|
Academic Open Internet Journal |
Volume 15, 2005 |
Genetic Algorithm applied to Optimal Location of FACTS Device in a Power
System Network considering economic saving cost.
J. Baskaran#, Dr. V. Palanisamy$
#Teaching research associate, $ principal.
Government
Abstract: The introduction of flexible AC
transmission system (FACTS) in a power system improves the stability, reduces
the losses, reduces the cost of generation and also improves the loadability of
the system. In the proposed work, a non-traditional optimization technique,
genetic algorithm is used to optimize the various process parameters involved
in introduction of FACTS devices in a power system. The various parameters taken
into consideration were the location of the device, their type, and their rated
value of the devices. The simulation was performed on a 30-bus power system
with various types of FACTS controllers, modeled for steady state studies. The
optimization results clearly indicate that introduction of FACTS devices in a
right location increases the loadability of the system and genetic algorithm
can be effectively used for this kind of optimization.
Keywords: Genetic Algorithm, Optimization, loadability, FACTS, optimal power flow.
INTRODUCTION:
In recent years,
with the deregulation of the electricity market, the traditional concepts and
practices of power systems are changed. This led to the introduction of
Flexible AC Transmission system (FACTS) such as Thyristor Controlled Series
Compensations (TCSC), Thyristor controlled phase angle Regulators (TCPR),
Unified Power Flow Controllers (UPFC) and Static Var Compensator (SVC). These
devices controls the power flow in the network, reduces the flow in heavily loaded
lines there by resulting in an increase loadability, low system losses,
improved stability of network and reduced cost of production [2,10,11,13]. It
is important to ascertain the location of these devices because of their
significant costs. S.Jerbex et al [4]
provides an idea regarding the optimal locations of fact devices, without
considering the investment cost of FACTS device and their impact on the
generation cost. L.J.Cai et al [5] later studied about the optimal location
considering the generation cost of the power plants and investment cost of the
devices.J.baskaran et al [16], discussed optimal location problem by power loss
reduction.
The
main objective of this paper is to develop an algorithm to find and choose the
optimal location of FACTS devices based on the Economic saving function, which
obtained by energy loss reduction.
The different
types of FACTS devices and their different location have different advantages.
In realizing, for the proposed objective function, the suitable types of FACTS
device, their location, and their rated value must be determined
simultaneously. This combinatorial analysis problem is solved by Genetic
algorithm.
This paper is organized as follows: following
the introduction, different FACTS devices mathematical models are described in
section II. Then in section III, objective functions are described. In section
IV, the genetic algorithms for optimal location of FACTS devices are discussed
in detail. The simulation results are given in section V.
II MATHEMATICAL MODEL OF FACTS DEVICES:
A. Facts Devices:
In an interconnected power
system network, power flows obey the Kirchoff’s laws. The resistance of the
transmission line is small compared to the reactance. Also the transverse
conductance is close to zero. The active power transmitted by a line between
the buses i and j may be approximated by following relationships:
Vi Vj
Pij = sinδij.
Xij
Where:Vi and Vj are voltages at buses i and j;Xij: reactance of the line;
δij: angle between the Vi and Vj.
Under the normal operating
condition for high voltage line the voltage Vi =Vj and θij is small. The
active power flow coupled with θij and reactive power flow is linked with
difference between the Vi-Vj. The control of Xij acts on both active and
reactive power flows. The different
types of FACTS devices have been choose and locate optimally in order to
control the power flows in the power system network. The reactance of the line
can be changed by TCSC.TCPAR varies the phase angle between the two terminal
voltages and SVC can be used to control the reactive power. UPFC is most power
full and versatile device, which control line reactance, terminal voltage, and
the phase angle between the Buses.
In this paper, four different typical FACTS devices have been selected: TCSC, TCPAR, SVC and UPFC. Their block diagrams are shown in Fig 1.
Fig.1 Block diagram of the considered FACTS devices: a) TCSC b) TCPST c) UPFC d) SVC
The above-mentioned FACTS devices can be applied to control the power flow by changing the parameters of power systems, so that the power flow can be optimized.
Mathematical Models:
The power-injected model is a good model for FACTS devices because it will handle them well in load flow computation problem. Since, this method will not destroy the existing impedance matrix Z; it would be easy while implementing in load flow programs. In fact, the injected power model is convenient and enough for power system with FACTS devices. The Mathematical models of the FACTS devices are developed mainly to perform the Steady state research. The TCSC, TCPAR, SVC and UPFC are modeled using the power injection method [4,5,8,13]. Furthermore, the TCSC, TCPAR, SVC and UPFC mathematical model are integrated into the model of the Transmission line. Fig: 1 shows a simple transmission line, the parameter are connected between bus i and bus j.the voltages and angles at the buses i and j are Vi, δi and Vj, δj respectively. The real and reactive power flow between the buses i to bus j can be written as
Pij =Vi2Gij-ViVj [Gijcos (δij) +Bijsin (δij)].
Qij = -Vi2 (Bij+Bsh)-ViVj [Gijsin (δij)-Bijcos (δij)].
Where the δij =δi-δj, similarly, the real and reactive power flow between the bus j to bus i is
Pji =Vi2Gij-ViVj [Gijcos (δij)-Bijsin (δij)].
Qji =-Vi2(Bij+Bsh)+ViVj
[Gijsin (δij) +Bijcos (δij)].
TCSC:
The model of a transmission line with a TCSC connected between the buses i and j is shown n fig: 1. The change in the line flows due to series reactance. The real power injection at buses i and bus j (Pi (com)) and Pj(com)can be expressed as
Pi (com) =Vi2 ΔGij-ViVj [ΔGijcos (δij) +ΔBijsin (δij)]
Pj (com) =Vj2 ΔGij-ViVj [ΔGijcos (δij)-ΔBijsin (δij)]
Similarly, the reactance power injected at bus i and j (Qi (com)) can be expressed as
Qi (com) =-Vi2 ΔBij-ViVj [ΔGijsin (δij)-ΔBijcos (δij)]
Qj (com) =-Vj2 ΔBij+ViVj
[ΔGijsin (δij) +ΔBijcos (δij)]
Where
XcRij (Xtcsc-2Xij)
ΔGij =
(Rij2+Xij2)(Rij2+(Xij-Xtcsc) 2)
-Xtcsc
(Rij2-Xij2 +XtcscXij)
DBij =
(Rij2+Xij2)(Rij2+(Xij-Xtcsc) 2)
TCPAR:
The voltage angle between the buses i and j can be regulated by TCPAR.The model of a TCPAR with transmission line as shown in fig.1. The injected real and reactive power at buses i and j having the phase shifter are
Pi (com) =-Vi2 S2Gij-ViVjS [Gijsin (δij)-Bijcos (δij)]
Pj (com) =-ViVjS [Gijsin (δij)+Bijcos (δij)]
Qi (com) =-Vi2S2 Bij+ViVjS [Gijcos (δij)+Bijsin (δij)]
Qj (com) =-ViVjS [Gijcos (δij)-Bijsin (δij)]
Where S=tanφtcpar
UPFC:
A series inserted voltage and phase angel of inserted voltage can model the effect of UPFC on network. The inserted voltage has a maximum magnitude of Vt=0.1Vm, where the Vm is rated voltage of the transmission line, where the UPFC is connected. It is connected to the system through two coupling transformers [8,113].
The real and reactive power injected at buses i and j can expressed as follows
Pi (com) = -Vt2 Gij -2ViVjGijcos (φupfc-δij) +ViVj [Gijcosφupfc+Bijsinφupfc].
Qi(com)=ViVj[Gijsin (φupfc-δij) +Bijsinφupfc].
Pj (com) =VjVt [Gijcosφupfc -Bijsinφupfc].
Qj (com) =-VtVj [Gijsinφupfc+Bijcosφupfc].
SVC:
The primary purpose of SVC is usually control of voltages at weak points in a network. This may be installed at midpoint of the transmission line. The reactive power output of an SVC can be expressed as follows:
Qsvc
=Vi (Vi-Vr) /
Xsl.
Where, Xsl is the equivalent slope reactance in p.u.equal to the slope of voltage control characteristic, and Vr are reference voltage magnitude. The exact loss formula of a system having N number of buses is [1].
N N
Pltc= Σ Σ
[αjk(PjPk+QjQk)+βjk(QjPk-PjQk)].
J=1 k=1
Where Pj, Pk and Qj, Qk respectively, are real and reactive power injected at bus-j and αjk, βjk are the loss coefficients defined by
Where
Rjk
αjk = cos (δj-δk)
ViVk
Rjk
βjk = sin(δj-δk ).
ViVk
Where Rjk is the real part of the j-kth element of [Zbus] matrix. The total loss if a FACTS device, one at a time, is used, can be written as follows [12].
Pl k
= (Pl kc- [Pi (com) +Pj (com)].
More than one device used at time, can be expressed as
Nd
Pl k = ( Pl kc ─ Σ [Pi (com) +Pj (com)])
d=1
Where, Nd is number of device is to be
located at various lines.
III.Objective
Function:
The aim is that to
utilize the FACTS device for optimal amount of power in a system is to supply
without overloaded line and with an acceptable voltage level. The optimal
location of FACTS device problem is to increases as much as possible capacity
of the network.i.e loadability. In this work, the FACTS devices have been
considered to Economic saving function, which obtained by energy loss, it
requires calculation of total real power losses at the day and light load
levels.
Objective function is
Min F (u) is N
PL (V,d, S) = å PLt*Eloss*ΔT
-Cin]---(1)
i=1
Subject to
F
(b, v) =0
F1(s)
<M1,
F2 (v)
<M2.
Where, u- set of parameters that indicates the location, devices and rated values.
F (b, v): conventional power flow equations,
and ΔT –time duration.
Eloss is energy loss cost.
Cin is investment cost of FACTS
device.
F1(s) <M1, and F2
(v) <M2 are inequality constraints for FACTS devices, and
conventional power flows.
The
FACTS devices can be used to change the power system parameters. These
parameters derive different results on the objective function (1). Also various
FACTS device locations, rated value and types have also influences on the
objective function. The above-mentioned parameters are very difficult to
optimize simultaneously by conventional optimization methods. To solve this
type of combinatorial problem, the genetic algorithm is employed. The genetic
algorithms are well developed and utilized effectively for this work. The C
computer coding are developed and for simulated.
IV.Genetic Algorithm:
Heuristic methods may be used to solve
complex optimization problems. Thus, they are able to give a good solution of a
certain problem in a reasonable computation time, but they do not assure to
reach the global optimum [3,4,5]. In case of GAs (Genetic Algorithm) are global
search technique, based on the mechanisms of natural selection and genetics;
they can search several possible solutions simultaneously.
The GAs start with random generation of
initial population and than the selection, crossover and mutation are produced
until the best population is found.
Encoding:
The
main objective of the optimization is to find the best locations for the given
number of FACTS devices within the defined constrains. The configuration of
FACTS devices is obtained by three parameters: the location of the devices,
their types and their rated values. [4,5]. Each individuals is represented by nfacts
number of strings, i.e. number of FACTES devices to be used this
optimization problem. The first values of the each string indicate the location
information. Only one device in a transmission line, the second value of the
string is represent the type of the devices: TCSC for 1, TCPAR for 2, SVC for
3, UPFC for 4 and zero for no device is connected. The last value stands for
rated value of the each device. According to the model of the FACTS devices,
the rated values (RV) of each FACTS device is converted into the real
compensation as follows:
TCSC: The TCSC has a working rang
between -0.8 Xij and 0.2 Xij, where Xij is the
reactance of the transmission line, where the TCSC installed.
Xtcsc
= RV ´ 0.45 -0.25.
TCPAR: The working range of the TCPAR
is between the -5 degrees to +5 degrees.
jtcpar =RV ´5(degree).
SVC: The working range of the SVC is
between -100Mvar and +100Mvar. The SVC has been
considered as a reactive power sources with the above limit.
Vsvc=
RV ´ 100 (Mvar).
UPFC: The working range of the UPFC is between -180 degrees to +180 degrees.
jupfc = RV ´ 180(degree).
Investment cost:
The
different FACTS devices cost function are developed by the based on the Siemens
AG Database [15]. The cost function of SVC, TCSC and UPFC are related to
operating ranges but, incase of TCPAR is depends on the operating voltage and
current of the circuits, it is fixed, where it is located, the cost function
can expressed as
Cin= Tlimit +
installation cost, where Tlimit is thermal limit of the line.
The
cost function for SVC, TCSC and UPFC is:
Cinsvc=0.0003S2–0.3051S+127.38(US$/Kvar).
Cintcsc =0.0015S2
–0.7130S+153.75(US$/Kvar).
Cinupfc =0.0003S2
–0.2691S+188.22(US$/Kvar).
Where
S is the operating rating of the FACTS devices in Mvar.and Cinsvc, Cintcsc,
are in US$/Kvar.
Fig 2: investment cost curve.
Initial
population:
The initial population is generated from the
following parameters [4,5]:NFACTS is the number of FACTS devices to
be located, the possible location of the devices i.e. Nlocation,
types of the devices i.e. Ntypes, and Nind is the number
of individuals of the population. The first, a set of NFACTS numbers
of strings are produced. For each string, the first value is randomly chosen
from the possible locations Nlocation .The second value, which
represented the types of FACTS devices, is obtained by randomly drawing numbers
among the selected devices. The third value of each string, which contains the
rated values of the FACTS devices, is randomly selected between the -1 and +1.
To obtain the entire initial population, the above operations are repeated Nind
times.
The objective function is computed for every
individuals of the population. In our case, the objective function is defined
in order to quantify the impact of the FACTS devices on the state of the power
system network. The inverse of the objective function is used to compute the
fitness value of each individual in the population.
Fitness
= 1/ Objective function+1.
Reproduction:
The biased roulette wheel selection [3,4,5]
is used in this paper for reproduction, According to their fitness values; the
individual is selected to move to a new generation.
Crossover:
Crossover is technique, which is used to
rearrange the information between the two different individuals and produce new
one. In this paper a two-point crossover is employed and the probability (Pc)
of the crossover is 0.75.
Mutation:
The probability of mutation is less than
0.05. Mutation is used to random alteration of bits of string position. The bit
will be changed from ±0.5. The above process summarized
given below in the flowchart.
SIMULATION TOOL:
Power
flows are solved with help of AU Power software package. Simulation was carried
out on IEEE 30 Bus test system, it consists of 30 Bus, 41 lines, generator are
modeled as PV-node, loads are modeled as PQ- node, the line is modeled using
the classical- Õ scheme.
V. SIMULATION RESULTS:
The modified IEEE 30 bus
test system as shown in fig 4 is used to verify the effectiveness of the
proposed algorithm. Whose line and load data can be found in [14]. In this
paper, the FACTS device location considered Economic
saving function, which obtained by energy loss reduction. The different
operating conditions are simulated for the optimal location of FACTS devices
problem; reducing the transmission real power loss changes the transmission
line capacity. In case of single device optimization: the simulation results
are (shown in Table1) TCSC and SVC provide relatively less additional reduction
in total active power loss while TCPAR provides 7% more reduction, and it
significantly reduces the total real power loss in MW and increase the revenue
saving per day as shown in table 4. The FACTS device not only reduces the real
power loss but also improves the loadability, stability of the system and
improves the voltage. The Table2 shows the results of voltage increases due to
location of FACTS devices in a network. Fig
3 shows the number of devices required to reduce the total real power loss of
the system. From the results declared that, the UPFC effectively reduces the
losses up to 89-90% of the total loss, and incase of, TCSC, TCPAR, and SVC
reduces the losses up to 75%, 70-73% and 55% of total power loss reduction
respectively. Less number of devices used is to obtain 89-90% of loss reduction
by UPFC, but for other cases the number of devices will be increased. From the
results it is clear that UPFC is the most powerful FACTS device while comparing
other devices. Since the initial investment cost of UPFC is very high. Other devices
like: TCSC, TCPAR, and SVC.
Table 1: energy
loss cost.
|
Load levels |
Cost [$/KWh] |
|
Day load |
0.60 |
|
Light load |
0.44 |
Fig: 3 Number of devices required for
power loss reduction.
Table
2:economic saving cost.
|
Device |
Economic saving/day. (Day load) |
Economic saving/day. (Light load) |
|
1.TCSC |
$0.3368 |
$0.3105 |
|
2.SVC |
$0.3204 |
$0.2818 |
|
3.TCPAR |
$0.5181 |
$0.4843 |
|
4.UPFC,Vt=0.03. |
$0.5323 |
$0.4891 |
Table 3: shows the voltage difference after and before location of FACTS devices
Before After
|
Bus 1 |
1.060 |
Bus1 |
1.060 |
|
Bus25 |
0.94866 |
Bus25 |
0.98866 |
|
Bus26 Bus29 |
0.92965 0.92991 |
Bus26 Bus29 |
0.949645 0.9301 |
|
Bus30 |
0.91747 |
Bus30 |
0.91747 |
VI.CONCLUSION:
In this paper, the proposed algorithm is to
determine the location of given number of FACTS devices in a power system;
their type and rated value are simultaneously optimized. Four different type
of device are simulated: TCSC, TCPAR, SVC and UPFC. The overall system real
power loss reduction, significantly improves the system performance. The simulation
results certify that, the efficiency of the proposed algorithm, also simultaneously
optimize the location, type and rated value of the device. This algorithm
is suitable to search several possible solutions simultaneously. Further,
this algorithm is practical and easy to be implemented into the power system.
Fig 4:IEEE 30 bus system.
Table 4:shows
the simulation results.
|
From line |
To line |
Type of the device |
Rated value |
Total Power loss |
%Power loss reduction. |
|
2 |
5 |
TCSC |
-18%Xline |
0.3268 |
14.32%` |
|
24 |
25 |
SVC |
9.8Mvar |
0.3268 |
13.62% |
|
9 |
6 |
TCPAR |
3°(degree) |
0.3268 |
22.02% |
References:
[1] I.O.Elgrd, “Electric Energy System
Theory-An Introduction”, McGraw Hill Inc.,
[2] G.H. Hingorani, “flexible AC transmission
system”, IEEE spectrum, Apr 1993.
[3]. D.E, Goldberg,
Genetic Algorithms in Search Optimization and Machine Learning: Addison-Wesley Publishing
Company, Inc., 1989.
[4] S.Gerbex,R.cherkaoui, and A.J.Germond,
“Optimal location of multi-type FACTS devices in a power system by means of
genetic algorithm.”IEEE trans.power system, vol.16, pp.537-544, August 2001.
[5] L. J. Cai and I. Erlich, “Optimal choice
and allocation of FACTS devices using genetic algorithms”IEEE Trans, Power
system pp,1-6,
[6] T.S.Chung,
and Y.Z.Li, “A hybrid GA approach for OPF with consideration of FACTS
devices,”IEEE power engineering Review, pp.47-57, February, 2001.
[7] F. D. Galiana, K. Almeida, M. Doussaint,
J. Grffin and D. Atanackovic,
“Assesment and control of the impact of FACTS devices on power
system performance, IEEE trans. Power
system, Vol 11 no 4, 1996.
[8] K. S. Verma, S. N. Singh and H. O. Gupda,
“Location of unified power flow
controller for congestion management”, Electric power system research
Vol 58, PP 89-96, 2001.
[9] T.T.Lie and W. Deng,”Optimal flexible AC transmission systems
(FACTS) devices allocations”,
Electrical power and energy system, Vol 19, PP 125-134, 1997.
[10] D.J.Gotham and G.T.Heydt, “Power flow
control and Power flow studies for system with FACTS devices,”IEEE trans,Power
System,vol.13,no.1,feb,1998.
[11] Preecha Preedavichit and S.C.Srivastava,
“Optimal reactive Power dispatch Considering FACTS devices”, Electrical power
research vol, 48, pp, 251-257, 1995.
[12] S. N. Singh and A. K. David, “Congestion
management by optimizing FACTS
device location”, Electric Power System Research vol, 58.pp, 71-79.
2001.
[13] H.C.Leung and T.S.chung Optimal power flow
with a versatile FACTS controller by Genetic algorithm approach.proceeding of
the 5th international conference on advances in power system
control,operation and management,APSCOM 2000 october,pp.178-183.
[14] The 1996 version of the Reliability Test System was published in Grigg, C., "The IEEE reliability test system: 1996", Paper 96 WM 326-9 PWRS, IEEE Winter power meeting 1996.
[15] K.Habur and D.Oleary,FACTS-flexible AC transmission system for cost effective and reliable transmission of electrical eergy,”http://www.siemenstd.com/transSys/pdf/costEffectiveReliabTrans.pdf.
[16] J.Baskaran, V.Palanisamy,”Optimal
location of FACTS device in a power system network considering power loss using
genetic algorithm” EE-Pub on line journal, march 7,2005.www.ee-pub.com.
VII.BIOGRAPHIES.
J.Baskaran received the B.E
(Electrical and Electronics)& M.E (Power System) in 1997and 2001,
respectively. He is now a PhD candidate at Government College of Engineering in
Dr.V.Palanisamy received the B.E
(Electronic and communication), M.E (Communication Engineering) and PhD Communication
Engineering in 1972,1974 and 1987 respectively. Since 1974,he has been the
faculty of Electronics and Communication Engineering and Served at various
Government engineering colleges. At present, he is the principal at
