Lithium-ion Battery Modeling for the Automotive Engineer

Most people are aware of the dramatic and fast-paced trend towards electrification within the automotive industry which has led to the increased use of Lithium-ion (Li-ion) batteries for energy storage in electrified vehicles. Here at Gamma Technologies, we work with many modeling, simulation, and controls engineers in the automotive industry, and one thing I have noticed is that this trend towards electrification is not only a shift in the products that OEMs sell, but also a personal shift for many automotive engineers. I’ve spoken to many engineers who have historically worked on conventional vehicles and are now being asked to focus more on electrified vehicles. Because of this, I decided to write a blog introducing the basics of Li-ion technology and popular modeling techniques for these automotive engineers trying to keep up with this major trend in the industry.

There are many ways to model a battery, but the two most commonly-used are electrical-equivalent behavioral models and electrochemical physical models. Both methods provide value for engineers, and each one takes a different approach to modeling the behavior of batteries. In this blog, you’ll learn about the basic operation of Li-ion batteries, how these different approaches model the behavior of a battery, and the benefits and tradeoffs associated with each.

How does a Lithium-ion battery work?

Before I go into detail about different modeling methods, let’s make sure we understand how a Li-ion battery operates. Figure 1 shows a cross-sectional view of a Li-ion cell.

Shown on the left and right sides of this cross-sectional view, the positive and negative terminals allow electrical connections between them.  This is where battery or cell voltage can be measured. During charging and discharging, Li-ions (Li⁺) shuttle back and forth between the cathode and anode through the separator (from the cathode to anode while charging, and from the anode to cathode while discharging). Within the cathode and anode, Li⁺ reacts with the active materials, releasing or absorbing electrons in the process that are then able to flow between positive and negative terminals.

What’s Important in a Battery Model?

For most applications using battery models, it is generally important to accurately predict the electrical characteristics of the battery, including the voltage across it and the current flowing through it. Additionally, an estimation of State of Charge (SOC, a normalized estimation of how much chemical energy is stored in a cell) is required. If battery models are linked to thermal management simulations, accurate heat dissipation from the battery must be captured.

As anyone with a cell phone, tablet, or laptop can tell you – Li-ion batteries degrade over time. There are many electrochemical factors that lead to the degradation of a Li-ion battery.  For instance, the active materials in the cathode and anode tend to crack over time and there are undesirable side reactions that lead to growth of films on active material particles in both the cathode and anode.  Additionally, under extreme conditions, Li⁺ may react with electrons to form Lithium metal in the anode during a process referred to as Lithium plating, which can be very detrimental to the health of a battery.

Safety simulation and testing is also an important topic. Abuse conditions such as nail penetration, as well as extremely hot or cold environments could be catastrophic for the battery. This is where predictive 3D models of cells and the conditions around them are required in order to capture the electrothermal response of the battery.

Electrical-Equivalent Modeling

Now that we understand more about Li-ion batteries, let’s take a look at the different modeling methods used, starting with electrical-equivalent modeling.  This modeling method is done primarily to give electrical representations of how batteries react under certain loading conditions.

Non-Dynamic (Resistive Models)

The simplest test done on a battery or cell is a constant-current discharge/charge test, where cells are discharged and charged to and from 0% and 100% state of charge at a constant current.  During these tests, the terminal voltage of the battery is observed to be similar to Figure 2.

Similarly, these discharge/charge tests can be done at multiple currents.  Figure 3 shows what a typical Li-ion cell’s terminal voltage may be for constant-current discharge tests at multiple currents.

The behavior observed here is that the voltage changes while the battery depletes depending on the direction of the voltage and the current.  Additionally, the terminal voltage drops with increasing currents.

With electrical-equivalent modeling, this type of behavior is represented in an electrical circuit using the resistive battery model, pictured in Figure 4.  In this model, the open circuit voltage and internal resistance are often characterized as functions of temperature and state of charge.  Using this model, the behavior observed in constant-current charge and discharge cycles can be replicated quite accurately.

Dynamic (Thevenin Models)

The resistive models are good representations of a battery’s electrical behavior observed in steady-state conditions; however, if loads on a battery are more dynamic, the resistive model may not follow observed behavior.  For instance, when Li-ion batteries are loaded with pulses of current, the voltage response can be very non-linear.  Figure 5, below, shows how a typical Li-ion cell reacts to a pulse of discharge current and a pulse of charge current.

With a resistive electrical-equivalent model, the non-linear, exponential-decay portion of the voltage response would not be captured.  In order to be able to capture the exponential decay behavior in the voltage response, one or multiple resistor-capacitor (RC) branches can be included in the electrical-equivalent model.  See Figure 6 for a circuit diagram of such a battery model, often referred to as a Thevenin battery model.

With this type of model, the step changes in the voltage captured are represented with the internal ohmic resistance (R0) and the exponential decay of the voltage response is captured with the RC branches.

SOC Estimation and Aging

In each of these electrical-equivalent models, there are a few ways to estimate SOC of a cell or battery.  The simplest and most common way is a process called “Coulomb Counting” where the model counts the charge (integral of current over time) moving across the battery and very simply adds or subtracts that charge from the initial charge of the battery.

With these electrical-equivalent models, heat generation of the battery is calculated by the summation of the power losses across each resistor (I2R losses).  Aging phenomena of Li-ion cells are often characterized as capacity fade and resistance growth over time with non-physics based empirical models.

Summary

It’s important to note that electrical-equivalent battery modeling is not inherently a physics-based approach. Both the dynamic and non-dynamic approaches are electrical representations of how the terminal voltage of a battery may react to different battery loads. The capacitors and resistors are not meant to represent physical capacitances and resistances but the dynamics of the battery.

The circuit parameters are often characterized at multiple temperatures and states of charge by matching experimental results.  This means that electrical-equivalent models are not predictive outside of calibrated temperature or SOC range.

Electrochemical Modeling

If this predictive capability outside of calibrated temperatures and states of charge, or if insight into cell operation is desired, physics-based electrochemical models are available to model Li-ion batteries.  For Li-ion batteries, the widely accepted electrochemical modeling approach is often referred to as the “Newman Pseudo 2D model,” named after John Newman, the creator of this model.

In the Newman Pseudo 2D (P2D) model, illustrated below in Figure 7, the cathode, separator, and anode are discretized in the thickness direction (horizontal direction in Figure 7) using a finite control volume approach.  Additionally, in each sub-volume of the cathode and anode, there is a spherical representation of an active particle, each of which are discretized using the finite control volume approach in the radial direction.  This combination of horizontal and radial discretization is where the term “Pseudo 2D” comes from.  The governing equations for the charge transfer and Li⁺ diffusion are all solved using this finite control volume approach in the model.

In these electrochemical battery models, the concentration of Li⁺ in different parts of the cell is solved, ultimately leading to a physics-based estimation of state of charge.  These models are also able to predict the heat generated from Li-ion batteries, including heat generated ohmic losses, reaction losses, and entropic heating.

With electrochemical models, physics-based representations of aging mechanisms are used. For instance, the SEI layer, cathodic film layer, and their growth over time can be modeled. Additionally, Lithium plating and Li+ isolation due to active material cracking can also be modeled.

These physics-based aging models have many benefits, including:

• Decreasing the amount of battery testing time required
• Understanding how batteries age in real-world scenarios
• Understanding how system-level performance degrades over time
• Understanding how charging strategies can affect battery life

 

How Do These Methods Compare?

Now that we have an understanding of how each method works, let’s compare the two to understand the advantages and tradeoffs associated with each.

First up – electrical-equivalent models. With this method of modeling, it is very easy to build and calibrate a battery model. There are standard curve-fitting methods to calibrate electrical-equivalent battery models to match a voltage.  Because these models have a simple calibration process, they usually give good results for voltage, current, SOC, and heat rate.

Next – electrochemical models. Unlike electrical-equivalent models, electrochemical models give insight into what occurs inside the cell and they can be used outside the calibrated temperature range. Another key difference is the ability to use physics-based (as opposed to empirical) aging models, which give insight into growth rate of the SEI and cathodic film layers, material isolation due to cracking, and Lithium plating. These models also give cell designers the ability to quickly iterate on cell design parameters without having to re-calibrate an electrical-equivalent model.

I know that’s a lot of information, so some advantages of each modeling approach are summarized in Figure 8.

When Do I Use These Models and How Do I Use Them?

As you can see, both modeling methods offer their own unique set of advantages and tradeoffs, but it still may not be clear when electrical-equivalent models and electrochemical models should be used.

For many system-level and thermal engineers, electrical-equivalent models are all that is required because these models give accurate results for battery voltage, current, SOC, and heat rates.  However, depending on the questions that are trying to be answered with simulation, electrical-equivalent models may not be sufficient.

Electrochemical models are often used in more advanced applications of battery modeling. For instance, if a model needs to predict the aging of a Li-ion cell, physics-based aging models offer a more flexible and predictive solution than the empirical aging models available in electrical-equivalent models.  Additionally, when designing a cell, choosing a charging strategy, or studying battery behavior in extreme climates, electrical-equivalent models may not provide enough insight into the behavior of the cell, which is often required for these applications.

Because both the electrical-equivalent and the electrochemical approaches to modeling Li-ion batteries provide value to simulation engineers, Gamma Technologies offers accurate capabilities for both methods.  When electrical-equivalent models are required, engineers are able to use GT-SUITE’s flexible solution for a resistive or Thevenin (flexible number of R-C branches) battery model. When electrochemical models are required, AutoLion provides cell designers and system simulation engineers accurate and fast-running electrochemical models.  These two tools can also be combined in order to incorporate electrochemical battery models into multi-domain system-level models.

What’s Next?

I know that this was a long read, but I hope this blog helped make Li-ion batteries feel less like “black magic” and that it built up an understanding of both electrical-equivalent and electrochemical modeling approaches to them.

If you’d like to learn more or are interested in trying GT-SUITE or AutoLion for battery simulation, Contact us!

NOTE: This piece was originally published on July 2018

 

Tolerance Study of a Diesel Fuel Injector Model using Sensitivity Analysis and Variability Analysis in GT-SUITE

Tolerance Study of a Diesel Fuel Injector Model using Sensitivity Analysis and Variability Analysis in GT-SUITE
This example demonstrates a tolerance study using GT-SUITE. The application is a detailed diesel injector model, but the concepts and tools described here can apply to a tolerance study applied to any other model or engineering domain. It demonstrates ranking of influential factors, identification and removal of negligible factors, evaluation of probability distributions of output variables, and execution of what-if studies to predict improvements to the output variable distribution. These objectives are accomplished by running a couple different Designs of Experiments (DOE) and performing various analyses in GT-SUITE’s DOE post-processor (DOE-POST).

Problem Description
We consider a detailed diesel injector model where the model map layout and component schematic is shown here:

Although the application details are not the primary focus of this writing, more details about diesel fuel injectors are included here for readers that are interested. In a diesel injector the fuel flow to the cylinder is governed by a large number of parameters. In this type of injector, a solenoid actuates the control valve, which connects the high and low pressure sides of the fuel system. The resulting flow passes through the control chamber, for which an inlet and outlet orifice diameter significantly influences the static pressure drop. Because the injector’s needle, which is close to the cylinder, is still subject to higher pressure, an upward motion of the control rod and needle releases fuel to the cylinder. The transient mass flow, or rate shape, is an important characteristic for the control of the combustion processes quality and is dependent on a large number or parameters. Aside from the actuation duration of the solenoid, mechanical parameters such as spring characteristics and clearances, as well as flow parameters such as restriction diameters at various locations, are important factors and can interact with each other. If the control piston and needle never reach their designed upper stop, the injector is referred to as being operated in the ballistic regime. Because of the floating nature of the needle, this regime is most sensitive to manufacturing tolerances.

For this study 11 known sources of variability are investigated. A single operating point is studied at 1300 bar rail pressure and 0.5 ms energizing time, which puts the injectors in the ballistic regime.

The 11 input variables, or factors, are listed in the table below, along with their known tolerances. It is assumed that all variations conform to normal distributions such that 95% of the variance falls within the tolerances listed, and therefore the standard deviation is half of the tolerance value. For example, the standard deviation for peak current duration is 0.025 ms, such that the real operating duration is between 0.095 and 0.105 ms 95% of the time (+/- 2 standard deviations).

The main output, or response, of interest is the injected fuel mass. Another key output is the cumulative flow through the control valve for each injection event, which represents fuel mass for which energy is expended to push through the control valve, but which doesn’t get injected. Ideally this mass would be minimized. The objectives of this study are the following:

1. Use factor screening to rank the 11 factors with respect to their influence on the two responses.
2. In accordance with the first objective, identify negligible factors that can be omitted from further analysis.
3. Evaluate the expected probability distributions of the two responses caused by the variation in the factors.
4. Predict the improvement in the injected mass probability distribution if the two most influential factors can be adjusted.

The third objective requires evaluating the model with Monte Carlo sampling, where the factor values are sampled from their normal distributions. The second objective is important for achieving the third, because as the number of factors increases, the number of Monte Carlo model evaluations will need to increase to obtain confidence in the results. If the number of factors can be decreased, the Monte Carlo model evaluations can either decrease or provide more resolution for the results.

Identifying Important and Unimportant Factors
We approach the first two objectives by performing the Morris Method on the model. The Morris Method is a global sensitivity analysis that utilizes one-at-a-time step changes in factor values. It calculates k different elementary effects in different areas of the factor domain, where an elementary effect, EE, is the change in response, R, that occurs with a step change in a factor, F.

It is computationally efficient and only requires k(F+1) model evaluations, where k is typically 15-30. The results of the analysis get conveniently summarized in a single plot.

For a given factor, the mean and standard deviation of the multiple elementary effects are calculated and placed on a plot of “EE standard deviation” vs. “EE mean”, with one point per factor. Factors whose points lie near the origin (0, 0) have negligible effect on the response. Factors whose points have large “EE mean” have large main effect on the response, and factors whose points have large “EE standard deviation” contain higher-order effects or interaction effects. However, the Morris Method cannot distinguish between higher-order effects and interaction effects, and it cannot identify specific interaction terms.

For this study, k was chosen to be 20, resulting in 20(11+1) = 240 model evaluations, and the lower and upper values in the table were used as variable bounds. The Morris sampling was configured in the DOE Setup (within Case Setup) as shown here:

The Morris sampling is a reduced version of a 4-level full-factorial scheme which includes interior points and not just the lower and upper bounds of the factor ranges. The parallel coordinates plot shown below, which is available in DOE-POST’s Select Experiments page, also illustrates the spread of the sampling for the 11 factors. In contrast, a 2-level full-factorial sampling scheme would result in 2^11 = 2048 points, but would not contain any interior points. A 3-level full-factorial sampling scheme would result in 3^11 = 177,147. As a result, Morris sampling has a computational advantage over 2-level and 3-level full-factorial methods.

After running the DOE simulations, the resulting Morris Method plots are provided in the Analyze Experiments page of the DOE post-processor and are shown below, where the analysis uses standardization and normalization such that the maximum allowed mean and standard deviation are 1.0. Using a maximum y-axis scaling of 1.0, the first observation from these plots is that the standard deviation is very low and negligible for all factors, meaning there are no higher-order or interaction effects within the relatively small ranges over which they were varied.

For easier readability, the y-axis is scaled to better show the individual points.

The plots show that, according to x-axis magnitude which represents the first-order effect, the OutletOrificeDiameter has the largest effect on the injected mass, followed by InletOrificeDiameter and CtrlValvePreload. For the control valve mass loss response, the OutletOrificeDiameter has the largest effect, followed by CtrlValvePreload, CtrlValveLift, and SolenoidCrossSectionalArea.
The full set of tabulated Morris results are provided in this table.

The Morris results are most useful for determining which factors can be excluded from further analysis. One might apply a threshold of 0.05 or 0.1 to the mean and standard deviations of the elementary effects to determine which factors are worth keeping. A threshold of 0.05 will be used for this example. The goal is to exclude factors which have EE Mean less than 0.05 for both responses. Those consist of CtrlValveStiffness, NozzleDiam, and NeedleSpringStiffness. The example will proceed with the remaining 8 factors.

Predict the Probability Distributions of the Responses
To determine the probability distributions of the responses, a new Monte Carlo DOE with 2000 experiments is configured in DOE Setup in GT-ISE. This screenshot shows the configuration which applies normal distributions to the 8 factors using the syntax normdist(mean, standard deviation).

 

After running the DOE simulations, the Variability Analysis page of the DOE post-processor is used to analyze the results. The resulting probability distributions for the two output distributions of interest are shown below, where they appear to conform to normal distributions. For the injected mass, 90% of the values fall between 10.85 and 14.24 mg, representing a relative spread of 2.9/12.6 = 27%, where 12.6 mg is the baseline injected mass. Relatively little variation is present in the control valve mass loss, where 90% of the values fall between 6.0 and 6.3 mg, with a relative spread of 0.3/6.14 = 4.9%, and as a result, the injected mass will take the remainder of the focus of this study.

The relatively large variation in injected mass is typical of an injector in the ballistic phase, where the needle is not at the upper stop. Injectors in the ballistic phase tend to be dynamic and unstable, as minimal force differences can cause substantial variation in injected mass. This behavior often causes difficulty in calibrating an injector model to measurement data, because these slight variations in input variables can cause a wide range of injected mass values. This variability can discourage the modeler by unnecessarily making them think that either something is wrong with the model or something is wrong with the measurement.

The modeler or design engineer might want or need to determine some worst-case scenarios for the injector. For example, it’s clear that the injected mass profile has a bell-shaped probability distribution that makes it possible for some injectors to inject as little as 8.5 mg or as much as 16.5 mg at the operating point of interest, even though none of the 2000 experiments resulted in these two values. This injector might be installed in tens of thousands of vehicles, and each vehicle would have multiple injectors, one for each cylinder. As a result, hundreds of thousands of this injector might be produced, making it likely for these more extreme injected mass values to occur.

To explore these worst-case scenarios, it is necessary to fit the injected mass data to an ideal distribution. This utility is included in the Variability Analysis page of the DOE post-processor. By enabling this feature, a distribution line representing the best fit is overlayed with the distribution plot, and a table appears that shows the metrics of different distributions. Changing the checkbox selection updates the plot so that the user can see how each distribution appears to fit the data. A few different distribution selections are shown below. The lower the “Error” metric in the table, the better the fit. The table also provides the parameters necessary to reproduce the distribution in the right-most column. The normal and log-normal distributions clearly fit the data best, but there is very little visual distinction between the two. Because of its lower error, the normal distribution will be used.

With the desired distribution selected, a calculator utility can be opened to determine worst-case scenarios. For example, the probability of the injected mass being as little as 8.5 mg is 0.000040, meaning it is likely to occur 40 times out of a million. The probability of the injected mass being as high as 16.5 mg is 1 – 0.999939 = 0.000061, meaning it is likely to occur 61 times out of a million.

Alternatively, the calculator utility can be used to enter cumulative probability values to calculate corresponding response values. For example, it might be desirable to determine the response values for the 0.1% and 99.9% cumulative probabilities. These are 9.4 and 15.7 mg, respectively.

Given the wide range of injected mass values that can be expected at this operating point, it might be necessary to ensure a narrower range of values in the context of injector design. For demonstration, we’ll assume that lower injected mass values are more problematic and that 99% of the time, at least 11 mg of fuel needs to be delivered. In the Variability Analysis page, the injected mass slider bars serve as specification limits. The lower bar is positioned at 11 mg, and the upper-right corner of the page displays the percentage of experiments that are out-of-spec according to these specification limits. 6.6% of the experiments yield injected mass less than 11 mg. The right-side table also provides process capability metrics, and the common metric Cpk is 0.57.

Predicting Improvements to the Response Distribution
The Variability Analysis page within the DOE post-processor serves as a powerful analysis tool for performing fast what-if studies to predict changes in response distributions according to changes in the factor variances. To experiment with changing the factor distributions, one should understand which factors should be focused on. We have already seen from the Main Effects Ranking plot that the OutletOrificeDiameter, InletOrificeDiameter, and CtrlValvePreload have the largest first-order effects on the injected mass. As a result, these three factors would be most appropriate for experimenting with adjusting the response distribution. These Main Effects rankings are indicative of using all the data, or in other words the entire factor domain. However, in some situations, a different factor can have a larger effect on a response in a smaller, specific region of the response. It is worth checking, since we are particularly interested in determining which factors mainly affect injected mass at the lower values.
To accomplish that task, which is known as Monte Carlo Filtering, we view the factor CDF plots in the Variability Analysis page. These plots are provided below, where the in-spec and out-of-spec CDF is provided for each factor. In summary, they show that higher values of InletOrificeDiameter and lower values of OutletOrificeDiameter cause the most significant discrepancy between the injected mass being in-spec and out-of-spec. SolenoidCrossSectionalArea and CtrlValvePrelaod also have a statistically significant effect on this discrepancy, but we will focus on the two diameters since their effects are so much larger than that of the other two.

Because the higher values of InletOrificeDiameter cause the injected mass to violate the specification limit, it is necessary to adjust the mean or nominal value, and attempting to improve its variance will not be sufficient. The same is observed for OuletOrificeDiameter. To test the effect of adjusting their means, we run a new Monte Carlo analysis, but we can do so directly within the DOE post-processor; it is not necessary to run additional DOE experiments from GT-ISE. To run them from the DOE post-processor, a metamodel is needed. It has already been shown that a linear metamodel without interaction effects can be used for the range of the factors being studied. The regression plot showing how well the metamodel’s predicted points align with the original data points is shown here.

After creating a linear metamodel in the Create Metamodels page, a new Monte Carlo experiment set is configured in the Variability Analysis page, where we experiment with adjusting these two diameters by 5 micron. In addition, we use a larger number of 5000 Monte Carlo experiments for each of these case studies, since the metamodel evaluations are very fast and practically free. We test three modifications to the input variables:

1. Decreasing the InletOrificeDiameter mean by 0.005 mm.
2. Increasing the OutletOrificeDiameter mean by 0.005mm.
3. Making modifications 1 and 2 simultaneously.

 

 

The plots below compare the original injected mass distribution with those of the three tests, and the table below the plots summarizes the effects of the modifications. Making a modification to either the InletOrificeDiameter or OutletOrificeDiameter is enough to decrease the probability of having the injected mass be less than 11 mg. Using these results, the design engineer can assess making one of these changes in the product.

Conclusions
This study demonstrated using sensitivity analysis and variability analysis to analyze and improve an injector design in GT-SUITE. A sensitivity analysis utilizing the Morris method identified the most influential factors on the two responses of interest, and three factors were found to be negligibly important for both responses and were therefore omitted from further analysis. Then normal distributions were applied to the remaining eight factors using a 2000-point Monte Carlo DOE. After running the simulations, the results were analyzed in DOE-POST, where the response distributions were plotted and observed. The response data was fit to a normal distribution so that worst-case scenarios could be calculated based on cumulative probabilities. Finally, a regional sensitivity analysis was conducted to determine how best to avoid injected mass values at the lower end of the distribution, and three fast what-if studies were conducted to predict improvements in the injected mass distribution.

 

By Ryan Dudgeon

Robust Battery Pack Simulation by Statistical Variation Analysis

Simulating Battery Packs – Not All Cells are the Same

When simulating a large battery module, typically we assume that all the cells in the module are going to be the same. However, that is not always the case. Factors such as the capacities and resistances of the cell can vary from cell-to-cell. This brings up the question – How can we model the variance of different cells within the module?

In v2021 of GT-SUITE, we added some new features to help model this cell-to-cell difference. One new feature is a new statistical variance analysis tool.

This new tool opens a wizard which walks users through choosing an object to select and vary the mean and standard deviation for the attribute variation. This will create unique parameters for each part associated with the object. To put it simply, each cell uses part overrides to define different capacities and resistances for each cell in a battery module.

Another new feature is in our design of experiments setup. The Monte Carlo method has been added as a new DOE distribution method in DOE Setup. This allows users to vary any parameter according to a normal distributed mean or standard deviation.

Let’s take a look at this example below.

In this example, we have a battery module with 444 cylindrical cells – 74 in series and 6 in parallel. We were told that the cell capacity was 3.2 Ah. Additionally, we were given distributions of the capacity and the resistance of 200 cells of the same type. The distributions followed a standard normal distribution and included the mean and standard deviation of the distribution.

With the statistical variance tool, we can add unique parameters for the capacity and resistance multiplier for each of the 444 cells with our simple wizard. Once that is done, we can open up DOE Setup and select how many experiments we want to run to see how the distribution of capacity and resistance affect our module. GT’s Monte Carlo solution enables normal distribution to be setup for the capacity and resistance multiplier parameters

After running the model, we can look at the responses for each individual cell in the module including the state of charge and total energy dissipated.  The boundary conditions for this model include discharging at a 2C rate and using a simple thermal model of a 1-D convective boundary condition at an ambient temperature of 25^oC and a convective heat transfer coefficient of 10 W/m²K. The total energy dissipated varies by around 3% and the SOC varies by around 1% within the various cells in our module.

Those these results may seem small, but depending on the ambient temperature, discharging/charging protocols, or other factors, they can have a great effect on the battery module. In some instances, we might be able to see that one section of the battery module is heating much faster than another, meaning that some cells might need to be replaced faster than others or need to be designed to allow for more cooling compared to other areas of the module.

With these new tools and with GT-AutoLion, users can take large battery modules like these and analyze the responses of each individual cell and extrapolate to various C-rates and temperatures with physics-based modeling – allowing the user to gain more insight into their battery module, evaluate the battery degradation, and improve their BMS in the process.

Written by Vivek Pisharodi

Gerotor Pump Model Optimization via Process Integration of GT-SUITE and Gerotor Design Studio

Overview

GT-SUITE gerotor pump models are powerful design tools that provide accurate predictions of flow and thermal behavior while also being computationally fast.  Necessary inputs to these models are the gerotor profiles for volume, surface areas, clearance gaps, and pressure force areas.  Gerotor Design Studio (GDS) is a unique CAD software solution for designing, analyzing, and manufacturing gerotor pumping elements.  More specifically, GDS can take detailed gerotor pump geometry and calculate the gerotor profiles required by GT-SUITE.  The partnership between GT-SUITE and Gerotor Design Studio provides sophisticated, accurate, and fast pump modeling capabilities to pump design engineers.

This post provides some background on gerotor pump models in GT-SUITE and GDS and details how the two software tools can complement each other through process integration for powerful optimization runs.

GT-SUITE Gerotor Pump Models

GT-SUITE is an ideal tool for studying the detailed flow and thermodynamic behavior of a variety of pumps and compressors, including gerotor, vane, external gear, reciprocating, swashplate, scroll, screw, and others.  These models can handle either positive or variable displacement, and key output predictions include:

• Performance vs. speed, pressure rise, and temperature
• Flow and pressure pulsations, and cavitation behavior
• NVH issues, resonance, and fluid borne noise
• Dedicated friction model for vane and gerotor machines
• Interaction with relief valve dynamics
• Bearing loading caused by internal pressurization

More specifically, gerotor pump models can be created directly from CAD using the GEM3D application, where four basic shapes are specified to define the inner gear, outer gear, inlet volume, and outlet volume.  With this basic template filled, the GEM3D model can be automatically exported to a .gtm model file in GT-ISE where all flow parts are connected and volume, port area profiles, and pressure force areas have been calculated.

Gerotor Design Studio Pump Models

The GDS software provides a user-interface for designing gerotor profiles, designing porting, specifying fluid and material properties, and visually inspecting the gerotor design.  The software performs many detailed physics calculations to predict flows, powers, efficiencies, and pressure waves.  It also has some powerful integration capabilities with GT-SUITE, where GDS can directly create GEM3D (.gem) models of the gerotor geometry while providing the gerotor input profiles to be used in a GT-SUITE pump model.  In addition, a command line version of the software is available that does not require the graphical user interface, and this command line version makes it possible to integrate with GT-SUITE for model-based optimization runs.

Motivation for Integrating GT-SUITE and GDS

Each software tool has unique advantages that complement the other.  More specifically, design changes made in GDS, such as detailed geometry inputs, will impact the angle-resolved gerotor profiles that the GT-SUITE pump model relies on.  A pump design engineer may want to run optimization or Design of Experiments (DOE) studies to analyze the effects that input geometry variables entered in GDS have on important flow and thermal output variables that are predicted by GT-SUITE.

Integrating GT-SUITE and GDS for Optimization and DOE Studies

Optimization and DOE studies require an automated approach to integration, which, for any combination of input GDS input variables, will first run the GDS model to generate the gerotor pump profiles, and then run a simulation of the GT-SUITE pump model that is configured to use those profiles.

The command line version of GDS becomes very beneficial for this type of automated approach.  It relies on an input text file that provides all the geometry to a GDS gerotor model.  Then an executable called GDS_GTS.exe can be run, which invokes the GDS solver to read the input file, perform its calculations, and generate the gerotor profiles.  A section of a GDS input file is shown here.

Process integration refers to automated sequencing of a series of processes that might include running CAE simulations, executing scripts or executables, and managing input and output variables that might transfer between processes.  GT-SUITE provides a process integration tool called Process Map which is part of the GT-Automation license.  Process Map models are graphically constructed in GT-ISE and provide organization of parameters, configuration of multiple cases in Case Setup, activation of the GT optimizer, and creation of Designs of Experiments.  The Process Map model for this integration is shown below and consists of five processes that are executed from left to right.

The first process handles transfer of Process Map parameter values to GDS, specifically by modifying the GDS input text file.  This component appears as follows, where four GDS variables are designated for replacement using syntax that targets the specific locations of the text file.  Four port variables are used in this example, and the parameters are used to define the replacement values in the Process Map model’s Case Setup.

The second process is a Python script that executes GDS_GTS.exe to perform the GDS calculations, generate the gerotor profiles, and generate .stp CAD files.  It also performs additional tasks to check for GDS errors.

The third process takes a GEM3D (.gem) gerotor model, which is preconfigured to point to the .stp CAD files that GDS generates, and exports or discretizes it as a 1D GT model file.  A screenshot of a GEM3D gerotor model is shown here.

The GT model exported from GEM3D happens to have a few missing inputs that need to be filled, so the fourth process is a Python script that utilizes the GT Python API to automatically fill those missing inputs.  A preview of the Python script that fills some Case Setup parameter values is shown below.

Finally, the fifth process executes the simulation of the GT-SUITE gerotor model.  The key results of the workflow are output variables (RLTs) from this GT simulation, such as mass flow rate, power consumption, and pressure wave amplitude.  The entire workflow takes about 90 seconds to execute.

With the Process Map model configured, the optimizer can be enabled.  This example focused on varying the four port variables previously mentioned.  The optimization objectives were to simultaneously minimize the pressure wave amplitude and minimize the power consumption.  A multi-objective Pareto approach was chosen to achieve these goals.  The optimization search algorithm was a genetic algorithm, specifically NSGAIII.  The following screenshots show a couple aspects of the optimization setup.

The main result of the optimization is a Pareto plot which puts the two objectives on the two axes.  The red points are non-optimal points, while the blue points are Pareto optimal.  The Pareto points are considered to be equally optimal and represent the trade-off between achieving the two objectives; if lower pressure amplitude is desired, then an increase in power consumption must be accepted.  The design engineer therefore must use additional criteria to choose a final design from among the available Pareto points.

Gamma Technologies is committed to continued research, testing, and improvement of its optimization and data analysis capabilities to provide its users with increased confidence in using these tools for their own projects.  For any questions, support, or further discussion, please reach out to us at [email protected].

Written by Ryan Dudgeon

Piston Group Dynamics: An Approach for Friction Reduction Simulation

Stricter demands on emission norms, fuel economy and performance require internal combustion engines to be optimized with respect to their frictional losses and wear. Different investigations show that the piston group, consisting of piston skirt and rings, cylinder liner and conrod bearings, contributes a major part to the overall frictional losses. Although the ICE exists for over a century now and many improvements have been made, its efficiency can still be increased and simulation tools like GT-SUITE have become a major contributor to achieve these targets. This blog illustrates the workflow how a predictive friction model for the piston group assembly can be set up in detail using GT-SUITE and how the results correlate with measurements. The built-in design optimizer and DOE tool (design of experiments) can be used to minimize frictional losses, while ensuring lubrication of all involved parts.

The outlined approach enables not only solving common problems for conventional vehicles like improving warmup strategies to stay within emission limits and reducing fuel and oil consumption. But especially also rather new effects introduced by the increasing amount of electrified powertrains are captured. Just to name a few, questions like how do measures like stop-start and pure electric drive over longer distances impact engine friction, can be answered.

Model Setup

The GT-SUITE software package offers a CAD driven process to obtain a model based on the 3D-CAD geometry of the system. All geometric and mass properties will be automatically transferred to the model after assigning the corresponding material (Fig. 1).

Based on this exported standard Cranktrain model, that can be used for various investigations from rigid balancing up to torsional damper modeling, the focus in the next sections will be put on some friction relevant parts and how GT-SUITE takes into account their properties:

• Piston Ring definition
• Piston Skirt profile and Cylinder Wall deformation
• Lubricant properties and surface roughness
• Cylinder Pressure (Profile): Depending on the modeled condition (fired or motored)

The piston ring objects are used to represent each of the individual rings in the ring pack. Detailed modeling involves calculation of ring radial and twist motions under the influence of ring tension, land pressure and countered by hydrodynamic and asperity forces at the ring running face. The piston rings can be incorporated into a more comprehensive blowby model with GT-POWER to evaluate sealing effectiveness and crankcase ventilation. In the context of predicting friction, these physics are simplified and instead the cylinder pressure is applied as the boundary condition for the compression ring groove and is scaled and applied to the scraper ring using our suggested values. This level of model fidelity can accurately predict the friction physics and its effect on the Cranktrain torque.  The shape of the piston ring can be represented by various geometric approaches. These are shown in Fig. 2 with symmetric profiles for the top (cylinder side) and bottom (crankcase side) section.

In case the actual ring shape differs from the ones shown above, GT offers full flexibility in allowing a user defined profile. The necessary inputs will be concluded by specifying material and mass properties as well as the surface texture and roughness.

Another main contributor to the friction is the piston skirt to cylinder wall interface. In order to consider the piston secondary motion (lateral motion and tilting effects), the skirt profile will be described in terms of axial and ovality profiles (Fig. 3). Also thermal deformation can be considered.

 

The other side of the interface is determined by the cylinder wall. The calculated clearances to allow ideal piston motion inside the cylinder can be considered as a function of circumferential angle and axial position. Furthermore, the deformed shape of the bore resulting from thermal expansion and mechanical bolt clamping loads can be included (Fig. 3). This information, together with the surface roughness, are used to determine the ring face and skirt oil film viscosity and ring-bore conformance, both of which affect oil film and friction calculations.

This brings us to the Lubricant that needs to be defined for this calculation. GT-SUITE offers a wide range of different oils available in the standard library that ships with the installation. If the user does not find a specific lubricant, it’s easy to define it as a new reference object in the model. The tribology models in GT-SUITE consider viscosity as a function of temperature, pressure, and shear rate to properly characterize the wide variety of oil blends used in industry.

Oil film temperature is calculated by averaging the piston skirt temperature (assumed to be uniform), and a bore temperature profile as a function of axial position.

Non-Newtonian shear thinning can be modelled by a variety of Carreau-like methods, all of which follow the Power Law.  After providing GT-SUITE with viscosity data as a function of temperature and shear strain rate, GT-SUITE will fit high-shear viscosity , characteristic time , and power law exponents m/p.  The former two are physically-based functions of temperature.

Pressure dependence can be defined explicitly via viscosity vs pressure/temperature maps, or use of Barus or Roelands exponents.

At runtime, thinning and pressure effects are applied on-the-fly using the average shear rate and film pressure.  Averaging is performed using a geometric mean for each pad, and lookups are performed at each timestep.

Shown below are classical Stribeck curves for the piston group, shown for 3 oil weights in a typical cranking scenario – adiabatic cylinder, no firing.  In general, increasing viscosity allows the surfaces to escape asperity load (transition from mixed to hydrodynamic lubrication) more easily, but carries a penalty of increased hydrodynamic shear friction.

Since the surface finish is another important influencing factor on the oil film extension and therefore on the friction behavior, the user can choose from different ways to define the asperity mesh. Next to pre-defined surfaces in the GT library and the possibility to enter measured profilometer data, that GT-SUITE uses to extract the corresponding parameters to characterize the surface, a new feature also allows the possibility to investigate different patterns and investigate their influence on the oil film extension. A demonstration of such a pattern for the piston skirt axial profile can be seen in Fig. 6.

Last, but not least, the cylinder pressure curves should be defined for an accurate prediction. The common approach is to either use measured profiles or generate these using an engine performance model (integration of GT-POWER model with predictive friction model).

 

Results

The standard procedure to perform this simulation is to run multiple steady-state simulations for the whole engine operating speed range, increasing the engine speed from idle in small increments to maximum speed. The runtime for these models usually is in a range of minutes, which makes them attractive to be used in large DOE’s and/or optimizations.

GT-SUITE’s post-processing tool GT-POST allows to analyze and customize the simulation results in every way. Summarizing plots, like the stacked plot below, can be visualized as well as individual component friction losses. In Fig. 5, the contribution of individual combine to provide the overall friction for the entire engine speed range and is compared to measured strip down test data. The contribution of the piston-cylinder (ring and skirt) is dominating for most operational points and emphasizes the importance of investigating this interface in more detail.

Fig. 5 shows the friction force for a top ring at different engine speeds and with different cylinder pressures. It can be seen that the GT solution is capable of following the measured floating liner forces in a quite accurate manner. Beside these results, the detailed motion of the piston ring as well as the contact behavior to the cylinder side (hydrodynamic and asperity) can be investigated and further improved, if necessary.

The other major contributor to the overall friction, the piston skirt to cylinder interface power loss, is shown for one engine cycle and a specific steady-state condition (fixed engine speed) in Fig. 6. For this specific layout and operating condition, there is no asperity contact in contact surface. That means that all forces in lateral direction are carried by the oil film which would ensure a sufficient lubricated contact here. Furthermore, the friction power is higher during upstroke than during the downstrokes. The reason can be the piston pin offset in order to abet the downstroke secondary motion behavior that usually causes the higher friction forces.

Finally, in addition to 2D line plots, there are also several results that can be visualized in 2D and 3D plots or even in animations. Fig. 8 shows one of these animations for the piston skirt to cylinder interface and color contours the fluid film pressure according to its magnitude. This unwrapped view and animation gives the user the possibility to detect any uncommon behavior in the important oil film extension and can give ideas for areas where the design might need to get improved.

Conclusion and Outlook

GT-SUITE offers a complete solution to model the frictional behavior of internal combustion engines. The special features are that the solution is:

• Predictive: Underlaying models (e.g. oil film models, Stribeck curve etc.) in combination with detailed input data allow to provide fast and accurate results for day-to-day use in design trade-off and optimization studies.
• Validated: The approach and methodology has been validated with several industrial partners, which has been implemented by the GT team of development and application specialists.
• Integrated: The integration of different sub-systems (e.g. cranktrain, valvetrain, timing drive etc.) and different physical domains (e.g. engine performance model, lubrication circuit etc.) allows to capture interacting effects on the overall friction studies.

Considering this complete solution in the well-known and established, user friendly environment of GT-SUITE, allows the development engineers to meet their targets with simulation, in addition to test engines on test benches.

Preview: The above shown model can be enhanced by compliant piston-liner model to capture flexible effects based on the interacting forces. The same setup can serve as a starting point to investigate oil consumption mechanism like oil evaporation, blowby/blowback and oil throw-off. More information will follow in one of the next blogs. Stay tuned.

Written by Marcel Schmädicke

Virtual Calibration of xEV Thermal Management Systems

Reducing the emission of the conventional vehicles by means of electrification of the powertrain brings new trends and new challenges for automotive engineers, especially in the field of thermal management and thermal component security. Thermal management systems for xEVs show a high degree of topological complexity, integration of new functions, more interaction between the different circuits, new thermal management strategies, and high level of complexity of the controls algorithms. The aim is to validate these new technologies early and without the presence of hardware, lowering the test costs and shortening development timeframes. Because of these requirements to design controls systems without prototype hardware, the focus is shifting to virtual testing (XiL) of vehicle systems: including Hardware in the Loop (HiL) and Software in the Loop (Sil) simulations.

XiL simulations tend to underline the software changes which may lead to the final market product. The key to keep pace with the changing requirements is efficient and simple workflow: minimization of modeling tools that are time intensive to interface, and a flexibility of a simulation model that allows for versatile model utilization of different stakeholders in an organization.  Ideally the same model would be used for detailed hydraulics, transient warmup component sizing, and controls’ development for HiL and SiL.

With GT-POWER-xRT, Gamma Technologies is offering a “settled in market” engine modeling tool, capable of bringing physical, predictive performance and combustion simulation on a HiL system. Similar opportunities exist for models for thermal management system or thermal component models. Delivering fast running thermal management models increases development efficiency and allows to explore new thermal management strategies.

With the increase demand for XiL cooling simulations, the ultimate objective is to be able to run the GT-SUITE cooling models on dedicated HiL machines.

GT-SUITE is capable to run fast, complex, and multi-physical thermal management models. The example that will be discussed is a Through The Road (TTR) hybrid vehicle with its thermal management system. The TTR powertrain has an ICE that drives one axle and an electric motor that drives the other. The plant includes a detailed thermal management system with:

• 3DFE thermal representation of the engine
• Detailed battery pack module
• Quasi 3D Underhood model
• Parametric thermal representation of the electric motor
• Two-Phase system for battery cooling and passenger comfort
• Cabin model
• Detailed piping network for low and high temperature cooling circuits

Such a model is usually assembled by components and systems from several contributors, who may have different expectations on model accuracy and runtime. If the individual components and systems are not optimized for fast runtime, the resulting model will likely run slower than real time. In the described state, the example TTR model has a real time factor of 8:  meaning that it ran 8 times slower than real time. In order to make such a model accessible for stakeholders in SiL and HiL activities, GT-SUITE offers a set of comprehensive tools to guide through model changes while maintaining model accuracy.

For circuit setup, GT-SUITE is equipped with the “Circuit Definition” wizard to help identify the different numerical circuits in a system and set optimal and therefore fast numerical settings. In the TTR example the flow circuits are divided automatically between engine cooling, engine lubrication, battery cooling, e-motor cooling, underhood air, cabin air and the refrigerant. Through analysis of the model circuits GT-SUITE will select appropriate settings for fast model execution automatically.

Complex thermal management systems also contain a large number of flow volumes. The “Combine Flow Volume Wizard” is another tool within GT-SUITE that allows the user to reduce the total number of flow volumes for faster runtime. The wizard is a guided tool which in addition to automatically merging flow volumes also auto-calibrates the pressure drop of those simplified flow branch.  This automatic calibration maintains high result accuracy while decreasing the model runtime.

GT-SUITE also comes with a comprehensive tool for Design of Experiments. The user can perform any variation of the model inputs for the purpose of predicting the model outputs by means of a meta/surrogate model. In addition, the guided workflows as well as the visual and interactive plots facilitate the task and increase the work efficiency.

Another very useful tool for thermal management XiL modeling is GT-SUITE Integrated Optimizer which allows the user to automatically calibrate the models without any user interaction or guidance. The tool can also optimize the model to automatically achieve certain targets in Pareto-style optimizations, for example minimizing the warm-up time or maximizing the driving range.

 

When creating a thermal component model in GT-SUITE, e.g., of battery, e-machine or inverter, users typically capitalize on the GT-SUITE unique 1D-3D synergetic approach for fast runtimes with high accuracy. This approach usually results in a 1D flow network coupled to a full 3D-FEM thermal structure model which can be computationally expensive. To allow SiL and HiL stakeholders to efficiently work with those models, GT-SUITE allows changing the modeling approach from a 3D-FEM to a lumped thermal mass approach by the click of a button. The information needed to characterize a lumped thermal mass, such as distance to mass center and heat transfer areas, is extracted automatically from the 3D FE. With this new approach, the user does not have to maintain different models for component, SiL and HiL simulation.

Throughout the described stages, GT-SUITE’s FRM Converter offers a convenient way to organize files and view/compare results.

By using these GT-SUITE tools, we have derived, in a meaningful way, a fast-running simplified model from the previous detailed TTR example. The derived model has a real time factor of 0.7 while still respecting the physics of the model. Throughout the process, the fast-running model shows a high result accuracy when compared to the detailed model, as demonstrated in the following plots of the coolant, the battery, and the cabin temperature.

Because the physics of the system are maintained, the fast-running model keeps the predictability of the detailed physical model. For many late design changes during the project, such as scaling a heat exchanger or substituting the pump, fan, or valves, the derived fast-running model can predict the right behavior. To demonstrate this the HT radiator is scaled down in the detailed and in the fast-running TTR plant model. This scaled down heat exchanger will affect not only the heat transfer rate to the coolant, but also the air distribution in the underhood model, the power consumption of the pump and other important system parameters. The following plots prove that the simplified model keeps the high predictability level characteristic thanks to physics-based model optimization. The scaled down heat exchanger succeeded to predict and capture the same behavior of the heat transfer rate, the coolant temperature and the SOC of the battery in both models.

Finally, GT-SUITE’s flexibility allows to partition a full model into parallel sub-models by means of FMI, thereby allowing to utilize parallel cores on a HiL machine to further speed up model execution or run model with even higher physical modeling depth.

Utilizing GT-SUITE’s XiL tools for thermal system and component modeling enables efficient, accurate and convenient modeling including HiL applications. This allows physically descriptive and predictive models to be used throughout the engineering program. The following graph shows the results of the temperature of the engine, battery, and the cabin of the HiL capable TTR model over a WLTC cycle. At the end, the TTR detailed model runtime was reduced by 96% leading to HiL capable model run with a real time factor of 0.3.

In summary, GT-SUITE offers different ways to help the user transform their cooling model into a Real Time capable model. Gamma Technologies is committed to continue to develop new tools and improve its solution to provide the users the confidence to use the tool for their current projects and extend it to new usage in the future. For any questions or support related to runtime, please contact us at [email protected].

Written by Hanna Sara

Simulating Battery Thermal Runaway Propagation with GT-SUITE

Learn how to use a model to evaluate battery pack safety during thermal runaway events

Designers of battery packs are tasked with a very challenging problem: to package a set of cells as tightly as possible and minimize the amount of non-cell weight in the battery while maintaining proper temperature levels of cells, protecting against premature cell degradation, and ensuring safe operation.  The last item on the list is, of course, the most important: ensuring that the battery pack is safe under any circumstance.

The most common challenge to ensuring battery safety is thermal runaway.  Thermal runaway is a phenomenon that occasionally occurs in Lithium-ion (Li-ion) cells when extreme temperatures are reached.  During thermal runaway, undesired exothermic side reactions heat up the cell, and as the cell heats up, the rate at which the undesired reactions occur accelerates, eventually causing a catastrophic loop of events that concludes with a destroyed Li-ion cell and a lot of heat released.  This loop of events is summarized in the image below.

There are many potential causes of thermal runaway.  For example, if a cell is heated to extreme temperatures, thermal runaway can occur.  If a cell is pierced by a nail or crushed, this can cause an internal short which eventually leads to thermal runaway.  Other times, thermal runaway can occur for seemingly no reason at all – in these cases it is often manufacturing issues or even internal dendrite growth that lead to internal shorts inside the Li-ion cell.

With all these potential causes for thermal runaway, as a pack designer, how are you supposed to protect your cells from entering thermal runaway?  The unfortunate answer: you can’t.

In fact, this is the wrong question for a pack designer to be asking.  Because thermal runaway can occur for so many different reasons, and occasionally for no apparent reason, pack designers must assume that at some point a cell in a battery pack will enter thermal runaway.  The correct question to be asking is, “Is my pack designed well enough to withstand one cell entering thermal runaway without starting a chain reaction of neighboring cells entering thermal runaway?”

Thermal Runaway Propagation

Thermal Runaway Propagation is the key phenomenon to consider when designing a safe battery pack, this refers to the event of a single cell entering thermal runaway, releasing a large quantity of heat, and heating neighboring cells to the point of thermal runaway, essentially starting a chain reaction in which all cells in a battery pack are eventually destroyed.

There are various levels of success for this type of thermal runaway propagation scenario.  There are the intuitive “pass” or “fail” results where a “pass” would mean that after a cell enters thermal runaway, it does not cause a chain reaction and a “fail” would mean that after a cell enters thermal runaway, it does cause a chain reaction.  There is a less intuitive middle ground in these scenarios, too.  For instance, maybe a chain reaction is set off, but the time delay between the first cell entering thermal runaway and the entire battery pack being destroyed is a long period of time, this may also be a “passing” result, depending on the application.  If a cell is sensed to have entered thermal runaway while a vehicle is at highway speeds, does a family have enough time to stop and safely exit the vehicle before a fast-moving chain reaction is set off?  If a cell enters thermal runaway during an EVTOL flight, is a pilot able to land before the chain reaction becomes unstable?

Without Simulation

Testing the design of a battery pack against thermal runaway propagation is an expensive and dangerous endeavor.  First, expensive prototype versions of battery packs must be assembled, then a single cell is selected (either at random or with engineering discretion to determine which would be most likely to cause the undesired chain reaction), and finally thermal runaway is intentionally induced on the selected cell (either with a nail or by heating it to extreme temperatures).  After that, it is up to the design of the pack to determine whether or not neighboring cells enter thermal runaway, and if they do, how fast.

This experimental setup has two major downsides.  First, battery packs are expensive, and prototype versions of battery packs are even more expensive.  To build these and intentionally destroy them can result in a high cost for battery safety testing.  Second, this physical test is often done very late in the development cycle for the battery-powered product (e.g battery electric vehicle, EVTOL, electric bicycle).  If a battery pack fails this test, it can be a major setback for the release schedule of the product, which can be detrimental to businesses.

With Simulation

Using simulation to run virtual thermal runaway propagation tests for Li-ion battery packs is a great way to avoid the costs and risks associated with experimental testing.  In addition to that, single cells do not need to be picked out at random.  Instead, multiple tests can be setup testing the “what if” scenario for every cell in a battery pack.

GT-SUITE is the ideal platform to run virtual thermal runaway propagation tests.

Modeling Thermal Runaway Propagation in GT-SUITE

In a paper published with NASA, who has extensive experimental data on thermal runaway of Li-ion cells, GT-SUITE was used to model the propagation effect of thermal runaway in a small battery module.  The thermal runaway propagation model was built by converting CAD geometry and validated with experimental data.

Nominal Electrothermal Model of Battery Module

The study shows a number of test cases, including two of the battery modules during normal operation, which do not have cells entering thermal runaway.  The animation below shows one of these tests, a battery module discharging at a C-rate of 1C.  In the animation below, the blue – red contour animates local temperatures where blue is cool temperatures and red is hot temperatures.  From the animation below, we can see the battery slowly warms up while being discharged at 1C.

 

To take this electrothermal battery model and setup the thermal runaway propagation model, a few extra steps were required.

Cell-Level Experimental Thermal Runaway Tests

NASA has created specialized bomb calorimeters that impose thermal runaway on a single cell through a variety of causes (internal short, nail penetration, excessive heating).  With this type of cell-level testing, NASA was able to measure the amount of energy released during a thermal runaway event.  Some example results from their testing of cylindrical cells are shown below.

Alterations to Battery Model

The nominal battery model that was setup for the previous electrothermal model was upgraded to include a model of thermal runaway.  This included the following changes:

• The Trigger: If any jelly roll temperature rose above 180°C, the cell would immediately enter thermal runaway
• The Heat Release: Once a cell entered thermal runaway, the cell would release energy in the form of heat (in this case 70 kJ)
  • 40% of the heat released would be absorbed by the jelly roll in 1.5 seconds
  • 60% of the heat released would be released as ejecta in 1.5 seconds
• The Electrical Disconnection: Once a cell entered thermal runaway, it would no longer participate in the module, which means the neighboring cells, which are placed in parallel, would have more current flowing through them.

Module-Level Model of Thermal Runaway Propagation

Once these alterations were made to the battery model, any cell in the module can be selected as the “trigger” cell by applying an external heat until the trigger temperature of 180°C is reached.

In the first study, a cell in the corner of the module was selected to be the trigger cell.  It was artificially heated to its runaway temperature of 180°C and it immediately entered thermal runaway.  The animation below shows the results of the thermal runaway simulation with the corner cell (top of the image) selected as the trigger cell.  Once again, blue cells are relatively cool and red cells are hot.  From viewing the animation, we can see that the corner cell does not cause a chain reaction of neighboring cells entering thermal runaway.

Since no real battery modules were destroyed in this simulation, this simulation can be repeated under different conditions.  The next study conducted was to test how the module behaves when a cell in the center of the module enters thermal runaway.  The image below shows how the module reacts when a cell in the center of the module is the trigger cell for thermal runaway.  Once again, we can see that the thermal runaway event does not propagate to neighboring cells.

The virtual thermal runaway propagation tests shown above both show “passing” results.  The trigger cell self-heats to extremely high temperatures; however, the neighboring cells do not pass the 180°C threshold to enter thermal runaway.

In order to illustrate a “failing” test result, some changes were made to the module to make it more likely to propagate thermal runaway to neighboring cells.  The busbar in the module was included, which increased the amount of heat conducted between neighboring cells.  Additionally, the ratio of self-heat and heat released as ejecta was altered to be 30%-70% instead of the 40%-60% previously mentioned.

With these changes, the following results were observed.  In this case, the trigger cell very quickly causes a chain reaction among neighboring cells and causes a much more catastrophic event than the previous two test cases presented.

Time-to-Results

Because time is one of the most important resources of battery pack designers, one of the key considerations when faced with a modeling challenge such as thermal runaway propagation is the total time that it takes to get results.  The time that it takes to get results is the sum of the time it takes to build a model (“time-to-model”) and the time that it takes the model to run (“time-to-run”).  With GT-SUITE, both time-to-model and time-to-run are minimized.

Time-to-Model

In the examples given above, the CAD geometry was converted into a GT model using GT’s built-in CAD geometry pre-processing tool GEM3D and models were further setup using GT’s integrated simulation environment in roughly half of a day.

Time-to-Run

In the examples given above, the models run roughly 2-4 times faster than real-time on a laptop PC, resulting in a 30-minute simulation taking 7-15 minutes to run.  The finite element structure in this model consisted of 6,000 nodes and 13,000 elements.

This fast time-to run enables users to experiment with some of the uncertainty that comes with battery thermal runaway propagation.  Which cell initiates thermal runaway? How much heat does it release?  How is that heat released?  How much material is ejected from it?  All of these are sources of variability that can be explored with the help of fast-running models (look for a future blog on this specific topic!).  This type of variability analysis would not be possible when using extremely detailed 3D CFD models.

Conclusion

When designing a battery module or a battery pack, the battery’s response to a cell entering thermal runaway needs to be studied to analyze whether or not the cell causes a chain reaction of cells entering thermal runaway, known as thermal runaway propagation.  This can be done experimentally by building prototype modules and packs and imposing thermal runaway on a trigger cell; however, this can be extremely expensive and if the pack fails the test, can be a substantial setback in the development of the battery.

With GT-SUITE, these thermal runaway propagation tests can be done virtually.  This provides a number of advantages, including the large cost advantage and the ability to run any number of hypothetical thermal runaway propagation tests.

If you’d like to learn more or are interested in trying GT-SUITE to virtually test a battery pack for thermal runaway propagation, Contact us!

Written by Joe Wimmer and Jon Harrison

Predicting Lithium-ion Cell Swelling, Strain, and Stress using GT-AutoLion Simulation

Lithium-ion batteries (LIBs), used in most commercial electronics and portable devices, occupy a highly privileged position in the energy storage sector and have emerged as a versatile and efficient option for the electrification of automotive transportation and integration of renewable energies. The global market for LIB technology is projected to be over $90 billion by the year 2025. Therefore, the reliability of LIBs is very crucial in such largescale applications and has a direct impact on the societal economics.

It has become increasingly evident that the next-generation high-energy-density batteries will not be realized without understanding the degradation mechanism from the mechanics perspective. On one side, the repetitive volumetric strain in electrodes, ranging from a few percentages (graphite, layered/spinel/olivine oxides) to a few hundred percentages for the materials of ever-increasing energy density, disrupts the structural stability in batteries and deteriorates the capacity retention over cycles. On the other side, the mechanical stress influences the kinetics of electrochemical processes, such as mass transport, charge transfer, interfacial reactions, and phase transitions, thereby impacting the performance, capacity, and efficiency of batteries. Some battery pack designs also contain cooling fins, thermistors, foam separators, and repeating frame elements to hold the cells, maintain temperature, and manage this volume change.

Successful battery engineering at all levels (cell-level, module-level, and pack-level) requires an understanding of the complex linkages between mechanical and electrochemical phenomena in. The mechano-electrochemical model in GT-AutoLion effectively captures this linkage to allow cell engineers, module engineers, and pack engineers  to accelerate the development of battery technology while decreasing the required testing load and cost.

How does the mechano-electrochemical model work?

The electrochemical processes such as the lithiation and de-lithiation process leads to significant volume change in the active material. This volume change leads to a substantial change in cell performance. Thus, to simulate this change in cell performance, a flexible swelling model capable of predicting cell performance under various conditions is implemented in AutoLion. These models include various mechanical strain mechanisms such as casing constraint, foam packing constraint, and an applied cell pressure constraint. The mechanical constraints applied here are analogous to the conditions that occur during battery testing or regular battery usage. Based on this analogy, the conditions can be broadly classified into three major categories (i) Rigid Wall (zero strain and high stress), (ii) Free Expansion (high strain and zero stress), and (iii) Realistic scenario with mixed constraints (non-zero stress and strain), as shown in the figure below.

How are the stresses, strains, and changes in porosity on each component captured?

To accurately simulate the cell’s mechanical behavior (e.g., the thickness change, pressure generation, etc.), each cell component’s mechanical response properties are incorporated. The porous electrodes’ mechanical properties are defined based on linear elasticity, porous rock mechanics, or measured stress-strain response of an electrode saturated with incompressible electrolyte. In an electrochemical cell system, the anode and cathode layers will contribute from both externally applied pressure and electrode layer expansion/contraction caused by the active material volume change to their overall strain response. The magnitude of the active material’s volume change is related to the active material state-of-lithiation. The total strain is captured from both these components, and the corresponding stresses are calculated through the constitutive relationships in mechanics.

The balance between the change in porosity and the change in dimension/strain is captured using the material balance. The sample result shown below shows the effect of change in porosity and strain for different stiffness casing constraints.

The material balance also accounts for the change in kinetics through the porosity change and, therefore, the cell’s electrochemical performance. A sample result for a graphite anode with an applied cell pressure is shown below, describing the change in strain and porosity.

The AutoLion model allows for a non-ideal lithiation behavior for anode and cathode, which increases the model’s accuracy, showing the importance of accounting for individual active material volume change behavior on cell level predictions.

How are these results useful?

Cell and pack designers currently rely on extensive electrochemical and mechanical testing to appropriately account for the volume change and the developed stresses. This mechano-electrochemical model predicts this volume change, which may reduce the required number of electrochemical and mechanical tests.

This model can help designers estimate cell-level volume change using knowledge of particle-level lithiation-based volume change behavior. The theoretical predictions of individual component strain, capacity balance effects, porosity, and pressure change effects can also be explored using this model. Also, the performance of the cells is highly dependent on the swelling strain evolution as shown in the sample results below.

The resulting understanding from the model may aid in cell design or determining operational parameters to mitigate adverse effects from active material volume change. Additionally, this model may prove useful to consider how mechanical and electrochemical phenomena intertwine as promising new chemistries such as silicon or Li metal are considered.

Written by Ajaykrishna Ramasubramanian and Joe Wimmer

How to Optimize Electric Vehicle (EV) Drivetrains in Less Than 1 Day Using Simulation

Improving Hybrid Electric Vehicle Controls:

The recent proliferation of hybrid electric vehicles has greatly complicated the world of vehicle controls engineers. Multiple energy sources and propulsion systems applied to sophisticated hybrid drivetrains necessitate a much more intricate controls strategy than conventionally powered vehicles.

Determining when to distribute power to the engine, motor(s), or both is no simple task, and the time typically taken to develop these controls strategies reflects that. Even developing controls for simple hybrid vehicle models can take precious time away from the rest of the design process, and cutting corners can lead to sub-optimal fuel economy and vehicle performance results during simulation. Fortunately, GT-SUITE’s embedded tools include two different methods to automatically generate optimized, charge-sustaining hybrid controls strategies on a per drive cycle basis:

• Equivalent Consumption Minimization Strategy (ECMS)
• Dynamic Programming

Using these tools allows for quick evaluation of a hybrid system’s peak capabilities without the hassle of developing and testing multiple controls options.

Model Generation & Evaluation In Minutes Vs. Days:

In Part 1 of this blog series, we employed GT-DRIVE+, Integrated Design Optimizer, and JMAG-Express to properly size and characterize an electric motor for a P4 hybrid system in a compact passenger car. These tools streamlined a traditionally time-consuming design process, with model generation and evaluation taking minutes rather than days. The goal was to select a motor for a P4 hybrid to meet the following requirements:

Metric	Requirement
Acceleration (0-60 mph)	8.5 seconds
Fuel Economy (City/Highway)	50/52 mpg

 

This blog will build upon our previous work, applying two of GT-SUITE’s hybrid controls optimization solutions to evaluate the previously selected motor’s impact on drive cycle fuel economy. Applying these tools within our workflow allows us to evaluate estimated fuel economy under optimized control without spending time developing complex hybrid controls.

Previous evaluation of our example model revealed that our 27.5 kW motor selection met the acceleration and highway fuel economy requirements but could not meet the city fuel economy demand. These tests, however, were performed using a rule-based control strategy that was not necessarily optimized for city or highway driving. Applying ECMS and Dynamic Programming to the city drive cycle should provide a better idea of this configuration’s fuel economy capabilities.

Equivalent Consumption Minimization Strategy (ECMS)

ECMS in GT-SUITE assigns a “fuel consumption” rate to energy pulled from the vehicle’s battery. Calculation of this energy-equivalent rate is influenced by several user-defined parameters including:

• Equivalence Factor – this represents the relationship between battery energy and fuel energy
• Target State of Charge – this sets a target SOC to develop a charge-sustaining strategy
• Penalty Function Exponent – this influences a penalty function that increasingly penalizes battery energy consumption as the battery deviates farther from the target state of charge

For an ECMS run, the user specifies a variety of independent control variables that are altered at every timestep with the goal of minimizing combined ‘fuel’ consumption from both the engine and the battery. For our example, the following variables were selected:

Variable	Values
P4 Motor Torque (27.5 kW motor)	-105 Nm to 105 Nm
Transmission Gear Number	1st to 6th Gear
Vehicle Mode	Hybrid, Electric, or Conventional

 

At every timestep, all combinations of the independent control variable values are considered. Any combinations that can meet the drive cycle power demand while obeying the defined constraints are evaluated to determine total fuel consumption. This calculation is heavily influenced by the battery energy-equivalent rate parameters. For example, if the SOC deviates too far from its target, then a larger penalty will be levied on battery consumption to incentivize a charge-sustaining strategy – this means scenarios where more engine power and less motor power is used may be deemed more favorable at that timestep. The variable combination that locally optimizes fuel consumption is then selected, and the process repeats for the remaining timesteps. The process at each timestep is summarized below:

Applying an ECMS control strategy to our city driving cycle, we will see a significant improvement in fuel economy that meets our initial requirements:

 

	FTP-75 (City) Minimum Fuel Economy Requirement	Reported FTP-75 (City) Fuel Economy
Heuristic Control	50 mpg	42.93 mpg
ECMS Local Optimization	50 mpg	58.30 mpg

 

 

Despite evaluating 612 different control scenarios at every timestep, this ECMS run completed in less than 3 minutes. After completion, we can see that our motor selection will be sufficient to meet the initial fuel economy requirements – all it needed was a better control strategy. However, optimizing locally at each timestep will likely result in slightly sub-optimal performance over the entire drive cycle.

In other words: This is good, but we can do even better.

Dynamic Programming (Global Optimization)

Dynamic Programming will provide an even clearer picture of our example vehicle’s fuel economy capabilities under optimal control. Dynamic Programming uses similar strategies to minimize fuel consumption but seeks to do so in the context of an entire drive cycle. A global cost function is created and minimized using similar parameters to those defined for ECMS. The run begins at the end of the drive cycle and marches backwards in time to the initial state, where the fuel costs for all possible states and controls are calculated and saved. By referencing these saved values, a controls solution is determined by computing the ‘optimal cost-to-go’. This may not necessarily minimize fuel consumption at every timestep but will produce a solution that cumulatively has the lowest fuel consumption from start to finish.

Applying dynamic programming to our city driving cycle, we will see fuel economy further improve to 62.3 mpg:

 

This blog series has demonstrated 5 different GT-SUITE tools that will significantly streamline your design process. In our motor sizing example, this increased efficiency was apparent:

• GT-DRIVE+ instantly generated a P4 HEV vehicle model to use for evaluation – 5 minutes
• Integrated Design Optimizer automatically selected the correct motor size to meet our acceleration requirements – 20 minutes
• JMAG-Express instantly created an efficiency map from our selected motor characteristics – 10 minutes
• Optimization Tools generated controls for our drive cycles to understand motor/vehicle performance under optimal control – 2 hours

One iteration of this design process could conceivably take less than one day. If we are unhappy with the results after evaluating this final design, we can easily iterate through again – tweaking our initial model and motor characteristics and applying all the tools again with relatively little time lost. If you are interested in learning more about any of these tools, feel free to contact us for additional information!

How to Optimize Hybrid Vehicle Design using Simulation

As emissions regulations tighten and an electrified future grows more and more imminent, automotive engineers have been tasked with applying decades of traditional vehicle engineering knowledge to increasingly complex xEV architectures. The good news is that automakers have become very proficient at building conventionally powered vehicles – so much so that they still comprise the basic underpinnings for most electric propulsion architectures. But even implementing hybrid-electric components into an existing conventional vehicle architecture introduces a long list of questions, such as:

• Where in my driveline should I integrate my motor?
• What size battery do I need to meet design requirements?
• And how should I optimally distribute power between the engine and (potentially multiple) motors?

Fortunately, GT-SUITE offers a variety of embedded tools that help answer these questions.

This will be the first blog in a two-part blog series highlighting solutions for hybrid-electric component sizing, assisted electric motor design, power split controls optimization, and much more. Proper use of these tools will significantly aid development and increase efficiency throughout various stages of the design process.

Hybrid Component Integration and Optimization

To demonstrate the power of incorporating these tools into your hybrid vehicle design process, we will walk through a simple example of hybrid component integration and optimization. The goal of the exercise will be to appropriately size and optimize control of an electric motor in a standard compact passenger vehicle.

This process can traditionally be burdensome. Assessing multiple motor configurations often requires repeated manual manipulation of models. Defining motor characteristics typically relies on data from expensive testing, and developing effective hybrid controls strategies is often a time-intensive, trial-by-error process. Fortunately, GT-SUITE’s embedded tools address these problems within one easy workflow. The efficiency of these tools also allows extra time to continually iterate and fine-tune your design.

Requirements:

For this example, we will focus on hybthat are reasonable for a compact hybrid sedan. Selecting a smaller, lower output motor will save costs, so we will seek to minimize motor size while still meeting these requirements.

Metric	Requirement
Acceleration (0-60 mph)	8.5 seconds
Fuel Economy (City/Highway)	50/52 mpg

 

Quickly generate a hybrid vehicle model

GT-DRIVE+ starts with a model generator that allows for easy generation of vehicle systems and quick evaluation between multiple architectures and components. When creating a hybrid vehicle, the user will be presented with several options for vehicle architectures as well a large library of pre-defined engines, transmissions, electric motors, batteries, and drive types.

The components were selected in the model generator to closely match many of the hybrid vehicle offerings currently on the market:

 

Hybrid Configuration	P4
Vehicle	Compact Car
Drive Type	FWD
Battery	Lithium-Ion 247 V 5Ah
Engine	Gasoline Direct Injection, 1.4 L Turbocharged I4
E-machine	To be configured within model
Transmission	6 Speed Automated Manual

 

Now, after just a few simple selections, a full vehicle model is generated – complete with test cases for city/highway driving cycles, and a pre-configured hybrid control strategy. If necessary, the exact same components can also be generated within a P0, P2, or P0/P4 hybrid architecture to compare how motor placement impacts vehicle performance.

Evaluate motor sizing

Next, maximum and minimum motor torque curves can be modulated to determine the minimum acceptable motor output. This can be done by configuring GT’s integrated design optimizer to sweep through one or more parameters to target a specific output. Here, the 8.5 second acceleration performance requirement is targeted. The design optimizer can be setup to modify torque values, run the model, evaluate the outcome, then modify torque values again, rerunning until results converge on the requirement. In this case, 151 possibilities were automatically evaluated in under 10 minutes. Upon completion, the design optimizer outputs several plots that help visualize the evaluation process, along with an updated model containing the final optimized parameter values.

 

After doing so, a motor with the following characteristics was selected to meet the acceleration performance requirement:

Note that while two of the requirements are satisfied, city fuel economy does not meet the 50 mpg requirement. This is not cause for immediate concern. GT-DRIVE+ automatically generates a rule-based hybrid controls strategy that effectively follows standard drive cycles but is not necessarily optimized for city or highway driving. A hybrid control optimization tool should be applied to this model to better understand city/highway fuel consumption. The second blog posting in this series will demonstrate the application of these optimization tools to this example.

 

Generate motor efficiency maps

GT has partnered with JSOL to bring their motor design tool, JMAG-Express, directly into GT-SUITE. The approximated motor characteristics determined in our initial investigation can be input directly into this integrated tool to calculate a complete motor efficiency map, as well as estimate many other fundamental motor characteristics, in only a few minutes.

This efficiency map can be pulled into our initial model to more accurately characterize the efficiency and power demands of a motor this size.

Instantly generating efficiency and loss maps eliminates the need to choose between over-simplifying motor efficiency for convenience, or spending time and money to test motor hardware. Instead, we can quickly calculate efficiency of our 27.5 kW machine, plug it in to our original model, and move on towards applying our hybrid controls optimization tools.

In this blog, we walked through three different GT tools that facilitate the hybrid vehicle design process. These tools assist and accelerate a highly iterative design process where components can be evaluated, optimized, changed, and evaluated again without sacrificing large amounts of time or resources. The next blog entry showcases GT’s hybrid control optimization solutions and how it can be used in the context of the example presented here.

If you would like to learn more about GT’s integration with JMAG-Express, [CLICK HERE] to read an additional blog post on the topic.

 

Exploring and Improving the GT-SUITE Genetic Algorithm

Mathematical optimization is the search for optimal model input parameters (factors) to minimize or maximize one or more of its predicted outputs (responses).  Optimization is a powerful tool to the modeler for two main tasks, both of which can enhance the modeler’s understanding of the relationship between factors and responses, and therefore the model in general.  The first task is model calibration, which is the process of tuning model inputs, whose values have a reasonable degree of uncertainty, to get one or more desired model outputs to align better with measurement data, thereby achieving a more accurate model.  The second task is engineering design, which is the process of finding optimal design parameters for which the design engineer is responsible, for the purpose of improving a real component, product, or system.

To avoid the rote task of simulating every possible combination of factor values within their specified bounds and with an acceptable degree of resolution, an optimizer employs a search algorithm to more efficiently find the optimal solution in as few model evaluations (referred to as design iterations) as possible.

Genetic algorithms are commonly used for optimization problems, as they include stochastic methods to more thoroughly search the design space, which is the multi-dimensional region between the lower and upper bounds of the factors.  Stochastic methods attempt to balance two processes, exploitation and exploration, to further improve upon solutions that are already known while continuing to find new solutions in unexplored areas of the design space.  The genetic algorithm included in GT-SUITE, NSGA-III, was developed by Kalyanmoy Deb and Himanshu Jain [1] and is well-regarded in the optimization community. A genetic algorithm mimics biological evolution by applying mathematical equivalents of selection, cross-over, and mutation to a population of agents over multiple generations.  An agent is a specific combination of factor values, thereby representing one design iteration.  A key genetic algorithm setting is the population size, which, after getting initialized with a set of agents, proceeds to evolve from generation to generation.  The total number of model evaluations or design iterations is the population size multiplied by the number of generations.

The performance of an optimization run generally consists of viewing the change in the response variable plotted against the design iteration number.  To evaluate optimization performance, we introduce the term progress, which is defined as the best response value at any given design iteration.  The performance of an optimization run can be evaluated using a single plotted line that represents the progress.  Because of the stochastic nature of a genetic algorithm, multiple optimizations (referred to as trials) must be run on the same problem using different random seeds to fairly evaluate the progress.  For these studies, 20 trials were run on each model, and the median and maximum progress were calculated and plotted to compare the two algorithms.  The maximum progress is a measure of the worst performance that can be expected.  The plot below is an example of 20 trials that were run for a particular optimization model, along with the median and maximum progress.

Again, the genetic algorithm’s population size is an important setting that influences the performance that can be achieved.  Smaller population sizes generally allow the optimizer to “turn over” and learn from itself faster, given an equal number of total design iterations.  In other words, with a smaller population size, more generations fit within a prescribed number of total design iterations.  As a result, smaller population sizes generally provide faster progress to be made for any given optimization run.  However, if the population size is too small, it might lack sufficient diversity of agents and converge to a local optimum.  This concept is illustrated in the following plot where the median progress is shown for four different population sizes for a given model.  The smaller population sizes achieve faster earlier progress within the first 400 design iterations, but population sizes 10 and 20 converge to local optimums and fail to continue to make progress.  The larger population sizes of 30 and 40 are slower to converge, but continue to make progress.

Gamma Technologies recently improved the genetic algorithm in V2021 by incorporating metamodeling during optimization runs.  Also referred to as a response surface or surrogate model, a metamodel is a mathematical representation of response data that uses factors as input variables.  The known data points are used to train the metamodel for the purpose of predicting response values between the known points.  The improved search algorithm, which is referred to as the Accelerated GA, seamlessly uses metamodels behind-the-scenes to intelligently estimate where the optimal solution might be located.   The following graphic is a basic representation of this concept, where a metamodel (represented by the surface contour) is fit through 9 datapoints.  If the optimizer is trying to find the maximum response, it can quickly determine that the starred location is the estimated maximum by using the metamodel.

More details about this approach are given in a white paper recently published to the Gamma Technologies website.  The paper also provides a comprehensive performance comparison between the standard genetic algorithm and the Accelerated GA using 25 complex optimization test models that were used to develop the modified algorithm.  Finally, the paper provides some helpful background on the genetic algorithm, including an exploration of the relationship between its two main parameters, the population size and number of generations.  The paper can be accessed using this link:

https://www.gtisoft.com/wp-content/uploads/2020/12/Exploring-and-Improving-the-GT-SUITE-Genetic-Algorithm.pdf

A few results of the final comparison are included here.  The plots below show median progress (solid lines) and maximum progress (dashed lines) for the standard genetic algorithm and Accelerated GA for four physics-based models.  For all of these four models, the Accelerated GA not only finds better final solutions, but does so faster and with less variance (as indicated by the maximum progress lines).  Considering the DIPulse-B model for example, the Accelerated GA is often finding better solutions multiple hundreds of design iterations sooner than the standard genetic algorithm, as measured by the horizontal distance between red and blue lines.

In summary, the GT-SUITE genetic algorithm’s exploitation process has been improved by incorporating metamodeling using the optimization data, and these metamodels provide an estimate for where the real optimum might exist.  The resulting Accelerated GA provides better performance than the standard genetic algorithm for almost all 25 of the models tested.  As a result, the modeler can use larger population sizes and fewer generations to increase diversity without substantially increasing the total number of design iterations.  The Accelerated GA should provide the modeler more confidence in finding better optimization solutions in fewer total design iterations.

Gamma Technologies is committed to continued research, testing, and improvement of its optimization and data analysis capabilities to provide its users with increased confidence in using these tools for their own projects.  For any questions, support, or further discussion, please reach out to us at [email protected].

Written by Ryan Dudgeon

References

[1]  K. Deb and H. Jain, “An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints,” in IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, pp. 577-601, Aug. 2014.

Using Design of Experiments and Distributed Computing to Optimize Microgrid Design

Learn how to use GT’s advanced productivity tools to explore a microgrid’s design space.

As mentioned in a previous blog posting, GT-SUITE is a powerful tool for evaluating the economics of a microgrid.  However, in that previous blog post, only one combination of input variables was selected to be analyzed; for instance, the wind generation system was sized to be 105 kW and the solar system was sized to be roughly 90 kW.  One of the main challenges of planning a microgrid is that the design space is very large, and the sizing of every component should be optimized, including the wind turbine system, the solar array, and the battery.  Changing the sizes of these subsystems results in different upfront cost and power generation metrics for microgrids; ultimately, these will develop into different payback periods, returns on investment, and maximum battery backup time for islanding mode.

 

To accurately quantify how the sizing of the subsystems in a microgrid affect the economics of a microgrid, we will use GT’s integrated Design of Experiments (DOE) and Distributed Computing capabilities to quickly explore the design space of the microgrid.

Model Setup

The first step to exploring a design space using GT’s DOE is to define the inputs and responses of the system.  The tables below summarize the system inputs and the system responses.

System Inputs

Input Name	Description
NumberOfWindTurbines	Number of 3 kW Wind Turbines installed in microgrid
SolarPanelArea	Area of solar panels (m^2)
Battery_NSeries	Number of series-connected cells in battery
Battery_NParallel	Number of parallel-connected cells in battery

System Responses

Response Name	Description
Initial_Cost	Initial Cost of microgrid installation (USD)
NetReturn_##Years	Net Savings of microgrid after 10, 20, and 30 years (USD)
Payback_Period	Payback period of microgrid investment (years)
ROI	Return on investment (%) after 30 years
Annualized_ROI	Annualized ROI (%) after 30 years
Islanding_Time	Amount of time (hours) microgrid can operate in islanding mode

 

Next, to properly explore the design space of the microgrid, GT’s DOE tool was used to setup a full factorial of simulations that varied the four system inputs.  To do this, each input requires a minimum, a maximum, and a # of levels (to determine how finely or coarsely to search each system input) to be defined.  The image below shows the settings used for the microgrid deign of experiments.  As shown in the image below, this configuration resulted in 10,368 experiments to be setup.

As mentioned in the previous blog, each 30 year simulation takes rough 90 seconds to complete.  This means that the 10,368 simulations would take over 10 days to complete if run on a single core.  With this in mind, we utilized GT’s ability to distribute this job using a high-performance computing (HPC) cluster and 50 simulations at a time, meaning this DOE could be run in less than 6 hours.

Post-Processing Model

Post-processing and understanding over 10,000 cases of simulation is no easy task; however, with GT’s DOE Post-processor, we are able to setup an easy-to-use and highly visual interface to quickly explore the design space of the microgrid.

In GT’s DOE Post-processor, users create metamodels that are trained by the large number of experiments that are run.  After the metamodels are created, Case predictions are made in the visual interface that is shown below.  This interface allows sliders to quickly adjust the values of the input variables (number of wind turbines, solar panel area, battery sizing) and see how these changes affect the results in plots on the right that are dynamically updated based upon the input values selected.  The response which is plotted is determined by which response is selected in the “Metamodel Tree” on the left side of the screen.

The image above shows a series of “single factor response” plots where the responses are plotted as functions of only changes in a single input variable.  Two factor response plots are also automatically created by GT’s DOE Post-processor.  Examples of these are shown in the image below, which show how the responses vary across two different input variables.

With the plots from the previous two images, we can conclude that as we increase the size of the battery, the annualized ROI of the system decreases This lines up with our expectations because the batteries are expensive and their primary purpose is to provide sufficient amounts of backup power, they’re not installed for profitability.  We can also see that increasing the number of wind turbines and solar panels will increase the annualized ROI, which lines up with our expectations because the wind turbines and solar panels are what will allow a microgrid to save money on the cost of electricity.

In addition to annualized ROI, these intuitive interfaces can be constructed to explore the design space of a micro grid and understand how changes in the design affect other responses like the payback period, net return, initial cost, and islanding time, among many other possible outputs.  For a more interactive demonstration, we’ve created the video below to show how this can be done.

Conclusion

With the microgrid model introduced in a previous blog, GT’s integrated Design of Experiments (DOE), and GT’s Distributed Computing capabilities, GT-SUITE is a powerful tool to explore the design space and optimize the design of any microgrid.  Want to evaluate GT-SUITE to study your microgrid?  Contact us!

Written by Holden Symonds and Joe Wimmer

Using Simulation to Evaluate Microgrid Design

Learn how to use a model to evaluate energy usage and cost of a microgrid.

According to the United States’ Environmental Protection Agency, the generation of electricity accounts for over a quarter of the greenhouse gas emissions in the United States and is the second leading source of such gases, behind only transportation.  It is well known that GT-SUITE from Gamma Technologies plays a leading role supporting automotive and commercial vehicle OEMs to decrease the greenhouse gases that their cars and trucks release, but what is less known are the capabilities that GT-SUITE has to model and help develop cleaner and more efficient electricity infrastructure.

Microgrids are a relatively new technology that communities, campuses, and governments are investigating to modernize and decentralize their electrical infrastructure.  These microgrids combine renewable energy, energy storage, and advanced controls to give communities and campuses the ability to restructure how they generate, store, transmit, and consume electrical energy.

What is a microgrid?

The U.S. department of energy microgrid exchange group defines a microgrid as “a group of interconnected loads and distributed energy resources within clearly defined electrical boundaries that acts as a single controllable entity with respect to the grid. A microgrid can connect and disconnect from the grid to enable it to operate in both grid-connected or island-mode.”

In short, microgrids enable communities to integrate decentralized generation (i.e. renewable energy and backup generators), as well as energy storage in batteries into the larger electrical grid.  Additionally, microgrids integrate advanced controls to enable precise energy management within the community and disconnect from the larger grid and operate in an islanding mode.

Why install a microgrid?

A microgrid’s battery backup and islanding feature enable microgrids to continue to operate during power outages, which has the potential to save lives during natural disasters.

Microgrids can also be a good financial investment. Microgrids generally have a high upfront cost to install renewable energy, controls, and energy storage, but over time, this has the potential to return on its investment with the money that is saved by purchasing less electrical energy.

Why model a microgrid?

Because of the steep upfront costs of microgrids, it is important to understand the expected return on investment and payback period before committing to installing a microgrid.  Because the upfront costs are so high, it is likely that zero prototypes will be built.

Additionally, it is beneficial to study the trade-offs between different design decisions in order to optimize the system (How large should the solar array be?  How many wind turbines should be installed?  How large of a battery should be used?). The optimal design will change for every project, based on the load of the system and the weather. For example, perhaps a business park in Arizona can expect a high load due to more air conditioning usage and may invest more into solar generation than wind because of the lack of cloud coverage.

All these factors mean that simulation is paramount for designers to optimize the various trade-offs associated with their microgrid project.

Modeling a Microgrid:

To demonstrate the capabilities and to evaluate the effectiveness of a microgrid, we built a comprehensive model in GT-SUITE. This model reflects the size and topology of a residential microgrid for a neighborhood of 20 homes.  The model includes renewable energy, a battery, the electrical consumption from the homes, and simplified controls to optimize energy usage. This model is parameterized so weather, load, and cost of electricity data can be customized to fit any application.

 

Each source of generation and the loads were converted to a simple power source/sink and a simple circuit that obeys Kirchhoff’s current law was created. This provides a full picture of the power flowing through the system and allows the cost of ownership of a microgrid to be easily calculated.

The power supplied by the renewable energy sources are based upon the weather data and specifications for specific wind turbine and solar panel models.  The model was setup such that new weather data can easily be brought into the model to calculate how the microgrid would behave in any climate.

In addition to differing weather, each microgrid’s electrical load will be unique as well. The load in the demonstration model is meant to represent a series of residential homes, so we have included a dependency on ambient temperature to increase power usage during times when heating or air conditioning are required. The daily energy usage of a home in the microgrid is defined using a piecewise function that defines three zones: heating, comfort, and cooling.  The comfort zone (when neither heating nor cooling is required) is defined as 55-65 degrees F.  Additionally, we have defined a baseline electrical energy usage for a household to be 20 kWh/day.  The piecewise function for daily power usage as a function of ambient temperature is shown below. This is of course flexible and can be altered to represent the electrical load from any system, like a hospital or college campus.

 

As mentioned earlier, another large benefit of microgrids is the increased control over the loads, generation, and connection to the grid. In the demonstration model, we have included some controls to take advantage of fluctuations in the price of electricity by charging the battery when the hourly price is low and discharging the battery when the price is high. Other control schemes can be tried and tested, allowing users to find new ways to save money and energy within their system.

Because the model is simple, we were able to run it with a timestep size of one hour, enabling simulations to be years long but only take seconds to run.  We setup the model to simulate 30 years of operation, which took less than 90 seconds to complete.

To understand the financial viability of the microgrid over the course of time, this demonstration model calculates financial results, including:

• Upfront cost of the microgrid
• Cost of electricity with and without the microgrid
• Net return of the microgrid
• Return on investment (ROI) of the microgrid
• Annualized ROI of the microgrid

Data Population

For this demonstration model, weather data from this website was used.  This is a paid service that provides historical weather data for locations around the world.  As an evaluation option, this web service provides historical weather data for Basel, Switzerland for free, which was used to build this demonstration model.  The data includes historical temperature, solar radiation, and wind speeds (all shown in the image below), but much more weather data is available on the website.  Please note that the simulation was setup such that day 0 is January 1^st and Day 365 is December 31^st.

In this demonstration model, we decided to use hourly pricing based upon historical data found on the website of Commonweath Edison (“ComEd”) Electricity Company.  ComEd is the local supplier of electricity in the Chicago area, which is the home of Gamma Technologies.

ComEd has given the public the ability to download historical prices of electricity here on their website.  For this demonstration model, the price of electricity during calendar year 2019 was used.  Additionally, to account for taxes and other fees, GT has applied multipliers and shifts onto this data.

Model Results:

In the image below, we have included the power generated by both solar and wind generation and the power consumed by the 20 homes in the microgrid over the course of one year.  The model uses a wind system that is rated at 105 kW and a solar system that is rated at 90 kW.  Clearly, the renewable energy sources are not operating at their maximum powers very frequently due to the highly transient weather data used in this simulation.

In addition to the amount of electrical power generated, stored, and consumed, the financial calculations were done over a 30 year period.  Below is a plot showing the cost comparison of the microgrid that was modeled (red line with a high initial investment) and the cost of electricity for the 20 homes if no microgrid was built (blue line).

In addition to the cost calculation, the return on investment (ROI) was calculated as a percentage, calculating the rate of return on the initial investment of the microgrid.  The payback period in this model was roughly 8.7 years and before that point, the ROI was negative.  Additionally, we calculated the annualized ROI, which asymptotes close to a 4% return on investment after 30 years.

Conclusion:

Using the simulation capability of GT-SUITE, we are able to evaluate the long-term power and aspects of installing a microgrid well before the initial investment for such a project would be made.  The results shown above reflect only a single simulation, but many more simulations can be done to experiment with and optimize the sizing of the wind turbines, solar arrays, and batteries.  Additionally, every microgrid will be different, so the electricity usage patterns, electricity price patters, and weather patterns need to be considered for each individual microgrid.  GT-SUITE is a powerful tool to be able to evaluate the economic viability of any microgrid.  Want to evaluate GT-SUITE to study your microgrid?  Contact us!

For those who already have GT-SUITE installed, we’ve uploaded the demonstration model to our secure downloads page.  To download the file, the username and credentials used to log onto our website are required.

Written by Holden Symonds and Joe Wimmer

Parametric Battery Pack Modeling in GT-SUITE for All Existing Cooling Concepts

Comprehensive System to Component xEV Simulation Using GT-SUITE and JMAG (Part II)

Accurate, Concept Level Electric Motor Design Using Simulation (Part I)

How to evaluate electric vehicle performance and behavior using simulation

A typical task of a vehicle simulation engineer is to evaluate the effect of different technologies or component selections on overall vehicle performance and behavior. One of the main challenges of this task is the lack of accurate data available for components, especially for engines, batteries, and electric motors. This lack of data availability can lead to false assumptions or extrapolations which may lead to inaccurate results. In this first blog of a two-part series, we will introduce a new integration between GT-SUITE and JMAG-Express Online that provides a method for accurate concept-level electric motor design. In the context of vehicle electrification, motors are a key powertrain component. What is required for a motor is not only high performance as a component but also high consistency with the system. This includes, for instance, matching the motor and battery sizes, but also cooling system size and performance as well. Figure 1 below shows an example of how different losses, and therefore cooling requirements, vary throughout the motor operating range. 

High-fidelity efficiency map-based modeling 

Vehicle engineers use either a map-based approach measured by the prototype or lower fidelity motor model-based approach at the system design phase. When using a map-based approach, the engineer commonly needs to wait for the prototype to be ready, or relies on other empirical approaches. Alternatively, using a lower fidelity motor model-based approach causes a lot of rework as the design matures. To eliminate these errors and inefficiencies, GT and JSOL have partnered together and are excited to release new software functionality. With GT-SUITE v2020, GT users can now create a high-fidelity motor model by using the embedded JMAG-Express Online interface. JMAG is a comprehensive software suite for electromechanically design and development. It enables users to make a high-fidelity efficiency map model with less than 1% error compared to measurement. It allows the user to see various kinds of motor characteristics within 1 second by changing motor types, slot combinations, dimensions and other machine parameters.  

Figure 2 shows a high-level overview of the workflow.

The above workflow is accomplished through an integrated interface, shown in Figure 3.

To the GT user, the experience of concept-level motor design is intuitive and seamless, as well as fast. In this embedded interface, the user has flexibility to change machine types, geometry, as well as requirements for torque, power, and maximum speed. It is also possible to add additional constraints on the system, such as voltage and current limitations, as well as geometry constraints such as maximum motor diameter or stack height, air gap, etc. Based upon “rules of thumb” and common motor design principles, JMAG-Express Online will create a motor which meets the requirements, subject to the constraints. The user can refine the design or proceed with the configured motor design. Because of JMAG’s history in the area of motor design, the end user does not need to be an expert in motor design to be effective in exploring different design possibilities.  

Through this embedded workflow, users quickly and efficiently analyze different motor types and create maps for each, such as in Figure 4. 

Because the JMAG-Express Online interface is natively integrated with GT-SUITE, users not only analyze the motor behavior in a standalone environment but integrate the JMAG motor models directly in a complete system-level model, as shown in Figure 5. 

Such a model can be exercised through standard drive cycles, and by reviewing the residency of plots for motor operating points by going through vehicle simulation, it enables users to reflect immediately on the motor specification and run the next simulations, shown in Figure 6. 

By connecting vehicle simulation engineers with parametric and template-driven motor design solutions with JMAG-Express Online, it is now possible to make earlier, and more confident design decisions, or motor selections. The push-button integration allows for design-space studies which more quickly explore all possibilities for the most effective motor solution at the vehicle level. Check out Part 2 of the blog series, where we discuss further integration possibilities between GT and JMAG, which move beyond map-based models into more predictive capabilities. 

Written By: Jon Zeman and Yusaku Suzuki  

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