Sampled-data modeling and dynamical effect of output-capacitor time-constant for valley voltage-mode controlled buck-boost converter

By analyzing the output voltage ripple of a buck-boost converter with large equivalent series resistance（ESR） of output capacitor, one valley voltage-mode controller for buck-boost converter is proposed. Considering the fact that the increasing and decreasing slopes of the inductor current are assumed to be constant during each switching cycle, an especial sampleddata model of valley voltage-mode controlled buck-boost converter is established. Based on this model, the dynamical effect of an output-capacitor time-constant on the valley voltage-mode controlled buck-boost converter is revealed and analyzed via the bifurcation diagrams, the movements of eigenvalues, the Lyapunov exponent spectra, the boundary equations,and the operating-state regions. It is found that with gradual reduction of output-capacitor time-constant, the buck-boost converter in continuous conduction mode（CCM） shows the evolutive dynamic behavior from period-1 to period-2, period-4, period-8, chaos, and invalid state. The stability boundary and the invalidated boundary are derived theoretically by stability analysis, where the stable state of valley voltage-mode controlled buck-boost converter can enter into an unstable state, and the converter can shift from the operation region to a forbidden region. These results verified by time-domain waveforms and phase portraits of both simulation and experiment indicate that the sampled-data model is correct and the time constant of the output capacitor is a critical factor for valley voltage-mode controlled buck-boost converter, which has a significant effect on the dynamics as well as control stability.

Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus

Based on the fact that the real inductor and the real capacitor are fractional order in nature and the fractional calculus,the transfer function modeling and analysis of the open-loop Buck converter in a continuous conduction mode（CCM） operation are carried out in this paper.The fractional order small signal model and the corresponding equivalent circuit of the open-loop Buck converter in a CCM operation are presented.The transfer functions from the input voltage to the output voltage,from the input voltage to the inductor current,from the duty cycle to the output voltage,from the duty cycle to the inductor current,and the output impedance of the open-loop Buck converter in CCM operation are derived,and their bode diagrams and step responses are calculated,respectively.It is found that all the derived fractional order transfer functions of the system are influenced by the fractional orders of the inductor and the capacitor.Finally,the realization of the fractional order inductor and the fractional order capacitor is designed,and the corresponding PSIM circuit simulation results of the open-loop Buck converter in CCM operation are given to confirm the correctness of the derivations and the theoretical analysis.

Analytical and computational modelling for wave energy systems：the example of oscillating wave surge converters

The development of new wave energy converters has shed light on a number of unanswered questions in fluid mechanics, but has also identified a number of new issues of importance for their future deployment. The main concerns relevant to the practical use of wave energy converters are sustainability, survivability, and maintainability. Of course,it is also necessary to maximize the capture per unit area of the structure as well as to minimize the cost. In this review, we consider some of the questions related to the topics of sustainability, survivability, and maintenance access, with respect to sea conditions, for generic wave energy converters with an emphasis on the oscillating wave surge converter. New analytical models that have been developed are a topic of particular discussion. It is also shown how existing numerical models have been pushed to their limits to provide answers to open questions relating to the operation and characteristics of wave energy converters.

Modeling and dynamics analysis of the fractional-order Buck-Boost converter in continuous conduction mode

In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode （CCM） are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck- Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.

Thermal Dissipation Modelling and Design of ITER PF Converter Alternating Current Busbar

Because the larger metallic surrounds are heated by the eddy current, which is generated by the AC current flowing through the AC busbar in the International Thermonuclear ExperimentM Reactor （ITER） poloidal field （PF） converter system, shielding of the AC busbar is required to decrease the temperature rise of the surrounds to satisfy the design requirement. Three special types of AC busbar with natural cooling, air cooling and water cooling busbar structure have been proposed and investigated in this paper. For each cooling scheme, a 3D finite model based on the proposed structure has been developed to perform the electromagnetic and thermal analysis to predict their operation behavior. Comparing the analysis results of the three different cooling patterns, water cooling has more advantages than the other patterns and it is selected to be the thermal dissipation pattern for the AC busbar of ITER PF converter unit. The approach to qualify the suitable cooling scheme in this paper can be provided as a reference on the thermal dissipation design of AC busbar in the converter system.

Gas–liquid mass transfer and flow phenomena in the Peirce–Smith converter: a water model study

A water model with a geometric similarity ratio of 1：5 was developed to investigate the gas-liquid mass transfer and flow charac- teristics in a Peirce-Smith converter. A gas mixture of CO2 and Ar was injected into a NaOH solution bath. The flow field, volumetric mass transfer coefficient per unit volume （Ak/V; where A is the contact area between phases, V is the volume, and k is the mass transfer coeffi- cient）, and gas utilization ratio （t/） were then measured at different gas flow rates and blow angles. The results showed that the flow field could be divided into five regions, i.e., injection, strong loop, weak loop, splashing, and dead zone. Whereas the Ak/V of the bath increased and then decreased with increasing gas flow rate, and n steadily increased. When the converter was rotated clockwise, both Ak/F and t/increased. However, the flow condition deteriorated when the gas flow rate and blow angle were drastically increased. Therefore, these para- meters must be controlled to optimal conditions. In the proposed model, the optimal gas flow rate and blow angle were 7.5 m3.h-1 and 10°, respectively.

Power Maximization of A Point Absorber Wave Energy Converter Using Improved Model Predictive Control

This paper considers controlling and maximizing the absorbed power of wave energy converters for irregular waves. With respect to physical constraints of the system, a model predictive control is applied. Irregular waves’ behavior is predicted by Kalman filter method. Owing to the great influence of controller parameters on the absorbed power, these parameters are optimized by imperialist competitive algorithm. The results illustrate the method’s efficiency in maximizing the extracted power in the presence of unknown excitation force which should be predicted by Kalman filter.

Modeling and Current Programmed Control of a Bidirectional Full Bridge DC-DC Converter

Modelling of bidirectional full bridge DC-DC converter as one of the most applicable converters has received significant attention. Mathematical modelling reduces the simulation time in comparison with detailed circuit response;moreover it is convenient for controller design purpose. Due to simple and effective methodology, average state space is the most common method among the modelling methods. In this paper a bidirectional full bridge converter is modelled by average state space and for each mode of operations a controller is designed. Attained mathematical model results are in a close agreement with detailed circuit simulation.

LARGE SIGNAL DISCRETE-TIME MODEL FOR PARALLELED BUCK CONVERTERS

As a number of switch combinations are involved in operation of multi converter system, conventional methods for obtaining discrete time large signal model of these converter systems result in a very complex solution. A simple sampled data technique for modeling distributed dc dc PWM converters system (DCS) was proposed. The resulting model is nonlinear and can be linearized for analysis and design of DCS. These models are also suitable for fast simulation of these networks. As the input and output of dc dc converters are slow varying, suitable model for DCS was obtained in terms of the finite order input/output approximation.

Mathematical Modeling of the Efficiency Gadolinium Based Neutron Converters

Procedures of mathematical modeling of thin solid-state converters of neutrons are described and converters a foil from natural gadolinium and its 157 isotopes are viewed. Algorithms of calculation of absorption of neutrons in a material of converters, probabilities formation of secondary electrons, probability of an exit of electrons from a material of the converter and efficiency of converters are given. Calculation is made for various thicknesses of converters, and various wavelengths of neutrons. The optimal converter thicknesses are chosen.

Numerical Simulation of Cold-Start Emission for the Three-Way Catalytic Converter: Mathematical Model and Result Analysis

This paper integrated a two-dimensional axisymmetrical transient model applicable to cold-start emission applications. The model can be used to simulate and explain effects of the flow and temperature distribution on performance of a converter. The evolutions of distribution of the temperature and concentration in the monolith during the cold-start period and the effects of flow distribution in the monolith on the cold-start performance are simulated in terms of the integrated model. The investigation indicates that the axial and radial gradients of temperature of the solid become steeper as the inlet gas temperature ramp increases; this furthermore results in the movement of reaction region in the monolith, and the flow distribution in the monolith affects the radial distribution of temperature of the solid;the radial gradients of temperature of the solid become greater as the flow uniformity index decreases, whereas the light-off time doesn't always increase as the flow uniformity index decreases. The analyses on the distribution of temperature and concentration in the monolith show that the catalytic reaction zone concentrates in central area near the front face. The predicted curves of the velocity distribution have a good agreement with the experimental data.

Analysis and Modeling of Buck Converter in Discontinuous-Output-Inductor-Current Mode Operation

The Buck converter with LC input filter operating in discontinuous output current mode has a high power factor with a constant duty cycle. A Buck converter in this operation mode can reduce the reverse recovery loss of the freewheeling diode thus increase the efficiency. The operation, power factor analysis and modeling of the converter are studied in this paper. Experimental results are presented to verify the theoretical predictions.

H-bridge Hybrid Converter Modeling and Synthesize with Power Sharing Analysis

In this paper hybrid converters with double inputs are investigated. Mainly any possible topologies are constructed and only one of them is chosen and modeled in none ideal format, by state space averaging method. After that small signal model and equilibrium point of that model is calculated. Finally with power sharing analysis the best point in efficiency was calculated.

三电平辅助变流器寿命优化控制

辅助变流系统是动车组车辆上关键的电气组成部分,主要为空调机组、风机、照明等交流负载提供稳定的三相电源。结温是影响动车组三电平辅助变流器IGBT(Insulated-gate Bipolar Transistor)模块寿命的主要因素。为了提高动车组三电平中点钳位(Neutral-Point Clamped,NPC)型辅助变流器寿命,提出一种降低结温的模型预测电流控制(Model Predictive Current Control,MPCC)策略。首先,考虑传统MPCC在每个采样周期需要代入27个电压矢量循环计算,计算量较大,因此将三电平基本电压矢量划分在间隔60°的6个扇区中,通过计算电压矢量在两相静止坐标下的相角,进而判断参考电压矢量所处扇区,将备选矢量数目从27缩减至10,减少了计算量;其次,传统MPCC直接应用于动车组辅助变流器会使IGBT模块的结温较高,老化速度加快,对变流器安全稳定运行产生不可预测的损害,本文对IGBT模块的开关损耗和导通损耗进行近似等效,得到了和集射极电压、集电极电流相关的功率损耗因子。通过预测每相电流的方向,进而预测IGBT模块的开关和导通情况,动态加入功率损耗因子,并在代价函数中约束每相IGBT及其续流二极管(Free Wheeling Diode,FWD)的功率损耗,使得最优电压矢量在降低功率损耗的同时保证一定的控制性能。通过仿真与实验验证,本文所提方法相比传统MPCC策略降低了功率器件的结温,提高了变流器寿命。

Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part II: Discontinuous Conduction Mode

This paper follows on from the first paper, Part I, where a general formulation of a describing function approach to frequency response determination of switched linear networks, such as PWM converters, was simplified and updated. The models assume a piecewise linear state space equation description of the system and results in a closed form solution for the sought after frequency response. In Part I, model derivation was demonstrated for the case of PWM converters operating in the continuous conduction mode (CCM). This operating mode does not feature any state dependent switching times. In this paper, Part II, frequency response models for any transfer function for PWM converters operating in discontinuous conduction mode (DCM) are derived based on the theory presented in Part I. This operating model features state dependent switching times. The describing function models developed are exact and therefore, in terms of accuracy, are to be preferred over averaged models which are widely used. The example of a boost dc-to-dc converter operating in DCM is simulated to obtain the control to output and input to output frequency responses and are compared with the models derived here. Excellent agreement between the simulated and model responses was found. Matlab code implementing the analytical models is also presented which the user can adapt for any other PWM converter topology. The models derived here may be used as a basis from which simplified models may be derived while still preserving required accuracy.

Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part I: Continuous Conduction Mode

A general approach is presented by which the exact frequency response of any transfer function of switched linear networks can be determined. This is achieved with a describing function approach using a state space equation formulation. This work presents a somewhat simplified set of equations to one previously given by one of the authors. To demonstrate application of the general formulation, the frequency responses of switched networks used as PWM DC-to-DC converters operating in continuous conduction mode (CCM) under voltage mode control are derived. (The accompanying paper, Part II, will present results for converters operating in discontinuous conduction mode (DCM)). From the general sets of equations developed here, both the control to output and input source variation to output frequency responses are derived. The describing function approach enables exact frequency response determination, even at high frequencies where the accuracy using average models may be compromised. Confirmation of the accuracy of the derived models is provided by comparing the responses with those obtained using the commercial simulator PSIM on a PWM boost converter. The magnitude and phase responses are shown to match perfectly over the full range of frequencies up to close to half the switching frequency. Matlab code that implements the models is given such that the user can easily adapt for use with other PWM converter topologies.

Modeling and Dynamic Analysis of Fractional-Order Buck Converter in Continuous Conduction Mode

According to the fact that the actual inductor and actual capacitor are fractional, the mathematical and state-space averaging models of fractional order Buck converters in continuous conduction mode(CCM) are constructed by using fractional calculus theory. Firstly, the parameter conditions that ensure that the converter working in CCM is given and transfer functions are derived. Also, the inductor current and the output voltage are analyzed. Then the difference between the mathematical model and the circuit model are analyzed, and the effect of fractional order is studied by comparing the integer order with fractional order model. Finally, the dynamic behavior of the current-controlled Buck converter is investigated. Simulation experiments are achieved via the use of Matlab/Simulink. The experimental results verify the correctness of theoretical analysis, the order should be taken as a significant parameter. When the order is taken as a bifurcation parameter, the dynamic behavior of the converter will be affected and bifurcation points will be changed as order varies.

Study on Bifurcation and Chaos in Boost Converter Based on Energy Balance Model

Based on boost converter operating in discontinuous mode, this paper proposes an energy balance model (EBM) for analyzing bifurcation and chaos phenomena of capacitor energy and output voltage when the converter parameter is varying. It is found that the capacitor energy and output voltage dynamic behaviors exhibit the typical period-doubling route to chaos by increasing the feedback gain constant K of proportional controller. The accurate position of the first bifurcation point and the iterative diagram of the capacitor energy with every K can be derived from EBM. Finally, the underlying causes for bifurcations and chaos of a general class of nonlinear systems such as power converters are analyzed from the energy balance viewpoint. Com-paring with the discrete iterative model, EBM is simple and high accuracy. This model can be easily devel-oped on the nonlinear study of the other converters.

Semi-Automatic Modeling Technique of Torque Converter Flow Passage

The modeling technique of hydrodynamic torque converter flow passage was investigated. The semi-automatic modeling technique of torque converter flow passage was proposed. The flow passage model of each converter wheel is considered as a revolution entity sliced by two curved surfaces. In order to generate the revolution entity, a new approximation method, condition optimum arc approximation, was proposed. The method was used to approximate the meridional streamlines of the inner and outer wall. As a result, the three-dimensional revolution entity can be conveniently generated. In order to create slice surfaces, the central stream surface of flow passage was approximated with a quadric surface. The normal vector of the quadric surface and the thickness/thickness-function of bade were used to calculate the discrete point coordinates of blade surfaces. Via the rotation transformation to the coordinates, the discrete point coordinates of slice surfaces were obtained. A parameterized program code used for the hydrodynamic torque converter design and semi-automatic modeling was developed. Modeling errors were calculated and analyzed. The flow passage model was generated in several minutes with the help of the program code, Auto CAD and Solidworks software. Finally, the model was inputted into Gambit, and the pre-processing task used for the numerical simulation of torque converter flow field was successfully completed. The investigation results show that the semi-automatic modeling not only can ensure the accuracy of modeling, but also librates the research and design workers of torque converter from the time-consuming modeling work, which paves the way for the numerical simulation of the complex flow field of the hydrodynamic torque converter.