Performance analysis of series/parallel and dual side LCC compensation topologies of inductive power transfer for EV battery charging system

Abstract

In an inductive battery charging system, for better power transfer capability and attaining required power level, compensation is necessary. This paper analyzes series/parallel (S/P) and dual side inductor-capacitor-capacitor (LCC) compensation topologies for inductive power transfer of electric vehicle (EV) battery charging system. The design and modeling steps of inductive power transfer for electric vehicle battery charging system are presented. Besides, the equivalent electrical circuits are used to describe the circuit compensation topologies. The results convey that the efficiency of dual side LCC compensation is higher than that of S/P compensation at variable mutual inductance (misalignment).

Key words： series/parallel compensation; electric vehicle (EV); dual side LCC compensation; inductive power transfer

Introduction

The popularity of electric vehicle (EV) in the automobile industry sector has always been increasing due to various advantages offered by the EV of increased energy security, improved fuel economy, reduced fuel costs, and reduced emissions. The EV runs on electricity and is propelled by one or more electric motors powered by rechargeable battery packs. The EV has many positive aspects such as high energy efficiency, environment friendliness, better performance, and reduced energy dependence on fossil fuels. However, the use of the EV faces some challenges like driving range, recharge time, battery cost, and more bulk and weight. Thus, with the growing EV market, problems need to be overcome by stimulation new ideas and developments in this area. One such major concern of the EV is the conductive battery charging applications which introduce the inconvenience and risk of hazards. This can be overcome by the simple concept of inductive power transfer [¹–³]. This simple concept introduced almost 30 years long back has been applied in the recent developing technology of wireless power transfer(WPT) technique (inductive power transfer) for battery charging application in EVs [⁴,⁵]. WPT is the transfer of energy by using the air as the medium, without the use of cables. Wireless charging is the key to unlocking an EV revolution [²,⁶]. Apart from overcoming the problems of range anxiety and hassle of plugging faced by plug-in EV, WPT application provides the added advantages of charging time, range, cost, reliability, safety. So, wireless EV charging is to ease the consumer anxieties and accelerate EV adoption [⁷].

The EV with wireless battery charging application has been extensively studied [¹–¹⁶] and many different topologies for wireless charging circuits have been discussed [¹⁷–²⁸], such as series/parallel (S/P), and series/series (S/S) resonant inductive power transfer with an aim to improve the overall performance of EV battery charging [⁵, ¹⁰,¹¹]. Along with the wireless charging concept comes the idea of optimizing the performance of the IPT network. In the context of increasing the WPT battery charging performance in EVs, diversified methods have been proposed [¹⁸,²⁰]. Applications of compensation circuits on the transmitter and receiver side are some of the strategies in an advancement of IPT technology. LCC is one of the compensation circuits, which is discussed in this paper. This paper focuses on the compensation circuits, their performance and characteristics. Besides, it aims to compare S/P and LCC compensation circuits of inductive power transfer in the EV.

The approach in this paper compares the S/P and dual side LCC compensation circuits for inductive power transfer in battery charging application of EV. Also, calculating the parametric values of compensation circuit components is one of the main features of designing and developing a compensation circuit for IPT. These incredibly efficient circuits are applied on both sides of the IPT system. To obtain the optimized value of circuit parameters for efficient inductive power transfer, different approaches are developed. Thus, IPT is improved significantly to cover the aspects of power transfer efficiency, range and power rating.

A significant portion of the industry believes that WPT technology represents the future of PEV, and various charging topologies are the catalysts in improving in WPT system [¹⁷,¹⁹,²¹]. Thus, extensive research has been conducted on future developments in the EV area in the scope of wireless charging of EV. This paper gives an insight on current developments in wireless charging topologies, compensation circuits, their parameterization and its performance.

The basic block diagram representation of the wireless EV battery charging system is shown in Fig. 1 which gives the power flow in the WPT system. The WPT system representation block diagram consists of a high-frequency inverter, a transmitter, receiver compensation circuits, inductive coils, and a battery charging unit. The high-frequency inverter converts the DC input supply to a high-frequency AC supply. The output of the inverter is fed to power compensation circuits which are connected to performance improvement of the WPT system. The transmitter and receiver coil are connected to the respective compensation circuits. The power transfer takes place between the inductive coils maintained at the proper air gap. The battery charging unit includes suitable power converters and the battery pack to be charged which is connected to the receiver side of the system.

Fig.1 Basic block diagram of wireless EV battery charging system

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Wireless EV battery charging system

WPT system

Basic characteristics of WPT

WPT is the method of transmitting electrical power from one source to consuming devices without conductors. Resonant inductive power transfer is the most popular current WPT technology [¹,⁹]. The resonant inductive power transfer consists of two independent mutually coupled coils with power electronic converters on both the transmitter and the receiver side of the system. The transmitter side inductor coil is excited with a constant current. The receiver side inductor coil is connected to a diode rectifier to convert the high-frequency AC to a DC voltage which is connected to a load. The following parts describe the WPT system by using equivalent circuits. The equivalent circuit model is illustrated in Fig. 2.

WPT equivalent circuit model

The principle of the inductive WPT system is almost the same as that of a conventional transformer [²³,²⁴]. The equations of the inductive power transfer system can be obtained by using the equivalent circuit model as shown in Fig. 2. It is assumed that under a steady-state condition the transmitter is excited with a sinusoidal voltage and current. In Fig. 2, R₁, L₁, V₁, and I₁ are the transmitter coil resistance, the inductance, the supply voltage, and the current of the transmitter coil while R₂, L₂, and I₂ are the receiver coil resistance, the inductance, and the receiver coil current, respectively.

Fig.2 Equivalent circuit model of WPT system coils

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(1)V_1=\mathrm{j}\omega L_1{I}_1+R_1{I}_1–\mathrm{j}\omega M{I}_2,

(2)\mathrm{j}\omega M{I}_1=\mathrm{j}\omega L_2{I}_2+R_2{I}_2+R_{\mathrm{L}}{I}_2.

The current in the receiver coil is given by the ratio of induced emf to the equivalent impedance of the receiver coil.

(3)I_{\mathrm{2}}={\displaystyle \frac{\mathrm{j}\omega M{I}_1}{\mathrm{j}\omega L_2+R_2+R_{\mathrm{L}}}}={\displaystyle \frac{\mathrm{j}\omega M{I}_1}{Z_2}},

where Z₂ is the total impedance of the receiver side of the coil. By substituting Eq. (3) in Eq. (1), the transmitter side voltage can be written as Eq. (4), and the total impedance (Z_t) is

(4)V_1=j\omega L_1{I}_1+R_1{I}_1+\left({\displaystyle \frac{{\omega }^{\mathrm{2}}{M}^{\mathrm{2}}}{Z_2}}\right)I_1,

(5)Z_t=\mathrm{j}\omega L_1+R_1+\left({\displaystyle \frac{{\omega }^{\mathrm{2}}{M}^{\mathrm{2}}}{Z_2}}\right).

It is observed from Eqs. (1)–(5) that both the reflected voltage and the induced voltage are described in terms of mutual inductance (M) between the coils. The relation between the mutual inductance and the magnetic coupling coefficient (k) is as given by Eq. (7). The expression of the efficiency of the inductive coupled coils is given by Eq. (6) which depends on the internal resistance of the coupled coils, the mutual inductance, and the angular frequency of the supply. To improve the coil efficiency, receiver inductance compensation is needed, whereas to reduce the VA rating of the supply transmitter compensation is required.

(6)\eta ={\displaystyle \frac{R_{\mathrm{L}}}{R_{\mathrm{L}}+R_{\mathrm{2}}+R_{\mathrm{1}}\left\{{\displaystyle \frac{{(R_{\mathrm{2}}+R_{\mathrm{L}})}^{\mathrm{2}}+{(\omega L_{\mathrm{2}})}^{\mathrm{2}}}{{(\omega M)}^{\mathrm{2}}}}\right\}}}.

The transmitter and receiver coils are modeled in the FEM simulation tool (ANSYS Maxwell).The detailed coil specifications are mentioned in Table 1. The variable mutual inductance used in the simulation is used for the vertical variable distance of the receiver coil. The mutual inductance is obtained from the FEM simulation.

(7)k={\displaystyle \frac{M}{\sqrt{L_{\mathrm{1}}{L}_{\mathrm{2}}}}}.

The magnetic coupling coefficient of the inductive power transfer coil is very poor. In Eq. (7), the coupling coefficient depends on the self-inductances of the transmitter, the receiver, and the mutual inductance between them.

Tab.1 Parameters used in the implementation of PSO for boost converter

Description	Value
Population size, N	10
Acceleration coefficient, C1	1.2
Acceleration coefficient, C2	1
Inertia weight, w	0.9
Ending criteria-iterations	50

Compensation topologies of WPT

The compensation in the secondary is needed for boosting the power transfer capability by increasing the quality factor. The primary compensation is used so that the equivalent impedance observed from the source is totally resistive. Therefore, the VA rating required for the supply is minimized [²⁵,²⁸]. The resonant inductive power transfer uses the capacitors that operate at a resonance frequency [⁵]. A classic resonant inductive power transfer system consists of a resonant transmitter and a receiver. The transmitter and the receiver contain resonant capacitors C₁ and C₂. Various resonant compensation topologies are proposed in Ref. [⁴]. As noted in Refs. [⁴,²⁷], the primary functions of the resonant circuits include improves transferred power, transmitted power frequency variation controlling, providing certain source characteristics (current or voltage source), transmission efficiency optimization, magnetic coupling variation compensation, and magnetizing current compensation in transmitter coil.

The transmitter topology series or parallel would be chosen depending on the voltage or current limitation on the power supply. In series, the voltage at the transmitter winding is compensated with the voltage across the capacitance so that the required voltage rating of the power supply is lower. Similarly, a parallel capacitance drives the current which compensates the transmitter current so that the current rating of the power supply is lower. Combinations of both the parallel and the series topologies of the primary winding would offer the possibility of fulfilling both current and voltage limitations. Several studies have been conducted on the different possible resonant networks at the transmitter side like CC (series, parallel, capacitors at the input) LCC or LCL [²,⁴,⁸]. The conventional compensation topologies are demonstrated in Fig. 3.

Fig.3 Four conventional compensation topologies

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Series/parallel compensation topology

The most advisable basic topology in EV battery charging application would be the series-parallel(S/P). A series capacitor in the primary would be chosen to accomplish the voltage limit at the inverter’s MOSFET while a parallel capacitor at the output would act as a controllable current source ideal for EV battery charging applications. To study the characteristics of the S/P compensation, the equivalent mutual inductance circuit model is considered as displayed in Fig. 4 and the following equations are developed for the analysis. Assuming that transmitter and receiver voltage and currents are sinusoidal, the system consists of a high frequency inverter, resonating inductive coupled coils, a diode bridge rectifier, a DC-DC boost converter, and the battery. The inverter which converts DC into a high frequency AC is connected to the resonating transmitter coil. The transmitter coil produces the high frequency magnetic field which links the receiver coil. The diode bridge rectifier is connected to the receiver coil which converts the AC into a DC supply. The DC-DC boost converter is used for regulating the battery voltage. A Li-ion battery of 120 V, 50 Ah is used for the simulation. However, the selection of the battery for this application is not limited to the Li-ion battery.

Fig.4 Series/parallel compensation topology for WPT

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The equations of the series/parallel compensated IPT system are described in Eqs. (8) and (9) while the receiver current of the system is provided in Eq. (10).

(8)V_1=\mathrm{j}\omega L_1{I}_1+{\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_1}}{I}_1–j\omega M{I}_2,

(9)\mathrm{j}\omega M{I}_1=\mathrm{j}\omega L_2{I}_2+I_2\left({\displaystyle \frac{R_{\mathrm{L}}\left({\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_2}}\right)}{R_{\mathrm{L}}+\left({\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_2}}\right)}}\right),

(10)I_2={\displaystyle \frac{\mathrm{j}\omega M{I}_1}{\mathrm{j}\omega L_2+\left({\displaystyle \frac{R_{\mathrm{L}}\left({\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_2}}\right)}{R_{\mathrm{L}}+\left({\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_2}}\right)}}\right)}}.

By substituting receiver side current Eq. (10) in Eq. (8), Eq. (11) can be obtained.

(11)V_{\mathrm{1}}=\mathrm{j}\omega L_1{I}_1+{\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_{\mathrm{1}}}}{I}_{\mathrm{1}}+I_{\mathrm{1}}\left({\displaystyle \frac{{\omega }^{\mathrm{2}}{M}^{\mathrm{2}}}{\mathrm{j}\omega L_2+\left({\displaystyle \frac{R_{\mathrm{L}}\left({\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_2}}\right)}{R_{\mathrm{L}}+\left({\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_2}}\right)}}\right)}}\right).

It is observed from Eq. (11) that the total impedance observed from transmitter side is Z_t. Hence,

(12)Z_t=\mathrm{j}\omega L_1+{\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_{\mathrm{1}}}}+{\displaystyle \frac{{\omega }^{\mathrm{2}}{M}^{\mathrm{2}}}{\mathrm{j}\omega L_2+\left({\displaystyle \frac{R_{\mathrm{L}}\left({\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_2}}\right)}{R_{\mathrm{L}}+\left({\displaystyle \frac{\mathrm{1}}{\mathrm{j}\omega C_2}}\right)}}\right)}}.

Therefore, the current drawn from the source is given by Eq. (13)

(13)I_{\mathrm{1}}={\displaystyle \frac{V_{\mathrm{1}}}{Z_t}}.

To get the maximum power transfer capability, the receiver should operate resonance frequency. For that, the compensation capacitor values are given by Eqs. (14) and (15).

(14)C_{\mathrm{1}}={\displaystyle \frac{\mathrm{1}}{{\omega }_{\mathrm{0}}^{\mathrm{2}}(L_{\mathrm{1}}-{\displaystyle \frac{M^{\mathrm{2}}}{L_{\mathrm{2}}}})}},

(15)C_{\mathrm{2}}={\displaystyle \frac{\mathrm{1}}{{\omega }_{\mathrm{0}}^{\mathrm{2}}{L}_{\mathrm{2}}}}.

To get the maximum efficiency, the system should operate at resonance. From the fallowing expressions, the efficiency of the system can be obtained.

(16)G={\displaystyle \frac{\mathrm{j}{\omega }_{\mathrm{o}}(R_{\mathrm{L}}-\mathrm{j}{\omega }_{\mathrm{o}}{L}_{\mathrm{2}})}{{\omega }_{\mathrm{o}}^{\mathrm{2}}{L}_{\mathrm{2}}^{\mathrm{2}}}},

(17)P_{\mathrm{o}}=I_{\mathrm{2}}^{\mathrm{2}}{R}_{\mathrm{L}},

(18)P_{\mathrm{o}}={\displaystyle \frac{G{I}_{\mathrm{1}}^{\mathrm{2}}{\omega }_{\mathrm{o}}^{\mathrm{2}}{L}_{\mathrm{2}}^{\mathrm{2}}}{R_{\mathrm{L}}-\mathrm{j}{\omega }_{\mathrm{o}}{L}_{\mathrm{2}}}},

(19)\eta ={\displaystyle \frac{G^{\mathrm{2}}{\omega }_{\mathrm{o}}^{\mathrm{2}}{L}_{\mathrm{2}}^{\mathrm{2}}}{Z_t(R_{\mathrm{L}}-\mathrm{j}{\omega }_{\mathrm{o}}{L}_{\mathrm{2}})}}.

Dual side LCC compensation topology

In recent years, the dual side LCC compensation has become more popular and as compared to basic compensation topologies, it has an additional series inductor and parallel capacitor on both the transmitter, the receiver side and it is shown in Fig. 5. A symmetric topology has been considered.

(20){\omega }_{\mathrm{0}}={\displaystyle \frac{\mathrm{1}}{\sqrt{L_{\mathrm{f1}}{C}_{\mathrm{f1}}}}}={\displaystyle \frac{\mathrm{1}}{\sqrt{L_{\mathrm{f2}}{C}_{\mathrm{f2}}}}}={\displaystyle \frac{\mathrm{1}}{\sqrt{(L_1-L_{\mathrm{f1}})C_1}}}={\displaystyle \frac{\mathrm{1}}{\sqrt{(L_{\mathrm{2}}-L_{\mathrm{f2}})C_{\mathrm{2}}}}}.

Fig.5 Dual sided LCC compensation topology for WPT

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It is observed that the resonant frequency depends on inductances and capacitances only. It is independent on coupling coefficient, mutual inductance, and load conditions.

(21)I_{L_{\mathrm{f1}}}={\displaystyle \frac{M{V}_{\mathrm{out}}}{\mathrm{j}{\omega }_{\mathrm{o}}{L}_{\mathrm{f1}}{L}_{\mathrm{f2}}}}

(22)I_{L_{\mathrm{f2}}}={\displaystyle \frac{M{V}_{\mathrm{in}}}{\mathrm{j}{\omega }_{\mathrm{o}}{L}_{\mathrm{f1}}{L}_{\mathrm{f2}}}}

(23)I_{\mathrm{1}}={\displaystyle \frac{V_{\mathrm{in}}}{\mathrm{j}{\omega }_{\mathrm{o}}{L}_{\mathrm{f1}}}},

(24)I_{\mathrm{2}}={\displaystyle \frac{V_{\mathrm{out}}}{\mathrm{j}{\omega }_{\mathrm{o}}{L}_{\mathrm{f2}}}}.

In this compensation, the transmitter series inductor current I_Lf1 is in phase with the input voltage and its amplitude depends on the output voltage. The receiver side series inductor current I_Lf2 is obtained by the input voltage [²]. Among the input and output voltage, the resonant frequency and the mutual inductance are the determining factors for the maximum power transfer. Usually, the mutual inductance is limited because of the limited coil size, the gap between the transmitter and the receiver coil, and the misalignment position of the coils. Design of L_f1 or L_f2 in dual side LCC compensation is used as another design procedure for wireless charger system for proper efficiency.

(25)L_{\mathrm{f1}}=L_{\mathrm{f2}}=\sqrt{{\displaystyle \frac{k{V}_{\mathrm{0}}{V}_{\mathrm{in}}{L}_{\mathrm{1}}}{{\omega }_{\mathrm{0}}{P}_{\mathrm{0}}}}},

(26)C_{\mathrm{f1}}=C_{\mathrm{f2}}={\displaystyle \frac{\mathrm{1}}{{\omega }_{\mathrm{o}}^{\mathrm{2}}{L}_{\mathrm{f1}}}},

(27)C_{\mathrm{1}}=C_{\mathrm{2}}={\displaystyle \frac{\mathrm{1}}{{\omega }_{\mathrm{o}}^{\mathrm{2}}(L_{\mathrm{1}}-L_{\mathrm{f1}})}},

(28)P_{\mathrm{in}}=\mathrm{Re}(V_{\mathrm{in}}{I}_{L_{\mathrm{f1}}}^{*}),

(29)P_{\mathrm{out}}=\mathrm{Re}(V_{\mathrm{out}}{I}_{L_{\mathrm{f2}}}^{*}).

Control strategy for IPT system

Inverter switching strategy of the IPT system

The DC input is transformed to a high frequency AC power by a full-bridge inverter which is formed by MOSFET switches S1–S4. These inverter switches are supplied with open loop PWM pulses at a suitable required frequency and duty cycle. This switching is provided through an Arduino based controller to the inverter switches. The switches are triggered by a gate driver circuit whose switching pulses are given through the programmed controller at a specified operating frequency for its stable operation.

Battery control strategy for boost converter

For regulating the output voltage at the secondary side of the IPT system, a proportional integral (PI) controller has been implemented for the boost converter. The schematic diagram of closed loop boost converter is shown in Fig. 6. The gain values of this controller have been determined by using the particle swarm based optimization algorithm. This algorithm efficiently evaluates the system and yields the optimal K_P and K_I values for the controller. It basically controls the duty cycle of the boost converter to maintain a constant voltage at a constant reference value. The closed loop transfer function of the boost converter is formulated and given below. This expression is crucial for evaluating the parameters of the PI controller.

Fig.6 Schematic diagram of closed loop controller for boost converter

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The error signal is processed through the PI controller and the output of the PI controller is given as

(30)u(t)=K_{\mathrm{p}}e(t)+K_{\mathrm{I}}{\displaystyle \int }e(t)\mathrm{d}t.

The objective function is to minimize the sum square error which is given as

(31)\mathrm{Minimize}\hspace{0.17em}F(Ø\mathrm{)=}{\displaystyle {\sum }_{t=\mathrm{0}}^t}{(e(t\mathrm{))}}^2,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{subject\; to}{Ø}_{\mathrm{lower}}\le Ø\le {Ø}_{\mathrm{upper}}.

where Ø = {K_P& K_I} the controller structure, t is the start-up time, and Ø_lower and Ø_upper are the lower and upper bounds of controller constants, which are obtained using transfer function model. The parameters of the PSO are given in Table 1 and the convergence characteristics are exhibited in Fig. 7 which is plotted with global best particle at each iteration.

(32){\displaystyle \frac{V_{\mathrm{out}}}{V_{\mathrm{in}}}}={\displaystyle \frac{{\displaystyle \frac{R_{\mathrm{L}}}{L_{\mathrm{b}}}}}{[\mathrm{1}+\{\left({\displaystyle \frac{R_{\mathrm{L}}}{L_{\mathrm{b}}}}\right)*(K_{\mathrm{p}}+{\displaystyle \frac{K_{\mathrm{I}}}{s}})*(\mathrm{1}-D)\left\}\right]}}.

The pseudo code for the implementation of PSO is as follows:

Initialize the parameters’ max iteration, population size N, acceleration parameters C₁ and C₂, and inertia weight w.

Randomly generate N particles.

Initialize, for each particle, the p_best as current location.

While (k<Max Iteration)

While ()

For every particle,

Calculate the fitness value of the particle.

If the current fitness of the particle is better than the previous best position, update p_best.

i=i+\mathrm{1};

If the fitness of the best particle is better than the global best position, g_best reached so far, update the global best position, g_best.

Update the velocity and position of the particle based on its personal best position, p_best and the global best position, g_best.

k=k+\mathrm{1};

End.

Fig.7 Boost converter convergence graph with PSO based controller

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Results and discussions

Modeling of inductive coils in FEM

The modeling of the inductive coil has been developed in the FEM software (ANSYS MAXWELL). The detailed parameters are specified in Table 2. The setup developed in the FEM simulation tool is depicted in Fig. 8. The number of turns (N) considered for the transmitter and the receiver is 26. The transmitter coil is energized from a 5 A current source, the vertical variation in the distance (misalignment) is varied from 10 mm to 200 mm, and the mutual inductance between the coupled coils is measured. The plot between distance and mutual inductance is plotted in Fig. 8, and the magnetic flux distribution surrounding the coil is shown in Fig. 7.

Tab.2 Coil specifications for FEM simulation

Parameter	Specification
Number of turns in transmitter	26
Number of turns in receiver	26
Coil diameter/cm	30
Conductor radius/mm	5
Self-inductance of transmitter/µH	230
Self-inductance of receiver/µH	230
Vertical distance varied/mm	10–200
Mutual inductance/µH	5–50
Coil design type	Circular

Fig.8 (a) FEM coil setup; (b) magnetic flux density distribution between the coils

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The mutual inductance between the coupled coils varies as the distance is varied and the coupling coefficient between the coupled coils depends on the mutual inductance between the coils. The plot between the coupling coefficient, mutual inductance versus distance between the coils is shown in Fig. 9. It can be observed from the analysis that as the distance between coupled coils is increased, the mutual inductance decreases, therefore the coupling coefficient also reduces and the power transfer capability will be reduced.

Fig.9 Distance vs mutual inductance and coupling factor

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MATLAB Simulink results

A WPT system model has been designed and developed in MATLAB to simulate the performance of the proposed S/P and LCC compensation topology for WPT. The topologies undertaken to study are applied on both sides of the system i.e. on transmitter side as well as receiver side. The proposed system parameters and the specification for the S/P and LCC compensation topology are listed in Table 3. The distance between the coils are reflected by various coupling coefficients, namely k = 0.022 and k = 0.217, i.e., the mutual inductance M = 5 µH and M = 50 µH are considered for the study. The Li-ion battery of 120 V, 50 Ah is used for the simulation. However, the selection of battery for this application is not limited to Li-ion battery. The resonant frequency is the same as the inverter switching frequency. Thus, based on specified parameters and the analysis above, the MATLAB Simulink model has been developed to simulate the S/P and dual side LCC compensated WPT system. On the transmitter side, a simple open loop controller for the inverter has been designed. On the receiver side of the WPT system, a diode bridge rectifier has been developed to get a DC voltage. The battery voltage can be regulated by a DC-DC converter for constant voltage operation of the battery.

Tab.3 Specification and parameters of the system

Parameter	Description	S/P	LCC
Vdc	Input voltage/V	60	60
L1	Transmitter inductance/µH	230	230
L2	Receiver inductance/µH	230	230
f	Resonant frequency/kHz	20	20
Po	Maximum output power/W	600	600
M	Mutual inductance/µH	5–50	5–50
C1	Transmitter side capacitance/µF	27	0.329
C2	Receiver side capacitance/µF	27	0.329
Lf1	Transmitter series inductance/µH	-	37.79
Lf2	Receiver series inductance/µH	-	37.79
Cf1	Transmitter parallel capacitance/µF	-	1.677
Cf2	Receiver parallel capacitance/µF	-	1.677
RL	Load resistance/Ω	15	15

Fig.10 Calculated, simulated and measured currents of S/P and dual side LCC compensation system

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Figure 10 describes the transmitter current variation for S/P and dual LCC compensation topologies with respect to various mutual inductances. It is observed that in series/parallel compensation, the transmitter current changes with respect to the mutual inductance but in the case of dual side LCC compensation the transmitter current will change within small limits (Figs. 11 and 12). It is observed that in the case of S/P compensation, if mutual inductance is decreasing, the current drawn from the source will increase but in the case of dual side LCC compensation, the source current will be within a small variation. The receiver current in the case of S/P compensation, if mutual inductance is low, the source current as well as the receiver current is also high compared to other higher mutual inductance conditions. In the case of dual side LCC compensation, as mutual inductance increases the transmitter, the receiver currents are increased. Figure 13 shows the input and output power variations with respect to the mutual inductance for S/P and dual side LCC compensation topologies.

Fig.11 Transmitter current of S/P compensation

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Fig.12 Transmitter current of dual side LCC compensation

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Fig.13 Magnitudes of power for S/P and dual side LCC compensation system

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Experimental results

The analytical and simulated results are compared with the experimental results. The setup developed in the laboratory is shown in Fig. 14. The hardware setup contains spiral circular coils and a metal oxide semiconductor field effect transistor (MOSFET) based H-bridge inverter along with the driver circuit, to provide high switching frequency pulses to the inverter. An arduino microcontroller is used at the receiver side. The diode bridge rectifier and DC-DC boost converters are involved to provide the constant voltage for EV battery charging. The closed loop control is provided for varying the duty cycle of the DC-DC boost converter in the receiver side by using another microcontroller. Inverter output voltage, transmitter current, receiver voltage and receiver current of the IPT system are shown in Figs. 15–17 provides transmitter currents at different mutual inductance for S/P and dual side LCC compensation respectively.

Fig.14 The setup developed in the laboratory

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Fig.15 Series/parallel compensated IPT system

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Fig.16 Transmitter current of S/P compensation for different mutual inductance value

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Fig.17 Transmitter current of dual side LCC compensation for different mutual inductance value

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The closed loop control of the boost converter is accomplished using the particle swarm optimization algorithm based PI controller. The time response characteristics of the proposed controller are compared with those of the conventional PI controller (Ziegler Nicholas method) in Fig. 18. The proportional gain, integral gain, settling time, and steady-state error of the controllers are given in Table 4. It is inferred that the response of PSO based PI controller is better when compared to the conventional PI controller. Here the settling time and steady-state error of the proposed controller are lesser.

Tab.4 Comparison of time response of the boost converter with conventionally obtained controller and PSO-tuned controller

Parameter	Conventional method	PSO method
KP	0.126	9.216
KI	11.32	24.315
Settling time (ts)/ms	45	22.32
Steady-state error (ess)/V	1.46	0.35

Fig.18 Time response of the boost converter

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Comparative analysis of S/P and dual side LCC compensation topologies

Stresses on the components

For the same amount of WPT system in both S/P and dual side LCC compensation topology voltage and current stress on the transmitter and the receiver inductance (L₁, L₂) at the same aligned position, the voltage stress on C₁ and C₂ in dual side LCC compensated system is less compared to that in the S/P compensated system.

Comparison of efficiency and output power

Mutual inductance is a main impact factor on the output power and efficiency. The efficiency of the S/P compensated system is higher for high values of mutual inductance. For the dual side LCC compensated system, the efficiency is higher if mutual inductance is of low values.

Figure 19 is an analytical, simulated, and measured efficiency comparison between the S/P and dual side LCC compensation topologies. The efficiency of dual side LCC compensation is steady, even though the maximum and minimum changes in mutual inductance compared to the S/P compensation topology. The reason behind this is the loss of the compensation circuit element increase while the loss in transmitter coil decreases when mutual inductance increases.

In designing IPT systems, the S/P compensation topology is used for systems with a large mutual inductance. On the other hand, dual side LCC compensation topology is used for the system with a small mutual inductance. The output power can be regulated by controlling the input voltage. In S/P compensation topology, when mutual inductance is maximum, the input voltage will be higher than that of dual side LCC compensation topology. When the mutual inductance is minimum, the dual side LCC compensation WPT system efficiency is higher.

Fig.19 Calculated, simulated and measured efficiency of S/P and dual side LCC compensation system

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From the above comparison and analysis, it can be concluded that the power transfer capability of the dual-side LCC compensation topology is better than that of the S/P compensation topology. The voltage and current stresses of the dual-sided LCC compensation topology are lower than that of the SP topology when charging the same battery at the rated power.

Conclusions

In this paper, the series/parallel and dual side LCC compensation topologies for wireless EV battery chargers were described and compared. Generally, the variation in mutual inductance (misalignments) affects the electrical characteristics of these two topologies. Theoretical, simulated, and measured analysis prove that compared to S/P compensation, dual side LCC compensation is less sensitive for the variation of mutual inductance. Besides, the voltage and current stress on the elements of the dual side LCC compensation is smaller. For minimum value of mutual inductance, the efficiency is higher for the dual side LCC compensation compared to the S/P compensation topology.

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