1. Series Capacitor Compensation
Sudarshan B S
Assistant Professor
Dept. of EEE
RVCE, Bangalore

2. Introduction
Series capacitors are usually used to reduce the effective inductive reactance of transmission lines.
In steady state, they aid better voltage control, reactive power management, reduced losses and improved power factor.
It is important to note the behaviour of series capacitors during the transient, first- swing and oscillatory periods.

3. Series Capacitors – Transient State
By reducing the equivalent series resistance of a transmission line, the series capacitor makes the voltage less sensitive to most disturbances.
During large disturbances (for example, faults on power system), the capacitor protective equipment can have significant effect as discussed in chapter-2.
When certain faults cause overvoltages, the capacitive protective gear becomes significant. The differential CTs measure the difference current and send signals for the gap to sparkover and later trigger the bypass switch to close, thereby bypassing the series capacitors. In such a case, the capacitor gets isolated from the system during transient state.

4. Series Capacitors – First Swing State
Thermal considerations and transient or steady-state stability restrict the maximum power capability of a transmission system.
The series capacitors are used on long transmission lines to increase the power transfer capability and to improve system stability.
The power transfer through a transmission line is given by:
𝑃= 𝐸𝑉 sin 𝛿 𝑋 𝐿
Where delta is the angle between the sending end voltage (E) and the receiving end voltage (V).
With a series capacitor, the expression for power transfer is:
𝑃= 𝐸𝑉 sin 𝛿 𝑋 𝐿 − 𝑋 𝐶

5. Series Capacitors – First Swing State
Therefore, for a given phase difference between the voltages, the power transfer is greater with series capacitor.
Thus, by making a greater interchange of power possible, the normal load transfer and the synchronizing power flowing during transient condition are increased, thereby improving stability.
To transfer the same power, the power angle delta is smaller when a series capacitor is used, thus improving stability.

6. Series Capacitors – First Swing State
Consider a series-compensated radial system shown below.
Let us assume that the reactance without series capacitor is Xt. Now with the insertion of series capacitors, let us assume that the total reactance was reduced by 10% by using series capacitors in the two parallel lines.
The peak synchronizing power capability (Pmax) would be increased by 10%. The generator would have more stability margin for the same initial operating power.

7. Series Capacitors – First Swing State
The area A2 in the figure is called the decelerating area.
With 10% increase in synchronizing power, the decelerating area would also increase.
For the same initial power, same fault and the same fault clearing time, the system would be more stable on first swing with series capacitors than without.
With a corresponding increase in Pmax, the accelerating energy (area A1) would decrease in the direction toward first swing stability, if the series capacitor is not bypassed by its protective equipments.

8. Series Capacitors – First Swing State
Generally, series capacitors are automatically bypassed by their fast acting protective gear.
They may be the traditional spark gap – bypass switch, or the modern Varistor method.
One must remember that the series capacitor bypass equipment only act when the voltage across the capacitor exceeds the threshold.

9. Series Capacitors – First Swing State
Consider a worst case fault when the series capacitor bypass remains in effect on the unfaulted line long after the faulted line is removed.
From the power angle curve, we can see that the accelerating area (A1) is greater than the available decelerating energy (A2). Thus, the system will be unstable.

10. Series Capacitors – First Swing State
Consider the next case when the capacitors in the unfaulted lines reinserted when the transmission angle reaches δr1.
This will be the case when the system is just stable or critically stable.
In this case, the peak angular swing δmax equals the critical value δu.
There is no stability margin because the total available decelerating energy is fully utilized i.e. area A1 = area A2.

11. Series Capacitors – First Swing State
In this case, the capacitors in the unfaulted lines are reinserted even earlier.
The angle at the time of insertion δr2 is less than in the marginally stable case (δr1).
Also, δmax = δu.
While A2 = A1, A2 is less than the total available decelerating energy.
The unused portion of available synchronizing energy constitutes a margin of stability.

12. Series Capacitors – First Swing State
When a Varistor scheme is used (ZnO), the reinsertion is essentially instantaneous.
Therefore with the use of Varistors, even greater stability margin is achievable.
In practice, this extra margin would be partially used up by operating at a higher initial power transfer, thus utilizing the transmission system more effectively.

13. Series Capacitors – Oscillatory State
By the time the system reaches oscillatory period, even more capacitor banks will be reinserted into the system by their reinsertion schemes.
Therefore, the power and angle swings are further reduced when compared to the oscillations that would exist without the use of series capacitors.
Series capacitor compensation aids the system’s generators in developing the synchronizing torques.
In the previous discussion of first swing state, the curve S3 represents the postfault system with the capacitors bypassed. Curve S4 represents the results after reinsertion.
The curve S4 has a greater peak synchronizing power than S3. For any given oscillations in power, the angle oscillations are smaller in magnitude for curve S4 on curve S3.