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
Further growth in renewable energy and planned electrification and decentralization of transport and heating loads in future power systems will result in a more complex unit commitment problem (UCP). This paper proposes an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. This approach employs a direct numerical method. The considered collocation-type numerical method has the second-order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimization in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of the Island of Ireland.