Dc to Ac Conversion Inversion

7/28/2019 Dc to Ac Conversion Inversion

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22.5. DC TO AC CONVERSION: INVERSION

Dc to ac converters constitute a significant portion of power electronic

converters. These converters, also called inverters, are used in applications

such as electric motor drives, uninterruptible power supplies (UPS), and

utility applications such as grid connection of renewable energy sources.

Inverters for single phase ac and three-phase three-wire ac systems are

described in this section.

22.5.1. Single-Phase AC Synthesis

In an ac system both the voltage and the current should be able to reverse in

polarity. Further, the voltage and current polarities may or may not be the

same at a given time. Thus, a dc to ac converter implementation should be

able to output a voltage independent of current polarity. In the full bridge dc

to dc converter shown in Fig. 22-19a the primary circuit consisting of four

controlled switches, also called H-bridge, has two bi-positional switch

implementations. Each bi-positional switch has bidirectional currentcapability but only positive output voltage ( >, > 0). However, based

on the duty cycles, the difference of the outputs, V = , can

reverse in polarity. Thus the H-bridge is used for synthesizing single phase ac

voltage from a dc voltage.

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DC TO AC CONVERSION: INVERSION
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Figure 22.19. Single-phase inverter: (a) circuit, (b) quasi-square wave

synthesis.

22.5.1.1. Quasi-Square Wave Inverter.

The simplest form of dc to ac conversion, albeit with poor quality, is synthesis

of quasi-square wave ac instead of a pure sine wave. Diagonally opposite

switches in the H-bridge are turned on simultaneously. The pulse width of

each pair is controlled to adjust the magnitude of the fundamental

component, while the switching frequency is equal to the required output

frequency. The synthesized voltage waveform is shown in Fig. 22-19b. The

peak value of fundamental and harmonic components are

(22-31)

where d is the duty ratio and n the harmonic number. This converter is

widely used for low cost low power UPS applications where the voltage

waveform quality is not important. Incandescent lighting, universal input

motors, and loads with a diode bridge or power factor corrected front end

(discussed in Sec. 22.8) are not affected by the voltage waveform quality. The

load current, i , has harmonics based on the load characteristics.

Sometimes an LC filter is added at the output to reduce the harmonic

content. Low power low cost inverters such as those used to generate ac

from 14 V dc in automobiles usually have quasi square wave voltage output.

22.5.1.2. Single Phase Sinusoidal Voltage Synthesis.

AB
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For applications requiring low voltage and current distortion high-frequency

PWM is utilized to generate a sinusoidally varying average voltage. The

power converter used is the H-bridge shown in Fig. 22-19a. The duty ratio for

each bipositional switch, also called one leg of the inverter, is varied

sinusoidally. The switching signals are generated by comparison of a

sinusoidally varying control voltage with a trianglewave as shown in Fig. 22-

20. Equations relating the control voltages, duty ratios, and the averaged

output voltages are as follows:

Figure 22.20. Single-phase sinusoidal ac synthesis waveforms.

(22-32)
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(22-33)

(22-34)

(22-35)

(22-36)

(22-37)

(22-38

(22-39)

Here and are peak values of control voltage and the triangle wave

respectively, is the modulation index, = 2f is the

angular frequency of the sinusoid to be synthesized, while d (t) and d (t)

are duty ratios of switches S1 and S3, respectively. In Eq. (22-39) k may

be regarded as the gain of the power converter that amplifies the control

signal (t) to the average output voltage . The maximum peak value of

the output voltage, obtained for m= 1, is V . This is significantly lower than

that obtainable with the quasi square wave inverter (4V /). However,

harmonics in the output voltage are significantly reduced and are at much

higher frequencies: k f l f , where k and l are integers such that k +

l is odd. The switching frequency is much higher than the output frequency

f , which has a maximum value of about 50/60 Hz for standard applications

or 400 Hz for aerospace applications.

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If the load is inductive, such as a motor, the current harmonics are much

lower than the voltage harmonics. For several applications maximum

harmonic content for the voltage and current output from the inverter is

specified. In these cases an L-C filter similar to the buck converter is used.

Depending upon the application a two-stage L-C filter or a two-stage notch

filter (to suppress the dominant switching frequency harmonics) may beused. Further, it has to be ensured that when connected to the load, the filter

is adequately damped by a combination of passive selection and the control

loop. This aspect is particularly important for line connected applications

where the inverter is supplying power to the utility grid.

Equation (22-37) can be rewritten as

(22-40)

This clearly shows that on an average basis the "neutral point" for the output

of one inverter leg is V /2 above "N," i.e., at the mid-point of the input dc

bus. Thus using the same H-bridge a split-phase ac (two ac voltages 180 out

of phase with a common return) can be generated if the center point of the

dc bus is available as the neutral connection for the output. This type of

configuration is commonly used in generating 120/240 from the same

inverter. Furthermore, using three legs instead of two the converter can

generate three phase voltages with a neutral connection, with the flexibility

that the three phases may be loaded independently. Common applications

are inverters for interfacing photovoltaic systems to the utility grid and

exporting power from vehicles.

22.5.2. Three-Phase AC Synthesis

The last observation in the previous section leads us to three-phase inverters

without a neutral connection. The circuit consists of three legs, one for each

output with a common dc link as shown in Fig. 22-21a. Using sine triangle

PWM with control voltages offset by 120 (instead of 180 as in the single-

phase case) we obtain:

in
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(22-41)

(22-42)

k =A, B, C

(22-43)

Figure 22.21. Three-phase ac synthesis: (a) converter, (b) output

voltage vectors, (c) instantaneous waveforms.

The zero sequence component of the output voltages, = ( + +

)/3 = V /2, does not appear in the line-to-line voltages, and since there is

no neutral connection to the inverter, zero sequence currents do not flow.

The maximum peak value of the output line-to-line voltages is .

Using square wave inversion, similar to that for the single-phase case, we canobtain higher magnitude for the fundamental component of the output

voltages at the cost of adding harmonics. However, if, instead of all the

harmonics, only the fundamental and those harmonics of the square wave

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that contribute zero sequence component (triplen harmonics) are retained,

the output voltage amplitude increases without adding harmonics to the line-

to-line voltages and the line currents. Usually, addition of the third harmonic

component is sufficient. As described in Refs. 37 and 38 the most

effective method is to add the following zero sequence component to the

control voltages for each phase:

(22-44)

In terms of output voltage generation, this is equivalent to space vector

modulation (SVM).

22.5.3. Space Vector Modulation

This method has become extremely popular for three-phase inverters in the

low to medium power range. A very brief description will be presented here

and details can be found in Refs. 31, 35, and 37.

For three-phase systems with no zero sequence component, i.e., = ( +

+ )/3 = 0, the three-phase quantities are linearly dependent and canbe transformed to a two-phase orthogonal system commonly called the

system. Quantities in the system can be represented by complex numbers

and as two-dimensional vectors in a plane, called space vectors. The

transformation from the abc to quantities is given by

(22-45)

With negative sequence components absent, and components of steady

state sinusoidal abcquantities are also sinusoids with constant amplitude

and a 90 phase difference between them. Under transient conditions they

are arbitrary time varying quantities. Thus, for balanced sinusoidal

conditions, the space vector rotates in counter clockwise direction with

angular frequency equal to frequency of the abcvoltages, and describes a

circle of radius(3/2) being the peak of the phase voltage.

The instantaneous output voltages of the three-phase inverter shown in Fig.

22-21acan assume ei ht different combinations based on which of the six

35, 36

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MOSFETs are on. The space vectors for these eight combinations are shown

in Fig. 22-21b. For example, vector V denoted by (100) corresponds to

switch states = V , = 0, and = 0. The vectors V (000) and

V (111) have zero magnitude and are called zero vectors.

Synthesis utilizing the idea of space vectors is done by dividing one switching

time period into several time intervals, for each of which a particular voltage

vector is output by the inverter. These time intervals and the vectors applied

are chosen so that the average over one switching time period is equal to the

desired output voltage vector. For the reference voltage vector , shown in

Fig. 22-21b, the nonzero vectors adjacent to it (V and V ), and the zero

vectors (V and V ) are utilized as shown in Fig. 22-21c. Relative values of

time intervals t and t determine the direction, while ratio oft to the

switching time period determines the magnitude of the output vector

synthesized. The formulae for time intervals are as follows:

(22-46)

(22-47)

t /2 = T /2-(t + t )

(22-48)

where is the angle of the vector measured from the axis. The

maximum obtainable average vector lies along the hexagon connecting the

six nonzero vectors. As stated earlier, balanced three-phase sinusoidal

quantities describe a circle in the plane. Thus, to synthesize distortion

free and balanced three-phase sinusoidal voltages, the circle must be

contained within the hexagon, i.e., with a maximum radius of . This

gives the maximum peak value of line-to-line voltage obtained with SVM as

. This is significantly higher than that obtained using sine triangle

PWM: .

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Further, the sequence and choice of vectors applied can be optimized to

minimize number of switchings and ripple in the resulting currents. There

are several variations of SVM, each suited to a different application. SVM can

be easily implemented digitally using microcontrollers or DSPs, and is

advantageous in control of three-phase ac machines using vector control

and direct torque control (DTC). Experimental waveforms for an SVMinverter are shown in Fig. 22-22.

Figure 22.22. Experimentally measured PWM signal and line current

for one phase of a three-phase SVM inverter: (a) 60 Hz synthesis; (b)

20 Hz synthesis.

22.5.4. Multilevel Converters

The converter topologies described so far are based on a two-level converter

leg (bi-positional switch), where the output voltage of each leg ( ) can be

either zero or V . The converters are therefore called two-level converters.

39

40-44

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In two-level converters, all the switches have to block the full dc bus voltage

(V ). For high-power applications IGBTs and GTOs are used as the

semiconductor switches. These have higher voltage and current ratings and

lower on-state voltage drop compared to power MOSFETs, but cannot switch

as fast. In some applications like some motor drives and utility applications,

even the voltage ratings of available IGBTs and GTOs is not sufficiently high.

Simple series connection, to achieve a higher blocking voltage, has problems

of steady-state and dynamic voltage sharing. Moreover, due to the low

switching frequency of high-power switches, the output voltage and current

quality deteriorates. These issues are addressed by multilevel converters. In

a multilevel converter, the output of each phase leg can attain more than

two levels leading to improved quality of the output voltage and current. The

circuit comprising each leg and its proper operation ensure that voltage

blocked by the switches reduces as the number of levels is increased. In

addition, multilevel converters are modular to some extent, thereby making it

easy to scale voltage ratings by increasing the number of "cells."

22.5.4.1. Multilevel PWM.

For two-level PWM, comparison of the control voltage with a triangle wave

generates the switching signal for the top switch, while the bottom switch iscontrolled in complement to the top switch. Each of these two states

corresponds to the two levels of the output voltage. For multilevel

converters, there are more than two effective switch states, each of which

corresponds to an output voltage level. For example, in a three-level

converter there are three effective states q(t) = 0, 1, 2, corresponding to

output voltage levels (t) = 0, V /2, V . The control voltage (t) is

compared with two triangle waves to obtain two switching signals q (t) andq (t), and the effective switching signal can be obtained as q(t) = q (t) +

q (t) as shown in Fig. 22-23. The output voltage is then given by = q(t)

(V /2). Switching signals for the individual switches are derived using q(t)

and the circuit topology. For the waveforms in Fig. 22-23, f = 60 Hz and V

= 2 kV. Since the v waveform is closer to desired sinusoid in the three level

case, the output voltage has lower THD even if the switching frequency is

low. For three-phase converters, space-vector-based PWM can be used for

generating the switching signals, the advantage in the multilevel case

compared to the two-level case being the significantly higher number of

output voltage vectors.

in

45,46

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Figure 22.23. Multilevel triangle comparison.

22.5.4.2. Multilevel Converter Topologies.

The chief multilevel converter topologies are diode clamped, flying capacitor,

and cascaded full bridge.

22.5.4.2.1. DIODE CLAMPED CONVERTER.

Figure 22-24ashows one phase leg of a three-level diode-clamped

converter. The input dc bus is split by means of capacitors. Pairs of

switches are turned on to obtain three different voltage levels for the output

voltage = 0, V /2, V as shown in Fig. 22-24c. It is evident that this

circuit acts like a tri-positional switch connecting the output to one of three

positions of the input dc bus. The minimum voltage at point "b1," and the

maximum voltage at point "b2," is clamped to V /2 by the blocking diodes

D and D , respectively. Thus, all the switches have to blockV /2 during

their off state. This topology can be extended to more number of levels.

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However, it is eventually limited by the voltage rating of blocking diodes,

which have to block increasing voltages as the number of levels is increased.

One-phase leg of a five-level version is shown in Fig. 22-24b.

Figure 22.24. Diode clamped converters: (a) one phase of a three-

level converter, (b) one phase of fivelevel converter, (c) switching

states in a three-level converter.

22.5.4.2.2. FLYING CAPACITORCONVERTER.

Figure 22-25 shows the topology of a three-level flying capacitor converter.
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The basic idea here is that the capacitor C is charged to half the input dc

voltage by appropriate control of the switches. The capacitor can then be

inserted in series with the output voltage, either adding or subtracting V /2,

and thereby giving three output voltage levels.

Figure 22.25. Three-level flying capacitor converter.

22.5.4.2.3. CASCADED FULL BRIDGE CONVERTERS.

In this scheme, single-phase H-bridges shown in Fig. 22-19aare connected

in series at the output to form one single-phase circuit as shown in Fig. 22-

26a. Three separate circuits are required for a three-phase implementation.

A delta connection of cascaded converters is shown in Fig. 22-26b. Since all

the H-bridges are same, the circuit is modular and can be scaled by adding

more H-bridges. However, dc sources at the input of all H-bridges have to be

isolated from each other. It is also possible to combine different types of H-

bridgesIGBT-based fast switching type and GTO-based slower switching

typeor have different dc bus voltage magnitudes in different bridges to

optimize losses or increase effective number of levels. One example of the

cascaded approach is the multilevel drive offering from Robicon, now a part

of Siemens. In some solar inverters the dc input (PV panel) is common and

the isolation is carried out by transformers at the output of the H-bridges;

in

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the transformer secondaries are then connected in series to obtain the

stepped waveform construction of the AC voltage.

Figure 22.26. Cascaded converters: (a) one phase; (b) three-phase

connection in delta.

22.5.4.2.4. OTHERMULTILEVEL CONVERTERS.

The recently proposed modular multilevel converter uses series connected

cells that together generate the required voltage for each phase. The dc

voltages to each cell have to be isolated similar to the case of cascaded

converters. The major advantage of this approach is scalability and

redundancy. Other types of multilevel converters proposed recently are the

interconnected multilevel converter and the Hexagram converter.

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Citation

H. Wayne Beaty; Donald G. Fink: Standard Handbook for Electrical Engineers,

Sixteenth Edition. DC TO AC CONVERSION: INVERSION, Chapter (McGraw-Hill

Professional, 2013), AccessEngineering

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