Dual-Loop PI Control for a Dynamic Wireless Electric Vehicle Charging System with Dual-transmitters using 3D Modeling of DD Coils

Summary

This work presents a simulation-based dynamic wireless power transfer (DWPT) system using a double-D (DD) coil structure in a dual-transmitter single-receiver (DTSR) topology and dual-loop proportional–integral (PI) control strategy, demonstrating regulated voltage and power delivery under coupling variation, misalignment effects, and a 150 mm air gap.

Abstract

Dynamic wireless power transfer (DWPT) is an emerging technology for supplying electric vehicles (EVs) with energy while in motion; however, its performance is significantly affected by coupling variation, coil misalignment, and load fluctuations. To address these challenges, this study presents a simulation-based protocol that integrates electromagnetic modeling, circuit-level co-simulation, and coordinated control evaluation for a dual-transmitter single-receiver (DTSR) DWPT system. The methodology begins with three-dimensional electromagnetic modeling of a double-D (DD) coil configuration using a finite-element solver to characterize self- and mutual-inductance variations under misalignment conditions. These parameters are then incorporated into a resonant circuit model to optimize power transfer performance. The complete DTSR system is subsequently implemented in a system-level simulation environment, where a dual-loop proportional–integral (PI) control strategy is applied to regulate output voltage and power under time-varying coupling conditions. The results demonstrate stable power delivery and effective regulation performance across dynamic operating scenarios, including a fixed air gap of 150 mm and varying misalignment conditions. The proposed framework enables systematic evaluation of system dynamics, control response, and power stability. This protocol provides a structured and reproducible workflow for analyzing and validating DTSR-based DWPT systems and supports the development of robust control strategies for dynamic EV charging applications.

Introduction

Electric vehicles (EVs) have emerged as a competitive alternative for transportation due to their advantages in environmental friendliness, isolation, and safety^1,2. However, EVs face several constraints, most notably limited battery autonomy, which results in restricted driving range, high cost, and lengthy charging times^3,4. Wireless power transfer (WPT) technology is considered a key enabler for overcoming these limitations by providing convenient and continuous energy supply. This charging technology can be categorized into two groups: static charging, where the vehicle is stationary over the charger, and dynamic wireless power transfer (DWPT), which enables power transmission while EVs are in motion^5–8. DWPT has emerged as a promising approach for reducing battery dependency, improving mobility, and saving time⁹.

In EV-DWPT technology, the primary research areas include coil design and system topology. Various coil structures have been proposed, among which the double-D (DD) coil is widely adopted for EV-DWPT applications¹⁰. Coil sizing and optimization with respect to coupling coefficient, cost, and efficiency have been extensively studied^11,12. In addition, modular EV-DWPT topologies with different configurations have been investigated to maintain high efficiency^13–16. The efficiency of EV-DWPT systems is strongly influenced by the design of transmitter and receiver pads^10,17,18, as coil geometry affects coupling coefficient, self-inductance, misalignment tolerance, electromagnetic field (EMF) exposure, and power transmission characteristics¹⁹. Design parameters include coil geometry, shielding, materials, axial and lateral misalignment, and dimensions. Although several pad geometries exist (circular, rectangular, DD, DDQ, etc.), DD pads are widely used due to their high mutual inductance (M) and industry adoption, as recommended by the Society of Automotive Engineers (SAE J2954)²⁰. Recent studies have investigated the calculation of self- and mutual inductance under misalignment conditions using analytical, numerical, experimental, and simulation approaches^21–25.

Most existing research focuses on conventional single-transmitter single-receiver (STSR) EV-DWPT systems, which face limitations in high-power applications and rapid charging capability^16,26. To address these limitations, dual-transmitter single-receiver (DTSR) configurations have been proposed to increase power transfer capacity by providing multiple transmission paths. Optimized DTSR designs using DD coils with LCC compensation have been developed to enhance power transfer efficiency²⁷, while theoretical modeling and impedance matching techniques have been investigated to further improve performance under dynamic conditions²⁸. However, misalignment reduction in multi-transmitter systems remains a significant challenge, and various design strategies have been proposed to mitigate this issue²⁹. Additionally, DTSR systems operating at a common resonance frequency with energy-saving techniques have been introduced and experimentally validated³⁰.

Despite these advancements, optimal system performance in EV-DWPT cannot be achieved without effective control strategies. Control methods are generally classified into primary-side, secondary-side, and dual-side control approaches³¹. For instance, a DC–DC converter with a proportional–integral (PI) controller has been used on the secondary side to regulate output voltage under varying load and coupling conditions³². On the primary side, the phase-shift angle of the full-bridge inverter is commonly controlled to regulate power transfer while maintaining zero-voltage switching (ZVS) at resonance^33,34,35. However, existing DTSR DWPT studies typically address electromagnetic design, resonant compensation, or control strategies separately. In contrast, this work integrates these components within a unified system-level framework to evaluate their combined impact under dynamic operating conditions.

The proposed procedure combines three-dimensional finite-element modeling and magnetic optimization of DD coils, circuit-level co-simulation for compensation network design and efficiency assessment, and coordinated control implementation using a dual-loop PI structure. The inner control loop regulates the secondary-side DC–DC buck converter to stabilize the load voltage under variable conditions, while the outer loop adjusts the phase shift of the primary-side full-bridge inverter to achieve adaptive power transfer in response to coupling variations.

The system adopts a series–series (SS) compensation network to minimize reactive power at resonance and improve overall efficiency, with the operating frequency fixed at 85 kHz to ensure consistent parameter evaluation³⁶. Rather than proposing a new control algorithm, this study's contribution lies in the systematic integration of a conventional dual-loop PI controller into a complete electromagnetic–circuit–control co-simulation framework for DTSR DWPT systems, enabling coordinated voltage and current regulation.

The resulting framework demonstrates stable power delivery under representative dynamic charging conditions and extends the applicability of established dual-loop PI control strategies to DTSR EV charging systems. The proposed methodology is particularly suitable for resonant inductive EV charging systems with similar pad geometries and operating conditions, though adaptation may be required for non-resonant architectures or highly nonlinear, time-varying loads. A workflow diagram illustrating the simulation stages is provided in Figure 1.

Protocol

The research tools employed are listed in the Table of Materials.

1. 3D finite-element modeling of DD coils

The electromagnetic modeling and optimization of transmitter and receiver DD coils were implemented using a 3D finite-element electromagnetic solver. The transmitter coil dimensions were optimized by sweeping length and width, while the receiver coil dimensions and the distance between the coils were kept fixed. The magnetic coupling between both sides was measured, and its mathematical representation is given by³¹:

   (1)

where  represents the coupling coefficient describing magnetic coupling between the coils,  denotes the self-inductance of the transmitter coil, and  represents the self-inductance of the receiver coil.

Based on the recorded maximum magnetic coupling, the transmitter length and width were selected. The receiver coil was designed with a smaller width than the transmitter to improve misalignment tolerance and mid-range coupling²⁹. The optimized dimensions and specifications were presented in Figure 2 and Table 1.

During modeling, the coils were excited with sinusoidal current sources at 85 kHz, and magnetic resonance coupling was enabled via series compensation capacitors. Adaptive meshing was employed, with refinement concentrated in regions of high magnetic field intensity, particularly around the transmitter and receiver coils. The self-inductance, mutual inductance, and coupling coefficient were directly extracted from the field solutions using built-in parameter-extraction tools.

2. WPT circuit co-simulation

To evaluate the system power transfer efficiency (PTE) at the selected frequency, the extracted electromagnetic parameters were imported into a circuit simulation environment (see Table of Materials), and WPT circuit co-simulation was performed. A time-domain circuit solver was used to simulate the interaction between the power electronic converter and the coupled coil model under dynamic operating conditions. The compensation elements were tuned to satisfy the resonance condition defined by:

    .(2)

where  represents the primary compensation component.

The air gap between the coils was fixed at 150 mm. The maximum PTE was estimated at approximately 0.0851 MHz as the operating frequency under the given spacing constraints. The maximum PTE was estimated at approximately 0.0851 MHz at an operating frequency under the given spacing constraints. The results indicated that magnetic resonance-based coupling achieved higher efficiency at mid-range distances compared to alternative wireless power transfer approaches, supporting its suitability for dynamic charging applications.

3. DWPT system implementation

The 3D coil model of the DTSR system implemented in the finite-element electromagnetic solver was presented in Figure 3. The receiver coil motion was defined along the Y-axis (lateral misalignment), while the X-axis displacement was assumed to be zero. The Z-axis represented the air gap between the coils, which was set to 150 mm. The mutual inductance became a function of displacement, expressed as .

The receiver coil moved from (0, −80, 150) mm to (0, 1400, 150) mm in the xyz coordinate system, resulting in a total lateral displacement of 2700 mm along the Y-axis. The simulation was performed to evaluate the variation of with lateral misalignment. The numerical results presented in Figure 4 and Supplementary Table 1 indicated peak mutual inductance at positions 9 and 22, corresponding to alignment with transmitter 1 and transmitter 2, respectively.

The circuit diagram of the proposed DWPT system was shown in Figure 5. The system consisted of two grounded transmitters  and  , and one moving receiver . The transmitters were supplied by a DC source connected to a full-bridge inverter, which converted DC voltage into high-frequency AC required for magnetic resonance coupling. The output was fed into a compensation network to achieve resonance, improve efficiency, and enhance power transfer³⁷. Common compensation topologies were discussed in previous studies³⁸.

The proposed system adopted a series–series (SS) compensation network, which minimized impedance at resonance and reduced reactive power. Capacitors  and  formed the primary compensation network, while  represented the secondary compensation component.

The DWPT system was simulated at the system level using the parameters given in Table 2. The induced voltage depended on the mutual inductance , which varied with coil displacement during motion. The system behavior under varying lateral displacement was analyzed by observing mutual inductance, voltage, and current in both transmitter and receiver coils. For simulation purposes, a vehicle speed of 27 m s⁻¹ (~60 mph) was used.

The mutual inductance, transmitter voltage, and current are shown in Figure 6, where a zero-phase shift indicates operation at resonance. The receiver voltage and current were presented in Figure 7. The load voltage and current are shown in Figure 8, and the output power is shown in Figure 9. Variations in load characteristics were observed due to changes in mutual inductance and coupling coefficient, which were addressed through the control strategy described in the next section.

4. Control methodology

A dual-side control approach was employed due to its effectiveness in enhancing power transfer and system efficiency under varying coupling conditions^39,40. A dual-loop proportional–integral (PI) control strategy was adopted to regulate both voltage and current.

The controller parameters were selected based on cascade control design principles rather than empirical tuning. The inner current loop, associated with the secondary-side DC–DC buck converter, was designed with a higher bandwidth to ensure fast response and disturbance rejection. The outer loop, controlling the primary-side phase-shift full-bridge (PSFB) inverter, operated at a lower bandwidth to maintain loop decoupling.

The PSFB control strategy involved continuous measurement of output voltage or current at the receiver, which was fed back to the inverter. The output power was controlled by adjusting the phase shift between the inverter legs, with a larger phase shift resulting in increased power transfer. The PI controller determined the required phase shift and generated pulse-width modulation (PWM) signals for switching control. The overall control structure was illustrated in Figure 10.

The control system was implemented in a discrete-time simulation environment with a fixed sampling period sufficient to capture the 85 kHz switching dynamics. Controller gains were tuned to achieve stable operation with minimal overshoot and acceptable settling time under variations in load and coupling conditions, while maintaining adequate stability margins.

Validation of the control design was achieved when the cascaded PI structure produced rapid, smooth voltage recovery under disturbances and when the inner current loop responded faster than the outer voltage loop. Deviations from these characteristics indicated potential inconsistencies in parameter extraction, compensation tuning, or controller configuration.

Results

Coil optimization sweep
The dimensions of the primary and secondary DD coils were determined based on the parametric sweeping procedure described in the protocol. The measured magnetic coupling between both sides during primary coil dimension sweeping indicated that the maximum coupling coefficient was achieved at a transmitter length of 500 mm and a width of 370 mm, with values of 0.349204 and 0.337464, respectively, as shown in Figure 11. Based on these results, the op...

Discussion

The main research gap addressed in this work concerned the limited dynamic stability and regulation accuracy of conventional single-loop or uncontrolled DWPT systems, particularly under load variations and coupling fluctuations caused by vehicle motion, as highlighted in previous studies on dynamic wireless charging systems^7,8. The results demonstrated that the proposed dual-loop PI control architecture for the DTSR configuration directly addressed this limitatio...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
ANSYS Electronics Desktop (Maxwell 3D)	Ansys, Inc.Maxwell  (version 2018)	N/A	Integrated electromagnetic platform hosting ANSYS Maxwell  used for finite-element electromagnetic modeling of DWPT coils
ANSYS Electronics Desktop (Simplorer)	Ansys, Inc.Simplorer  (version 2018)	N/A	Commercial circuit-level simulator used to implement resonant DWPT model
MATLAB/Simulink	MathWorks, Inc.(version R2023b)	N/A	Control design and simulation environment used for controller implementation and dynamic system simulation