Fundamental Harmonic Approximation Research Articles

A Detailed Analysis and Gain Derivation of Reconfigurable Voltage Rectifier-Based LLC Converter

In this paper, a complete analysis of an LLC resonant converter with a customized rectifier structure is presented. The converter is intended for wide, low-input, high-output voltage DC bus applications. The performance of the converter is assessed using comprehensive time-domain and fundamental harmonic approximation (FHA), which demonstrates its capacity to operate across an ample range of voltages by precisely adjusting the rectifier structure. The converter’s capability is illustrated by deriving and discussing detailed mode operation, steady-state analysis, and DC gain equations. In order to verify the theoretical analysis, a prototype with a power output of 250 watts is constructed and subjected to testing. The results of the testing demonstrate that the converter is both feasible and effective. The experimental findings illustrate its capacity to manage vast voltage ranges while upholding high efficiency. In addition, the converter utilizes a frequency switching modulation (FSM) to connect with a photovoltaic (PV) panel and control the high output voltage. This demonstrates its adaptability in renewable energy applications. The validation is in accordance with theoretical predictions, demonstrating the converter’s high-efficiency performance and versatility.

DAB-Based Bidirectional Wireless Power Transfer System with LCC-S Compensation Network under Grid-Connected Application

To realize two-way power transfer without physical connections under a grid-connected application, bidirectional wireless power transfer (BDWPT) is introduced. This paper proposes an LCC-S compensated BDWPT system based on dual-active-bridge (DAB) topology with the minimum component counts. LCC-S is designed to be a constant voltage (CV) network. To obtain the power transmission characteristics of the system, a mathematical model based on the fundamental harmonic approximation (FHA) method is established, and the result shows that the direction and amount of transfer power can be controlled by changing the magnitude of output voltages of either/both side of H-bridges. The reactive power of the system can be controlled to be zero when the output voltages of two H-bridges are in the same phase. Compared with DAB-based BDWPT systems with constant current (CC) compensation networks, the proposed structure has better transfer power regulation capability and easier control of the direction of power flow. A 1.1 kW experimental prototype is built in the laboratory to verify the characteristics of the proposed system. The results indicate that the power transfer characteristics of the proposed BDWPT system match its mathematical derivation results based on the FHA model.

Analysis of the time‐domain model of the LLC series resonant converter with frequency and single phase shifted control

AbstractLLC series resonant converter (LLC‐SRC) has attracted much attention due to its simple circuit structure and easy realization of soft‐switching. To get a better efficiency, rectifier stage can be realized by the active switches instead of the diodes. Meanwhile, more control variables can be selected besides the switching frequency, such as single phase shifted (SPS) angle, dual phase shifted (DPS) angle, and extended phase shifted (EPS) angle. Considering the simplicity of the implementation of the control strategy, this paper focused on the converter model with frequency and SPS control. Different from the common modelling method with the Fundamental Harmonic Approximation (FHA), the precise time‐domain mathematic model is built. By a comparison between the two modelling results, it can be proved the FHA model may be failure in some operating condition while the proposed time‐domain model can still show a good accuracy. According to the proposed model, two simple fixed‐frequency SPS control strategies are proposed. The first one can realize infinite soft‐switching margin with no restrictions on the transformer magnetizing inductance. The second one can greatly improve the efficiency of the converter. All the theoretical results are verified by a 1‐kW experiment prototype.

A receiver-side power control method for series-series magnetic topology in inductive contactless electric vehicles battery charger application

Wireless power transfer (WPT) can be used to charge the battery conveniently and efficiently. In this paper, the investigation of high-efficiency S/S resonant magnetic topology in inductive wireless battery charging of electric vehicles (EVs) is analyzed, designed, and controlled. To regulate the output power efficiently rather than controlling the supply voltage, novel bidirectional switches are introduced to control the output power by using the duty cycle control method. The output power of the secondary side is derived and discussed based on the fundamental harmonic approximation (FHA) approach. A 1.5 kW, 120 mm distance, and 85 kHz resonance frequency are verified in MATLAB/Simulink.

Zero-Backflow Power Control Scheme of Dual Bridge Series Resonant DC–DC Converters With High-Accuracy Time Domain Modeling

In the fundamental harmonic approximation (FHA) modelling of dual bridge series resonant DC-DC converters (DBSRCs), the approximation error of the FHA model will lead to low accuracy of optimization schemes, which will reduce the efficiency of DBSRCs. In this paper, firstly, the time domain analysis (TDA) modelling of the DBSRC is adopted, which can describe the characteristics of the DBSRC accurately. Secondly, the extended phase shift (EPS) modulation based on the TDA modelling is discussed, and the backflow power model with the TDA of the DBSRC is developed. On this basis, a zero-backflow power optimization scheme is proposed. In addition, the effects of dead time are analyzed and the compensation method is proposed. The proposed backflow power optimization method with dead time compensation can achieve zero-backflow power and improve the efficiency of the DBSRC. Especially, the proposed method with TDA modelling is more excellent when DBSRC operates in wide voltage range conditions. Finally, a comprehensive experiment comparison of DBSRC under the minimum current trajectory (MCT) with FHA modelling and the proposed method with TDA modelling is discussed. The experimental results have verified the effectiveness of the proposed scheme.

Eigenfrequency Identification Scheme for Strongly Coupled Series-Parallel Compensated Wireless Power Transfer System

This brief proposes an eigenfrequency identification scheme (EIS) based on circuit theory in time domain for a series-parallel compensated wireless power transfer (SP-WPT) system with the pure capacitance filter. In the SP-WPT system, the high nonlinear features (HNFs), including the strong magnetic coupling and diode rectifier influence the system operation by causing the distortion and discontinuity of the voltages and currents. Thus, the effectiveness of fundamental harmonic approximation is influenced, especially when the impact of HNF becomes serious under the strong magnetic coupling and light load conditions. Consequently, the time domain analysis is developed for the diode rectifier-equipped strongly coupled SP-WPT system. Three operation modes of the diode rectifier are analyzed in detail, where the influence of constant dc-link voltage is investigated. Besides, the two eigenfrequencies of the SP-WPT system can be analytically calculated by using the coupling coefficient, k and resonant frequency in the proposed EIS, which reveals the relationship between k and the operation characteristic of the system. Eigenfrequency is the inherent characteristic of the system, which is different from odd and even frequency. Finally, the effectiveness and accuracy of the proposed EIS are verified by experiments on an SP-WPT platform.

Envelope-Detection-Based Accurate Small-Signal Modeling of Series Resonant Converters

Resonant converters have many desirable characteristics such as high efficiency, low component count and low electromagnetic interference production. The resonance phenomenon that enables this also makes their design and control a challenging process. Attempts have been made to determine the small signal control to output dynamics for resonant converters, however they either involve complex mathematics or numerical solutions which do not provide much insights and make it difficult to design controllers. This paper uses Fundamental Harmonic Approximation to model the different stages of Series Resonant Converter. Herein the small signal perturbations in control variable i.e. the switching frequency, result in perturbations in inductor current envelop that is analysed in the Laplace Domain. This current envelop is then used to analytically derive the control to output transfer function for the Series Resonant Converter. The modeling process is verified and validated by comparing the analytical frequency response with that obtained from Simulink simulation and experimental results. For wide output voltage application designs, the system performance and stability vary with the changing operating point. An example demonstrating the utility of the developed model in analysing such systems is also presented.

An Intuitive and Noniterative Design Methodology for CLLC Chargers Employing Simplified Operation Modes Model

This paper mainly focuses on the simplified operation modes (SOM) model and resonant parameter design for the CLLC charger. Based on the mathematical and detailed operation waveform assumptions, the voltage gain model expressions and the operation mode boundaries are calculated directly, providing the high efficiency and high reliability of the CLLC converter. The proposed SOM model is more accurate in depicting the voltage gain compared with the conventional fundamental harmonic approximation (FHA) model. Moreover, the SOM model is more intuitive and has less computational complexity than the complicated and unsolvable time-domain model. As for the parameter design process, the inductance ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> and characteristic impedance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z_{0}$</tex-math></inline-formula> are selected instead of specific inductances and capacitances. Relying on the SOM model, a step-by-step parameter design methodology is studied, which avoids repetitive iterations and streamlines the procedure. The voltage gain range, efficiency, soft-switching operation, mode boundaries, and system stability are considered comprehensively and realized in this process. The simulations and experiments validate that the proposed SOM model is accurate, and the design methodology is straightforward through a 1-kW CLLC charger prototype with 97% peak efficiency.

Development of 80-kW High-Voltage Power Supply for X-ray Generator

This paper describes the development of an 80kW high voltage power supply (HVPS) to drive an X-ray tube. Since the developed HVPS is based on an LCC resonant converter with a symmetrical bipolar voltage multiplier (SBVM), it shows many superior features such as soft switching capability and low voltage imbalance among stages. In addition, the proposed circuit has high power density because a series resonant capacitor is removed by using a method converting the SBVM into capacitors and the full-wave rectifier. Furthermore, a suggested transformer achieves high insulation performance and effective winding area utilization by applying half of the output voltage to the core. The detailed design based on the fundamental harmonic approximation (FHA) is presented for the practical use of the LCC resonant converter with the SBVM in high voltage and high power applications. Also, some significant issues in the implementation are addressed. The performance of the developed HVPS is verified by simulations and experimental results.

High-Gain Bidirectional LCLC Resonant Converter With Reconfigurable Capability

A reconfigurable gain circuit is proposed for an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCLC</i> resonant converter with bidirectional capability considering wide varying redox flow battery source. A suitable hybrid control scheme for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCLC</i> resonant converter with secondary synchronous rectifier is proposed in this work. The proposed reconfigurable circuit enables to configure secondary bridge as an active voltage doubler, full-bridge circuit during forward power transfer mode and reverse power transfer mode, respectively. The reconfigurability helps significantly to design a transformer with lower secondary turns and achieve desired high gain. The reduced transformer secondary turns result in reduced transformer parasitics. The presence of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCLC</i> resonant tank helps to provide the additional gain; the hybrid control scheme ensures zero-voltage switching turn- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> for the primary, and secondary synchronous <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mosfets</small> throughout the operating range. The proposed converter is analysed using fundamental harmonic approximation. The proposed reconfigurable gain circuit and hybrid control scheme is verified experimentally for an 800 V/1 kW hardware prototype fed from 24 to 54 V input.

Analysis of two-section phase-controlled resonant voltage converter

Analysis of two-section resonant DC-to-DC converter with phase power control is carried out in this paper. Two-section converter is considered as a boundary case of the multi-section converter with only one controlled section and other uncontrolled sections. The converter sections are parallel resonant half-bridge voltage inverters with a common resonant capacitor connected to the load through a matching transformer, center-tapped rectifier and smoothing filter. One of the sections is the reference, relative to which the phase shift of the output pulses of the other section is adjusted. The switching frequency of the converter is constant, which improves its electromagnetic compatibility. Analysis is carried out by the fundamental harmonic approximation method. Analytical expressions for voltage and current phasors in both sections of the converters have been established. The dependence of the converter power on the phase shift between the pulses of the half-bridge inverter sections was obtained. The dependence of the efficiency of the converter on the power was analyzed. It is shown that the efficiency slightly decreases when the power is reduced in a wide range of powers and only at powers less than 10% of full load power it drops sharply. The problems of operation of section transistor switches in their zero-voltage switching mode is considered. Verification of the conducted analysis was carried out by simulation of the converter circuit using the PSIM program for modeling power electronics devices. The simulation results are in a good agreement with the analysis results.

Minimum Current Optimization of DBSRC Considering the Dead-Time Effect

In a dual-bridge series resonant converter (DBSRC) working at a high switching frequency, the dead-time effect is a serious issue. When the minimum current trajectory (MCT) method is applied, the inductor current cannot be minimized due to the dead-time effect, and the range of the soft switching is reduced. Considering the dead-time, this paper first presents a theoretical analysis of the transmission power and the soft-switching characteristics based on the fundamental harmonic approximation (FHA) approach. Then, a minimum current trajectory method considering the dead-time (MCT-d) is proposed to achieve the minimum inductor current by compensating for the dead-time. This method can extend the soft-switching range as well. Finally, the experimental results validate the theoretical analysis and the improvement of the converter’s efficiency.

Accurate Steady-State Modeling and Design Based on State Trajectory Analysis for LCC Resonant Converter With Voltage Doubler Rectifier

The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCC</i> series–parallel resonant converter with a voltage doubler rectifier, widely used in X-ray machines, is required to meet an extremely wide output range. However, state-of-the-art models are based on fundamental harmonic approximation and cannot maintain good accuracy over the entire output range. The state trajectory method has the potential to achieve a full range of high accuracy without high complexity, but it only applies to simple topologies, like <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCC</i> with a full-bridge rectifier. For <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCC</i> with a voltage multiplier, the capacitors in the multiplier are involved in the resonance, which can be modeled as a five-element resonant circuit. Moreover, the conduction sequence of components in the minor mode is different from that in the major mode, which is usually ignored in the steady-state model. The influence of the output capacitance of power transistors on the state trajectory is so unclear that the model accuracy decreases considerably at high frequencies. In this article, the equivalent parallel resonant capacitance is derived through the current distribution. The steady-state model of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCC</i> converter with a voltage doubler rectifier is developed for both major mode and minor mode. The deviation of the state trajectory and modeling accuracy induced by the output capacitor is investigated. Based on the proposed model and device stress analysis, the design procedure for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCC</i> under a wide operation range is presented. The simulations and experiments verify the accuracy of the model and the validity of the design method. The simulation mismatches are less than 2.3% over the entire output range. The maximum experimental mismatch is 15%.

Analysis and Verification of a Half-Dual Bridge Resonant Converter with Voltage Match Modulation

To overcome the weakness of the narrow conversion gain of dual bridge resonant converter, a half-dual bridge resonant converter (H-DBRC) with voltage match modulation (VMM) is proposed and implemented for wide voltage range applications. The H-DBRC, including a full bridge on the primary side and a half bridge on the secondary side, is adopted to realize the bidirectional power flow and wide voltage operation. Owing to the synergy between the H-DBRC structure and VMM strategy, the converter can operate in full-bridge state and half-bridge state with maximized ZVS (zero-voltage switching) operation and minimized circulating current. The steady-state analysis is performed and the solutions for both forward and backward modes could be obtained uniformly by using the fundamental harmonics approximation approach. The soft-switching characteristics, implementation process and design example are analyzed in detail. Finally, to confirm the theoretical analysis and feasibility, both simulation and experimental verifications are demonstrated in this paper. Since the converter consistently achieves voltage-matching operation, the optimal ZVS range can be obtained when the voltage gain M is between 0.5 to 1. Moreover, the economic cost and control complexity are greatly reduced because only six switches are required in the converter.

Operation of a semi dual-bridge resonant converter with a tunable resonant tank

In this paper, a control strategy to minimize the root-mean-square (rms) current and eliminate the backflow power over a wide operation range is proposed to enhance the conversion efficiency of a semi dual-bridge resonant converter (SDBRC). Steady-state analysis of the converter is performed using the fundamental harmonic approximation approach. Optimal operating states are then found with the minimum resonant current and zero backflow power for both buck and boost operation. The switching conditions of the optimal operating trajectory are also elaborated in detail. The converter is enabled to work under the optimal operating condition in a wide load range by adjusting the switch-controlled capacitor based tunable resonant tank continuously. Finally, a prototype converter rated at 500 W is built and extensive experimental tests have been done to evaluate the proposed switch-controlled capacitor based topology converter and its optimal modulation. Performance improvement brought up by the proposed converter with its modulation could be confirmed by means of comparisons with previous works.

Real Time Hardware-in-Loop Implementation of LLC Resonant Converter at Worst Operating Point Based on Time Domain Analysis

The inductor inductor capacitor (LLC) resonant topology has become more popular for deployment in high power density and high-efficiency power converter applications due to its ability to maintain zero voltage switching (ZVS) over a wider input voltage range. Due to their ease of operation and acceptable accuracy, frequency domain-related analytical methods using fundamental harmonic approximation (FHA) have been frequently utilized for resonant converters. However, when the switching frequency is far from the resonant frequency, the circuit currents contain a large number of harmonics, which cannot be ignored. Therefore, the FHA is incapable of guiding the design when the LLC converter is used to operate in a wide input voltage range applications due to its inaccuracy. As a result, a precise LLC converter model is needed. Time domain analysis is a precise analytical approach for obtaining converter attributes, which supports in the optimal sizing of LLC converters. This work strives to give a precise and an approximation-free time domain analysis for the exact modeling of high-frequency resonant converters. A complete mathematical analysis for an LLC resonant converter operating in discontinuous conduction mode (DCM)—i.e., the boost mode of operation below resonance—is presented in this paper. The proposed technique can confirm that the converter operates in PO mode throughout its working range; in addition, for primary MOSFET switches, it guarantees the ZVS and zero current switching (ZCS) for the secondary rectifier. As a function of frequency, load, and other circuit parameters, closed-form solutions are developed for the converter’s tank root mean square (RMS) current, peak stress, tank capacitor voltage, voltage gain, and zero voltage switching angle. Finally, an 8 KW LLC resonant converter is built in the hardware-in-loop (HIL) testing method on RT-LAB OP-5700 to endorse the theoretical study.

Analytical modeling of resonant converters in frequency domain for wireless power transfer: Continuous current mode (CCM) operation

The major topology for wireless power transfer is resonant converters, which use fundamental harmonic approximation as a general analysis method. The accuracy of fundamental harmonic approximation (FHA) is unsatisfactory in some wireless power transfer applications, as the current has distortions due to the non-linear diode-bridge rectifier. Some frequency-domain models also consider harmonics beside fundamental component and indeed have a higher resolution. However, due to the difficulty of modeling the non-linear rectifier, most models are oversimplified by assuming a voltage source on the output to eliminate the rectifier. Moreover, the value of the voltage source is often treated as a fixed given number, which is not true for a resistive load. To cover a general case, this paper proposes a frequency-domain analytical model for resonant converters in continuous current mode (CCM) with the capability of considering any load and source situations in kHz frequency range. In terms of computation complexity, the proposed model only involves matrix operation (first-order). A simple algorithm has been chosen to demonstrate the fast convergency and high accuracy of the proposed model. The main findings are verified by the comparison between the theoretical calculation, time-domain simulation and experimental results, where the estimation of output power has 10% improvement than the FHA method.

Unified analysis and output estimation for strong coupling contactless slipring system

Contactless slipring (CS) system utilizing inductive-power-transfer (IPT) technology is a good candidate for the traditional mechanical slipring assemblies. However, suffering from the high harmonic currents in strong coupling CS system, the output power will deviate from the theoretical values estimated by the fundamental harmonic approximation (FHA) and its extension method, i.e., E-FHA, in which the power are transferred by both the fundamental current and the high order harmonic currents. In order to achieve high precise output estimation, a unified analysis is proposed in this paper. Firstly, Fundamental-harmonic Double Resonance Phenomenon is revealed via impedance analysis, to address the nature of the high harmonic currents in strong coupling system. Then, a unified output current expression owning high precision is derived, followed by a unified fundamental load impedance. Discussions show that both the output and the fundamental load impedance of FHA, and E-FHA are all the special cases of the unified expressions proposed. FHA, and E-FHA are precise enough for the loose coupling system, whereas the proposed method is indispensable for the strong coupling system with k>0.4. Finally, simulations and experimental measurements of a 1.6kW CS system, as well as the comparative studies among FHA, E-FHA, and the proposed method, are presented, indicating that the proposed method are effective for high precise output estimation.

Current Sharing Analysis for Novel Paralleled CLLLC Converters

In the field of high-capacity bidirectional converters, paralleled LLC converters are usually used to increase the output power and system power density. However, because of the production tolerances the parameters of the resonant components for each paralleled unit may not be completely identical. The gain characteristic of the LLC resonant converter is sensitive to the parameters of the resonant components. For the paralleled converters, because voltage gains can be slightly different from each other for a same input, system output current may be poorly shared among the parallel units. In this paper, novel paralleled CLLLC converters are proposed. For the proposed converters, the load current sharing performance is not sensitive to component parameter differences or derivations. Equal load sharing can be realized easily. And no additional components or controllers are needed. The gain characteristics are analyzed and they are similar with that of a single CLLLC resonant converter. The mathematical model of the paralleled converters is deduced based on fundamental harmonic approximation (FHA) method. And the load current sharing errors for the conventional and proposed paralleled CLLLC converters are compared or analyzed by introducing variables such as the load current sharing coefficient. It is shown that for the same set of component parameters, when the conventional paralleled converters are used most of the load may be supported by a single converter while the output power of another one is small. On the other hand, for the cases of parameter derivations, the current sharing performance of the novel proposed paralleled converters is obviously much better. And finally the effectiveness of current sharing for the proposed paralleled CLLLC converters is verified by simulations and experiments.

Differential Equation Model of the LLC Resonant Converter in the Ideal Case

The LLC resonant converter has been widely used in direct current (DC) power supply applications. However, fundamental harmonic approximation or other simplified analyses will introduce inevitable deviations. Therefore, the differential equation model with numerical solution of the LLC converter is proposed in this paper based on the operational principle of the ideal case. In order to solve the differential equation, initial values need to be substituted. The accurate LLC model based on time interval analysis is very complicated and cannot be used. In this paper, solution methods of the initial values corresponding to different switching frequencies are proposed. The initial values can be solved conveniently. Furthermore, the voltage gain curve is modified by the idealized analysis. Lastly, all the above research is verified by PSIM simulation. The work is helpful to understand the operational principle of the LLC resonant converter.