Iaetsd static network equivalents for large power systems

1. STATIC NETWORK EQUIVALENTS FOR LARGE POWER SYSTEMS
S. Mouli
M.E, PSA
rajmouli.245@gmail.com
Andhra University college of Engineering
Dr. V. Bapiraju
Professor
drbapibv@yahoo.com
Andhra University college of Engineering
ABSTRACT:
This paper describes static network equivalents
for power flow studies. Steady state equivalents
are of important for the study of the static
characteristics of a large power system when the
solution time must be decreased. An effort is
made in this paper to understand and
implement few types of equivalents such as REI
equivalents, ward and extended ward. These are
tested on several IEEE test systems for power
flow solutions under normal and outage
conditions. Several equivalents are examined
and compared. Among all the equivalent
techniques available ward equivalents are
widely used in the industries. Test load flow
results will be presented in order to assess the
accuracy of the examined equivalents. The
major conclusion of the paper is that as long as
there exists some reactive power support from
the equivalent it will perform satisfactorily.
I INTRODUCTION
Steady state equivalents are of great important
when there is an interest in studying a small part of
a large system. In such a case it would be desirable
to equivalize the system around the area of interest
and experiment with the reduced system instead of
the large system. Considerable interest is currently
being shown in load-flow equivalence especially
for control-centre applications. In any country the
overall economic development depends on the
availability of electric power. The ever-increasing
demand for electric power due to rapid
industrialization and urbanization the electric
power networks are growing in size and complexity
years after year. These power systems have several
inter connections. Due to this interconnectivity the
modern electric power systems are characterised by
their large size and complexity with enormous
number of generating units transmission lines
transformers and other related compensating
devices etc., distributed over long distance over
several hundreds of kilometres. Several types of
equivalence techniques have been considered to
date. Since all equivalents are calculated from a
solved base case load flow they are exact only for
the base case. one of the most widely used
equivalence methods is the due to ward. The major
problem with the ward equivalent is that it does not
allow for reactive power support in the equivalize
area. This can be explained by noticing that
although the real power is always specified for
every bus the slack bus the reactive power is not
specified for every bus and may vary.
If the equivalent assumes that the reactive power at
the regulated buses will remain at its base case
value even under out ages the results are really
unacceptable. For the ward equivalent once the
equivalent has been formed there is no way of
producing more or less reactive power in the
equivalize area if the out aged case so requires.
Therefore it is expected that the behaviour of an
equivalent network with the reactive power support
capabilities would be closer to the behaviour of the
unreduced network. Several equivalence techniques
such as REI ward equivalent with buffer and
extended ward equivalent satisfy the above
requirement.
Experiments were conducted with the REI
equivalent and the ward equivalent with a buffer
zone and although the REI type equivalent
performed satisfactorily the final conclusion was
that the ward equivalent with a carefully selected
buffer zone is a very good equivalence method.
This equivalent is the easiest to implement and
understand and thus it has been recommended for
future usage.
II BASIC ISSUES OF
EQUIVALENCING
Fig illustrates the general problem being deal with.
Load flow type studies are to be performed on an
interconnected system. An internal system is to be
modelled in detail. The remaining external system
is to be represented by some equivalent attached at
the boundary buses. The solved load flow model of
the entire interconnected system is available. The
aim of equivalence is simply computational
economy, through reduction of the system size. The
general problem can be formally stated as follows.
Given a solved load flow model of an
interconnected power system PS and an area of
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2. interest AI with in PS find a new equivalent load
flow model PE that has a smaller number of buses
and branches than PS. PE should be such that for
changes of the operating conditions within AI the
results of PE are close to the results of PS. If AE=
{PS}-{AI} then schematically the steady state
equivalent problem is as shown.
Fig 1
If PS were a linear system then the problem posted
would be easily and exactly solved. This can be
seen from the following matrix manipulations.
Since it was assumed that PS can be described by a
set of linear equations and without loss of
generality these could be the nodal
Equations then


















E
I
E
I
EEEI
IEII
I
I
V
V
YY
YY
AE
AI
(1)
Solving for V1
V1=Y11
-1*
Y12*V2+Y11
-1
*I1 (2)
Substituting in to (1)
Y22EQ*V2=I2EQ (3)
Where Y22EQ = Y22 -Y21 * Y11
-1
* Y12
I2EQ= I2 - Y21 * Y11
-1
* I1
According to the previous definition of PE the set
of equations (3)is a description of the equalised
system and it contains the same number of buses as
AI. If any elements of AI are altered the solution of
PE is exactly the same with the solution of PS
because AE Does not change whenever AI
changes.
III REI EQUIVALENT
The equivalent that has been suggested is the REI
(radial equivalent independent) equivalence
technique. In this case AE is transformed in to
passive network by aggregating all the generation
of AE in one bus and all the load of AE in another
new bus so that the rest of AE becomes passive.
Schematically the REI equivalent inserts a lossless
network NREI between the eliminated buses and
their aggregated injections as shown where NL is
the number of load buses and NG is the number of
generator buses. The REI equivalent (NREI) is
formed as a function of the injected power of the
buses included in the equivalent and the base
voltage of these buses.
Fig 2
Fig 3
From fig letting VG=0, then
SR= i
iS IR = i
I i
VR=SR/*IR YR=*SR/VR
2
YI=- Si*/Vi
2
Notice that the network NREI is a lossless network
for the base case conditions. In fact by construction
the power injected into R is SR= Si and the power
injection in to the ith
bus of the REI equivalent is
equal to Si.
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3. It is essential to have voltage magnitudes of all the
buses and in particular the voltage controlled buses
close to 1pu to achieve load flow convergence. The
equivalent did not make and provisions to avoid
this low voltage condition at the newly created
buses. Even if all the generators are grouped
together a low voltage condition may exist at the
REI buses. So care should be taken in building the
equivalent. It should be avoided to have
incorporating both negative and passive values of
the net injected power in the same equivalent. This
is avoided if two REI equivalents are formed one
for PV buses and one for PQ buses for each
equivalized area.
COMPUTER SIMULATION OF REI
EQUIVALENT STEP BY STEP ALGORITHM
Step 1: Read bus data of a power system and also
data for lines transformers, shunts, all the bus
voltages and powers.
Step 2: From the line, transformer and shunt data Y
bus .
Step 3: Base power flow is carried out to obtain
base case solution before the system is reduced.
Step 4: From the original Y bus only those rows
and columns are selected that belong to external
and boundary buses. Then, the resulting admittance
matrix is of the form.






BBEB
EBEE
YY
YY
Step 5: To this admittance matrix node ‘R’ and
node ‘G’ are added by inserting rows and columns
calculating values corresponding to these nodes
using the formula given above. Then, we get Y bus
of the form
















RRRBRGRE
BRBBBGBE
GRGVGGGE
EREBEGEE
YYYY
YYYY
YYYY
YYYY
Y
Step 6: From the above admittance matrix all
external nodes and node ‘G’ are eliminated using
gauss elimination, then it results new connections
between node R and boundary buses.
  






BBRB
BRBB
eq
YY
YY
Y
Step 7: Now the reduced system [YR] contains
these connections and original lines that are in
between internal system buses and that are in
between internal and boundary buses.
Step 8: If all the eliminated buses are of PQ type,
then bus ‘R’ is being considered as PQ type. If all
are of PV type, then bus ‘R’ is considered of PV
type.
Step 9: With all these values we can formulate REI
equivalent that are from REI 1 to REI 7.
IV WARD EQUIVALENT
One of the most widely used equivalence method is
the one due to ward. This ward technique was
proposed by ward himself in 1949. This equivalent
can be applied to load flow analysis and
contingency analysis. This method suffers from
poor accuracy for security related studies due to
problems in the designation of boundary bus type.
Off line equivalent overcomes this deficiency by
using buffer zones but these can’t be used on line.
The major problem with the ward equivalent is that
it does not allow for reactive power support in the
equivalized area. This can be explained by this. In
any power system the real power is always
specified for every bus except at the slack bus. The
reactive power is specified for few buses and may
vary. If the equivalent assumes that the reactive
power at the regulated buses will remain at its base
case value even under outage, the results are
unacceptable. So for the ward equivalent once the
equivalent has been formed, there is no way of
producing more or less reactive power in the
equivalize area if the out aged case so requires.
Therefore the behaviour of an equivalent network
with reactive power support capabilities would be
closer to the behaviour of the unreduced network.
Fig 4
COMPUTER SIMULATION OF WARD
EQUIVCALENT
Algorithm
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4. Step 1: Read system data, bus data of a power
system and also data for lines transformers and
shunts.
Step 2: From the line transformer and shunt data,
Y bus is constructed.
Step 3: Base case power flow is carried out to
obtain base case solution before the system is
reduced.
Step 4: From the original Y bus only those rows
and columns are selected that belong to external or
boundary buses.
Step 5: From this Y bus by performing gauss
elimination on the columns of external buses
eliminate external buses. Then one gets Yeq of
equivalent network and new connections between
boundary buses.
Step 6: The reduced system Y bus contains these
new connections and original lines that are in
between internal system buses and between internal
and boundary buses.
RESULTS FOR 30BUS SYSTEM FOR
DIFFERENT EQUIVALENTS
Step 7: With the reduced system Y bus and base
case voltage and angles compute the power
injections at the boundary buses. These are the total
power injections and are kept constant as long as
the eliminated network remains same.
Step 8: With this injected power starting with initial
values of the reduced system, power flow is carried
out.
V EXTENED WARD
In this equivalence technique a different way of
providing reactive power support is considered. It
involves the creation of a number of new
generators equal to the number of boundary load
buses. That is one new fictitious generator is
connected to each boundary load bus in such a way
as to not affect the base case solution of the
reduced system. The new generators do not
produce any real power but are capable of
producing reactive power whenever the internal
system so requires. For multisystem planning
applications the number of additional generator
buses would in general be large.
B.NO TYPE
GENERATION LOAD DEMAND BUSVOLTAGES
REAL REACT REAL REACT VOLTAG ANG(deg)
1 3 2.3873 -0.1765 0 0 1.06 0
2 1 0.4 0.5204 0.217 0.127 1.045 -5.0361
3 1 0.2 0.1917 0 0.3 1.01 -9.8046
4 1 0 0.2271 0.3 0 1.082 -18.3703
5 1 0 0.3574 0.942 0.19 1.01 -13.5302
6 1 0 0.1931 0 0 1.071 -15.0062
7 2 0 0 0 0 1.0399 -15.1913
8 2 0 0 0.058 0.02 1.0244 -16.1105
9 2 0 0 0.112 0.075 1.0458 -15.0062
10 2 0 0 0 0 1.0792 -15.5341
11 2 0 0 0.076 0.016 1.0151 -8.7828
12 2 0 0 0.228 0.109 1.0026 -12.0551
13 2 0 0 0 0 1.0105 -10.1343
14 2 0 0 0.062 0.016 1.0311 -15.9467
15 2 0 0 0.082 0.025 1.0267 -16.0779
16 2 0 0 0.035 0.018 1.0293 -15.7442
17 2 0 0 0.09 0.058 1.0204 -16.2135
18 2 0 0 0.032 0.009 1.0135 -16.8029
19 2 0 0 0.095 0.034 1.0089 -17.0388
20 2 0 0 0.022 0.007 1.0119 -16.8652
21 2 0 0 0.175 0.112 1.0154 -16.5169
22 2 0 0 0 0 1.0171 -16.4866
23 2 0 0 0.032 0.016 1.0206 -16.5169
24 2 0 0 0.087 0.067 1.021 -16.7487
25 2 0 0 0 0 1.0518 -16.1605
26 2 0 0 0.035 0.023 1.0348 -16.5526
27 2 0 0 0.024 0 1.0239 -7.2915
28 2 0 0 0 0 1.0121 -10.7532
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5. 29 2 0 0 0.024 0.009 1.0605 -16.6375
30 2 0 0 0.106 0.019 1.0497 -17.427
Table 1:30 bus system for base case
Total generation =2.9873+i1.3132
Total load=2.8340+i1.2500
Real loss=0.1533
Reactive loss=0.0632
BUS TYPE GENERATION LOAD DEMAND BUS VOLTAGES
REAL REACTIVE REAL REACTIVE VOLTAGE ANGLE
1 3 2.3873 -0.1765 0 0 1.06 0
2 1 0.4 0.5204 0.217 0.127 1.045 -5.0361
3 1 0.2 0.1917 0 0.3 1.01 -9.8046
4 1 0 0.2271 0.3 0 1.082 -18.3703
5 1 0 0.3574 0.942 0.19 1.01 -13.5302
6 1 0 0.1931 0 0 1.071 -15.0062
7 2 0 0 0 0 1.0399 -15.1913
8 2 0 0 0.058 0.02 1.0244 -16.1105
9 2 0 0 0.112 0.075 1.0458 -15.0062
10 2 0 0 0 0 1.0792 -15.5341
11 2 0 0 0.076 0.016 1.0151 -8.7828
12 2 0 0 0.228 0.109 1.0026 -12.0551
13 2 0 0 0 0 1.0105 -10.1343
14 2 0 0 0.062 0.016 1.0311 -15.9467
15 2 0 0 0.082 0.025 1.0267 -16.0779
16 2 0 0 0.035 0.018 1.0293 -15.7442
17 2 0 0 0.09 0.058 1.0204 -16.2135
20 2 0 0 0.022 0.007 1.0119 -16.8652
21 2 0 0 0.175 0.112 1.0154 -16.5169
22 2 0 0 0 0 1.0171 -16.4866
27 2 0 0 0.024 0 1.0239 -7.2915
28 2 0 0 0 0 1.0121 -10.7532
31 2 0 0 0.411 0.177 1.0269 -16.9978
Table 2: 30 bus system for REI equivalence
Total generation=2.9873+i1.3132
Total load=2.8340+i1.2500
Real loss=0.1533
Reactive loss=0.0632
BUS TYPE GENERATION LOAD DEMAND BUS VOLTAGES
REAL REACTIVE REAL REACTIVE VOLTAGE ANGLES
1 3 2.3873 -0.1765 0 0 1.06 0
2 1 0.4 0.5204 0.217 0.127 1.045 -5.0361
3 1 0.2 0.1917 0 0.3 1.01 -9.8046
4 1 0 0.2271 0.3 0 1.082 -18.3703
5 1 0 0.3574 0.942 0.19 1.01 -13.5302
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6. 6 1 0 0.1931 0 0 1.071 -15.0062
7 2 0 0 0 0 1.0399 -15.1913
8 2 0 0 0.058 0.02 1.0244 -16.1105
9 2 0 0 0.112 0.075 1.0458 -15.0062
10 2 0 0 0.1777 0.0667 1.0792 -15.5341
11 2 0 0 0.076 0.016 1.0151 -8.7828
12 2 0 0 0.228 0.109 1.0026 -12.0551
13 2 0 0 0 0 1.0105 -10.1343
14 2 0 0 0.062 0.016 1.0311 -15.9467
15 2 0 0 0.1563 0.0664 1.0267 -16.0779
16 2 0 0 0.035 0.018 1.0293 -15.7442
17 2 0 0 0.09 0.058 1.0204 -16.2135
20 2 0 0 0.1184 0.0403 1.0119 -16.8652
21 2 0 0 0.175 0.112 1.0154 -16.5169
22 2 0 0 0.0668 0.0449 1.0171 -16.4866
27 2 0 0 0.024 0 1.0239 -7.2915
28 2 0 0 0 0 1.0121 -10.7532
Table3:30bus system for ward equivalence
Total generation=2.9873+i1.3132
Total load=2.8381+i1.2594
Real loss=0.1492
Reactive loss=0.0539
VI CONCLUSION
In this thesis an attempt is made to study and
analyze the static network equivalents of the power
system. The static equivalent reduces the size of the
system. The reduced dimensionality of the network
would pave the way for real time applications.
Ideally the power flow Solution of the unreduced
network and the power flow solution of the reduced
Network should be same at the identifiable buses.
However, in reality due to various reasons, the
solutions would slightly differ from each other and
also the overall system losses would differ. Some
of the issues have been addressed in this thesis.
There are several equivalents such as ward;
extended ward and REI are in vogue. These
equivalents have their merits and demerits. There is
no one single type of equivalent which is applicable
for all kinds of situations. Most of the times the
problems are associated with the reactive power
support. This very issue has resulted in different
kinds of equivalents. Some of these issues are
being tried to understand in this work. Interestingly
all these equivalents are designed interconnected
systems where in distinct classifications such as
study network/systems external systems, which are
needed to be equivalence and the interconnectivity
of these two systems, called as boundary buses. An
attempt is made in this thesis to apply definitions to
a single area system itself so that three groups of
buses could be formulated. The first group of buses
forms a set surrounding the disturbed condition,
second group of buses from another set, which is
being equivalence and located at the boundary
buses. A simple and convenient top down tree
model is developed starting from the slack bus
growing down as roots of a tree based on the
connectivity. Now the grouping of buses can easily
be incorporated dividing the network in to the
categories of buses. For equivalence the loads are
represented as constant admittances using either
flat start voltage or an already known base case
voltage and conventional gauss elimination
technique are used to obtain reduced equivalent. At
this stage it is worth mentioning the developed
algorithm will segregate all the PQ buses in to the
external area without losing the generality for
convenience of elimination. However, in this
process of segregation if a PV bus falls in to the
external area the algorithm takes care about the
situation by creating islands of PV buses
surrounded by PQ buses. Now each island is again
subjected the same rigor of demarcations as if it is
an independent network. This situation tantamount
to the external network would be reduced to
number of PV buses falling in to that group which
in turn would be interface to boundary buses. This
algorithm would immensely help in contingency
analysis for large size networks where in the
network size can easily be reduced to the smallest
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7. possible dimension and power flow solutions can
speedily be obtained using conventional already
available power flow methods. The accuracy of the
power flow solution greatly depends on the quality
of equivalence. In this regard a simple effort is
made in representing the loads by constant
admittance with appropriate node voltages and
reduced networks are tried for several test systems
such as IEEE 14, IEEE 30 and IEEE 118 bus test
systems. For all these test systems the power flow
solutions obtained for reduced networks are in
close agreement with those of the unreduced
systems.
VII References
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assessment of power systems", ERDA and EPRI
Conf. Publication CONF-750867, Henniker, Aug.
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enhancement for power systems", ibid.
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