Week 7 State of charge estimation

Week 7 Challenge - State of Charge Estimation

Q1) What is coulomb counting?

Q2)How does a BMS implement coulomb counting for SOC estimation?

ANS 1:

The state of charge (SOC) of a battery is a measure of the available charge or remaining charge in that battery. It is defined as the ratio of the amount of extractable charge at a specific point in time of a battery to the full capacity of that battery. A battery that is fully charged is said to have a state of charge of 100% whereas a battery that is fully discharged is said to have a state of charge of 0%. The state of charge can be expressed mathematically by the formula below:

`SOC (t) = (Q(t))/Q_n`

An alternative parameter to express the amount of charge available in a cell is referred to as the 'Depth of Discharge' or DoD. This parameters tells us how much a battery has been discharged from its full capacity and so a DoD of 1 means a fully discharged condition and 0 means a fully charged condition.

For the application of rechargeable batteries in HEVs and EVs, the SOC is a very important parameter and is the equivalent of a fuel gauge in conventional vehicles. A fuel gauge tells us how much fuel is available in the fuel tank whereas the SOC tells us how much charge is available in the batteries. For a user to be able to control their HEV or EV properly, they need to know the SOC and this has to be measured by electrical and electronic systems. The SOC has to be estimated accurately because it has to be used by a battery management system (BMS). The BMS, with the SOC measurement can inform the user of how much charge is available before needing to recharge, and will implement control strategies to keep the battery operating within its limits to improve the battery life. However, the SOC cannot be measured directly because that would require accurately measuring the lithium content at the electrodes. So instead, the SOC can be measured by a few indirect methods which involve measuring some other parameter of a battery which correlates with the SOC. These indirect methods are listed and explained below:

• Chemical method
• Voltage method
• Current Integration method
• Kalman Filtering method
• Pressure method

Chemical Method

The chemical method is only applicable to cells that give open access to their liquid electrolyte e.g. non sealed lead acid batteries. The SOC of such batteries is measured from the pH or the specific gravity of their electrolyte. The pH can be measured using a pH meter which will measure the potential difference between the pH electrode and a reference electrode. The specific gravity can be measured using a hydrometer. A known volume of the electrolyte has to be taken and weighed and the specific gravity is given by the ratio of the mass of the electrolyte to its volume (the density of the electrolyte) divided by the density of water. Using a lookup table, we can find the SOC from the specific gravity measurement. Recently, immersion refractometry has been used for the continuous monitoring of the SOC of a battery.

Voltage Method

This method measures the present voltage of a battery to find its SOC using the discharge characteristics of the voltage vs the SOC. This method is not preferred because the voltage in is more affected by the current in the battery and the battery temperature. This method does not take in to account the temperature variations that can cause the terminal voltage of a cell to vary from its open circuit voltage (OCV). Considering an LFP cell, its discharge characteristics are rather flat showing a linear relation between the OCV and the SOC and this decreases the accuracy of the SOC measurement further. Instead of using the voltage reading, another measurement that is proportional to the current should be used and a lookup table of the OCV vs temperature can be referred to.

Current Integration Method

This method is also known as the 'coulomb counting' method and involves measuring the current entering the battery (charging) and leaving the battery (discharging) over the time. The area under a current vs time graph will tell us the charge supplied or removed. Since charge is measured in Coulombs and this method measures the amount of charge entering or leaving a cell, this method is referred to as Coulomb counting as well. A device called a coulomb counter will measure the current consumed or supplied to the cell, finds the total current flowing in or out of the cell over a period of time and compares it with the pre - programmed battery capacity to find the SOC.

Even though this method is the most accurate way of measuring the SOC, it is not perfect. For instance, the method suffers from long term drift and a lack of a reference point because the measurement is limited by the sensor accuracy. This means that the SOC has to be re-calibrated regularly back to 100% every time a battery is fully charged. This method also does not consider the efficiency of the battery which is very important factor in considering the relevance of the SOC measurement. This is because battery temperatures are subject to change depending on their charging / discharging currents and this will affect their efficiencies accordingly. The cycle life of a battery also affects the coulomb counting method because at a certain point in the working life of a cell, its efficiency and its usable capacity would have decreased over time. This in turn affects the SOC measurement.

The current integration method can be expressed mathematically as shown below:

`SOC (t) = SOC(t_0) - 1/Q_n int_(t_0)^t eta(t) *i(t) dt`

where,

The current SOC - `SOC(t)`

The previous SOC - `SOC(t_0)`

Starting time of charging/discharging - `t_0`

End time of charging/discharging - `t`

Declared/Nominal capacity of cell - `Q`

Efficiency of cell presently - `eta`

Current flowing at end time - `i`

Time interval - `dt`

This above integral can be further simplified when expressed like so:

`SOC(t) = SOC(t_0) - [(i(t))/Q_n * deltat]`

From the equation above, we can see that the SOC estimation requires the main information of the previous estimated SOC value and the charging / discharging current and the time interval for which the charge / discharge takes place.

Modified Coulomb Counting Method

To improve upon the shortcomings of the coulomb counting method, the modified coulomb counting method was developed. The main difference in the modified version is that it uses 'corrected' values of the current in order to improve the accuracy of the SOC estimation. The corrected current is a function of the discharge current and there exists a quadratic relationship between the two parameters. The corrected current is calculated using the mathematical expression below:

`I_c(t) = k_2I(t)^2 + k_1I(t) + k_0`

where,

Corrected current - `I_c(t)`

Discharge current - `I`

Constants from experimental data - `k_2, k_1, k_0`

Time - `t`

This corrected current is then used in the traditional coulomb counting equation to find the improved SOC value. The modified coulomb counting equation is shown below:

`SOC(t) = SOC(t) - (I_c(t))/Q_n*deltat`

Kalman Filtering Method

This method is used to overcome the disadvantages and problems with measuring the SOC using the voltage method and current integration method. This method implements a Kalman filter which will use the electrical model of a battery to predict its over voltage due to the current. It can be used together along with the current integration method to accurately measure the SOC. The main advantage of a Kalman filter is that it is able to adjust its trust of the battery voltage and coulomb counting in real time.

Pressure Method

This method is most commonly used with NiMH type of batteries (Nickel Metal Hydride) whose internal pressure varies depending upon the amount of charge stored in them. The internal pressure of the battery increases when the battery is being charged, and so decreases when the battery is being discharged. The pressure method can be improved upon when used together with Peuker's Law which is given by:

`C_p = I^k*T`

where,

Peukert's Capacity (Ah) - `C_p`

Current (Amps) - `I`

Peukert's Coefficient - `k`

Time (hours) - `T`

ANS 2:

A battery management system (BMS) is an electronic system that combines hardware and software to manage a rechargeable battery. The BMS performs a variety of functions to make sure that a battery is always within its safe operating limits and has the longest possible working life. Without a BMS, a user has no control over the way a battery gets charged or discharged because the battery itself is not aware. For instance, a battery does not know how its own SOC, it does not know when to stop charging etc. In the application of EVs and HEVs, BMS have the following functions:

• Monitoring
• Energy recovery
• Thermal management
• Computation
• Communication
• Protection
• Optimization

Monitoring

This feature involves the BMS watching over the various parameters of the battery to be able to sense the state of the battery. The different parameters that a BMS monitors are:

• Voltage - this can be for the individual cells as well as for the overall battery pack
• Current
• Temperature - this can be for the individual cells as well as for the overall battery pack
• State of Charge (SOC)
• State of Health (SOH) - this parameter tells us the ratio of the current capacity of the battery to its original capacity

Energy Recovery

In vehicles that are capable of regenerative braking, the BMS will control the usage of the current produced by the regenerative braking to charge the battery by directing the flow of current from the motor/generator to the battery pack.

Thermal Management

The BMS is responsible for monitoring the temperature of the battery pack and to make sure that the temperatures remain within the operating ranges of the cells (as mentioned in their data sheet). It is important to monitor and control the temperature because charging and discharging currents and environmental conditions can influence the temperature to exceed their tolerances. The thermal management may be active (requires extra energy) or passive (requires no extra energy) and the cooling medium may be liquid, air or some substance that undergoes a phase change.

Passive cooling is reliant on the convection of the surrounding air. However, air cooling is quite inefficient in that it requires more power than liquid cooling and the components of air cooling systems are heavier which reduces the efficiency of the batteries. Liquid cooling is preferred by some automakers because liquids e.g. water have higher thermal conductivities than air and therefore have higher natural cooling potentials. The batteries may be submerged in the coolant or the coolant may flow in the BMS without coming in contact with the batteries.

Computation

This feature of a BMS involves being able to perform calculations based on sensed parameters and current conditions of the battery. For instance, the BMS performs calculations to be able to tell us the SOC of the battery pack, to be able to tell us the available range achievable with the amount of charge available in the battery pack. The BMS can even tell us the age of the battery pack by counting the number of cycles it has been charged/discharged for.

Communication

This feature is about the BMS being able to communicate with other systems in order to work together efficiently. For instance, the central controller of the BMS is able to communicate with its own hardware at the cell level and can even communicate externally.

Protection

The BMS is responsible for the protection of the battery pack in that it ensures that the battery is always operating within its safe limits (as mentioned in the cell data sheet) without causing any harm to it or to the user. For instance:

• Over current discharge - This is when the battery is being discharged at a higher C rate than recommended which is not advisable.
• Over current charge - This is when the battery is being charged at a C rate higher than recommended which is dangerous.
• Discharging below cutoff voltage - This is when the battery is discharged to a level below the cutoff voltage which is not advisable.
• Charging above full charge voltage - This is when the battery is charged to a voltage level above the full charge voltage.
• Temperature - The battery should not be at a temperature outside its safe operating range in any instance. This includes over temperature and under temperature.

Optimization

This feature of a BMS involves making sure that the battery is used as efficiently as possible by ensuring that the maximum capacity of a battery is usable and that the cell balancing occurs. Cell balancing is needed when individual cells are not at the same voltage level, or are not at the same SOC, or are not charging / discharging with the same current. Cell balancing is done by two main ways: active and passive. Active balancing involves shuffling energy from the highest charged cells to the lesser charged ones. This makes sure that no charge is wasted. Passive balancing is when the extra energy in the more charged cells is dissipated as heat energy by connecting them to some load.

Battery management systems can use different methods to estimate the SOC of the battery, however one of the main ways used is the coulomb counting method. The BMS implements the coulomb counting method to measure the SOC using an algorithm which is shown in the diagram below:

We can see that after 'Start', the algorithm first checks the serial number of the battery being used. From here, the first split in the algorithm occurs. If the battery being used is the same type of battery used previously, it will load the historical data of the previous battery from the memory. The memory will contain the important data needed for the coulomb counting method to start e.g. the initial SOC, SOH and DoD. Because of this, the BMS can go straight to monitoring the battery voltage and current. However, if the battery being used is different from the previous type, the BMS will have to determine the initial SOC, SOH and DoD and perform some sensing operations and computations. The SOH is taken as 100% because the BMS assumes that this is a fresh battery. Then only can the BMS proceed to measuring the battery voltage and current.

From the battery current, the algorithm can take the next decision is to compute whether the battery current is lesser than zero, greater than zero or equal to zero. If the battery current is lesser than 0 i.e. negative, the algorithm will interpret the battery being in a discharging mode. If the battery current is greater than 0 i.e. positive, then the algorithm will interpret the battery being in a charging state. If the battery current is equal to 0, then the algorithm interprets the battery being in the open circuit mode. For this algorithm, the convention taken is that the charging current is positive.

If the battery is in the discharging mode, the next decision is to compute whether or not the battery voltage is greater than the minimum voltage i.e. cutoff voltage. If the battery voltage is greater than the cutoff voltage, then the depth of discharge is calculated using initial DoD, the operating efficiency and the difference in the DoD over the operating period. If the battery voltage is lesser than the cutoff voltage, then the battery should be used no longer and should be charged. The SOH value is reevaluated with the DoD measurement. In both cases, the SOC and SOH is indicated.

If the battery is in the charging mode, the next decision is to detect whether the battery is fully charged. If the battery is fully charged, the BMS will know because the battery voltage will be equal to the full charge voltage and the battery current will be equal to the lower limit of the current (during charging). If this condition is met, then the SOH of the battery is reevaluated with the SOC value. If the voltage and current conditions are not met, the BMS will know that the battery is not fully charged and will calculate the DoD and the SOC using the same information and formulas as that of the discharging mode.

If the battery is in the open circuit mode, the BMS will directly indicate the SOC and SOH. In all other instances, the BMS will eventually indicate the SOC and SOH after performing the required computations. From the SOC and SOH indication, the algorithm then makes the BMS return to the previous stage of monitoring the battery voltage and current and the process repeats. The monitoring stage will make the BMS ensure that the voltage and current remain within their operating limits while charging or discharging.