Hello, and welcome to week three of this course. Last week we looked at how to collect data to create an open-circuit voltage relationship for our battery cells. This week, we begin by looking at how to collect data to determine that dynamic portion of an equivalent circuit model of our battery cells. Later we will also look at how to use these data in order to find the parameter values of an enhance to self-correcting cell model. The data that we must collect to tune the dynamic parameter values must be captured while exercising a physical battery cell with a low demand that is representative of the final application. So this means for example, if the final application is an automobile, then the profile of load versus time should be representative of the demand versus time from an automobile. Or if the final application is a consumer electronics device, then the profile of load versus time should be representative of that device. Now, the reason for this is that the equations that we have developed to describe the operation of a battery cell are not perfect, there is some inaccuracy. And the process that we will use to make the model fit the captured data from the laboratory as well as possible is essentially a dynamic curve fit. And because of this, the model will be somewhat biased towards representing well the application from which the data was taken to find the model parameter values. So, if we collect the data that looks like an automotive application, the model will be somewhat biased toward being able to predict automotive type behaviors better than for example, consumer electronics type behaviors. Or, if the data we collected were from a cell that was exercised using a consumer electronics load profile, then that model will better predict a consumer electronics type application than it would in automotive type application. The figure on this slide shows a sample profile of electrical current versus time for an automotive application. You can see that there are many points in time when the sign of current is positive, or current as in the discharge direction. And there are many other points in time when the sign of current is negative, or in the charging direction. And this application discharging current happens when the vehicle is attempting to accelerate and places a load on the battery. And the charging points in time happen when the vehicle is either coasting or braking and some of the kinetic energy of the vehicle is converted through the power electronics back into electric chemical energy charging the battery system. Now, this particular profile comes about by simulating a vehicle performing the "urban dynamometer driving schedule", or UDDS drive cycle profile. This is the profile of load versus time that the Environmental Protection Agency, or EPA in the United States uses when testing a conventional gasoline powered or diesel powered vehicle in order to determine the fuel economy of the vehicle when driving in a city. The EPA would put a vehicle on a dynamometer, and execute a certain profile of load versus time and then use that to determine the fuel efficiency. So, we can apply the same profile of load versus time to an electric vehicle and see what the demand would be on the battery system when we do so and the result is that we obtain for at least one example this particular profile of load current versus time. If you choose to take the honors section of this course, then you also will be able to simulate the profile of load versus time on an actual electric vehicle platform, simulation platform and you will replicate this result here as well. When we execute this profile of electrical current versus time on a battery cell, it has the effect of reducing the state of charge of the battery cell by about five percent. In order to collect data then over the entire operating range of this cell, we must execute this profile repeatedly in order to move the state of charge throughout the entire range of interest. So, roughly speaking, the idea is that we will load the battery cell with a profile of load versus time repeated multiple times in order to exercise the battery cell as desired. While we do so, we will collect measurements of voltage, and current, and temperature, ampere-hours charged and ampere-hours discharged on a regular basis. The sampling interval is what you will use in your final model, so that is a design parameter but something on the order of one hertz should be a reasonable sampling rate. So, with that introduction to the basic idea, we will now look in more detail at the actual testing steps that need to be performed. Remember that when we were collecting data to determine the open-circuit voltage relationship last week, we divided the process into several different test programs or test scripts. We're going to do the same basic thing. The first dynamic test script is executed at the test temperature of interest. For example, if we are collecting data that is designed to create a cell model to describe the cell at 35 degrees Celsius, then this testing profile should be done on a physical battery cell that is soaked in an environment of 35 degrees Celsius. We assume that the test script begins with the cell fully charged before anything happens at a 100 percent calibrated state of charge point. And then the first step in our test script is to soak the battery cell for at least two hours at the test temperature to ensure that there is a uniform temperature throughout the cell construction. The second step and test script number one is to discharge the cell at a constant-current rate away from the 100 percent state of charge point. If you go back to the previous slide and examine the profile of load current versus time, remember that there were certain points in time where we saw that they were charging currents. And if we were to leave the cell at 100 percent state of charge before we did any further testing, whenever we hit any of those charging steps in the profile, we would be very likely to overcharge the cell or have an over voltage situation. So the purpose of this step number two is to move the state of charge somewhat away from 100 percent state of charge in order to minimize the risk of over-voltage to this cell and whatever subsequent aging that might cause or even safety considerations that might cause. Now the exact distance away from 100 percent state of charge is not necessarily critical, and you can design that based on your application. But here, I am suggesting that you might discharge the cell 10 percent down to a 90 percent state of charge point by executing a one C discharge for six minutes. But again, you could specify that yourself. The third step is to execute dynamic profiles over the entire state of charge range of interest in your application. So, this might be from a range going from 90 percent down to 10 percent state of charge for example. And the figures on this slide show representative output from test script number one. On the left hand side, you see the entire output, and on the right hand side I zoom in to one portion so that you can see some of the finer details. If you look at the left figure closely, you see that we start out at a voltage of 4.15 volts. This is the 100 percent state of charge point for this cell. The cell rests at that point for two hours which appears relatively short on this scale because I've actually, I believe cut off a little bit of that data here to emphasize the remainder of the test. Then we see this constant-current discharge profile which is bringing the cell voltage down. And then after that before I start the dynamic load profiles versus time, I allow the cell to rest to allow the cell voltage to approach open-circuit voltage before doing a dynamic profile. Then I execute a dynamic profile and then a rest again to allow the open- circuit volt or the voltage to recover closer to open-circuit voltage and other dynamic profile and rest and so forth. I believe there are 19 profiles or at least partial profiles that you can see on this figure. The test stops when we reach a termination condition. You might imagine that we would execute a certain constant number of dynamic profiles that we have predetermined to be the right number, that's not what I did here. You might also imagine that we could proceed until the state of charge reaches some final value but again, that's not what I did here. Instead what I did was I monitored the terminal voltage under load at every point in time during the test, and whenever that terminal voltage dropped below some criteria, I would stop the test. And if you look carefully at the 19th cycle, you can see it's somewhat shorter than the others because partway through that profile, we hit the under voltage condition and stopped the test. Now, if you look at the other end of the spectrum at the beginning of the test, remember we started at 100 percent state of charge which had a rest voltage of 4.15 volts. And then if you look a little bit past their point, you can see that sometimes the terminal voltage exceeds that 4.15 volts. But remember from the cell models that you've already learned about that the terminal voltage in the open circuit voltage or different quantities. And because of the impedance of the cell, the open-circuit voltage actually is never above 4.15 volts in the entire test, it's only the terminal voltage which sometimes exceeds 4.15 volts on a dynamic basis. And you have to be careful, you don't want to do this too much or too often, but if you confer with your cell manufacturer, they will probably give you some advice for how long you can have over-voltage pulses in what magnitude of over-voltage pulses they would recommend as a maximum value. And so, in this case, overcharging just a little bit above 4.2 volts for very short periods of time did not represent a safety concern nor did it really represent a degradation concern and so it was permitted. You might also put limits in fact I suggest you put limits and you're testing profiles that say, if the voltage ever goes above some maximum voltage like maybe 4.3 volts or 4.4 volts, that we stop immediately so that we don't damage the cell and we don't cause a safety problem. When the first test script completes, we expect the cell to be at a low state of charge but not exactly at zero percent state of charge. So, test script number one is calibrated at its beginning point to 100 percent state of charge, but the endpoint is not precisely calibrated. And since we don't know precisely what the total capacity of this cell is at this point in history, even though last week we might have calibrated it for the open-circuit voltage test. And we don't know exactly what the coulombic efficiency of this cell is for this particular test, we cannot at this point calibrate every data point that we have collected for test script number one. So, the goal of test scripts number two and three is to collect further data that will allow us to calibrate the data and test script number one, to use it for generating the parameter values of our models. Now, what we're going to do is we are going to discharge the battery cell down to zero percent state of charge just like we did last week to calibrate the OCV test, and then to charge the cell and calibrate it at 100 percent state of charge again, sort of like what we did last week for the OCV tests. So, in order to discharge to zero percent, remember that zero percent is really only well-defined as a voltage at 25 degrees Celsius. So we configure our thermal chambers back to a 25 degree Celsius set point, and we allow the cell to rest at 25 degrees Celsius in order to soak the cell, so it has a uniform temperature throughout its construction at 25 degrees. So, the next step is to bring the cell voltage to Vmin. Hopefully, the cells open-circuit voltage to Vmin, either by charging or discharging at a slow rate, maybe at C divided by 30 rate. We expect the cell state of charge at the end of test script number one to be above zero percent. So normally, we would consider discharging down to this terminal voltage but perhaps at some temperature, we actually discharge below zero percent in test number one. And so, we have to at least consider the possibility of needing to charge up to Vmin in this step here. So we either discharge or charge at a slow rate back up to the Vmin point. Now the objective of this test script is to bring the cell to a calibrated zero percent state of charge. And by doing a constant- current, constant-voltage type of approach, we can certainly approximate that, but you understand that because of hysteresis, that might not be sufficient. And so step 5b, is an optional step that you can perform but I recommend it in order to attempt to eliminate hysteresis to the greatest extent possible by using these dither profiles versus time. Now, the figure on the slide shows a representative output for the entirety of test program number two. You can see that the original two hours rest does not really change the cell voltage very much as the cell soaks in a different temperature. And then we do a discharge from 3.45 volts down to Vmin, which is three volts for this cell. And that happens quite quickly, and then we execute six follow-on dither profiles. And you can see those voltage versus time responses in this plot. So, after dynamic test script number two executes, the cell is at a calibrated zero percent state of charge set point. If we were to assume that the coulombic efficiency of the cell are perfect, then we could use all of the information from script number one and test script number two, to calibrate every point in test script number one and we would have what we need. However, we already know from last week that the dynamic or the coulombic efficiency is not perfect and therefore, we can't assume that it's 100 percent when we're calibrating the data. So, that's the purpose of test trip number three. The purpose is to bring the cell back up to a 100 percent state of charge point, so that we can use the remaining data to calibrate the coulombic efficiency. This test script also executes a 25 degrees Celsius but the previous test script was already at 25 degrees Celsius, so there's no need to change the environmental chamber temperature, it's already at the right point. There is no need to soak the cell, it's already at the right point. And so we proceed immediately by charging the battery cell up to 100 percent state of charge using the manufacturer recommended guidelines. Perhaps at a 1C charge rate up to Vmax followed by a constant voltage step until the current drops below some value. We can also execute follow-on dither profiles to eliminate hysteresis to the greatest degree possible, and I do recommend doing so. The figure on this slide shows a representative output from the test script number three. You can see that the voltage quickly rises from Vmin up to Vmax, and then under a constant-current, and then constant-voltage holds it at Vmax for actually a fairly short period of time until the current drops below some threshold, and then you can also see that there are six follow-on dither profiles that were executed. So at this point, the data that we have collected gives us information about the dynamic response of the battery cell, to a dynamic input profile of load versus time, and it also gives us enough information to calibrate the total capacity of the cell and the coulombic efficiency of the cell at this point in time at this date in history. To summarize then, in this lesson, you have learned that this cell must be exercised with a profile of load versus time that is representative of what the cell will see in its final application. And while doing this, we must collect data such as voltage, and current, and temperature, and ampere-hours charged, and ampere-hours discharged at regular intervals in order to use those data to train the unknown parameter values in an enhanced self-correcting cell model. The first test script repeats this dynamic profile over the entire anticipated range of state of charge that we expect to see in the final application and we'll use these data to train the model parameter values so that the model will be able to describe all expected operating conditions. You've also learned that the remaining test scripts number two and number three calibrate the cell zero percent state of charge point and 100 percent state of charge point, and that will allow us just like last week to calibrate the coulombic efficiency for this test, and the total capacity of this cell at this point in time. This suite of all three test scripts is executed over the entire temperature range at discrete points. So, we might say over a grid across the temperature range so that the final model that we generate is able to describe the behavior of the battery cell well at any point in temperature, at any point in state of charge as the battery pack is operated in its final application. That brings us to the end of this lesson. As we proceed through this week, you're going to learn more details about how to use these data that you've collected to train the parameter values of the model, and then furthermore, how to use the model to simulate the response of a battery cell to a different load profiles.
