Thermal–electrical averaging model of resonant converters based on extended describing function method

The series parallel resonant converter (SPRC) is known to have combined merits of the series resonant converter (SRC) and parallel resonant converter (PRC). However, the presence of a three-element LCC structure makes the SPRC's transient dynamics complex and its quick control difficult. This paper provides an analysis and a solution for this problem. It firstly presents the SPRC dynamics using the state-plane analysis technique and then provides a method to derive the optimal trajectory during transients for the SPRC. The method minimizes the transient response of the SPRC to within one switching cycle by deriving two optimal switching instances. The derivation of the optimal state trajectory during transients for the SPRC is described. Simulation results validate the method and show significant improvement in transient response compared to that of a step change in frequency control.

The analysis of resonant converters including the capacitance of the switches is presented. New dc characteristics are obtained for the series, parallel, and series-parallel resonant converters (SPRC). The operating regions where the converters operate with zero-voltage switching (ZVS) are determined as a function of the switch capacitance. The more pronounced effect can be seen in the series resonant converter (SRC), while the parallel resonant converter (PRC) is the most insensitive. The results of the analysis have been verified on an experimental prototype.

This paper presents a new circuit topology known as series-parallel resonant converter (SPRC), which is a combination of both the series resonant converter (SRC) and the parallel resonant converter (PRC) topologies. This topology has several advantages when compared to the individual SRC and PRC. For example, the SPRC can operate under open load conditions, and it allows for zero-current switching operation. Using the steepest descent algorithm, the state-plane equations are numerically solved to obtain the performance characteristic curves. Based on these curves, a converter design procedure can be devised. A specific design example is given.

A general analytical procedure is presented for the equivalent circuit modeling of resonant converters, using the series and parallel resonant converters as examples. The switched tank elements of a resonant converter are modeled by a lumped parameter equivalent circuit. The tank element circuit model consists, in general, of discrete energy states, but may be approximated by a low-frequency continuous time model. These equivalent circuit models completely characterize the terminal behavior of the converters and are solvable for any transfer function or impedance of interest. With the approximate model it is possible to predict the lumped parameter poles and zeros, and to quickly determine the relevant DC gains of the output impedance and the control to output transfer function. Closed-form solutions are given for the equivalent circuit models of both converter examples. Experimental verification is presented for the control-to-output transfer functions of both series and parallel resonant converters, and good agreement between theoretical prediction and experimental measurement is obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A novel analytical methodology is proposed and applied to investigate the steady-state processes in voltage-fed parallel and series-parallel resonant DC-DC power converters with a capacitive output filter. In this methodology, the rectifier, output capacitor and load are replaced by an equivalent circuit which includes a capacitor and resistor connected in parallel. Excellent agreement was obtained when comparing the numerical values calculated by the proposed model to cycle-by-cycle SPICE simulation and to the numerical results of earlier studies.

Because of their reduced switching losses, DC-to-DC resonant converters have been used extensively in the design of smaller size and lighter weight power supplies. The steady state and dynamic behaviors of both the conventional series and parallel resonant converters have been thoroughly analyzed and small-signal models around given nominal operating points have been obtained. These models have been used in the past to design controllers that attempted to keep the output voltage constant in the presence of input perturbations. However, these controllers did not take into account neither load nor components variations, and this could lead to instability in the face of component or load changes. Moreover, prediction of the frequency range for stability was done a posteriori, either experimentally or by a trial and error approach. In this paper we use /spl mu/-synthesis to design a robust controller for a series resonant converter. In addition to robust stability the design objectives include rejection of disturbances at the converter input while keeping the control input and the settling time within values compatible with a practical implementation. >

A practical method for the steady-state design of parallel resonant DC/DC power converters is presented. The method uses a set of pre-derived equations from an LLCC-type series-parallel resonant converter (LLCC-SPRC). Although four tank elements are used in an LLCC-SPRC, only two ratios of these tank elements are needed during design. The values of the four tank elements can be found from the design results. In addition to designing an LLCC-SPRC, the prederived equations can also be used to design and analyze conventional LCC-type series-parallel (LCC-SPRC), LLC-type parallel (LLC-PRC), and LC-type parallel (LC-PRC) resonant power converters. In other words, four power converters can be designed by the same equations. A design procedure along with design examples is given. Experimental circuits are implemented and measured based on the design results to verify the validity of the derived equations and the design procedure.

The authors present an analysis of the series-parallel resonant power converter (SPRC) that includes the capacitance of the switches. New DC characteristics are obtained, and the regions where the converter operates with zero voltage switching are determined as a function of the switch capacitance. The analysis is also valid for series and parallel resonant converters. The analysis is verified experimentally on a 50 W, 1 MHz SPRC converter. >

LowQ resonant converter, such as series-series resonant converter, series resonant converter, and parallel resonant converter (PRC), are highly flexible and highly tolerant to coil misalignments. However, these kinds of topologies cannot be employed to the wide air-gap, low-coupling transformers because of their inadequate magnetizing inductance. On the other hand, highQ multiple-resonant converters such as series-PRC) and series-SPRC are very suitable for low-coupling compact wireless transformer applications. However, because these multiresonant topologies have several resonant pairs resonating at a single frequency, these parameter values ought to be consistent throughout the operating conditions to resonate at the same frequency. However, since the wireless power transfer (WPT) applications are required to be flexible and convenient to the customers, the wireless transformers are not supposed to be rigid and stationary. To solve the problem, a controllable inductor for a highQ multiresonant WPT system is proposed to extend the soft switching region and to keep the resonant circulating energy minimum even at resonant mismatch conditions caused by the misalignments or temperature variations of the wireless transformer coils. The performance enhancement of the multipleresonant wireless converter is validated using the proposed controllable inductor technique, and also the feasibility of the proposed technique is proven under different mismatch conditions through 200-W hardware experimental results.

Because of their reduced switching losses, allowing a higher operating frequency, dc-to-dc resonant converters have been used extensively in the design of smaller size and lighter weight power supplies. The steady state and dynamic behavior of both the conventional series and parallel resonant converters have been thoroughly analyzed and small-signal models around given nominal operating points have been obtained. These models have been used in the past to design controllers that attempted to keep the output voltage constant in the presence of input perturbations. However, these controllers did not take into account either load or components variations, and this could lead to instability in the face of component or load changes. Moreover, prediction of the frequency range for stability was done a posteriori, either experimentally or by a trial and error approach In this paper we use /spl mu/-synthesis to design a robust controller for a series resonant converter (SRC). In addition to robust stability the design objectives include rejection of disturbances at the converter input while keeping the control input and the settling time within values compatible with a practical implementation.

The authors describe a rectifier unit using a series resonant power converter designed for rack-mounted DC power systems. For a light load, this converter is controlled by voltage resonance formed with a parallel resonant circuit. An averaged circuit model is proposed. It approximates the parallel and series resonant circuit as a simple series resonant circuit with the capacitor which has frequency-dependency capacitance. The averaged model was verified with detailed model simulation and experimental results. Characteristics of a rectifier unit using the resonant converter with AC three-phase 200 V input and DC 56 V 50 A output are presented. A weight of 11.5 kg for the unit has been achieved with natural air cooling. The efficiency was 90% or higher at output currents from 10 A to 50 A and 92.8% at 50 A. >

Series resonant converter can only operate efficiently within a narrow voltage gain range, which limits the use for battery charging applications. Thus, this article proposes a turn-off delay-controlled bidirectional series resonant (TFD-BSR) converter to extend the voltage gain range and enhance the efficiency. Instead of frequency modulation, the turn-off delay of the corresponding bottom switches is adopted to regulate the direction and amplitude of power flow. First, high peak and low valley voltage gain is obtained at fixed switching frequency. As a result, wide voltage range is extended. Second, the voltage gain is independent of auxiliary and magnetizing inductors, and hence, a large value for the two inductors, which depresses the circulating losses significantly, can be designed just considering zero-voltage switching (ZVS) conditions. In addition, all the active switches can operate with ZVS, which further enhances the efficiency. Operation principles, voltage gain characteristics, ZVS analysis, and design method of the proposed TFD-BSR converter are analyzed in detail. Finally, the feasibility and performance of the proposed converter are validated by simulations and experimental results from a 3.5-kW prototype.

A new contactless power converter topology for a seriously low coupling (less than 0.15) using low-cost commercialized ferrite core transformer with high efficiency and wide air-gap (23 mm) is presented in this paper. Among the typical resonant converter topologies for contactless power transferring systems, Series-Series Resonant Converter (SSRC) and Series-Parallel Resonant Converter (SPRC) are widely used in number of power electronic applications. Because of the simple strategy and superior response irrespective of coupling factor and load changes, SSRC topology is widely applied in contactless transformer applications. However, in seriously low coupling and wide air-gap applications, the switching frequency must be increased to several MHz range in order to operate the converter at the optimized operating region. Unless some high-cost, low resistance windings are selected, due to skin effect and proximity effect, the ac conduction loss will be dangerously high when the converter is operating at the high frequency range. To solve this problem, a modified and improved topology of series-series parallel resonant converter for wide-gap (23 mm) contactless power transfer applications with the coupling rate of 0.15 is proposed.

A resonant converter using nonresonant coupling between the rectifier and resonant circuits is presented. This converter has many advantages over a conventional parallel resonant converter (PRC), such as better control characteristics, lower component stress, lower converter gain, and better stability. It uses a capacitive (instead of an inductive) output filter, which has the advantages of smaller physical size and less component cost. Analysis and design of this converter are given for three modes of converter operations. By comparing the characteristic curves with those of the conventional PRC, it is seen that the present converter has a lower converter gain for a given Q/sub p/. This present converter should have better stability than the conventional PRC. Since the capacitor voltage is clamped at +or-V/sub 0/, the size of the state-plane diagram is limited for a given gain. This assures that a runaway problem in the converter is not encountered. >

A generalized average model of a Series Resonant Dual Active Bridge (SRDAB) converter with variable phase shift control is proposed in this paper. The transformer current in SRDAB is sinusoidal, so the requirement of negligible ripple current for the conventional averaging technique is not satisfied here. This proposed model uses the output filter capacitor voltage, resonant capacitor voltage, and resonant inductor current as state variables. The dc component and the fundamental component of state variables are used to develop the proposed model. The transformer's leakage resistance is considered for more accurate modeling. With the help of the model proposed, the average model and the small-signal model of the converter are derived and verified using simulation results. The beat frequency dynamics often seen in the resonant converters could be predicted using this proposed model. The analytical expression for small signal control to output transfer function for phase shift control is derived, which aids in the control loop design.