The document discusses GTO controlled series capacitor (GCSC) compensation for power transmission systems. GCSC consists of a series capacitor with two GTOs connected in anti-parallel to allow control of the capacitor voltage through delay angle control. By adjusting the delay angle of the GTO switches, the effective voltage across the capacitor can be varied each half cycle, providing a means to control the series capacitive reactance and compensate for varying line current. Mathematical expressions are presented relating the fundamental component of the capacitor voltage and reactance to the delay angle control. GCSC allows maintaining either a constant compensating voltage or maximum compensating reactance over a range of line currents.

1. COMPENSATION USING
POWER ELECTRONIC
DEVICES
PRESENTED BY
Himal Chaulagain
Paschimanchal Campus

2. GTO Controlled Series Capacitor
 Consists of a series fixed capacitor with two GTOs
connected in anti parallel
 Have the capability of varying capacitor voltage by
delay angle control
 Operation is based on the fast commutating
switches, which permit the higher degree of
controllability with respect to thyristor devices

3. Circuit diagram, operation and waveform
 Main objective is to control the ac voltage ‘𝑢 𝑐’ across the
capacitor at a given line current i
 Figure below shows the circuit diagram for controlled operation
of GCSC

4.  When GTO is closed, 𝑢 𝑐=0 and when it is open, 𝑢 𝑐=maximum
 For controlling 𝑢 𝑐,the closing and opening of GTO switches is
carried out in each half cycle in synchronism with the ac system
frequency
 GTO switch is stipulated to close automatically whenever the
capacitor voltage crosses the zero
 The turning off of the switch is controlled by a delay angle 𝛿
with respect to the peak of the current i.e. the adjustment of the
capacitor voltage can only take place once in each half cycle
 Figure below shows the waveform of operation:

6.  If T1 and T2 are turned off for positive and negative half cycle of
𝑢 𝑐 respectively, then the whole line current flows through the
capacitor and 𝑢 𝑐 will be the sine wave lagging by 90° wrt line
current i. This corresponds to turn off angle 𝛾= 𝜋
2 (i.e. T1 is
turned off at 𝜋
2 and T2 turned off at 3𝜋
2 )
 For turn off angle 𝛾= 𝜋
2, the scheme provides full value of series
capacitive compensation

7.  If T1 and T2 are turned off lately (or with some delay angle 𝛿 ) for
positive and negative half cycle of 𝑢 𝑐 (i.e. T1 and T2 are kept ON for
fraction of positive and negative cycle of 𝑢 𝑐), the line current flows
through T1 and T2 resulting zero current through the series capacitor
and resulting zero voltage across the series capacitor. Then the
resulting waveform of capacitor voltage will be a chopped sinewave
as shown above.
 Therefore, the effective value of 𝑢 𝑐 varies with turned off angle 𝛾.
 Let the line current I = 𝐼 𝑚 cos 𝜔𝑡 be the reference waveform

8.  In general, the voltage across the capacitor is given by
𝑢 𝑐(𝛾) =
1
𝐶 𝛾
𝜔𝑡
𝑖 𝑑𝑡 =
1
𝐶 𝛿
𝜔𝑡
𝐼 𝑚 cos 𝜔𝑡 𝑑𝑡
=
𝐼 𝑚
𝜔𝐶
[sin 𝜔𝑡 - sin 𝛿]
= 𝑢 𝑐𝑚𝑎𝑥 sin(𝜔𝑡) + 𝑢 𝑐𝑚𝑎𝑥 sin 𝛿
variable with 𝜔𝑡 constant whose
value only depend on 𝛿

9.  As seen from the figure, the waveform posses odd
symmetry
∴ 𝑎0 = 𝑎 𝑛 = 0
We know,
𝑓 𝑥 = 𝑎0 + 𝑛=1
∞
𝑎 𝑛 cos 𝑛𝜔𝑡 + 𝑏 𝑛 sin 𝑛𝜔𝑡
∴ 𝑢 𝑐(𝑡) = 𝑛=1
∞
𝑏 𝑛 sin 𝑛𝜔𝑡
So, 𝑏 𝑛=
2
𝜋 0
𝜋
𝑢 𝑐(𝑡) sin 𝑛𝜔𝑡 d𝜔𝑡
=
2
𝜋 𝛿
𝜎+𝛿 𝐼 𝑚
𝜔𝐶
[ sin 𝜔𝑡 − sin 𝛿] sin 𝑛𝜔𝑡 d𝜔𝑡

10.  Taking fundamental component only and 𝜎 = 𝜋-2𝛿
𝑏1=
2
𝜋 𝛿
𝜋− 𝛿 𝐼 𝑚
𝜔𝐶
[ sin 𝜔𝑡 − sin 𝛿] sin 𝜔𝑡 d𝜔𝑡
=
2
𝜋
𝐼 𝑚
𝜔𝐶 𝛿
𝜋− 𝛿
sin2
𝜔𝑡 − sin 𝛿 sin 𝜔𝑡 d𝜔𝑡
=
2
𝜋
𝐼 𝑚
𝜔𝐶
[ 𝛿
𝜋− 𝛿
(
1−𝑐𝑜𝑠2𝜔𝑡
2
)d𝜔𝑡− sin 𝛿 𝛿
𝜋− 𝛿
𝑠𝑖𝑛 𝜔𝑡d𝜔𝑡
=
2
𝜋
𝐼 𝑚
𝜔𝐶
[
𝜋
2
- 𝛿+sin 2𝛿/2-sin 2𝛿]
𝑢 𝑐*√2 =
𝐼 𝑟𝑚𝑠√2
𝜔𝐶
[1-
𝑠𝑖𝑛2𝛿
𝜋
-
2𝛿
𝜋
]
∴ 𝑢 𝑐=
𝐼
𝜔𝐶
[1-
𝑠𝑖𝑛2𝛿
𝜋
-
2𝛿
𝜋
]

11.  So,the fundamental component of 𝑢 𝑐
𝑢 𝑐1(𝛾) =
𝐼
𝜔𝐶
[1 −
2𝛿
𝜋
−
𝑠𝑖𝑛2𝛿
𝜋
]
In general, 𝛾 =
𝜋
2
+ 𝛿 𝛿 = 𝛾-
𝜋
2
Substituting the value of 𝛿 in the above equation, we get
𝑢 𝑐1(𝛾) =
𝐼
𝜔𝐶
[2 −
2𝛾
𝜋
−
𝑠𝑖𝑛2𝛾
𝜋
]
or,
𝑢 𝑐1( 𝛾)
𝐼
=
1
𝜔𝐶
[2 −
2𝛾
𝜋
−
𝑠𝑖𝑛2𝛾
𝜋
]
𝑋𝑐(𝛾) =
1
𝜔𝐶
[2 −
2𝛾
𝜋
−
𝑠𝑖𝑛2𝛾
𝜋
]

12. Fig: Fundamental component of the series capacitor voltage vs. the turn-off
delay angle γ.

13.  This variable series capacitive reactance of the schemes as a function of turn off
angle 𝛾.
 Hence, by controlling turn off angle 𝛾 we can control the voltage across the
capacitor.
 In a practical application the GCSC can be operated either to control the
compensating voltage, uC(γ), or the compensating reactance, XC(γ). In the
voltage compensation mode, the GCSC is to maintain the rated
compensating voltage in face of decreasing line current over a defined
interval Imin<= I <=Imax as illustrated in Figure (a1).

14.  In the impedance compensation mode, the GCSC is to maintain
the maximum rated compensating reactance at any line current up to
the rated maximum. In this compensation mode the capacitive
impedance is chosen so as to provide the maximum series
compensation at rated current, XC = ucmax/Imax, that the GCSC can
vary in the 0 <= XC(γ) <= XC range by controlling the effective
capacitor voltage uC(γ),

15. THANK YOU