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BMS functions and EV range numerical

Short answer

BMS monitors cell voltage/temp, estimates SoC/SoH, protects against overcharge/discharge, balances cells, manages thermal. Usable energy 0.9×40=36 kWh, range 36000/160=225 km. Charging energy (0.8-0.2)×40=24 kWh; effective power 7.4×0.92=6.81 kW; time 24/6.81≈3.53 h (3 h 32 min).

(a) State the main functions of a battery management system (BMS). (b) An electric car has a 40 kWh battery of which 90 % is usable and consumes 160 Wh/km. Find its range. It is charged from 20 % to 80 % of the 40 kWh capacity through an AC charger of 7.4 kW rated output with 92 % efficiency. Find the charging time.

(a) Functions of a BMS

  1. Monitoring of cell voltages, pack current and temperature.
  2. State of charge (SoC) and state of health (SoH) estimation.
  3. Protection against over-charge, deep discharge, over-current, short circuit and over-temperature, by tripping the contactors.
  4. Cell balancing (passive, using resistors, or active, by transferring charge), so that all cells have the same SoC.
  5. Thermal management: control of cooling or heating.
  6. Communication with the vehicle ECU and the charger over CAN, including limits on charge and discharge power.

(b) Numerical

Range

Eusable=0.9×40=36 kWh,Range=36 000160=225 kmE_{usable} = 0.9 \times 40 = 36\ \text{kWh}, \qquad \text{Range} = \frac{36\,000}{160} = 225\ \text{km}

Charging time

Energy to be stored =(0.80−0.20)×40=24= (0.80 - 0.20) \times 40 = 24 kWh.

Taking 7.4 kW as the AC power the charger supplies and 92 % as the charging efficiency, the power reaching the battery is:

Peff=7.4×0.92=6.81 kW,t=246.81=3.53 hP_{eff} = 7.4 \times 0.92 = 6.81\ \text{kW}, \qquad t = \frac{24}{6.81} = 3.53\ \text{h}

The energy drawn from the supply is 24/0.92=26.124/0.92 = 26.1 kWh. (If instead the full 7.4 kW reached the battery, the time would be 24/7.4=3.2424/7.4 = 3.24 h. In practice the charging rate tapers near 80 % SoC.)

Answer: range =225= 225 km; charging time ≈3.53\approx 3.53 h (3 h 32 min).

✓ Answer checked by Claude Opus 5.5 (high effort)

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