Week-11 Challenge: Braking

1. For a defined driving cycle, calculate the energy required for braking.

To calculate the energy required for braking over a defined driving cycle, first determine the vehicle's kinetic energy at each time step using $KE = \frac{1}{2} m v^2$.

When velocity decreases, compute the change in kinetic energy ($\Delta KE$ΔKE), as this represents the energy that must be dissipated by braking.

Next, account for resistive forces, including aerodynamic drag ($F_{\text{drag}} = \frac{1}{2} C_d A \rho v^2$) and rolling resistance ($F_{\text{rolling}} = mg C_r$Frolling​=mgCr​), which naturally slow the vehicle.

The resistive power ($P_{\text{resistive}} = (F_{\text{drag}} + F_{\text{rolling}}) v$) is integrated over braking periods to find $E_{\text{resistive}}$

​. The total braking energy is then given by $E_{\text{brake}}=\sum \mathrm{\Delta }KE-E_{\text{resistive}}$

${}_{\text{<br>}}$$E_{\text{battery}}={\eta }_{\text{regen}}{E}_{\text{brake}}$

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This method provides an estimate of the energy required for braking, considering both mechanical dissipation and potential energy recovery.

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2.Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?

An electric motor’s ability to generate braking torque at high speeds differs from its ability to generate starting torque due to the following reasons:

1. Back Electromotive Force (Back-EMF)
• At high speeds, the motor generates a significant back-EMF, which opposes the applied voltage and limits the current available for braking. Since braking torque is directly proportional to current, the available torque decreases.
2. Field Weakening at High Speed
• Many electric motors (especially induction and PMSM motors) use field weakening beyond the base speed. This reduces the magnetic field strength, which in turn lowers the available braking torque at high speeds.
3. Regenerative Braking Limitations
• In regenerative braking, the motor acts as a generator, converting kinetic energy into electrical energy. However, at very high speeds, the power electronics and battery may not be able to handle the high voltage generated, limiting regenerative braking capability.
4. Inverter and Power Electronics Constraints
• The inverter controlling the motor has operational limits on voltage and current. At high speeds, voltage saturation can occur, preventing the motor from developing sufficient braking torque.
5. Torque-Speed Characteristics
• Motors provide high torque at low speeds (constant torque region) but have reduced torque in the high-speed range (constant power region). This affects braking performance, just as it affects acceleration.

Electric and mechanical brakes are coordinated through brake blending to ensure efficient, smooth, and safe deceleration. The coordination process involves:

1. Regenerative Braking Priority
• The system first prioritizes regenerative braking to recover energy and recharge the battery.
2. Transition to Mechanical Brakes
• If the required braking force exceeds the regenerative braking capability (e.g., at low speeds or during emergency braking), mechanical brakes (friction brakes) supplement the braking effort.
3. Brake Control System (Blending Algorithm)
• A Brake Control Unit (BCU) or Vehicle Control Unit (VCU) continuously monitors speed, driver input, and braking torque demand to distribute braking force between the motor and mechanical brakes.
4. ABS and Stability Control Integration
• Mechanical brakes provide higher reliability in emergencies and are necessary for ABS (Anti-lock Braking System) and stability control, which operate independently of regenerative braking.
5. Creep Mode and Low-Speed Braking
• At very low speeds, regenerative braking becomes ineffective, so mechanical brakes fully take over to bring the vehicle to a complete stop.

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3.Make a MATLAB program which plots contour of given motor speed, torque and efficiency values. Attach the code as a .m file attach a screenshot of all the plots.

% MATLAB Program to Plot Motor Efficiency Contour

OUTPUT :

Figure 1

figure 2

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