Electro-thermal modelling of a supercapacitor and experimental validation
Introduction
Electricity is a widely-used form of energy which offers considerable advantages compared to other energy vectors, being easy to convert into other forms of energy and simple to transport [1]. However, its major disadvantage is that it is difficult to store [2], [3], [4]. Whilst a broad spectrum of electricity storage technologies are available, the most appropriate one will depend on the application in question [5], [6], [7], [8]. For those applications requiring the management of large power peaks with rapid dynamics, those technologies offering the best response include supercapacitors (SCs), flywheels and superconducting magnetic energy storage systems [9], [10], [11]. Applications of this type are increasingly in demand due to the growing integration of renewable energies into the electricity grid, the advancement of electric microgrids based on renewable energies and smart loads, the development of electric vehicles, etc. [12], [13], [14].
Given the fact that SCs store energy as an electric field, with no need to convert it into another type of energy, this is the most suitable technology to cover those applications requiring the management of rapid power variations. The result is high efficiency and reliability with a simple installation and integration process [15], [16], [17]. Supercapacitors are very high surface area activated capacitors that use a molecule-thin layer of electrolyte as the dielectric to separate charge. SCs are formed by two porous electrodes immersed in an electrolyte solution. Both electrodes are separated by an electrically insulating membrane that prevents short circuits. As a result of the extensive contact surface area between the electrode and electrolyte and the small gap between the opposing positive and negative charges, extremely high capacitance values can be obtained [15], [18], [19]. Electronic double layer capacitors (ELDCs) comprising carbon-based electrodes immersed in a liquid electrolyte, are currently the most developed and used SC technology [20], [21], providing a very high power output and longer cycle life than other types of SC, whilst the production process is simpler and the materials used are less expensive. EDLCs are being marketed by companies such as Maxwell Technologies [22] and the Tecate Group [23].
The modelling of the electrical behaviour of SCs has been widely studied in the literature through a number of models used to predict performance. Some are relatively simple [24], [25], [26], [27], whilst others are based on more complex mathematical models requiring longer simulation times [28], [29], [30]. The classical equivalent circuit is one of the most widely used electric models, comprising a capacitor representing the SC capacitance, a series resistor representing the ohmic losses and a parallel resistor representing the SC self-discharge [24]. This is a useful model for quick estimate or sizing purposes. However, if a detailed analysis is required or high frequency behaviour needs to be studied, this model is insufficiently accurate, ignoring important physical phenomena such as ion desolvation on penetration in the electrode pores. Zubieta et al. [31] propose a three branch model, with three parallel-connected branches, each of which is formed by the series connection of a capacitor and a resistor. These branches have different time constants, being the fastest of them of few seconds, the medium of tens of seconds and the slowest time constant of few minutes. Although this model accurately predicts the performance of the SC at low frequencies, it does not model the ion penetration process in the electrode pores or the SC parasitic inductance, both of which are particularly significant during high frequency operation. Mention should also be made of a dynamic SC model developed by Maxwell Technologies Inc. [15], which offers good performance at medium and high frequencies. Its main innovation relates to an RC branch connected in series with the main capacitor, representing the instantaneous response of the SC. Being designed for a high frequency SC operating mode, this model ignores physical phenomena such as ion solvation and desolvation. Devillers et al. [32] published a study comparing the operation of the classical model, branch model and dynamic model in a number of operating environments, concluding that the three models are complementary and that the use of one or the other depends on the specific application. De Levie [28] suggests a complex SC model based on the capacitance of the porous electrodes. The model configuration is based on a distributed capacitance with an electrolyte resistance which is also distributed and which covers the entire depth of each electrode pore. This detailed analysis is suitable in the design process of a SC or in the improvement of its chemical characteristics. However, for simulation purposes, more general models are usually preferred. Torregrossa et al. [33] accurately model the diffusion phenomenon of the supercapacitor residual charge through two current sources. Although this model is extremely accurate for long simulations (2000–4000 s) due to the current sources, it does not model the drop in the SC capacitance observed at high frequencies.
The use of a thermal model to predict the SC temperature has also been widely studied. The SC thermal models can be divided into two broad groups. On the one hand, some studies propose differential equations based on the SC geometry and composition, which are solved either by the finite-differential method [34] or by the finite-element method [35], [36]. With these models the inner temperature distribution of each cell can be predicted, nevertheless, for applications in which there is no need for a precise prediction of temperature, the computational cost of these extremely accurate models is too high. On the other hand, there are comprehensive models where the SC is considered to be a compact, homogeneous body, which are usually represented as equivalent electric circuits. In these models, heat is assumed to be generated uniformly in SC interior. Al Sakka et al. [37] consider a conduction process inside each cell and a convection process between them. In other studies [38] the authors study the reversible heat generation and calculate experimental model parameters. Chiang et al. [39] apply extended Kalman filter to SC SOC and temperature estimation. These comprehensive models produce some manageable linear equations for the simulation, with an acceptable accuracy for most applications.
In this paper we model an EDLC, model BMOD0083 manufactured by Maxwell [22] with a rated capacitance of 83 F and rated voltage of 48 V. The aim is to predict its electric and thermal performance based on the physical and chemical phenomena taking place therein. We are therefore proposing an electric model to provide the SC voltage and a thermal model to determine its operating temperature. Each model is represented by an electrical equivalent circuit, making the models easier to understand and allowing them to be readily incorporated into simulation software. A number of experiments served to validate the electric and thermal models developed for a wide range of operating currents, frequencies and temperatures. These experiments included a real operating environment based on the integration of an SC bank in an electric microgrid located at the Public University of Navarre (UPNa).
Section snippets
Supercapacitor description and experimental setup
The experimental work reported herein was performed at the UPNa Renewable Energies Laboratory which is equipped with several Maxwell BMOD0083 supercapacitors [22]. Each SC comprises 18 series-connected BCAP1500 P270 cells, each having a rated capacitance of 1500 F and a rated voltage of 2.7 V, giving the BMOD0083 supercapacitor a rated capacitance of 83 F and a rated voltage of 48 V. The EDLC cells comprise two activated porous carbon electrodes, separated by a cellulose membrane, and an
Double layer effect and charge distribution
The alignment of charges of opposite polarity at the interface between each electrode and the electrolyte in the supercapacitor cells is known as the double layer effect. The electrode charges are electronic whilst those in the electrolyte are ionic [40]. An increase in the voltage applied to this double layer intensifies the electric field in this zone, thereby increasing the force of attraction, compressing the ionic layer and reducing the effective separation distance between the positive
Thermal model
The thermal energy generated in the SC interior during operation is dissipated into the environment as heat. This energy transfer can be expressed overall through a balance of heating powers [52]:
In the expression above, is the generated heat, in other words the electric power converted into heat. The term is the dissipated heat from the SC into the environment. is the net heat, contributing to the SC heat energy variation. This heating power conditions the SC
Methodology and experimental design to obtain the parameters
This section details the process to obtain the SC electric model (Fig. 6) and thermal model (Fig. 7) parameters implemented in Sections 3 Electric model, 4 Thermal model respectively. To do so, three experiments were conducted: a, b and c. Experiment a consisted in subjecting the SC to charge and discharge steps from 1 V up to 46 V and vice versa, with a value of iSC = ±75 A for 10 h, followed by a further 10 h with the SC idle. In this way, operating temperature T increased during the first
Introduction to the validation of the electro-thermal modelling
The validation of the electro-thermal modelling was based on three experiments in which the SC was made to work in different operating modes. The experiments were programmed on the DSP controlling the electronic charge and the power source. In turn, these experiments were reproduced in MATLAB-Simulink® using the electric model (Fig. 6) and thermal model (Fig. 7) in order to compare the results obtained by simulation with the data measured in the said experiments. The input magnitudes for the
Conclusions
This paper reports on the electro-thermal modelling of a commercial 83 F 48 V BMOD0083 supercapacitor (SC) by Maxwell, based on the physicochemical phenomena taking place in each cell. For this purpose, we have presented an electric model and a thermal model in the form of electrical equivalent circuits in which each significant phenomenon is represented. The configuration of the SC electric model is principally based on the following phenomena: double layer; solvation and desolvation of the
Acknowledgements
We would like to acknowledge the support of the Spanish Ministry of Economy and Competitiveness under grant DPI2010-21671-C02-01 and the Government of Navarre and FEDER funds under project “Microgrids in Navarra: design and implementation”.
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