Coulomb Counting for Capacity of battery

Initial Notes

SoC (State of Charge) of a battery can be described as the ratio of its current capacity to its nominal capacity (which represents the maximum amount of charge that can be stored in the battery).

There are a variety of different methods to estimate the SoC (State of Charge) of a battery. In general, these different methods can be divided into four categories:

1. Direct measurement: these methods use physical battery properties, such as the voltage and impedance of the battery

2. Book-keeping estimation: these methods use discharging current as the input and integrates the discharging current over time to calculate the SoC

   1. Basically keeps track of how much energy we are drawing from an initially “full” pack

3. Adaptive systems: adaptive systems are self-designing and can automatically adjust the SoC for different discharging conditions.

4. Hybrid methods: hybrid models benefit from the advantages of each SoC estimation method and allow a globally optimal estimation performance.

Open

Table showing different SoC estimation methods divided into the four categories.

Direct measurement methods

Determining state-of-charge from a single measurement (no sense of history).

• Open Circuit Voltage (OCV) Method: The open circuit voltage method relies on finding a relationship between the battery terminal voltage and its SoC, and then using this relationship to estimate the SoC from the battery terminal voltage. This is more useful when there is a roughly linear relationship between SoC and OCV (seen in lead-acid batteries). However, Li-ion batteries do not have this linear relationship. Additionally, as the OCV-SoC differs among batteries, this relationship needs to be specifically measured to accurately estimate the SoC. I also believe that OCV refers to measuring a disconnected battery, so probably not very useful for our car where the battery needs to be connected at all times (ideally).

• Terminal Voltage Method: The terminal voltage method is based on the terminal voltage drops due to internal impedances when the battery is discharging, so the electromotive force (EMF) of the battery is proportional to the terminal voltage. Since the EMF of batteries are approximately linear proportional to the SoC, the terminal voltage of a battery is also approximately linear proportional to the SoC. But at the end of battery discharge, the estimated error of this method is large as a battery’s terminal voltage suddenly drops near the end of discharge.

• Impedance Method: Impedance measurements provide knowledge of several parameters, which may or may not depend on the SoC of the battery. Need a wide range of impedance experiments for identification and use of impedance parameters for estimating the SoC of a given battery. Not sure how we can measure impedance during the race.

• Impedance Spectroscopy Method: Measures battery impedances over a wide range of ac frequencies at different charge and discharge currents. The values of the model impedances are found by least-squares fitting to measured impedance values. SoC may be indirectly inferred by measuring present battery impedances and correlating them with known impedances at various SoC levels. Also not sure how we can measure impedances during the race.

Book-Keeping Estimation

Methods that uses the history of the cell to estimate the present capacity.

• Coulomb Counting Method: The Coulomb counting method measures the discharging current of a battery and integrates the discharging current over time in order to estimate SoC. This estimation is based on the discharging current, I(t) and previously estimated SoC values:

  • Open

    

    Qn here is the battery cell capacity, basically subtracting the amount of energy drawn out from the battery each time delta, and then using the new estimation for the next calculation

  • Requires an accurate initial SoC “measurement” of the cell.

    • One way would be to charge to maximum cell voltage which can be used as a reference point

  • Can be prone to drifting? Needs a way to “recalibrate” over some period of time, possibly using a direct measurement?

  • There are several factors that affect the accuracy of Coulomb counting including temperature, batter history, discharge current, and cycle life

    • As well as sources of error in the data collection

      • Starting SoC accuracy

      • Current measurement accuracy

      • Current integration error

      • Uncertainty in battery capacity

      • Timing error

    • Which can be impacted by:

      • Components used for cell voltage measurement

      • Voltage sense wires, connectors and connection locations

      • Current sensors

      • Voltage and current measurement channel accuracy

      • Timing circuit

      • The code

• Modified Coulomb Counting Method: This method uses the corrected current to improve the accuracy of estimation. The corrected current is the function of discharging current. There is a quadratic relationship between the corrected current and discharging current of battery:

  • Where k2, k1, and k0 are constant values obtained from the practice experimental data

  • The SoC is then calculated by:

  • This modified method has been shown to be superior to the conventional Coulomb counting method

    • Not sure why the measured discharging current is less accurate though → where is the extra energy lost (heat?)

      • The intuition here is from rate-dependent capacity. If you discharge a cell at 0.1C, you will measure a higher capacity than you would if you discharged at 1C or 3C. This is why manufacturers state a ‘standard discharge current’ for the capacity measurement of the cells.

      • When more ions are moving back and forth across the cell separator, there are more that will get stuck or may not make it into the structure on the other side.

      • Heat does play into this as well, where a hotter cell will make it easier for the chemical reactions to occur, but also slightly changes material properties so there is a different resistance inside the cell.

Adaptive Systems

These systems mainly have to do with artificial intelligence. Essentially using some neural networks(?) to map various inputs (terminal voltage, discharge current, temperature, etc.) to an output (SoC). Feel free to explore if interested.

We may need to collect lots of experimental data for these methods? Will probably need to order extra cells in that case, since extensive testing may wear out the cells.

• BP Neural Network ← most popular type?

• RBF Neural Network

• Fuzzy Logic Method

• Support Vector Machine

• Fuzzy Neural Network

• Kalman Filter ← possibly interesting to explore?

  • “Unscented Kalman Filter (UKF)”

  • This article references an article “Adapted unscented Kalman filtering for state of charge estimation of a lithium-ion battery for electric vehicles”, possibly relevant to us

Hybrid Methods

Combine different models to benefit from the advantages of each method.

• Coulomb Counting and EMF Combination: Combines battery EMF measurement during the equilibrium state and Coulomb counting during discharge state. Not sure what equilibrium state means here, maybe keeping track of the loss during time when the car is off (but wouldn’t the solar panels be charging the batteries then?)?

• Coulomb Counting and Kalman Filter Combination: “KalmanAh method” uses the Kalman filter method to correct for the initial value used in the Coulomb counting method. The Kalman filter method is used to make the approximate initial value converge to its real value. Then the Coulomb counting method is applied to estimate the SoC for the long working time.

  • I think this may be reasonable?

• Per-Unit System and EKF Combination: Something

Initial Timeline (Tasks (Goals) + Deliverables + Estimated Time)

I think first we should do some deeper background research on all of the different methods, and see which one is most feasible and accurate for our timeline.

Week 1:

• Do research into the direct measurement, book-keeping measurement, and hybrid methods, and determine which ones we want to use.

  • Deliverables: Confluence page or presentation documenting the research, pros and cons of each method, and decisions on which methods to explore (most likely some combination of Coulomb counting and a direct measurement method)

• Adaptive systems are optional, likely out of scope of our project.

Resources

• The State of Charge Estimating Methods for Battery: A Review

  • Introduces a large variety of different methods to measure SoC, includes references to papers that go into more detail for each method

  • Most of the initial info was from here

• Enhanced Coulomb Counting Method

• Implementation of an Improved Coulomb-Counting Algorithm Based on a Piecewise SOC-OCV Relationship for SOC Estimation of Li-Ion Battery

• https://uwmidsun.atlassian.net/wiki/spaces/~karlding/pages/620036100

• A Lossy Counting-Based State of Charge Estimation Method and Its Application to Electric Vehicles

• A Closer Look at State of Charge (SOC) and State of Health (SOH) Estimation Techniques for Batteries

• Estimation of state of charge for lithium-ion batteries - A Review

• https://uwmidsun.atlassian.net/wiki/search?text=coulomb counting

Battery Performance

Initial Notes

Not tooooo sure what this task is, want to clarify what this task is

Initial Timeline (Tasks (Goals) + Deliverables + Estimated Time)

Resources

Cooling System Optimization

Initial Notes

Generally, small fans are used to aid in creating airflow within the vehicle. This is mainly used in two cases:

1. Cooling the cabin of the vehicle (so driver doesn’t die)

2. Cooling the battery box (so driver doesn’t die)

Typically these fans are PC fans, such as those developed by Noctua. This task would be an investigation into the effectiveness of these fans, how many fans we want (probably some kind of diminishing return from adding more and more fans, need to consider the power draw (and I guess the weight lol)), and how fast we want to run the fans. The fan speed may also be variable depending on how much we want to cool the pack during different segments of the race.

I believe most fans can be controlled using PWM (Pulse Width Modulation). I assume that a higher duty cycle (leading to higher RPM) leads to a higher current draw. The first thing to check for this assignment is how significant the current draw of the fan(s) are (relative to the overall current draw of the vehicle or to the capacity of the battery pack). If the current draw is significant enough, we can look deeper into projects that help optimize fan control for cooling the battery pack.

Note that if a fan is too weak it may even REDUCE airflow

Initial Timeline (Tasks (Goals) + Deliverables + Estimated Time)

• Determine whether or not the fan power draw is significant enough to warrant a deeper investigation

  • Deliverables would be numbers / charts and graphs representing:

    • Min and max current / power draw of typical (can probably look into the past cars) fans

      • Comparison with the overall current draw of vehicle, or the total capacity of battery pack

      • Can find a number for total power consumed if we were to keep fans at max speed throughout entirety of race

    • Respective min and max airflow

      • How this relates to the cooling effect on battery pack

    • Pressure?

• Brainstorm ideas for testing methods which investigate fan optimizations

  • Fan model

  • Number of fans

  • Fan speed @ different conditions

• One of the deliverables could be also doing research on different fans and how different models affect the cooling performance (and balance between cooling performance and power draw)

  • Could be used to help decide on what fans to use in the car

Resources

• Fan Control ADT7476A Note

  • Some pretty good documentation on one of the fans I believe we used in the past

• https://noctua.at/en/products/fan/nf-a20-pwm/specification

  • Sample fan specifications, some specs to take note of:

    • Blade geometry

    • Rotational speed

    • Min rotational speed at 20% PWM

    • Airflow

    • Static Pressure

    • Max input power

    • Max input current

    • Operating voltage

    • Voltage PWM signal

• This may involve some simulations in SimScale that @Darton has been working on for modelling the cooling of our pack

  • Module Spacing Investigation

  • Darton’s documentation on his investigations so far

Battery Module Testing

Initial Notes

Basically want to discharge a module similar to how the pack may be discharged throughout the race.

The battery pack will consist of 9 modules connected in SERIES. This means that the same current will be drawn from all of the modules, which will be equal to the current drawn by the car overall. The main difference between the pack and one of the modules is that the pack is at a much higher voltage (9x the voltage of one module).

We want to create a test bench and setup which will draw a custom current (e-load?) while also supplying a custom current (power supply?) to simulate the current draw of the vehicle and the power supply of the solar array during the race. During this simulation, we can monitor certain characteristics of the module such as its voltage, temperature, and internal impedance. We can analyze this data to see whether we are “on track” to a safe battery pack. We can additionally use the data to further optimize the design of the modules and stuff.

For the temperature monitoring, we will likely need to install lots of thermistors throughout the module. Each thermistor can measure the temperature at a certain point in the module. It would be cool to be able to create some kind of visualization of where the hottest points are in the module (2D or 3D).

Initial Timeline (Tasks (Goals) + Deliverables + Estimated Time)

• I imagine most of the work will be “borrowing” Micah’s battery testing script and adding the functionality of importing a “complex” current draw routine (this might already be a thing in his code idk lol but check for it)

• Develop race models for the current draw of one of the past routes

• Develop model for the solar array input over one of the past routes

• Design physical test bench

  • Previous test setup was a cardboard enclosure with an air inlet on one end, and a fan on the opposite end

  • Thermistors were distributed throughout the module, check the “Production Testing” documentation below

• Perform tests

• Analyze data

Resources

• https://github.com/mbA2D/Test_Equipment_Control/blob/master/battery_test.py

  • Micah’s script for battery testing

  • I imagine we would have something very similar to this with the setup described above

  • Main difference would be we would want to code a custom current draw routine that simulates what the current draw might be based on the route conditions (and weather data?), as well as code a custom power supply routine that simulates the current supplied by the solar array

• Battery Module - Production Testing

  • Outlines the testing procedure

• Testing - Airflow Through Modules

  • Shows the cardboard setup

• Testing - Cooling Methods and Temperature Distribution under High Loads

  • Shows the visualizations of the temperature distribution in a module

Battery Type Testing

Initial Notes

We have a pretty good testing script curtesy of Micah: https://github.com/mbA2D/Test_Equipment_Control/blob/master/battery_test.py

However, we don’t have great documentation on a solid testing procedure and data analysis. It would be great for the future car (we already bought cells for this car rip) to have a method to collect data and most importantly analyze it to determine which cell model is optimal for our car.

The old testing procedure is listed in the Resources part, I’m just gonna note down some thoughts I had with the testing procedure while I was doing testing.

• The main problem was finding a solid way of analyzing the data after collecting it. It would be great to have some kind of system figured out to compare the different measured characteristics such as voltage, capacity, internal impedance, etc. to see which cell is the best.

• Testing procedure was pretty slow, each cell would take at least 1 hour to perform one test

  • And there are various tests that need to be done such as different current levels (1A, 5A, etc.) as well as internal impedance tests

• This lead to not having enough data to really perform any significant analysis

• Difficult to create the same initial conditions

  • Difficult to see when cells are at “full” charge, one way is to monitor the charging current and stop once the current drops to a certain level

• Cells are also expensive so that also leads to fewer data points

  • Only tested 8 of each cell model

• Would be great to have some kind of system to test cells in parallel at the same time, while keeping the same initial conditions

  • Limited to one test a time due to only having one e-load

• Micah’s 64 channel DAQ USB port connection broke so that might need to be fixed lol

Initial Timeline (Tasks (Goals) + Deliverables + Estimated Time)

• Low priority, but important task for the next car

• Improve testing procedure (and code if needed)

• Improve test data analysis

Resources

• Sample Cell Testing Procedure

  • Current testing procedure

• Cell Chemistry Testing - 5A Discharge Data

  • Most recent data from my testing

• https://github.com/mbA2D/Test_Equipment_Control/blob/master/battery_test.py

  • Testing code

• Single Cell Testing - Data Processing Guide

  • Test data processing guide