Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Analysis of the impact of stationary energy storage systems in trolleybus grids using Simulink-based modelling

The voltage profile of the catenary between traction substations (TSSs) is affected by the trolleybus current intake and by its position with respect to the TSSs: the higher the current requested by the bus and the further the bus from the TSSs, the deeper the voltage drop. When the voltage drops below 500V, the trolleybus is forced to decrease its consumption by reducing its input current. This thesis deals with the analysis of the improvements that the installation of an BESS produces in the operation of a particularly loaded FS of the DC trolleybus network of the city of Bologna. The stationary BESS is charged by the TSSs during off-peak times and delivers the stored energy when the catenary is overloaded alleviating the load on the TSSs and reducing the voltage drops. Only IMC buses are considered in the prospect of a future disposal of all internal combustion engine vehicles. These trolleybuses cause deeper voltage drops because they absorb enough current to power their traction motor and recharge the on board battery. The control of the BESS aims to keep the catenary voltage within the admissible voltage range and makes sure that all physical limitations are met. A model of FS Marconi Trento Trieste is implemented in Simulink environment to simulate its daily operation and compare the behavior of the trolleybus network with and without BESS. From the simulation without BESS, the best location of the energy storage system is deduced, and the battery control is tuned. Furthermore, from the knowledge of the load curve and the battery control trans-characteristic, it is formulated a prediction of the voltage distribution at BESS connection point. The prediction is then compared with the simulation results to validate the Simulink model. The BESS allows to decrease the voltage drops along the catenary, the Joule losses and the current delivered by the TSSs, indicating that the BESS can be a solution to improve the operation of the trolleybus network.