## 1. Introduction

Information technology has shaped the form of the market in this recent years. The conventional market has been changing progressively in the online market. According to the prediction of Forrester Research cited in a DHL report, online retail in Europe grows by 10% year-on-year. China market will be equal to the combined market of France, Germany, Japan, the United Kingdom, and the United States by 2020 [

1]. Logistic robots represent an emerging trend in online retail or supply chain companies because they can work more efficiently, effectively, and accurately. A logistic robot should be autonomous and able to replace humans in several parts of the process, such as the selection, packing, and delivery of the products. According to a report published by Bloomberg [

2]. Amazon has approximately 30,000 Kiva robots in its warehouses across the globe which will be increasing in the future. A logistic robot should be flexible such that it is not powered by a wired power supply but using a rechargeable energy storage device. The amount of stored energy in a battery is proportional to the size and the weight of the battery. Besides the larger size and heavier weight, to have more stored energy lead to a longer operational hour and charging time. As a case, LocusBots [

3] has an unloaded weight of 36 kg and a maximum payload of 46 kg. Thus, this robot uses its energy approximately 45% of its energy to carry its body, which could be a drawback. However, using a smaller battery also lead to a frequent recharging process which is inconvenient for the user.

Wireless power transfer (WPT) can be a solution to the previously mentioned problems because it is flexible, safe, and free of dust/dirt, and enables in motion charging system [

4,

5,

6]. It should be noted that this benefit can be obtained if the system has been conformed to the existed regulation such IEEE Std C95.1™-2005 for safety level. More comprehensive study about the Electromagnetic Compatibility (EMC) and shielding method for WPT have been published in [

7,

8]. The WPT technology has very wide applications such as for Medical Implants [

9,

10], Unmanned Aerial Vehicles (AUV) [

11,

12], and transportation system like Tram [

13]. The in-motion-charging feature enables the use of a small battery, which is lightweight without causing anxiety about running out of power, and frequent docking. The in-motion charging system in which the charging process is in progress while the receiver is moving is only possible if the Dynamic Wireless Power Transfer (DWPT) is applied. However, DWPT is subjected to the variation of the load and the coupling coefficient. Thus, the charging system should be able to respond robustly to these variations. Some developments in DWPT have been published in the recent years. In [

14,

15] the authors focused on the control method of the DWPT and used the Series-Series (SS) compensation in their studies. The SS compensation has a simple topology, an independent load, and against frequency. However, as discussed in [

16], the independent coupling coefficient frequency only available for symmetric compensator in which the resonant condition of the transmitter and receiver is similar and at a certain value of the load. In another word, the frequency cannot be maintained constant for various coupling coefficient and load. By contrast, another type of compensator that consists an inductor, two capacitors in the transmitter side, and a series connected capacitor in the receiver side which is named the LCC-S or LCC-C compensation topology provides a constant transmitter coil current, and a robust power characteristic against coupling coefficient variation if the design is optimized [

17]. This characteristic makes LCC-S compensation suitable for DWPT.

This study extends the application of the LCC-S compensated DWPT for a logistic robot that requires a smaller and lighter receiver part. The contribution of this includes the study of the LCC-S topology with a segmented lumped coil which is more practical for DWPT compared to a single symmetric coil as studied in [

17]. This proposed topology has less sensitivity to load variation, and more predictable behavior against the mutual coupling variation. The independent load transmitter coils current characteristic also can limit the maximum voltage stress of the compensator capacitor. In addition to the contribution, the presented analysis, practical design guideline may be useful for the implementation of the system in near future. We also expect that this study could encourage the idea of using DWPT for logistic robot application that could be a promising technology in this decade. In the subsequent sections, the analysis, modeling, design, hardware implementation, and testing procedures will be discussed.

## 2. Analysis and Characteristic of LCC-S DWPT

A complete system of a DWPT consists of AC-DC converter, inverter, resonant compensation circuit of the primary and secondary side, transmitter and receiver coil, rectifier, and post-regulator stage if needed. The AC-DC converter is necessary to convert the AC voltage from the utility AC grid to the DWPT system to serve as the power factor corrector (PFC). The inverter provides the square AC voltage to the compensation circuit and again reconverted to DC voltage by the rectifier, and in some cases, it is connected to the post regulator converter.

Figure 1 illustrates two types of transmitter coil configuration. It can be either a long single track, as depictured in

Figure 1a, or a segmented lumped coil, as depictured in

Figure 1b. The utilization of a long single track transmitter has been reported in [

18] under a platform called Roadway Powered Electric Vehicle (RPEV).

This configuration has a more robust coupling coefficient variation, but it suffers from the small coupling and stray magnetic field. In contrary, the segmented lumped coils suffer from the coupling variation, such that system has to be optimized to have the robust power transfer against the coupling coefficient. In this study, a segmented lumped transmitter is selected and optimization is implemented by optimizing the compensator design.

The analysis in this section only focuses on the DC-DC stage. Therefore, the output of AC-DC voltage is represented as the DC input voltage (

V_{in}_{(DC)}).

Figure 2 shows that compensator consists of a series resonant inductor (

L_{pr}), a parallel resonant capacitor (

C_{pp}), a series capacitor in the transmitter (

C_{ps}), and a series capacitor in the receiver side (

C_{ss}). This is why it’s named as the LCC-S or LCC-C DWPT. A segmented three lumped coils can be considered as a transmitter inductor (

L_{p}) as expressed in (1). Mutual inductance (

M) between the transmitter and receiver is expressed in (2), wherein

k is the coupling coefficient. In this section, the analysis of the system is based on the AC analysis by means first harmonic approximation (FHA). We also have presented this analysis for a static WTP system in [

19]. In this method, only the fundamental frequency is considered [

10]. All of the components are assumed ideal for simplicity.

Based on the FHA, the square wave inverter voltage can be expressed as (3) followed by its magnitude r.m.s value in (4). The output AC voltage and equivalent AC load also can be converted from the output DC voltage and DC load as expressed in (5) and (6) respectively. From (4) and (5) we know that the magnitude gain of the DC-DC stage voltage is equal to the magnitude gain of compensator circuit. Therefore, the behavior of the system can be analyzed by analyzing the compensator circuit.

An AC equivalent circuit of the compensator parameter is depicted in

Figure 3a. As expressed in (1), the transmitter inductor can be modeled as a single inductor by assuming that the coupling coefficient between each lumped coil of the transmitter can be ignored. The circulating current in the transmitter induces the magnetic field to the receiver coil and vice versa that generates the induced voltage at both side coils as expressed in (7). Equation (8) expresses the impedance of the receiver side (

Z_{s}) which can be reflected to the transmitter side as

Z_{ref} as shown in (9). By doing so, the circuit can be simplified as illustrated in

Figure 3b.

The current of the primary coil can be obtained by applying Kirchhoff’s law as shown in (10). Since the inverter current (

I_{inv}) is the total current flow through

C_{pp} (

I_{Cpp}) and transmitter (

I_{p}), (10) can be modified become (11). If the switching frequency is equal to

${\omega}_{o}=1/\sqrt{{L}_{pr}{C}_{pp}}$ then (12) is valid and the impedance of the LC resonant can be eliminated. Thus, the relationship between the primary current and the AC input voltage is written in (13). It shows that the primary coil current (

I_{p}) is independent of load variation and can be maintained constant by maintaining the inverter output voltage and the switching frequency constant [

20].

The voltage gain characteristic of the LCC-S WPT is very important to understand how the circuit works and how to control the system. The fundamental resonant angular frequency is selected to be

ω_{o}. The input impedance of DWPT,

Z_{in}, is expressed in (14) and the output to input voltage gain can be derived result in (15). The plots of the gain curve for various loads and mutual inductances in

Figure 4 is based on the

Table 1 parameters. These parameters can be selected freely depends on the desired design. However, in this paper, the selected parameters are same as the used parameters for hardware implementation.

Figure 4 provides the information that the voltage gain of the DWPT system varies with the operation frequency, load, and mutual inductance. In terms of the load variation, this WPT has an independent load voltage gain at the designed frequency for a same mutual inductance. However, the variation of mutual inductance is proportional to the variation of voltage gain. Based on the presented curves, we can also see that the independent load frequency does not change with a different mutual coupling. This characteristic could be used to predict the output voltage if the system works at a fixed frequency. These curves contain information about the capacitive and inductive region which is useful to determine the Zero Voltage Switching (ZVS) and Zero Current Switching (ZCS) region. The ZVS transition frequency range is in the negative slope frequency range and ZCS transition frequency is in the range of positive slope frequency. However, the operation with switching frequency far from the independent load frequency could result in a lower efficiency due to the higher circulating current of the compensation loop.