How to Measure State-of-charge

Explore SoC measurements and why they are not accurate.

Voltage Method

Measuring state-of-charge by voltage is simple, but it can be inaccurate because cell materials and temperature affect the voltage. The most blatant error of the voltage-based SoC occurs when disturbing a battery with a charge or discharge. The resulting agitation distorts the voltage and it no longer represents a correct SoC reference. To get accurate readings, the battery needs to rest in the open circuit state for at least four hours; battery manufacturers recommend 24 hours for lead acid. This makes the voltage-based SoC method impractical for a battery in active duty.

Each battery chemistry delivers its own unique discharge signature. While voltage-based SoC works reasonably well for a lead acid battery that has rested, the flat discharge curve of nickel- and lithium-based batteries renders the voltage method impracticable.

The discharge voltage curves of Li-manganese, Li-phosphate and NMC are very flat, and 80 percent of the stored energy remains in the flat voltage profile. While this characteristic is desirable as an energy source, it presents a challenge for voltage-based fuel gauging as it only indicates full charge and low charge; the important middle section cannot be estimated accurately. Figure 1 reveals the flat voltage profile of Li-phosphate (LiFePO) batteries.

Figure 1: Discharge voltage of lithium iron phosphate.
Li-phosphate has a very flat discharge profile, making voltage estimations for SoC estimation difficult.

Lead acid comes with different plate compositions that must be considered when measuring SoC by voltage. Calcium, an additive that makes the battery maintenance-free, raises the voltage by 5–8 percent. In addition, heat raises the voltage while cold causes a decrease. Surface charge further fools SoC estimations by showing an elevated voltage immediately after charge; a brief discharge before measurement counteracts the error. Finally, AGM batteries produce a slightly higher voltage than the flooded equivalent.

When measuring SoC by open circuit voltage (OCV), the battery voltage must be “floating” with no load attached. This is not the case with modern vehicles. Parasitic loads for housekeeping functions puts the battery into a quasi-closed circuit voltage (CCV) condition.

In spite of inaccuracies, most SoC measurements rely in part or completely on voltage because of simplicity. Voltage-based SoC is popular in wheelchairs, scooters and golf cars. Some innovative BMS (battery management systems) use the rest periods to adjust the SoC readings as part of a “learn” function. Figure 2 illustrates the voltage band of a 12V lead acid monoblock from fully discharged to full charged.

Figure 2: Voltage band of a 12V lead acid monoblock from fully discharged to fully charged.Source: Power-Sonic

Hydrometer

The hydrometer offers an alternative to measuring SoC of flooded lead acid batteries. Here is how it works: When the lead acid battery accepts charge, the sulfuric acid gets heavier, causing the specific gravity (SG) to increase. As the SoC decreases through discharge, the sulfuric acid removes itself from the electrolyte and binds to the plate, forming lead sulfate. The density of the electrolyte becomes lighter and more water-like, and the specific gravity gets lower. Table 2 provides the BCI readings of starter batteries.

Approximate state-of-charge	Average specific gravity	Open circuit voltage
		2V	6V	8V	12V
100%	1.265	2.10	6.32	8.43	12.65
75%	1.225	2.08	6.22	8.30	12.45
50%	1.190	2.04	6.12	8.16	12.24
25%	1.155	2.01	6.03	8.04	12.06
0%	1.120	1.98	5.95	7.72	11.89

Table 2: BCI standard for SoC estimation of a starter battery with antimony.
Readings are taken at 26°C (78°F) after a 24h rest.

While BCI (Battery Council International) specifies the specific gravity of a fully charged starter battery at 1.265, battery manufacturers may go for 1.280 and higher. Increasing the specific gravity will move the SoC readings upwards on the look-up table. A higher SG will improve battery performance but shorten battery life because of increased corrosion activity.

Besides charge level and acid density, a low fluid level will also change the SG. When water evaporates, the SG reading rises because of higher concentration. The battery can also be overfilled, which lowers the number. When adding water, allow time for mixing before taking the SG measurement.

Specific gravity varies with battery applications. Deep-cycle batteries use a dense electrolyte with an SG of up to 1.330 to get maximum specific energy; aviation batteries have an SG of about 1.285; traction batteries for forklifts are typically at 1.280; starter batteries come in at 1.265; and stationary batteries have a low specific gravity of 1.225. This reduces corrosion and prolongs life but it decreases the specific energy, or capacity.

Nothing in the battery world is absolute. The specific gravity of fully charged deep-cycle batteries of the same model can range from 1.270 to 1.305; fully discharged, these batteries may vary between 1.097 and 1.201. Temperature is another variable that alters the specific gravity reading. The colder the temperature drops, the higher (more dense) the SG value becomes. Table 3 illustrates the SG gravity of a deep-cycle battery at various temperatures.

Electrolyte temperature		Gravity at full charge	Table 3: Relationship of specific gravity and temperature of deep-cycle battery. Colder temperatures provide higher specific gravity readings.
40°C	104°F	1.266
30°C	86°F	1.273
20°C	68°F	1.280
10°C	50°F	1.287
0°C	32°F	1.294

Inaccuracies in SG readings can also occur if the battery has stratified, meaning the concentration is light on top and heavy on the bottom. (See BU-804c: Water Loss, Acid Stratification and Surface Charge.). High acid concentration artificially raises the open circuit voltage, which can fool SoC estimations through false SG and voltage indication. The electrolyte needs to stabilize after charge and discharge before taking the SG reading.

Coulomb Counting

Laptops, medical equipment and other professional portable devices use coulomb counting to estimate SoC by measuring the in-and-out-flowing current. Ampere-second (As) is used for both charge and discharge. The name “coulomb” was given in honor of Charles-Augustin de Coulomb (1736–1806) who is best known for developing Coulomb’s law. (See BU-601: How does a Smart Battery Work?)

While this is an elegant solution to a challenging issue, losses reduce the total energy delivered, and what’s available at the end is always less than what had been put in. In spite of this, coulomb counting works well, especially with Li-ion that offer high coulombinc efficiency and low self-discharge. Improvements have been made by also taking aging and temperature-based self-discharge into consideration but periodic calibration is still recommended to bring the “digital battery” in harmony with the “chemical battery.” (See BU-603: How to Calibrate a “Smart” Battery)

To overcome calibration, modern fuel gauges use a “learn” function that estimates how much energy the battery delivered on the previous discharge. Some systems also observe the charge time because a faded battery charges more quickly than a good one.

Makers of advanced BMS claim high accuracies but real life often shows otherwise. Much of the make-believe is hidden behind a fancy readout. Smartphones may show a 100 percent charge when the battery is only 90 percent charged. Design engineers say that the SoC readings on new EV batteries can be off by 15 percent. There are reported cases where EV drivers ran out of charge with a 25 percent SoC reading still on the fuel gauge.

Impedance Spectroscopy

Battery state-of-charge can also be estimated with impedance spectroscopy using the Spectro™ complex modeling method. This allows taking SoC readings with a steady parasitic load of 30A. Voltage polarization and surface charge do not affect the reading as SoC is measured independently of voltage. This opens applications in automotive manufacturing where some batteries are discharged longer than others during testing and debugging and need charging before transit. Measuring SoC by impedance spectroscopy can also be used for load leveling systems where a battery is continuously under charge and discharge.

Measuring SoC independently of voltage also supports dock arrivals and showrooms. Opening the car door applies a parasitic load of about 20A that agitates the battery and falsifies voltage-based SoC measurement. The Spectro™ method helps to identify a low-charge battery from one with a genuine defect.

SoC measurement by impedance spectroscopy is restricted to a new battery with a known good capacity; capacity must be nailed down and have a non-varying value. While SoC readings are possible with a steady load, the battery cannot be on charge during the test.

Figure 4 demonstrates the test results of impedance spectroscopy after a parasitic load of 50A is removed from the battery. As expected, the open terminal voltage rises as part of recovery but the Spectro™ readings remains stable. Steady SoC results are also observed after removing charge during when the voltage normalizes as part of polarization.

Figure 4: Relationship of voltage and measurements taken by impedance spectroscopy after removing a load. Battery is recovering after removing a load. Spectro SoC readings remain stable as the voltage rises.