I. Introduction
Wireless power transfer (WPT) has attracted a great deal of attention in recent years, in view of its ability to provide convenience to customers by allowing electrical devices to remain permanently unplugged. WPT has three international standards, namely Qi, PMA, and A4WP [1]. Qi and PMA adopt magnetic induction for WPT and utilize a low frequency range from 100 to 300 kHz, while A4WP selects a magnetic resonance for WPT and uses a higher frequency of 6.78 MHz, which is suitable for mid-range applications. In 2007, MIT researchers established the theory of nonradiating WPT via strongly coupled magnetic resonance and verified its possibility as a mid-range solution experimentally [2]. Thereafter, a number of studies on WPT with multiple resonators were conducted to improve system performances in various aspects [3]–[10]. In a relay WPT, an optimal relay position was investigated to maximize efficiency [3], [4], and it was shown that the use of relay can ensure stability of the efficiency, even in a strongly coupled region [5]. In a multiple-receiver WPT, optimal load conditions for maximizing the overall system efficiency were derived [6], and some effective methods for distributing the required power to receivers, e.g., impedance matching [7] and frequency selectivity [8], were proposed. In addition, the optimal condition was discussed, in which the same power is transferred to multiple loads over various distances [9] and Lee and Chae [10] provided a comparative analysis of an intermediate relay and a receiver in a 3-coil WPT system. Even though some studies have considered a multiple-receiver WPT system [6]–[10], to our best knowledge, there are no research on methods for reducing the system charging time
The system charging time is defined as the time that it takes for all receivers to become fully charged.
for a multiple-receiver array.