## 2-1 Introduction

In some applications such as battery coursers and a category of District of Columbia and ac motor thrusts it is necessary for the dc electromotive force T be governable. The Ac to controlled-dc transition is accomplished in line0frequency phase-controlled convertors by agencies of thyistor. In the yesteryear, these convertors were used in a big figure of applications for commanding the flow of the electric power. Owing to the increasing handiness of better governable switches in high electromotive force and current evaluations, new usage of these thyistor convertors nowadays is chiefly in three-phase, high-octane applications. This is peculiarly true in applications, most of them at high power degrees, where it is necessary or desirable to be able to command the power flow in both waies between the Ac and the District of Columbia sides. Example of such applications are convertors in high-voltage District of Columbia power transmittal and some dc motor and ac motor and ac thrusts with regenerative capablenesss.

As the name of there convertors implies, the line-frequency electromotive forces are present on their ac side. In these convertors, the blink of an eye at which a thyistor begins or ceases to carry on depends on the line-frequency Ac electromotive force wave forms and the control inputs. Furthermore, the transportation or commuting of current from one device to the following occurs of course because of the presence of these ac electromotive forces.

A to the full controlled convertor is shown in Fig 2-1a in block diagram signifier. For given ac line electromotive forces, the mean dc-side electromotive force can be controlled from a positive upper limit to a negative minimal value in a uninterrupted mode. The convertor District of Columbia current can non alter way. Therefore, a convertor of this type can run in merely two quarter-circles ( of the plane ) , as shown in Fig 2-1b. Here, the positive values of imply rectification where the power flow is from the Ac to the dc side. In a inverter manner, becomes negative ( and the power is transferred from the District of Columbia to the ac side. The inverter manner of operation on a sustained footing is possible merely if a beginning of power such batteries, is present on the dc side.

( a ) ( B )

Fig2-1 line frequence controlled convertor.

## 2-2 Thyistor circuits and their control

For given Ac input electromotive forces, the magnitude of the mean end product electromotive force in thyistor convertors can be controlled by detaining the blink of an eyes at which the thyistor are allowed to get down conductivity. This is illustrated by the simple circuits of Fig2-2.

## 2-2-1 basic thyistor circuits

In Fig2-2a, a thyistor connects the line-frequency beginning to a burden opposition. In the positive half-cycle of, the current is zero until, at which clip the thyistor is supplied a positive gate pulsation of a short continuance. With the thyistor conducting, . for the remainder of the positive half-cycle, the current wave form follows the ac electromotive force wave form and becomes zero at. Then the thyistor blocks the current from fluxing during the negative half-cycle of. the current corsets nothing until, at which clip another short-duration gate pulsation is applied and the following rhythm of the wave form begins. By seting, the mean value of the burden electromotive force can be controlled.

In Fig2-2b, the burden consists of both Rand L. ab initio, the current is nothing. The thyistor conductivity is delayed until. Once the thyistor is fired or gated on at during the positive half-cycle of when the electromotive force across the thyistor is positive, the current begins to flux and. the electromotive force across the inductance can be written as

( 2-1 )

where. In Fig 2-2b, is plotted and is shown as the difference between. During is positive and the current additions, since

( 2-2 )

where is a variable of integrating. Beyond, becomes negative and the current begins to worsen. The blink of an eye at which the current becomes zero and corsets zer due to the thyistor is dictated by Eq2-2.graphaically in Fig 2-2b, is the blink of an eye at which are peers country and the current becomes nothing. These countries represent the clip built-in of, which must be zero over one rhythm of repeat in steady province. It should be note that the current continues to flux for a piece even after has become negative. The ground for this has to make with the stored energy in the inductance, a portion of with is supplied to R and the other portion is absorbed by when it becomes negative.

In Fig 2-2c, the burden consists of an inductance and a dc electromotive force. Here, with the current ab initio zero, the thyistor is rearward biased until, as shown in Fig2-2c. Therefore, in can non carry on until. The thyistor conductivity is farther delayed until, when a positive gate pulsation is applied. With the current flowing

In footings of,

where is an arbitrary variable of integrating. The current extremum at where. the current goes to zero at, at which instant country peers country, and the clip built-in of the inductance electromotive force over one clip period of repeat becomes zero.

( a )

( B )

( degree Celsius )

Fig2-2 basic thyistor convertor

## 2-2-2 Thyistor Gate triping

By commanding the blink of an eye at which the thyistor is gated on, he mean current in the circuits of Fig3-3 can be controlled in a uninterrupted mode from nothing to a maximal value. The same is true for the power supplied by the Ac beginning.

Versatile integrated circuits, such as the TCA780, are available to supply delayed gate trigger signals to the thyistor. A simplified block diagram of a gate trigger control circuit is shown in Fig3-3. Here, a proverb tooth wave form is compared with the control signal, and the hold angle with regard to the positive nothing crossing of the ac line electromotive force is obtained in footings of and the extremum of the proverb tooth wave form:

another gate trigger signal can easy be obtained, delayed with regard to the negative nothing crossing of the ac line electromotive force.

Fig 2-3 Gate trigger control circuit

## 2-2-3 Practical Thyistor Converters

Full-bridge convertors for individual and three-phase public-service corporation inputs are shown in Fig2-4. The dc-side induction may be a portion of the burden, for illustration, in dc motor thrusts, prior to analysis of the full-bridge convertor in Fig 2-4 ; it will be helpful to analyse some simple and perchance conjectural circuits. This simplification is achieved by presuming ac-side induction to be zero and the dc side current to be strictly dc. Following, the consequence of on the convertor wave forms will be analyzed. Finally, the consequence of the rippling in will be included. These convertors will besides be analyzed for their inverter manner of operation.

( a ) ( B )

Fig2-4 Practical thyistor convertor

## 2-2-4-1 Single-phase thyistor convertor and inverter

The practical circuit of Fig 2-4a, with the premise of and a strictly dc current, is shown in Fig2-5a. it can be redraw as in Fig 2-5b. the current flows through one thyistor of the top group ( thyistor 1 and 3 ) and one thyistor of the bottom group ( 2 and 4 ) . If the gate currents to the thyritor were continuously applied, the thyistors in Fig2-5 would act as rectifying tubes and their operation would be similar. The electromotive force and current wave forms under these conditions are shown in Fig2-6a.

( a ) ( B )

Fig2-5 single-phase thyistor convertor with and changeless District of Columbia current

The blink of an eye of natural conductivity for a thyistor refers to the blink of an eye at which the thyistor would get down to carry on of its gate current were continuously applied. Therefore, in Fig 2-6b, the blink of an eye of natural conductivity is for thyistors 1 and 2 and for thyistor 3 and 4.

( a )

( B )

Fig 2-6 Waveform in the convertor of Fig 2-5

Following see the consequence of using gate current pulsations that delayed by an angle ( called the hold angel or firing angle ) with regard to the blink of an eye of natural conductivity. Now prior to, the current is fluxing through thyistor 3 and4, and. as shown in Fig2-6b, the electromotive force across thyistor 1 becomes frontward biased beyond, but it can non carry on until when a gate current pulsation is applied. The state of affairs is indistinguishable for thyistor2. As a effect of this finite hold angle, becomes negative during the interval from 0 to.

At, the commuting of current from thyistor 3 and 4 to thyistor 1 and 2 is instantaneous due to the premise of. When thyistor 1 and 2 are contributing, . Thyistor 1 and 2 behavior until when thyistor 3 and 4 are triggered, delayed by the angle with regard to their blink of an eye of natural conductivity ( . A similar commuting of current takes topographic point from thyistor 1 and 2 to thyistor 3 and 4.

Comparing the consequence of the hold angel on the wave form in Fig 2-6b with that in Fig2-6a shows that the mean value can be obtained as

Let be the mean value of the dc electromotive force in Fig2-6a with and =0, where

Then, the bead in the mean value due to is

This “ lossless ” electromotive force bead in is equal to the volt-radian country shown in Fig 2-6b divided by.

The fluctuation of as a map of is shown in Fig2-7, which shows that the mean dc electromotive force becomes negative beyond. This part is called the inverter manner of operation and is discussed subsequently. The mean power through the convertor can be calculated as

With a changeless District of Columbia current ( ,

Fig 2-7 Normalized as a map of

## 2-2-4-2 inverter manner of operation of single-phase thyistor convertor

It was mentioned in chapter2-1 that the thyistor convertors can besides run in an inverter manner, where has a negative value, as shown in Fig 2-1b, and therefore the power flows from the dc side to the ac side. The easiest manner to understand the inverter manner of the operation is to presume that the dc side of the convertor can be replaced by a current beginning of changeless amplitude, as shown in Fig2-5a. For a hold angle greater than 90Es but less than 180Es , the electromotive force and current moving ridge signifiers are shown in Fig2-8b. The mean value of is negative, given by

Where 90Es . Therefore, the mean power is negative, that is, it flows from the District of Columbia to the ac side. One the ac side, is besides negative because.

( a )

( B )

Fig 2-8 ( a ) Inverter presuming a changeless District of Columbia current ( B ) wave forms

There are several points deserving observing here. This inverter manner of operation is possible since there is a beginning of energy on the dc side. On the ac side, the ac electromotive force beginning facilitates the commuting of current from one brace of thyistor to another. The power flows into this ac beginning.

By and large, the District of Columbia current beginning is non a realistic dc-side representation of systems where such a manner of operation may be encountered, Fig 3-6a shows a electromotive force beginning on the dc side that may stand for a battery, a photovoltaic beginning, or a dc electromotive force produced by a wind-electric system. It may besides be encountered in a four-quadrant District of Columbia motor supplied by a back-to-back connected thyistor convertor.

An premise of a really big value of allows us to presume to be a changeless District of Columbia, and therefore the wave forms of Fig 2-8b besides apply to the circuit of Fig 2-9a. Since the mean electromotive force across is zero,

The equations is exact if the current is changeless at, otherwise, a value of at, should be used in this Eq alternatively of. Fig 2-9b shows that for a given value of, for illustration, , the intersection of the District of Columbia current and therefore the power flow.

During the inverter manner, the electromotive force wave form across one of the thyistor is shown in Fig 2-10. An extinction angle is defined to be

during which the electromotive force across the thyistor is negative and beyond which it becomes positive. As the extinction clip interval should be greater than the thyistor turn-off clip. Otherwise, the thyistor will prematurely get down to carry on, ensuing in the failure of current to commutate from one thyistor brace to the other, an unnatural operation that can ensue in big destructive currents.

( a ) ( B )

Fig2-9 ( a ) thyistor inverter with a dc electromotive force beginning ( B ) versus

Fig 2-10 Voltage across a thyistor in the inverter manner

## 2-2-5 Three-phase Converters and Inverters

The practical circuit of Fig 2-4b with the premise of and a strictly dc current is shown in Fig 2-11a. It can be redrawn as in Fig 2-11b. The current flows

Fig2-11

Though one of the thyistor of the top group ( thistor1, 3, 5 ) and one of the bottom group ( 2. 4. 6 ) . If the gate currents were continuously applied, the thyistor in Fig2-11 woud behave as rectifying tube and their operation would be similar to that described in the old chapter. Under these conditions ( ) , the electromotive forces and the current in stage are shown in Fig 2-12a. the mean dc electromotive force is as in Equivalent:

( 2-3 )

Using the same definition as in 2-2-4-1, blink of an eyes of natural conductivity for the assorted thyistor are shown in Fig 2-12a by 1, 2aˆ¦ The consequence of the fire or hold angle on the convertor moving ridge signifiers are shown in Figs 2-12b to d. Concentrating on the commuting of current from thyistor 5 to 1, we see that thyistor 5 supports on carry oning until, at which instant the current commutates outright to thyistor 1 due to zero. The current in stage is shown in Fig 2-12c. Similar hold by a angle takes topographic point in the conductivity of the other thyistor. The line to line Ac electromotive forces and the District of Columbia end product electromotive force are shown in Fig2-12d.

The look for the mean dc electromotive force can be obtained from the wave forms in Figs 2-12b and d. the volt-second country ( every 60 ) consequences in the decrease in the mean dc electromotive force with a hold angle compared to in Fig 2-12a. Therefore,

( 2-4 )

From Fig 2-12b, the volt-radian country is the built-in of. This can be confirmed by Fig 2-12d, where is the built-in of. With the clip origin chosen in Fig 2-12,

Therefore,

Substituting in Eq.2-4 and utilizing Eq.2-3 for output

( 2-5 )

The above process to obtain is straightforward when. For we get the same consequence but an alternate derivation may be easier

Equation 2-5 shown that is independent of the current magnitude so long as flows continuously ( and =0 ) . The control of as a map of is similar to the single-phase instance shown by Fig 2-10. The dc electromotive force wave form assorted values of is shown in Fig 2-13. The mean power is

Fig 2-12 Waveform in the convertor of Fig 2-11

Fig2-13 the dc-side electromotive force wave form as a map of where

## 2-2-5-1 Inverter manner of three-phase thyistor convertor

To understand the inverter manner of operation, we will presume that the dc side of the convertor can be represented by a current beginning of changeless amplitude, as shown in Fig 2-14. For a hold angle greater than 90Es but less than 180Es , the electromotive force and current wave forms are shown in Fig 2-15a. The mean value of is negative harmonizing the Eq. . On the ac side, the negative power implies that the stage angle between and is greater than 90Es , as shown in Fig 2-15b.