Based on the finite element method, a flexible catenary model incorporating a single dropper fracture and a lumped mass pantograph model are developed. The pantograph-catenary system is coupled using the penalty function method. The Newmark integration method is used to solve the system’s dynamic equations, and the effect of dropper fracture on current collection performance is analyzed. Results show that the broken dropper primarily affects the span in which the faulty dropper is located, as well as the adjacent spans. The impact of the fracture of the 2# dropper on the contact force between the pantograph and the catenary is more pronounced compared to that of the 3# dropper fracture. Following the fracture of the 2# dropper, the minimum contact force decreased from 67.4 N under normal dropper conditions to 28.4 N, representing a reduction of approximately 58%. Concurrently, the standard deviation of the contact force increased from 36.2 N to 41.6 N, indicating a rise of approximately 15%.