Last week, you learned about the equations that define the enhanced self-correcting or ESC cell model of a lithium ion battery cell. You also learned about a simple set of laboratory procedures that could be performed in order to find the unknown constant parameter values of these equations in certain specific cases in particular, when the model had only a single resistor capacitor pair and when no hysteresis was being considered in the model description. This week, we're going to start looking in more detail at finding parameter values and more general cases and more accurately. And we're thinking about the case where we might have multiple resistor capacitor pairs and when also we want to have a model of hysteresis. We will be more careful to define the exact laboratory tests that must be performed in the entire data collection process and reduction process including introducing you to some Octave or Matlab code that can perform the data reduction itself. So, that is our focus is turning to finding the model parameter values to describe a particular physical lithium ion battery cell. So, to describe some particular cell, we must collect data from the cell using carefully defined procedures, and then we must process that data to generate the unknown parameter values of the model. You might remember that in the ESC model, there are portions of the model that describe static elements of behavior and portions that describe dynamic or instantaneous elements of behavior also. And the cells open circuit voltage is a static function of state of charge and temperature, that's what we're going to emphasize this week. A separate cell tests in the laboratory are required to collect data for the open circuit voltage relationship versus the tests required for the dynamic relationships. And this week, we look at the tests that are required to collect data for the open circuit voltage relationship and how to process those data. Next week, we will turn our attention to the dynamic aspects of the model instead. When determining the model parameters that describe a specific cell, we collect data from that cell in the lab. And it's very important that the data we collect be as representative as possible of how the cell will perform in the final application. We don't want the data to be biased by the measurements setup itself, for example. So, for that reason, it's really important to use a 4-wire or a Kelvin connection in the test setup. And the figure on the slide shows a battery under load as the green rectangle and it's terminals as the red circles. The test equipment that sources and sinks current to the battery cell is connected to that cell through two wires that are drawn in this illustration as the thicker wires. And the current that goes through this wires we denote as I. The test equipment also measures the voltage response of the battery cell to this input current stimulus and it measures the voltage through two different wires that are drawn on this illustration as thinner wires connected to a volt meter that is denoted by the letter V on this diagram. Large currents can be sourced by the test equipment and so there can be large voltage drop over the current supply wires, the thick wires connected to the battery cell. So, if we were to measure voltage using the same wires that we use to source current, then we're not going to measure only the battery cell voltage, but we're additionally measuring the voltage drop over these wires due to the resistance of the wires. And this is why we don't use two wires to connect to the device under test because our model must describe the cell and not the test equipment wires that connect to the cell. When we connect the battery using 4-wires as illustrated, the active sensing the cell voltage through the thin wire draws essentially zero current, and so there is essentially zero voltage drop over these voltage centers wires themselves. And this means that the volt meter will accurately measure the true terminal voltage of the battery cell. So, I recommend that in every scenario where you're testing a battery cell that you use a 4-wire connection as drawn. When we are collecting data from a battery cell, we use lab equipment that is known as battery-cell cyclers or a battery-cell test equipment. One example that we have here in our laboratory at the University of Colorado, Colorado Springs was manufactured by Arbin Instruments, and it's shown in the figure. This equipment is able to control each cell's current or power as a function of time according to some user-designed test program and at the same time it records the actual cell current and voltage and temperature response. This particular unit is configured with 12 testing channels where each channel can be connected to an individual battery cell under test, so we can conduct up to 12 tests simultaneously. In the photograph, each of the thicker white cables that you see internally contains four separate wires and together corresponds to a single test channel using a 4-wire or Kelvin connection. And in this Arbin equipment, internally it has all of the power electronics and the processing required to execute the user's desired profile of current versus time or power versus time on the battery cell and then to measure the response. You might also notice that there are some thinner white wires in this diagram, and those happen to be connected to thermistors to measure temperature. And internal to those cables there's only two wires that connect the thermistor to the test equipment. Battery-cell test equipment is usually designed to the customer's specifications. And so, this example I show you is intended for illustration only. There's a lot of variety and how many test channels you can configure for any particular piece of test equipment. There's a lot of variety in the current ranges that you can command. On this particular device, there's 10 channels that can command up to 20 amps of current each, and two channels that can command up to 200 amps of current each. But this is highly configurable depending on your needs. And there's also great variability in the types of programming environments that the different manufacturers offer that allow you to customize the type of testing that you can do. In addition to controlling the input current or power to a battery cell, most tests must be conducted in controlled temperature environments as well, in ambient temperatures that are regulated. The photograph on this slide shows an environmental chamber manufactured by Cincinnati Sub-Zero. This particular unit has eight cubic feet of interior space and is capable of maintaining constant ambient temperatures between negative 45 degrees Celsius and positive 190 degrees Celsius. It can even command profiles of temperature versus time. And again though, this example is representative of what a thermal chamber might look like and systems can be purchased from different vendors configured in different ways. Some of them will have humidity control settings and some of them will have different temperature ranges. Some even have extremely rapid cooling to investigate thermal shock and even more than that. To summarize our introduction to this week's topic, we're beginning to look at how to identify the parameter values of an enhanced self-correcting cell model. Importantly, when conducting laboratory experiments to gather data from the cell in order to do this, the cell must be connected with a 4-wire measurement setup for accurate voltage measurements that are not biased by the measurement configuration itself. Cell-test equipment will supply a profile of current versus time or power versus time to the cell, and it will then also measure the actual current versus time and the voltage and so far, responses of the battery cell. Environmental or thermal chambers maintain a constant ambient temperature to make sure that the tests are calibrated properly for a certain operating regimes. And you've seen example photographs of two pieces of such test equipment from different vendors. By the end of next week, you will understand all of the testing requirements necessary to characterize a cell model. And this will give you insight into the specifications for test equipment that you might require in order to do so. And that brings us to the end of this lesson, and as we proceed from here, we'll be studying more this week about how to collect data to characterize the open circuit voltage relationship of this cell, and how to write computer programs to analyze those data to find the parameter values that we need. So, that's what's coming up next, hope you're looking forward to it.
