Theoretical Analysis of Fully Wireless-Power-Transfer Node Networks

Abstract

SUMMARY The performance of a fully wireless-power-transfer (WPT) node network, in which each node transfers (and receives) energy through a wirelesschannelwhenithassufficient(andinsufficient)energyinitsbattery,wastheoreticallyanalyzed.Thelostjobratio(LJR),namely,istheratioof (i)theamountofjobsthatcannotbedoneduetobatteryofanoderunningoutto(ii)theamountofjobsthatshouldbedone,isusedasaperformance metric.Itdescribestheeffectofthebatteryofeachnoderunningoutandhowmuchadditionalenergyisneeded.AlthoughitisknownthatWPT can reduce the probability of the battery running out among a few nodes within a small area, the performance of a fully WPT network has not been clarified. By using stochastic geometry and first-passage-time analysis for a diffusion process, the expected LJR was theoretically derived. Numerical examples demonstrate that the key parameters determining the performance of the network are node density, threshold switching of statuses between “transferring energy” and “receiving energy,” and the parameters of power conversion. They also demonstrate the followings: (1) The mean energy stored in the node battery decreases in the networks because of the loss caused by WPT, and a fully WPT network cannot decrease the probability of the battery running out under the current WPT efficiency. (2) When the saturation value of power conversion increases, a fully WPT network can decrease the probability of the battery running out although the mean energy stored in the node battery still decreases in the networks. This result is explained by the fact that the variance of stored energy in each node battery becomes smaller due to transfer of energy from nodes of sufficient energy to nodes of insufficient energy. key words: