Modelling and state-of-charge estimation for ultracapacitors in electric vehicles

University of Technology Sydney. Faculty of Engineering and Information Technology.In order to cope with the global challenges like fossil fuel depletion and environmental pollution, electrified vehicles (EVs) have been widely accepted as an enabling option for future ground mobility. In comparison to conventional combustion engine vehicles, EVs have the advantage of high efficiency, environment-friendly operation and excellent control flexibility. There is a proviso here that the electricity used by the EV is from a green source such as hydro, wind or solar. The energy storage system (ESS) is a key ingredient of an EV, and significantly affects its driving performance and cost-effectiveness. The exploration of a vehicular ESS poses a formidable challenge, because of high power/energy demands and unpredictable driving environments. Li-ion batteries represent a main choice for this use, but suffer the drawbacks of low power density and poor recyclability. Recently, ultracapacitors (UCs), also referred to as supercapacitors (SCs) or electric double-layer capacitors (EDLCs), have gained increasing attention in the energy storage community, thanks to their high power density, high efficiency, fast charge, wide temperature window and excellent recyclability. These advantages make UCs a good augmentation to high-energy ESSs (e.g., fuel cells, lithium-ion batteries). This combination represents a hybrid energy storage system (HESS) that can fully leverage the synergistic benefits of each constituent device. To ensure efficient, reliable and safe operations of UC systems, numerous challenges including modelling and characterization, and State-of-Charge (SOC) estimation should be effectually surmounted. In order to meet the above mentioned challenges, the main research presented in this dissertation includes: 1. A special test rig for UC characteristic investigation has been established. A test procedure is proposed to collect comprehensive test data. A plethora of tests have been conducted on this test rig including capacity calibration, experimental impedance investigation under different temperatures and SOC values, and dynamic cycling including pulse tests and driving-cycle-based tests under different temperatures, resulting in a wide-ranging UC database. 2. The impedance characteristics of UCs are experimentally investigated under different temperatures and SOC values. The results show that the impedance is highly sensitive to temperature and SOC; and the temperature effect is more significant. In particular, the coupling effect between the temperature and SOC is illustrated, and the high-efficiency SOC window is highlighted. 3. For UC modelling, three commonly used equivalent circuit models are systematically examined in terms of model accuracy, complexity and robustness in the context of EV applications. A genetic algorithm (GA) is employed to extract the optimal model parameters based on the Hybrid Pulse Power Characterization (HPPC) test data. The performance of these models is then evaluated and compared by measuring the model complexity, accuracy, and robustness against “unseen” data collected in the Dynamic Stress Test (DST) and a self-designed pulse (SDP) test. The validation results show that the dynamic model has the best overall performance for EV applications. 4. Online parameter identification of UC models is researched. The extended Kalman Filter (EKF) is proposed to recursively estimate the model parameters using the DST dataset, in which the dynamic model is used to represent the UC dynamics. The effectiveness and robustness of the proposed method is validated using another driving-cycle-based dataset. 5. A novel robust H-infinity observer is presented to realize UC SOC estimation in real-time. In comparison to the state-of-the-art Kalman filter-based (KF-based) methods, the developed robust scheme can ensure high estimation accuracy without prior knowledge of process and measurement noise statistical properties. More significantly, the proposed H-infinity observer proves to be more robust to modelling uncertainties arising from the change of thermal conditions and/or cell health status. 6. A novel fractional-order model is put forward to emulate the UC dynamics. In contrast to integer-order models, the presented fractional-order model has the merits of better model accuracy and fewer parameters. It consists of a series resistor, a constant-phase-element (CPE), and a Warburg-like element. The model parameters are optimally extracted using GA, based on the time-domain Federal Urban Driving Schedule (FUDS) test data acquired through the established test rig. By means of this fractional-order model, a fractional Kalman filter is synthesized to recursively estimate the UC SOC. Validation results show that the proposed fractional-order modelling and state estimation scheme is accurate and outperforms the current practice based on integral-order techniques. 7. An optimal HESS sizing method using a multi-objective optimization algorithm is presented, in which the primary goal is reducing the ESS cost and weight while prolonging battery life. To this end, a battery state-of-health (SOH) model is incorporated to quantitatively investigate the impact of component sizing on battery life. The wavelet-transform-based power management algorithm is adopted to realize the power coordination between the battery and UC packs. The results provide prudent insights into HESS sizing with different emphases

Accurate Parameters Identification of a Supercapacitor Three-Branch Model

Supercapacitors are becoming increasingly important storage system components. To effectively control their terminal voltage, even in real time, numerous circuit models capable of faithfully simulating their behavior in energy systems and various applications are being explored. The three-branch supercapacitor model appears to be a good compromise between simplicity and accuracy. Typically, this model lacks accuracy in dynamic cycling and long stand-by periods. In this study, a new model identification method based on the state equations of the circuit is described and tested on a 400 F supercapacitor, and the obtained results are validated by measurements. Such an approach, suitably optimized, provides good agreement with the measurements, with discrepancies below 50 mV even in repeated cycles. In the static identification, after 90 minutes of self-discharge, the discrepancy was approximately 5 mV. The study also discusses the sensitivity of the model output to the circuit parameters, which is useful for choosing the appropriate timespan for parameter optimization and introduces variable leakage resistance and a method for its determination. Through this parameter, good agreement with the measurements is observed during the long self-discharging phases. A discrepancy of less than 50 mV between the measured and computed results is observed after one week. The union of the circuit state equations based model and the nonlinear leakage resistance determination allows the three-branch circuit model to achieve a high accuracy both in real-time simulation and in the presence of long stand-by phases

Buck-boost DC-DC converter with fractional control

This paper deals with the fractional modeling of a DC-DC buck-boost converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. Although the modeling and design of the controller is carried out for this particular DC-DC converter, it can be easily extended to other kind of switching converter. In addition, the comparison between integer-order plant/controller and fractional-order plants/controller is carried out. The article also shows that, under the same design conditions, the fractional-order controller has a better performance and behaviour than the classical integer-order controller in both situations, that is, with integer-order plant and fractional-order plant models.Postprint (published version

Various analytical models for supercapacitors: a mathematical study

Supercapacitors (SCs) are used extensively in high-power potential energy applications like renewable energy systems, electric vehicles, power electronics, and many other industrial applications. This is due to SCs containing high-power density and the ability to respond spontaneously with fast charging and discharging demands. Advancements in material and fabrication techniques have induced a scope for research to improve the application of SCs. Many researchers have studied various SC properties and their effects on energy storage and management performance. In this paper, various fractional calculus-based SC models are summarized, with emphasis on analytical studies from derived classical SC models. Study prevails such parameterized resistor- capacitor networks have simplified the representation of electrical behavior of SCs to deal with the complicated internal structure. Fractional calculus has been used to develop SC models with the aim of understanding their complicated structure. Finally, the properties of different SC models utilized by various researchers to understand the behavior of SCs are listed using an equivalent circuit

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15–30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced b attery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted

Advances in Supercapacitor Technology and Applications

Energy storage is a key topic for research, industry, and business, which is gaining increasing interest. Any available energy-storage technology (batteries, fuel cells, flywheels, and so on) can cover a limited part of the power-energy plane and is characterized by some inherent drawback. Supercapacitors (also known as ultracapacitors, electrochemical capacitors, pseudocapacitors, or double-layer capacitors) feature exceptional capacitance values, creating new scenarios and opportunities in both research and industrial applications, partly because the related market is relatively recent. In practice, supercapacitors can offer a trade-off between the high specific energy of batteries and the high specific power of traditional capacitors. Developments in supercapacitor technology and supporting electronics, combined with reductions in costs, may revolutionize everything from large power systems to consumer electronics. The potential benefits of supercapacitors move from the progresses in the technological processes but can be effective by the availability of the proper tools for testing, modeling, diagnosis, sizing, management and technical-economic analyses. This book collects some of the latest developments in the field of supercapacitors, ranging from new materials to practical applications, such as energy storage, uninterruptible power supplies, smart grids, electrical vehicles, advanced transportation and renewable sources