Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 293.
Transmission Loss Minimization and UPFC Installation
Cost using Evolutionary Computation for Improvement of
Voltage Stability
Nor Rul Hasma Abdullah
Ismail Musirin and Muhammad Murtadha Othman
Faculty of Electrical & Electronics Engineering
Universiti Malaysia Pahang
Kuantan, Pahang, Malaysia
norrul78@yahoo.com
Faculty of Electrical Engineering
Universiti Teknologi MARA
Shah Alam, Selangor, Malaysia
i_musirin@yahoo.co.uk & mamat505my@yahoo.com
supply using the existing transmission lines. There are few
other methods available in solving the problems. In couple of
years, the electromechanical equipments were used. Those
equipments were switched inductors or capacitors banks and
phase-shifting transformer. However all this equipments are
not reliable or not efficient enough due to the certain problems
related to this equipments. They are not only relatively slow
but they also cannot be switched frequently because they tend
to wear out quickly [1]. In this context, one possible solution
to improve the system operation was the use of Flexible AC
Transmission Systems (FACTS) technologies. It opens up
new opportunities for controlling the power, decreasing the
losses and enhancing the unstable capacity of existing
transmission lines [1]. However not all can be provided by
FACTS devices and it is important to select the type of
devices in order to achieve the purpose. FACTS devices are
solid state converters that have the ability to control various
electrical parameters in transmission networks.
Unified
Power Flow Controller (UPFC) is one of the suitable
approaches to be chosen according to the purpose. UPFC can
effectively control both the active and reactive flows on the
lines and voltage magnitudes at the buses. In addition, UPFC
can independently provide either positive or negative reactive
power injections. The application of UPFC as the main
instrument to improve voltage profile has also been addressed
in various researches [7, 9, 11]. Some optimization techniques
have been applied for the optimal placement of multi-type
FACTS devices such as Genetic Algorithms (GAs), Tabu
Search (TS) and Simulated Annealing (SA) [4-5]. An
evolutionary programming approach to determine the optimal
allocation of multi-type FACTS devices [6-7], a Genetic
Algorithm technique which proposed for solving the optimal
location of FACTS [8, 9] and a particle swarm technique for
optimal location of FACTS devices[10-11]. Preedavichit and
Srivastava [12] proposed a loss sensitivity approach for
placement of series capacitors, phase shifters and static VAR
compensators. In this study, EP technique was used as one of
the optimization technique. By using EP technique to optimize
the size of UPFCs, the loss can be minimized and voltage
profile can be improved. Therefore the recovered supply can
be used to support the increasing electrical energy demand in
Abstract - A critical factor effecting power transmission
systems today is power flow control. The increment of load
variation in a power transmission system can lead to potential
failure on the entire system as the system has to work under a
stressed condition. Thus, the Flexible AC Transmission System
(FACTS) are integrated in power system to control the power
flow in specific lines and improve the security of transmission
line. This paper presents Evolutionary Programming (EP)
techniques for solving reactive power problem incorporating
Unified Power Flow Controller (UPFC). The objective of the
study is to employ EP optimization technique for loss
minimization along with installation cost calculation and voltage
profile monitoring. The optimizations are made based on two
parameters: the location of the devices and it sizes. The UPFC
devices are installed in the system in order to enhance the system
security; performed on the IEEE 30-bus RTS for several loading
conditions. The simulations results are compared with those
obtained from the Artificial Immune System (AIS) technique in
the attempt to highlight its merit.
Index Terms - UPFC; Loss Minimization; Evolutionary
Programming; Artificial Immune System; Installation Cost.
I.
INTRODUCTION
Nowadays, the power transmission systems have been
changed a lot. The voltage deviation due to load variation and
power transfer limitation were observed due to reactive power
unbalances has drawn attention to better utilize the existing
transmission line. It also causes a higher impact on power
system security and reliability in the world. Hence, the
electrical energy demand increases continuously from time to
time. This increase should be monitored or observed because
few problems could appear with the power flows through the
existing electric transmission networks. If this situation fails to
be controlled, some lines located on the particular paths might
become overloaded [1]. Due to the overloaded conditions the
transmission lines will have to be driven close to or even
beyond their transfer capacities.
Building a new transmission line will not be an efficient
way to solve the problems since it is quite complicated and
due to the environmental and political reasons [2]. Therefore
the only way to overcome this major problem is by developing
a new way of transmitting more efficient and economical
825
the system. EP is optimization technique implemented in
solving power optimization problems. This method has been
thoroughly discussed since its introduction by Fogel in 1960
[13]. It has also been successfully applied to various areas of
power systems to solve the optimization problem related to
unit commitment [14], optimal reactive power dispatch [14]
and reactive power planning [15-16]. Another technique
which can address optimization technique is Artificial
Immune System (AIS).
This paper presents the application of EC to minimize
losses and improve voltage profile in power system along with
calculation of installation cost. The technique determines the
location of UPFC installation based on voltage stability index
as the fitness and their optimal sizing. The EP and AIS
methods performed on the IEEE 30-bus reliability test system
have indicated that the proposed methods are worth in loss
minimization scheme.
II.
Z ij = Z L + jX TCSC , X TCSC = rTCSC . X L
(1)
where ZL is the impedance of the transmission line, XTCSC is
the reactance of the line where TCSC is located and rTCSC is
the coefficient which represents the compensation degree of
TCSC.
Fig. 2 Block diagram of the considered TCSC devices.
The SVC can be operated as both inductive and capacitive
compensation which can control bus voltage by absorbing or
injecting reactive power [10]. The SVC is modelled as a shunt
variable susceptance added at both ends of the line. Hence, it
is modelled as ideal reactive power injections to perform the
steady-state condition at bus i, as shown in Fig. 3 [17].
PROBLEM FORMULATION
Flexible AC transmission system (FACTS) devices have
several types namely, Unified Power Flow Controller (UPFC),
Static VAR Compensator (SVC), static compensator
(STATCOM), Thyristor Controlled Phase Angle Regulator
(TCPAR) and Thyristor Controlled Static Compensator
(TCSC). The optimization of SVCs for solving reactive power
control problem involve several equation and constraint;
equality constraint and inequality constraint. The equality
constraints are the nodal power balance equations, while the
inequality constraints are the limits of all control or state
variables. The objective function is optimization of real power
losses in the power system.
Fig. 3 Block diagram of the considered SVC devices.
The injected power at bus i is
ΔQis = Qsvc .
(2)
where QSVC is the reactive power injected by the SVC placed
bus in MVAR.
Hence, the UPFC device constraint limit is given by [18],
A. Unified Power Flow Controller (UPFC) design
UPFC mode is illustrated in Fig. 1. It consists of two
voltage-source converters, which is connected back to back
through a DC capacitor.
− 0.8 X L ≤ X TCSC ≤ 0.2 X L
(3)
− 200MVAR ≤ QSVC ≤ 200 MVAR
(4)
B. Unified Power Flow Controller (UPFC) placement
The placement of the UPFCs in the network must be
determined and then, the setting of the control parameters of
UPFC is optimized by controlling the device parameters.
Locations of FACTS devices in the power system are obtained
based on the performance using the voltage stability index
measured each line for the same operating conditions. UPFCs
are installed in the weakest buses and heavily loaded areas to
reduce stressed condition in the system. The Static Voltage
Stability Index (SVSI) technique was applied as the tool to
indicate the UPFCs location into the network. When the load
flow program was run, stability indices are calculated for
UPFC placed in every line one at a time for the same
operating conditions and the system identified five line buses
with the highest SVSI for the purpose of installing the UPFC.
The EP optimization technique is then used to determine the
Fig. 1 UPFC model.
In this study, the UPFC is modelled by the simultaneous
presence of several FACTS devices in the same power
transmission line [18]. A TCSC in the line and SVC at a bus
in an adjacent branch incorporated as an UPFC in this paper.
The mathematical models of TCSC, is shown in Fig. 2. TCSC
can be operated as the inductive or capacitive compensation
by decreasing or increasing the reactance of the transmission
line branch. Its value is function of the reactance of the line XL
where the TCSC is located [17].
826
suitable value of the UPFC. The concept of the SVSI is
demonstrated through a simple two-bus system model. The
mathematical formulation for SVSI [1] is given as in equation
(5);
SVSI ji =
2
(X
2
ji
+R
2
ji
)(P
2
ji
+Q
2
ji
)
1) Initialization: An initial population of xi parent
individual is selected randomly within their feasible range as
denote below:
xim = [ xTCSC( y ) i , xTCSC( y ) i , xTCSC( y ) i , xTCSC ( y ) i ,
1
(5)
5
2
where, i is the sending bus, j is the receiving bus, Rji is the line
resistance Xji is the line reactance, Pji is the real power at the
receiving end, Qji is the reactive power at the receiving end
and Vi the sending end voltage. SVSI has a value between 0
and 1, in which 0 represents the no-load condition and 1
represents unstable condition. Therefore, to obtain stability in
the system, SVSI has to be maintained far below 1.
C. Cost of Installation
The cost of installation of UPFC devices has been
mathematically formulated and is given by [2]
(6)
where IC is the installation cost of UPFC devices in US$ and
CUPFC is the cost of UPFC devices in US$/KVAR.
Installation cost includes the sum of installation cost of all
the devices and it can be calculated using the cost function
given by [2]:
CUPFC = 0.0003 S 2 − 0.2691S + 188 .22 (US $ / KVAR )
(7)
S = Q2 − Q1
(8)
4
1
2
3
4
(9)
5
where i= 1,2,3,4,…m. The variable, m indicated the
population size from a set of random distributions ranging
from
min
max
min
max
to xTCSC and Qsvc to Qsvc . It represents the
xTCSC
compensation degree of UPFC. The variables y1 until y5
indicated the five bus at the sensitive line. The initial parent
should verify the constraints which is the fitness function of
the system.
2) Mutation: During mutation, the Gaussian mutation
operator is performed to generate new population (offspring)
to the selected individual (parents), xi,j randomly by using a
standard deviation, σ which is the square root of the variance.
The standard deviation decides the features of offspring
produced related to its parent. Each element of the offspring
individual is calculated according to the following equation:
(
)
xi +m, j = xi , j + N 0, σ i2, j ,
⎛ fi ⎞
⎟⎟
⎝ f max ⎠
σ i , j = β (x j max − x j min )⎜⎜
(10)
where
xi+m = mutated parent (offsprings)
xi,j = parent
N (μ , σ 2 ) = Gaussian random variable with mean μ and
variance σ2
β = mutation scale. 0< β <1
xj max=maximum random number for every variable
xj min =minimum random number for every variable
fi= fitness for the ith random number
fmax= maximum fitness
The mutation scale, β can be manually adjusted to achieve
better convergence. The lower value of β, convergence of EP
is expected to occur more quickly and vice versa.
3) Tournament Selection: EP employs a selection
through the tournament scheme as to choose the survivals to
the next generation. This selection is used to identify the
candidates that can be transcribed into the next generation
from the combined population of the parents and offspring. In
this tournament, an individual is randomly selected from the
set of parents and offsprings population. The populations of
individuals with better fitness function were sorted in
ascending order. The first half or the population would be
retained as a new individuals or parent to the next generation
and the others will be removed from the pools. The process is
continued until a convergence is reached.
4) Convergence Criterion: The convergence criterion is
based on the difference between the maximum and minimum
where, S is operating range of UPFC in MVAR, Q1 is reactive
power flow through the branch before UPFC installation and
Q2 is reactive power flow through the branch after UPFC
installation.
III.
3
xTCSC( y ) i , Qsvc( y ) i , Qsvc( y ) i , Qsvc( y ) i , Qsvc ( y ) i , Qsvc( y ) i ]
Vi − 2 X jiQ ji − 2 R ji Pji
IC = CUPFC × S × 1000 .
2
EVOLUTIONARY PROGRAMMING
In this study EP is used as the main optimization
technique to solve the reactive power dispatch problem; which
involves initialization, fitness computation, mutation,
combination, tournament selection and transcription of next
generation. The process for the optimal solution is started by
determining a population of candidate solution over a number
of generations randomly. The strength of each of candidate
solution is determined by its fitness function which is
evaluated based on the constraint in the objective function of
the minimization respectively. The individuals that survived
according to fitness function referred to as the objective
function. If the individuals pursue the fitness setting range
during the initialization, the fittest individuals will survive to
the next generation, while others will be combined through a
process of mutation to create new populations. Finally, the
new population is evaluated and the process is repeated. The
procedure of the proposed method is summarized as follows:
827
fitness of the objective function. The optimal solution is
achieved when there is no significant changed between the
new generation and the last generation. If fitnessmax and
fitnessmin represent the maximum and minimum values of the
objective functions inside a given parent generation, the
convergence criterion process will be achieved if:
fitnessmax – fitnessmin ≤ 0.0001
START
size of UPFCs to be installed and transferred into the load
flow programme for evaluating the total losses. Tests are
performed at several loading conditions. Several inequality
constraints are set in this study so as to achieve the optimal
solution.
V. RESULT AND DISCUSSION
(11)
The proposed method has been tested on a IEEE 30-bus
RTS system, which consist of 5 voltage control buses, 24 load
buses, 1 slack bus, 41 interconnected lines and 4 transformer
tap changers. The base power is 100MVA.
There were two constraints assigned before the UPFCs
sizing is optimized. The constraints were total loss to be less
than the loss_set and voltage at the loaded bus higher than
V_set. The loss_set and V_set are the total loss and voltage at
the loaded bus before the optimization process was conducted.
Result for losses minimization and voltage profile
improvement at bus 26 is tabulated in Table I. From the table,
bus 26 was subjected to variation of loading conditions.
Loading factor, λ is increased gradually in order to observe the
effect of total losses with the installation of UPFCs to the
system.
Find the 5 sensitive line and
assign x to UPFC parameter
Set the loading factor
Calculate fitness by running
load flow programme to
evaluate total loss
Run load flow
Calculate index
Determine the maximum,
minimum, average and
summation of fitness
Sort index in descending
order
Mutate the parents
(Generate offsprings)
Display 5 highest index
(Sensitive Line)
29
Find Qline before UPFCs
installation
Set the UPFCs constraints
Total Losses at bus 26 (MW)
Recalculate fitness by
running load flow
programme to evaluate total
loss
Combine parent and
offsprings
Generate random no,x as a
control variable of UPFC
(x1,x2,...xn)
n= no. of UPFCs
installation
Perform selection by
ranking process
27
25
23
21
19
17
2
Fig 5. Transmission loss profiles using EP and AIS with bus 26 loaded
Solution converge?
Fill in population pool
1.5
Yes
Find Qline after UPFCs
installation
Voltage at bus 26 (p.u)
Yes
3.2
Total Losses after optimised with AIS
No
No
3
Total Losses after optimised with EP
Yes
Polulation pool
is full?
λ at bus 26 (p.u)
Total Losses before installation of UPFC
Transcribe new generations
Constraint
violation?
2.5
Calculate cost of
installations
Determine xi min and x i max
END
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
a
0.6
0.5
2
Fig. 4 Flowchart of EP for UPFC Implementation
2.5
3
λ at bus 26 (p.u)
Voltage before installation of UPFC
IV. METHODOLOGY
Voltage after optimised with EP
Voltage after optimised with AIS
The Evolutionary Programming (EP) optimization
technique was implemented in the following procedures as
shown in Fig. 4. Ten initial variables i.e. x1, x2, x3, x4, x5, x6, x7,
x8 , x9 and x10 are generated randomly. These values will be the
Fig 6.
828
Voltage profiles for bus 26 loaded
3.2
TABLE I
EFFECT OF UPFC INSTALLATION FOR LOSS MINIMIZATION AND COST INSTALLATION AT BUS 26
λ factor
(p.u.)
2.0
2.5
3.0
3.2
Analysis
SVSI
(p.u.)
Total Loss
%
∆Loss
Pre-UPFC
0.3197
(MW)
20.3
Post-UPFC
0.395
18.3
Pre-UPFC
0.3636
22.3
Post-UPFC
0.2974
18.7
Pre-UPFC
Post-UPFC
Pre-UPFC
Post-UPFC
0.538
0.3965
0.6431
0.431
26.2
19.1
28.9
19.5
Vm
(p.u.)
Cost
(US$)
0.845
9.6
10,764.80
1.115
0.783
16.1
11,762.92
1.013
0.688
1.153
0.636
1.080
27.2
32.7
21,223.23
28,559.57
TABLE II
LOCATION AND SIZE OF UPFC WHEN BUS 26 WAS REACTIVELY LOADED
λ factor
(p.u.)
2.0
2.5
3.0
3.2
Vm
(p.u.)
Analysis
X1
X2
X3
X4
X5
Q1
Q2
Q3
Q4
Q5
2
0.19
Per Unit
15
0.26
34
0.38
6
0.18
5
0
2
0
MVAr
15
0
34
0
6
0
Line No
Pre-UPFC
0.845
5
0.20
Post-UPFC
1.115
0.17
-0.23
-0.53
-0.67
-0.65
-92.49
-26.45
-41.64
-29.90
45.73
34
0.38
-0.22
34
0.38
-0.21
15
0.38
-0.22
5
0.20
0.19
5
0.20
-0.28
5
0.20
0.07
2
0.19
-0.07
2
0.19
-0.37
2
0.19
-0.04
15
0.26
-0.69
15
0.26
-0.54
12
0.26
0.04
6
0.18
-0.29
6
0.18
-0.43
6
0.40
-0.10
34
0
-22.22
34
0
-42.79
15
0
-44.43
5
0
-10.22
5
0
-21.25
5
0
173.81
2
0
17.95
2
0
-9.64
2
0
42.08
15
0
33.98
15
0
-44.87
12
0
-55.41
6
0
-140.71
6
0
-88.28
6
0
15.65
Line No
Pre-UPFC
Post-UPFC
Line No
Pre-UPFC
Post-UPFC
Line No
Pre-UPFC
Post-UPFC
0.783
1.013
0.688
1.153
0.636
1.080
.TABLE III
COMPARISON RESULTS FOR UPFC BETWEEN EP AND AIS WHEN BUS 26 WAS REACTIVELY LOADED
λ
factor
(p.u.)
Post UPFC
Pre UPFC
EP
AIS
Voltage
Loss
Voltage
Loss
%∆Loss
Cost
Voltage
Loss
%∆Loss
Cost
2.0
0.8445
20.3
1.1148
18.3
9.6
$10,764.80
1.1876
20.2
0.1
$11,913.93
2.5
0.7831
22.3
1.0133
18.7
16.1
$11,762.92
1.0261
22.2
0.3
$39,406.71
3.0
0.6878
26.2
1.1528
19.1
27.2
$21,223.23
1.3877
25.9
1.0
$19,413.65
3.2
0.6358
28.9
1.0797
19.5
32.7
$28,559.42
1.2584
28.4
1.7
$28,559.57
The loading factor, λ was increased up to 3.2 p.u.. The five
location of UPFCs installation in the network are also
identified by using SVSI technique and shown in the Table II.
Different loading condition shows a different location for
UPFCs placement in the system as it depends on which line
are the weakest subjected to loading factor variation. The
application for minimization of losses as the objective
function using EP has significantly reduced the losses and
increased the voltage profile value at the loaded bus; hence
improving the voltage stability in a system. It is observed that
the total losses value decreased accordingly and the voltage
profiles for post-UPFC are higher with the increment in the
loading factor. This implies that with the implementation of
UPFC optimization, voltage has been improved, while total
losses have been reduced indicating voltage stability
improvement.
For instance, at loading condition of 3.2 p.u. the losses
have been reduced from 28.9 MW to 19.5 MW with the
reduction of 32.7%. In order to achieve this reduction, the
values of UPFCs are -0.22 p.u. and -44.43 MVAR, 0.07 p.u.
and 173.81, -0.04 p.u. and 42.08 MVAR, 0.04 p.u. and -55.41
MVAR, -0.10 p.u. and 15.65 MVAR which should be
installed at line number 15, 5, 2, 12 and 6 respectively.
Comparative study was performed by implementing similar
scheme using AIS. The comparisons are made in terms of total
loss minimization, voltage profile and installation cost. Table
III tabulates the results of comparative studies using EP and
AIS. From Table III and Fig. 5, it is observed that when EP
was used to optimize the size of UPFC, it gives better results
as compared to AIS in terms of total losses. However, as
shown in Fig. 6, it is observed that when AIS was used to
optimize the size of UPFC, it outperformed EP in term of
829
voltage profile enhancement. At loading factor, λ = 3.2 p.u.,
AIS methods has improved the voltage profile from 0.6358.u.
to 1.2584p.u. as compared to EP which can only manage to
increase the voltage up to 1.0797 p.u.. As for the installation
cost, at loading factor equal to 2.5 p.u., an installation cost of
five UPFCs devices equal to $11,762.92 is obtained by EP
technique, while for the same number of UPFCs devices the
installation cost obtained by AIS technique is
$39,406.71which is higher whereas the reduction of total
losses is lower than EP.
[11]
[12]
[13]
[14]
VI. CONCLUSION
[15]
This paper has presented the application of evolutionary
computation technique for loss minimization and UPFC
installation cost. In this study, EP and AIS methods are
applied at bus 26 for the minimization of real power loss as
the objective function. Simulation is carried out on the IEEE
30-bus RTS system. Both the EP and AIS techniques
performed well in most cases. Simulation results demonstrated
that the proposed EP technique is feasible for loss
minimization scheme in other power system network. For
future work, other FACTS devices such as TCSC, SVC and
TCPAR can be incorporated together to achieve similar task.
[16]
[17]
[18]
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VIII. BIOGRAPHIES
Nor Rul Hasma Abdullah was born in Pahang,
Malaysia on 1978. She received her BEng from
Universiti Teknologi Malaysia in 2002 and MEng
from Kolej Universiti Tun Hussein Onn, Malaysia.
She is currently pursuing her PhD in power system at
Universiti Teknologi MARA Malaysia. Her research
interests include power system stability and Artificial
Intelligent techniques. She has written more than 5
technical papers in the international conferences and
journals.
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Associate Professor Dr. Ismail Musirin obtained
Diploma of Electrical Power Engineering in 1987,
Bachelor of Electrical Engineering (Hons) in 1990;
both from Universiti Teknologi Malaysia, MSc in
Pulsed Power Technology in 1992 from University
of Strathclyde, United Kingdom and PhD in
Electrical Engineering from Universiti Teknologi
MARA, Malaysia in 2004. He has published 2 books
and more than 120 technical papers in the
international and national, conferences and journals.
His research interest includes power system stability, optimization techniques,
distributed generation and artificial intelligence. To date he is currently the
Chair, IEEE Malaysia-Power and Energy (PES) Chapter.
Dr. Muhammad Murtadha Othman received
B.Eng. (Hons) from Staffordshire University,
England in 1998; M.Sc from Universiti Putra
Malaysia in 2000 and Ph.D from Universiti
Kebangsaan Malaysia in 2006. His area of research
interests are artificial intelligence, transfer
capability assessment and reliability studies in a
deregulated power system. To date, he is currently
the Chair, Centre for Electrical Power Engineering
Studies (CEPES) (Formerly known as the Head of
Department), Faculty of Electrical Engineering, Universiti Teknologi MARA,
Malaysia. He is also a member of IEEE. He has published more than 50 papers
in the international and national, conferences and journals.
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