Modeling and characterization of supercapacitors for wireless sensor network applications
Research highlights
▶ An equivalent circuit is developed to model supercapacitors. ▶ The charging, redistribution and self-discharge are characterized. ▶ The model predicts self-discharge better than two- and three-branch models. ▶ The model provides a better tool for supporting self-powered WSN research.
Introduction
Harvesting energy from ambient environment to power wireless sensor networks (WSNs) has been investigated to extend system lifetime [1], [2], [3], [4], [5], [6], [7], [8]. Rechargeable batteries such as NiMH [1] and Li-ion [2] were first selected to serve as primary energy storage devices. While rechargeable batteries have high capacity and low leakage, the cycle life of rechargeable batteries limits the lifetime of wireless sensors [3], [5], [6]. The cycle life of a rechargeable battery is defined as the number of charge–discharge cycles before its capacity falls below 80% of its initial rated capacity. The aging process during the charge–discharge cycles results in a gradual reduction in capacity and an increase in internal resistance over time [9]. By the end of the cycle life, the capacity of a rechargeable battery is reduced by 20% and the useful energy drops to 50% because the higher internal resistance causes premature end of life [3]. Due to limited cycle life, typically ranges from 100 s to 1000 s [10], a wireless sensor node will require battery replacement after 1–2 years [3], [5], [6]. Compared with rechargeable batteries, supercapacitors have a much longer cycle life and higher charge–discharge efficiency in addition to fast charge–discharge characteristic [3], [5], [6], [7], [11], [12]. Some authors have proposed to use supercapacitors alone to store harvested energy [3], [12] or use supercapacitors in combination with rechargeable batteries [5], [6], [7], [11] to achieve “perpetual lifetimes” for wireless sensor networks.
Due to wide range of potential applications of self-powered WSNs, there is considerable research interest in developing efficient power storage systems [11], [12], power management algorithms [13] and communication protocols [14]. A supercapacitor model is an important tool for evaluating these researches using analytical methods or simulation before being demonstrated in practical deployments. Currently adopted supercapacitor models in WSN research are developed from the supercapacitor leakage power profiles [5], [11], [12], [14], [15], which are called the energy recursive equation (ERE) models in this paper. The ERE model assumes the capacitance of a supercapacitor is constant, and uses a long-term leakage power profile to determine leakage at any time [12]. However, the physics of the supercapacitor suggests that its capacitance depends on the terminal voltage across the device and the supercapacitor usually experiences internal charge redistribution during and after charge and discharge cycles [16]. Without capturing these properties, the terminal voltage estimated using the ERE model may have significant deviation from the actual value. The voltage deviation can cause improper decision making in a power management system for self-powered wireless sensors that harvest ambient energy and experience frequent charge–discharge cycles. The improper decision may even lead to failure of a wireless sensor network.
A simple equivalent circuit model for supercapacitors that can accurately model charging, redistribution and self-discharge processes is presented in this paper. A supercapacitor with rated capacitance of tens Farads, typical capacity for WSN applications, is used as an example to illustrate the modeling and characterization process. The performance of the developed model is compared with that of models used in power electronics applications that often target supercapacitors with rated capacitances of kilo-Farads. In addition, the developed model is compared with the ERE model in analyzing a simplified energy storage system for wireless sensors. The results demonstrate that the new model provides a more accurate estimation of terminal voltages across the supercapacitor than the currently used ERE model and hence a better alternative for supporting research on storage system design and power management in WSNs.
Section snippets
Modeling and characterization of supercapacitors
The electrochemical impedance spectroscopy (EIS) is a general approach to measure the complex impedance of energy storage devices such as supercapacitors and batteries [17]. The nature of impedances in various frequency ranges can be determined by analyzing the frequency dependencies of the real part and the imaginary part [18]. Various equivalent circuit models [19], [20] have been developed using the porous electrode theory [21], [22], [23], [24], [25], [26] to interpret the impedance
Modeling supercapacitor self-discharge
A charged supercapacitor is in a state of higher Gibbs energy than in its discharged state [33]. Therefore a thermodynamic “driving force” results in spontaneous decline of Gibbs energy [33]. This decline manifested as decay in supercapacitor voltage is the self-discharge. The rate of self-discharge, which usually diminishes with time, actually determines the shelf-life of supercapacitors [34]. Fig. 3 shows the self-discharge of a 22F supercapacitor. The open circuit voltage of the
Evaluation of the VLR model
The VLR model for a 22F supercapacitor from Cooper Bussmann [37] was developed following the characterization process described in Sections 2 Modeling and characterization of supercapacitors, 3 Modeling supercapacitor self-discharge. The charging, redistribution and self-discharge processes were performed for identifying model parameter values. During the charging and redistribution processes, the initially completely discharged supercapacitor was charged for 610 s using a constant current
Comparison of the VLR and ERE models in self-powered wireless sensor networks
Supercapacitors have been used as alternative energy storage devices for self-powered wireless sensor networks [3], [5], [12] due to their long charge–discharge cycle lives. Accurate supercapacitor models are critical for designing efficient energy storage systems and supporting power management related research. The current commonly used models, ERE models, are based on leakage characteristics of supercapacitors [5], [12]. In this section, performance of the VLR model is compared with that of
Conclusions
An equivalent circuit model of supercapacitors is proposed and the characterization process is illustrated. A variable leakage resistance (VLR) is connected in parallel with two resistor–capacitor branches to model the nonlinearity of supercapacitor self-discharge. The VLR represents both leakage due to diffusion-controlled Faradaic redox reactions, which is a nonlinear process, and internal ohmic leakage. The proposed VLR model increases model accuracy while maintaining simplicity of circuit
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