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INTRODUCTION
In India, the distribution systems losses is about 12% of the
generation, which is high when compared to developed countries. In
attempting to reduce distribution system losses, a thorough
knowledge of distribution system losses, a thorough knowledge of
distribution system loss calculation has to be understood.
Presently computers are widely used to solve utility
engineering problems. New programs are being developed for load
flow stability, short circuit, and for control of power systems.
Considering the utility investment in the distribution system, new
tools are essential to save engineering time and to reduce
investment. In solving distribution problems, tedious hand
calculations can be avoided with the help of new algorithms and
preferably with small computing systems.
A power system is an inter connected system composed of
generating stations, which convert fuel energy into electricity.
Substations that distribute electrical power to loads (consumers)
and transmission lines that tie the generating stations and
distribution substations together. According to voltage levels an
electric power system can be viewed as consisting of generating
system, a transmission system and a distribution system.
The distribution system is generally categorized into two
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subdivisions.
1. Primary Distribution
Which carries load at higher than utilization voltages from the
substation (or other source) to the point where the voltage is to be
stepped down to the value at which the energy is utilized by the
consumer.
2. Secondary Distribution
Which includes the part of the system operation at utilization
voltage, upto the meter at the consumer's premises.
Primary distribution system include the following basic types.
i. Radial system and
ii. Loop systems.
Chapter 2 explains in detail about the innovative technique for
load flow calculations reactive power analysis of distribution
networks. A method for reducing a radial network into a single line
equivalent, known as Dist flow method has been developed by
G.B. Jasmon and L.H.C.C. Lee which simplifies lengthy calculations of
an unreduced network. This reduced network also enables the fast
computation of load flow solutions of distribution networks. The
conditions for voltage collapse to occur are easily derived form the
single line equivalent.
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The complete simplification of equations involved are given in
Chapter 2.
Application of this Dist flow method for two test systems is
explained using software programme in Chapter 4 and the results
thus obtained are given in Chapter 5.
1.1 DISTRIBUTION SYSTEMS
1.1.1 Introduction
An electric distribution system, or distribution plant as it
sometimes called, is all of that part of an electric power system
between the bulk power source or sources and the consumer's
service switches. The bulk power sources are located in or near the
load area to be served by the distribution system and may be either
generating stations or power substations supplied over transmission
lines. Distribution system can, in general, be divided into six parts,
namely, subtransmission circuits, distribution substations,
distribution transformers, secondary circuits (or) secondaries, and
consumer's services connections and meters (or) consumer's
services.
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The subtransmission circuits extend from the bulk power
source or sources to the various distribution substations located in
the load area. They may be radial circuits connected to a bulk power
source at only one end or loop and ring circuits connected to one or
more bulk power sources at both ends. The subtransmission circuits
consist of underground cable, aerial cable, or overhead open-wire
conductors carried on poles, or some combination of them. The
subtransmission voltage is usually between 11 and 33 kv, inclusive.
Each distribution substation normally serves its own load area,
which is a subdivision of the area served by the distribution system.
At the distribution system substation the subtransmission voltage is
reduced for general distribution throughout the area. The substation
consists of one or more power-transformer banks together with the
necessary voltage regulating equipment, buses, and switch gear.
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The area served by the distribution substation is also
subdivided and each subdivision is supplied by a distribution or
primary feeder. The 3- primary feeder is usually run out from the
low voltage bus of the substation to its load centre where it
branches into three phase subfeeders and 1- laterals. The primary
feeders and laterals may be either cable (or) open wire circuits.
The distribution plant occupies an important place in any
electric power system. Briefly, its function is to take electric power
from the bulk power source or sources and distribute to deliver it to
the consumers. The effectiveness with which a distribution system
fulfills this function is measured in terms of voltage regulation,
service continuity, flexibility, efficiency and cost.
1.2 Types of Distribution Systems
1.2.1 The Radial System
The radial type of distribution system, a simple form. It is used
extensively to serve the light and medium density load areas where
the primary and secondary circuits are usually carried over head on
poles. The distribution substation or substations can be supplied
from the bulk power source over radial or loop subtransmission
circuits or over a subtransmission grid or network. The radial system
gets its name from the fact that the primary feeders radiate from
the distribution substations and branch into subfeeders and laterals
which extend into all parts of the area served. The distribution
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transformers are connected to the primary feeders, subfeeders, and
laterals, usually through fused cutouts, and supply the radial
secondary circuits to which the consumer's services are connected.
Fundamentally the advantages of the radial distribution
system are simplicity and low first cost. These result from a straight
forward circuits arrangement where a single (or) radial path is
provided from the distribution substation, and sometimes from the
bulk power source, to the consumer. With such a circuit
arrangement the amount of switching equipment is small and the
protective relaying is simple. Although simplicity and low first cost
account for the wide spread by of the radial system they are not
present in all forms of the system.
The lack of continuity of service is the principal defect of the
radial system of distribution. Attempts to over come this defect
have resulted in many forms and arrangements of the radial
system. Frequently the system is radial only from the distribution
substations to the distribution transformers. Because of the many
system arrangements encountered is some times difficult to
determine in what major type of a system should be classified. To
aid in such classification and to allow more readily the discussion of
radial systems, it should be remembered that a radial system is a
system having a single path over which current may flow for a part
or all of the way from the distribution substation or substations to
the primary of any distribution transformer.
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1.2.2. The Loop System
The loop type of distribution system is used most frequently to
supply bulk loads such as small industrial plants and medium (or)
large commercial buildings, where continuity of service is of
considerable importance. The subtransmission circuits of the loop
system should be parallel (or) loop circuits or a subtransmission
grid. These subtransmission circuits should supply a distribution
substation (or) substations. The reason for this is that as much or
more reliability should be built into the system from the low-voltage
bus of the distribution substation back to the bulk power source (or)
sources as is provided by the loop primary feeders. The use in a
loop system of a radial subtransmission circuit or circuits and a
distribution substation (or) substations, which may not provide good
service continuity, does not give a well coordinated system. This is
because a fault on a subtransmission circuit or in a distribution
substation transformer results in a interruption of service to the
loads supplied over the more reliable loop primary feeders. The
subtransmission circuits and distribution substations are often
common to both radial and loop type distribution systems.
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MODELING OF DISTRIBUTION SYSTEMS
2.1. Load Flow Analysis
Distribution system has not received much attention unlike
load flow analysis of transmission systems. However, some work has
been carried out on load flow analysis of a distribution network but
the choice of a solution method for a practical system is often
difficult. Generally distribution networks are radial and the R/X ratio
is very high. Because of this, distribution networks are ill-
conditioned and conventional Newton Raphson (NR) and fast
decouple load flow (FDLF) method are inefficient at solving such
networks.
Baran and Wu [1], obtained the load flow solution in a
distribution system by the iterative solution of three fundamental
equations representing real power, reactive power and voltage
magnitude. These three equations are very useful, since they deal
to the use in real physical systems than in other traditionally known
forms, in this dissertation work, equations, have been further
developed in which the loss terms in two of the fundamental
equations are grouped and represented in a single line equivalent.
Present work extends the single line equivalent network to be used
for load flow calculations and for deriving the condition for voltage
collapse to occur. Due to simplicity of the single line equivalent
technique, stability analysis based on this equivalence is much
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simplified making it most suitable for use in real time distribution
system monitoring. A further special feature of the method
illustrated in this work is that all voltage terms are eliminated from
the equations for solving the load flows there by simplifying the
equations for iterative solution.
In India, all the 11 KV rural distribution feeders are radial and
too long. The voltages at the far end of many such feeders are very
low with very high voltage regulation more preferable. Another
advantage of the distflow method is that it requires less computer
memory. Convergence is always guaranteed for any type of
practical radial distribution network with a realistic R/X ratio while
using the distflow method. Loads in the present formulation have
been represented as constant power. However, the dist flow method
can easily include composite load modelling. Several practical rural
radial distribution feeders in India have been successfully solved
using the dist flow method. The data of various radial systems can
be obtained using the On line production of load data in substations
[10] system described by Schrock and K.C.Kwong[10].
2.2. On Line Production of Load Data in Substations
The acquisition of statistical data on a power system is a
necessary part in its operation and planning. The essential
information, such as average daily load curve and maximum
demand is often derived by a combination of pulse summation and
computer analysis. A microprocessor based system has been
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developed which captures and analyses voltages and currents on
feeders and produces a set of reduced data which fully describes
the recent load pattern locally in the substation. Such a system is
described by F.S.Schroder and K.C.Kwong.
The load on a power system is characterised by the fact that it
is determined by the consumer and not the electricity authority.
Consequently, it must be metered firstly so that it can be controlled
and secondly so that a record is kept for later analysis. A
microprocessor systems is chosen so that the load data could be
fully analysed locally in the substation and only the minimum
amount of data consistent with the provision of all the necessary
information to describe what loads have occured is outputed. A
number of such statistical metering schemes are available
commercially. In the system developed by the author[10] the
statistical data is on-line and could be displayed on the screen of a
Video Display Unit or on a printer at any time. This data is also in a
much condensed format and is immediately usable for planning and
system operation purposes from the hard-copy printer output.
Alternatively the data could be transferred onto a cassette tape for
archive and
for further analysis.
The system as developed is aimed for the acquisition of
statistical data in a medium size substation. It caters for the
measurement of both balanced and unbalanced feeder loads using
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a flexible combination of input channels.
The data returned by the data acquisition system can be
accessed for functions such as
detection of power failures (when the voltage drops to below
20% of the rated value).
measurement of time when the voltage value falls outside the
+6% limits.
detection of maximum demands and their times of
occurrence. to predict the voltage collapse (point of
occurrence).
This system is a joint effort between the South East
Queensland Electricity Board & The Capricornia Institute of
Advanced Education.
2.3 Methodology
Distflow Method
2.3.1. Mathematical formulation of Techniques
Governing equations of a single-line system.
Before proceeding to the actual system we first derive the
equations that characterize the behaviour of a single-line system.
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Consider the single line in fig. 1 which has the following
parameters.
Where
P : Injection of real power
Q : Injection of reactive power
r : Resistance of the line
x : Reactance of the line
PL : Real load
QL : Reactive load
V : Voltage magnitude
From fig. (1) the real and reactive power equations have been
derived as
P = resistive loss in the line + real load
i.e. P = I2r+PL
the current through the line, I in terms of P and Q is
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I2 =2
22
V
QP +
Therefore the equation becomes
P = L2
22
PV
QPr +
+ (1)
Similarly the reactive power
Q = L2
22
QV
QPx +
+ (2)
From equations (1 and 2), we can eliminate the
+2
22
V
QPterms.
From equation (1)
P = L2
22
PV
QPr +
+
r
PP
V
QP L2
22 =
+ (3)
and from the equation (2)
Q = L2
22
QV
QPx +
+
X
V
QP L2
22 =
+ (4)
From equations (3) and (4) the resultant equation can be written as
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2
22LL
V
QP
x
r
PP +=
=
x
r
PP LL =
)PP(x L = r(Q-QL)
By rearranging5
)PP(x L = r(Q-QL)
(Q-QL) = )PP(r
xL
Q = LL QPPr
x+ )(
Squaring on both sides,
)(2)( 22
222
LLLL PPQr
xPP
r
xQQ ++=
( )r
)PP(xQ2PP2PP
r
xQQ LLL
2L
2
2
22L
2 +++=
Now this Q2 substitute in equation (1)
( ) LLLL2L222
2L
2
2P
r
)PP(xQ2PP2PP
r
xQP
V
rP +
++
+=
+
+= L2
22L2
22
2
22L
22
PP2r
xP
r
xP
r
xPP
V
r
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LLLL P
r
PxQ2
r
PxQ2+
The voltage at the sending end is the reference voltage and
its magnitude is kept constant, and in this case V2=1.
Therefore the equation becomes
0PPr
Qrx2Px
r
Qrx2xP2P
r
xrPQPr L
L2L
2L
2L
2222
L =+
+
++
From this equation a quadratic equation in terms of P is
obtained as follows:
0rPP)PQrx2Px()Qrx2xP2(P)xr(PrQ LLL2
L2
L2
L2222
L =++++
0rPPrQPrxQ2Px)rxQ2xP2(P)xr(p L2LLL
2L
2L
2L
222 =++++
Finally we get,
0rPPrxQ2rQPx)rrxQ2xP2(P)xr(PLLL
2
L
2
L
2
L
2
L
222 =+++++
From the above equation, the expression for P can be obtained as
( ) ( ) ( )
( )
+
++
=22
222
LL2
LL2
xr2
xr4rrxQ2Px2rrxQ2Px2
P
( )}
( )
+
++22
2/1
LLL2L
22L
2
xr2
rPQrxP2PxQr (6)
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Similarly for the reactive power Q,
Rearranging the equation (5) and eliminating P in equation (2)
( ) ( )LL QQrPPx =
( ) ( )L1 QQx
rPP =
P = ( ) LL PQQx
r+
Squaring on both sides,
( ) ( )LL2
L2
22L
2 QQx
rP2QQ
x
rPP
+
+=
( ) ( )LLL2L222
2L
2 QQr
xQ2QQ2QQ
x
rPP
++
+
Substitute this value of P in equation (2)
( ) ( ) L2LLL2L222
2L2
QQQQr
xP2QQ2QQ
x
rP
V
xQ +
+
++
+=
=
++
2L
2L
L2
2L2
L2 x
Qr
x
rP2Q
x
Qr
x
rP2QP
V
x
L22L
2
x
QQr2+
+
+++=
2
2L
2LL
2
22L2
L2 x
Qr
x
rPQ2
x
Qr
x
rQP2P
V
x
L2
2L
2
QQx
QQr2+
+
Q =
+
++ 2 L
2
L2
22
22L2 x
rxP2rQ2Q
x
xrQP
V
x
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L2
LL2L
2
Qx
PrxQ2Qr+
The above equation can be written as
+
++
2L
2L
2
2222
L2 x
rxP2rQ2Q
x
xrQP
V
x
0QQx
PrxQ2QxL2
LL2L
2
=+
+
+
+ xrxP2xQ2
V
Q
x
xr
V
Q
PV
x L2
L
2
22
2
22
L2
0QQx
PQrx2Qx
V
1L
LL2L
2
2=+
(Since V2=1).
Therefore the equation becomes,
++
x
rxP2rQ2Q
x
xrQPx L
2L
2222
L
+ 0QQx
PQrx2QrL
LL2L
2
=
0
x
QxxQPrxQ2QrrxP2rQ2QxrQxP LLL2L
2L
2L
2222L =
++++
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( ( ( 0xQxQPQrx2QrrxP2rQ2QxrQxP LLL2L2L2L2222L =++++
( ) ( ) ( ) 0xQrQPrxQ2PxxrxP2rQQxrQ L2LLL2L2L22L222 =++++++
This is the quadratic equation interms of Q.
From the above equation, the expression fro reactive power Q can
be obtained as
( ) ( )
( ) ( )( )22
LLL2L22
L222
2
LL2
LL2
xr2
x QQr x P2QrPxxr4
xr x P2Qr2xrx P2Qr2
Q+
+++
++
= (7)
2.3.2. Power Flow Equations:
Consider the radial network
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Fig. 4: Online Diagram of a radial Network
We represent the line with impedance iii jxrZ += and loads as
constant power sinks LLL jQPS += power flow in a radial distribution
network can be described by a set of recursive equations that are
structurally rich and conductive for computationally efficient
solutions. Those power flow equations are called DISTFLOW Branch
equations, that use the real power, reactive power and voltage
magnitude at the sending end of a branch i.e., P i, Q i, Vi respectively
to express the same quantities at the receiving end of the branch as
follows:
1iP + =
+
2
2
i2
iii
V
QPrP - ILiP + (8)
1iQ + =
+
2
2
i2
iii
V
QPxQ - ILiP + (9)
2IiV
+ = ( ) ( )
++++
2
i
2
i2
i2i
2
iiiii2
iV
QPxrQxPr2V (10)
Hence if P1, Q1, V1 at the first node of the network is known or
estimated, then the same quantities at the other nodes can be
calculated by applying the above branch equations successively. We
shall refer to this procedure as a FORWARD UP DATE.
Dist flow branch equations can be written backward too, i.e.,
by using the real power, reactive power and the voltage magnitude
at the receiving end of a branch Pi, Qi, Vi to express the same
quantities at the sending end of the branch. The result is the
following recursive equations, called the BACKWARD branch
equations.
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1iP =( ) ( )
Li2
i
21
i
21
iii P
V
QPrP +
++ (11)
1iQ + = ( ) ( ) Li2i
21
i1
iii Q
V
QPxQ +
++ (12)
1iQ = ( ) ( )( ) ( )
+++++
2
i
21
i
21
i2i
2
i1
ii1
ii2
iV
QPxrQxPr2V (13)
Where 1iP = Lii PP +
1
iQ = Lii QQ +
The procedure is referred as BACKWARD UPDATE. Similar to
forward update, a Back ward update can be defined.
Start updating from the last node of the network assuming the
variables nnn V,Q,P at that point are given and proceed backward
calculating the same quantities at the other nodes by applying (11),
(12) and (13) successfully. Updating process ends at the first node
(i.e., at node 1) and will provide the new estimate of the power
injections into the network P1 and Q1.
Note that by applying backward and forward update schemes
successively one can get a power flow solution.
2.3.3. Reduction of Real Network to a Single Line
Equivalent
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In this section we will show how a given power distribution
network can be reduced to a single line equivalent.
The real and reactive power flows in any line are given by
1iP + =
+
2
i
2
i2
iii
V
QPrP - 1LiP +
1iQ + =
+
2
i
2
i2
iii
V
QPXQ - 1LiQ +
The real and reactive loss terms in the above equations are
iLP =
+2
i
2
i2
ii
V
QPr (14)
iLQ =
+2
i
2
i2
i
i V
QP
x (15)
Using equation (2.14) the ratio of real losses (LPi) between
branch i and proceeding branch i+1 can be computed as,
i1i
LPLP + =
+
+
+
+++
2
i
2
i2
i1
2
1i
2
1i2
1i1i
V
QPr
V
QPr
= ( )2i
2
ii
2
1i2
1i1i
QPr
QPr
+
+ +++
+2
1i
2
i
V
V (16)
By considering the current flow in the branch i,
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+2
i
2
i2
i
V
QP=
( ) ( )
+++
+
++++2
1i
2
1Li1i2
1Li1i
V
QQPP
From the above equation the voltage ratio between branches i and
i+1 is
+2
1i
2
i
V
V=
( ) ( )
+++
+
++++2
1Li1i2
1Li1i
2
i2
i
QQPP
QP (17)
equation (2.17) can be submitted in equation (2.16) to get the ratio
of real losses
i
1i
LP
LP +=
( ) ( )
+++
+
+
+
++++
+++2
1Li1i2
1Li1i
2
i2
i2
i2
i
2
1i2
1i
i
1i
QQPP
QP
QP
QP
r
r
i
1i
LP
LP +=
( ) ( )
+++
+
++++
+++
21Li1i21Li1i
2
1i2
1i
i
1i
QQPP
QP
r
r
Similarly for the ratio of reactive losses
i
1i
LQ
LQ +=
+
+
+
+++
2
i
2
i2
ii
2
1i
2
1i2
1i1i
V
QPx
V
QPx
.
=(( )2
i2
ii
2
1i2
1i1i
QPx
QPx
+
+ +++
+2
1i
2
i
V
V
i
1i
LQ
LQ +=
( ) ( )
+++
+
++++
+++2
1Li1i2
1Li1i
2
1i2
1i
i
1i
PPPP
QP
X
X (19)
For a given distribution network the total injected real and reactive
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powers are:
P = Lii PLP + (20)
Q = Lii QLQ +
(21)
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From the equation (18) and (19) it can be seen that the losses
in the distribution network are ratios of the losses in the preceding
branch of the network.
Hence
P = ( ) Li22eq PQPr ++ (22)
Q = ( ) Li22eq QQPx ++ (23)
Since (V2 = 1)
Where
req is the equivalent resistance of the single line
and xeq is the equivalent reactance of the single line
Hence we have now reduced the real distribution network consisting
of many branches into a system with only one line.
The values of req and xeq can be obtained by
eqr = ( )2i2
iQP
TLP
+ (24)
xeq = ( )2i
2
iQP
TLQ
+ (25)
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Where
TLP = LPi is the total real power losses in the system with a
power injection of ii jQP + .
TLQ = LQi is the total reactive power losses in the system with a
power injection of ii jQP + .
Power Factor: Power factor is defined as Ratio of active power (in
KW) to the apparent power (in KVA).
22 QP
P.f.p
+
= (26)
Where p is active power.
q is reactive power
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REACTIVE POWER COMPENSATION
INTRODUCTION
Shunt and series reactive compensation using capacitors has
been 3 widely recognized and powerful method to combat the
problems of voltage drops, power losses, and voltage flicker in
power distribution networks. The importance of compensation
schemes has gone up in recent years due to the increased
awareness on energy conservation and quality of supply on the part
of the Power Utility as well as power consumers. This article (in two
parts) amplifies on the advantages that accrue from using shunt and
series capacitor compensation. It also tries to answer the twin
questions of how much to compensate and where to locate the
compensation capacitors.
3.1 SHUNT CAPACITOR COMPENSATION IN
DISTRIBUTION SYSTEMS:
Fig. 1 represents an a.c. generator supplying a load through a
line of series impedance (R+jX) ohms, fig. 2(a) shows the phasor
diagram when the line is delivering a complex power of (P+jQ) VA
and Fig. 2 -(b) shows the phasor diagram when the line is delivering
a complex power of (P+jO) VA i.e. with the load fully compensated.
A thorough examination of these phasor diagrams will reveal the
following facts. which is higher by a factor of
2
Cos
1
compared to
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the minimum power loss attainable in the system.
2. The loading on generator, transformers, line etc is decided by
the current flow. The higher current flow in the case of
uncompensated load necessitated by the reactive demand
results in a tie up of capacity in this equipment by a factor of
Cos
1i.e. compensating the load to UPF will release a capacity
of (load VA rating X Cos ) in all these equipment.
3. The sending-end voltage to be maintained for a specified
receiving-end voltage is higher in the case of uncompensated
load. The line has bad regulation with uncompensated load.
4. The sending-end power factor is less in the case of an
uncompensated one. This due to the higher reactive
absorption taking place in the line reactance.
5. The excitation requirements on the generator is severe in the
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case of uncompensated load. Under this condition, the
generator is required to maintain a higher terminal voltage
with a greater current flowing in the armature at a lower
lagging power factor compared to the situation with the same
load fully compensated. It is entirely possible that the required
excitation is much beyond the maximum excitation current
capacity of the machine and in that case further voltage drop
at receiving-end will take place due to the inability of the
generator to maintain the required sending-end voltage. It is
also clear that the increased excitation requirement results in
considerable increase in losses in the excitation system.
It is abundantly cleat from the above that compensating a
lagging load by using shunt capacitors will result in
i. Lesser power loss everywhere upto the location of capacitor
and hence a more efficient system
ii. Releasing of tied-up capacity in all the system equipments
thereby enabling a postponement of the capital intensive
capacity enhancement programmes to a later date.
iii. Increased life of eqipments due to optimum loading on them
iv. Lesser voltage drops in the system and better regulation
v. Less strain on the excitation system of generators and lesser
excitation losses.
vi. Increase in the ability of the generators to meet the system
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peak demand thanks to the released capacity and lesser
power losses.
Shunt capacitive compensation delivers maximum benefit
when employed right across the load. And employing compensation
in HT & LT distribution network is the closest one can get to the
load in a power network. However, various considerations like ease
of operation end control, economy achievable by lumping shunt
compensation at EHV stations etc will tend to shift a portion of shunt
compensation to EHV & HV substations. Power utilities in most
countries employ about 60% capacitors on feeders, 30% capacitors
on the substation buses and the remaining 10% on the transmission
system. Application of capacitors on the LT side is not usually
resorted to by the utilities.
Just as a lagging system power factor is detrimental to the
system on various counts, a leading system pf is also undesirable. It
tends to result in over-voltages, higher losses, lesser capacity
utilisation, and reduced stability margin in the generators. The
reduced stability margin makes a leading power factor operation of
the system much more undesirable than the lagging p.f operation.
This fact has to be given due to consideration in designing shunt
compensation in view of changing reactive load levels in a power
network.
Shunt compensation is successful in reducing voltage drop
and power loss problems in the network under steady load
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conditions. But the voltage dips produced by DOL starting of large
motors, motors driving sharply fluctuating or periodically varying
loads, arc furnaces, welding units etc can not be improved by shunt
capacitors since it would require a rapidly varying compensation
level. The voltage dips, especially in the case of a low short circuit
capacity system can result in annoying lamp-flicker, dropping out of
motor contactors due to U/V pick up, stalling of loaded motors etc
and fixed or switched shunt capacitors are powerless against these
voltage dips. But Thyristor controlled Static Var compensators with a
fast response will be able to alleviate the voltage dip problem
effectively.
3.2. SERIES CAPACITOR COMPENSATION IN
DISTRIBUTION SYSTEMS:
Shunt compensation essentially reduces the current flow
everywhere upto the point where capacitors are located and all
other advantages follow from this fact. But series compensation
acts directly on the series reactance of the line. It reduces the
transfer reactance between supply point and the load and thereby
reduces the voltage drop. Series capacitor can be thought of as a
voltage regulator, which adds a voltage proportional to the load
current and there by improves the load voltage.
Series compensation is employed in EHV lines to 1) improve
the power transfer capability 2) improve voltage regulation 3)
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Series capacitors, with their inherent ability to add a voltage
proportional to load current, will be the ideal solution for handling
the voltage dip problem brought about by motor starting, arc
furnaces, welders etc. And, usually the application of series
compensation in distribution system is limited to this due to the
complex protection required for the capacitors and the consequent
high cost. Also, some problems like self-excitation of motors during
starting, ferroresonance, steady hunting of synchronous motors etc
discourages wide spread use of series compensation in distribution
systems.
3.3. SHUNT CAPACITOR INSTALLATION TYPES:
The capacitor installation types and types of control for
switched capacitor are best understood by considering a long feeder
supplying a concentrated load at feeder end. This is usually a valid
approximation for some of the city feeders, which emanate from
substations, located 4 to 8 Kms away from the heart of the city. Ref
Figs 3 & 4.
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Absolute minimum power loss in this case will result when the
concentrated load is compensated to up by locating capacitors
across the load or nearby on the feeder. But the optimum value of
compensation can be arrived at only by considering a cost benefit
analysis.
The reactive demand of the load varies over a day and a
typical reactive demand curve for a day is given in fig. 5.
It is evident from fig.5 that it will require a continuously
variable capacitor to keep the compensation at economically
optimum level throughout the day. However, this can only be
approximated by switched capacitor banks. Usually one fixed
capacitor and two or three switched units will be employed to match
the compensation to the reactive demand of the load over a day.
The value of fixed capacitor is decided by minimum reactive
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demand as shown in Fig 5.
Automatic control of switching is required for capacitors
located at the load end or on the feeder. Automatic switching is
done usually by a time switch or voltage controlled switch as shown
in Fig 5. The time switch is used to switch on the capacitor bank
required to meet the day time reactive load and another capacitor
bank switched on by a low voltage signal during evening peak along
with the other two banks will maintain the required compensation
during night peak hours.
3.4 ECONOMIC JUSTIFICATION FOR USE OF
CAPACITORS:
The increase in benefits for 1 kVAR of additional compensation
decrease rapidly as the system power factor reaches close to unity.
This fact prompts an economic analysis to arrive at the optimum
compensation level. Different economic criteria can be used for this
purpose. The annual financial benefit obtained by using capacitors
can be compared against the annual equivalent of the total cost
involved in the capacitor installation. The decision also can be based
on the number of years it will take to recover the cost involved in
the Capacitor installation. A more sophisticated method would be
able to calculate the present value of future benefits and compare it
against the present cost of capacitor installation.
When reactive power is provided only by generators, each
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system component (generators, transformers, transmission and
distribution lines, switch gear and protective equipment etc) has to
be increased in size accordingly. Capacitors reduce losses and
loading in all these equipments, thereby effecting savings through
powerless reduction and increase in generator, line and substation
capacity for additional load. Depending on the initial power factor,
capacitor installations can release at least 30% additional capacity
in generators, lines and transformers. Also they can increase the
distribution feeder load capability by about 30% in the case of
feeders which were limited by voltage drop considerations earlier.
Improvement in system voltage profile will usually result in
increased power consumption thereby enhancing the revenue from
energy sales.
Thus, the following benefits are to be considered in an
economic analysis of compensation requirements.
i. Benefits due to released generation capacity.
ii. Benefits due to released transmission capacity.
iii. Benefits due to released distribution substation capacity.
iv: Benefits due to reduced energy loss.
v. Benefits due to reduced voltage drop.
vi. Benefits due to released feeder capacity.
vii. Financial Benefits due to voltage improvement.
Which are the benefits to be considered in capacitor
application in distribution system? Capacitors in distribution system
will indeed release generation and transmission capacities. But
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when an individual distribution feeder compensation is in question,
the value of released capacities in generation and transmission
system are likely to be too small to warrant inclusion in economic
analysis. Moreover, due to the tighty inter-connected nature of the
system, the exact benefit due to capacity release in these areas is
quite difficult to compute. Capacity release in generation and
transmission system is probably more relevant in compensation
studies at transmission and sub- transmission levels and hence are
left out from the economic analysis of capacitor application in
distribution systems.
3.4.1. Benefits due to released distribution substation
capacity:
The released distribution substation capacity due to
installation of capacitors which deliver Qc MVARs of compensation
at peak load conditions may be shown to be equal to
c2
c
c
2/1
2
c
22
cc S1
S
SinQ
S
CosQ1S
+
=
In general and SinQS cc when1 0
SQ CC