Fuel Cell System Modeling - MATLAB & Simulink
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    Fuel Cell System Modeling

    Learn how Simulink®, Simscape™, and Model-Based Calibration Toolbox™ are used to model a polyelectrolyte membrane (PEM) fuel cell system. Model a fuel cell using a physics-based approach that shows:

    • Aspects of fuel cell electrochemistry
    • Model balancing of the fuel cell plant
    • Fuel cell optimization
    • Fuel cell system response for an electric vehicle drive cycle

    Next, simulate the fuel cell using a statistics-based method that focuses on using data, lookup tables, and statistics to develop less detailed models better suited for system integration and supervisory control studies.

    Published: 22 Jun 2022

    We'll discuss two different types of approach to model the fuel cell systems. One approach focused on the physical and chemical process of fuel cell. We call that thermodynamics oriented. It use the physical modeling tools to model the electrochemical equations of the stack and the physical process in the balance of a plant. The models built this way usually have more details and higher fidelity and can be used for designing or optimizing the fuel cell system itself.

    The other approach is more data-driven. It looks at the fuel cell system as a whole, as an energy source, without worrying too much how that happens-- the detail physics. We call this a system-integration oriented method. They tend to be more statistical in nature and has a sort of input and output type of structure using usually lookup tables or empirical equations to represent the response from a fuel cell system.

    This type of model contains less details, runs faster, and is suitable for system integration study or designing supervisory controllers. We'll next show you an example of each approach. The model built with either of these two approaches works well with the virtual vehicle framework we have just discussed.

    So we'll start with the first approach that's based on the thermodynamic physics. What is shown here on the right is a shipping example in the latest release of MATLAB, our release 2021a. It is a PEM fuel cell system. The equation of the stack is implemented in Simscape language, including the electrical chemistry for the voltage, hydrogen oxygen consumption, water generation and transport, and heat generation as well.

    The balance of the plant in this model include the compressor, humidifier, cooling systems, recirculation for the hydrogen, as well as some water management-- basically typical components you'll see in the fuel cell system. So this example model itself include a few scenarios and codes to visualize the results, and we can take a look at a couple of those in the next slide.

    So on the left, we're showing a few characteristic curves for the stack using a current sweep-- basically, linear increase the current-- as the input. We can see that the voltage will drop as current increase and the power output actually increase with the current until a certain point. That's where the maximum current is.

    The bottom left figure shows the thermal efficiency. It tends to drop when you have a higher current and how much hydrogen and oxygen are being consumed from inlet of the stack to the outlet. So this is a sort of idealized case you do through your current sweep, checking out the characteristic of the stack itself.

    So on the right, it's closer to a real-life scenario. So this is based on the power demand from FTP75 drive cycle. The power demand is actually prerecorded from a full vehicle simulation. The model output from this give us an idea of the power generated by the stack, as well as the amount consumed by the balance of a plant. That's on the first figure on the top.

    The one in the middle shows us the amount of hydrogen consumed. And as a result, the tank pressure decreases. On the bottom, we're showing the temperature in different part of the fuel cell system, the anode, cathode, as well as the coolant itself around the radiator, how it's been cooled.

    So this contains the details on the electrical chemistry of the stack and all the thermal fluids aspect modeled in the balance of plant. With these details, we can actually use it to study and optimize the design of the fuel cell system itself, size the component, and develop some local controllers. And next we'll show you another approach that does not include these details, and of course with different goals and applications.

    So this approach is geared towards system-integration study. So it treats the fuel cell system as something that provide electrical power without worrying how it provide the power, therefore can represent the system as lookup tables or empirical equations instead of a particular model that works for every scenario.

    What we're actually want to discuss is a workflow to build such a model using statistical tools for MathWorks. The model can be built using lab data sets or from high-fidelity simulations. We can apply a statistical modeling tools to fit and describe the data sets and arrive at a fast-running model, which is especially suitable for system integration study and supervisory control development.

    One example of MathWorks tools for this task is the model-based calibration toolbox. It's a set of apps and tools for modeling and calibrating complex nonlinear systems. There are a lot of application of this tool for engine calibration or motor control. And we have had some success using this tool to generate lookup table models for fuel cell system as well.

    So on the right this is a typical workflow using this tool. You can use it to design experiment, use that design to collect data, model those data, and generate or export the statistical model or lookup tables from this, and eventually use that to either implement on the control hardware or for further simulation study.

    So here is example of application of this workflow for fuel cell modeling. We skip the first two step, the DOE and the data collection, because data is readily available. Argonne National Lab has done this test on a Toyota Mirai and made the data available, so here's the citation for that.

    We import this data into the model-based calibration toolbox, model the data, generate the statistical model, export that for further simulation work. Then we can compare the simulation result with the original data set. The current here on the middle left is the input, so they match, of course.

    Then we look at whether we can get a match in the voltage. For most of the time, yes. And when the current is 0, we see the transient. They disagree a little bit. That's OK. We know this is the price we're going to pay. Lookup table models tends to not include those details, and it's not surprising to us.

    But also because the current is 0 whenever this happens, the actual power output from the stack is actually very well captured. We're getting an excellent agreement on the bottom right here. This means we can use this model to predict the power output, fuel consumption efficiency, et cetera, and enable the supervisory control design.

    So this workflow overall provide a fast track from lab data to a simulation model without digging too much to the physical details. We have also include an example of the lookup table model built using this approach in the fuel cell EV reference application you saw earlier.