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Python implementation of a longitudinal dynamic control model for electric buses, trains, and other ground vehicles, including speed, acceleration, energy, and CO₂ emission simulations

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Longitudinal Dynamic Control Model for Ground Transportation Systems

This project implements a control algorithm for traction and braking, applicable to electric vehicles such as cars, buses, and trains.
The controller is based on longitudinal dynamics evaluating speed, acceleration, power, and torque over a given route.

In addition, the framework allows the estimation of energy consumption and approximate CO₂ emissions (depending on the energy source), providing insights into the environmental impact of different control strategies.

🚀 Project Overview

Efficient traction and braking control is essential for modern mobility systems.
This project provides a simple yet effective approach to:

  • Control vehicle acceleration and deceleration.
  • Analyze dynamic performance (velocity, acceleration, power, torque).
  • Estimate energy demand during a trip.
  • Approximate CO₂ emissions, useful for comparing scenarios.

The project can be extended to different transport modes (passenger cars, heavy vehicles, or rail systems).

📊 Results - Case Study

A real-world case study was carried out for a bus route between Dallas Fort Worth International Airport (Terminal E) and AT&T Stadium.

🚍 Vehicle Selection

The Yutong IC15E was selected for the route operation. It proved a capable operational characteristics. Specially, reaching and maintaining >100 km/h, ideal for U.S. highways.

📈 Key Performance Indicators

A set of key performance indicators (KPIs) was selected to evaluate the bus's performance along its designated route. The Table shows the results of a single trip from Terminal E at Dallas Fort Worth International Airport to Dallas AT&T Stadium. For this evaluation, the bus operated at 85% of its maximum load capacity; in addition, stops at traffic lights were considered.

KPI Value
Total Distance Travelled 21.93 km
Trip Moving Time 21m 41s
Total Trip Time (incl. stops) ~34m 11s
Max Speed 104.3 km/h
Average Speed 58.3 km/h
Max Acceleration 1.09 m/s²
Max Deceleration 0.90 m/s²
Total Energy Required (traction) 107.5 MJ
Recovered Energy (regen braking) 35.5 MJ
Net Energy Consumption (w/ aux) 131.1 MJ (40.5 kWh)

Simulation Results

In the bus simulation, the vehicle reached a maximum speed of ~105 km/h with an average of ~58 km/h, closely following the reference speed profile and adapting well to local speed restrictions. Acceleration remained within comfort and safety limits (≤ 1.2 m/s² for traction and ≥ -0.9 m/s² for braking), with peaks mainly around stops and speed changes. The motor power stayed below the 500 kW limit, showing positive peaks during acceleration and negative values during regenerative braking, with minor oscillations due to road slope variations. Overall energy demand for the 21 km trip was ~107.5 MJ, reflecting both traction phases and the contribution of regenerative braking.

Speed profile Bus Speed Profile

Acceleration profile Bus Acceleration Profile

Motor Power profile Bus Motor Power Profile

Energy Consumption profile Bus Energy Profile

⚡ Energy & Emissions

The total energy consumption for the 21 km bus trip was estimated at ~131.1 MJ, including both traction (107.5 MJ) and auxiliary loads such as HVAC, lighting, and onboard electronics (~23.6 MJ). Accounting for a 10% charging loss, the well-to-wheel energy demand rises to ~145.7 MJ (≈40.5 kWh). Using the Dallas–Fort Worth (ERCOT All) grid emission factor of 332.9 g CO₂/kWh, the trip generates approximately 13.5 kg CO₂, or 0.615 kg CO₂ per kilometer, highlighting the environmental advantage of electric buses even under a fossil-heavy electricity grid.

  • Total trip energy demand: 40.5 kWh (including auxiliaries and charging losses).
  • Estimated CO₂ emissions (using Dallas–Fort Worth grid intensity, ERCOT All):
    • 13.5 kg CO₂ per trip
    • ≈ 0.615 kg CO₂ / km
  • Comparison to diesel: Typical diesel bus emits ~1.3 kg CO₂/km.
    → The electric bus reduces emissions by ~50% under the fossil-heavy Texas grid mix.

📎 References

A. N. and W. J. D. Gent, Pneumatic Tire, Ohio, US: Mechanical Engineering Faculty Research, 2006.
S. M. T., S. M. K.-K., A. e. a. Skarlis, “Towards Electrification of Urban Buses Using Model Based,” London, 2018.
H. M., Y. Y., Z. Z., T. X., Y. C., X. L., Tao Zhu, “An Optimized Energy Management Strategy for Preheating Vehicle-Mounted Li-ion Batteries at Subzero Temperatures,” 2017.
A. & L. T. Lajunen, “Lifecycle cost assessment and carbon dioxide emissions of diesel, natural gas, hybrid electric, fuel cell hybrid and electric transit buses,” 2016.
M. v. d. H., E. L. A., S. D. U. Rogge, “Electric bus fleet size and mix problem with optimization of charging infrastructure,” 2018.
T. L., Antti Lajunen, “Lifecycle cost assessment and carbon dioxide emissions of diesel, natural gas, hybrid electric, fuel cell hybrid and electric transit buses,” 2016.
U. S. E. P. Agency, “EPA. United States Environmental Protection Agency,” 2023. [Online]. Available: https://www.epa.gov/egrid/power-profiler#/ERCT
C. Goodall, How to live a low-carbon life: the individual's guide to stopping climate change, London, Washington, DC: Earthscan, 2007.

👤 Author

Daniel Avila, Mobility Engineering MSc Student

📄 License

This project is licensed under the MIT License. See the LICENSE file for details.

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Python implementation of a longitudinal dynamic control model for electric buses, trains, and other ground vehicles, including speed, acceleration, energy, and CO₂ emission simulations

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