International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
Optimal Transformer Tap Settings and TCSC Size
for Transmission Congestion Management
S. Sakthivel1, D. Priyanga2, S. Sumathi3
1
Associate Professor
Department of Electrical and Electronics Engineering
V.R.S. College of Engineering and Technology
Villupuram, Tamil Nadu, India.
2&3
UG Scholars
Department of Electrical and Electronics Engineering
V.R.S. College of Engineering and Technology
Villupuram, Tamil Nadu, India.
violation especially in the scenario of deregulated power
markets. Congestion is posing threats to the security of power
systems as it may cause line outage and voltage collapse.
During congestion, price volatility and market imbalance may
also result and consequently the consumers will suffer and this
will shake the very purpose of supplying power at competitive
price to the consumers [3]. The other major problem caused
by congestion being it imposes barriers on existence of new
contracts [4]. Hence congestion management is an important
issue to be addressed in restructured markets.
Numerous methods have been proposed in the literature for
congestion management [5]-[7]. Transmission congestion is
relieved by way of generation reschedule, forced outage of
lines, load curtailment, insertion of FACTS devices and
transformer tap settings [8]-[9]. Among the above mentioned
methods, use of FACTS devices and control of transformer
tap settings are cost free methods since they do not involve
any marginal cost [10]-[11] except the capital cost (cost free
methods).
Keywords— Transformer tap settings, TCSC, FACTS,
FACTS devices are long been used for power system
Congestion management, BB-BC algorithm, Real Power
control
and congestion management [12]-[13]. Series FACTS
performance index.
devices are relatively better than shunt FACTS devices for
power flow control. Use of series FACTS controllers like
I. INTRODUCTION
In deregulated electricity markets, the transmission lines TCSC will help controlling of power flow for congestion
are operated much closer to their thermal limit due to large management. Sensitivity based approaches are attempted for
number of bilateral and/or multilateral transactions. Under optimal location of TCSC for congestion management in
such stressed operating conditions, there is a risk of power recent researches [14]. TCSC is a low cost FACTS device and
flow limit violation what is termed as transmission congestion. widely used for congestion relief.
Benefits of FACTS devices are more when they are located
Relieving congestion is vital for making power transfer
in
a most suitable position in the power system [15]-[17].
agreements for the near future. Congestion can be alleviated
Intelligence
techniques are used for maximizing the benefits
by constructing new transmission lines but it is not straight
forward and needs long time for realisation [1]. Moreover of FACTS devices in congestion management [18]. The
there is lack of coordination between GenCos (Generator recently developed PSO algorithm is attempted for congestion
Companies) and TransCos (Transmission Companies) and it management by load curtailment and/or generation reschedule
results in relative decline in investment for transmission (non cost free methods).
In this paper, transmission congestion is managed by
systems [2].
optimizing
the real power performance index which is a
Congestion is defined as capacity violation of generators or
measure
of
quantity of line MW flow. Transformer tap
transformers or transmission lines. Now-a-days the word
settings
and
TCSC
sizes are the decision variables for real
congestion is used mainly to refer to the line flow limit
Abstract— Power transmission congestion is a critical challenge
in a deregulated energy market. Transmission congestion
management is very much necessary for realising all the desired
power transactions and to avoid line outages due to heavy power
flow. In this paper, a cost free congestion method by real power
performance index based approach is presented. The real power
settings correspond to optimal power flow results they are not
disturbed for congestion management only the line flows are
adjusted for relieving line over loads. Power flows are adjusted
via transformer tap positions and inserting thyristor controlled
series capacitor (TCSC) in transmission lines. Transformer tap
settings and location and size of two thyristor controlled series
capacitor (TCSC) are considered as control variables for
congestion relief objective. Optimal values of control parameters
are obtained by implementing the simple, free from large
number of parameters and easy to realise big bang-big crunch
(BB-BC). The proposed work is validated by testing it in the
medium sized IEEE 30 bus test system and the results obtained
are really encouraging.
ISSN: 2231-5381
http://www.ijettjournal.org
Page 608
International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
power flow minimization. The control parameters are varied
in a coordinated manner and improved results are obtained in
this work.
RPPI =
II. MODELLING OF TCSC
TCSC is a low cost but rapid response FACTS controller
and is a series connected FACTS device that decreases or
increases the effective line reactance, by adding a capacitive
or inductive reactance correspondingly. TCSC is highly
suitable for line flow control by changing the transfer
reactance of the line. The TCSC is modelled as a variable
reactance, where the equivalent reactance of line Xij is
defined as:
Where,
P = Mega Watt flow of line k.
Pk max = Mega Watt capacity of the line.
NL = Number of lines in the system.
n = Specified exponent.
εk = Weighting factor of line ‘k’, which may be used to
reflect the importance of some lines.
In this paper, we consider that n=1 and εk =1. RPPI will be
small when all the lines are within their limits and reach a
high value where there are overloads.
The objective is subjected to the following constraints
=
+
(1)
where, XLine is the transmission line reactance before
insertion of TCSC, and XTCSC is the TCSC reactance. The
degree of the applied compensation of the TCSC usually
varies between 20% inductive and 80% capacitive to avoid
).
over compensation (−0.8X
≤X
≤ 0.2X
The load flow studies model of a TCSC is shown in figure
1.
Bus ‘i’
XTCSC
Bus ‘j’
XL
P
ε
(2)
P
B. Equality constraints
P −P −
|V | V Y cos δ − δ − θ
= 0(3)
Q −Q −
|V | V Y sin δ − δ − θ
= 0 (4)
Where, P and P are the real power generation and load
at bus ‘i’; Q and Q are the reactive power generation and
load at bus ‘i’.
C. Inequality constraints
Bi
Line real power flow limit
Bj
MW (δ, V) ≤ MW
(5)
Power generation limit
Fig 1. Model of a TCSC
The addition of TCSC changes only the elements
corresponding to the buses i and j of the admittance matrix
and therefore modelling of TCSC for load flow studies is
simple.
III. CONGESTION MANAGEMENT PROBLEM FORMULATION
The Congestion management can be achieved by
minimizing the real power flow through the lines that are
carrying increased power. Sum of real power performance
index of all the lines in the system is taken as the objective
value for location of TCSC.
A. Objective function
The objective of this work is to minimize the total real
power performance index (RPPI) value [19]for congestion
relief. Therefore the objective functions can be written as:
ISSN: 2231-5381
P
≤P ≤P
Q
≤Q
(6)
≤Q
(7)
TCSC reactance limit
x
≤x ≤x
(8)
Bus voltage magnitude limit
V
≤V ≤V
(9)
IV. BIG BANG – BIG CRUNCH ALGORITHM
A. Overview
http://www.ijettjournal.org
Page 609
International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
A new nature inspired optimization technique which has
low computational time and high convergence speed called
BB-BC is introduced recently [20]-[22]. It has two phases,
Big bang phase
2. Big crunch phase.
In Big Bang phase, candidate solutions are randomly
distributed over the search space and in the Big Crunch phase,
randomly distributed particles are drawn into an orderly
fashion.
The Big Bang-Big Crunch optimization method generates
random points in the Big Bang phase and shrinks these points
to a single point in the Big Crunch phase after a number
sequential Big Bangs and Big Crunches.
The Big Crunch phase has a convergence operator that has
many inputs but only one output, which is named as the
‘‘centre of mass”, since the only output has been derived by
calculating the centre of mass. The point representing the
centre of mass is denoted by Xc and is calculated according to
the following equation.
1
X
f(X )
X =
(10)
1
∑
f(X )
∑
There are 4 Tk’s and 2 XTCSC in the IEEE-30 system and
hence a candidate is a vector of size 1x6.
Step 2: Calculate the fitness function values of all candidate
solution by running the NR load flow. The control variable
values taken by different candidates are incorporated in the
system data and load flow is run. The total line loss
corresponding to different candidates are calculated.
Step 3: Determine the centre of mass which has global best
fitness using equation (10). The candidates are arranged in the
ascending order their fitness (fitness) and the first candidate
will be the candidate with best fitness (minimum loss).
Step 4: Generate new candidates around the centre of mass
by adding/subtracting a normal random number according to
equation (11). It should be ensured that the control variables
are within their limits otherwise adjust the values of ‘r’ and
‘α’.
Step 5: Repeat steps 2-4 until stopping criteria has not been
achieved.
Where Xi is the ith candidate in an D-dimensional search
space, f(Xi) is a fitness function value of this point, NP is the
population size in Big Bang phase.
After the Big Crunch phase, the algorithm creates new
candidates to be used as the Big Bang phase of the next
iteration step. This can be done in various ways, the simplest
one being identifying the best candidate in the population. In
this work, the new candidates are generated around the centre
of mass and knowledge of centre of mass of previous iteration
is used for better convergence. The parameters to be supplied
to normal random point generator are the centre of mass of the
previous step and the standard deviation. The deviation term
can be fixed, but decreasing its value along with the elapsed
iterations produces better results.
X
=X +
rα(X
−X
t
)
Start
Initialize the population
within the limits
Calculate the fitness
of each agent
Gen=Gen+1
Form the new agents
around the centre of
mass
Run NR load flow and
calculate the fitness
(11)
Where r is a normal random number, α is a parameter
limiting the size of the search space, Xmax and Xmin are the
upper and lower limits, and t is the iteration step. Since
normally distributed numbers can be exceeding ±1, it is
necessary to limit the population to the prescribed search
space boundaries. This narrowing down restricts the candidate
solutions into the search space boundaries.
B. Big Bang Big Crunch applied to loss minimization
Big Bang Big Crunch algorithm involves the steps shown
below in reactive power flow control.
Step 1: Form an initial generation of NP candidates in a
random manner respecting the limits of search space. Each
candidate is a vector of all control variables, i.e. [Tk, XTCSC].
ISSN: 2231-5381
Identify the centre of
mass
Is gen<=
max gen?
Print the global best
Stop
Fig. 2 Flow chart for BB-BC algorithm
V. RESULTS AND DISCUSSIONS
The proposed BB-BC algorithm based congestion
management is tested on the standard IEEE-30 bus test system
[23]. The single line diagram of the test system is shown in
http://www.ijettjournal.org
Page 610
International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
figure 2. The algorithm is coded in MATLAB 7.6 language
tool. The test system is described in table I. The system is
considered under base load condition and the real power
settings correspond to OPF results for base load.
affected by the parameter values. Therefore tuning of the
parameters is necessary and it is not very easy. BB-BC being
with only one parameter is easy for implementation and
produces better results. The algorithm converges when
number of individuals is taken as 30 and run for 200 iterations.
TABLE. I
SYSTEM PARAMETERS
Sl.No
1
2
3
4
5
Variables
Buses
Branches
Generators
Shunt capacitors
Tap-Changing transformers
TABLE. III
OPTIMAL VALUES FOR CONTROL PARAMETERS
Quantity
30
41
6
2
4
Sl.
no
1
2
3
T6-9
T6-10
T4-12
Initial
value
0.978
0.969
0.932
Final
value
0.9801
0.9708
0.9602
T28-27
0.968
0.9344
Parameter
4
Values of all the 6 control parameters are adjusted
respecting their bounds to relieve the line congestion.
Transformer tap settings are changed and two TCSCs are
located in suitable locations with proper settings. The optimal
values of control variables obtained are shown in table III. It
may be noted that TCSC1 is located in the line connected
between buses 1-3 and takes capacitive compensation. But the
second TCSC takes inductive compensation. Table IV shows
the location and level of compensation of the TCSCs.
TABLE. IV
LOCATION OF FACTS DEVICE
FACTS
device
TCSC1
TCSC2
Fig. 3 Single line diagram of the test system
There are four tap changer transformers in the test system
and two TCSCs are recommended for better power flow
control through the lines. These six control variables are found
to be suitable for congestion management and loss reduction.
The upper and lower bounds of the six variables are given in
table II.
Parameter
No of individuals (NP)
Distribution parameter ( )
Number of iterations
Optimal value
30
±1
200
The BB-BC algorithm based optimization approach is with
only one parameter, the distribution parameter. In most of the
population based algorithms their performance is greatly
ISSN: 2231-5381
1-3
23-24
Level of
compensation
-0.5106
0.1401
Nature of
compensation
Capacitive
Inductive
When the real power settings corresponding to OPF results,
line flow in line 1 is 114.772 MVA and this is 88.28% of its
capacity. Power flow in a line above 80% of its capacity is
considered as congestion. For economic operation of the
power system for the given loading conditions (base load of
the system) the real power settings should be intact and at the
same time congestion is to be relieved. Change in power flow
pattern by adjusting the tap positions and TCSC parameters
relies the congestion. Table V shows that the underutilized
lines are better utilized and congested lines are relieved.
TABLE. V
LINE POWER FLOWS
MVA flow
TABLE. II
BB-BC PARAMETER VALUES
Sl. no
1
2
3
Location
Li
ne
no
1
2
3
4
5
6
Before
optimiz
ation
After
optimiz
ation
114.772
61.971
33.054
57.644
63.542
43.901
96.903
96.903
24.975
74.585
60.837
37.984
http://www.ijettjournal.org
M
V
A
li
mi
t
130
130
65
130
130
65
MVA flow
Li
ne
no
22
23
24
25
26
27
Before
optimiz
ation
After
optimiz
ation
6.618
3.228
6.890
9.349
6.571
21.879
6.379
3.025
7.208
9.676
7.606
21.626
M
V
A
li
mi
t
16
16
32
32
32
32
Page 611
International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
7
8
9
10
11
12
13
14
15
16
17
18
19
20
49.352
14.238
34.399
13.438
26.419
14.232
19.051
31.673
36.931
14.465
8.214
19.152
8.422
1.706
58.370
16.711
37.073
15.002
25.509
13.877
19.406
31.339
34.224
18.052
7.908
18.177
7.801
1.413
90
70
130
32
65
32
65
65
65
65
32
32
32
16
21
4.401
3.963
16
28
29
30
31
32
33
34
35
36
37
38
39
40
41
6.902
0.854
5.388
6.845
2.590
1.394
4.261
3.835
17.328
6.409
7.282
3.753
3.137
14.862
5.778
0.577
4.357
5.746
1.760
2.327
4.259
6.555
21.197
6.400
7.272
3.750
3.055
16.077
-------
-------
32
32
16
16
16
16
16
16
65
16
16
16
32
32
---
The congestion relief offers other benefits like voltage
profile improvement in the load bus areas. Figure 5 depicts
that the voltage magnitudes in buses 25 to 30 are improved.
VI. CONCLUSIONS
This work proves the effectiveness of a cost free congestion
management scheme incorporating TCSC devices. Congestion
management by the proposed method do not affect the
customer benefits since the real power schedule remains
unchanged. It is obvious from the numerical results that the
congestion relief is very much encouraging. The system
operator can use this method to relive the congestion and all
contracted power transactions can be accommodated without
violation of line flow limits. Further, all the lines in the system
are left with sufficient loading margins and therefore the
system becomes capable of transmitting increased amount of
power flows.
The very purpose of supplying power to consumers at
competitive price can be ensured to consumers. This approach,
a cost free one, implemented through BB-BC algorithm will
be a better alternative to non cost free methods of congestion
management. Moreover, the BB-BC algorithm is simple and it
could be implemented easily.
REFERENCES
[1]
[2]
[3]
Fig. 4 Convergence of BB-BC algorithm
[4]
Number of iterations taken for the optimization process is
200 and the best results are obtained in the 50th iteration.
Less number of iterations for convergence to the better results
proves the efficiency of the algorithm.
[5]
[6]
Volgae magnitude
Before
After
[7]
1.1
[8]
1.05
[9]
1
[10]
0.95
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Bus number
[11]
Fig. 5 Bus voltage magnitude
[12]
ISSN: 2231-5381
Seyed M.H. et al, “Social welfare improvement by TCSC using real
code based genetic algorithm in double-sided auction market”,
Advances in Electrical and Computer Engineering, Vol. 11, No.2, 2011.
E. Hirst, U.S. Transmission Capacity: Present Status and Future
Prospects, Edison Electric Institute and Office of Electric Transmission
and Distribution, U.S. Department of Energy, 2004.
Srinivasa Rao Pudi et al, Optimal placement of TCSC based on a
sensitivity approach for congestion management, Fifteenth National
Power System Conference, December 2008.
Sujatha Balaraman et al, “Congestion management in deregulated
power system using real coded genetic algorithm”, International
Journal of Engineering Science and Technology, Vol. 2, No. 11, pp.
6681-6690, 2010.
A.K. David, “Dispatch methodologies for open access transmission
systems”, IEEE Transactions on Power Systems, Vol. 13, No. 1, pp 4653, 1998.
R. S. Fang, and A. K. David, “Transmission congestion management in
electricity market”, IEEE Transactions on Power Systems, Vol. 14, No.
3, pp. 877-883, 1999.
Harry Singh, Shan You, and Alex Papalexopalos, “Transmission
congestion management in competitive electricity market”, IEEE
Transactions on Power Systems, Vol. 13, No. 2, pp. 672-680, 1998.
Acharya N, Mithulananthan N. Locating series FACTS devices for
congestion management in deregulated electricity markets. Electric
Power System Research, Vol. 77, pp. 352–60, 2007.
Besharat H, Taher SA. “Congestion management by determining
optimal location of TCSC in deregulated power systems”, International
Journal of Electrical Power Energy Systems, Vol. 30, pp. 563–8, 2008.
Nguyen TT, Nguyen VL. Application of wide-area network of phasor
measurements for secondary voltage control in power systems with
FACTS controllers. In: Power engineering society general meeting,
IEEE2005, Vol. 3, pp. 2927–34.
Rahimzadeh S, Tavakoli Bina M, “Looking for optimal number and
placement of FACTS devices to manage the transmission congestion.
Energy Conver Manage, Vol. 52, pp.437–46, 2011.
T. S. Chung, and Y. Z. Li, “A hybrid GA approach for OPF with
consideration of FACTS devices”, IEEE Power Engineering Review,
pp. 47-50, 2001.
http://www.ijettjournal.org
Page 612
International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
P. Bhasaputra and W. Ongasakul, “Optimal power flow with multitype of FACTS devices by hybrid TS/SA approach”, in Proc. IEEE
ICIT 2002, Bangkok, Thailand, pp.285-288.
Abouzar samimi et al, “A new method for optimal placement of TCSC
based on sensitivity analysis for congestion management”, Smart Grid
and Renewable Energy, Vol.3, pp. 10-16, 2012.
P. Preedavichit, S.C. Srivastava, “Optimal reactive power dispatch
considering FACTS devices, Electric Power System Research, Vol. 46,
pp 251–257, 1998.
S.N. Singh, A.K. David, “A new approach for placement of FACTS
devices in open power markets”, IEEE Power Engineering Review,
Vol. 21, No. 9, pp. 58–60, 2001.
H. Mori, Y. Goto, “A parallel Tabu search based method for
determining optimal allocation of FACTS in power systems in”,
International Conference on Power System Technology Proceedings,
Vol. 2, pp. 1077–1082, 2000.
S. Gerbex, R. Cherkaoui, J. Germond, “Optimal location of multi-type
FACTS devices in a power system by means of genetic algorithms”,
IEEE Transactions on Power Systems Vol.16, No. 3, pp. 537–544,
2001.
Smt. Ushasurendra, S. S. Parathasarthy Congestion management in
deregulated power sector using fuzzy based optimal location technique
for series flexible alternative current transmission system (FACTS)
device Journal of Electrical and Electronics Engineering Research
Vol. 4(1), pp. 12-20, August 2012.
K. Erol Osman, Ibrahim Eksin, “New optimization method : Big BangBig Crunch”, Elsevier, Advances in Engineering Software 37 (2006),
pp. 106–111.
Dr. H. K. Verma, Yogesh Manekar, “Big Bang Big Crunch
Optimization for Determination of Worst Case Loading Margin”,
International Journal of Engineering Research and Applications, Vol. 2,
No. 4, pp. 421-426, August 2012.
S. Sakthivel, D. Mary, “Reactive Power Optimization Incorporating
TCSC Device through Big Bang-Big Crunch Algorithm for Voltage
Stability Limit Improvement”, Wulfenia Journal, Vol. 19, No. 10, 2012.
Power Systems Test Case, 2000, The University of Washington
Archive,
http://www.ee.washington.edu/research/pstca.
ISSN: 2231-5381
BIOGRAPHIES
S. Sakthivel received the Degree in Electrical and Electronics Engineering in
1999 from Madras University and Master Degree in Power
Systems Engineering in 2002 from Annamalai University.
He is pursuing the Ph.D., Degree in Electrical Engineering
faculty from Anna University of Technology, Coimbatore,
India. He is presently working as an Associate Professor in
Electrical and Electronics Engineering at V.R.S.College of
Engineering and Technology, Villupuram, Tamil Nadu,
India. His research areas of interest are Power System control, Optimization
techniques, FACTS, Economic load dispatch, Power system deregulation and
Voltage stability improvement.
S. Priyanka is an undergraduate student in the Department of Electrical and
Electronics Engineering at VRS College of Engineering
and Technology, Villupuram, Tamil Nadu, India. She is
interested in power system operation optimization by using
intelligent techniques.
S. Sumathi is an undergraduate student with the Department of Electrical and
Electronics Engineering at VRS College of Engineering
and Technology, Villupuram, Tamil Nadu, India. Optimal
power flow using evolutionary algorithms is her important
area of interest.
http://www.ijettjournal.org
Page 613