Series and Shunt Compensation Explained for Power System Stability and Transmission Capacity

Series Compensation
Series compensation is basically a powerful tool
to improve the performance of EHV lines. It
consists of capacitors connected in series with
the line at suitable locations.

Advantages of Series Compensation
1. Increase in transmission capacity
– The power transfer capacity of a line is given by
sin
.
X
VE
P 
where, E is sending end voltage
V is receiving end voltage
X is reactance of line
δ is phase angle between E and V

• Power transfer without and with compensation:
KXXXX
X
P
P
XX
VE
P
X
VE
P
LCCL
L
CL
L









1
1
)/1(
1
)(
sin
)(
.
sin
.
1
2
2
1


where K is degree of compensation.
The economic degree of compensation lies in the range of 40-70%
(K < 1, i.e. 0.4-0.7)

2. Improvement of System Stability
• For same amount of power transfer and same value of E
and V, the δ in the case of series compensated line is less
than that of uncompensated line.
L
CL
CL
L
X
XX
XX
VE
P
X
VE
P
)(
sin
sin
sin
)(
.
sin
.
1
2
2
1









• A lower δ means better system stability
• Series compensation offers most economic solution for
system stability as compared to other methods (reducing
generator, x-mer reactance, bundled conductors, increase
no. of parallel circuits

3. Load Division between Parallel
Circuits
• When a system is to be strengthen by the addition
of a new line or when one of the existing circuit is
to be adjusted for parallel operation in order to
achieve maximum power transfer or minimize
losses, series compensation can be used.
• It is observed in Sweden that the cost of the series
compensation in the 420 kV system was entirely
recovered due to decrease in losses in the 220 kV
system operating in parallel with the 420 kV
system.

4. Less installation Time
• The installation time of the series capacitor is
smaller (2 years approx.) as compared to
installation time of the parallel circuit line (5
years approx.)
• This reduces the risk factor.
• Hence used to hit the current thermal limit.
• The life of x-mission line and capacitor is
generally 20-25 years.

Disadvantages
1. Increase in fault current
2. Mal operation of distance relay- if the degree
of compensation and location is not proper.
3. High recovery voltage of lines- across the
circuit breaker contacts and is harmful.

4. Problems of Ferro-resonance
• When a unloaded or lightly loaded transformer is
energized through a series compensated line, Ferro-
resonance may occur.
• It is produced due to resonance occurred in between the
iron-created inductance (i.e., due to iron parts in the
transformer) and in the reactance of the compensated
line.
• This will cause a flow of high current.
• It rarely happens and may be suppressed by using shunt
resistors across the capacitors or by short circuiting the
capacitor temporarily through an isolator or by-pass
breaker.

5. Problems due to sub-synchronous
resonance
• The series capacitors introduces 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 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.

Sub-Synchronous Resonance
• We know that, with the series compensation
used, the power handling capacity of line is
)1()(
sin
.
KXXXX
X
VE
P
LCL 
 
• where, K = XC/XL is degree of compensation
and reactances are at power frequency ‘f0’

Sub-Synchronous Resonance
(continued …)
XC = K. XL
1/ ωC = K ωL (1)
As at certain resonant frequency (fr) it is possible that
LC
f
Cf
Lf
LfX
Cf
X
r
r
r
r
fr
L
r
fr
C





2
1
2
1
2
2;
2
1



Replacing LC = 1/K(2πf)2 from (1)
Kf
fK
fr 


2
)2( 2 As K is 0.4-0.7; fr < f
Hence called sub-synchronous
frequency

Location of Series Capacitor
• The choice of the location of the series
capacitor depends on many technical and
economical consideration.
• In each case, a special system study
concerning load flow, stability, transient
overvoltage, protection requirements, system
voltage profile etc. is necessary before the
optimal location is chosen.

1. Location along the line
• In this method the capacitor bank is located at
the middle of the line (if one bank) or at 1/3rd
distance along the line (if two banks).
• This has advantage of better voltage profile
along the line, lesser short circuit current
through the capacitor in the event of fault and
simpler protection of capacitor.
• The capacitor stations are generally
unattended.

2. Location at one or both ends of line
section on the line side in the switching
station
• The main advantage of this location is that the
capacitor installation is near the manned sub-
stations.
• However, requires more advanced line
protection.
• For the same degree of compensation, more
MVAr capacity is needed as compared to
method 1.
3. Location within bus bars within Switching Stations

Shunt Compensation
• 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.

Shunt Compensation (continued…)
• 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.

• If XC = 1/ωC be the reactance of the shunt
capacitor then the reactive power generated of
leading VAr supplied by the capacitor:
CV
X
V
Q
C
C 
2
2
2
2

• where, |V2| is the magnitude of receiving end
voltage.

• 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 capacitor. 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.

• If XL = ωL be the reactance of the shunt reactor
(inductor) then the reactive VAr absorbed by
the shunt rector:
LV
X
V
Q
L
L /
2
2
2
2

• where, |V2| is the magnitude of receiving end
voltage.

• 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.

Degree of series compensation
We know that the surge impedance
LC xx
Cj
Lj
C
L
Z 


Suppose Cse is the series capacitance per unit length for series compensation.
Therefore total series reactance will be
 se
L
cse
se
sese
Lj
X
X
Lj
LC
Lj
Lj
Lj
C
j
Lj
C
j
LjLj























11
1
1
.'
2
where γse is known as degree of series compensation. Therefore, virtual
surge impedance
)1(
)1('
seC
se
C Z
Cj
Lj
Z 






Degree of shunt compensation
We know that the surge impedance
LLC xx
Cj
Lj
C
L
Z 


Suppose shunt inductance Lsh per unit length is used for shunt compensation.
Therefore the net shunt susceptance will be
 sh
Lsh
c
sh
shsh
Cj
X
X
Cj
CL
Cj
C
C
L
j
Cj
Lj
CjCj























11
1
1
.
1
'
2
where γsh is known as degree of shunt compensation. Therefore, virtual
surge impedance
)1()1(
'
sh
C
sh
C
Z
Cj
Lj
Z







• Considering both series and shunt compensation
simultaneously:
sh
se
C Zc
Cj
Lj
Z







1
1
'
''
• Therefore, the virtual surge impedance loading
se
sh
C PcP





1
1'
• It is clear that a fixed degree of series compensation and
capacitive shunt compensation decreases the virtual surge
impedance of line.
• However, inductive shunt compensation increases the virtual
surge impedance and decreases the virtual surge impedance
loading of line. If inductive shunt comp. is 100%, the virtual
surge impedance becomes infinite and loading zero.

• Suppose, we want flat voltage profile corresponding to 1.2 PC
without series compensation, the shunt capacitance
compensation required will be:
pu
PP
PcP
sh
shCC
shC
44.0
12.1
1'






• Now, assuming shunt compensation to be zero, the series
compensation required corresponding to 1.2 PC :
pu
PP
PcP
se
seCC
seC
306.0
1/2.1
1/'






• However, because of lumped nature of series capacitor,
voltage control using series capacitors is not recommended.
• Normally used for improving stability limits of the system.

Active Compensation
• Synchronous condensers are the active shunt
compensators and have been used to improve the
voltage profile and system stability.
• When machine is overexcited, it acts as shunt
capacitor as it supplies lagging VAr to the system
and when under excited it acts as a shunt coil as it
absorbs reactive power to maintain terminal
voltage.
• The synchronous condenser provides continuous
(step less) adjustment of the reactive power in
both under excited and overexcited mode.

Flexible AC Transmission System
(FACTS)
• Using high speed thyristors for switching in or out
transmission line components such as
capacitors, reactors or phase shifting transformer for
desirable performance of the systems.
• Power transfer between two systems interconnected
through a tie-line is given as
sin
.
X
VE
P 
• The FACTS devices can be used to control one or
more of voltages at the two ends, the reactance of the
tie-line and the difference of the voltage angles at the
two ends.

FACTS Devices
• The various devices used are
– Static VAr compensator (SVC)
– Static Condensors (STATCON)
– Advanced Thyristor Controlled Series
Compensation (ATCSC)
– Thyristor Controlled Phase Shifting Transformer

Active Compensation using SVC
Static VAr Compensators (without rotating part)
• An static VAr system consists of two elements in
parallel (a rector and a bank of capacitors).
• Used for surge impedance compensation and for
compensation by sectioning a long transmission line.
• Also for load compensation to maintain constant
voltage for
– Slow variation of Load
– Load rejection, outage of generator/line
– Under rapid variation of Load
• Improves system pf and stability.

Static VAr Compensators
(continued…)
• An ideal static reactive power compensator must be
capable of step-less adjustment of reactive power
over an unlimited range (lagging and leading) without
any time delay.
• Some important compensators used in transmission
and distribution networks are:
– Thyristor controlled reactor (TCR)
– Thyristor switched capacitor (TSC)
– Saturated rectors (SR)

Common feature in Static
compensators
• A fixed capacitor in parallel with controlled
susceptance. The fixed capacitors are usually
tuned with small reactors to harmonic
frequencies to absorb harmonics generated by
controlled susceptance.

Thyristor Controlled Reactor (TCR)
The controlled element is the
reactor and the controlling element
is the thyristor controller consisting
of two opposite poled thyristors
which conduct every half cycle of
the supply frequency.
Currently available thyristors can
block voltage upto 4000-9000 V
and conduct current upto 3000-6000
A.
Practically 10-20 thyristors are
connected in series to meet the
required blocking voltage .

 


sinsin)(
cos)(


t
L
V
ti
tVtv
m
L
m
• The current in the reactor can be controlled by the
method of firing delay angle control. The closure of
the thyristor valve is delayed wrt the peak of the
applied voltage in each half-cycle. Let the firing delay
angle is α, applied voltage is v.
• The amplitude ILF(α) of the fundamental reactor
current iLF(α) can be expressed as:






 



 2sin
12
1)(
L
V
I m
LF

• The admittance as a function of angle α, can be
written directly from the current equation.






 



 2sin
12
1
1
)(
L
BL
• Evidently, the admittance BL(α) varies with α
in the same manner as the fundamental current
ILF(α).
• If the switching is restricted to a fixed delay
angle, usually =0, then it becomes thyristor-
switched reactor (TSR). The TSR provides
fixed inductive admittance.

• As the SCR’s are fired then the distortion in the
sine-wave is observed with the production of odd-
harmonics.
• Arranging the TCR and coupling X’mer
secondary in delta cancels the third harmonics
and its multiple. But 5th, 7th, … harmonics are still
present.
• Small reactors are usually included in the fixed
capacitor branches, which tunes with these
branches as filters for 5th and 7th harmonics.

Operating V-I area of the TCR (a) and of the TSR (b).

Thyristor Switched Capacitors (TSC)
• In this scheme TSC’s are used
with TCR’s.
• The TCR’s and capacitance
changed in discrete steps. The
susceptance is adjusted by
controlling the no. of parallel
capacitors.
• The capacitors serve as filters
for harmonics when only the
reactor is switched.
• Advantage: Dynamic stability
is better
• Disadvantages: more no. of
SCRs, more cost

Basic TSC (a) and associated waveforms (b)

• Normally a relatively small surge current limiting
reactor is used in series with the TSC branch. This is
needed primarily to limit the surge current in the
thyristor valve under abnormal condition (switching at
wrong time).
• Transient free switching:
‘switching in’
• Case 1: vC <= V
– at vC =v or vsw = 0 (dv/dt should be 0) and
• Case 2: vC > V
– α = 0 and vsw = min.
‘switching out’ at i = 0.

Transient free switching of TSC with
different residual voltages

Operating V-I area of single TSC

TCR-FC
• The TCR-FC system provides continuously
controllable lagging to leading VArs through
thyristor control of reactor current.
• Leading VArs are supplied by two or more fixed
capacitor banks. The TCR is generally rated larger
than the total of fixed capacitance so that net
lagging VArs can also be supplied.
• The variation of current through the reactor is
obtained by phase angle control of back to back
pair of thyristors connected in series with the
reactor.

Basic TCR-FC and
its VAr demand vs VAr output characteristics

TSC-TCR
Basic TSC-TCR type static var generator and its VAr demand vs VAr output characteristic.

Operating V-I area of the TSC-TCR type VAr generator with two thyristor-switched
capacitor banks

Mechanically Switched Capacitors
(MSC)
• In this scheme MSC’s are
also used with TCR’s.
• Uses conventional
mechanical or SF6 switches
instead of thyristors to
switch the capacitors.
• More economical when
there are a large no. of
capacitors to be switched
than using TSCs.
• The speed of switching is
however longer and this
may affect transient
stability.
• This method is suitable for
steady load conditions, where
the reactive power
requirements are predictable

Saturated Reactors (SR) Scheme
• In some schemes for compensation saturated
reactors are used.
• Three-phase saturated reactor having a short
circuited delta winding which eliminates third
harmonic currents from the primary.
• Fixed capacitors are provided as usual.
• A slope-correction capacitor is usually connected
in series with the saturated reactor to alter the B-
H characteristics and hence the reactance.

• A three-phase saturated reactor having a short
circuited delta winding which eliminates third
harmonic currents from the primary winding.
• The SR compensator is maintenance free, it
has no control flexibility and it may require
costly damping circuits to avoid any possibility
of sub harmonic instability.
• Has the overload capability which is useful in
limiting overvoltage.

Static Condenser (STATCON)
or Static Compensator (STATCOM)
The basic elements of a Voltage
Source Inverter (VSI) based
STATCON are an inverter, a DC
capacitor and a transformer to
match the line voltage
When inverter fundamental
output voltage is higher than the
system line voltage the
STATCON works as a capacitor
and reactive VAr is generated.
However, when the inverter
voltage is lower than the system
line voltage, the STATCON acts
as an inductor thereby absorbing
the reactive VArs from the
system.
STATCON is a GTO (Gate Turn off) based compensation system.

For purely reactive power flow, the three-phase induced
electromotive forces (EMFs), ea, eb and ec of the synchronous
rotating machine are in phase with the system
voltages, va, vb, and vc. The reactive current I drawn by the
synchronous compensator is determined by the magnitude of the
system voltage V, that of the internal voltage E, and the total
circuit reactance (synchronous machine reactance plus
transformer leakage reactance plus system short circuit
reactance) X:
2
1
V
X
V
E
Q
X
EV
I




By controlling the excitation of the machine, and hence the
amplitude E of its internal voltage relative to the amplitude V
of the system voltage, the reactive power flow can be
controlled.

• From a DC input voltage source, provided by the charged capacitor CS, the
converter produces a set of controllable three-phase output voltages with
the frequency of the ac power system. Each output voltage is in phase
with, and coupled to the corresponding ac system voltage via a relatively
small (0.1-0.15 p.u.) tie reactance (which in practice is provided by the per
phase leakage inductance of the coupling transformer).
• By varying the amplitude of the output voltages produced, the reactive
power exchange between the converter and the ac system can be
controlled in a manner similar to that of the rotating synchronous machine.
• That is, if the amplitude of the output voltage is increased above that of
the ac system voltage, then the current flows through the tie reactance
from the converter to the ac system, and the converter generates reactive
(capacitive) power for the ac system.
• If the amplitude of the output voltage is decreased below that of the ac
system, then the reactive current flows from the ac system to the
converter, and the converter absorbs reactive (inductive) power. If the
amplitude of the output voltage is equal to that of the ac system
voltage, the reactive power exchange is zero.
• Hence, also known as Static Synchronous Generator (SSG).

• The main difference between the SVC and STATCON is that in case
of SVC the current injected into the system depends upon the system
voltage, but in case of STATCON it is independent of system voltage.
• STATCON generate or absorb reactive power without the use of
capacitor or reactors.
• The STATCON current I is made perpendicular to the system voltage
V. The STATCON coordinators adjust the phase of I so that it leads or
lags wrt to V.
Advantages:
• The steady state load ability of the line is improved.
• The voltage rises due to capacitor switching is substantially reduced
both in magnitude and duration.
• Voltage variation due to customer’s loading is reduced.
STATCON is more expensive than switched capacitors or static VAr
compensation on a per unit steady-state MVA basis, however, the
performance of the STATCON outweights the increase in cost.

GTO Thyristor-Controlled Series
Capacitor (GCSC)
It consists of a fixed
capacitor in parallel with
a GTO thyristor (or
equivalent) valve (or
switch) that has the
capability to turn on and
off upon command.
Fig. (a) Basic GTO-Controlled Series Capacitor, (b) principle of
turn-off delay angle control, and (c) attainable compensating
voltage waveform

• The objective of the GCSC scheme is to control the ac voltage vc across the
capacitor at a given line current i. Evidently, when the GTO valve, sw, is
closed, the voltage across the capacitor is zero, and when the valve is
open, it is maximum. For controlling the capacitor voltage, the closing and
opening of the valve is carried out in each half-cycle in synchronism with
the ac system frequency.
• The GTO valve is stipulated to close (through appropriate control
action) whenever the capacitor voltage crosses zero. (Recall that the
thyristor valve of the TCR opens whenever the current crosses zero.)
• When the valve sw is opened at the crest of the (constant) line current
(γ = 0), the resultant capacitor voltage vc will be the same as that
obtained in steady state with a permanently open switch. When the
opening of the valve is delayed by the angle γ with respect to the crest
of the line current, the capacitor voltage can be expressed with a
defined line current, i(t) = I cos ωt, as follows:
 



sinsin
1
)(
1
)(   t
C
dtti
C
tv
t
C
The amplitude of fundamental capacitor voltage can be expressed as a function
of γ
)2sin
12
1()( 



 
C
I
VCF
where γ is the amplitude of the line current, C is the capacitance of the GTO
thyristor controlled capacitor, and ω is the angular frequency of the ac system.

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

This impedance can be written as )2sin
12
1(
1
)( 



 
C
XC
In a practical application the GCSC can be operated either to control the
compensating voltage, VCF(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).
In this compensation mode the capacitive reactance XC, is selected so as to
produce the rated compensating voltage with I= Imin, i.e., VCmax = XC Imin. As
current Imin is increased toward Imax, the turn-off delay angle γ is increased to
reduce the duration of the capacitor injection and thereby maintain the
compensating voltage with increasing line current.

• 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 = Vcmax/Imax, that the GCSC can
vary in the 0 <= XC(γ) <= XC range by controlling
the effective capacitor voltage VCF(γ), i.e.,
XC(γ) = VCF(γ)/I.

Thyristor-Switched Series Capacitor
(TSSC)
• The operating principle: the degree of series compensation
is controlled in a step-like manner by increasing or
decreasing the number of series capacitors inserted. A
capacitor is inserted by turning off, and it is bypassed by
turning on the corresponding thyristor valve.
• A thyristor valve commutates "naturally," that is, it turns
off when the current crosses zero. Thus a capacitor can be
inserted into the line by the thyristor valve only at the
zero crossings of the line current.

• Since the insertion takes place at line current zero, a full half-cycle
of the line current will charge the capacitor from zero to
maximum and the successive, opposite polarity half-cycle of the line
current will discharge it from this maximum to zero.
• As can be seen, the capacitor insertion at line current
zero, necessitated by the switching limitation of the thyristor
valve, results in a dc offset voltage which is equal to the amplitude
of the ac capacitor voltage. In order to minimize the initial surge
current in the valve, and the corresponding circuit transient, the
thyristor valve should be turned on for bypass only when the
capacitor voltage is zero. With the prevailing dc offset, this
requirement can cause a delay of up to one full cycle, which would
set the theoretical limit for the attainable response time of the
TSSC.

Thyristor-Controlled Series Capacitor
(TCSC)
It consists of the series compensating capacitor
shunted by a TCR. In a practical TCSC
implementation, several such basic
compensators may be connected in series to
obtain the desired voltage rating and operating
characteristics. This arrangement is similar in
structure to the TSSC and, if the impedance of
the reactor, X1, is sufficiently smaller than that
of the capacitor, XC, it can be operated in an
on/off manner like the TSSC. However, the
basic idea behind the TCSC scheme is to
provide a continuously variable capacitor by
means of partially canceling the effective
compensating capacitance by the TCR.






sin2
)(
)(
)(
)(




LL
CL
LC
TCSC
XX
XX
XX
X

Thyristor-Controlled Phase Shifting
Transformer (TCPST)
In general, phase shifting is obtained by
adding a perpendicular voltage vector
in series with a phase. This vector is
derived from the other two phases via
shunt connected transformers. The
perpendicular series voltage is made
variable with a variety of power
electronics topologies. A circuit concept
that can handle voltage reversal can
provide phase shift in either direction.
This Controller is also referred to as
Thyristor-Controlled Phase Angle
Regulator (TCPAR).

Series and Shunt Compensation Explained for Power System Stability and Transmission Capacity

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Series and Shunt Compensation Explained for Power System Stability and Transmission Capacity