Control of accuracy on Taylor-collocation method for load leveling problem

High penetration of renewable energy sources coupled with the decentralization of transport and heating loads in future power systems will result in even more complex unit commitment problem solution using energy storage system scheduling for efficient load leveling. This paper employees an adaptive approach to load leveling problem using the Volterra integral dynamical models. The problem is formulated as the solution of the Volterra integral equation of the first kind which is attacked using Taylor-collocation numerical method which has the second-order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. Also, the CESTAC method is applied to find the optimal approximation, optimal error and optimal step of the collocation method. 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.
Comment: Submitted to the Bulletin of Irkutsk State University - series Mathematics