# Vehicle-Driven Operation of an Adaptive IPT System with Tolerance to Large Magnetic Coupling Coefficient Variations

Fco. Javier López-Alcolea<fnref n="1" />, Emilio J. Molina-Martínez<fnref n="2" />, Alfonso Parreño Torres<fnref n="1" />, Jaime García Jiménez<fnref n="3" />, Javier Vázquez<fnref n="2" />, Pedro Roncero-Sánchez<fnref n="3" />

E-Mail: FJavier.Lopez@uclm.es,

This publication is part of the projects TED2021-132233B-I00 funded by MICIU/AEI/10.13039/501100011033 and by the European Union "NextGenerationEU"/PRTR, and the PID2022-141100OB-C21 project funded by MICIU/AEI/10.13039/501100011033 and by the European Regional Development Fund (ERDF). This work was supported by the University of Castilla-La Mancha (UCLM) and the ERDF under the pre-doctoral scholarship 2020-UNIVERS-9820.

**Index Terms**—Bi-directional, Charging Infrastructure for EV's, Contactless Energy Transfer, Control Strategy, Vehicle-to-Grid.

**Abstract**—This paper proposes an adaptive operation of a bidirectional inductive power transfer (IPT) system designed for the wireless charging of electric vehicles (EVs). It is composed of two controllers and an expert control layer that monitors the operation, giving the system this adaptability feature. Experimental results demonstrate its correct operation.

## I. INTRODUCTION

Relative displacement between transmitting and receiving coils presents a persistent challenge in inductive power transfer (IPT) systems, particularly in the context of wireless charging of electric vehicles (EVs). Factors such as misalignment and various parameters influencing the distance between coils (e.g., tire pressures or vehicle load) results in an uncertainty in the coupling coefficient ($k$) value of the magnetic coupler.

The low $k$ values achieved (typically below 0.4 in EV charging applications [1]) leads to substantial percentage variations of this parameter. As a result, the IPT system operating point may undergo significant changes in the presence of relatively large displacements between coils.

Therefore, it is important to ensure robustness against variations in $k$ when designing such types of IPT systems. To achieve this, one could modify the magnetic pad

or the compensation network to obtain a lower variation of $k$ in response to coil displacements or minimize its influence [2], [3], or even use aid-positioning systems [4]–[6].

However, this may lead to an increase in cost, weight or volume. Therefore, a second (and more interesting) solution involves enhancing the robustness of the IPT system through control strategies. By implementing and/or modifying the existing control algorithms, it is possible to change the system behavior, thereby improving its response against variations in the operating point.

This paper proposes a control strategy that enhances the adaptability of an IPT system when variations in $k$ occur. It extends upon the research previously presented in [7], incorporating changes to a double-sided LCC compensation network, a different filtering stage in the DC-DC converter, and providing experimental validation of the proposed control structure. To increase the robustness of the IPT system operation, the addition of an expert control layer is proposed. This layer monitors the operation of two different PI controllers that regulate the vehicle DC bus voltage and battery current. The main contributions of this paper are:

1. The robustness of the IPT system operation against changes in $k$ is increased.

2. The power transferred is regulated with smooth transients in the battery current.

<footnote n="1">¹School of Industrial Engineering, University of Castilla-La Mancha, Albacete, Spain</footnote>

<footnote n="2">²School of Industrial Engineering, University of Castilla-La Mancha, Ciudad Real, Spain</footnote>

<footnote n="3">³Institute of Energy Research and Industrial Applications, University of Castilla-La Mancha, Ciudad Real, Spain</footnote>
<figure><img src="image_1.png" /><figcaption>Fig. 1: Proposed IPT system operation.</figcaption></figure>

### 3. Experimental validation of the proposed control strategy is provided.

For this purpose, the rest of the paper is organized as follows: Section II offers a description of the proposed system operation. In Section III, the mathematical development required for the design of the controllers is addressed, and Section IV explains the proposed control strategy and its design. Finally, Section V presents an analysis of the experimental results obtained, while Section VI summarizes the main conclusions extracted from this work.

## II. PROPOSED SYSTEM OPERATION

Fig. 1 depicts the operation of the proposed IPT system. The magnetic coupler uses an LCC network to operate at a resonance frequency $f_0$, and the system can be divided into two main parts: the ground (GA) and vehicle (VA) assemblies.

The GA has a DC bus connection so that it can be connected, for example, to a DC microgrid. It also includes an H-bridge inverter and a compensated coil placed in the parking space. On the other hand, the VA comprises a second compensated coil integrated in the vehicle, another H-bridge inverter, and a DC-DC converter that interfaces the IPT system and the EV battery.

In the proposed IPT system operation, the H-bridge inverter located in the GA operates in a square wave configuration with frequency $f_0$ without any control loop applied. As a result, the regulation tasks are solely driven by the EV. This approach eliminates the need for real-time data exchange between GA and VA, thereby ensuring that communication delays do not compromise

the stability of the system. Furthermore, the absence of regulation algorithms in the parking space simplifies the interoperability between an EV and different GAs, as system stability relies solely on hardware, avoiding potential interactions between GA and VA control loops.

The EV adjusts the VA DC bus voltage $V_{VA,DC}$ using the duty cycle $D$ applied to the DC-DC converter. For this purpose, a proportional-integral (PI) controller is implemented on a digital platform. A second proportional-integral-derivative (PID) controller is employed for the regulation of the power delivered to/absorbed from the battery. It modifies the phase-shift angle $\alpha_{VA}$ applied to the VA H-bridge inverter, regulating the battery current $I_{Bat}$. In doing so, power regulation is achieved in both grid-to-vehicle (G2V) and vehicle-to-grid (V2G) power flow directions.

As it will be shown later in Section III, the power transferred can be adjusted by varying the DC bus voltage $V_{VA,DC}$ for a given $\alpha_{VA}$ that remains constant. Consequently, it is possible to adapt the IPT system operation to changes in $k$ by modifying the voltage control loop reference voltage. For this purpose, three control layers are implemented in a digital platform (see Fig. 2). They are classified based on their proximity to the hardware, with the lower control layer encompassing the hardware and software protections, as well as the modulations of the inverters and the DC-DC converter.

The second layer comprises the voltage and current controllers, and in the third layer an expert controller is implemented. This expert controller monitors the operation of the PI and PID regulators and determines whether the adaptation of the IPT system is necessary by following the criteria outlined in Section IV. If so, the
<figure><img src="image_2.png" /><figcaption>Fig. 2: Control layers implemented in the proposed system.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 3: Equivalent model of the LCC-compensated magnetic coupler.</figcaption></figure>

expert controller halts the current controller operation, sets the $\alpha_{VA}$ applied to the VA H-bridge inverter, and modifies the DC bus voltage reference to change the operating point of the system.

### III. ANALYTICAL DESCRIPTION OF THE SYSTEM

#### A. IPT System

The electrical scheme of the LCC-compensated magnetic coupler is shown in Fig. 3. This compensation network has been widely studied in literature [8]–[10]. When the IPT system operates at the resonance frequency, the expressions for the currents $I_{GA}$, $I_{VA}$, $I_1$ and $I_2$ are [9]:

$$I_{GA}(j\omega_0) = -\frac{k\sqrt{L_1L_2}}{j\omega_0L_{f1}L_{f2}}V_{VA}(j\omega_0) \quad (1)$$

$$I_{VA}(j\omega_0) = \frac{k\sqrt{L_1L_2}}{j\omega_0L_{f1}L_{f2}}V_{GA}(j\omega_0) \quad (2)$$

$$I_1(j\omega_0) = \frac{1}{j\omega_0 L_{f1}} V_{GA}(j\omega_0) \quad (3)$$

$$I_2(j\omega_0) = -\frac{1}{j\omega_0 L_{f2}} V_{VA}(j\omega_0) \quad (4)$$

where $\omega_0 = 2\pi f_0$.

According to [7], the DC component of the current at the DC side of the VA H-bridge inverter, $I_{Rect,DC}$, can be expressed as a function of $\alpha_{VA}$:

$$I_{Rect,DC} = \sum_{h=1,3,5,...}^{n} \frac{2}{h\pi} I_{VA}^{h} \cos(\varphi_{h}) \cos(h\alpha_{VA}) \quad (5)$$

where $I_{VA}^h$ and $\varphi_h$ represent the amplitude and phase angle between $V_{VA}$ and $I_{VA}$ of the harmonic component $h$.

In the IPT system, the power transferred is carried mainly by the fundamental component. Hence, the first harmonic approximation can be employed, resulting in the following expression:

$$I_{Rect,DC} = \frac{2}{\pi} I_{VA}^{1} \cos(\alpha_{VA}) \quad (6)$$

Therefore, it is possible to linearize around the equilibrium point obtained for a given value of $\alpha_{VA}^0$. Moreover, since the time constant of the IPT system $\tau_{IPT}$ will be usually significantly lower than that of the DC-DC converter, $\tau_{DC}$, the dynamic behavior of the IPT system can be represented as a simplified first-order system. Consequently, the following expression is obtained [7]:

$$\Delta I_{Rect,DC}(s) = -\frac{2}{\pi} \frac{1}{\tau_{IPT}s + 1} I_{VA}^{1} \sin(\alpha_{VA}^{0}) \Delta\alpha_{VA}(s) \quad (7)$$

#### B. DC-DC Converter

The connection of the DC-DC converter to the DC side of the VA H-bridge inverter is regarded as a current source, as shown in Fig. 4. The DC bus capacitance $C_{DC}$ is placed on the inverter-side of the DC-DC converter, while a T-filter is employed to establish a connection to the EV battery. When a given duty cycle $D^0$ is applied to the converter, the following equilibrium point is obtained:

$$I_{Bat}^{0} = \frac{I_{Rect}^{0}}{D^{0}} \quad (8)$$

$$V_{VA,DC}^{0} = \frac{(R_{Lconv} + R_{Lbat} + R_{Bat})I_{Bat}^{0} + V_{B}^{0}}{D^{0}} \quad (9)$$

For a given $\alpha_{VA}$, the amplitude of the voltage $V_{VA}$ at the fundamental frequency is [11]:

$$V_{VA}(j\omega_0) = \frac{4V_{VA,DC}}{\pi} \cos(\alpha_{VA}) \quad (10)$$
<figure><img src="image_4.png" /><figcaption>Fig. 4: DC-DC converter with a T-filter.</figcaption></figure>

Therefore, from (9) it can be inferred that, by solely modifying $D^0$, $V_{VA,DC}$ can be adjusted. Consequently, according to equation (10), $V_{VA}$ is modified by $V_{VA,DC}$ if $\alpha_{VA}$ is kept constant. Since $I_{VA}$ does not depend on $V_{VA}$, the variation in $D$ does not affect $I_{Rect}$ either and, thus, both currents are kept constant. Consequently, the variation in both $V_{VA}$ and $V_{VA,DC}$ leads to a change in the transferred power. This is the mechanism employed in this work to adapt the IPT system operation.

After linearizing the system around the equilibrium point, the two transfer functions of interest, $P_{Vva}(s) = \Delta V_{VA,DC}(s)/\Delta D(s)$ and $P_{Rect}(s) = \Delta I_{Bat}(s)/\Delta I_{Rect,DC}(s)$, are obtained:

$$P_{Vva}(s) = \frac{\beta_7 s^3 + \beta_6 s^2 + \beta_5 s + \beta_4}{s^4 + \beta_3 s^3 + \beta_2 s^2 + \beta_1 s + \beta_0} \quad (11)$$

$$P_{Rect}(s) = \frac{\beta_{10}s^2 + \beta_{9}s + \beta_{8}}{s^4 + \beta_{3}s^3 + \beta_{2}s^2 + \beta_{1}s + \beta_{0}} \quad (12)$$

where the coefficients $\beta_0$ to $\beta_{10}$ are the ones collected in TABLE I. $R_{Cdc}$ is the equivalent series resistance (ESR) of $C_{DC}$, and $R_{LConv}$, $R_C$, $R_{L Bat}$ and $R_{Bat}$ are the ESRs of the components $L_{Conv}$, $C$, $L_{Bat}$ and the battery.

From equations (7) and (12), the transfer function $P_{Ibat}(s) = -\Delta I_{Bat}(s)/\Delta \alpha_{VA}(s)$ is then obtained:

$$P_{Ibat}(s) = \frac{2\sqrt{2}}{\pi} I_{VA,RMS}^1 \sin(\alpha_{VA}^0) \frac{1}{\tau_{IPTS} + 1} P_{Rect}(s) \quad (13)$$

# IV. PROPOSED CONTROL STRATEGY

## A. Voltage Control Loop

Fig. 5 illustrates the block diagram of the voltage control loop in the discrete domain. It is composed of a pre-filtering stage $H_V(z)$ and a PI controller $R_V(z)$. The expert controller modifies, if necessary, the reference voltage $\Delta V_{Ref}(z)$ by adding the signal $\Delta V_{Exp}(z)$ to $\Delta V_{VA,DC}^*(z)$. The sharp transitions in $\Delta V_{Ref}(z)$ are

<figure><img src="image_5.png" /><figcaption>Fig. 5: Block diagram of the voltage control loop.</figcaption></figure>

smoothed by the transfer function $H_V(z)$, which is defined as a second-order low pass filter with a cut-off frequency $\omega_{HV}$:

$$H_V(z) = \frac{(1 - e^{-\omega_{HV} T_s})^2}{(z - e^{-\omega_{HV} T_s})^2} \quad (14)$$

where $T_s$ is the sampling period.

The smoothed evolution of $\Delta V_{Ref}(z)$ is then compared with the measured value of $\Delta V_{VA,DC}(z)$. Then, the regulator $R_V(z)$ adjusts the duty cycle of the DC-DC converter to drive the error signal $e_V(z)$ to zero. $R_V(z)$ is defined as:

$$R_V(z) = K_{PV} + K_{IV} \frac{1}{z - 1} \quad (15)$$

being $K_{PV}$ and $K_{IV}$ the proportional and integral gains of the regulator.

## B. Current Control Loop

The current controller uses a PID regulator, as depicted in Fig. 6. It compares the desired battery current, $\Delta I_d^*(z)$, with the measured value and determines the phase-shift angle $\Delta \alpha_{Ctrl}(z)$ that must be applied. The signal $\Delta I_d(z)$ is generated by smoothing the reference signal $\Delta I_{Bat}^*(z)$ using $H_I(z)$, which has the same definition as $H_V(z)$ in (14) but with a cut-off frequency $\omega_{HI}$.

The expert control layer determines whether the $\Delta \alpha_{Ctrl}(z)$ provided by the PID regulator should be applied to the VA H-bridge inverter. If the current controller operation has to be interrupted, the Exp\_Ctrl signal will change its value so that the $\Delta \alpha_{VA}(z)$ applied to the inverter will have a predefined fixed value. Additionally, a saturation block is employed to ensure that the applied $\Delta \alpha_{VA}(z)$ remains within the minimum and maximum applicable values. Therefore, during the operation of the system it is possible to find that $\Delta \alpha_{Ctrl}(z) \neq \Delta \alpha_{VA}(z)$, which could result in the saturation of the PID controller integral part. To mitigate the effects of this saturation, an anti-windup action is implemented.

## C. Expert Controller

The expert controller evaluates the operation of the voltage and current control loops. It monitors the evolution of the desired and measured values of $V_{VA,DC}(z)$
<table><caption>TABLE I: Coefficients of the transfer functions $P_{Vva}(s)$ and $P_{Rect}(s)$.</caption><tr><td>β<sub>10</sub></td><td>D<sup>0</sup>R<sub>C</sub>R<sub>Cdc</sub>/L<sub>Bat</sub>L<sub>Conv</sub></td><td>β<sub>9</sub></td><td>CR<sub>C</sub> + C<sub>DC</sub>R<sub>Cdc</sub>/CC<sub>DC</sub>L<sub>Bat</sub>L<sub>Conv</sub></td></tr><tr><td>β<sub>8</sub></td><td>D<sup>0</sup>/CC<sub>DC</sub>L<sub>Bat</sub>L<sub>Conv</sub></td><td>β<sub>7</sub></td><td>L<sub>Conv</sub>I<sup>0</sup><sub>Bat</sub> + C<sub>DC</sub>R<sub>Cdc</sub>D<sup>0</sup>V<sup>0</sup><sub>VA,DC</sub>/C<sub>DC</sub>L<sub>Conv</sub></td></tr><tr><td>β<sub>4</sub></td><td>D<sup>0</sup>V<sup>0</sup><sub>VA,DC</sub> + I<sup>0</sup><sub>Bat</sub>(R<sub>Lbat</sub> + R<sub>LConv</sub> + R<sub>Bat</sub>)/CC<sub>DC</sub>L<sub>Bat</sub>L<sub>Conv</sub></td><td>β<sub>0</sub></td><td>(D<sup>0</sup>)<sup>2</sup>/CC<sub>DC</sub>L<sub>Bat</sub>L<sub>Conv</sub></td></tr><tr><td>β<sub>6</sub></td><td>1/CC<sub>DC</sub>L<sub>Bat</sub>L<sub>Conv</sub>[D<sup>0</sup>V<sup>0</sup><sub>VA,DC</sub>[CC<sub>DC</sub>R<sub>Cdc</sub>(R<sub>Lbat</sub> + R<sub>C</sub> + R<sub>Bat</sub>) + CL<sub>Bat</sub>]+CI<sup>0</sup><sub>Bat</sub>[L<sub>Bat</sub>(R<sub>LConv</sub> + R<sub>C</sub>) + L<sub>Conv</sub>(R<sub>LBat</sub> + R<sub>C</sub> + R<sub>Bat</sub>)]]</td><td></td><td></td></tr><tr><td>β<sub>5</sub></td><td>1/CC<sub>DC</sub>L<sub>Bat</sub>L<sub>Conv</sub>[D<sup>0</sup>V<sup>0</sup><sub>VA,DC</sub>[C<sub>DC</sub>R<sub>Cdc</sub> + C(R<sub>Lbat</sub> + R<sub>C</sub> + R<sub>Bat</sub>)]+I<sup>0</sup><sub>Bat</sub>[L<sub>Bat</sub> + L<sub>Conv</sub> + C[R<sub>LConv</sub>(R<sub>LBat</sub> + R<sub>C</sub> + R<sub>Bat</sub>) + R<sub>C</sub>(R<sub>LBat</sub> + R<sub>Bat</sub>)]]</td><td></td><td></td></tr><tr><td>β<sub>3</sub></td><td>(L<sub>Bat</sub>(R<sub>LConv</sub> + R<sub>C</sub>) + L<sub>Conv</sub>(R<sub>Lbat</sub> + R<sub>C</sub> + R<sub>Bat</sub>) + L<sub>Bat</sub>R<sub>Cdc</sub>(D<sup>0</sup>)<sup>2</sup>)/L<sub>Bat</sub>L<sub>Conv</sub></td><td></td><td></td></tr><tr><td>β<sub>2</sub></td><td>1/CC<sub>DC</sub>L<sub>Bat</sub>L<sub>Conv</sub>[C<sub>DC</sub>(L<sub>Bat</sub> + L<sub>Conv</sub>) + CC<sub>DC</sub>[R<sub>Cdc</sub>(R<sub>Lbat</sub> + R<sub>C</sub> + R<sub>Bat</sub>)(D<sup>0</sup>)<sup>2</sup>+R<sub>LConv</sub>(R<sub>Lbat</sub> + R<sub>C</sub> + R<sub>Bat</sub>) + R<sub>C</sub>(R<sub>Lbat</sub> + R<sub>Bat</sub>)] + CL<sub>Bat</sub>(D<sup>0</sup>)<sup>2</sup>]</td><td></td><td></td></tr><tr><td>β<sub>1</sub></td><td>(C<sub>DC</sub>[R<sub>Lbat</sub> + R<sub>LConv</sub> + R<sub>Bat</sub> + R<sub>Cdc</sub>(D<sup>0</sup>)<sup>2</sup>]+C(R<sub>Lbat</sub> + R<sub>C</sub> + R<sub>Bat</sub>)(D<sup>0</sup>)<sup>2</sup>)/CC<sub>DC</sub>L<sub>Bat</sub>L<sub>Conv</sub></td><td></td><td></td></tr></table>

and $I_{Bat}(z)$, the control variables $D(z)$ and $\alpha_{VA}(z)$, and determines if it is necessary to change the operating point of the IPT system. It functions during the initialization and operation of the current control loop.

Prior to initializing the current controller, $I_{Bat}$ is desired to be close to the initial reference value, which helps minimizing the transient caused by the regulator when it starts its operation. For this purpose, the minimum and maximum values of $I_{Bat}$ that are allowed to start the current control loop operation are established. The expert controller will evaluate if the measured $I_{Bat}$ is within this band, and will act according to the following criteria:

* If $|I_{Bat}(\kappa)| > |I_{max}^X|$, then $\Delta V_{exp}(\kappa) = \Delta V_{Exp}(\kappa - 1) - \Delta V$.

* If $|I_{Bat}(\kappa)| < |I_{min}^X|$, then $\Delta V_{exp}(\kappa) = \Delta V_{Exp}(\kappa - 1) + \Delta V$.

* If $|I_{min}^X| \le |I_{Bat}(\kappa)| \le |I_{max}^X|$, then $\Delta V_{Exp}(\kappa) = \Delta V_{Exp}(\kappa - 1)$ and $Exp\_Ctrl = 0$.

where $I_{min}^X$ and $I_{max}^X$ represent the minimum and maximum desired values of $I_{Bat}$ when operating in the G2V or V2G power flow directions.

This process will be repeated at regular time intervals until $I_{Bat}$ is reached or $V_{VA,DC}$ exceeds its minimum or maximum allowed values. If the former is achieved, the current control loop operation will start. Otherwise, an error signal will be triggered, stopping the system operation.

After initializing the current control loop, the expert controller will monitor if the desired value for $I_{Bat}$ can be reached. A band is generated around $I_d(\kappa)$ by using the parameter $\delta_I$ so that the measured value of $I_{Bat}(\kappa)$ falls within the range $[(1 - \delta_I)I_d(\kappa), (1 + \delta_I)I_d(\kappa)]$. If $I_{Bat}(\kappa)$ is outside this band while the minimum or maximum value of $\alpha_{VA}$ ($\alpha_{VA,min}$ and $\alpha_{VA,max}$) is exceeded, the expert controller determines that an adaptation of the IPT system must occur. For this purpose, the current controller operation is interrupted, $Exp\_Ctrl = 1$, and the following rules apply:
<figure><img src="image_6.png" /><figcaption>Fig. 6: Block diagram of the current control loop.</figcaption></figure>

* If $|I_{Bat}(\kappa)| > (1 + \delta_I)|I_d(\kappa)|$ and $\alpha_{VA} > \alpha_{VA,max}$, then $\alpha_{Exp}(\kappa) = \alpha_{VA,max} - 5^{\circ}$ and $\Delta V_{Exp}(\kappa) = \Delta V_{Exp}(\kappa - 1) - \Delta V$.

* If $|I_{Bat}(\kappa)| < (1 - \delta_I)|I_d(\kappa)|$ and $\alpha_{VA} < \alpha_{VA,min}$, then $\alpha_{Exp}(\kappa) = \alpha_{VA,min} + 5^{\circ}$ and $\Delta V_{Exp}(\kappa) = \Delta V_{Exp}(\kappa - 1) + \Delta V$.

* Otherwise, $Exp\_Ctrl = 0$.

When the expert controller determines that the target $I_{Bat}$ can be followed ($Exp\_Ctrl = 0$), the current controller resumes its operation. During the adaptation process, an error signal will be triggered if $V_{VA,DC}$ falls outside its minimum or maximum allowed values.

## V. EXPERIMENTAL RESULTS

With the aim of validating the proposed IPT system operation, the experimental setup shown in Fig. 7 was assembled. Two 16 kW Regatron TC.GSS DC voltage sources were employed to emulate both the 400V GA DC bus connection and the 220V EV battery. Two CGD15FB45P1 SiC MOSFET Driver and two CCS050M12CM2 three-phase SiC Power Module from Wolfspeed were used for the GA and VA H-bridge inverters and the DC-DC converter MOSFET branch. In the GA, only two branches of the three-phase module were employed while, in the VA, two branches were used for the H-bridge inverter and the remaining one was utilized for the DC-DC converter, achieving a compact solution.

The control algorithms were implemented in a dSPACE MicroLabBox control platform with a $T_s = 100$ µs and the operating frequency of the IPT system was set to $f_0 = 81$ kHz. The experimental data was recorded in the control platform and a Yokogawa DL 850 ScopeCorder. The parameters of the IPT system are collected in TABLE II, while those of the DC-DC converter are presented in TABLE III. The design of the PI and PID controllers was accomplished using

<table><caption>TABLE II: Registered values for the LCC-Compensated IPT system.</caption><thead><tr><td>Parameter</td><td>Value</td><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>L<sub>1</sub> (μH)</td><td>157.70</td><td>L<sub>2</sub> (μH)</td><td>158.71</td></tr><tr><td>C<sub>1</sub> (nF)</td><td>38.33</td><td>C<sub>2</sub> (nF)</td><td>34.21</td></tr><tr><td>C<sub>f1</sub> (nF)</td><td>66.42</td><td>C<sub>f2</sub> (nF)</td><td>89.99</td></tr><tr><td>L<sub>f1</sub> (μH)</td><td>51.6</td><td>L<sub>f2</sub> (μH)</td><td>39.92</td></tr></tbody></table>

<table><caption>TABLE III: Registered values for the DC-DC converter.</caption><thead><tr><td>Parameter</td><td>Value</td><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>L<sub>Conv</sub> (mH)</td><td>1.05</td><td>L<sub>Bat</sub> (μH)</td><td>102</td></tr><tr><td>C<sub>DC</sub> (μF)</td><td>890.94</td><td>C<sub>1</sub> (μF)</td><td>2.01</td></tr><tr><td>R<sub>LConv</sub> (mΩ)</td><td>265</td><td>R<sub>LBat</sub> (mΩ)</td><td>180</td></tr><tr><td>R<sub>Cdc</sub> (mΩ)</td><td>214</td><td>R<sub>C</sub> (mΩ)</td><td>58</td></tr></tbody></table>

the *Control System Designer* tool from MATLAB, and the control gains are displayed in TABLE IV. It is worth to mention that in the voltage control loop the same gains could be employed since the plant $P_{Vva}(z)$ did not exhibit a significant variation. However, in the plant $P_{Ibat}(z)$ there was a change in the sign depending on whether the system operates in the G2V or the V2G power flow direction. Therefore, different gains were chosen for each power mode. The minimum and maximum allowed values for $V_{VA,DC}$ and $\alpha_{VA}$ were set to 200 V and 450 V and 3° and 85°, respectively.

<table><caption>TABLE IV: Control Gains</caption><thead><tr><th rowspan="2">Gain</th><th rowspan="2">Value</th><th rowspan="2">Gain</th><th colspan="2">Value</th></tr><tr><th>G2V</th><th>V2G</th></tr></thead><tbody><tr><td>K<sub>PV</sub></td><td>-0.0005</td><td>K<sub>P</sub></td><td>-0.00475</td><td>0.00475</td></tr><tr><td>K<sub>IV</sub></td><td>-2.5 · 10<sup>-5</sup></td><td>K<sub>I</sub></td><td>-0.00025</td><td>0.00025</td></tr><tr><td>K<sub>A</sub></td><td>0.001</td><td>K<sub>D</sub></td><td>-0.02025</td><td>0.02025</td></tr></tbody></table>
<figure><img src="image_7.png" /><figcaption>Fig. 7: Experimental setup: (1) GA H-bridge inverter, (2) GA compensation network, (3) GA coil, (4) VA coil, (5) VA compensation network, (6) VA on-board electronics, (7) dSPACE MicroLabBox rack, (8) ScopeCorder and (9) DC voltage sources.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 8: Experimental waveforms of $I_{Bat}$ (up) and $V_{VA,DC}$ (down) for an air gap of (a) 100 mm (G2V) and (b) 180 mm (V2G).</figcaption></figure>

The experimental validation was carried out with two different coil separations: 100 mm and 180 mm with $k$ values of $k = 0.4447$ and $k = 0.2014$, respectively. Therefore, a magnetic coupling coefficient variation of more than 100% is achieved. Both configurations were tested with the same programmed scenario:

1. The DC-DC converter operation is enabled at $t = 0$ s with $D^0 = 0.93$.

2. The IPT system operation is enabled at $t = 500$ ms with $\alpha_{VA}^0 = 80^\circ$ (G2V) or $\alpha_{VA}^0 = 75^\circ$ (V2G).

3. The voltage control loop is activated with $V_{VA,DC}^* = 250$ V at $t = 1$ s.

4. The current regulation is enabled at $t = 1.5$ s.

5. The expert controller initializes the current control loop with $I_{Bat}^* = 4$ A (G2V) or $I_{Bat}^* = -4$ A (V2G).

6. The value of $I_{Bat}^*$ changes to 13.6 A (G2V) or -13.6 A (V2G).

7. $I_{Bat}^*$ returns to 4 A (G2V) or -4 A (V2G).

Fig. 8.a presents the experimental data recorded when an air gap of 100 mm was employed in the G2V power flow direction. At this operating point, the battery
current is already within the [2, 6] A range established
for the initialization of the current control loop. Conse-
quently, when the expert controller starts its operation in
step 4, it quickly determines that the current controller
can be initialized in step 5. Following a minor transient
due to the regulator initialization, the reference is tracked
by modifying α<sub>VA</sub>. Then, the transition from 4 A to
13.6 A (≈ 3 kW) is achieved smoothly, as in the last
step. Throughout this process, the voltage control loop
successfully maintains V<sub>VA,DC</sub> at the initial reference
voltage by adjusting D.

In the second experiment, shown in Fig. 8.b, the
decrease in k caused the IPT system to significantly
reduce the maximum power transferred for the initial
V<sub>VA,DC</sub>. When the expert controller begins its operation
in step 4, the initial current is outside the [-6, -2] A
band. As a result, the reference voltage is modified twice
until I<sub>Bat</sub> enters the range at V<sub>Ref</sub> = 270 V. At this
point, step 5 is reached and the current controller is
initialized. At this operating point, the -13.6 A reference
current cannot be reached. Therefore, when the system
approaches this value, the expert control layer detects
a deviation of I<sub>Bat</sub> from I<sub>d</sub> while α<sub>VA,min</sub> is reached.
Hence, the expert controller halts the operation of the
current control loop and modifies V<sub>Ref</sub> until 370 V are
reached. At this new operating point, the target I<sub>Bat</sub> can
be achieved and the operation of the current controller
resumes. Finally, the step from -13.6 A to -4 A is
followed satisfactorily. It is possible to find a more noisy
I<sub>Bat</sub> in Fig. 8.b. According to other experiments carried
out in the laboratory in open-loop operation that are
out of the scope of the article, it was inferred that the
cause is an interaction between the IPT system and the
DC voltage source that models the battery pack at some
operating points.

VI. CONCLUSION

In this work, an adaptive operation for a bidirectional
IPT system designed for the wireless charging of EVs
was proposed. For this purpose, two different control
loops were implemented for regulating the VA DC bus
voltage and the EV battery current. The adaptability
feature was provided by an expert controller located in
a higher control layer that monitors the operation of the
two implemented control loops and determines if it is
necessary to adapt the system operation.

The mathematical description of the IPT system was
presented, as well as the operation of each implemented
controller. The validation of the system operation was
carried out using a 3 kW experimental prototype. Ex-
perimental results have shown a robust operation of the

system for variations of *k* of more than 100%, with
smooth transitions when tracking the reference current
and a stable VA DC bus voltage.

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