Three-phase line commutated controlled rectifier
Three-phase line commutated controlled rectifier
A DC motor is powered by a three-phase line commutated controlled rectifier like shown in figure 1.
This rectifier is controlled by the most common method, which means that the thyristors are turned into conduction at a predetermined phase of the sinusoidal voltage waveform. So the output voltage v
D
becomes controllable depending on the phase angle 𝛼 . i
D
1 v
13 v
12
2 v
23
3
L
1d
L
2d
L
3d
L
1y
L
2y
L
3y v
1 v
2 v
3
T
1
T
2
T
3 v
D
L
A v
A
Figure 1: Three-phase half-wave controlled rectifier
Hints:
• Please use the appended waveform graphs
• The following coherencies are very useful for this exercise cos(x − y) = cos(x) ⋅ cos(y) + sin(x) ⋅ sin(y) sin(𝑥 + 𝑦) − sin(𝑥 − 𝑦) = 2 ⋅ cos(𝑥) ⋅ sin(𝑦) sin � 𝜋 cos �
3� = 𝜋
3� =
√3
1
2
2
Problem 1
Sketch the voltage waveform of the output voltage assuming a continuous output current i
D
. v
D
(t) for 𝛼 = 0, 𝛼 = 90° and 𝛼 = 180° and
Problem 2
Calculate the output current i
D
(t) .
Problem 3
What are the steady state conditions for i
D
(t) ?
Problem 4
Sketch the output current waveform conditions for i
D
(t) are fulfilled. i
D
(t) for 𝛼 = 0, 𝛼 = 90° and 𝛼 = 180°.
Calculate the phase cutting angle 𝛼 for the case of an undistorted output current flow and when the steady state
Problem 5
Sketch the voltage waveform of the output voltage three thyristors for 𝛼 = 30° . v
D
(t) and the voltage waveform across one of the
Problem 6
Calculate the extremes of i
D
(t) when the phase cutting angle 𝛼 is treated as an independent variable. Calculate the angle 𝛼 when the output current starts with a horizontal tangent.
Problem 7
Calculate the phase cutting angle 𝛼 𝑐𝑟𝑖𝑡 when the output current ripple is at maximum.
Problem 8
Calculate the amplitude of the maximum current ripple.
Problem 9
Determine the mean value of the output current 𝐼
𝐷 𝑚𝑖𝑛 at the given phase angle 𝛼 = 𝛼 𝑐𝑟𝑖𝑡 and when the rectifier operates at boundary condition. Calculate the value of the relative current ripple
Δ𝑖
𝐷
𝐼
𝐷 𝑚𝑖𝑛
.
Problem 10
Use the results of problem 9 and determine a formula to calculate the inductor L
A given 𝐼
𝐷 𝑚𝑖𝑛
= 1 A and a given RMS value for the secondary windings of 𝑈
1,2,3
𝑅𝑀𝑆
. Calculate
= 230 V .
L
A
for a
Help-sheet for problem 1
Help-sheet for problem 3 and 6
Help-sheet for problem 4
Help-sheet for problem 5
Help-sheet for problem 8
π /3 0 π /3
3
π /3 0 π /3
