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Power Electronics Dr.Mohammed Tawfeq

Tutorial Sheet No. (3)

Controlled rectification 1. The single-phase half-ware controlled rectifier shown in fig.1 is operating at

α1=90º . The thyristor Th2 is connected across the load and operating with a delay

angle α2 of 45º .Assume the load is highly inductive such that IL is continuous

.Plot waveforms of V2, I th1 , I th2 ,I L , V th1 and V th1. Derive an expression for the

average load voltage Vdc as a function of α1 and α2 (with α1< α2).

{Ans:Vdc =Vm/2π[cos α1 +cos α2]}

TH1

TH2 VL

iL

vmsinwt

Fig.1

2. The single-phase half-controlled rectifier operating at a delay angle of 45º

.Assuming the load is resistive, plot V2 , Ith , IL ,and ID. Express Vdc as a function

of α. Calculate Vdc.

Fig.2

TH1

V2 D1

Vs= Vmsinwt

V1

1:1

R

[Ans:Vdc =Vm/2π(cos α +3)] Vdc =0.59v

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3. A single-phase Full-ware fully-controlled bridge rectifier supplying

highly inductive load as shown in fig.3.The r.m.s value of the a.c. input voltage is

230V.The firing angle is maintained constant at 45 so that the load current is

continuous at a value of 5A.

(a) Calculate the dc output Voltage. [Ans: 146.4V].

(b) Assume that load resistance remains the same; find the current if a

freewheeling diode DF is used at the output. [Ans: 6.03A].

(c) If Th3 is open circuited, find the load voltage and current while

freewheeling diode DF is still connected and α is the same.

[Ans: 88.3V, 3.02A].

TH1 TH3

TH4 TH2

Df

230V r.m.s

S

LOAD

Fig.3

4. A fully-controlled single-phase bridge rectifier is supplied from a 50HZ, 230/100V

transformer .The rectifier supplying a highly inductive load of 10Ω resistance. For a

firing angle of 45º, determine the rectified voltage, the rectified current and the power

factor.

[Ans: 63.7V, 6.37A, 0.637].

5. A single –phase, fully-controlled bridge rectifier supplies a constant current to a

highly inductive load.

Derive an expression for the average d.c. output voltage from the bridge and also the

R.M.S. value of the fundamental component of the alternating line current assuming

(a) that there is no freewheel diode , and (b) that a freewheel diode is used.

{Ans: Vdc = (2Vm/ π) cosα, IL=( 2√2)Idc/ π , Vdc= (Vm/ π)(1+cosα) ,

IL=[( 2√2)Idc/ π] cos(α/2) }

6. For a single- phase, fully – controlled, bridge rectifier derive an expression for the

power dissipated in a resistive load as the triggering angle is varied. If one thyristor

remains in the non-conducting state , calculate the firing angle which results in 25%

of maximum power dissipation in the load.

[ Ans: Vm2

{ π –α +½ sin 2 α}/{2 πR}] ;90º ]

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7.The circuit of Figure ( 4 ) consists of identical resistors R1= R2 =100 ohms, an

ideal diode D and an ideal thyristor T supplied from an ideal power supply e = 100 sin

wt. Sketch, roughly to scale, corresponding waveforms of the supply voltage and the

currents in R1, R2, D and T if the thyristor firing angle is 90°. What is the average

value of the current in R1 for a supply cycle?

Fig. 4

8. A single-phase controlled full-wave rectifier shown in Fig .5, has a source of 220 V

r.m.s at 50 Hz, and is feeding a load R = 20 Ω and L = 40 mH. The firing angle is a

45◦ and the extinction angle is, β= 230°.

(a) Specify whether the current is continuous or discontinuous

(b) Sketch the voltage and current waveforms (VL, iL) and show the SCR triggering

sequence of the conducting devices.

(c) Determine the average load voltage and current.

(d) Determine the r.m.s load voltage and current.

(e) Determine the a.c and d.c powers absorbed by the load.

(f) Determine the efficiency of the converter.

Fig.5

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