MODULE -5B: REACTIVE POWER COMPENSATION IN EHVAC LINES-

PART B – PASSIVE SERIES & SHUNT COMPENSATION (CONTD.)

5.3.4 Protection Schemes for Series Capacitor

When the fault or overload occurs the large current will flow across the series capacitor of the
line. Thus, the excessive voltage drop (=Ifault*XCse) occurs across the capacitor and it may
rupture. For protecting the capacitors from such abnormal voltages, spark gaps and surge
diverter are connected to the capacitor terminal. A circuit breaker (bypass switch) is also
connected in parallel with it to remove or re- insert the series capacitor in the line manually.
Some of the methods of series capacitor insertion/removal are shown below.

5.4 Problems associated with Series capacitor introduction (SSR)

Southern California has a great demand for electric power, and in the 1970's additional
generating plants in Arizona were connected to the Los Angeles area by 500-kV series-
compensated lines. A surprise occurred in 1970 when a generating unit in the then new
Mohave plant suffered breakage of a shaft between the exciter and the main generator. The
cause of this accident was not understood at first. The generating unit was repaired and
restored to service. About a year later, the same accident recurred. This time the phenomena
were thoroughly studied, and much knowledge was gained on what is now called sub-
synchronous resonance (SSR). Sub-synchronous resonance cannot occur unless the
transmission system has at least one natural frequency that is sub-synchronous, that is, lower

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 than the generated frequency. A series-compensated transmission system has one or more
sub-synchronous frequencies.
Shunt-compensated lines, on the other hand, if not too long and too heavily compensated,
have no sub-synchronous natural frequencies but only super synchronous ones.
Some of the problems associated with the series-capacitor application are given below in
details

 The series compensated line produces series resonance at frequencies lower than power
frequencies. This is known as sub-synchronous resonance. The sub-synchronous produces
mechanical stress due to which high torsional stress occurs in the rotor shaft. The problem of
sub-synchronous resonance mostly occurs during faults or switching operation.

The series capacitors introduce a sub-synchronous frequency (proportional to the square-root

of the compensation) in the system. In some case this frequency may interact with weak steam
turbine generator shaft frequencies and give rise to high torsional stress.

In hydro-turbine generators, the risk of sub-synchronous resonance is small because the

torsional frequency is about 10 Hz or even less

We know that, with the series compensation used, the power handling capacity of line is

E.V
P sin 
X
X  ( X L  X C )  X L (1  K )

where, K = XC/XL is degree of compensation and reactances are at power frequency ‘f0’

(1)

As at certain resonant frequency (fr) it is possible that

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X Cfr  ; X Lfr  2f r L
2f r C
1
2f r L 
2f r C
1
fr 
2 LC

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 Replacing LC = 1/K(2πf)2 from (1)above , we get:

K (2f ) 2
fr   f K
2

 The problem of sub-synchronous resonance with series compensated lines is overcome by the
following methods.

(a) By using a filter.

(b)By passing the series capacitor bank under resonance conditions.

(c) By tripping off the generator under sensing of the initiation of the resonance.

5.5 Shunt Compensation- An Introduction

For high voltage transmission line the line capacitance is high and plays a significant role in
voltage conditions of the receiving end. When the line is loaded then the reactive power
demand of the load is partially met by the reactive power generated by the line capacitance
and the remaining reactive power demand is met by the reactive power flow through the line
from sending end to the receiving end.

Inductive loading

When load is high (more than SIL) then a large reactive power flows from sending end to the
receiving end resulting in large voltage drop in the line. To improve the voltage at the receiving
end shunt capacitors may be connected at the receiving end to generate and feed the reactive
power to the load so that reactive power flow through the line and consequently the voltage
drop in the line is reduced. To control the receiving end voltage a bank of capacitors (large
number of capacitors connected in parallel) is installed at the receiving end and suitable
number of capacitors are switched in during high load condition depending upon the load
demand. Thus the capacitors provide leading VAr to partially meet reactive power demand of
the load to control the voltage.

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If XC = 1/ωC be the reactance of the shunt capacitor at the line end , then the reactive power
generated of leading VAr supplied by the capacitor

2
V2
QC   V2 C
2

XC
where, |V2| is the magnitude of receiving end voltage.

Capacitive loading

When load is small (less than SIL) then the load reactive power demand may even be lesser
than the reactive power generated by the line capacitance. Under these conditions the reactive
power flow through the line becomes negative, i.e., the reactive power flows from receiving
end to sending end, and the receiving end voltage is higher than sending end voltage (Ferranti
effect).

To control the voltage at the receiving end it is necessary to absorb or sink reactive power. This
is achieved by connecting shunt reactors at the receiving end. Shunt reactors are inductive
loads that are used to absorb reactive power to reduce the over voltages generated by line
capacitance. To maintain the voltage rise within certain limits, we may use more than one
shunt reactor placed at appropriate points along the line length (as shown). The magnitude of
the reactor reactance and its locations will decide the ultimate shape of the voltage profile over
the line length.

If XL = ωL be the reactance of the single shunt reactor (inductor) at the line end then the
reactive VAr absorbed by the shunt rector:

2
V
QL  2  V2 / L
2

XL
where, |V2| is the magnitude of receiving end voltage.

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Although shunt reactors are inductive loads similar to transformers but they are different than
transformers in terms of construction and some electrical characteristics.

Their major applications are: • Preventing over voltages that occur when the line is lightly
loaded (Ferranti Effect). • Providing voltage control. • Compensating for line charging reactive
power demand of the open-circuit line. • Suppressing the secondary arc current for successful
single pole reclosing

In summary:

• To control the receiving end voltage generally one shunt rector is installed and switched
in during the light load condition.

• To meet the variable reactive power demands requisite number of shunt capacitors are
switched in, in addition to the shunt reactor, which results in adjustable reactive power
absorption by the combination. This is shown :

In long transmission lines, both series and/or shunt compensations may be used. A variety of
possible configurations may be tried. Some of these are shown:

Note: SE = sending end RE = receiving end

The suitability of schemes are tested in terms of power capacity improvements, voltage profiles
over the line, stability of lines, fault current MVA etc.

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5.6 Analysis of Mixed Compensation schemes

Long transmission lines performance is analyzed using the ABCD parameters as given below:

The ABCD parameters depend on the line parameters R, L and C.

When series or shunt or mixed compensation schemes are used, the ABCD parameters will
change. The new values of the ABCD parameters can be designated as A T, BT, CT and DT
respectively. To compute the overall ABCD parameters with the inclusion of the
series/shunt/mixed compensation, we need to use the chain rule. This rule tells us that if we
divide the entire line configuration (with the compensation schemes) into discrete blocks, then
the overall ABCD parameters will be the matrix multiplication of the ABCD parameters of the
individual discrete blocks.

Now we need to define the ABCD parameters of the series capacitor and the shunt reactor.
These are given as follows:

Series capacitor ABCD parameters

Hence A=1, B=-jXc, C=0, D=1

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Shunt reactor ABCD parameters

Zsh =jXsh and Bsh=1/ Xsh .

ABCD parameters are A =1, B=0, C=-jBsh, D=1

The application of the chain rule is illustrated with the following example:

Consider a compensation scheme in which two reactors are placed at ends of a EHVAC line. Let
the reactance of each be Zsh. Let the line ABCD parameters be given as

Then by the chain rule we have overall ABCD parameters as:

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Note : when there is no reactor, Zsh= ∞. Then : Bsh=0 .Hence,

As another example, let us find the overall ABCD parameters of an EHVAC line with a series
capacitor at the middle of the line as shown in the figure below:

Then by the chain rule assuming that the ABCD parameters of each half of the line (i.e. length
L/2) is

We have:

This expression may be simplified to give the overall ABCD parameters

Similarly with more complex mixed schemes the chain rule can be accordingly used/ applied to
get the overall ABCD parameters of the line.

*****************************END OF MODULE 5B******************************