Tài liệu Power Electronic Handbook P6 ppt

Multilevel Converters Diode-Clamped Multilevel Converters • Flying-Capacitor Multilevel Converters • Cascaded H-Bridge Multilevel Converters • Multilevel H-Bridge Converters Cascaded Mul

Multilevel Converters

Diode-Clamped Multilevel Converters • Flying-Capacitor Multilevel Converters • Cascaded H-Bridge Multilevel Converters • Multilevel H-Bridge Converters

Cascaded Multilevel Converters • Cascaded Multilevel H-Bridge Converters

Three-Level Diode-Clamped Inverter • The Cascade-3/2 Inverter • The Cascade-5/3H Inverter

6.1 Introduction

Multilevel power conversion was first introduced 20 years ago [1] The general concept involves utilizing

a higher number of active semiconductor switches to perform the power conversion in small voltagesteps There are several advantages to this approach when compared with traditional (two-level) powerconversion The smaller voltage steps lead to the production of higher power quality waveforms and alsoreduce the dv/dt stresses on the load and reduce the electromagnetic compatibility (EMC) concerns.Another important feature of multilevel converters is that the semiconductors are wired in a series-typeconnection, which allows operation at higher voltages However, the series connection is typically madewith clamping diodes, which eliminates overvoltage concerns Furthermore, since the switches are nottruly series connected, their switching can be staggered, which reduces the switching frequency and thusthe switching losses

One clear disadvantage of multilevel power conversion is the larger number of semiconductor switchesrequired It should be pointed out that lower voltage rated switches can be used in the multilevel converterand therefore the active semiconductor cost is not appreciably increased when compared with the two-level case However, each active semiconductor added requires associated gate drive circuitry and addsfurther complexity to the converter mechanical layout Another disadvantage of multilevel power con-verters is that the small voltage steps are typically produced by isolated voltage sources or a bank of seriescapacitors Isolated voltage sources may not always be readily available and series capacitors requirevoltage balance To some extent, the voltage balancing can be addressed by using redundant switchingstates, which exist due to the high number of semiconductor devices However, for a complete solution

to the voltage-balancing problem, another multilevel converter may be required [2–4]

In recent years, there has been a substantial increase in interest in multilevel power conversion This

is evident by the fact that some Institute of Electrical and Electronic Engineers (IEEE) conferences areKeith Corzine

University of Wisconsin–Milwaukee

now holding entire sessions on multilevel converters Recent research has involved the introduction ofnovel converter topologies and unique modulation strategies Some applications for these new convertersinclude industrial drives [5–7], flexible AC transmission systems (FACTS) [8–10], and vehicle propulsion[11, 12] One area where multilevel converters are particularly suitable is that of medium-voltage drives [13].This chapter presents an overview of multilevel power conversion methods The first section describes

a general multilevel power conversion system Converter performance is discussed in terms of voltagelevels without regard to the specific topology of the semiconductor switches A general method ofmultilevel modulation is described that may be extended to any number of voltage levels The next sectiondiscusses the switching state details of fundamental multilevel converter topologies The concept ofredundant switching states is introduced in this section as well The next section describes cascadedmultilevel topologies, which involve alternative connections of the fundamental topologies The finalsection shows example multilevel power conversion systems including laboratory measurements

6.2 Multilevel Voltage Source Modulation

Before proceeding with the discussion of multilevel modulation, a general multilevel power converterstructure will be introduced and notation will be defined for later use Although the primary focus ofthis chapter is on power conversion from DC to an AC voltages (inverter operation), the materialpresented herein is also applicable to rectifier operation The term multilevel converter is used to refer to

a power electronic converter that may operate in an inverter or rectifier mode

motor load is shown on the AC side of the converter However, the converter may interface to an electricutility or drive another type of load The goal of the multilevel pulse-width modulation (PWM) block

is to switch the converter transistors in such a way that the phase voltages v as, v bs, and v cs are equal tocommanded voltages , , and The commanded voltages are generated from an overall supervisory

FIGURE 6.1 Multilevel converter structure.

cs

cs

control [14] and may be expressed in a general form as

(6.1) (6.2)

(6.4)

Because an inverse of the matrix in Eq (6.4) does not exist, there is no direct relationship betweencommanded phase voltages and line-to-ground voltages In fact, there are an infinite number of voltagesets {v ag v bg v cg} that will yield a particular set of commanded phase voltages because any zero sequencecomponents of the line-to-ground voltages will not affect the phase voltages according to Eq (6.4) In athree-phase system, zero sequence components of {v ag v bg v cg} include DC offsets and triplen harmonics

of θc To maximize the utilization of the DC bus voltage, the following set of line-to-ground voltagesmay be commanded [16]

(6.5)

(6.6)

(6.7) where m is a modulation index It should be noted that the power converter switching will yield line-to-ground voltages with a high-frequency component and, for this reason, the commanded voltages inEqs (6.5) to (6.7) cannot be obtained instantaneously However, if the high-frequency component isneglected, then the commanded line-to-ground voltages may be obtained on a fast-average basis Bysubstitution of Eqs (6.5) to (6.7) into Eq (6.4), it can be seen that commanding this particular set ofline-to-ground voltages will result in phase voltages of

2 –1 –11

6 cos(3θc)–

+

=

v bg∗ vdc

2 - 1 m θc

2π3 -–

6 cos(3θc)–

+

=

v cg∗ vdc

2 - 1 m θc

2π3 -+

6 cos(3θc)–

=

vˆ bs

mvdc

2 - θc

2π3 -–

2π3 -+

cos

=

where the symbol denotes fast-average values By comparing Eqs (6.8) to (6.10) with Eqs (6.1) to

(6.3), it can be seen that the desired phase voltages are achieved if

(6.11)

It should be noted that in H-bridge-based converters, the range of line-to-ground voltage is twice that

of converters where one DC voltage supplies all three phases (as in Fig 6.1) The modulation method

here can accommodate these converters if the modulation index is related to the commanded voltage

magnitude by

(6.12)

The modulation process described here may be applied to H-bridge converters by substituting m H for m

in the equations that follow The benefit of including the third harmonic terms in Eqs (6.5) to (6.7) is

an extended range of modulation index [16] In particular, the range of the modulation index is

(6.13)

It is sometimes convenient to define a modulation index that has an upper limit of 100% or

(6.14)

The next step in the modulation process is to define normalized commanded line-to-ground voltages,

which will be referred to as duty cycles In terms of the modulation index and electrical angle, the duty

cycles may be written:

(6.15)

(6.16)

(6.17)

To relate the duty cycles to the inverter switching operation, switching states must be defined that are

valid for any number of voltage levels Here, the switching states for the a-, b-, and c-phase will be denoted

s a, s b, and s c, respectively Although the specific topology of the multilevel converter is covered in the next

section, it may be stated in general for an n-level converter that the AC output consists of a number of

6 cos(3θc)–

6 cos(3θc)–

6 cos(3θc)–

+

=

voltage levels related to the switching state by

line-to-ground voltages for two-level, three-level, and four-level converters In each case, the fast-average of

v ag will equal the commanded value However, it can be seen that as the number of voltage levels

increases, the converter voltage yields a closer approximation to the commanded value, resulting in lowerharmonic distortion

The next step in multilevel modulation is to relate the switching states s a , s b , and s c to the duty cyclesdefined in Eqs (6.14) through (6.16) Here, the multilevel sine-triangle technique will be used for this

purpose [17, 18, 19] The first step involves scaling the duty cycles for the n-level case as

(6.22) (6.23) (6.24) The switching state may then be directly determined from the scaled duty cycles by comparing them to

a set of high-frequency triangle waveforms with a frequency of f sw For an n-level converter, n − 1 trianglewaveforms of unity amplitude are defined As an example, consider the four-level case Figure 6.3a shows

the a-phase duty cycle and the three triangle waveforms offset so that their peaks correspond to the nearest switching states In general, the highest triangle waveform has a minimum value of (n − 2) and

a peak value of (n − 1) The switching rules for the four-level case are fairly straightforward and may bespecifically stated as

(6.25)

similar to that of Fig 6.2d and, therefore, the resulting line-to-ground voltage according to Eq (6.17)will have a fast-average value equal to its commanded value These switching rules may be extended to

any number of levels by incorporating the appropriate number of triangle waveforms and definingswitching rules similar to Eq (6.25) It should be pointed out that the sine-triangle method is shownhere since it is depicts a fairly straightforward method of accomplishing multilevel switching In practice,the modulation is typically implemented on a digital signal processor (DSP) or erasable programmablelogic device (EPLD) without using triangle waveforms One common method for implementation isspace-vector modulation [20–22], which is a method where the switching states are viewed in the voltagereference frame Another method that may be used is duty-cycle modulation [23], which is a directcalculation method that uses duty cycles instead of triangle waveforms and is more readily implementable

on a DSP It is also possible to perform modulation based on a current-regulated approach [22, 24],which is fundamentally different than voltage-source modulation and results in a higher bandwidthcontrol of load currents

FIGURE 6.2 Power converter line-to-ground output voltages.

ag

ag dc

ag

dc

ag dc

6.3 Fundamental Multilevel Converter Topologies

This section describes the most common multilevel converter topologies In particular, the diode-clamped[25–28], flying capacitor [29, 30], cascaded H-bridge [31–33], and multilevel H-bridge [34] structuresare described In each case, the process of creating voltage steps is illustrated and the relation to thegeneralized modulation scheme in the previous section is defined For further study, the reader may beinterested in other topologies not discussed here, such as the parallel connected phase poles [35], ACmagnetically combined converters [36, 37], or soft-switching multilevel converters [38]

Diode-Clamped Multilevel Converters

One of the most common types of multilevel topologies is the diode-clamped multilevel converter[25–28] Figure 6.4 shows the structure for the three-level case Comparing this topology with that of astandard two-level converter, it can be seen that there are twice as many transistors as well as addeddiodes However, it should be pointed out that the voltage rating of the transistors is half that of thetransistors in a two-level converter Although the structure appears complex, the switching is fairlystraightforward Figure 6.5 shows the a-phase leg of the three-level diode clamped converter along with

the corresponding switching states Here, it is assumed that the transistors act as ideal switches and thatthe capacitor voltages are charged to half of the DC-link voltage As can be seen in Fig 6.5b, in switching

state s a = 0, transistors T a3 and T a4 are gated on and the output voltage is v ag= 0 Similarly, switching state

s a = 2 involves gating on transistors T a1 and T a2 and the output voltage is v ag = vdc These switching states

produce the same voltages as a two-level converter Switching state s a= 1 involves gating on transistors

T a2 and T a3 as shown in Fig 6.5c In this case, the point a is connected to the capacitor junction through the added diodes and the output voltage is v ag = vdc/2 Note that for each of the switching states, the transistorblocking voltage is one half the DC-link voltage When compared with the two-level converter, theadditional voltage level allows the production of line-to-ground voltages with lower harmonic distortion,

as illustrated in Fig 6.2 Furthermore, the switching losses for this converter will be lower than that of

a two-level converter Switching losses are reduced by the lower transistor blocking voltage and increased

by the higher number of transistors However, it can be seen by inspection of Figs 6.2 and 6.5 that each

transistor is switching only during a portion of the period of d a, which again reduces the switchinglosses Maintaining voltage balance on the capacitors can be accomplished through selection of the

FIGURE 6.3 Four-level sine-triangle modulation technique.

a

tr3

tr2

tr1

FIGURE 6.4 Four-level converter topology.

FIGURE 6.5 Three-level converter switching states.

as

cs bs dc

a dc

redundant states [27] Redundant switching states are states that lead to the same motor voltages, butyield different capacitor currents As an example, consider the three-level converter redundant switching

states sw = 24 and sw = 9 shown in Fig 6.6 It can be shown through Eq (6.4) that either switching statewill produce the same voltages on the load (assuming the capacitor voltages are nearly balanced) However,from Fig 6.6 it can be seen that the current drawn from the capacitor bank will be different in each case

In particular, if the a-phase current is positive, the load will discharge the capacitor that it is connected

to In this case, the load should be connected across the capacitor with the highest voltage On the other

hand, if the a-phase current is negative, it will have a charging effect and the load should be connected

across the capacitor with the lowest voltage Therefore, capacitor voltage balancing through redundantstate selection (RSS) is a straightforward matter of selecting between the redundant states based on whichcapacitor is overcharged with respect to the other and the direction of the phase currents This infor-mation may be stored in a lookup table for inclusion in the modulation scheme [25, 27] Figure 6.7

shows a block diagram of how an RSS table may be included in the modulation control There, themodulator determines the desired switching states as described in the previous section The desiredswitching state as well as the capacitor imbalance and phase current direction information are used asinputs to the lookup table, which determines the final switching state As a practical matter, this tablemay be implemented in a DSP along with the duty-cycle calculations or may be programmed into anEPLD as a logic function

FIGURE 6.6 Redundant switching state example.

FIGURE 6.7 Redundant switching state example.

xs xs

a b c

Figure 6.8 shows the topology for the four-level diode-clamped converter Proper operation requiresthat each capacitor be charged to one third of the DC-link voltage The transistor switching is similar to

that of a three-level converter in that there are (n − 1) adjacent transistors gated on for each switching

state The switching results in four possibilities for the output voltage v ag = {0 vdc vdc vdc} In thistopology, each transistor need only block one third of the DC-link voltage The diode-clamped conceptmay be extended to a higher number of levels by the expansion of the capacitor bank, switching transistors,and clamping diodes However, there are some practical problems with diode-clamped converters of four

voltage levels or more The first difficulty is that some of the added diodes will need to block (n − 2)/

(n − 1) of the DC-link voltage [28] As the number of levels is increased, it may be necessary to connectclamping diodes in series to block this voltage It should also be pointed out that capacitor voltage balancethrough RSS works well for the three-level topology, but for converters with a higher number of voltagelevels there are not enough redundant states to balance the capacitor voltages when the modulation index becomes greater than 60% [27] In these cases, another multilevel converter, such as a multilevelrectifier [25] of multilevel DC-DC converter [25] must be placed on the input side for voltage balance

Flying-Capacitor Multilevel Converters

behind this converter is that the added capacitor is charged to one half of the DC-link voltage and may

be inserted in series with the DC-link voltage to form an additional voltage level [29, 30] Figure 6.10

shows how this is accomplished through the transistor switching As can be seen, switching states s a= 0

and s a= 2 involve gating on the two lower and upper transistors as was done with the diode-clamped

structure In this topology, there are two options for switching to the state s a= 1, as can be seen in Fig

DC-link voltage In essence, there is switching redundancy within the phase leg Since the direction of thecurrent through the capacitor changes depending on which redundant state is selected, the capacitor

FIGURE 6.8 Four-level converter topology.

c5 b5

1 dc 2

1 3 2 3

m

voltage may be maintained at one half the DC-link voltage through the redundant state selection withinthe phase.

Cascaded H-Bridge Multilevel Converters

Cascaded H-bridge converters consist of a number of H-bridge power conversion cells, each supplied by

an isolated source on the DC side and series-connected on the AC side [31–33] Figure 6.11 shows the

a-phase of a cascaded H-bridge converter, where two H-bridge cells are utilized It should be pointed

out that, unlike the diode-clamped and flying-capacitor topologies, isolated sources are required for eachcell in each phase In some systems these sources may be available through batteries or photovoltaic cells[32], but in most drive systems transformer/rectifier sources are used Figure 6.12 illustrates the switchingstate detail for one H-bridge cell As can be seen, three unique output voltages are possible In accordancewith the convention used here, the lowest switching state will be labeled state 0 When these cells arecombined in series, an effective switching state can be related to the switching states of the individualcells By defining switching states in this way, the modulation scheme of the previous section may beapplied to this converter as well The output voltage of the inverter may be determined from the switchingstates of the individual cells by

(6.26)

where p is the number of series H-bridge cells.

If the DC voltage applied to each cell is set to the same value, then the effective number of voltagelevels may be related to the number of cells by

(6.27)Therefore, the converter shown in Fig 6.10 would operate with five voltage levels To obtain a clearercomprehension of how the voltage levels are produced, Table 6.1 shows the overall switching state as well

as the switching states of the individual cells and the resulting output voltage As can be seen, there isquite a bit of switching state redundancy within one phase leg of the cascaded H-bridge converter for

states s a = 1, sa = 2, and sa = 3 This redundancy may be exploited to increase the number of voltage levels

FIGURE 6.9 Three-level flyback converter topology.

a2

a3

a4

ag dc