The droop control is an advantageous approach for stand-alone supply systems consisting of multiple batteries, allowing among various inverters without intercommunication. The droop coefficients of batteries always vary with their state-of-charge (SoC) and charge/discharge mode, resulting in small-signal instability. Nevertheless, the existing impedance-based approaches can only assess the droop coefficients stability point, but not the stability region. Therefore, this article proposes a droop coefficients stability region analysis approach. First, the charge/discharge SoC-based droop controlled battery, the P&Q controlled distributed generator and the constant power load are separately discussed. Meanwhile, the state matrix and return-ratio matrix are established, respectively. Furthermore, the novel forbidden region criterion based on the return-ratio matrix is constructed, which reduces conservatism compared with norm-based impedance criteria and partial forbidden region criteria. Such a forbidden region criterion is first switched to the Hurwitz identification problem regarding the equivalent return-ratio matrix. Combined the state matrix and the equivalent return-ratio matrix, the generalized incidence matrix is constructed to simultaneously identify subsystem stability and interactive stability. Based on the generalized incidence matrix, an adaptive step search strategy is proposed to obtain the droop coefficients coordinated stability region. Finally, the simulation and experimental results illustrate the validity of the proposed method.

中文翻译：

---

具有恒定功率负载的独立供电系统的电池基于SoC的下垂系数稳定性区域分析

对于由多个电池组成的独立供电系统，下垂控制是一种有利的方法，可以使各种逆变器之间无需相互通信。电池的下降系数始终随其充电状态（SoC）和充电/放电模式而变化，从而导致小信号不稳定。然而，现有的基于阻抗的方法只能评估下垂系数的稳定点，而不能评估稳定区域。因此，本文提出了一种下垂系数稳定区域分析方法。首先，分别讨论基于充电/放电SoC的下垂控制电池，P＆Q控制的分布式发电机和恒定功率负载。同时，分别建立状态矩阵和收益率矩阵。此外，构造了基于收益率矩阵的新型禁区准则，与基于规范的阻抗准则和部分禁区准则相比，降低了保守性。首先将这种禁区标准切换到关于等效回报率矩阵的Hurwitz识别问题。结合状态矩阵和等效收益率矩阵，构造广义关联矩阵以同时识别子系统稳定性和交互稳定性。基于广义关联矩阵，提出了一种自适应步长搜索策略来获得下垂系数协调稳定区域。最后，仿真和实验结果证明了该方法的有效性。与基于规范的阻抗标准和部分禁止区域标准相比，这降低了保守性。首先将这种禁区标准切换到关于等效回报率矩阵的Hurwitz识别问题。结合状态矩阵和等效收益率矩阵，构造广义关联矩阵以同时识别子系统稳定性和交互稳定性。基于广义关联矩阵，提出了一种自适应步长搜索策略来获得下垂系数协调稳定区域。最后，仿真和实验结果证明了该方法的有效性。与基于规范的阻抗标准和部分禁止区域标准相比，这降低了保守性。首先将这种禁区标准切换到关于等效回报率矩阵的Hurwitz识别问题。结合状态矩阵和等效收益率矩阵，构造广义关联矩阵以同时识别子系统稳定性和交互稳定性。基于广义关联矩阵，提出了一种自适应步长搜索策略来获得下垂系数协调稳定区域。最后，仿真和实验结果证明了该方法的有效性。首先将这种禁区标准切换到关于等效回报率矩阵的Hurwitz识别问题。结合状态矩阵和等效收益率矩阵，构造广义关联矩阵以同时识别子系统稳定性和交互稳定性。基于广义关联矩阵，提出了一种自适应步长搜索策略来获得下垂系数协调稳定区域。最后，仿真和实验结果证明了该方法的有效性。首先将这种禁区标准切换到关于等效回报率矩阵的Hurwitz识别问题。结合状态矩阵和等效收益率矩阵，构造广义关联矩阵以同时识别子系统稳定性和交互稳定性。基于广义关联矩阵，提出了一种自适应步长搜索策略来获得下垂系数协调稳定区域。最后，仿真和实验结果证明了该方法的有效性。提出了一种自适应步长搜索策略来获得下垂系数协调稳定区域。最后，仿真和实验结果证明了该方法的有效性。提出了一种自适应步长搜索策略来获得下垂系数协调稳定区域。最后，仿真和实验结果证明了该方法的有效性。