⚡ electrical engineering

Eco-Driving Control for Electric Vehicles with Multi-Speed Transmission: Optimizing Vehicle Speed and Powertrain Operation in Dynamic Environments

This paper proposes a real-time eco-driving controller for electric vehicles with multi-speed transmissions that co-optimizes vehicle speed and powertrain operation using traffic prediction constraints, achieving up to an 11.36% reduction in energy consumption in dynamic mixed-traffic environments.

Original authors: Suiyi He, Zongxuan Sun

Published 2026-01-28

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CC BY 4.0

Original authors: Suiyi He, Zongxuan Sun

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are driving an electric car (EV). Most electric cars today have a transmission that is like a single-speed bicycle: it has one gear ratio. No matter if you are crawling up a steep hill or zooming down a highway, the engine is always spinning at a speed relative to your wheels. This is simple, but it's not always the most efficient way to use energy.

This paper proposes a smarter way to drive these cars by giving them a multi-speed transmission (like a bicycle with 3 gears) and a "super-smart" driving brain that decides exactly when to shift gears and how fast to drive, all while looking ahead at traffic.

Here is a breakdown of the paper's ideas using simple analogies:

1. The Problem: The "One-Size-Fits-All" Gear

Think of a single-speed EV like a runner who can only jog at one specific pace. If they need to sprint, they have to push incredibly hard (wasting energy). If they need to walk slowly, they are still moving their legs too fast (also wasting energy).

The Paper's Solution: Give the car a 3-speed transmission. Now, the car can "shift gears" just like a cyclist. It can use a low gear for climbing hills (high torque, low speed) and a high gear for cruising on the highway (low speed, high efficiency).

2. The "Super-Brain" (The Eco-Driving Controller)

Having 3 gears is great, but if you shift them at the wrong time, you waste energy. The authors created a computer algorithm that acts as a co-pilot.

Simultaneous Thinking: Instead of just deciding "how fast to go" and then "which gear to pick" separately, this brain does both at the same time. It asks: "If I shift to 3rd gear now and slow down slightly, will I save more battery than if I stay in 2nd gear and speed up?"
The Crystal Ball (Traffic Prediction): The car isn't just reacting to the car in front of it; it's predicting the future. Using data from traffic lights, other connected cars, and sensors, the algorithm acts like a crystal ball. It knows a red light is coming up 500 meters away. Instead of speeding up and then slamming on the brakes (which wastes energy), the car gently slows down early, coasting to a stop. This is called "Eco-Driving."

3. The Challenge: The Math is Hard

Trying to calculate the perfect speed, the perfect gear, and the perfect braking moment for every second of a drive is a massive math puzzle. It involves "mixed integers" (discrete gears) and complex curves.

The Trick: The authors simplified this giant puzzle. They turned the complex, non-linear math into a format that a standard computer can solve in less than a second. This means the system can run in real-time while you are actually driving, not just in a simulation.

4. The Results: Saving Energy in the Real World

The team tested this system in two ways:

Virtual Driving: They simulated a car driving through a city with traffic lights and other cars.
Real-World Driving: They drove a test vehicle on a real highway in Minnesota (Trunk Highway 55) with 22 intersections.

The Outcome:

In the simulation, the 3-speed car used 12% less battery than the single-speed car.
In the real-world test drive (an 18 km trip), the 3-speed car saved 11.36% more energy.

Why did it save so much?

Better Gear Selection: The motor stayed in its "sweet spot" (where it is most efficient) more often.
Smarter Braking: The car used "regenerative braking" (turning the motor into a generator to recharge the battery) more effectively because it could manage the speed better.
Less Waste: By predicting traffic, the car avoided the "stop-and-go" energy waste that happens when you have to brake hard and then accelerate again.

5. What It Doesn't Do (Limitations)

The paper is honest about what it leaves out. The current system does not account for battery temperature. Just like a human gets tired in extreme heat or cold, batteries change how they perform based on temperature. The authors note that adding temperature management is the next step for future research, but this specific study focused purely on speed, gears, and traffic prediction.

Summary

This paper presents a "smart driver" for electric cars with multiple gears. By combining gear shifting with predictive traffic awareness, the car can drive more like a pro cyclist (coasting and shifting efficiently) rather than a robot stuck in one gear. The result is a significant drop in energy consumption, meaning the car can go further on a single charge without needing bigger batteries.

Technical Summary: Eco-Driving Control for Electric Vehicles with Multi-Speed Transmission

Problem Statement

The paper addresses the challenge of maximizing energy efficiency in Connected and Autonomous Electric Vehicles (CAEVs) equipped with multi-speed transmissions. While single-speed transmissions are standard in EVs for simplicity, multi-speed systems offer potential improvements in driving range and acceleration. However, existing eco-driving controllers often struggle to optimize these systems in real-time due to the computational complexity of mixed-integer nonlinear programming (MINLP). Furthermore, many current approaches rely on hierarchical structures that decouple speed and gear optimization, or they simplify powertrain dynamics by ignoring mechanical braking forces, leading to suboptimal energy management in dynamic traffic environments. The core problem is to develop a real-time, co-optimization controller that simultaneously manages vehicle longitudinal speed and discrete gear shifts while adhering to safety constraints derived from traffic predictions.

Methodology

Traffic Prediction Framework

To enable proactive control, the system employs a traffic prediction algorithm based on a discretized second-order Payne-Whitham (PW) traffic flow model.

Data Integration: The algorithm fuses real-time Signal Phase and Timing (SPaT) data, GPS data from the ego vehicle, and V2V/V2I data from Connected Vehicles (CVs).
Estimation: An Unscented Kalman Filter (UKF) estimates traffic speed and density ahead of the immediate preceding vehicle.
Prediction: The model propagates traffic flow dynamics over a prediction horizon to forecast the longitudinal trajectory of the vehicle directly ahead, accounting for signalized intersections and mixed traffic conditions.

Co-Optimization Formulation

The core of the proposed controller is a simultaneous co-optimization of vehicle speed and powertrain operation.

System Dynamics: The model integrates longitudinal vehicle dynamics (including acceleration and position), battery state of charge (SOC) dynamics using an internal resistance model, and a comprehensive powertrain model.
Powertrain Model: Unlike previous studies that often assume zero mechanical braking, this formulation explicitly models the interaction between regenerative braking and hydraulic braking. It includes constraints for low-speed regenerative braking cutoffs and motor torque limits based on speed.
Objective Function: The cost function minimizes a weighted sum of battery energy consumption ( $P_b$ ), acceleration (for comfort), and the deviation of the ego vehicle's terminal position from a desired safe following distance behind the predicted trajectory of the lead vehicle.

Problem Simplification for Real-Time Implementation

The original problem is a nonlinear mixed-integer optimization problem due to discrete gear selection and bilinear terms (e.g., motor torque $\times$ gear ratio). To enable real-time execution, the authors apply several simplification techniques:

Big-M Technique: Discrete gear selection variables are converted into a set of linear inequality constraints.
Piecewise Linear Approximation: Quadratic terms (such as air drag $v^2$ ) and nonlinear motor efficiency maps are approximated using Special Ordered Sets of type 2 (SOS2) and polynomial fitting, respectively.
McCormick Relaxation: Bilinear terms involving motor speed and torque are convexified into linear inequalities.
Soft Constraints: Hard traffic constraints are relaxed using slack variables to ensure feasibility, penalized within the cost function.

The resulting simplified problem is solved within a Model Predictive Control (MPC) framework using the Gurobi solver.

Key Contributions

Simultaneous Co-Optimization: Unlike hierarchical methods that separate speed and gear planning, this controller concurrently optimizes vehicle longitudinal speed, motor operation, and discrete gear shift maneuvers.
High-Fidelity Powertrain Modeling: The formulation incorporates realistic interactions between regenerative and mechanical braking, as well as battery dynamics, avoiding the oversimplification of assuming zero mechanical braking forces.
Computational Efficiency: By employing Big-M techniques, SOS2 approximations, and McCormick relaxations, the complex mixed-integer problem is transformed into a form solvable in real-time (average solve time of ~0.27s per cycle).
Safety-Critical Constraints: The controller integrates traffic predictions to enforce safe car-following distances and smooth traffic flow in dynamic environments with signalized intersections.

Results

Numerical Simulations

The algorithm was validated using the Simulation of Urban MObility (SUMO) tool with a platoon of 10 vehicles traversing an 1800 m road section with two signalized intersections.

Performance: Compared to a baseline controller for an EV with a single-speed transmission (using the same optimization framework), the multi-speed controller reduced battery SOC consumption by 12.01%.
Energy Economy: The energy consumption improved from 203.6 Wh/km to 179.1 Wh/km.
Operational Insights: The multi-speed transmission allowed the motor to operate consistently within a more efficient range, particularly during acceleration and high-speed cruising, reducing the need for high-current battery discharge.

Real-World Road Tests

Validation was conducted on Trunk Highway 55 (TH55) in Minnesota, covering an 18 km route with 22 intersections.

Setup: Real-world traffic data, including SPaT and vehicle trajectories, was recorded and used to simulate the preceding vehicle's behavior for the ego vehicle.
Performance: The proposed controller achieved an 11.36% reduction in energy consumption (battery SOC usage) over the 18 km drive compared to the single-speed counterpart.
Observation: The results confirmed that the multi-speed transmission enables the motor to operate in a more efficient regime, validating the approach in a realistic, mixed-traffic environment.

Significance and Limitations

The paper claims that the proposed algorithm successfully bridges the gap between theoretical energy efficiency gains of multi-speed transmissions and the practical requirements of real-time control in dynamic traffic. By demonstrating double-digit percentage improvements in energy efficiency through both simulation and real-world testing, the work validates the viability of co-optimizing speed and gear selection for CAEVs.

The authors modestly note a primary limitation: the framework currently excludes battery thermal effects. Since temperature significantly influences battery efficiency and degradation, the authors identify integrating thermal dynamics as a necessary next step to evolve the controller into a holistic powertrain management system. The paper does not propose specific future applications beyond this thermal integration or other hardware modifications.