Modeling, Analysis, and Implementation of Series-Series Compensated Inductive Coupled Power Transfer (ICPT) System for an Electric Vehicle

+is paper focuses on the modeling and implementation of an Electric Vehicle (EV) wireless charging system based on inductively coupled power transfer (ICPT) technique where electrical energy can be wirelessly transferred from source to vehicle battery. In fact, the wireless power transfer (WPT) system can solve the fundamental problems of the electric vehicle, which are the short battery life of the EV due to limited battery storage and the user safety by handling high voltage cables. In addition, this paper gives an equivalent electrical circuit of the DC-DC converter for WPT and comprises some basic components, which include the H-bridge inverter, inductive coupling transformer, filter, and rectifier. +e input impedance of ICPT with series-series compensation circuit, their phases, and the power factor are calculated and plotted by using Matlab scripts programming for different air gap values between the transmitter coil and receiver coil. +e simulation results indicate that it is important to operate the system in the resonance state to transfer the maximum real power from the source to the load. A mathematical expression of optimal equivalent load resistance, corresponding to a maximal transmission efficiency of a wireless charging system, was demonstrated in detail. Finally, a prototype of a wireless charging system has been constructed for using two rectangular coils.+e resonant frequency of the designed system with a 500× 200mm transmitter coil and a 200×100mm receiver coil is 10 kHz. By carefully adjusting the circuit parameters, the implementation prototype have been successfully transferred a 100W load power through 10 cm air gap between the coils.


Introduction
Nowadays, the automotive sector is extremely motivated by the development of electric vehicles (EVs) with a projected growth of 6 million by 2020, to reduce air pollution and global warming [1]. In addition, the need to move towards clean energy resources has led to the progressive electrification of vehicles. However, some questions are still pending, in particular, on the EV battery recharge time and user safety by handling high-voltage cables, especially when rain and snow are present [2]. In this context, the wireless power transfer (WPT) system is a promising solution due to its high safety and convenience, which are particularly important for electrical vehicles [3]. e purpose is to transfer energy without cable from the power source (the ground) to the load (onboard battery) [4]. erefore, the WPT technology can fundamentally solve their problems of short battery life of the electrical vehicle due to limited battery storage or high initial cost due to installation of a large number of batteries [5]. In fact, the wireless charging system can be deployed as a stationary system to charge EV in garages or public parking spaces. Additionally, there is another possibility of charging EVs while they are in transit which is called EV dynamic wireless charging. In this paper, the focus is on type of stationary wireless charging to make the charging process safer and less complicated in terms of infrastructure [6]. As users of EV manipulate a lower number of components (two coils), the robustness is another advantage of wireless charge.
Several works have focused on the wireless methods of the EV battery charging system, which treats the different ways that this technology can be used. In fact, the EV wireless charging technologies essentially depend on the frequency of the electromagnetic field and the air gap between the power emitter/receiver (installed in the vehicle). Accordingly, these two parameters determine whether the wireless power transfer will be in a far-field over long distance or a near-field over low and medium distance [7,8]. In a far-field approach, generally labeled the microwave power transfer (MPT) technology, the energy can be wirelessly transferred between transmitting antennas and receiving antennas (also named as rectenna), as same technology of wireless communication [9]. e MPT has the advantage that the capability to transfer power over long distances via radio waves with frequencies ranging from 1 to 30 GHz [7,10]. However, this technology has the disadvantage of increasing the cost and the size of the antenna. Taking into account the typical distance ranges between the transmitter coil and the receiver coil (10-30 cm) for EV application, the near-field category can be divided into two groups: inductive power transfer (IPT) [11] and inductively coupled power transfer (ICPT) [12,13]. In the IPT method, a transmitter coil (in the ground) is excited with an alternating (AC) current, which generates a magnetic field. erefore, when the magnetic field traverses the receiver coil, an induced voltage is created to charge the EV battery, as explained by Faraday's laws. However, this method is limited by the capability of transmission distance, necessity of very low air gap between coils to keep the power transmission more efficient. In most WPT for EV application, the IPT technology is not largely used due to its poor magnetic coupling between the transmitter and the receiver coils (usually 0.05∼0.2), which result in large equivalent leakage inductance [14]. Indeed, as the WPT system would be fixed in a vehicle, it is important to verify that the values of the electromagnetic field around the vehicle are in the safety limits of human exposure, as recommended by the Word Health Organization [15,16].
In addition, the ICPT method is based on the same principle of IPT technology, with the only difference that the compensation capacitors are connected in series (S) or in parallel (P) with coils to create a "strong coupled between transmitter and receiver coils." e ICPT technology has advantages to transfer the maximum real power from the source to the load by compensating the leakage energy stored in the coils [17]. Based on the connection to the coils, four compensation topologies, labeled as series-series (SS), series-parallel (SP), parallel-series (PS), and parallel-parallel (PP), are possible for ICPT technology [13,[18][19][20]. To compensate the total leakage inductance seen by the input circuit, the primary capacitor C p in series is used to get input voltage and current in phase, known as zero-phase-angle (ZPA) approach. At this point, the reactive power will be equal to zero and so the real power transferred to the load is maximum. Most researchers of resonant topologies have selected the SS compensation type as a preferable topology due to several reasons: it assures that the series primary compensation (C p ) is independent on the mutual inductance and the equivalent load resistance, so it is not necessary to retune or change the conception of the system every time that the load changes [13,18]. In particular for high power applications, it is found that the SS topology is more economical than other topologies in terms of required copper mass for fabricating an inductively coupled coil set [12]. In an important work [4], Ibrahim et al. have developed a wireless charging of EV based on ICPT technology with series-series compensation. However, the detailed theoretical analysis of input impedance and efficiency of the system have been not studied.
Accordingly, a high efficiency wireless charging system for an EV based on ICPT technology is presented and analyzed in this paper. e input impedance of ICPT with a series-series compensation circuit, their phases, and the power factor is calculated and plotted by using Matlab scripts programming for different air gap values between the transmitter coil and receiver coil. e importance of the power factor (PF) that it is useful to determine the size and cost of the inverter used in the WPT system, so as PF is much less than one, then the inverter cost will be high. Additionally, an expression of optimal load resistance, corresponding to the maximal transmission efficiency, was demonstrated in this paper. Furthermore, the transmission efficiency characteristic of the proposed system was determined and plotted as a function of air gap. Finally, a wireless charging system prototype based on two rectangular coils has been built and tested under different transmission distance. e experimental results show a good performance of the proposed wireless charging system.

Proposed Wireless Charging System
A generalized configuration of EV wireless charging is proposed in this paper, as shown in Figure 1. e primary side is the one shown outside the vehicle, which includes a power source, a rectifier, and a high-frequency inverter (Power Electronics) all connected to the transmitter coil. e secondary side (power pickup system) is placed inside the vehicle. It also includes the power electronic converter and the onboard EV battery to be wirelessly charged. In fact, the EV wireless charging system can be operated in a resonance state by carefully integrated compensation topologies (the primary capacitor C p and the secondary capacitor C s ) in both the primary and the secondary sides of the system.

Calculation of Self and Mutual Inductances.
Recently, the wireless charging EV systems have been in development because they are easy to use and robust. is technology of transferring power, without cable over an air gap, is based in the magnetic coupling between inductive coils. e inductive coupling transformer consists of two coils, the transmitter (stationary), and the receiver (pick-up). In fact, the performance of the WPT system for EV charging depends significantly on the design (dimensions and shapes such as circular and rectangular) of the coils [4,12,[21][22][23]. In order to transfer the power efficiency, two rectangular coils were constructed in this work ( Figure 2). e resistance R i and self-inductance L i of a rectangular coil can be calculated as follows [12,22]: where N i is the number of turns � a i + b i , β � (a 2 i + b 2 i ) 0.5 , i � p is used for the transmitter (primary) coil, and i � s for the receiver (secondary) coil. In fact, the equivalent radius of the coil r i ( Figure 2) can be determined by the following expression [12]: where S i is the section of the wire. Assuming that the transmitter coil is longer than the receiver coil (b 1 ≫ b 2 ), the mutual inductance M between two parallel rectangular coils can be calculated analytically by [23] where N 1 and N 2 are number turns of the transmitter and receiver coils, respectively; d is the air gap (distance between the transmitter and receiver coils); μ 0 is the permeability of vacuum (μ 0 � 4 × 10 − 7 ); b 2 is the length of the receiver coil; and a 1 width of the transmitter coil. In addition, the coupling coefficient, which can be used to qualify the magnetic coupling, is defined as In order to see the influence of the transmission distance h, Figure 3 shows the simulation result of mutual inductance and coupling coefficient as a function of air gap d using the practical dimensions coils. From these curves, it can be observed that the mutual inductance M and coupling coefficient decrease rapidly when the distance between the transmitter and receiver coils increases. erefore, it is important to integrate compensation capacitors in series (S) or parallel (P) with coils to create a strong coupling between the transmitter and receiver coils.

Equivalent Circuit of the ICPT System.
e literature review shows several equivalent circuit model of inductive power transfer systems [4,5]. A typical equivalent electrical circuit (EEC) of the resonant series-series ICPT system is shown in Figure 4, where the left side of the circuits is the transmitters and the right side is the receiver. is circuit consisted of two resonant circuits, which coupled magnetically by mutual impedance (M) and the indices "p" and "s" indicate, respectively, the primary and secondary circuits. In this equivalent circuit, R p and L p are the resistance and selfinductance of the transmitter coil, R s and L s are the resistance and self-inductance of the receiver coil, R L is the load resistance, and C p and C s are series capacitors in transmitting and receiving compensation circuit, respectively. M is the mutual inductance between the two coils. For analysis simplicity, the rectifier, filter, and resistive load circuit (RFRC) in Figure 4(a) can be replaced with an effective AC resistance R e , as in [4].
e expression of the equivalent load resistive denoted R e is given by

Journal of Electrical and Computer Engineering
Due to the full bridge inverter configuration and the fundamental harmonic analysis (FHA), the amplitude of V 1 can be determined as e induced voltage in the secondary side due to the primary current I 1 is equal to − jωMI 1 , while the reflected voltage in the primary due to the secondary current I 2 is equal to jωMI 2 . Indeed, the voltage induced in the secondary coil is proportional to the operating frequency (ω s � 2πf s ), the mutual inductance M, and the current of the primary coil I 1 . According to equivalent electrical circuit depicted in Figure 4(b) and using Kirchhoff voltage law, the corresponding equation system at both primary and secondary circuit sides can be expressed as where X p and X s are equivalent reactance of the primary and secondary circuits, respectively.
erefore, the primary and secondary circuits can be reduced to two impedances Z p and Z s respectively, as shown in Figure 4(b). As a result, the secondary reflected and the input impedance Z in of whole circuit equations are respectively given by In order to ensure maximum power transfer to the load, it is desirable to operate the inverter at the resonance frequency f 0 . At this frequency, the reactance of the circuits perceived by the power source is zero where the input Rectifier, Filter, and Resistive load Circuit impedance seen by the source is purely resistive (Z in � R p + (ω 2 M 2 /R s + R e )). In this paper, the self-inductances values (L p and L s ) of coils are determined analytically by using equations (2), and its experimental values are given in Table 1. e resonance frequency f 0 is assumed to be equal 10 kHz due to the limited switching frequency of our inverter. us, the primary and a secondary compensation capacitors can be calculated, respectively, by In fact, the amplitude of the primary current and operating point of the system can be determined by the input impedance modulus [24]. erefore, the equivalent input impedance Z in in equation (10) is plotted in Figure 5 for different air gap distances d (m). ese values of mutual inductance M given in Table 1 are found from the simulation results mentioned in Figure 3, and the values of coupling coefficient are determined by equation (5).
From Figure 5, it can be noted that the impedance Z in is purely resistive and minimum (Z in � R p + (ω 2 M 2 /R s + R e )) if the operating frequency f s is equal to resonance frequency f 0 , which means that the normalized frequency f N � (f s /f 0 ) � 1.
In addition, the power factor (PF) can be obtained from the phase of the impedance Z in as expressed by following equation: e power factor is useful to determine the size of Volt-Ampere (VA) ratings, so Figure 6 shows the PF as function of normalized frequency for different air gap d (m) values. en, it can be concluded that the power factor have a maximum value as the normalized frequency f N � 1. is means that the module of the input impedance seen by the source is resistive at this frequency. At this point, the reactive power will be zero, so the VA value of the source is minimal. From these results, we can notice that it is essential to operate the wireless power transfer system in the resonance state.

Maximum Efficiency Condition for ICPT.
In this section, a novel approach to determine the efficiency of the ICPT system is presented. An optimum load resistance for the maximum efficiency is demonstrated from the efficiency equation. In Figure 4(b), P in and P L represent real powers at the source and load ports, respectively, and they can be expressed as follows: en, the efficiency of the ICPT system can be determined as In fact, by considering only the powers losses in coils, the efficiency of the system can be rewritten as follows: To simplify the study, it is assumed supposed that both Z p and Z s are defined as the impedances of primary and secondary circuit as follows: (8), it is possible to determine the current of transmitter coil I 1 � and receiving coil I 2 , as Substituting the secondary current I 2 in equation (18) into equation (16) yields erefore, the efficiency of the ICPT system mainly depends on the operating frequency (ω s � 2πf s ), the mutual inductance M between two coils, and the equivalent load resistive. Accordingly, if it is desired to increase the efficiency power transferred from the source to the load for a given application, at least one of these three parameters must be increased. Generally, the ICPT system is worked at resonance frequency where the coils are both constructed to operate at the resonance frequency (f 0 � (1/2π) ���� L s C s ). en, the expression of the power transfer efficiency in equation (19) at resonance frequency can be simplified by equation (20) when the equivalent reactance of receiver coil X s is equal to zero: where ω r � 2πf 0 . By differencing equation (21), we can get the optimal load resistance R e for the maximum efficiency of ICPT system as follows: Now and after simplification by using several hypotheses (R e ≠ 0, and M ≠ 0), the optimal load resistance at maximum efficiency is given by Once the air gap distance and the coils dimensions are selected, the design process of the WPT system begins with the calculation of the resistances, self-inductances of coils, and mutual inductance. Figure 7 shows a flow diagram describing the principal steps to design a WPT system. If the optimal load resistance is determined; applying equation (22), a maximum efficiency of WPT system can be found. In fact, an interactive calculation has been done using Matlab program and the obtained values of parameters of the system are illustrated in Table 2. From these optimal values, the test bench prototype will be constructed.
For fixed values of coil resistances, resonance frequency f 0 � 10 kHz, and mutual inductance M � 223 μH at 10 cm gap, it has been found that a load resistance R L of 20 Ω is optimal for the proposed ICPT system. Figure 8 shows the efficiency of ICPT system as a function of the transmission distance at different load resistances. It can be noted that the air gap between the transmitter and receiver coils has a strong influence on the transmission efficiency of the ICPT system.

Experimental Test
e scheme used to provide experimental tests of the proposed wireless charging system is given in Figure 9. It consisted of four major components: a power source, an inverter (DC/AC converter consists of four switches IGBTs),   an inductive coupler (two rectangular coils), and a rectifier and a load resistive. A photograph of the experimental setup is shown in Figure 10. e key parameters used in the proposed prototype are summarized in Table 2. In order to limit losses due to skin and proximity effects, we will use Litz wire of 1.5 mm 2 section to construct the two rectangular coils of the coupler. e equivalent radius of the primary and secondary coils have been found, respectively, equal to r 1 � 5.8 mm and r 2 � 6.9 mm (Figure 2).
A dSpace DS1104 processor board generates the switch control signals to the inverter. For as witching operating frequency f s � 10 kHz, the compensation capacitors are calculated from equations (11) and (12). Figure 11 presents the scheme of the designed compensation capacitances, the primary C p and the secondary C s , which are used in this paper. e experimental results are obtained using a digital oscilloscope during transfer power to optimally resistive load 20 Ω with switching frequency f s � 10 kHz and DC input voltage V dc � 60 V. e voltages and currents across input and output of the ICPT system are displayed in  In the first experimental test, the receiver coil is placed at 10 cm gap from the transmitter coil. Figure 12 shows the input voltage V 1 (output voltage of the inverter bridge) and the output voltage V 2 (input voltage of the rectifier bridge), while Figure 13 presents the input current I 1 (transmitter coil current) and the output current I 2 (receiver coil current). However, the input and the output currents are nearly sinusoidal. According to these results, it is important to notice that the RMS value of output voltage V 2 and output current are equal to 50 V and 2.16 A, respectively, at 10 cm air gap, as shown in Figures 12 and 13. In addition, the load power P L can be determined by the product of load voltage U L and load current I L . It is measured as 101 W. e power transfer efficiency (PTE), from DC input to DC output, is thereafter calculated as 80%. is value of the efficiency is compared to simulated result (ɳ � 86%) at 10 cm air gap shown in Figure 8. e obtained values show a good coherence between the simulated and experimental results.
In order to see the influence of air gap between coils in the proposed system, the receiver coil is placed at 15 cm gap. erefore, Figure 14 demonstrates the input and the output voltages, and Figure 15 displays the input and the output currents. According to the observation of these curves, it can be noted that the RMS values of output voltage V 2 and output current I 2 are equal to 17 V and 0.85 A, respectively. From these experimental results, as the distance transmission increases, the output power and efficiency were reduced mainly, where the load power was at 14.45 W at 9.5% efficiency with 15 cm air gap. To summarize, as the distance between transmitter and receiver coils is increased, the power transfer capability of the ICPT system is rapidly decreased.
Calculation of resistances (R p , R s ) and inductances (L p , L s ) of coils, apply Equations (1) and (2) Geometry of coils, N 1 , N 2 , V dc , f s , air gap d Select a proper value of resonance frequency f r and determine the compensation capacitors using Equations (11) and (12) Using Equation (22) and find optimal load resistance R e-opt Regulate the load resistance to optimal value R e_opt for obtaining a maximum efficiency of the WPT system End Figure 7: Flow diagram describing the principal steps to design a WPT system.  Finally, as we compare our work system to other works, the authors have described an advanced wireless charging system for real electric vehicle in [4], where the efficiency of    Journal of Electrical and Computer Engineering wireless charging system is not determined. However, a mathematical modeling and simulation of a wireless charging system based on the ICPT method have been studied and analyzed in our work with experimental validation. is paper also investigates the optimal load resistance corresponding to the maximum transmission efficiency in the series-series compensated WPT system.

Conclusion
In this paper, a novel wireless charging system based on equivalent electrical circuit of ICPT technology was studied. us, the input impedance of ICPT with a series-series compensation circuit, their phases, and the power factor are calculated and plotted by using Matlab scripts programming for different air gap values between the transmitter coil and receiver coil. Furthermore, a prototype of the wireless charging system has been built by optimizing the coils and compensating capacitance parameters. e experimental results were presented, and it was also demonstrated that the power transfer capability of the system is decreased if the air gap between coils increases. Finally, the presented system can be a good solution for electric vehicle battery charge and can be installed on highways to increase the EV usages.

EV:
Electrical vehicle WPT: Wireless power transfer ICPT: Inductively coupled power transfer SS: Series-series topology f s : Switching frequency (circuit operating frequency) ω s : Switching angular frequency (ω s � 2πf s ) ω r : Operating resonant pulsation (ω r � 2πf 0 ) R p : Resistance value of the transmitter coil L p : Self-inductance value of the transmitter coil R s : Resistance value of the receiver coil L s : Self-inductance value of the receiver coil M: Mutual inductance value between coils d: Distance between coils C p : Capacitance value of the primary sides C s : Capacitance value of the secondary sides C F : Output filter capacitance N 1 : Number of turns in the transmitter coil N 2 : Number of turns in the receiver coil V dc : Input DC voltage of the wireless charging system V 1 : ICPT circuit input voltage (AC) (output voltages of the inverter) V 2 : ICPT circuit output voltage (AC) (input voltage of the rectifier) i 1 : Transmitter (primary) coil current i 2 : Receiver (secondary) coil current V L : Load voltages I 0 : Load currents R L : Load resistance RFRC: Rectifier, filter, and resistive load circuit.

Data Availability
e data used to support the findings of this study are included within the article.  Journal of Electrical and Computer Engineering 9