BMS-08 — SOC Estimation

1. There’s No Sensor That Measures SOC Directly

SOC represents the lithium distribution inside a cell’s electrodes — its internal chemical state. No sensor observes that directly; the BMS has to estimate SOC from current, voltage, and temperature measurements. An accurate estimate is critical for the range indicator, protection limits, and energy management.

2. Coulomb Counting: Simple but Forgetful

You integrate current over time to compute the charge that’s passed:

SOC(t) = SOC(0) - (1/C_nominal) ∫ i(t) dt

Simple and direct, but error accumulates — the initial SOC error and current-sensor offset both grow over time. A constant +20 A offset produces a 20 Ah error in charge accounting over 1 hour (BMS-05); in our hypothetical 225 Ah pack, that alone is a ~8.9% deviation.

3. OCV Feedback Resets the Error

OCV, measured while a cell is resting (current ≈ 0), has a strong, repeatable relationship with SOC — this relationship is calibrated as the OCV-SOC curve. By catching rest periods and measuring OCV, the BMS can periodically zero out Coulomb counting’s accumulated error.

In NMC this curve is usually a steep, distinctive S-shape; in LFP there’s a very flat plateau across the middle SOC range (~20-80%) (see the diagram below).

4. Why You Can’t Just Look at Voltage

Under load, terminal voltage deviates from OCV due to the internal-resistance drop and polarization:

V_terminal = OCV(SOC) - I × R_internal   (during discharge; the sign flips during charge)

With OCV(50%) = 3.7 V, R_internal = 2 mΩ, and a 200 A discharge current: V_terminal = 3.7 - 0.4 = 3.3 V. In other words, even though the cell is really at 50% SOC, only 3.3 V is read under load — feeding that value directly into the OCV-SOC curve gives the wrong SOC. The problem gets worse for flat-plateau chemistries like LFP: voltage already barely moves against SOC, so voltage alone can’t discriminate.

ASSUMPTION — The OCV and R_internal values in this example are representative; the real curve and resistance are determined through lab characterization specific to cell chemistry, temperature, and aging.

Because capacity and internal resistance change with temperature and aging, the SOC algorithm also uses temperature and SOH data to compensate for these effects (BMS-09).

5. Model + Observer: Combining Both

The model-based approach represents a cell with an equivalent circuit model (R-C networks); current/voltage/temperature measurements feed into the model, which estimates SOC and internal states (polarization voltages). An observer is a feedback structure that continuously corrects the model’s prediction against measurement. A Kalman Filter, and its EKF variant for nonlinear systems, statistically balances measurement noise against model error to produce an optimal estimate — combining Coulomb counting’s directness with OCV feedback so it both reduces accumulated error and stays accurate under dynamic load.

6. When Things Go Wrong

Typical things that corrupt SOC estimation: current sensor offset, voltage measurement error, an incorrect OCV-SOC table, and long stretches without a rest period (no chance for OCV correction). In these cases the BMS can lower SOC confidence and apply more conservative power limits (SOP).

7. How It’s Calibrated in Production

The OCV-SOC curve and model parameters (R-C values) are determined through cell characterization tests at different temperature/aging levels and loaded into the BMS software. HIL testing simulates different SOC/temperature scenarios to verify the algorithm’s accuracy (BMS-19, BMS-20).

8. How It Connects to Other Systems

SOC is the direct input to the SOP calculation (BMS-10), the target quantity for cell balancing (BMS-11), and the source of the range/percentage information shown to the driver (via BMS-15).

Interactive Tool

Use the SOC/Coulomb Counting Simulator below — enter a current and duration and watch how SOC changes, and how an offset accumulates error over time.

Summary

• SOC can’t be measured directly; it’s estimated.
• Coulomb counting is simple but accumulates error; OCV feedback zeroes it out but needs a rest period.
• Kalman/EKF fuses measurement and model for a robust estimate.
• The OCV-SOC table and model parameters are calibrated in production.

Sources

• Gregory L. Plett, Battery Management Systems, Volume I & II — SOC, EKF, observer.