外文翻譯---雙向全橋dc-dc變流器的建模與仿真（英文）

1、Energy and Power Engineering, 2012, 4, 107-116 http://dx.doi.org/10.4236/epe.2012.43015 Published Online May 2012 (http://www.SciRP.org/journal/epe) 107Modeling and Current Programmed Control of a Bidirectional Full

2、Bridge DC-DC Converter Shahab H. A. Moghaddam, Ahmad Ayatollahi, Abdolreza Rahmati School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran Email: shahab.h.moghaddam@gmail.com, {ayatoll

3、ahi, rahmati}@iust.ac.ir Received February 7, 2012; revised February 28, 2012; accepted March 16, 2012 ABSTRACT Modelling of bidirectional full bridge DC-DC converter as one of the most applicable converters has received

4、 signifi- cant 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 methodolog

5、y, 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 desig

6、ned. Attained mathematical model results are in a close agreement with detailed circuit simulation. Keywords: Average State Space; Bidirectional; Detailed Circuit Simulation; Full Bridge DC-DC Converter; Mathematical

7、Modeling 1. Introduction Modeling of DC-DC converter as one of the most appli- cable industrial converters has aroused a lot of interest. Since modeling gives us information about static and dynamic of the system, it

8、is a crucial factor in design and control. Moreover, attained mathematical model can re- duce the simulation time in comparison with the simula- tion time provided by “cycle by cycle” solving the dif- ferential equati

9、ons of the circuit, as is the case in matlab/ simulink. With respect to renewable energy systems and optimum use of regenerated energy, interface converters should be capable of transferring power in both directions.

10、 So bidi- rectional DC-DC converters (BDC) are one of the most important interfaces that have applications such as: hybrid or electrical vehicles [1], aerospace systems [2], tele- communications, solar cells, battery

11、 chargers [3], DC motor drive circuits [4], uninterruptable power supplies [5-7], etc. so far many BDCs topologies have been in- troduced and surveyed [8,9]. In applications that trans- ferred power is more than 750

12、watts, full bridge topology is a proper one [10]. Bidirectional full bridge (FB) converters have been studied in many papers like [11-13]. A general modeling method that develops the discrete time average model is p

13、roposed in [12]. The operation period is divided to 3 intervals, the equivalent circuit and the differential equa- tions for each interval are written in matrix form. After solving equations and applying approximation

14、 of Taylor expansion, the averaging state vector in half cycle gives us the final answer. Since time domain method employs numerical integration to solve differential equations the analysis is complicated and computat

15、ionally intensive. Moreover the information about the dependence of the converter’s operating conditions on the circuit parameters is not provided [14]. Reference [13] proposes a discrete Small signal model with the

16、 amount of considerable calculation, just to pre- dict the peak response of state vectors. There are also some identification-based methods like NARMAX [15, 16] and Hammerstein [17,18] to model the DC-DC con- verter.

17、 Hammerstein model involves of a static nonlin- earity followed by a linear discrete-time and time-in- variant model, but identification based methods consider the system as a black/gray box, therefore they do not pr

18、ovide any insight into circuit details. So many refer- ences use circuit oriented methods to model the converter. Vorperian and Tymerski et al. [19,20] provide the circuit switch model with replacing the PWM switch wi

19、th its equivalent circuit in order to model the converter. This method may pose some complexity especially in non- basic topologies. Another circuit oriented method that is introduced by Middlebrook and Cuk [21-23] i

20、n 1977 is the average state space. An advantage of the state-space averaging method is its efficiency compared to that of the switched model because there is not any switching fre- quency ripple and, consequently, th

21、e simulation time required by the averaged model is much lower than re- quired by the switched model. Among all methods of Copyright © 2012 SciRes.

22、 EPE S. H. A. MOGHADDAM ET AL. 109With turning off the switches, next interval starts. Al- though the existence of leakage inductance prevents the switches go off immediately after applying gate turn

23、off pulses and conduction of switches will continue through parasitic capacitors and diodes, but it is assumed that these subintervals are very short and can be neglected. In off time, the secondary side is only fed

24、by the inductor stored energy, so the inductor current decreases propor- tional to output voltage. Next half switching cycle is the same, and only applied voltage of HV side is negative that is rectified in LV side.

25、3. Small Signal Modeling Using Average State Space Employing average state space method is divided into three phases: 1) With respect to switch conditions, the circuit is di- vided into different subintervals and sta

26、te equations are written in the matrix form in each interval. State vectors are defined as inductors currents and capacitors voltages. 2) Averaged equations are formed by taking weighted average of state equations of

27、 each interval. 3) Averaged equations are written in differential form then linearization is done by perturbing variables. Em- ploying Laplace transform and omitting additional AC and DC terms (only first order AC te

28、rms), needed transfer functions are achieved. For simplicity of modeling the following assumptions can be employed: ? Switches are ideal, there is no parasitic effect in switches; ? Inductor has no resistance; ? T

29、ransformer is ideal and there are no leakage and magnetizing inductances; ? Filter capacitors have low ESR (equivalent series re- sistance) that can be neglected; ? Load is constant and for modeling of the load chang

30、e an additional current source has been added at the out- put; ? Each mode (buck or boost modes) starts with zero ini- tial condition. State equations will be written in each mode separately and with some mathemat

31、ical operations one can derive needed transfer functions. 3.1. Boost Mode State Equations As we saw in Section 2.1 in this mode two main intervals can be assumed. When all four switches conduct the equivalent circuit

32、will be the same as shown in Figure 4 and the differential equations can be written as follows: d d 1d dL LIN v L ? ? IN i i v t t L ?(1) d d 1 1d dc c cz z C v v v C i i v R t t C RC ? ? ? ? ?(2) d 1 0 0 0 d 1 1d 0 0 d

33、LL INC Z ci i v t L v i v RC C t? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?(3) This state lasts for (d – 0.5)Ts where 1 s s is pe- riod of switching, T f ?on s d t

34、 T ?is the effective duty ratio and n is turn ratio of secondary to primary windings. In the next interval when diagonal switches conduct, the equivalent circuit can be sketched as the same in Figure 5 and the state

35、equations can be written as below: d d 1 1 0 d dC L LIN IN C v i i v L v v t n t L nL ? ? ? ? ? ? ?(4) d d 1 1 1d dC C C LZ L Z C v v v i i c i i v n R t t nC C RC ? ? ? ? ? ? ?(5) d 1 1 0 0 d 1 d 1 1 0 dLL INC Z ci i v

36、t nL L v i vC nC RC t? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? 0 1 0 0 L IN C o c C Zi v Y v v Y v i? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?(6) (7) This sta

37、te lasts for (1 – d)Ts. The output state in both intervals is the same as Equation (7). Now averaging the state equations during half switching cycle will result in the equation that has the characteristic of two inte

38、rvals: 2( 1) 1 0 0 & 1 2(1 ) 1 0t tdnL L A B dC nC RC? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?(8) Figure 4. Equivalent circuit of boost mode operation with four LV switches on. Figure 5. Circuit of b