Patin Power Electronics Applied to Industrial Systems and Transports, Volume 3

Switching Power Supplies
1. Auflage 2015
ISBN: 978-0-08-100462-3
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 184 Seiten

Some power electronic converters are specifically designed to power equipment under a smoothed DC voltage. Therefore, the filtering part necessarily involves the use of auxiliary passive components (inductors and capacitors). This book deals with technical aspects such as classical separation between isolated and non-isolated power supplies, and soft switching through a special converter. It addresses the problem of regulating the output voltage of the switching power supplies in terms of modeling and obtaining transfer of SMPS functions.Power Electronics for Industry and Transport, Volume 3, offers a case study of an isolated flyback power which the complete design is presented: the active and passive components are sized based on the specifications initially set. Particular attention is given to the converter output capacitors and all the surrounding organs. - Introducing Essential notions in power electronics from both the theoretical and technological perspectives - Detailed chapters with a focus on switch-mode power supplies, another key area in which power electronics is used is in the supply of energy to a variety of electronic equipment for signal and information processing - Presented from a user's perspective to enable you to apply the theory of power electronics to practical applications

Nicolas Patin's research activities are based around PWM inverter circuits (electric and hybrid vehicles) and the aging of electrolytic capacitors.

Autoren/Hrsg.

Patin, Nicolas

Leseproben

1

Non-Isolated Switch-Mode Power Supplies

Abstract

The buck converter is a single-quadrant chopper, as studied in Chapter 1 of Volume 2 [PAT 15b]. The “load” is made up of an inductance L in series with the association of the actual load (presumed to be a current source Is) in parallel with a filtering capacitor C. In these conditions, for a correctly dimensioned power supply, the assembly (Is,C) may be considered to be analogous to the electromotive force (e.m.f.) Ea of a direct current (DC) machine, and the inductance L may be considered to play the same role as the armature inductance in the machine.

Keywords

Boost converters

Buck converters

Critical conduction point

FeSi core

Forward isolated power supply

Inductive storage chopper

Power factor correctors (PFCs)

1.1 Buck converters

The buck converter is a single-quadrant chopper, as studied in Chapter 1 of Volume 2 [PAT 15b]. The “load” is made up of an inductance L in series with the association of the actual load (presumed to be a current source Is) in parallel with a filtering capacitor C (see Figure 1.1).

Figure 1.1 Diagram of a buck converter

In these conditions, for a correctly dimensioned power supply, the assembly (Is,C) may be considered to be analogous to the electromotive force (e.m.f.) Ea of a direct current (DC) machine, and the inductance L may be considered to play the same role as the armature inductance in the machine. Consequently, the results established in Chapter 1 of Volume 2 [PAT 15b] are applicable here. In the case of continuous conduction, an output voltage of s=a.Ve is obtained, where a is the duty ratio of the transistor control. Moreover, in cases of discontinuous conduction (i.e. for a current which cancels out in the inductance), the output voltage will be higher than in the continuous conduction case, in accordance with the characteristic shown in Figure 1.4 (see Chapter 1 of Volume 2 [PAT 15b]). A summary of the characteristics of this converter is shown in 1.1. The constraints applicable to the switches are similar to those for a one-quadrant chopper powering a DC machine, but we should also analyze the quality of the voltage supplied to the load. The waveforms produced are the same as those shown in Figure 1.2 (Volume 2, Chapter 1 [PAT 15b]), as the ripple of the output voltage Vs is considered to be a second-order phenomenon, negligible when calculating the ripple of current iL in inductance L (constant Vs, as for the e.m.f. Ea of a DC machine). Thus, this current may be considered (as in the case of a machine power supply) to be a time-continuous, piecewise-affine function, which may be written (presuming that the load current is is constant and equal to Is) as:

Lt=Is+i˜Lt

  [1.1]

Figure 1.2 Current in the inductance and voltage at the capacitor terminals in a buck converter

where ˜Lt is a signal with an average value of zero, with a “peak-to-peak” ripple ?iL expressed as:

iL=a.1-a.VeL.Fd

  [1.2]

where Fd = 1/Td is the switching frequency and a the duty ratio of the control of transistor T.

Second, given the current ripple ˜Lt, the (low) ripple of the output voltage ?s(t) may be deduced, insofar as:

st=Vs+?˜st

  [1.3]

with:

s=a.Ve

  [1.4]

and:

˜st=?˜st0+1C?t0t0+tiCt.dt=?˜st0+1C?t0t0+ti˜Lt.dt

  [1.5]

Using this result, it is then easy to deduce the peak-to-peak ripple ??s of voltage ?s (t):

?s=1C.·12·Td2·?iL2=a.1-a.Ve8L.C.Fd2

  [1.6]

These results are illustrated in Figure 1.2.

Remark 1.1

In practice, it is important to dimension the capacitor correctly so that the ripple of the output voltage is low in relation to its average value (e.g. 1%) in order to guarantee the validity of the reasoning used above. The current ripple was calculated based on the assumption that the output voltage is constant; strictly speaking, this assumption is not fulfilled, but the simplification is verified in practice. The decoupling of inductance and capacitor dimensioning is widespread when designing switch-mode power supplies, and will be used again when studying other structures. While this reasoning approach may appear artificial, it is based on “auto-coherence” between the initial hypotheses and the desired dimensioning objective. In practice, the output voltage should be as constant as possible when powering electrical equipment using switch-mode supplies (DC/DC converters).

Table 1.1

Summary of continuous conduction in the buck converter

Quantities

Values

Maximum transistor voltage VTmax

Ve

Maximum inverse diode voltage Vdmax

– Ve

Current ripple in inductance ?iL

.1-a.VeL.Fd

Average output voltage <Vs>

a.Ve

Output voltage ripple ??s

.1-a.Ve8L.C.Fd2

Maximum current in transistor and diode

s+?IL2

Average current in transistor <IT >

a.Is

Average current in diode <Id>

(1–a).Is

RMS current in transistor (for ?iL  Is)

.Is

RMS current in diode (for ?iL  Is)

-a.Is

Note that the calculation of the output voltage ripple (used in dimensioning the filter capacitor C) corresponds to a continuous mode of operation. This is not strictly applicable for discontinuous mode, but this choice presents certain advantages:

– simpler calculations using this operating mode;

– the results obtained allow satisfactory dimensioning of capacitors (on the condition that a minimum safety margin is respected) for all possible cases;

– continuous conduction is often the most critical case with regard to the output ripple, although this is not true for buck converters. The output ripple is proportional to the charge current (for boost and buck-boost converters, described in the following sections), and is higher in continuous mode (discontinuous conduction = low charge).

1.2 Dimensioning a ferrite core inductance

For iron core windings (as discussed in Chapter 5 of Volume 1 [PAT 15a]), a simple magnetic circuit was considered, characterized on the sole basis of three geometric parameters (reduced to two parameters) which needed to be established. While the equation model of the inductance and the applicable usage constraints remain identical, the geometry of a ferrite core is required, and a core must simply be selected from the lists supplied in manufacturer catalogs. The first stage in this process is to choose a family of ferrite cores: this choice depends on the application and the available space. Note the existence of “E,I” structures (alongside double E structures); in power electronics, however, the RM and PM families are most interesting in terms of electromagnetic compatibility, as they are relatively “closed” and produce limited radiation into the immediate environment. Two examples of these families of cores are shown in Figure 1.3.

Figure 1.3 RM a) and PM b) ferrite cores

Once a family of cores has been selected, we need to choose a specific model in accordance with a given specification. To do this, the expressions of Ae (iron section) and Sb (windable section) are used. Note that two surfaces are linked to constraints relating to ferrite (magnetic flux density Bmax) and copper (current density...