How to Measure State-of-charge

Voltage Method

Measuring state-of-charge by voltage is the simplest method, but it can be inaccurate. Cell types have dissimilar chemical compositions that deliver varied voltage profiles. Temperature also plays a role. Higher temperature raises the open-circuit voltage, a lower temperature lowers it, and this phenomenon applies to all chemistries in varying degrees.

The most blatant error of voltage-based SoC occurs when disturbing the battery with a charge or discharge. This agitation distorts the voltage and no longer represents the true state-of-charge. To get accurate measurements, the battery needs to rest for at least four hours to attain equilibrium; battery manufacturers recommend 24 hours. Adding the element of time to neutralize voltage polarization does not sit well with batteries in active duty. One can see that this method is ill suited for fuel gauging.

Each battery chemistry delivers a unique discharge signature that requires a tailored model. 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. And yet, voltage is commonly used on consumer products. A “rested” Li-cobalt of 3.80V/cell in open circuit indicates a SoC of roughly 50 percent.

The discharge voltage curves of Li-manganese, Li-phosphate and NMC are very flat, and 80 percent of the stored energy remains in this flat voltage profile. This characteristic assists applications requiring a steady voltage but presents a challenge in fuel gauging. The voltage method only indicates full charge and low charge and cannot estimate the large middle section accurately. 

 Lead acid has diverse 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. Temperature also affects the open-circuit voltage; heat raises it while cold causes it to 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, the battery voltage must be truly “floating” with no load present. Installed in a car, the parasitic load present makes this a closed circuit voltage (CCV) condition that will falsify the readings. Adjustments must be made when measuring SoC in the CCV state by including the load current in the calculation. In spite of the notorious inaccuracies, most SoC measurements rely on the voltage method because it’s simple. Voltage-based state-of-charge is popular for wheelchairs, scooters and golf cars.

Hydrometer

The hydrometer offers an alternative to measuring SoC, but this only applies to flooded lead acid and flooded nickel-cadmium. Here is how it works: As the 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 1 provides the BCI readings of starter batteries.
  


Approximate state-of-charge

Average
specific gravity

Open circuit voltage

2V

6V

8V

12V

100%
75%
50%
25%
0%

1.265
1.225
1.190
1.155
1.120

2.10
2.08
2.04
2.01
1.98

6.32
6.22
6.12
6.03
5.95

8.43
8. 30
8.16
8.04
7.72

12.65
12.45
12.24
12.06
11.89
Table 1: BCI standard for SoC estimation of a maintenance-free starter battery with antimony. The readings are taken at room temperature of 26°C (78°F); the battery had rested for 24 hours after charge or discharge.
 

While BCI specifies the specific gravity of a fully charged starter battery at 1.265, battery manufacturers may go for 1.280 and higher. When increasing the specific gravity, the SoC readings on the look-up table will adjust upwards accordingly. Besides charge level and acid density, the SG can also vary due to low fluid levels, which raises the SG reading because of higher concentration. Alternatively, the battery can be overfilled, which lowers the number. When adding water, allow time for mixing before taking the SG measurement.

The specific gravity also varies according to battery type. Deep-cycle batteries use a dense electrolyte with an SG of up to 1.330 to get maximum runtime; aviation batteries have a SG of 1.285; traction batteries for forklifts are at 1.280; starter batteries come in at 1.265 and stationary batteries are at a low 1.225. Low specific gravity reduces corrosion. The resulting lower specific energy of stationary batteries is not as critical as longevity.

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 is, the higher (more dense) the SG value becomes. Table 2 illustrates the SG gravity of a deep-cycle battery at various temperatures.
 

Temperature of
the Electrolyte

Gravity at full charge
Table 2: Relation of specific gravity and temperature of deep-cycle battery
Colder temperatures provide higher specific gravity readings.

40°C
30°C
20°C
10°C
0°C

104°F
86°F
68°F
50°F
32°F

1.266
1.273
1.280
1.287
1.294

Errors can also occur if the acid has stratified, meaning the concentration is light on top and heavy on the bottom. 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 as a SoC indication. This method works on the principle of measuring the current that flows in and out of the battery. If, for example, a battery was charged for one hour at one ampere, the same energy should be available on discharge. This is not the case. Inefficiencies in charge acceptance, especially towards the end of charge, as well as losses during discharge and storage reduce the total energy delivered and skew the readings. The available energy is always less than what had been fed to the battery, and compensation corrects the shortage.

Disregarding these irregularities, coulomb counting works reasonably well, especially for Li-ion. However, the one percent accuracy some device manufacturers advertise is only possible in an ideal world and with a new battery. Independent tests show errors of up to 10 percent when in typical use. Aging causes a gradual deviation from the working model on which the coulomb counter is based. The result is a laptop promising 30 minutes of remaining runtime and all of a sudden the screen goes dark. Periodic calibration by applying a full discharge and charge to reset the flags reduces the error. See Calibration.

There is a move towards electrochemical impedance spectroscopy and even magnetism to measure state-of-charge. These new technologies get more accurate estimation than with voltage and can be used when the battery is under load. Furthermore, temperature, surface charge and acid stratification do not affect the readings noticeably.

Impedance Spectroscopy

Impedance spectroscopy evaluates the battery on the impedance values of the Randles model and works on flooded and sealed lead acid. The battery does not need to rest before taking the reading and parasitic loads do not affect the outcome. Figure 3 illustrates an incorrect SoC reading because of voltage drop when a load is applied; Figure 4 shows the correct result under the same conditions with impedance spectroscopy.
BCI*-based SoC reading SoC based on impedance spectroscopy
Figure 3: BCI*-based SoC reading.
A parasitic load distorts voltage-based SoC readings. Voltage recovery takes 4–8 hours.		 Figure 4: SoC based on impedance spectroscopy. A parasitic load does not affect the SoC reading.

* BCI (Battery Council International) measures state-of-charge by open circuit voltage. The voltage methods works well if the battery has no load and has rested after charge or discharge.

Courtesy of Cadex

Quantum Magnetism

In pursuit of a better way to measure battery state-of-charge, researchers are exploring radically new methods, one of which is quantum magnetism (Q-Mag™). Q-Mag by Cadex reads magnetism through spin-dependent tunneling. Here is how it works.

When discharging a lead acid battery, the negative plate changes from lead to lead sulfate, which has a different magnetic susceptibility to lead. Measuring the resulting change of the magnetic field with a sensor responding to magnetism provides linear SoC information. The magnetic change also works with lithium-ion, and the feedback is more pronounced than with lead acid. Figure 5 shows the concept on a starter battery.
Quantum Magnetism

Figure 5: State-of-charge measurement by quantum magnetism
Lead fights the applied magnetism less than lead sulfite, allowing SoC measurement by magnetism. Li-ion also responds well to magnetic SoC measurement.

Courtesy of Cadex

The sensor consists of two metal alloys separated by a thin insulator in the nanometer range (thickness of few atoms). The electrons in a magnetic field tunnel through the insulator more easily than in a neutral state, leading to a resistive change. Q-Magä interprets state-of-charge using mathematical models. The error is +/–7 percent over the entire SoC range, an accuracy that is unthinkable with voltage measurement, hydrometer and coulomb counters.

All batteries behave in a similar way in that the composition of the electrodes changes, which affects the magnetic characteristics. Q-Mag works on new as well as aged batteries and the technology is immune to voltage distortion caused by loading, charging or surface charge on lead acid. Figure 6 shows how magnetic measurements can track discharge/ charge activities of a lead acid battery independent of voltage. The circles represent the voltage under charge and the triangles reveal the state-of-charge.
 
Discharge/charge profile of a starter battery

Figure 6: Discharge/charge profile of a starter battery
SoC is being traced with magnetism from 0 to 100 percent against the voltage curve. Q-Mag tests have been carried out in the laboratories of Cadex Electronics Inc. (2010).

Test method: The battery was first discharged at 20A, followed by a constant charge of 9A to 14.4V and subsequent float charge.

Courtesy of Cadex

Measuring the intrinsic state of a battery rather than relying on voltage enables more precise full-charge detection. This feature can be used to improve charge methods and diagnose battery deficiencies, including predicting end-of-life by measuring battery capacity. Q-Mag works also with lithium-ion in non-ferric enclosures. Many of these technologies are proprietary and are in various experimental stages at Cadex.

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Comments

On September 21, 2011 at 12:51pm
Joe Accetta wrote:

There is yet another and quite accurate means of measuring SOC in open port lead acid batterieis through the use of refractometry. The index of refraction of the electrolyte is directlly proportional to the SG. JSA Photonics has developed an in-cell immersion refractometer that yields accurate 24/7 SOC information along with cell temperature for monitoroing and temp correction and in some instances electrolyte level. The sensor replaces the existing battery cap. See www.jsaphotonics.com.

On October 13, 2011 at 4:02am
Josep wrote:

I’m investigating about, and I read that the most common, easy, and accurate way of measuring OSC is Ampere Hour Counting.

http://www.sciencedirect.com/science/article/pii/S0378775301005602#sec2.2

On November 29, 2011 at 7:15am
Qaisar Azeemi wrote:

Its really nice information about SOC is given here. But i request to please include measurement steps for all methods mentioned above.
Thank you

On January 20, 2012 at 5:05am
kishore kumar wrote:

Its good to know about soc. There is metal detector to detect metal likewise I need to know how to detect a battery? Can anyone help me.

On January 25, 2012 at 1:34pm
Diego wrote:

All,
the problem of establishing the SOC is not trivial, expecially with LiFePO4 batteries. An interesting article “Fine Tuning TI-impedence Track (TM) battery fuel gauge with LiFePO4 cells in shallow discharge application” can be found at this link

http://www.ti.com/lit/an/slyt402/slyt402.pdf

On February 20, 2012 at 2:11am
Kumar wrote:

Please provide me the positive and negative plate behaviour of a lead acid battery during charge & discharge when it is measured with a cadmium rod as reference.