. 最后，通过一个仿真实例说明了论文的结果。通过这样做，我们能够证明传统的下垂控制策略不一定能实现网格拓扑中的预期目标。因此，我们专注于闭环系统的一致性动力学，推导出简单的测试以得出其行为的结论，并提出基于线性矩阵不等式 (LMI) 的程序来验证可以实现控制目标的电压偏差区域. 最后，通过一个仿真实例说明了论文的结果。