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Batteries are ubiquitous in modern life, powering everything from our smartphones to electric vehicles and even entire power grids. Understanding the behavior of batteries is crucial for optimizing their performance, extending their lifespan, and developing efficient energy storage solutions.

In this blog, we'll delve into the world of battery modeling using Simulink, a powerful tool in the Simulink ecosystem. Specifically, we'll explore a simple, yet insightful battery model developed in Simulink, which provides a foundation for understanding battery behavior and designing control systems for various applications. Here, we'll break down the components of our battery model, discuss the underlying physics and principles, and demonstrate how to implement it in Simulink.

As we delve deeper into the realm of battery modeling, it's essential to grasp the diverse landscape of battery chemistries employed in electric vehicles (EVs). The choice of battery chemistry profoundly influences the performance, cost, and environmental impact of EVs, making it a critical consideration for manufacturers and researchers alike. From the widely adopted lithium-ion batteries, renowned for their high energy density and longevity, to emerging technologies like solid-state batteries promising enhanced safety and energy efficiency, the array of chemistries available reflects ongoing efforts to push the boundaries of energy storage capabilities.

Among the notable contenders are lithium iron phosphate (LFP) batteries, celebrated for their thermal stability and suitability for high-power applications, and nickel-manganese-cobalt (NMC) batteries, striking a balance between energy density and lifespan.

Fig 1. Battery Chemistry and Energy Density

Battery energy density is paramount for maximizing power output in relation to size. Higher energy density enables compact yet long-lasting batteries, ideal for smartphones and handheld devices. However, heightened energy density also raises safety concerns, particularly with volatile liquid electrolytes in lithium-ion batteries, necessitating safety features at the expense of compactness.

Lithium-ion batteries dominate with energy densities ranging from 260 to 270 Wh/kg, revolutionizing energy consumption and portability. Advances in battery chemistry enable engineers to manipulate electrochemistry, enhancing energy density and power density [1]. At the forefront is the lithium cobalt-oxide battery, offering unparalleled energy density and widely employed in compact devices like smartphones, laptops, and even Electric Vehicles (EVs).

Electric vehicles (EVs) stand at the forefront of battery pack applications, commanding significant research attention owing to their pivotal role in the transition towards sustainable transportation. As society increasingly prioritizes emissions reduction and energy efficiency, EVs emerge as a compelling solution, propelled by advancements in battery technology.

Battery packs serve as the lifeblood of EVs, driving their performance, range, and overall viability. Researchers are vigorously exploring avenues to enhance battery packs for EVs, focusing on improving energy density, reducing charging times, and ensuring long-term reliability.

Moreover, innovations in battery management systems and integration with renewable energy sources hold promise for further enhancing the capabilities of EVs and enabling grid flexibility through vehicle-to-grid (V2G) applications. In essence, the evolution of battery packs for electric vehicles not only drives technological progress but also plays a crucial role in shaping the future of sustainable mobility.

The Li-air battery operates on a chemistry where lithium undergoes oxidation at the anode while oxygen undergoes reduction at the cathode. In the early 2010s, this system was heralded as the "holy grail" of batteries due to its theoretical potential to achieve the highest specific energy, around 3500 Wh/kg based on the formation of lithium peroxide (Li2O2) at the cathode. However, the Li-air battery faces numerous challenges, primarily stemming from side reactions induced by the high oxidative strength of the discharge product Li2O2. These side reactions can lead to the oxidation of organic materials, attack on the electrolyte, and degradation of the cathode's carbonaceous catalyst support. Moreover, the battery's lithium metal component reacts not only with oxygen but also with other ambient air components such as water and carbon dioxide, necessitating filtration to prevent irreversible reactions.

Laboratory experiments typically utilize oxygen mixed with inert gases due to these challenges. Additionally, the battery's practical energy density is limited to around 400–450 Wh/kg due to auxiliary units and the system's limited areal capacity. As such, mitigating risks and addressing technical limitations are essential steps towards realizing the commercial viability of Li-air batteries [3].

Another recent chemistry is Lithium-sulfur (Li-S) option. These batteries offer high theoretical capacity and specific energy, but face challenges such as the need for a significant amount of conductive matrix, typically carbon, to counter sulfur's insulating nature. Additionally, high volumes of electrolyte are required to prevent degradation from polysulfide intermediates. Despite their potential for high gravimetric capacities (~350 Wh/kg), Li-S batteries are primarily considered for airborne or space applications due to their comparably low volumetric capacity. Companies like OXIS Energy and Sion Power have developed prototype systems, but challenges remain, with OXIS Energy facing insolvency and Sion Power shifting focus to lithium metal batteries [3].

A key goal in lithium-ion battery (LIB) development is the integration of a lithium metal anode, which would substantially increase anodic capacity from 372 mAh/g to 3861 mAh/g, potentially boosting battery pack capacity by 30%–40%. To achieve this, the Solid-State Battery (SSB) concept has emerged, offering several advantages such as higher storage capacity, faster charging, and improved safety by replacing liquid electrolytes with polymeric or inorganic alternatives. In current designs, the cathode remains similar to conventional LIBs, while the solid electrolyte acts as a mechanical barrier against dendrite growth.

However, challenges persist in maintaining sufficient ionic conductivity and intimate contact between materials over numerous charge cycles, particularly with thin ceramic layers. While numerous research groups and companies are actively pursuing SSB development, uncertainties remain regarding commercialization timelines and competitiveness against conventional LIBs. Commercialization may not occur before 2025, given the complexities of scaling up from laboratory cells to industrial production and integration into vehicles [3].

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Having covered recent advancements in battery chemistry for electric vehicles (EVs), let's now shift our focus to various battery modeling techniques. These methods play a crucial role in understanding battery behavior and optimizing performance. We'll explore different modeling approaches, from empirical to physics-based simulations, to gain insights into battery systems and drive further innovations in EV technology.


Electrochemical Models:

Physically based models at the material level are considered the most accurate and often serve as reference points for comparison with other models. However, they are complex and demand numerous input parameters for simulations, rendering them unsuitable for real-time applications due to poor computational efficiency.

Empirical models, while simpler, sacrifice some accuracy by relying solely on experimental data and approximations of battery behavior. These models require fewer input parameters and offer higher computational efficiency, making them suitable for real-time predictions of basic parameters like State of Charge (SoC) and State of Health (SoH).

Analytical and equivalent electrical circuit models strike a balance between accuracy and simplicity, with input parameters readily available from manufacturers' datasheets. The equivalent circuit model, capable of capturing I-V characteristics, is particularly useful for integration into broader electrical systems.

Hybrid models, which combine approaches to increase accuracy without significant computational overhead, are designed for specific applications, offering a practical compromise between complexity and precision.

Monitoring the State of Charge (SoC) and State of Health (SoH) of a battery requires a precise and robust mathematical model working in tandem with an accurate estimation strategy. In the context of electric vehicle (EV) applications, SoC and SoH monitoring poses significant challenges due to the multitude of interacting parameters influencing battery performance. Batteries operate in dynamic environments characterized by acceleration and deceleration, influenced by factors such as cell imbalance, self-discharge, aging effects, capacity fade, and temperature variations, which are not always provided by battery manufacturers. While electrochemical model parameters can be measured experimentally through cell examination, this approach is often costly, time-consuming, and may not yield all required parameters.

Analytical Models:

Analytical models, simplified versions of electrochemical models, incorporate nonlinear capacity effects and offer runtime predictions with a reduced set of equations. This simplification makes them user-friendly and applicable in various scenarios. Analytical models provide a higher level of abstraction compared to electrochemical and electrical circuit models, performing well for State of Charge (SOC) tracking and runtime prediction under specific discharge profiles. Peukert's law, the simplest analytical model, depicts the nonlinear relationship between battery runtime and discharge rate but does not consider the recovery effect. Another notable analytical model is the kinetic battery model (KiBaM).

Stochastic Models:

Stochastic models, akin to analytical models, introduce randomness into the discharging and recovery processes. They focus on the recovery effect, modeling battery behavior as a Markov process with probabilities based on electrochemical cell characteristics. These models represent battery states using discrete-time Markov chains, where each state corresponds to the available charge units. Charge units are either consumed or recovered at each time step, determining the battery's behavior until it reaches an empty state or consumes its theoretical capacity.

Electrical circuit-based models employ equivalent electrical circuits, comprising voltage and current sources, capacitors, and resistors, to simulate battery characteristics. Some of these models incorporate State of Charge (SOC) tracking and runtime prediction using sensed currents and/or voltages, enabling co-design and co-simulation with other electrical circuits and systems. While these models do not integrate nonlinear capacity behaviors, they come in handy due to its electric output characteristics and easy implementation to system simulation models.

Given the complexities involved in accurately monitoring battery performance, especially in electric vehicle (EV) applications, where factors like accelerations and decelerations, significantly impact battery behavior, opting for a simplified approach becomes imperative. Hence, we move forward with an electric-circuit model for battery emulation. This model, while not capturing all the nuances of electrochemical and stochastic models, offers a practical compromise by simulating battery characteristics using equivalent electrical circuits. By focusing on electric output characteristics and ease of implementation within system simulation models, the electric-circuit model provides a streamlined solution to understand the electrical behavior of battery packs in EV applications without introducing unnecessary complexities into the system. But why do we require battery emulation in the first place; let’s look into it.


Fig 8. Impedyme’s CHP Cabinet

The Impedyme’s emulation solutions mimic your MATLAB Simulink models that can be used for high power tests, up to a few Mega Watts scale, for bandwidths up to 20 kHz. Simply connect the optical links to our cabinets and deploy your models to begin the testing.

The cabinets have multiple optical links each up to 12.5 giga-bits per second. For simulations with ultra-low step-times, the equipment supports FPGA-based tests, that allows you to have time steps as low as a few nanoseconds. Moreover, the FPGA brings in a better performance for your real-time emulation since the processing speed of an FPGA is much higher than that of a CPU.

Also, for high-speed emulations, the individual FPGAs of the drawers can communicate among them. The testing using Impedyme’s CHP is straightforward as it uses Simulink designs. Our products come with a wide range of pre-designed models, which you can customize the designs according to your needs and requirements.

Furthermore, if we were to emulate both the input and the output side of the power systems, we can have a circulating power flow. Since the power is recirculated, we only must feed in power losses from the grid. By having such a technology can reduce the power requirements of your lab for testing large power systems.

Moreover, during the real-time emulation of your models, our integrated thermal management utilizes an advanced liquid + air cooling technology that ensures that does not require any additional chiller for cooling. Thus, we use Impedyme’s CHP to emulate the developed impedance testing model. 

Now that we have developed a battery model, let us see how the connections are given to kickstart the testing process.

Fig 9. 

Electric Circuit-based Models:


[1] K. S. Song, S. -J. Park and F. -S. Kang, "Internal Parameter Estimation of Lithium-Ion Battery Using AC Ripple With DC Offset Wave in Low and High Frequencies," in IEEE Access, vol. 9, pp. 76083-76096, 2021, doi: 10.1109/ACCESS.2021.3082148.

[2] R. H. Lasseter, Z. Chen and D. Pattabiraman, "Grid-Forming Inverters: A Critical Asset for the Power Grid," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 2, pp. 925-935, June 2020, doi: 10.1109/JESTPE.2019.2959271.

Fig 2. Cross-Section of an EV Battery Pack

Today, most electric vehicles (EVs) rely on lithium-ion batteries, a mature technology also prevalent in laptops and cell phones. Decades of development have driven down costs and improved performance, enabling EVs to rival gas-powered cars in price and travel hundreds of miles on a single charge. These batteries also find use in grid-scale electricity storage to stabilize renewable energy sources like wind and solar. However, there's ongoing research to enhance lithium-ion batteries, focusing on increasing capacity, reducing charging times, and cutting costs for broader adoption in both EVs and grid storage.


Alternatively, sodium-ion batteries offer potential cost savings due to cheaper materials, though their suitability for EVs remains uncertain.

In the stationary storage sector, iron-based batteries are emerging as promising alternatives. Companies like Form Energy and ESS are developing iron-based batteries that could offer cost-effective and efficient energy storage solutions. Form Energy recently announced plans for a $760 million manufacturing facility in Weirton, West Virginia, while ESS has begun manufacturing operations in Wilsonville, Oregon [2]. Additionally, advancements in research have led to innovations such as lithium-sulfur (Li-S) batteries, offering the potential for significantly higher energy densities, and lithium-air batteries, envisaged as breakthroughs in achieving unparalleled energy storage capacities. Understanding the nuances of these battery chemistries is pivotal for designing tailored solutions that meet the diverse needs of EV manufacturers, consumers, and sustainability goals.

Now that we've explored the recent advancements in battery technologies for electric vehicles (EVs), let's delve into two emerging innovations poised to shape the future of automotive electrification.

Fig 3. Lithium-Air Battery Chemistry


Battery emulation serves as a pivotal component in the development and advancement of various technologies, particularly in the domains of electric vehicles (EVs), renewable energy systems, and grid storage solutions. The necessity for battery emulation arises from several key factors.

Firstly, in the context of EVs and renewable energy systems, battery emulation allows for comprehensive testing and validation of battery management systems (BMS) and power electronics. By simulating battery behavior and responses to different operating conditions, developers can assess the performance and reliability of BMS algorithms, charging strategies, and power converters without the need for physical batteries. This not only reduces costs associated with hardware testing but also accelerates the development cycle by enabling rapid prototyping and iteration.

Moreover, battery emulations support the development of advanced control algorithms and energy management strategies for optimizing battery operation and utilization within complex energy systems. By emulating battery responses, developers can fine-tune control algorithms for maximizing energy efficiency, extending battery lifespan, and ensuring safe and reliable operation under dynamic conditions.

Overall, battery emulation plays a vital role in accelerating the innovation and deployment of energy storage solutions, contributing to the transition towards sustainable and electrified transportation, renewable energy integration, and grid stability. By providing a flexible and scalable platform for virtual testing, validation, and optimization of battery systems, emulation technologies pave the way for the realization of efficient, reliable, and environmentally sustainable energy storage solutions in various applications.


Battery models are crucial tools in understanding and optimizing performance in various applications, typically in electric vehicles. One commonly used model is the single RC model, which represents the battery's behavior using a resistor (R) and capacitor (C) in series. However, conventional single RC models often assume fixed internal parameters regardless of the battery's state of charge (SoC).

Fig 4. Simulink Battery Model

To address this limitation, a dynamic single RC battery model for each sub-module of the battery pack has been developed, where internal parameters and open circuit voltage (OCV) are adapted based on the battery's SoC. Moreover, the SoH of the battery is estimated based on the nominal battery voltage and measured counterparts.

Fig 5. Battery pack’s sub-module equivalent Circuit

In the model, the internal parameters of the battery are selected according to the battery's SoC [1]. To accurately capture these dynamics, the model continuously updates the internal parameters based on the changes in SoC, ensuring a more realistic representation of the battery's behavior.

In addition to auto-selection of internal parameters, the battery model also incorporates SoC-dependent OCV behavior. The open circuit voltage of a battery varies with the state of charge. As the SoC is varied, the OCV curve shifts accordingly. By incorporating this SoC-dependent OCV behavior into the model, it can accurately model the battery under different charge and discharge conditions.

Furthermore, the state of charge is calculated based on the Coulombic counting method.

Fig 6. SoC Calculation Model

State of Health (SoH) is determined by comparing the measured voltage of a battery pack to its nominal voltage. The SoH expresses the battery's current condition as a percentage, with values below 100% indicating degradation. This calculation helps assess battery health and anticipate performance changes over time.

Fig 7. SoH Estimator Model


Fig 8. Discharging Mode Dynamics

Fig 9. Charging Mode Dynamics

Fig 10. Current Step Changes


EV Powertrain Emulation :

Fig 11. EV Powertrain

The Figure above depicts the powertrain configuration wherein a high-voltage battery is linked to the motor via the inverter, which provides the necessary voltage for the motor's operation directly from the battery. The developed battery model can be used to emulate a HV Battery pack.  

We allocate the first drawer, that is the top-most drawer, for the battery model and the second drawer for the inverter drive. Likewise, finally, the third drawer is dedicated for the motor model for the EV. The last two, that is the two bottom-most drawers are dedicated for the Active Front end Converters that provide the DC coupling for the emulation. 

The power connections are given on the backside of the cabinets. The DC supply from the active front end drawer is given to the battery model drawer and the battery voltage is provided to the inverter’s input supply. The second drawer emulates the action of an inverter and converts the DC from the battery to 3-phase AC (purple connections), which are subsequently provided to the motor drawer below, and finally the DC coupling is given back to the active front end drawer from the motor to have a circulating power flow.

Fig 12. EV Powertrain Emulation Using Impedyme’s CHP

Grid-Connected Inverter Emulation:

Grid-connected inverters are pivotal components in modern electrical grids, facilitating the efficient transfer and management of power between energy sources, such as batteries, solar panels or wind turbines, and the grid. Real-time emulation and analysis are essential for thoroughly understanding and optimizing the performance of grid-connected inverters.

Fig 13. Typical Grid-Connected Inverter

Impedyme offers advanced solutions in this regard, utilizing Combined Hardware and Power-Hardware-in-the-Loop (CHP) technology. By integrating MATLAB Simulink models with their cutting-edge systems, Impedyme enables seamless testing and evaluation of grid-connected inverters in real-world scenarios. Their CHP solutions provide a secure testing environment, allowing for comprehensive assessments of inverter performance under various conditions and parameters.

Fig 14. Grid-Connected Inverter Emulation Using Impedyme’s CHP

CHP seamlessly integrates hardware-in-the-loop (HIL) and power hardware-in-the-loop (PHIL) capabilities, offering unparalleled accuracy and efficiency in EV development. With CHP, engineers can simulate real-world scenarios with precision, testing EV components and systems under dynamic conditions. From battery management systems to motor controllers, CHP empowers manufacturers to optimize performance, enhance reliability, and accelerate time-to-market for their EVs. Its modular design ensures flexibility to adapt to evolving testing needs, while its intuitive Simulink interface streamlines the testing.

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