Effect of pulsed current on charging performance of lithium-ion batteries

IEEE Transactions on Industrial Electronics

Published On 2021/10/27

The pulsed current has been proposed as a promising battery charging technique to improve the charging performance and maximize the lifetime for lithium-ion (Li-ion) batteries. However, the effect of the pulsed current charging is inconclusive due to the changeable current mode and conditions. This article systematically investigates the effect of various pulsed current charging modes, i.e., positive pulsed current mode, pulsed current-constant current mode, negative pulsed current mode, alternating pulsed current mode, sinusoidal-ripple current mode, and alternating sinusoidal-ripple current mode on battery performance. Moreover, a comprehensive analysis of the frequency impact on the quality of the current mode is performed. The current modes in this work are evaluated considering the maximum rising temperature, discharging capacity, and charging speed according to experimental results. Furthermore …

Journal

IEEE Transactions on Industrial Electronics

Published On

2021/10/27

Volume

69

Issue

10

Page

10144-10153

Authors

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

Position

Professor at

H-Index(all)

104

H-Index(since 2020)

72

I-10 Index(all)

0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

Cited By

0

Research Interests

Power Electronics

Smart Batteries

AI

University Profile Page

Daniel Stroe

Daniel Stroe

Aalborg Universitet

Position

Head of Battery Storage Systems Research Programme at

H-Index(all)

49

H-Index(since 2020)

46

I-10 Index(all)

0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

Cited By

0

Research Interests

Lithium-ion Batteries

Energy Storage

Electric Vehicles

Renewable Energy

Energy Management

University Profile Page

Wenjie Liu

Wenjie Liu

Aalborg Universitet

Position

H-Index(all)

12

H-Index(since 2020)

11

I-10 Index(all)

0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

Cited By

0

Research Interests

power electronics

University Profile Page

Other Articles from authors

Daniel Stroe

Daniel Stroe

Aalborg Universitet

Data in Brief

Dataset of lithium-ion battery degradation based on a forklift mission profile for state-of-health estimation and lifetime prediction

Lithium-ion (Li-ion) batteries are becoming an increasingly integral part of modern society, through consumer electronics, stabilisation of the electric grid, and electric vehicles. However, Lithium-ion batteries degrade in effectiveness over time; a degradation which is extremely dependent on the usage of the battery. Therefore, to study how a battery cell degrades under dynamic conditions, a realistic load profile was constructed based on the operation of forklifts. This profile was used to age three Lithium-ion battery cells at 45, 40, and 35°C and the response of the cells was measured on a second-by-second basis. Periodically the ageing was halted to perform a reference test of the cells allowing for the tracking of their degradation.

Daniel Stroe

Daniel Stroe

Aalborg Universitet

On the Use of Randomly Selected Partial Charges to Predict Battery State-of-Health

As society becomes more reliant on Lithium-ion (Li-ion) batteries, state-of-health (SOH) estimation will need to become more accurate and reliable. Therefore, SOH modelling is in the process of shifting from using simple and continuous charge/discharge profiles, to more dynamic profiles constructed to mimic real operation, when ageing the Li-ion batteries. However, in most cases, when ageing the batteries, the same exact profile is just repeated until the battery reaches its end-of-life. Using data from batteries aged in this fashion to build a model, there is a very real possibility that the model will rely on the built-in repetitiveness of the profile. Therefore, this work will examine the dependence of the performance of a multiple linear regression on the number of charges used to train the model, and their location within the profile used to age the batteries. The investigation shows that it is possible to build models using randomly selected partial charges while still reaching errors as low as 0.5%. Furthermore, it shows that only two randomly sampled partial charges are needed to achieve errors of less than 1%. Lastly, as the number of randomly sampled partial charges used to create the model increases, then the dependence on particular partial charges tends to decrease.

Daniel Stroe

Daniel Stroe

Aalborg Universitet

Batteries

Lithium-Ion Supercapacitors and Batteries for Off-Grid PV Applications: Lifetime and Sizing

The intermittent nature of power generation from photovoltaics (PV) requires reliable energy storage solutions. Using the storage system outdoors exposes it to variable temperatures, affecting both its storage capacity and lifespan. Utilizing and optimizing energy storage considering climatic variations and new storage technologies is still a research gap. Therefore, this paper presents a modified sizing algorithm based on the Golden Section Search method, aimed at optimizing the number of cells in an energy storage unit, with a specific focus on the unique conditions of Denmark. The considered energy storage solutions are Lithium-ion capacitors (LiCs) and Lithium-ion batteries (LiBs), which are tested under different temperatures and C-rates rates. The algorithm aims to maximize the number of autonomy cycles—defined as periods during which the system operates independently of the grid, marked by intervals between two consecutive 0% State of Charge (SoC) occurrences. Testing scenarios include dynamic temperature and dynamic load, constant temperature at 25 °C, and constant load, considering irradiation and temperature effects and cell capacity fading over a decade. A comparative analysis reveals that, on average, the LiC storage is sized at 70–80% of the LiB storage across various scenarios. Notably, under a constant-temperature scenario, the degradation rate accelerates, particularly for LiBs. By leveraging the modified Golden Section Search algorithm, this study provides an efficient approach to the sizing problem, optimizing the number of cells and thus offering a potential solution for energy storage in off-grid PV systems.

Daniel Stroe

Daniel Stroe

Aalborg Universitet

Journal of Energy Storage

Identification of the aging state of lithium-ion batteries via temporal convolution network and self-attention mechanism

Deep learning methods have been widely used for battery aging state estimation with either manual or automatic features, while the contribution of multi-source features is rarely considered. To solve this problem, a hybrid method is proposed to combine the manual and automatic features based on a temporal convolution network (TCN) and a self-attention mechanism (SA). Specifically, the local voltage, capacity, and incremental capacity are manually extracted as battery aging features. Then, for extracting automatic features, TCN employs dilated convolution to capture the capacity regeneration phenomenon during battery degradation. Considering the contribution of multi-source features, we use SA to fuse the obtained manual and automatic features. Finally, the available capacity and remaining useful life of the battery are predicted using a fully connected neural network on one dataset from our lab, the Oxford …

Daniel Stroe

Daniel Stroe

Aalborg Universitet

Battery state-of-health estimation using machine learning

Over the years, lithium–ion batteries have developed as a key enabling technology for the green transition. Although many of these batteries’ characteristics, such as energy density, power capability, and cost, have gradually improved, uncertainties remain concerning their performance over their lifetimes. Thus, to ensure reliable and efficient battery operation, the battery's available performance, known as its state of health (SOH), must be known at every moment. This chapter introduces the most common battery SOH estimation methods, from direct measurements to deep neural networks, discussing their key performance metrics, advantages, and drawbacks.

Daniel Stroe

Daniel Stroe

Aalborg Universitet

Advanced Energy Materials

Unravelling the Mechanism of Pulse Current Charging for Enhancing the Stability of Commercial LiNi0.5Mn0.3Co0.2O2/Graphite Lithium‐Ion Batteries

The key to advancing lithium‐ion battery (LIB) technology, particularly with respect to the optimization of cycling protocols, is to obtain comprehensive and in‐depth understanding of the dynamic electrochemical processes during battery operation. This work shows that pulse current (PC) charging substantially enhances the cycle stability of commercial LiNi0.5Mn0.3Co0.2O2 (NMC532)/graphite LIBs. Electrochemical diagnosis unveils that pulsed current effectively mitigates the rise of battery impedance and minimizes the loss of electrode materials. Operando and ex situ Raman and X‐ray absorption spectroscopy reveal the chemical and structural changes of the negative and positive electrode materials during PC and constant current (CC) charging. Specifically, Li‐ions are more uniformly intercalated into graphite and the Ni element of NMC532 achieves a higher energy state with less Ni─O bond length variation …

Daniel Stroe

Daniel Stroe

Aalborg Universitet

Thermal state monitoring of lithium-ion batteries: Progress, challenges, and opportunities

Transportation electrification is a promising solution to meet the ever-rising energy demand and realize sustainable development. Lithium-ion batteries, being the most predominant energy storage devices, directly affect the safety, comfort, driving range, and reliability of many electric mobilities. Nevertheless, thermal-related issues of batteries such as potential thermal runaway, performance degradation at low temperatures, and accelerated aging still hinder the wider adoption of electric mobilities. To ensure safe, efficient, and reliable operations of lithium-ion batteries, monitoring their thermal states is critical to safety protection, performance optimization, as well as prognostics, and health management. Given insufficient onboard temperature sensors and their inability to measure battery internal temperature, accurate and timely temperature estimation is of particular importance to thermal state monitoring. Toward …

Daniel Stroe

Daniel Stroe

Aalborg Universitet

State-of-energy balancing control with cascaded H-bridge for second-life batteries

Battery energy storage systems (BESS) are fre-quently utilized to support the power grid. Second-Life batteries (SLBs) are considered as a potential solution to reduce the cost of BESS in stationary applications. However, using SLBs has certain challenges due to the non-uniform State-of-Charge (SOC) and State-of-Health (SOH) among the battery modules. This study examines two control strategies for a cascaded H-bridge (CHB) topology used for BESS applications. The possibilities for flexible control of the BESS are enabled by employing a CHB topology. By utilizing the CHB topology, each battery module can be individually charged and discharged. Two battery energy management system (BEMS) techniques are proposed based on the batteries' State-of-Energy (SOE): 1) continuous and 2) discrete balancing techniques. The experimental tests demonstrate the advantages of the proposed solutions in terms of …

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

IEEE Transactions on Industrial Electronics

Health Prediction for Lithium-Ion Batteries Under Unseen Working Conditions

Battery health prediction is significant while challenging for intelligent battery management. This article proposes a general framework for both short-term and long-term predictions of battery health under unseen dynamic loading and temperature conditions using domain-adaptive multitask learning (MTL) with long-term regularization. First, features extracted from partial charging curves are utilized for short-term state of health predictions. Then, the long-term degradation trajectory is directly predicted by recursively using the predicted features within the multitask framework, enhancing the model integrity and lowering the complexity. Then, domain adaptation (DA) is adopted to reduce the discrepancies between different working conditions. Additionally, a long-term regularization is introduced to address the shortcoming that arises when the model is extrapolated recursively for future health predictions. Thus, the short …

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

IEEE/ASME Transactions on Mechatronics

Online Sensorless Temperature Estimation of Lithium-Ion Batteries Through Electro-Thermal Coupling

Owing to the nonnegligible impacts of temperature on the safety, performance, and lifespan of lithium-ion batteries, it is essential to regulate battery temperature to an optimal range. Temperature monitoring plays a fundamental role in battery thermal management, yet it is still challenged by limited onboard temperature sensors, particularly in large-scale battery applications. As such, developing sensorless temperature estimation is of paramount importance to acquiring the temperature information of each cell in a battery system. This article proposes an estimation approach to obtain the cell temperature by taking advantage of the electrothermal coupling effect of batteries. An electrothermal coupled model, which captures the interactions between the electrical and the thermal dynamics, is established, parameterized, and experimentally validated. A closed-loop observer is then designed based on this coupled model …

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

Artificial Intelligence-Based State-of-Health Estimation of Lithium-Ion Batteries

The State of Health (SOH) estimation for automotive batteries is currently assessed with different techniques which may involve long testing procedure or require costly hardware to be implemented. This paper aims at contributing to this domain by exploiting the response of a lead-acid battery with respect to a short-term current profile using an Artificial Neural Network (ANN) classifier for SOH estimation. The method is applicable onboard the vehicle and no additional instrumentation is required on the retained vehicle. The design and validation of a SOH method with a short-term current profile using Artificial Intelligence (AI) in lead-acid batteries, which are commonly used in heavy-duty vehicles for cranking and cabin systems, are presented. The paper validates the considered approach with experimental data, which are representative of actual vehicle operations. In detail, the paper describes the retained …

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

arXiv preprint arXiv:2402.07777

Novel Low-Complexity Model Development for Li-ion Cells Using Online Impedance Measurement

Modeling of Li-ion cells is used in battery management systems (BMS) to determine key states such as state-of-charge (SoC), state-of-health (SoH), etc. Accurate models are also useful in developing a cell-level digital-twin that can be used for protection and diagnostics in the BMS. In this paper, a low-complexity model development is proposed based on the equivalent circuit model (ECM) of the Li-ion cells. The proposed approach uses online impedance measurement at discrete frequencies to derive the ECM that matches closely with the results from the electro-impedance spectroscopy (EIS). The proposed method is suitable to be implemented in a microcontroller with low-computational power, typically used in BMS. Practical design guidelines are proposed to ensure fast and accurate model development. Using the proposed method to enhance the functions of a typical automotive BMS is described. Experimental validation is performed using large prismatic cells and small-capacity cylindrical cells. Root-mean-square error (RMSE) of less than 3\% is observed for a wide variation of operating conditions.

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

IEEE Transactions on Industrial Informatics

A Battery Digital Twin From Laboratory Data Using Wavelet Analysis and Neural Networks

Lithium-ion (Li-ion) batteries are the preferred choice for energy storage applications. Li-ion performances degrade with time and usage, leading to a decreased total charge capacity and to an increased internal resistance. In this article, the wavelet analysis is used to filter the voltage and current signals of the battery to estimate the internal complex impedance as a function of state of charge (SoC) and state of health (SoH). The collected data are then used to synthesize a battery digital twin (BDT). This BDT outputs a realistic voltage signal as a function of SoC and SoH inputs. The BDT is based on feedforward neural networks trained to simulate the complex internal impedance and the open-circuit voltage generator. The effectiveness of the proposed method is verified on the dataset from the prognostics data repository of NASA.

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

IEEE Transactions on Industry Applications

Small-Sample-Learning-Based Lithium-Ion Batteries Health Assessment: An Optimized Ensemble Framework

Machine Learning is widely studied in battery state of health (SOH) estimation due to its advantage in establishing the non-linear mapping between measurements and SOH. However, the requirement of a big dataset and the lack of robustness limit the practical application, especially in small sample learning. To tackle these challenges, an optimal ensemble framework called BaggELM (bagging extreme learning machine) is proposed for battery SOH estimation. Specifically, the required dataset is reduced by optimizing the input voltage and the hyperparameters of the BaggELM algorithm. Moreover, a statistical post-processing method is used to aggregate multiple ELMs, and the final estimate is determined by the maximum probability density value. As a result, the effects of random parameterization of ELM and the training data size on SOH estimation are suppressed, thus improving the robustness and accuracy of …

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

Intelligent Cell Balancing Control for Lithium-Ion Battery Packs

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Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

Grid Impedance Shaping for Grid-Forming Inverters: A Soft Actor-Critic Deep Reinforcement Learning Algorithm

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Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

Electric vehicle battery charging strategy

As a key enabler for transportation electrification and a contributor toward the net-zero carbon future, battery plays a pivotal role in determining the energy management performance of electric vehicles. Technical challenges facing the development of advanced automotive battery charging arise from various contradictory objectives, immeasurable internal states, and hard constraints. This chapter presents a critical introduction to the state-of-the-art charging strategies for the electric vehicle battery and their key enabling technologies. Specifically, battery charging solutions for electric vehicles are first classified and discussed. Then, the battery models on which these solutions rest are stated, the related charging frameworks are summarized, and the advantages and drawbacks of the adopted technologies are discussed. Suggestions for overcoming the limitations of the discussed charging strategies are proposed …

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

Thermal state monitoring of lithium-ion batteries: Progress, challenges, and opportunities

Transportation electrification is a promising solution to meet the ever-rising energy demand and realize sustainable development. Lithium-ion batteries, being the most predominant energy storage devices, directly affect the safety, comfort, driving range, and reliability of many electric mobilities. Nevertheless, thermal-related issues of batteries such as potential thermal runaway, performance degradation at low temperatures, and accelerated aging still hinder the wider adoption of electric mobilities. To ensure safe, efficient, and reliable operations of lithium-ion batteries, monitoring their thermal states is critical to safety protection, performance optimization, as well as prognostics, and health management. Given insufficient onboard temperature sensors and their inability to measure battery internal temperature, accurate and timely temperature estimation is of particular importance to thermal state monitoring. Toward …

Daniel Stroe

Daniel Stroe

Aalborg Universitet

Applied Energy

Optimal battery thermal management for electric vehicles with battery degradation minimization

The control of a battery thermal management system (BTMS) is essential for the thermal safety, energy efficiency, and durability of electric vehicles (EVs) in hot weather. To address the battery cooling optimization problem, this paper utilizes dynamic programming (DP) to develop an online rule-based control strategy. Firstly, an electrical–thermal-aging model of the LiFePO 4 battery pack is established. A control-oriented onboard BTMS model is proposed and verified under different speed profiles and temperatures. Then in the DP framework, a cost function consisting of battery aging cost and cooling-induced electricity cost is minimized to obtain the optimal compressor power. By exacting three rules” fast cooling, slow cooling, and temperature-maintaining” from the DP result, a near-optimal rule-based cooling strategy, which uses as much regenerative energy as possible to cool the battery pack, is proposed for …

Remus Teodorescu

Remus Teodorescu

Aalborg Universitet

Reliability Engineering & System Safety

Predictive health assessment for lithium-ion batteries with probabilistic degradation prediction and accelerating aging detection

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IEEE Transactions on Industrial Electronics

Robust Diagnosis of Partial Demagnetization Fault in PMSMs Using Radial Air-Gap Flux Density Under Complex Working Conditions

Partial demagnetization fault (PDF) is a common problem for permanent magnet synchronous motor (PMSM). The PMSM usually operates under complex working conditions (dynamic speed and various load), leading to the difficulty in robust PDF diagnosis. Hence, how to reliably and accurately diagnose PDF under complex working conditions has become a key issue in ensuring its safe operation. To address this issue, a robust PDF diagnosis method for PMSM is proposed based on radial air-gap flux density in this article. First, the d -axis magnetic network model of PMSM is established to extract the fault feature from the radial air-gap flux density. Then, by subtracting the offline-calculated radial air-gap flux density of stator current excitation from the online measured value, the open-circuit radial air-gap flux density can be calculated. Next, the equiangular interval resampling method is used to obtain the open …

Zhongbao Wei(魏中宝)

Zhongbao Wei(魏中宝)

Beijing Institute of Technology

IEEE Transactions on Industrial Electronics

Cathodic Supply Optimization of PEMFC System Under Variable Altitude

The efficiency of the proton exchange membrane fuel cell (PEMFC) system drops remarkably with the changed ambient pressure and temperature under variable altitudes. To enhance the adaptability of PEMFC, this article proposes a hierarchical optimal control strategy (HOCS) that guarantees the efficient operation of the PEMFC system during changes in altitude. In particular, the sparrow search algorithm (SSA) is exploited to optimize the air supply strategy under different operating conditions. To support the HOCS, a variable altitude model of PEMFC is established, which integrates the environmental impacts on components. A sliding mode controller (SMC) is employed to achieve precise and fast control of the air supply system across various situations. Comparative results validate the superiority of the proposed method in terms of the efficiency of the air compressor and the net power output. In a typical driving …

Tianliang Li

Tianliang Li

National University of Singapore

IEEE Transactions on Industrial Electronics

Modular and Fault-Tolerant Three-Axial FBG-Based Force Sensing for Transoral Surgical Robots

Transoral robotic surgery (TROS) has met a significant challenge to precise control of surgical instruments and depress the injury risks without force feedback. Therefore, we develop a modular high-precision three-axial fiber Bragg grating (FBG) force sensor with nonlinear decoupling, fault tolerance, and temperature compensation (TC) for seamless integration into transoral robots. The sensor comprises a one-body elastomer housing four optical fibers engraved with FBG each, arranged at a constant interval of 90° along the circumference to enhance three-axial force perception through redundancy. A novel dung Beetle optimization extreme learning machine (DBO-ELM) algorithm is proposed to tackle nonlinear coupling, FBG fracture, and temperature interference challenges leading to excellent performances of accurate and reliable measurement. The maximum full-scale error is less than 4% in each dimension …

Chunhua Yang

Chunhua Yang

Central South University

IEEE Transactions on Industrial Electronics

Multimodel Self-Learning Predictive Control Method With Industrial Application

In industrial sites, system operation conditions fluctuate due to changes in raw material and equipment status, making it critical to identify the operation conditions and obtain appropriate controllers accurately. Additionally, even for a specific operation condition, fixed control strategies may result in mismatches due to varying operational stages. To address the accurate control of industrial processes across multiple operation conditions, this article proposes a multimodel self-learning predictive control (MSLPC) method to simultaneously improve the accuracy of offline condition partition and online control performance. Specifically, in the offline stage, for complex and multidimensional industrial data, condition indicators are selected based on expert systems and data analytics, and a “presetting precise-fusion” two-stage operation condition learning (TSOCL) algorithm is proposed to accurately identify the operation …

Choon Ki Ahn

Choon Ki Ahn

Korea University

IEEE Transactions on Industrial Electronics

Model-Free Filter-Based Single-Loop Output-Feedback System Design for PMSMs With Critically Damped Performance

This article designs a filter-based output-feedback system to regulate the speed of permanent magnet synchronous motors (PMSMs), which structures a simple single-loop form compensated by feed-forward terms. The proposed controller design framework considerably reduces the dependence level of the PMSM model by requiring partial nominal parameter values for control law and removing the model structure and whole parameter information for the filter. The main advantages consist of two parts. First, the proposed observer employs the second-order pole-zero cancelation (PZC) technique to continuously extract the speed and acceleration from noisy position measurements by the rotary encoder, independent from the PMSM model. Second, the PZC filter-based proportional–integral control forms a single-loop feedback system including the active damping injection and disturbance observer, which assigns …

Sang-Won Lee

Sang-Won Lee

Kongju National University

IEEE Transactions on Industrial Electronics

Quasi-Resonant Fly-Buck Converter With Active Switching for Improved Output Voltage Boosting and Regulation

This article proposes a quasi-resonant fly-buck converter using an active switching operation at the isolated load side. The proposed circuit overcomes the cross-regulation and low voltage gain problems of the conventional fly-buck converter with the simple quasi-resonance operation between the inherent leakage inductance of a transformer and an auxiliary capacitor at the isolated secondary side. The converter implements the high step-up operation using an auxiliary switch; therefore, the reduced winding ratio of the transformer improves the power density of the circuit. In addition, this circuit implements the soft switching at all active components, and does not suffer from the reverse recovery problem at a diode. A 20 W prototype having an input voltage of 12 V was built to prove the theoretical analyses, and it regulated 5 V for 10 W and 15 V for 10 W at the primary nonisolated and secondary isolated load sides …

Xiaoshan Bai

Xiaoshan Bai

Technische Universiteit Delft

IEEE Transactions on Industrial Electronics

Efficient Performance Impact Algorithms for Multirobot Task Assignment With Deadlines

This article investigates the multirobot task assignment problem with deadlines, where a group of distributed heterogeneous robots needs to collaborate effectively to first maximize the number of successful search and rescue missions and then minimize the robots' total service time. First, a distributed performance impact algorithm is designed to obtain the initial assignment solution, where each robot can compute its assignment solution independently. Subsequently, based on different local search strategies, a disturbance mechanism and two improvement strategies, namely, first, global task inclusion first and decoupled 1-opt second phase and, second, global task inclusion first and coupled 1-opt second phase, are proposed to disrupt and refine the initial solution. The integration of the distributed performance impact algorithm with the two refinement strategies leads to a decoupled performance impact algorithm …

zhiliang zhang

zhiliang zhang

Nanjing University of Aeronautics and Astronautics

IEEE Transactions on Industrial Electronics

Digital Synchronous Rectifier Control Using Extended Harmonics Impedance Model for High-Frequency GaN-Based LLC Converters

Conventional LLC synchronous rectifier (SR) schemes use detection circuits to sense the signals of voltage or current. But it typically operates below 500 kHz, which is unsuitable for high-frequency applications as it may lose large SR duty cycle caused by high dv/dt and GaN devices usage. To address the serious challenge, a digital SR control using extended harmonics impedance model is proposed for GaN LLC converters. By building the impedance model, the SR on-time is calculated accurately in the microcontroller. It not only minimizes the on-time of SR body diode with high precision, but also owns high immunity. A 650-kHz 1.5-kW GaN LLC converter was built. With the output of 28 V/53.5 A, the efficiency is as high as 98.1% at 1.5 kW by using the proposed SR. The power density is also up to 524 W/in 3 . Compared to the conventional SR, the efficiency improves 1.6% at full load.