The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical method based on the modified Newton–Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations. Second, the proposed numerical method was tested both on synthetic examples and real world problems related to the dynamic analysis of microgrids with energy storage systems.

中文翻译：

---

具有分段光滑核的Volterra方程非线性系统：数值解及其在电力系统运行中的应用

解决了存储系统的演化整体动力学模型。这样的模型基于具有分段光滑核的弱规则非线性Volterra积分方程组。这些方程式可以具有取决于自由参数的非唯一解。本文的目的是双重的。首先，提出了一种基于改进的牛顿-坎托罗维奇迭代过程的迭代数值方法，用于求解此类弱正则Volterra方程的非线性系统。其次，在合成实例和与带有储能系统的微电网动态分析有关的实际问题上，对所提出的数值方法进行了测试。