An Analytical Solution for Optimal Design of Stationary Lithium-Ion Capacitor Storage Device in Light Electrical Transportation Networks

Abstract

In the recent technical literature a high interest has been devoted to the employment of energy storage at the aim of improving the performances of electrified light transit systems. Some significant results have been obtained for deriving in a rational way a design procedure for ensuring contemporaneously desirable requirements as the energetic efficiency and the reduction of pantograph voltage droops. In particular, it has been verified that the optimization theory is a powerful and proper candidate for determining in a feasible way  the optimal characteristics of the storage devices both in stationary and on-board configuration. This problem was approached by exploiting the classical theory of calculus of variations. In this paper, by starting from this approach, a complete analytical solution to the problem of the optimal design storage is afforded. Without loss of generality, the analytical methodology is presented with respect to the stationary case. The formulation as classical isoperimetric problem is developed, based upon a current source for the electrical traction load. This mild assumption allows to obtain a closed analytical form to the storage current law, which in turns results very useful in performing the sensitivity analysis for choosing the free parameters appearing in the methodological framework. A great advantage of the procedure is related to the fact that the analytical expression of the storage currents could be employed for realizing an optimal open-loop law for controlling in real-time the storage device. In the paper in order to show the potentiality of the analytical methodology, a numerical application with respect to realistic light railway vehicles operation is performed. The various simulations confirm the feasibility and the goodness of the proposed methodology