The growing urbanization and the current transport demand have insisted on a new way of planning for transport from the municipalities. This issue is a reality that it has been happening into different cities and Cuenca city is not an exception. It is the main reason because it has searched a plan approached Modern Massive Transport System, this helps to reduce the increasing rate of motor vehicles and mitigate the negative impact on the environment. The Cuenca city municipality in Ecuador is implementing the 'Cuatro Ríos' project approached the public transport that is a very ambitious and important mobility project aimed to have less carbon dioxide emissions. Moreover, it is an alternative and efficient choice. This article presents the mathematical model of the 'Cuatro Ríos' transport system using Matlab-Simulink® software. This mathematical model examines technical characteristics of the DCvoltage filter and the actuating system so that it can identify which are the electric network impacts. Finally, the results clarify the behaviour of the four motors (bogie) traction system allowing to know what is the energy consumption and the effects in the sub-transmission network when the trolley car is operating in the city.