Power electronics digital notes b. Tech III year

Single phase half controlled converter with RLE load 
The diode D2 and D4 conducts for the positive and negative half cycle of the input voltage waveform 
respectively. On the other hand T1 starts conduction when it is fired in the positive half cycle of the input 
voltage waveform and continuous conduction till T3 is fired in the negative half cycle. Fig. shows the 
circuit diagram and the waveforms of a single phase half controlled converter supplying an R 
–
L 
–
E 
load. 
Figure: 2.5 single phase half controlled converter with RLE load 
Referring to Fig
T1 D2 starts conduction at ωt = α. Output voltage during this period becomes equal to 
vi. At ωt = π as vi tends to go negative D4 is forward biased and the load current commutates from
D2 to 
D4 and freewheels through D4 and T1. The output voltage remains clamped to zero till T3 is fired at ωt = 
π + α. The T3 D4 conduction mode continues upto ωt = 2π. Where upon load current again free wheels 
through T3 and D2 while the load voltage is clamped to zero. From the discussion in the previous 
paragraph it can be concluded that the output voltage (hence the output current) is periodic over half the 
input cycle. Hence

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Single phase half controlled converter with RLE load and freewheeling diode 
Figure: 2.6 single phase half controlled converter with RLE load and freewheeling diode 
Numerical problems
1.
A single phase 230V, 1 Kwheater is connected across 1 phase 230V, 50Hz supply through an 
SCR. For firing angle delay of 45
0
and 90
0
, calculate the power absorbed in the heater element. 
Solution: Heater resistance R = 230
2
/1000 
Ω

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The rms value of voltage is V
or
= 
= 
= 155.071V 
Power absorbed by the heater element for α = 45
0
is
= 454.57W 
for α = 90
0
the rms voltage is
V
or
= 
= 115V 
Power absorbed by the heater element for α = 90
0
is
= 250W 
2.
A resistive load of 10Ω is connected through a 
half-wave controlled rectifier circuit to 220V, 50 
Hz, single phase source. Calculate the power delivered to the load for a firing angle of 60
ᵒ
. Find 
also the value of input power factor
3.
A single phase semi converter delivers to RLE load with R=5Ω, L = 10m
H and E = 80V. The source 
voltage is 230V, 50Hz. For continuous conduction, Find the average value of output current for 
firing angle
 
= 50
o
.