Calculating the State of Charge of a Lithium Ion Battery System using a Battery Management System

Summary

In this Stifle Systems Insights video, Eric Staal discusses the concept of State of Charge (SOC) in battery packs, emphasizing its definition as the remaining capacity relative to the total capacity in amp-hours. He illustrates the difference between SOC based on capacity and SOC based on energy, highlighting the importance of understanding the energy available for applications like electric vehicles. Staal also explains the method of Coulomb counting for calculating SOC, the challenges of current sensor drift, and the role of open circuit voltage (OCV) lookup in ensuring accurate SOC estimation for reliable battery performance.

Takeaways

• 🔋 The state of charge (SOC) is defined as the remaining capacity in amp-hours or coulombs that can be discharged over the total capacity of the battery pack.
• 📉 SOC is measured in units of amp-hours, not energy, which is an important distinction because the voltage of a battery changes as it discharges.
• 📊 The discharge curve for lithium-ion batteries typically shows a varying downward slope, with higher voltage in the initial stages and lower voltage towards the end of discharge.
• 🚗 In electric vehicle applications, it's more useful to consider the energy available (SOC II) rather than just the capacity remaining, as it provides a more accurate fuel gauge algorithm.
• 🔍 The 50% SOC point on the discharge curve does not necessarily correspond to 50% of the energy remaining; it's where 50% of the amp-hours have been discharged.
• 🔄 Coulomb counting is the primary method for calculating SOC, which involves integrating the current over time to estimate the amp-hours discharged.
• 🛠 Current sensors used in Coulomb counting can have drift and integration errors, which is why open circuit voltage (OCV) lookup tables are used to correct and recalibrate the SOC estimation.
• 🔄 Depth of discharge (DOD) is the inverse of SOC and represents the percentage of the battery's capacity that has been used.
• 🔄 The BMS uses OCV lookup to determine the SOC when the battery is at rest, ensuring an accurate starting point for Coulomb counting and reliable SOC estimation.
• ⚙️ Accurate SOC and SOC II algorithms are crucial for the reliable and predictable operation of battery packs, preventing issues like sudden drops in estimated charge.

Q & A

What is the state of charge (SOC) of a battery pack?

The state of charge (SOC) is defined as the capacity remaining over the total capacity in amp-hours or coulombs that you can discharge over the total capacity of the battery pack.

How is the SOC percentage calculated?

The SOC percentage is calculated by dividing the remaining capacity by the total capacity of the battery pack. For example, if a battery pack has a total capacity of 100 amp-hours and 70 amp-hours are left, the SOC is 70%.

Why is it important to distinguish between SOC and energy units?

It's important because SOC is measured in amp-hours, which is a measure of capacity, whereas energy is measured in watt-hours. This distinction is crucial for applications like electric vehicles where the available energy, not just capacity, determines the range.

What is the significance of the discharge curve for lithium-ion batteries?

The discharge curve for lithium-ion batteries typically shows a varying downward slope in voltage as capacity is discharged. This curve is significant because it illustrates the relationship between voltage, capacity, and energy, which is essential for understanding battery performance.

What is the difference between SOC based on capacity (SOC I) and SOC based on energy (SOC II)?

SOC I is based on the remaining capacity in amp-hours, while SOC II is based on the available energy. SOC II provides a more accurate representation of the expected runtime or range, as it accounts for the varying energy output at different states of charge.

Why is Coulomb counting a primary method for calculating SOC?

Coulomb counting is a primary method for calculating SOC because it involves integrating the current over time to estimate the amp-hours discharged, providing a direct measure of the battery's state of charge.

What challenges does Coulomb counting face in accurately estimating SOC?

Coulomb counting faces challenges such as current sensor drift and integration error, which can lead to inaccuracies in the estimation of discharged amp-hours. To mitigate this, additional methods like open circuit voltage (OCV) lookup are often used.

What is open circuit voltage (OCV) lookup and how does it help in SOC estimation?

OCV lookup is a method where the BMS compares the actual voltage of the battery at rest with a lookup table to determine the corresponding state of charge or depth of discharge. This helps in recalibrating the SOC estimation, ensuring accuracy and reliability.

What is the relationship between depth of discharge (DOD) and SOC?

Depth of discharge (DOD) is the inverse of SOC. While SOC represents the remaining capacity, DOD represents the amount of capacity that has been used. For example, at 70% SOC, the DOD would be 30%.

Why is it crucial to have an accurate SOC estimation in applications like electric vehicles?

In electric vehicles, an accurate SOC estimation is crucial for predicting the remaining range and ensuring reliable operation. Inaccurate SOC estimation can lead to unexpected battery depletion, causing inconvenience and potential stranding of the vehicle.

Outlines

00:00

🔋 Understanding State of Charge (SOC) and Capacity

In this segment, Eric Staal, the president of Stoffels Systems, introduces the concept of State of Charge (SOC) in battery packs. SOC is defined as the remaining capacity of a battery pack expressed as a percentage of its total capacity. Using a 100 amp-hour battery pack as an example, if 70 amp-hours are left to discharge, the SOC is 70%. It's emphasized that SOC is measured in amp-hours, not energy, which is a critical distinction. The video also explains the voltage discharge curve of lithium-ion batteries, highlighting how voltage decreases as capacity is discharged. The importance of differentiating between energy and capacity is discussed, especially in applications like electric vehicles where energy available is more relevant than raw capacity. The concept of SOC II, which is energy-based, is introduced as a more accurate representation for fuel gauge algorithms.

05:07

🔬 Calculating SOC: Coulomb Counting and Open Circuit Voltage (OCV) Lookup

The second paragraph delves into how SOC is calculated, focusing on Coulomb counting as the primary method. Coulomb counting involves integrating the current over time to determine the amp-hours discharged, which is essential for calculating SOC. The discussion points out the challenges of current sensor drift and integration error, which can affect the accuracy of SOC estimation. To mitigate these issues, the Battery Management System (BMS) uses an open circuit voltage (OCV) lookup. This lookup compares the integrated current data with the actual cell voltage to recalibrate the SOC. The concept of depth of discharge (DOD) is also introduced as the inverse of SOC, and its importance in recalibrating the SOC after the battery has been at rest is explained. The video concludes by emphasizing the importance of accurate SOC and SOC II calculations for reliable battery pack operation, particularly in applications like electric vehicles where inaccurate readings could lead to stranded vehicles and safety concerns.

Keywords

💡State of Charge (SOC)

State of Charge (SOC) is a measure of the amount of charge left in a battery. It is defined as the ratio of the remaining capacity to the total capacity of the battery pack, expressed in amp-hours or coulombs. In the video, SOC is used to illustrate how much of the battery's capacity is left after a certain amount has been discharged. For instance, if a battery pack has a total capacity of 100 amp-hours and 70 amp-hours are left, the SOC is 70%. This concept is central to understanding the battery's health and capacity to deliver power.

💡Battery Pack

A battery pack refers to a combination of multiple battery cells that are connected together to provide a desired voltage and capacity. In the context of the video, the battery pack's total capacity is used to calculate the SOC. The video explains that the SOC is determined by the capacity remaining in the battery pack, which is crucial for applications such as electric vehicles where knowing the exact charge level is essential for range estimation.

💡Capacity

Capacity in the context of batteries refers to the amount of electric charge that a battery can store. It is typically measured in amp-hours (Ah). The video uses the term to explain the total capacity of a battery pack, which is the maximum amount of charge it can hold. The SOC is directly related to the capacity, as it represents the percentage of the total capacity that is still available.

💡Coulomb Counting

Coulomb counting is a method used to estimate the SOC by integrating the current flowing in or out of the battery over time. It involves multiplying the current by the time interval and summing these products to approximate the total charge that has flowed out of the battery. The video emphasizes that Coulomb counting is the primary method for calculating SOC and is essential for accurate battery management systems (BMS).

💡Discharge Curve

A discharge curve is a graphical representation of the voltage of a battery cell or pack as it discharges over time. The video describes how the discharge curve for lithium-ion batteries typically has a downward slope, with the voltage decreasing as the battery discharges. This curve is important for understanding the relationship between the SOC and the actual energy available from the battery.

💡Energy-Based SOC (SOC II)

Energy-Based SOC, or SOC II, is a more accurate representation of the battery's state that takes into account the varying energy content at different SOC levels. Unlike the simple capacity-based SOC, SOC II considers the energy available at each point of discharge, which is more relevant for applications like electric vehicles where the usable energy, not just the capacity, is critical. The video explains that SOC II is a more reliable indicator of the expected runtime or range of a battery.

💡Open Circuit Voltage (OCV)

Open Circuit Voltage (OCV) is the voltage of a cell when no current is flowing. The video mentions that BMS uses OCV lookup tables to compare the actual voltage of a cell with the expected voltage for a given temperature and SOC. This comparison helps in recalibrating the SOC estimation, ensuring that the battery's state is accurately represented, which is crucial for preventing inaccurate fuel gauge algorithms that could lead to unexpected battery depletion.

💡Depth of Discharge (DOD)

Depth of Discharge (DOD) is the inverse of SOC and represents the percentage of the battery's capacity that has been used. The video uses DOD to illustrate the relationship between the SOC and the voltage of the battery. For example, at a 70% SOC, the DOD would be 30%. Understanding DOD is important for battery management as it helps in determining the health and lifespan of the battery by monitoring how much of its capacity has been utilized.

💡Fuel Gauge Algorithm

A fuel gauge algorithm is a method used to estimate the remaining capacity or range of a battery, similar to how a fuel gauge in a car shows the amount of fuel left. The video discusses how confusing SOC with a fuel gauge algorithm can lead to inaccuracies because the energy available varies with the SOC. The correct approach, as highlighted in the video, is to use SOC II, which is based on energy, to provide a more accurate and reliable fuel gauge for applications like electric vehicles.

💡Battery Management System (BMS)

A Battery Management System (BMS) is an electronic system that monitors and controls the charging and discharging of battery cells to ensure optimal performance, prolong battery life, and prevent damage. The video explains that BMS uses techniques like Coulomb counting and OCV lookup to calculate the SOC and ensure accurate battery monitoring. The BMS is essential for managing battery packs in applications such as electric vehicles and renewable energy storage systems.

Highlights

Definition of State of Charge (SOC) as the remaining capacity relative to total capacity in amp-hours or coulombs.

Example illustrating SOC calculation with a 100 amp-hour battery pack.

Clarification that SOC is measured in amp-hours, not energy units.

Explanation of the typical discharge curve for lithium-ion batteries.

Importance of understanding the varying voltage slope during battery discharge.

Misinterpretation risks when conflating SOC with fuel gauge algorithms.

Introduction of SOC II, which is based on energy rather than capacity.

Practical example of calculating SOC II based on the area under the discharge curve.

Differentiation between energy-based SOC (SOC II) and capacity-based SOC.

Discussion on the importance of SOC II for accurate fuel gauge algorithms in applications like electric vehicles.

Introduction to Coulomb counting as the primary method for calculating SOC.

Description of how a BMS uses current sensing to perform Coulomb counting.

Challenges with current sensor drift and integration error in Coulomb counting.

Use of open circuit voltage (OCV) lookup for accurate SOC estimation.

Explanation of depth of discharge (DOD) as the inverse of SOC.

Process of recalibrating SOC using OCV lookup after the battery has been at rest.

The necessity of accurate SOC algorithms for reliable battery pack operation.

Transcripts

[Music]

welcome to the stifle systems insights

video series I'm Eric Staal president of

Stoffels systems the topic of today's

video is the state of charge of a

battery pack as estimated by a BMS so

what is the state of charge or SOC so

it's very simple the state of charge is

defined as the capacity remaining so

that total capacity in amp hours or

coulombs that you can discharge over the

total capacity of the battery pack so

let's give an example

so if we had a battery pack that was say

100 amp hour battery pack total capacity

and we had 70 amp hours left to

discharge that would give us a state of

charge of 70% so this would mean that if

we fully charge the battery pack up to

the 400 amp hours and then discharge 30

amp hours we would have 70 amp hours or

70 percent of the capacity remaining now

it's very important to note that this is

in units of amp hours not in units of

energy and why is that important well if

we look at the discharge curve for a

lithium-ion battery cell or a battery

pack for that matter with voltage here

on the exit y-axis and on the x-axis we

have amp hour discharged

what does the curve typically look like

so for most lithium-ion batteries for

example like an MMC or lco type

chemistry you would expect to see a

curve like this and it falls off towards

the end and so typically this is about

4.2 volts per cell and the end of

discharge is 2.5 volts per cell this

could be a little different for

different chemistry's but the point is

the same in general you have a varying

downward facing slope for the voltage as

you discharge capacity out of the pack

so for example if I took the 50% point

for the amp hours discharged so if we

took the example above and said that

this was a hundred amp hours or 100% and

this was 50 amp hours this is zero then

this would be the 50% state of charge

point which means that we've discharged

50 amp hours out of a hundred amp hours

and we have 50 amp hours left to go

before the battery reads reaches its

termination voltage so one thing to

notice is that look at the areas under

these relative curves one side is bigger

than the other so for example there's a

lot more energy on the left side of this

line than on the right side of the line

and why is that important because when

you confuse state of charge with a fuel

gage algorithm this happens which is

typically if you want to get a fuel gage

if you want to use a fuel gage for

example from electric vehicle

application or most applications you're

more interested in the energy available

as opposed to the capacity so for

example if we were doing an electric

vehicle design and we were trying to

determine okay this is a 200 mile range

at what state of charge would you have a

hundred miles of range remaining well

look at this the balance between this

side and this side is clearly imbalanced

because the voltage is higher in the

lower than the higher states of charge

and the voltage is lower in the lower

state to charge so it's important to

introduce the concept of soe II or SOC

based on energy so we denote this as

follows

I use the black pen for this so SOC c4

capacity or SOC II for energy and these

are different and this is actually what

most applications are interested in

because this is actually the more

accurate fuel gauge algorithm that tells

you how much expected runtime use

distance range you ever made so let's

look at look at this example again if we

say okay where is the actual 50% SOC II

point on this well that would be where

we would have approximately 50% of the

area under the curve on the left side of

the line as on the right side that would

be somewhere more like here say that

this corresponds to a point of 42% SOC

see but this equals 50% SOC II so it's

very important to understand the

distinction between energy state to

charge fuel gauge algorithms and

capacity states of charge in a future

video we'll discuss how the state of

charge is actually calculated it

typically has a number of more

sophisticated elements but for the

purposes of today I do want to discuss

Coulomb counting which is the primary

way that state of charge is calculated

so as I mentioned earlier in this

example we have a hundred amp hours and

we discharged 30 amp hours to have 70

amp hours remaining which means we're at

a c2 charge of 70% but how did we

determine that we discharged 30 amp

hours well from the first video we can

remember that a BMS typically has a

current sensor either a shunt or a Hall

effect device that can monitor the

current flowing in or out of the battery

pack and what are you doing to determine

amp hours since amp hours are in units

of current times time we are actually

performing an integration

called Coulomb counting so this is your

current and this is time so say that we

have a curve that looks like this

that is how much charge that's how much

current at any given time is coming out

of the pack the area under the curve

corresponds to the actual capacity

removed so this is in units of amp hours

and this is what Coulomb counting does

Coulomb counting is basically looking at

every single slice in a time slice

integration fashion multiplying the

current times the time interval and

summing that up to get an approximation

of the integral of this function and

what that does is that gives us an

accurate estimate of amp hours which

gives us a basis for SoC

now one of the things to note about

Coulomb counting and current sensing is

that the current sensor has drift and

integration error so you're not going to

get perfect alignment of all your

sensing with the actual current spikes

itself so it's important to note that

oftentimes you also need what's called a

ocv or open cell voltage lookup to

compare what you're integrating with

your actual voltage so we'll look over

here I'll draw on this plot voltage

times I'm gonna introduce a new term

called depth of discharge depth of

discharge is the inverse of state of

charge so for example at 70 percent SOC

you would have a depth of discharge of

30% so for example 30% SOC right depth

of discharge 60% depth of discharge and

say this is a hundred percent your

voltage is gonna go like this so when

the PAC has been at rest for a

considerable period of time what you do

is the BMS will look up with a lookup

table or something similar to see what

the open circuit voltage of the cell is

for a given temperature

and then it will equate that or

determine what the corresponding state

of charge or depth of discharge is for

that and then it will re cede the soc

function so that you have a basis upon

which to get an accurate understanding

of where you need to start Coulomb

counting again and this is very

important because you don't want to have

a fuel gauge algorithm that gets off so

you can imagine how frustrating it would

be if you had say you're driving along

and all of a sudden you went from 30% to

0% state of charge immediately because

there is an inaccurate estimation it

would leave you stranded at least

anxiety all sorts of problems like that

so the benefit of having both open

circuit voltage lookup and accurate

Coulomb counting is that you can

actually ensure a high degree of

accuracy for the state of charge

algorithm and the state of charge energy

algorithm such that your results are

expected in a reliable and predictable

operation of your battery pack that's

all for today thanks for watching see

you next time

[Music]

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