Effect of a split transformer leakage inductance in the LLC converter with integrated magnetics

As a result of the advantages such as high efficiency, continuous current and high stability margin, push-pull converter with continuous current (PPCWCC) is competitive for battery discharge regulator (BDR) which plays an important role in power conditioning unit (PCU). Leakage inductance yields current spike in low-ripple current of PPCWCCs. The operating modes are added due to leakage inductance. Therefore the steady state performance is affected, which is embodied in the spike of low-ripple current. PPCWCCs which are suitable for BDR can be separated into three types by current spike characteristics. Three representative topologies IIs1, IIcb2 and Is3 are analyzed in order to investigate the factors on the magnitude and duration of spike. Equivalent current sampling method (ECSM) which eliminates the sampling time delay and achieves excellent dynamic performance is adopted to prevent the spike disturbance on current sampling. However, ECSM reduces the sampling accuracy and telemetry accuracy due to neglecting the spike. In this paper, ECSM used in PPCWCCs is summarized. The current sampling error is analyzed in quality and quantity, which provides the foundation for offsetting and enhancing the telemetry accuracy. Finally, current sampling error rate of three topologies is compared by experiment results, which verify the theoretical analysis.

Effect of Transformer's Parameters on Harmonic Generation

Leakage inductance is one of the key parameters of a transformer, and it is often intentionally integrated into transformers. Rogowski’s equation is generally used for leakage inductance calculation; however, it is only applicable to concentric winding transformers where windings have the same height. Consequently, it has limited applications. This paper proposes a transformer leakage inductance calculation method using a double Fourier series. The limitation of Rogowski’s leakage inductance equation was analyzed in practical applications, and a new model for calculating the leakage inductance of a double-group-overlapping winding transformer was derived. Experimental prototypes of transformers were developed, and their simulation models were built in Ansys. The correctness of the proposed calculation method for transformer leakage inductance using a double Fourier series was verified by comparing the calculation results with the simulation and measured ones. A sensitivity analysis was also conducted by studying the variations in different parameters that might affect the leakage inductance value. The proposed calculation model gives an intuitive and simple method with less calculation and design effort while maintaining reasonable accuracy for leakage inductance calculation. In addition, the featured double Fourier series approach has a wider range of applications than Rogowski’s equation.

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.

The efficiency is affected by the parameters of components in the DC high current generator. The leakage inductance of the rectifier transformer will affect the output and filtering effect of the device and reduce the power quality of the public network. To improve the output and filtering effect of the DC high current generator, the 3-phase 6-pulsation rectifier bridge arm with the transformer T-type equivalent circuit is proposed. Through the topology model of each conduction state circuit of the semiconductor components, the expressions of load output, high-order harmonic content, and transformer leakage inductance are calculated. Then the actual generator is simulated in the MATLAB-Simulink module and variation law between the primary and secondary side leakage inductance and the output DC voltage, the total harmonic distortion(THD), and the fifth harmonic content rate is obtained. Finally, the output waveform is analyzed under the rated condition. The results show that the influence of transformer leakage inductance on output efficiency and high order harmonic filtering effect can be obtained by the proposed calculation method, and the simulation results verify the validity and correctness of the theoretical analysis.

An algorithm based on new circulated current model is proposed to analyze the circulating current in the multiphase LLC converter. First of all, a virtual-open concept is introduced and LLC phases are decoupled from each other, Thus, A circulating current model can be achieved from fundamental harmonic approximation (FHA). Secondly, the ac voltages on the equivalent resistor of different phases are assumed same magnitude but different angle viewing from the primary-side. From mentioned above, current sharing error can be calculated, two types calculated results are shown under two-phase independent LLC converter and two-phase common inductor LLC converter. Simulation results from different input voltage levels, different resonant component tolerances, and different total load are compared. A two-phase 600W prototype is built to verify the effectiveness of the proposed analysis method

The transformer leakage inductance (TLI) is an important parameter in the design phase of the isolated power supplies. Hence, the TLI estimation before the transformer construction is very useful for the designers. The previous works considered an ordered winding turn arrangement (WTA) for the transformers. This assumption considers only ideal windings which may result in a significant error from what will be achieved after the construction of the transformer. This article concentrates on the transformers with nonideal windings in which the turns are not ordered. The uneven distribution of the turns in the layers is mainly due to the wrapping machine error. Hence, for a specific transformer with determined electrical specifications, different WTAs will be possible. Thus, the corresponding TLIs will be different. This will cause uncertainties about the TLI values for the designer. The article proposes a method for considering a large number of possible WTAs of nonideal windings. Hence, the proposed method can be used as a probability tool to plot the probability distribution of the TLIs. Furthermore, based on the obtained results, effective guidelines are recommended for the designers to avoid critical situations according to the transformer specifications. The accuracy of the method is evaluated using finite-element (FE) analysis and experimental measurements. The FE and experimental results both are in conformity with the statistical analysis of the article.

This paper presents a general approach to compute the leakage inductances of power transformers with turn-to-turn winding faults. The leakage inductances are obtained by using well-known conventional formulas, adapted to the asymmetrical conditions produced by the interturn fault in the leakage flux distribution. Two methods for calculating the leakage inductances are presented: the first requires detailed information about the geometry of the windings whereas the second uses simplifying assumptions, allowing to express the leakage inductances as a function of the nameplate short-circuit inductance, the number of turns, and core dimensions. A leakage inductance model of the transformer with faulty turns is also proposed, which is based on the three-winding transformer theory. This leakage inductance equivalent circuit can be easily integrated into other electromagnetic transient simulators. The results obtained from the application of the analytical methods and the equivalent circuit are validated using data obtained from finite-element analysis and experimental short-circuit tests.

The leakage inductance of a high-frequency transformer affects the operating mode and performance in dc/dc converters, so it is necessary to calculate the leakage inductance accurately. In the existing analytical calculation methods of leakage inductance of high-frequency transformers with Litz wire winding, the nonarea-equivalent high-frequency analytical method is applied to calculate leakage inductance. However, the calculated leakage inductance value is lower than its actual value due to the neglect of the irregular region between turns. In order to improve the calculation accuracy, this article proposes an analytical calculation method of leakage inductance for the high-frequency transformer with Litz wire winding, which considers the irregular region between turns. The 2-D magnetic field distribution in the transformer window and attenuation caused by high-frequency effects on magnetic field energy are analyzed and applied in this proposed method, to take the energy stored in the irregular region between turns into account indirectly. Thus, the proposed analytical expression for leakage inductance is derived correspondingly. Finally, the accuracy of the proposed method is verified by simulations and experiments. The results indicate that the relative error of calculating leakage inductance can be reduced from 16.25% to 3.79% by the proposed method within a certain range of wire densities.

The paper at hand proposes to employ a multisource DC-DC converter to interconnect energy sources, storage devices, drives and the motion control unit of an electric vehicle. This converter topology is well suited to interconnect more than 2 sources/loads that need galvanic isolation. It is particularly advantageous in the case of different voltage levels to be connected, with the power flowing in any direction. The multisource DC-DC converter employs a single magnetic core with multiple windings. The maximum transmissible power for each pair of sources, the energy efficiency and the controllability of the system depend on the multiwinding transformer's leakage inductances. The paper presents a solution to adjust the leakage inductances in order to obtain a given converter characteristic. The approach works with uneven transformation ratios and is validated experimentally for 4 sources/loads.

The data centers of the telecommunication infrastructure are recently consuming more electric power than before. This increasing electrical burden is requiring a small but high-power isolated power converter with a high step-down ratio. Conventionally, the LLC converter is regarded to be a promising candidate, although this converter needs vacant space for galvanic isolation due to extremely high voltage caused by the resonance in the primary side, i.e. high voltage side, of the isolation transformer, which hinders the compact implementation inside the server computers in high power design. The purpose of this paper is to propose a novel LLC converter topology to reduce this extremely high voltage by locating the LC resonator on the secondary side. The performance analysis revealed that the proposed converter exhibits a similar frequency-voltage characteristic enabling the boost and buck operation modes as well as the small rectifier conduction loss similar to the full-wave rectifier with a center-tapped transformer. The simulation confirmed the operating principles and reduction of the resonance voltage amplitude of the proposed LLC converter in comparison with the conventional LLC converter. Furthermore, the experiment also supported the operating principles, which suggests the usefulness of the proposed converter for a high voltage dc power supply system.

29 - High-Frequency Inverters: From Photovoltaic, Wind, and Fuel-Cell-Based Renewable- and Alternative-Energy DER/DG Systems to Energy-Storage Applications

The dc-dc topologies with capacitive output filter are going to be widely used especially for high-output current applications because of its inherent advantages in the lower voltage stress on rectifiers and the smaller occupied printed circuit board layout area at the secondary side. However, the parasitic resonance between the equivalent leakage inductance of the power transformer and the equivalent output junction capacitance of the rectifier still practically exists in the center-tapped rectification configuration, which leads to considerable voltage ringing on the rectifier and then results in the utilization of the rectifier with much higher breakdown voltage rate and the decrease of conversion efficiency. Moreover, the relatively larger output-current ripple induces the both larger conduction loss in the secondary-side windings of the power transformer and the capacitive output filter. In this paper, a novel symmetrical rectifier configuration is proposed, which can effectively clamp the practical voltage stress on the rectifier without any parasitical voltage spike and reduce the output-current ripple due to the bypass effect of the auxiliary flying-balancing capacitors. The leakage inductance and the output filter capacitor can be treated as an inherent small LC filter to reduce the output voltage ripple further. Based on the theoretical analysis and the optimal design considerations, a 300-W lab-made LLC resonant dc-dc converter with this proposed configuration is built up to verify its advantages in high conversion efficiency.

Resonant converters rely on a precise knowledge of leakage inductance of the equipped transformers. Resonant circuit topologies such as LLC usually utilize the transformer leakage as an inductive component in the resonant tank, allowing for a drastic reduction in the converter weight, size and volume. The existence of the secondary leakage inductance affects the whole operation of the LLC resonant converter. This paper reveals that placing the secondary winding near the air gap would increase the resonant tank input impedance, vertically shrink the voltage-gain curve of the converter, and consequently minimize the frequency range (i.e frequency bandwidth with respect to load variation). On contrary, placing the secondary winding in a close contact with the magnetic core would decrease the resonant tank input impedance, vertically stretches the voltage-gain curve of the converter, and widen the frequency variation range. It has been reported that the winding location with respect to the air gap has an impact on the leakage inductance value. In other words, placing the secondary winding in a close contact with the magnetic core (zero mmf position) would maximize the leakage energy storage originated from the secondary winding, and hence maximize the secondary leakage inductance and vice versa. The theoretical discussion is presented which is merely based on Ampere's law and Dowell's model. Furthermore, transformer prototypes had been constructed and tested in a 390V/12V-220W LLC converter prototype to evaluate the proposed analysis.

This paper proposes a topology combination scheme to achieve wide-range operation for LLC resonant converters. Instead of directly adding an auxiliary current injection circuit for each individual LLC converter, the proposed scheme combines two LLC converters through coupled resonance. Then, one LLC circuit can be utilized to adjust the equivalent resonant parameters of the other LLC circuit. By only controlling the phase delay between the mosfet bridges, output voltage regulation is properly maintained without changing the switching frequency. Since the total power rating does not change and each converter can share the load, it does not have any extra cost of power components. The advantages of this design include higher power efficiency, smaller size, and optimized utilization of each converter at different load, since both converters can fulfill isolated power conversion with independent control. Also, by taking the benefit of suppressed frequency variation, a smaller leakage inductance and a lower ratio between the leakage inductance and the magnetizing inductance are allowed, so that the coupling of transformer windings and transformer efficiency just improve. In addition to detailed theoretical analysis, experimental results verify the feasibility and effectiveness of the proposed concept.