## 1 Introduction  
With the emergence of energy harvesting (EH) techniques, sensors can be equipped with EH modules to acquire additional energy from the ambient resources (i.e., solar radiation, wind, vibrations, radio-frequency (RF) power, etc.) Such EH sensors do not break down due to energy shortages as long as the energy consumption is less than the harvested energy, so they can operate perpetually with a desired performance level, which is called energy neutral operation (ENO) [1]. According to the controllability of energy sources, ENO approaches can be classified as ambient energy harvesting (AEH) or wireless power transfer (WPT). AEH is the process of transforming any ambient resource, such as solar radiation or wind, into readily utilizable energy [2]. In AEH, it is difficult to control the amount of energy supplied due to the random nature of the employed energy sources. Thus, by predicting the energy source activity, various adaptive energy management schemes, which control the duty cycles [3], transmission power [4], sampling rates [5], and routing paths [6] of sensor nodes, have been proposed to guarantee ENO. Meanwhile, WPT uses a controllable RF power source, such as a power beacon and hybrid access point (HAP) (While a power beacon only acts as a power transmitter, a HAP acts as both a power transmitter and a communication gateway.) Various radio resources (e.g., time, bandwidth, waveform, antennas, etc.) can be controlled to transfer the RFenergy efficiently while ensuring ENO [7, 8]. Such controllability at the RF power source adds a new dimension to the system optimization, and various optimization problems have been addressed to maximize system performance while ensuring ENO [9, 10]. The potential of WPT has recently begun to emerge in two major applications: wireless powered communication networks (WPCNs) [11] and simultaneous wireless information and power transfer (SWIPT) [12]. A WPCN consists of a dedicated power source (e.g., HAP) and wireless devices (e.g., sensors), where the wireless devices are powered by the RF waves sent from the HAP and then transmit data to the HAP using the harvested energy. On the other hand, SWIPT is a technique that enables both wireless information transmission (WIT) and wireless energy transfer (WET) to be attained simultaneously via the same electromagnetic wave [13]. To this end, one of two mode-switching techniques, namely power splitting (PS) or time switching (TS), is used to balance the ratio of WIT to WET [14]. One of the main challenges in the operation of wireless sensor networks (WSNs) is the limited battery time of the sensor nodes. WSNs typically consist of massive numbers of sensor nodes, so it is costly and impractical to replace their batteries regularly [15]. It is also very serious that sensing errors and link failures often occur when the battery life of a sensor node is almost over. Therefore, extending the lifetimes of sensor nodes while maintaining their sensing performance is a major problem in WSNs [16, 17]. To address this issue, we apply the WPT technology to a WSN. Firstly, we apply the basic WPCN concept to a hierarchical network structure, as many WSN applications use this structure to reduce the total cost of the transmission links [18]. In this wireless powered sensor network (WPSN) with a hierarchical structure, all of the nodes in the cell harvest wireless energy from the HAP, as in a WPCN. However unlike in a WPCN, the sensor nodes are clustered and transmit the sensing data to the cluster head (CH) without directly transmitting the data to the HAP. The CH gathers and aggregates all of the sensing data received from its member nodes and then transmits the aggregated data to the HAP at one time. If all of the sensor nodes perform the same task and thus generate sensing data of the same size, the maximum rate of the sensing data collected in the WSN will be limited by the worst sensor node with low harvesting energy and poor link budget [19, 20].