phones, leaf blowers, electric cars, etc?
It turns out most modern Battery Management Systems (BMS) use a combination of four variables to estimate the remaining charge in a battery.
1. Voltage Measurement: Used to provide quick and direct State Of Charge (SOC) estimates but can be inaccurate due to load variations. There are two measurements typically considered:
- Open-Circuit Voltage (OCV): This measures the voltage when the battery is not under load. Each battery type has a characteristic voltage curve that relates voltage to SOC.
- Under-Load Voltage (ULV): This measures the voltage while the battery is under load. Compensation is required to account for the voltage drop due to internal resistance.
2. Coulomb/Charge Counting: Precise over short periods but can drift over time due to measurement inaccuracies.
- Coulomb/Charge Counting involves tracking the current flowing in and out of the battery. By integrating the current over time, you can estimate the total charge added or removed. This method needs a known initial state of charge to be accurate.
3. Impedance Tracking: Provides additional data to refine SOC estimates but requires complex algorithms and computations.
- Impedance Tracking uses the battery's internal impedance (reciprocal resistance) which changes with the state of charge. By measuring the impedance, the state of charge can be estimated.
4. Temperature Compensation: Battery performance and voltage readings can be significantly affected by temperature.
- Temperature sensors are used to adjust the SOC calculations.
Battery Capacity
Battery capacity C for a new battery is a given and specified by the battery manufacturer in ampere-hours (Ah) or milliampere-hours (mAh) units, depending on the size of the battery. As an example, the iPhone 15 Pro is equipped with a single battery rated at 3274mAh. If you are wondering about your Tesla or Prius - batteries are wired in parallel – for example a 2020 Long Range Tesla Model 3 battery pack has 46 cells in parallel with each cell rated at 5 Ah. So that Tesla battery pack has about 46x5 Ah = 230 Ah capacity. Over time, battery capacity will decrease.
Some Variables
Let’s look at a couple of simple calculations used by our devices to calculate battery charge/percentage. Before we look at the formulas, let’s identify some variables used in the calculations.
Initial Calibration:
- Battery starts fully charged (100% SOC).
- OCV is measured to establish a reference point.
Discharge Phase:
- Voltage is continuously monitored.
- Coulomb counting tracks the charge removed.
- Impedance is checked periodically to refine the SOC estimate.
- Temperature compensation adjusts the readings.
State of Charge Calculation:
- Combining the voltage, coulomb count, and impedance data, the BMS computes the SOC.
- This value is then translated into a percentage to display the remaining battery life.
Finally - A Couple Formulas
There are two formulas commonly used - the first uses current (Coulomb Counting) and the second voltage (Voltage-Based SOC Estimation)
Formula for Coulomb Counting Estimation:
Formula for Voltage-Based SOC Estimation:
Battery percentage calculations rely on sensor measurements that account for the various factors affecting battery performance. Using real time sensor data, BMS algorithms continue to advance, providing estimates of remaining battery charge.
