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

Constrained least - squares parameter estimation for a double layer capacitor

This paper presents an estimation of the parameters for a Double Layer Super Capacitor (DLC) that is modelled with a two-branch circuit. The estimation is achieved using a constrained minimization technique, which is developed off-line and uses a single constraint to write the matrix equation. The model is algebraically manipulated to obtain a matrix equation, and a signal processing system is developed to prepare the signals for the identification algorithms. The proposed method builds on the results obtained using an unconstrained ordinary least-squares (OLS) technique. The method is tested both in simulation and experimentally, using a specially-designed experimental rig. A current ramp input is used to generate the corresponding output voltage and its derivatives. The results obtained from the constrained off-line minimization algorithm are compared with those obtained using a traditional off-line estimation method. The discussion of the results shows that the proposed method outperforms the traditional estimation technique. In summary, this paper contributes to the field of DLC parameter estimation by introducing a new off-line constrained minimization technique. The results obtained from the simulations and experimental rig demonstrate the effectiveness of the proposed method with two of three parameters showing relative errors less than 5%

Properties improvement of poly(o-methoxyaniline) based supercapacitors : experimental and theoretical behaviour study of self-doping effect

The support of this research by FAPESP (2011/10897-2, 2013/07296-2), CsF-PVE (99999.007708/2015-07), CAPES and CNPq is gratefully acknowledged. We also thank the University of Aberdeen for providing computational time on MaxwellPeer reviewedPostprin

Voltage equalisation techniques for high capacitance device modules

Phd ThesisTraditionally, the electrochemical battery has been the prime medium by which electrical energy is stored for future use. Increasingly, the demands of modern systems such as electric vehicles, renewable energy, distributed generation, smart grid and others has stretched the development of new chemistries, materials and assembly techniques for electrochemical batteries. Additionally, some load profiles in these applications demand extremely high dynamic behaviour which is either undeliverable by conventional electrochemical batteries or is undesirably damaging to these technologies. As such, a family of electrochemical storage, known generally as supercapacitors or ultracapacitors, have been developed and implemented for such applications. In recent years advancements in electrochemical technology has led to hybridisation of high capacitance devices. Lithium-ion capacitors that are used in this work are, with their higher cell voltage and modern packaging, expected to be among the next emerging families of state-of-the-art electrical energy storage devices. The relatively low cell voltage of high capacitance cells requires them to be connected in series to attain a system level voltage. During charging and discharging, manufacturing tolerances between the cells results in voltage mismatch across the stack. Mismatched voltages are an inefficient use of the energy storage medium and can lead to dangerous failures in the cells. Several techniques exist to limit the variance in cell voltages of supercapacitors across a series connected stack. These range from simple systems which discharge the cells at higher voltages through resistors to more complex active converter systems which equalise the cell voltages through charge redistribution via a power electronic converter. Whilst the simpler schemes are effective they are very inefficient and as such are not suitable for use in many applications. A number of active converter voltage equalisation schemes have been proposed in literature, however, each of these equalisation schemes exhibit flaws which either makes them less desirable or less effective for a broad range of applications. Therefore, a new equalisation converter topology is proposed which is designed for greater equalisation effectiveness, modularity and size. The proposed equalisation converter differs from previously published equalisation schemes by allowing energy transfer between any pair of cells without the cumbersome multi-winding transformers employed in existing equalisation converters. The new equalisation scheme uses a bi-directional arrangement of MOSFET switches for galvanostatic isolation allowing the converter to be multiplexed to the stack. This arrangement allows the total size of the equalisation scheme to be reduced whilst maintaining performance.EPSRC

Unified model of lithium-ion battery and electrochemical storage system

Nowadays, energy storage systems are of paramount importance in sectors such as renewable energy production and sustainable mobility because of the energy crisis and climate change issues. Although there are various types of energy storage systems, electrochemical devices such as electric double layer capacitors (EDLCs), lithium-ion capacitors (LiCs), and lithium-ion batteries (LiBs) are the most common because of their high efficiency and flexibility. In particular, LiBs are broadly employed in many applications and preferred in the mobility sector, where there is a need for high energy and high power. To ensure good operating conditions for a battery and limit its degradation, it is important to have a precise model of the device. The literature contains numerous equivalent circuit models capable of predicting the electrical behavior of an LiB in the time or frequency domain. In most of them, the battery impedance is in series with a voltage source modeling the open circuit voltage of the battery for simulation in the time domain. This study demonstrated that an extension of a model composed exclusively of passive elements from the literature for EDLCs and LiCs would also be suitable for LiBs, resulting in a unified model for these types of electrochemical storage systems. This model uses the finite space Warburg impedance, which, in addition to the diffusion process of lithium\lithium ions in the electrodes\electrolyte, makes it possible to consider the main capacitance of the battery. Finally, experimental tests were performed to validate the proposed model

The nonlinearities in the galvanostatic charging curves of supercapacitors provide insights into charging mechanisms

Supercapacitors are often charged using constant currents. The capacitance can be determined from the slope of the voltage-time curve if the measured voltage over the supercapacitor increases linearly with time. However, the resulting voltage-time curve is often nonlinear, which may lead one to interpret the capacitance as being either time or voltage dependent. In the current work, systematic experimental studies of the nonlinearity of galvanostatic charging curves as a function of applied current and temperature are undertaken for commercial supercapacitors in the range 1–1000 F. A consistent theory is developed to explain the available data. It is demonstrated that the nonlinearity in the voltage-time curve can be attributed to a constant capacitance in parallel with a resistance, the latter which is inversely proportional to the applied current. The influence of faradaic charge transfer reactions or surface charge reorganization on this parallel resistance is analyzed. The proposed theory is also used to analyze galvanostatic charging data available in the research literature, and the different types of nonlinearities observed provide new insight into the mechanisms occurring during charging of various types of supercapacitors.publishedVersio

Observability of a 2-branch Double-Layer-Capacitor

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