Unit ii

Rama Kishore Bonthu Associate Professor

Email: [email protected]

POWER ELECTRONICS - II

FILTERS:

A filter provides an output voltage as smooth as possible. If the filter is connected across rectifier input side, it is called ac

filters. If the filter is connected across rectifier output side, it is called dc filters. The more common ac & dc filters are of L,

C and LC type as shown in figures (a), (b),(c) and (d).

An inductor L in series with load R, Fig(a), reduces the ac

component, or ac ripples. It is because L in series with R offers

high impedance to ac component but very low resistance to dc.

Thus ac component gets attenuated. A capacitor C across load

R. Fig (b), offers direct short circuit to ac component, these are

therefore not allowed to reach the load. However, dc gets

stored in the form of energy in C and this allows the

maintenance of almost constant dc output voltage across the

load.

CAPACITOR FILTER (C-FILTER):

This diagram represents the diode bridge rectifier with R-load. A

capacitor C directly connected across the load, serves to smoothen out the

dc output wave. Source voltage vs = Vm sin wt is sketched in below

Fig.(a). Load voltage Vo is shown in Fig. (b). In this figure, from wt = 0

to wt =θ, source voltage Vs is less than capacitor discharges through load

resistance R. At wt = θ, V0 = Vc = V2 as shown in Fig. (b). Soon after wt = θ,



source voltage Vs exceeds Vo (= Vc), diodes D1, D2 get forward biased and begin to conduct. As a result, source voltage charges

capacitor from V2 to Vm at wt = π/2, as shown Fig.(b). Soon after wt = π/2, source voltage Vs begins to decrease faster

than the capacitor voltage Vc. it is because capacitor discharges gradually through R. Therefore, after wt = π/2, diodes Dl, D2

are reverse biased and capacitor discharges through R. The capacitor voltage falls exponentially, shown in Fig. (b).In the next

half cycle, Vc = V0= V2 at wt = (π + θ). Just after wt = (π + θ), Vs> Vc, diodes D3, D4 get forward biased and begin to

conduct. The capacitor voltage rises from V2 to Vm at wt = 3π/2. It is seen from figure (b) that voltage drop from maximum to

minimum is Vm -V2, or peak to peak ripple voltage, Vrp =Vm - V2.

In Fig. (c) is drawn the profile of ripple voltage with the help of Fig. (b). A horizontal line at a height 1/2(Vm + V2), from

reference line wt in Fig. (b) is now taken as the

reference line in Fig. (c) for plotting voltage profile Vr. Ripple voltage is seen to be almost triangular in shape.

From the Fig. (c), Peak to peak ripple voltage is Vrpp= Vm - V2

Peak ripple voltage Vrp = 1/2(Vm - V2)

Charging of Capacitor:

From wt =θ to π/2, capacitor charges from V2 to Vm . The equivalent circuit for capacitor

charging, shown below, gives the charging current is as under :

The charging current ic at wt = π/2 is ic= wcvmcos 900 = 0, but Vc =Vs= Vmsin900 = Vm.

Therefore, energy stored in C at wt = π/2 is 1/2(CVm2)

Discharging of capacitor:

KVL for the circuit model of below figure, for capacitor discharging gives

Charging time is usually small, therefore it can be neglected. As a result t1+t2 = t2 = T/2. But T = 1/f, therefore t2 = 1/2f



FIRING CIRCUITS FOR THYRISTORS:

SCR can be switched from off-state to on-state in several ways. Those are forward voltage

triggering, dv/dt triggering, temperature triggering, light triggering and gate triggering. The instant of the turning on the SCR

cannot be controlled by the first four methods listed above. However, gate triggering method turns-on the SCR accurately at

the desired instant. In addition gate triggering is reliable and efficient. In this method gate must be fired by using firing

circuits at a particular angle or instant.

RESISTANCE FIRING CIRCUITS:

Res i s t ance t r i gge r o r f i r i ng c i r cu i t s a r e t he simplest and

most economical. They however, suffer from a l imited range of

fir ing angle con t ro l (0 ° t o 90°) . In this circuit,R2 is the variable

resistance, R is the stabilizing resistance. In case R2 is zero, gate

current may flow from source, through load, R1, D and gate to

cathode. The function of R1 is to limit the gate current to a safe value as

R2 is varied. Resistance R should have such a value that maximum

voltage drop across it does not exceed maximum possible gate voltage

Vgm. As resistances R1, R2 are large, gate trigger circuit draws a

small current. Diode D allows the flow of current during Positive

half cycle only, i.e. gate voltage Vg is half-wave dc pulse.

The amplitude of this dc pulse can be controlled by varying R2.

The potent iometer setting R, determines the gate voltage amplitude. When R2 is large, current i is small and

the voltage across R, i.e. Vg = i . R is also small as shown in Fig.(a). As Vgp (peak of gate voltage vg) is less than



Vgt (gate trigger voltage), SCR will not turn on. Therefore, load voltage Vo = 0, io = 0 and supply voltage Vs

appears as VT across SCR as shown Fig. (a).

In Fig.(b), R, is adjusted such that Vgp = Vgt. This gives the value of firing angle as 90 0.

In Fig. (c), Vgp > Vgt. As soon as vg becomes equal to Vgt for the first time SCR is turned on. Increasing Vg above

Vgt turns on the SCR at firing angles less than 90°. When vg reaches Vgt for the first time, SCR fires, gate loses control

and Vg is reduced to almost zero (about 1 V) value as shown.

From the above analysis

Where α = firing angle of SCR

In this method, the resistance triggering cannot give firing angle beyond 90°.

RESISTANCE-CAPACITANCE (RC) FIRING CIRCUITS:

The limited range of firing angle control by resistance firing circuit can be overcome by RC firing

circuit. There are several variations of RC trigger circuits. Two of them are (i) RC half wave trigger circuit (ii) RC full

wave circuit

( i ) RC half -wave tr igger ci rcui :

By varying the value of R, firing angle can be controlled from 0° to 180°. In the negative half cycle, capacitor C

charges through D2. After wt = -900, source voltage vs decreases from -Vm at wt = - 900 to zero at wt = 0°. During this

period, capacitor voltage Vc may fall from –Vm at wt = - 90° to some lower value - oa at wt = 0° as shown in below figure.

Now, as the SCR anode voltage passes through zero and becomes positive, C begins to charge through variable

resistance R from the initial voltage -oa. When capacitor charges to positive voltage equal to gate trigger voltage V gt,

SCR is fired.

Diode D1is used to prevent the breakdown of cathode to gate junction through D2 during the negative half cycle.

In figure (a), R is more, the time taken for C to charge from -oa to Vgt is more, firing angle is more and therefore

average output voltage is low. In figure (b), R is less, the time taken for C to charge from -oa to Vgt is less, firing angle

is less and therefore average output voltage is more.

(ii) RC full wave circuit:

Diodes D1—D4 form a full-wave diode bridge. In this circuit, the initial voltage from which the capacitor C

charges is almost zero. When capacitor charges to a voltage equal to Vgt, SCR triggers and rectified voltage vd

appears across load as vo. In Fig. (a), for high value of R, firing angle α is more than 90° and in Fig. (b) for low value

of R ,α< 90°.



SINGLE PHASE HALFWAVE CONVERTER (RECTIFIER) WITH R-LOAD:

thyristor conducts from (wt = α to π, 2π+α to 3π and so

on. Over the firing angle delay α, load voltage Vo = 0 but

during conduction angle (π-α), Vo = Vs. As firing angle is

increased from zero to π the average load voltage

decreases from the largest value to zero.

Average voltage Vo across load R, for the single-phase

half-wave circuit in terms of firing angle a is given by



SINGLE PHASE HALFWAVE CONVERTER (RECTIFIER) WITH RL-LOAD:

A single-phase half-wave thyristor circuit with RL

load is shown in Fig. Line voltage Vs is sketched in

the top of Fig. At wt = α, thyristor is turned on by

gating signal. Then The load voltage V0 becomes

equal to source voltage Vs as shown. But the

inductance L forces the load current i0 to rise

gradually. After some time, i0 reaches maximum

value and then begins to decrease. At wt =π, V0 is

zero but i0 is not zero because of the load inductance

L. After wt = π, SCR is subjected to reverse anode

voltage but it will not be turned off as load current i0

is not less than the holding current. At some angle β,

i0 reduces to zero and SCR is turned of as it is

already reverse biased. After wt = β, V0, = 0 and i0 =

0. At wt = 2π + α, SCR is triggered again, Vo is applied

to the load and load current develops as before. Angle β is

called the extinction angle and β – α = γ is called the

conduction angle.

The Voltage equation for the above circuit, when SCR is ON

The load current i0 consists of two components, one steady-state component is and the other transient component i t. Therefore i0 = is + it

The transient component it can be obtained from force-free equation:

Constant A can be obtained from the boundary condition at wt = α, At this time t = α/w, i0=0

β can be determined by using the condition, when wt=β, t= β/w, i 0=0

This transcendental equation can be solved to obtain the value of extinction angle β, if β is known, the average voltage is given by



Single-phase Half-wave Circuit with RL Load and Freewheeling Diode :

The waveform of load current io in RL load circuit can

be improved by connecting a freewheeling (or

flywheeling) diode across load as shown in above

circuit, A freewheeling diode is also called by-pass or

commutating diode. At wt= 0, source voltage is

becoming positive. At some delay angle α, forward

biased SCR is tr iggered and source voltage

appears across load as At wt = π, source voltage Vs,

is zero and just after this instant, Vs tends to reverse,

freewheeling diode FD is forward biased through

the conducting SCR. As a result, load current i0 is

immediately transferred from SCR to FD asV s

tends to reverse. At the same time. SCR is

subjected to reverse voltage and zero current. it

is therefore turned off at wt = π. It is assumed

that during freewheeling period. load current does

not decay to zero until the SCR is triggered again at

wt=2π+α. Voltage drop across FD is taken as almost zero

the load voltage Vo is zero during the freewheeling

period.

The voltage variation across SCR is shown as VT in above waveform. It is seen from this waveform that SCR is

reverse biased from wt= π to wt = 2π.

Operation of the above circuit can he explained in two modes. In the first mode, called conduction mode, SCR conducts from

wt=α to π, to 2π + α to 3π and so on and FD is reverse biased. The second mode, called freewheeling mode, extends from π to

2π + α, 3π to 4π + α and so on. In this mode, SCR is reverse biased from π to 2π, 3π to 4π and so on.

conduction mode:

The load current i0 consists of two components, one steady-state component is and the other transient component i t. therefore i0 = is + it



Constant A can be obtained from the boundary condition at wt = α, At this time t = α/w, i0=I0

freewheeling mode:

SINGLE-PHASE HALF-WAVE CIRCUIT WITH R-L-E LOAD:

A single-phase half-wave controlled converter

with RLE load is shown above. The counter

emf E in the load may be due to a battery or a

dc motor. The minimum value of firing angle

is obtained from the relation Vm sin wt = E.

This is shown to occur at an angle θ 1 in

waveform. Where θ1 = sin-1(E/Vm).

In case thyristor T is fired at an angle w < θ1,

then E > V, SCR is reverse biased and therefore

it will not turn on. Similarly, maximum value

of firing angle is θ2 = π – θ1 shown in above

waveform. During the interval load current i0 is

zero, load voltage Vo = E and during the time

is is not zero, Vo follows Vs curve.



The solution of this equation is made up of two components, namely steady-state current component i s, and

the transient current component it. For convenience, is, the sum of is1 and is2, where is1 is the steady state

current due to ac source voltage acting alone and is2, is that due to dc counter emf E acting alone (according to

superposition theorem).

Unit ii

Engineering

Transcript of Unit ii