Curbing climate change requires significant efforts from all sectors, including transportation. The city's public transport system is a crucial component of the transport sector. Combining the tried-and-true trolleybus technology with the state-of-the-art battery technology creates the battery-trolleybuses, which offer significant environmental benefits in the fight against fossil fuel pollution in cities.The goal of this work is to develop a simulation model that can overcome limitations in accurately representing real-world conditions, such as traffic congestion, weather conditions, and passenger demand. This work also investigates the challenges of implementing many innovative features into modern trolleybus systems, such as battery-trolleybuses, photovoltaic systems, electric vehicle charging stations,and battery storage power stations. The simulation model will take into account various factors from both the traffic and electrical network parts that can affect the performance of trolleybus systems.The simulation model is a discrete-time model that identifies the trolleybus system state across time samples. As the buses move continuously, the topology of the traction network will vary with each time step. Thus, a new conductance matrix for the trolleybus traction network is determined at each time step. Moreover, the presence of unidirectional traction substations results in significant voltage rises whenever surplus power is produced. A specific approach is implemented to effectively determine the traction network's steady-state.This thesis makes a significant contribution to the fields of transportation and electric power engineering by introducing a novel simulation model. This model can help enhance the performance of current trolleybus systems, support decision-making for public transportation authorities, and promote the transition towards environmentallyfriendly public transportation systems, specifically battery-trolleybus systems.