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With the increasing awareness of carbon neutrality, the application of energy-efficient train control (EETC) to rail transportation systems continues to attract attention from industry and academia. In many classic EETC studies, train models are commonly simplified with pure regenerative braking and constant power characteristics during high speeds, to simplify the complexity of the model. In this paper, a realistic model incorporating hybrid braking characteristics combining regenerative and mechanical braking, and reduced-power characteristics at high speeds into the EETC problem is proposed to improve control precision of the train and the modeling precision of the energy consumption and time. This study addresses the minimum-time train control (MTTC) problem and EETC problem considering nonlinear traction characteristics based on the mixed-integer linear programming (MILP) method, and nonlinear traction and braking characteristics are approximated via a piecewise linear (PWL) modeling technique. Results indicate that the proposed alternative models achieves some deviations from the realistic model in terms of time, energy consumption, and control strategies. The deviations between models in energy consumption and time accumulate as the number of operating stations increases. Therefore, the choice of an appropriate model depends on the precision requirements of various scenarios. In scenarios demanding higher precision, selecting the proposed realistic model is crucial for more accurate computation of energy consumption and time and for obtaining more precise control strategies. • A novel MILP model addresses EETC and MTTC problems with varying nonlinear traction system characteristics, using PWL modeling for approximation. • The impact of realistic nonlinear traction system characteristics model on the EETC problem is considered, and the optimal train control strategy is derived. • Comprehensive case studies on urban rail transit and high-speed railways demonstrate the impact of realistic traction/braking forces on eco-driving strategies. • Sensitivity analysis of critical speed assesses energy consumption variations. [ABSTRACT FROM AUTHOR]