  Development of reliable methods for optimised energy storage and generation
is one of the most imminent challenges in moder power systems. In this paper 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. These integral equations efficiently solve such inverse problem taking
into account both the time dependent efficiencies and the availability of
generation/storage of each energy storage technology. In this analysis a direct
numerical method is employed to find the least-cost dispatch of available
storages. The proposed collocation type numerical method has 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 optimisation in real time. The efficiency of the proposed
methodology is demonstrated on the Single Electricity Market of Republic of
Ireland and Sakhalin island in the Russian Far East.
