IN PROGRESS
Also, make a battery basics page - links to MDPI pages
To get a better understanding of the equivalent circuit model of a cell, see this page (link).
Quick Overview and Recommendations:
The goal of cell testing:
The more data and the more informed we are about the status of our pack, the better.
Any imbalances present in the pack at the start will only get worse as the pack is cycled. Within series modules, this variance can be overcome with cell balancing, but within parallel cells there is no way to overcome this. (link study) Due to the nature of li-ion cells being a manufactured component, there is always some degree of tolerance from the manufacturer. This page will discuss the parameters that can vary and how they affect pack imbalance.
What parameters can be measured, and do they cause pack imbalance?
As-Received OCV - Assuming the cells were manufactured at the same point on the voltage curve, the as-received OCV is an indicator of the amount of self-discharge current of the cell. See the self-discharge method.
Cell Weight - The weight of a cell is an indicator of how much material is inside the cell. According to this paper (https://www.nature.com/articles/srep35051), the weight of a cell correlates loosely with the capacity of the cell, before factory screening occurs, as tested on 5473 Boston Power Li-ion cells (Swing 5300 5.3Ah). See capacity section for the effect of capacity on imbalance.
Self-Discharge - (https://literature.cdn.keysight.com/litweb/pdf/5992-2517EN.pdf?id=2911018). Keysight has developed a self-discharge measuring unit, which incorporates a super-high precision DC voltage source and a super high precision current measurement device (accurate to the tens of uA). The bucket method described in the document provides a quick (1 hour) test of the self-discharge current. A single cells having a significantly higher self-discharge current will cause the module to have a larger self-discharge current. Over long periods of time (such as sitting idle in the bay for a month), this self discharge current will cause an imbalance in SoC of the cells and lead to decreased pack capacity.
Capacity - The difference in capacity between cells in parallel groups causes current spikes in these cells at the end of charge or discharge cycles.
DC Internal Resistance - The DC Internal resistance (DCIR, DCR, RI, or IR) is modelled as a resistor in series with the cell. Measuring the resistor involves putting a pulse discharge current on the cell, and measuring the voltage drop. This voltage drop is attributed to the series resistance inside the cell. Typical values for DCIR are between 30-80mOhm for a new 18650 cells. For comparison, LiPo cells with high discharge ratings used in RC models typically have a DCIR in the range of 2-10mOhm.
AC Internal Impedance - The internal impedance of a cell is a similar measure to the DC internal resistance except measured with a 1kHz sinusoidal signal applied.
Electrochemical Impedance Spectroscopy (EIS) Measurements - For basics of EIS measurements, there is a great explanation here . EIS measurement, by sweeping the frequency of an applied signal across a wide range of frequencies determines the cell impedance at each of these frequency. Complex mathematical algorithms can fit many free parameters to this data, allowing measurement and evaluation of much more complex cell models, involving inductors, capacitors, and resistors to model the AC behaviour. As a research tool, this is a super powerful technique allowing characterization of all cell parameters except capacity. Nyquist plots are used to determine the real component of the series resistance at the zero-crossing point. EIS measurements take a long time to perform, and are not necessarily better than the other methods for our applications.
A comparison of EIS measurement and DC Pulse measurement of resistance is shown below (https://www.sciencedirect.com/science/article/pii/S2352152X18300732#bib0090). I don't claim to understand everything about EIS measurements, but according to this report (https://pdfs.semanticscholar.org/58a9/c593a684fa1a503492383ec807334b4aaaef.pdf?_ga=2.120996168.1162077320.1560615736-269352092.1559077519, page 17) explaining the Nyquist plot (blue) below, the intersection between the semicircle and the Warburg straight line represents the sum of all the internal resistances (the electrolyte, the solid electrolyte interface, and the electron transfer reaction). Notice how the DC IR curve intersects that corner at a pulse time of around 2s. The value obtained for the resistance matches the expected value when compared with calorimetry data in the same report calculating the amount of temperature rise in the system.
Initial Characterization Predicted Results
If we do go ahead with individual cell testing, what are the values that are expected, how much variation is expected, and are there outliers that will cause imbalance?
Below is a figure showing DCR and capacity tests for over 20,000 cells measured at beginning of life. The tests were performed on LiFePO4 cells, however the data is a good indication of the variance we should expect as the manufacturing processes are pretty much identical. The key thing to notice here is that while the capacities and DCR measurements at beginning of life follow a normal distribution, with fairly low variance from nominal (5.8% for DCR and 1.3% for capacity), there are outliers within the data at the edges of the normal distribution. It is these outlier cells that will cause issues in packs, due to previously mentioned imbalance factors (https://www.sciencedirect.com/science/article/pii/S037877531300116X?via%3Dihub) (blue/yellow graphs).
The second set of graphs show Initial Conditioning and Characterization Tests performed on 100 Panasonic NCR18650B cells, and a similar amount of outliers and standard deviation is noted. The Panasonic cells have been around for a long time. An email from Steve McMullen, ASC Inspector, notes that "Their testing was also with very mature technology Panasonic 18650 3.2AH cells that have been manufactured in the millions if not billions. The newer cells don’t have as much credibility. I believe your team is using LG CHEM INR 18650 MJI which is a variant of the technology to trade off Rate for Life and Weight for Capacity, so the cell is already working in realm different than the Panasonics". We should be aware that the MJ1 cells we are using could have more variation than the data from the panasonic tests noted below (https://www.hnei.hawaii.edu/sites/www.hnei.hawaii.edu/files/Initial%20Conditioning%20Characterization%20Test.pdf) (red/blue/black graphs).
Ideal situation: Test, Estimated Time Required per cell
Every cell Capacity (SoC/OCV curve), DC Ir, AC Im, As-Received OCV, Self-Discharge using Keysight bucket method, Weight
We have access (thanks to Keysight) to all the equipment necessary to perform all these tests.
Option 1:
No Testing
Option 2:
As-Received OCV as a measure of self-discharge during transport (accept cells within certain bounds?)
DC Ir (Show paper of why this is a much more useful term to measure) (bin cells per Ir)
AC Im (longer setup) Reject cells with elevated Im - as per this paper, can be an indicator of manufacturing defects.
Do we want to make a solar car, or do we want to make the best solar car? - 480mAh (20mAh difference per cell assumed) difference between modules = 0.48Ah x (36x3.7V) = 63Wh of energy. Assuming we travel at the efficiency of XXX, we will have XXX Km less range with a pack imbalanced by 0.48Ah
If balancing modules based on cells tests, one of the most important items to test is the individual cell capacity. Building the modules based on a minimum capacity deviation will allow us to perform less testing on the modules as the capacity is already determined. This will require more test time at the cell level on a tradeoff for less test time at the module level. With access to the right equipment (a large cell cycling machine, around 200 slots), it will take less time to test the cells than to test the 48 modules on 1 or 2 high current cyclers. Building modules with a capacity metric in hand will allow us to create packs with equal useable energy.
Why single cell testing is required (comparison against module/pack testing):
1 - A manufacturing error will be impossible to detect once we put the cells in modules
Once we put the cells in modules, the IR will be extremely low. Finding differences in the IR of the modules due to 1 bad cell will be next to impossible due to small contribution each cell has to the overall Resistance. If we take the internal resistance of each cell to be 50mOhm, then the IR of a 24P module will be 2.08mOhm. If one cell had an IR of 70mOhm (which would cause increased currents during the ends of charge/discharge cycles due to mismatched SOC-OCV curves), the total resistance would be 2.11mOhm. A 100A load connected to the module would produce a voltage drop of 0.208V if all cells were 50mOhm, and 0.211V if one cells was at 60mOhm. While this level of precision if achievable with our multimeters, the same voltage drop (0.211V would occur if all cells had an Ir of 51mOhm).Thus, to determine any imbalances in Ir, individual cell testing must be conducted.
While the capacity of the modules might be able to tell of a faulty cell, if other cells were picked such that the capacity was increased more than the average, the faulty cell could not be detected on a module level.
Self-Discharge is difficult to measure without extremely accurate and precise equipment (which may be available from Keysight). If one cell has an elevated self-discharge current of 20uA while all other cells have a self-discharge current of 10uA, a 24P module made up of 10uA self-discharge cells will have a self-discharge current of 240uA. If one cell in the module has an elevated self-discharge, then the total self-discharge will be 250uA.
2 - The cell life can be prolonged by avoiding exposure of the cells to high charge and discharge currents.
Every cell inside a pack with matched IR will be able to deliver the full energy in the cell due to the change in SOC-OCV curve at higher internal resistance (https://iopscience.iop.org/article/10.1088/1742-6596/795/1/012036/pdf).
3 - Once we put the cells inside the modules, they cannot be taken out. This is one of the reasons that we bought additional cells. Detecting a singular bad cell inside a module is possible in some cases, but we would never be able to identify the offending cell and replace it. If all the metrics (except capacity) of the individual cells are tested before being put into modules, we will know that there are no manufacturing defects in the cells.
Effects of an Internal Resistance imbalance in parallel connected cells
A cell-cell variation of internal resistance is +/- 15% (https://www.sciencedirect.com/science/article/pii/S2352152X18308156, Table 2), and follows a roughly normal distribution. This matches with results in several other reports, while a +/- 5% variation in capacity is noted from the same table.
Internal resistance mismatch between cells can lead to sudden capacity losses and a decrease in overall cycle life of around 40% (http://web.mit.edu/bazant/www/papers/pdf/Gogoana_2013_J_Power_Sources.pdf). While we are not concerned with the cycle life of our pack, sudden capacity losses must be avoided. The graph below shows that capacity suddenly drops by roughly 20% around the 100-150 cycle mark. The cells in these tests were LiFePO4 cells, and the internal resistance measured by a 15s 40A pulse, with a distribution shown above from 13.5 - 21.5 mOhm. This is a fairly large spread (50%) or IR and the currents that the pack were tested at are much larger than anything our cells will ever see. A high current test such as this decreases the time that the mismatch effects take to show up as the cells are performing at their peak characteristics.
The capacity loss shown in the figure happens after around 100 cycles, and is due to the mismatched cells being exposed to large charge/discharge currents as the ends of the charging and discharging cycles due to differing SoC-OCV curves cause by the mismatched resistance.
Internal resistance mismatch causes current mismatch on charge and discharge cycles. The current mismatch creates voltage drop difference and thus a difference in SoC between the cells in parallel groups. Thus there is an SoC mismatch between the cells when current is being drawn, which leads to internal current spikes when the external current flow stops.
A capacity drop in any one of our modules will affect the whole pack. If one cell in one module drops by 10% capacity due a an uncaught cell parameter outlier (increased IR), then we lose (3.5Ah * 10% * 3.7 * 36 = 47Wh) 47Wh of energy in our pack. That single cell will then also start to degrade quicker and the module will have to be replaced. Judging by the efficiencies of other winning solar cars, 47Wh could add an additional 1-2 Km of range to the car.
Thoughts on Temperature Variation:
Pack-Variation: As the temperature of a battery pack increases, the self-discharge rate also increases due to the increased rate of the chemical reactions inside the cell. An increase in 10 degrees Celsius will double the amount of self-discharge current. (Keysight link) The self-discharge will still be in the high-uA range (maybe low mA in the worst case), and thus not be an issue in module or pack balancing as the passive balancing circuit will take care of the pack-level variation in self-discharge. Assuming the temperature within the pack is only hotter when we are drawing current, the change in DC Internal Resistance will more than offset the change in self-discharge current.
Module-Variation: Temperature variation within a module, under extreme circumstances, can result in a positive feedback situation (until a certain delta OCV is reached). A decrease in internal resistance of the cell due to an increase in temperature will cause more current to be drawn from that cell, which will lower its OCV. Due to the close proximity of cells within a module, the temperature variation (unless caused by a cell with initially high IR) will be very small ans thus its effects negligible.
With temperature variation, the useable capacity of the cell will increase as the internal resistance decreases and thus we have less power loss in the cells due to IR. (Show IR-temp graph and Capacity-Temp Graph)
Module Testing
Once we build our modules, the next step is to test every module to ensure an even capacity in series-connected strings, and test for any possible manufacturing errors.