NPTEL Online Certification Course
<Power Electronics Applications in Power Systems>
<Assignment 06>: Detailed Solution
Indian Institute of Technology Guwahati
(Common data for Q1-Q7)
Consider a 3-phase, lossless TSC-TCR compensator unit consisting of three identical TSCs and one
TCR unit. The compensator is designed to provide 1 p.u. of capacitive compensation and 0.4 p.u. of
inductive compensation. Consider the magnitude of susceptance ( B ) of the step-down transformer
as 5 p.u. and system voltage as 1 p.u.
(Note: Consider the base reactive power of the SVC as the reactive power at full production of SVC
at a nominal voltage of 1 p.u.).
1. The rating of each TSC unit is
a. 0.833 p.u.
b. - 0.278 p.u.
c. 0.278 p.u.
d. 0.417 p.u.
Sol:
Let BC , BL , be the rated susceptance of each TSC unit and TCR unit, respectively, and BTSC −TCR be
the susceptance of the TSC-TCR unit under operation.
B (3BC + BL )
BTSC −TCR =
B + 3BC + BL
At maximum production limit of SVC, BL = 0 , and BTSC −TCR = 1 p.u.
Therefore,
B (3BC ) −5(3BC )
=1 = 1 BC = 0.278 p.u.
B + 3BC −5 + 3BC
2. The rating of the TCR unit is
a. 0.435 p.u.
b. – 0.370 p.u.
c. 0.370 p.u.
d. – 0.435 p.u.
Sol:
At maximum absorption limit of SVC, BC = 0 , and BTSC −TCR = − 0.4 p.u.
Therefore,
B ( BL ) − 5( BL )
= − 0.4 = − 0.4 BL = − 0.435 p.u.
B + BL − 5 + BL
3. If only 2 TSCs are ON, the SVC susceptance corresponding to maximum production and the
compensator current ( I SVC ) are
a. - 0.626 p.u. and 0.626 p.u., respectively
b. 0.626 p.u. and – 0.626 p.u., respectively
c. – 0.124 p.u. and 0.124 p.u., respectively
d. 0.124 p.u. and 0.124 p.u., respectively
Sol:
At maximum production, TCR is OFF.
Therefore,
B (2 BC ) −5(2 0.278)
BTSC −TCR = = = 0.626 p.u.
B + 2 BC −5 + 2 0.278
I SVC = − V BTSC −TCR = 1 0.626 = − 0.626 p.u. (-ve sign indicates that the current is capacitive.)
4. If only 2 TSCs are ON and TCR is fully ON, the SVC susceptance and the SVC current are,
respectively,
a. 0.124 p.u. and – 0.124 p.u.
b. 0.124 p.u. and 0.124 p.u.
c. – 0.626 p.u. and 0.626 p.u.
d. 0.626 p.u. and – 0.626 p.u.
Sol:
At minimum production TCR is ON.
Therefore,
B (2 BC + BL ) −5(2 0.278 − 0.435)
BTSC −TCR = = = 0.124 p.u.
B + 2 BC + BL −5 + 2 0.278 − 0.435
I SVC = − V BTSC −TCR = −1 0.124 = − 0.124 p.u.
5. If only 1 TSC is ON and TCR is fully ON, the subrange of the SVC susceptance is
a. [– 0.152, 0.294] p.u.
b. [– 0.294, 0.152] p.u.
c. [– 0.626, 0.124] p.u.
d. [0.124, 0.626] p.u.
Sol:
When TCR is fully ON,
B ( BC + BL ) −5(0.278 − 0.435)
BTSC −TCR = = = −0.152 p.u.
B + BC + BL −5 + 0.278 − 0.435
When TCR is fully OFF,
B BC −5 0.278
BTSC −TCR = = = 0.294 p.u.
B + BC −5 + 0.278
Therefore, the subrange of the SVC susceptance is [– 0.152, 0.294] p.u.
6. The susceptance range corresponding to maximum and minimum inductive compensation is
a. [– 0.4, 0] p.u.
b. [0, 0.434] p.u.
c. [-0.434, 0] p.u.
d. [0.434, 1] p.u.
Sol: For inductive compensation, all TSCs are OFF.
At minimum inductive compensation, TCR is also OFF, therefore, BTSC −TCR = 0 p.u.
At maximum inductive compensation, TCR is fully ON, therefore,
B BL −5 (−0.435)
BTSC −TCR = = = − 0.4 p.u.
B + BL −5 − 0.435
7. Mark the correct statements from the following.
a. When 3 TSCs are ON and TCR is off, the VAr production subrange of the SVC is continuous.
b. When 3 TSCs are ON and TCR is off, the VAr production subrange of the SVC is discrete.
c. When 3 TSCs are ON and TCR is also ON, the VAr production subrange of the SVC is discrete.
d. When 3 TSCs are OFF and TCR is ON, the VAr production range of the SVC is discrete.
8. A TSC unit is required to be turned ON. If the capacitor is pre-charged with a voltage ( VC 0 ) greater
than the peak of TSC bus voltage ( Vm ), the thyristor should be fired at
a. zero crossing of the TSC bus voltage.
V
b. firing angle equal to sin −1 C 0 .
V
c. the instant when the voltage across the valve is maximum.
d. the instant when the TSC bus voltage reaches the peak value.
9. A 3-phase TCR is delta connected to
a. eliminate only 3rd harmonics
b. eliminate 5th harmonics
c. eliminate all triplen harmonics
d. eliminate all non-triplen harmonics
10. Which of the following statements is correct about FC-TCR?
a. FC-TCR provides controllable reactive power only in the lagging power factor range.
b. FC-TCR provides controllable reactive power only in the leading power factor range.
c. A small tuning inductor is connected in shunt with the capacitor to eliminate harmonics of specific
harmonic order.
d. A small tuning inductor is connected in series with the capacitor to eliminate harmonics of
specific harmonic order.
