Battery management system: SoC, SoH and cell balancing

Why it matters

A lithium-ion pack is safe and long-lived only if every cell stays inside its voltage, current and temperature window, and the driver trusts an EV only if its range display is accurate. The battery management system (BMS) does both jobs: it protects hundreds of cells individually and estimates state of charge (SoC), state of health (SoH) and available power. BMS design, calibration and validation are among the most active EV engineering jobs in India.

Key ideas

What a BMS does.

• Sensing: voltage of every series cell group (to a few millivolts), temperatures at many points, pack current (shunt or Hall sensor), pack voltage, and insulation resistance between the high-voltage system and the chassis.
• Protection: limits for over-voltage, under-voltage, over-current, over- and under-temperature; opens the main contactors if limits are exceeded; controls the pre-charge sequence that charges the inverter's capacitors through a resistor before closing the main contactor.
• Estimation: SoC, SoH, state of power (how much charge and discharge power the pack can accept or deliver right now) and remaining range.
• Balancing: equalising cells so that the whole series string can use its capacity.
• Thermal control: requests cooling or heating from the thermal system.
• Charging control: sets the charger's current and voltage (constant current, then constant voltage) and talks to DC fast chargers.
• Communication and diagnostics: CAN messages to the vehicle control unit and charger; fault codes and data logging.

Architectures. Centralised (one board wired to every cell — simple for small packs such as two-wheelers), distributed or modular (cell-monitoring units on each module report to a master over an isolated link — common in cars).

State of charge. SoC is the remaining charge as a fraction of the cell's present full capacity (100 % full, 0 % empty). It cannot be measured directly; it is estimated by:

• OCV lookup: open-circuit voltage maps to SoC, but only after the cell has rested (often tens of minutes), and the curve is very flat for LFP over most of its range.
• Coulomb counting: integrate current over time from a known starting SoC. Accurate over short periods, but sensor offset and capacity errors accumulate, so it must be corrected periodically (e.g. at full charge or after a rest).
• Model-based estimation: an equivalent-circuit model (OCV source, series resistance, one or two RC pairs) with a Kalman filter blends the current integral with measured voltage to correct drift continuously. Temperature and ageing change both capacity and the voltage curve, so the estimator must compensate.

State of health. SoH describes ageing compared with a new pack. Capacity-based SoH is present capacity ÷ rated capacity; resistance-based SoH tracks the rise in internal resistance (which reduces power). End of life for traction use is commonly taken at about 70–80 % of rated capacity. Ageing comes from calendar ageing (time, temperature, high SoC storage) and cycle ageing (depth of discharge, C-rate, temperature).

Why cells drift apart and balancing. Cells differ slightly in capacity, self-discharge and temperature. In a series string the same current flows through all cells, so charging must stop when the highest cell reaches its maximum voltage and discharging when the lowest reaches its minimum. Unbalanced cells therefore waste usable capacity and, if unprotected, can be over-charged or over-discharged.

• Passive balancing: a resistor and switch across each cell bleed charge from the higher cells, usually near the top of charge. Simple and cheap, but the energy is lost as heat and balancing currents are small (typically tens to a few hundred mA).
• Active balancing: capacitors, inductors or transformers move charge from high cells to low cells. More efficient and faster, but more complex and costly.

Insulation monitoring. The high-voltage system is floating (isolated from the chassis). The BMS or a separate monitor checks the insulation resistance continuously; safety standards set a minimum in Ω per volt of working voltage (take the value from the applicable standard).

Formulas

SoC(t) = SoC₀ − (1 / Q_act) × ∫ η I dt

• SoC as a fraction, SoC₀: initial SoC, Q_act: present actual capacity (A·s or A·h), I: current (A, positive for discharge), η: coulombic efficiency (≈ 1 for Li-ion; < 1 when charging if losses are included), t (s or h, consistent with Q).

SoH_C = Q_act / Q_rated

• Capacity-based state of health (fraction).

SoH_R = (R_EOL − R_now) / (R_EOL − R_new)

• Resistance-based state of health (fraction): R_new: internal resistance when new, R_EOL: resistance defined as end of life, R_now: present value (Ω).

DoD = 1 − SoC

ΔSoC_error = I_offset × t / Q_act

• SoC drift from a current-sensor offset I_offset (A) over time t (h), Q_act (A·h).

I_bleed = V_cell / R_bleed, t_bal = ΔQ / I_bleed, P_bleed = V_cell² / R_bleed

• Passive balancing: bleed current (A), time to remove excess charge ΔQ (h if ΔQ in A·h), heat in the resistor (W).

V_t = OCV(SoC) − I × R₀ − V_RC

• Equivalent-circuit terminal voltage (V); R₀: series resistance (Ω), V_RC: voltage across the RC branch (V).

Worked examples

Example 1 (standard). A pack rated 66 A·h now has an actual capacity of 60 A·h and starts at 90 % SoC. It is driven for 45 min at an average 40 A discharge, then regenerates for 10 min at an average 12 A. Take coulombic efficiency as 1. Find the final SoC and the capacity-based SoH.

1. Charge removed = 40 × 0.75 = 30 A·h; charge returned = 12 × (10/60) = 2 A·h; net = 28 A·h.
2. SoC = 0.90 − 28 / 60 = 0.90 − 0.467 = 0.433.
3. SoH_C = 60 / 66 = 0.909.

Answer: SoC ≈ 43.3 %, SoH ≈ 90.9 %.

Example 2 (GATE level). (a) The current sensor of the pack in Example 1 has a 0.2 A offset. How large a SoC error builds up in 10 h of coulomb counting? (b) One cell group is 0.6 A·h higher than the rest at about 4.10 V. Its passive-balancing resistor is 47 Ω. Find the bleed current, the time to balance and the heat dissipated. (c) A cell's resistance was 1.5 mΩ new, end of life is defined at 3.0 mΩ, and it now measures 2.1 mΩ. Find SoH_R.

1. ΔSoC = 0.2 × 10 / 60 = 0.033 → about 3.3 % of SoC.
2. I_bleed = 4.10 / 47 = 0.0872 A; t = 0.6 / 0.0872 = 6.88 h; P = 4.10² / 47 = 0.358 W.
3. SoH_R = (3.0 − 2.1) / (3.0 − 1.5) = 0.6 → 60 %.

Answer: about 3.3 % drift; 87 mA, about 6.9 h, about 0.36 W; SoH_R = 60 %.

Common mistakes

• Dividing by the rated capacity instead of the present (aged) capacity when computing SoC.
• Confusing SoC (charge left now) with SoH (how much the pack has aged).
• Expecting an OCV reading under load or straight after driving to give an accurate SoC.
• Forgetting that coulomb counting drifts and must be re-anchored.
• Believing balancing increases the capacity of a weak cell. It only lets the string use the capacity the weakest cell has.
• Assuming passive balancing is fast; with tens of milliamps it takes hours.
• Treating pack voltage as a reliable SoC indicator for LFP; its voltage curve is too flat.

For GATE ME

BMS questions are mostly applications of charge and energy balance: integrating current over time, percentages and ratios, Ohm's law and resistor power, and series-string reasoning (weakest cell limits the pack). Practise keeping A·h, A·s, h and s consistent.

Quick check

1. Why does coulomb counting need periodic correction?
2. In a series string, which cell ends charging and which ends discharging?
3. A 100 A·h pack at 80 % SoC delivers 30 A for 1 h. What is the new SoC?
4. What is the main drawback of passive balancing?
5. What does a pre-charge circuit do?

Answers: 1. Sensor offset and capacity errors accumulate as drift. 2. The highest-voltage cell ends charging; the lowest ends discharging. 3. 50 %. 4. The excess energy is wasted as heat and balancing is slow. 5. Charges the inverter's DC-link capacitors through a resistor so the main contactor does not close onto a large inrush current.