2014 International Conference on Circuit, Power and Computing Technologies [ICCPCT]
Self-Adaptive Firefly Algorithm based Transmission Loss Minimization using Multi type FACTS Devices R. Selvarasu
M. Surya Kalavathi Professor, Department of EEE JNTUH, Hyderabad, India.
[email protected]
Research Scholar, Department of EEE, JNTUH, Hyderabad, India.
[email protected] Abstract-- Loss minimization is an important research issue in power system network. This can be minimized by reactive power compensation. Hence placements of multi type FACTS (Flexible AC Transmission System) devices have been suggested in this paper for optimal real and reactive power dispatch. Three different kinds of FACTS devices like Static Var Compensator (SVC), Thyristor Controlled Series Compensator (TCSC) and Unified Power Flow Controller (UPFC) are considered in this study. The placement of FACTS devices highly depends on its parameter and suitable location in the power system network. Thus a new Self Adaptive Firefly Algorithm is proposed to identify the type, optimal location and parameter of FACTS devices. This proposed strategy is tested on three IEEE test systems and their results are presented.
k max
Number of iterations
Ploss
Net transmission loss
nl l
Number of transmission lines Number of transmission of lines
Gl
Conductance of
Vi Vj
Voltage magnitudes at bus
N
m, n
j
δ ij
Voltage angle at bus i and
PGi
Real power generation at
QGi PDi QDi
Reactive power generation at
QG i
ith
generator
ith
generator
Real power drawn by the load at i bus Reactive power drawn by the load at bus i
min
NOMENCLATURE
BSVC nd
line
i and j respectively
Key words: Firefly Algorithm, Loss Minimization, SVC, TCSC, UPFC
FACTS SVC TCSC UPFC FA SAFA
l th
,
QG i
max
Minimum and maximum reactive power th
Flexible Alternating Current Transmission System Static Var Compensator Thyristor Controlled Series Compensator Unified Power Flow Controller Firefly Algorithm Self Adaptive Firefly Algorithm Susceptance of SVC
mth
Light intensity of the
α
γ
Absorption parameter Random movement factor
rm,n
Cartesian distance between
k
Number of iterations
γ TCSC
Line location of FACTS device VAR output Reactance of the transmission line Compensation factor of the TCSC I.
INTRODUCTION
Nowadays, the electrical energy demand is increasing continuously from time to time. To meet this situation, either construction of new generation facilities and transmission networks is required or the existing infrastructure of power system has to be improved. The construction of new generation system and laying of transmission lines involve huge installation cost, environment impact, political, large displacement of population and land acquisition. One of the
Attractiveness Parameter
978-1-4799-2395-3/14/$31.00 ©2014 IEEE
Type of FACTS device
QSVC X line
firefly
mth and nth
Tk Lk
Number of decision variables Maximum number of fireflies Number of fireflies
Im β m ,n
NF
generation of i generator respectively Number of FACTS devices
firefly
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2014 International Conference on Circuit, Power and Computing Technologies [ICCPCT]
achieving better convergence. Self Adaptive FA (SAFA) based strategies have been proposed to minimize the transmission loss through placing TCSCs [14] and UPFCs [15].
simplest way is to minimize the transmission loss rather than constructing new generation systems by providing optimal quantity of reactive power support at appropriate buses. The solid state converters based FACTS devices have been effectively used for flexible operation and control of the power system through controlling their parameters. They have the capability to control the various electrical parameters in transmission network in order to achieve better system performance. FACTS devices can be divided into shunt connected, series connected and a combination of both [1-2]. The Static Var Compensator (SVC) and Static Synchronous Compensator (STATCOM) belong to the shunt connected device and are in use for a long time. Consequently, they are variable shunt reactors, which inject or absorb reactive power in order to control the voltage at a given bus. [3]. Thyristor Controlled Series Compensator (TCSC) and Static Synchronous Series Compensator (SSSC) are series connected devices for controlling the real power in a line by varying the line reactance. They are in operation at a few places but are still in the stage of development [4]. Unified Power Flow Controller (UPFC) belongs to combination of shunt and series devices and is able to control real power, reactive power and voltage magnitude simultaneously or separately [5]. These devices can facilitate the control of power flow, increase the power transfer capability, reduce the generation cost, improve the security and enhance the stability of the power systems.
In this paper, a SAFA based strategy is proposed for multi type FACTS placement with a view of minimizing transmission loss besides maintaining the voltage magnitude of all the buses within the lower and upper bounds. The strategy identifies the optimal locations, the type of FACTS devices and their parameters. Simulations are performed on three IEEE test systems using MATLAB software package and the results are presented to demonstrate the effectiveness of the proposed approach. II.
FACTS DEVICES MODELLING
The real and reactive power transmitted by a line
l from bus i to j may be approximated by the following relationships.
Pi j =
Qi j =
In recent years, the FACTS devices attracts the system engineers and researchers for providing better adaptation to varying operational conditions and improve the usage of existing installations. The placement of FACTS devices can be described as an optimization problem with an objective of minimizing the network loss.
VV i j X ij
sin δ i j
1 (Vi 2 − Vi Vjcos δ i j ) X ij
(1)
(2)
The voltages at any two buses are approximately same at the high voltage transmission lines under normal operating conditions. Also the voltage angle differences between any two buses are very small. Real power flow depends on voltage angle difference and reactive power flow depends on voltage magnitude difference. Though, both of them can be controlled by varying the line reactance.
Several nature inspired meta-heuristic algorithms such as Genetic Algorithm (GA), Simulated Annealing (SA), Ant Colony Optimization (ACO), Bees Algorithms (BA), Differential Evolution (DE), and Particle Swarm Optimization (PSO) and Bacterial foraging optimization algorithm etc [6][10] have been applied in solving the FACTS placement problems. GA has been proposed to identify the optimal location of multi type FACTS devices in a power system to improve the loadability [7]. PSO has been applied to find the optimal location of FACTS devices considering cost of installation and system loadability. [8]. Bees Algorithm has been proposed to determine the optimal allocation of FACTS devices for maximizing the available transfer capability [9]. Bacterial Foraging algorithm has been proposed for loss minimization and voltage stability improvement [10]
Three different types of FACTS devices have been chosen for the optimal placement. The first one is shunt connected SVC, which injects or absorbs reactive power in order to control or maintain bus voltage. Reactive power drawn by SVC, which is also reactive power injected at bus i, is (3) Qsvc = Qi = −Vi 2 Bsvc Second one is the series connected TCSC, which acts either as a capacitive or inductive compensator respectively to decrease or increase the reactance of the line there by changes line flow. The net reactance X ij of the transmission line connected between the buses i to j , after placement of TCSC can be written as. (4) X ij = X line + X TCSC
Firefly Algorithm (FA), a nature-inspired metaheuristic algorithm, has been suggested for solving optimization problems and widely applied for solving real world optimization problems, such as economic dispatch [1112] and unit commitment [13] etc. However, the improper choice of FA parameters affects the convergence and may lead to sub-optimal solutions. There is thus a need for developing better strategies for optimally selecting the FA parameters with a view of obtaining the global best solution besides
X TCSC = γ TCSC X line
(5)
Finally, the UPFC consists of two controllers. The shunt controller injects or absorbs reactive power and the series controller injects the voltage that alters the line
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2014 International Conference on Circuit, Power and Computing Technologies [ICCPCT]
reactance, thereby control the real power flow. This device may be modeled for convenience as a combination of SVC and TCSC through Equations (3) and (4).
The value of
β max
is taken as 1.
nth firefly is larger than the intensity of the mth firefly, th th then the m firefly moves towards the n firefly and its th iteration is denoted by the following motion at the k
FA is a recent nature inspired meta-heuristic algorithms which has been developed by Xin She Yang at Cambridge University in 2007 [6]. The algorithm mimics the flashing behavior of fireflies. The total number of fireflies in the swarm is known as the population size, N . The population size selection depends on the specific optimization problem. The population size of 20 to 50 has been used for PSO and FA in many applications [8, 11]. th
Each m firefly is denoted by a vector
equation:
xm(k) = xm(k−1) + βm,n ( xn (k−1) − xm(k−1)) +α ( rand − 0.5) (12)
The random movement factor α is a constant whose value depends on the dynamic range of the solution space. At each iterative step, the intensity and the attractiveness of each firefly is calculated. The intensity of each firefly is compared with all other fireflies and the positions of the fireflies are updated using Equation (12). After an adequate number of iterations, each firefly converges to the same position in the search space and the global optimum is achieved.
xm as
xm = ⎡⎣ x1m , xm2 " , xmnd ⎤⎦
(6)
The search space is limited by the following inequality Constraints
B.
Self Adaptive Firefly Algorithm
v
x (min) ≤ x ≤ x (max) v = 1, 2," , nd (7)
In FA, each firefly of the swarm travel around the problem space taking into account the results obtained by others and still applying its own randomized moves as well. Performance of the FA can be improved by tuning three parameters. The random movement factor α is very effective on the performance of FA whose value is commonly chosen in the range 0 and 1. A large value of α makes the movement to explore the solution through the distance search space and smaller value of α tends to facilitate local search.
The positions of the fireflies are generated initially from a uniform distribution using the following equation
xmv = x v (min) + ( x v (max) − x v ( min) ) × rand
(8)
In the above “Equation (8)”, rand is a random number with the values between 0 and 1, taken from a uniform distribution. The primary distribution does not significantly affect the performance of the algorithm. Every time the algorithm is executed and the optimization process starts with a different set of initial points. However, in each case, the algorithm searches for the optimum solution. In the case of multiple possible sets of solutions, the proposed algorithm may converge on different solutions each time. Although each of those solutions will be valid as they all will satisfy the requirement. th
The influence of other solutions is controlled by the value of attractiveness of Equation (10), which can be adjusted by modifying two parameters β max and γ . In general the value of
I m = Fitness ( xm ) th
The attractiveness between the m is given by
and n
variation of attractiveness with increasing distance from communicated firefly. In general γ is chosen in the range of 0 to 10. Indeed, the choice of these parameters affects the final solution and the convergence of the algorithm. In this paper, the parameters α , β max and γ are tuned through a self –
firefly,
β m,n = ( β max,m, n − β min,m,n ) exp(−γ m rm,n 2 ) + β min,m ,n (10)
adaptive mechanism.
Where
rm,n = xm − xn =
is chosen in the range of 0 to 1 and two limiting cases
= 1 and only non-cooperative distributed random search with β max = 0. On the other hand, the value of γ determines the
(9) th
β max
can be defined: The algorithm performs cooperative local search with the brightest firefly strongly determining other fireflies positions, especially in its neighborhood, when β max
I m is given by
The light intensity of the m firefly,
β m ,n
another constant whose value is
of
A. Classical Firefly Algorithm
v
is taken as 0.2 and the value of
related to the dynamic range of the search space. The position of firefly is updated in each iterative step. If the light intensity
III. FIREFLY ALGORITHM
v
β min γ is
nd
∑( x v =1
k m
k n
−x
)
2
Each firefly for a problem with nd control variables will be defined to encompass nd +3 FA variables in the proposed formulation. The additional three variables represent α m , β min,m and γ m . A firefly is represented as
(11)
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2014 International Conference on Circuit, Power and Computing Technologies [ICCPCT]
xm = ⎡⎣ x1m , xm2 " , xmnd , α m , β min,m , γ m ⎤⎦ Each firefly possessing the solution vector,
the starting end of the chosen transmission line. The third and fourth variables QSVC , and γ TCSC correspond to injected
(13)
αm ,
reactive power and line compensation factor respectively. The parameter which is not required for a particular type of device is ignored. The last three variables represent FA parameters. The problem variables contain both integer value for representing Tk and Lk and real values to denote QSVC , ,
β min,m and γ m undergo the whole search process. During iterations, the FA produces better off-springs through Equations (10) and (12) using the parameters available in the firefly of Equation (13), thereby enhancing the convergence of the algorithm.
γ TCSC , α m , β min,m
IV. PROPOSED STRATEGY
Objective function
The objective is to minimize transmission loss, which can be evaluated from the power flow solution, and written as follows: Min Ploss =
nl
∑ G (V l
2
i
+ V j − 2VV i j cos δ ij ) 2
γm
T1
T2
...
TNF
L1
L2
...
LNF
QSVC ,1
QSVC ,2
...
QSVC , NF
γ TCSC ,1
γ TCSC ,2
...
γ TCSC , NF
αm
(14)
β min,m
l =1
B.
γm
Equality Constraints
Fig.1. Representation of SAFA variables
The equality constraints are the load flow equation given by
E.
PGi − PDi = Pi (V , δ ) for PV and PQ buses (15) QGi − QDi = Qi (V , δ ) for PQ buses C.
Light Intensity Function
The SAFA searches for optimal solution by maximizing the light intensity I m , which is like the fitness
(16)
Inequality Constraints
function in any other stochastic optimization techniques. The light intensity function can be obtained by transforming the power loss function into I m function as
Reactive Power generation limit
QG i min ≤ QG i ≤ QG i max for PV buses (17)
Max I m =
FACTS device Constraints
−100MVAR ≤ QSVC ≤ 100MVAR for SVC (18)
1 1 + Ploss
(20)
A population of fireflies is randomly generated and the intensity of each firefly is calculated using Equation (20). Based on the light intensity, each firefly is moved to the optimal solution through Equation (12) and the iterative process continues till the algorithm converges.
−0.8Xline ≤ γ TCSC Xline ≤ 0.2 Xline p.u for TCSC (19) Equations (18) and (19) for UPFC D. Representation of SAFA variables
V. SIMULATION RESULTS AND DISCUSSIONS The effectiveness of the proposed SAFA for optimally placing the FACTS devices to minimize the transmission loss has been tested on IEEE-14, -30 and -57 bus test systems using MATLAB 7.5. The line data and bus data for the three test systems are taken from [16]. The limits for the control and dependant variables and the chosen range for self adaptive parameters are given in Table I. The population size, N for all the test systems is taken as 30 and the number of iterations, Kmax, is considered as 200.
The FA variables that denote the type of the devices, their locations and parameters in vector form as shown in Fig.1. In this figure, the first variable Tk represents the type of k − th FACTS device. Integer numbers 1, 2 and 3 are used to represent SVC, TCSC and UPFC respectively. The corresponds to the location of the second variable Lk FACTS devices. It represents the number of the line
but the SAFA algorithm deals
with real numbers. Therefore, the values that correspond to first two variables are rounded off to the nearest integer values.
The problem is to place the appropriate FACTS devices with optimal device parameters at the best possible locations through an objective of minimizing the transmission loss for better utilization of the existing power system. This paper aims to develop a SAFA based methodology that performs FACTS device placement. A.
and
Lk
where the device is to be located. The devices are connected at
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2014 International Conference on Circuit, Power and Computing Technologies [ICCPCT]
TABLE 1.CONTROL VARIABLES Minimum Maximum
QSVC (MVAR)
-100
100
γ TCSC α β γ
-0.8
0.2
0
0.5
0.2
1
0
1
Self Adaptive Parameters
V. CONCLUSION This paper made an attempt to identify the optimal
Simulations are carried out with different number of FACTS devices for all the three systems and the resulting loss is presented in Table II. It is seen from this table that the real power loss is considerably reduced from 13.3663 MW to 13.2163 MW, when three FACTS devices are connected for IEEE 14 bus system. If the number of FACTS devices is further increased by one, loss is reduced to 13.2136 MW, which is insignificant. Hence the number of FACTS devices for the present study is therefore chosen as 3 for IEEE 14 bus systems. Similarly for IEEE 30 and IEEE 57 bus systems it is selected as 5 and 6 respectively. Variation of real power loss for IEEE 14, IEEE30 and IEEE57 bus system has shown in Figs. 2, 3 and 4 respectively.
Fig.3. Variation of Real Power Loss for IEEE 30 Bus System
TABLE II. REAL POWER LOSS WITH NUMBER OF FACTS DEVICES System IEEE 14 Bus
IEEE 30 Bus
IEEE 57 Bus
No of FACTS Devices 0 3 4 0 3 4 5 6 0 4 5 6 7
Real power Loss
Fig.4. Variation of Real Power Loss for IEEE 57 Bus System TABLE III TYPE OF FACTS DEVICES, OPTIMAL LOCATION AND PARAMETER OBTAINED IN SIMULATION
13.3663 13.2163 13.2136 17.5028 17.2541 17.1542 17.1196 17.2510 27.2233 25.3548 25.2428 25.2138 25.3407
System
No of FACTS Devices
IEEE 14 Bus
3
IEEE 30 Bus
5
IEEE 57 Bus
6
Type 3 2 3 3 2 3 1 1 3 3 1 2 1 2
Line Location 20 17 15 35 9 4 24 29 53 14 67 54 49 60
QSVC (MVAR) 7.474 29.628 5.448 22.056 6.743 16.645 42.267 31.435 38.407 13.186 -
γ TCSC 0.125 -0.800 -0.270 0.045 0.200 -0.570 -0.628 -0.068 -0.455 -0.133
The type of FACTS devices, location and their parameters are given in Table III. The proposed method requires one TCSC and two UPFC at line locations 17, 15 and 20 respectively for IEEE 14 bus system. For IEEE 30 bus system two SVC, one TCSC and two UPFC is required at line
Fig.2. Variation of Real Power Loss for IEEE 14 Bus System
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2014 International Conference on Circuit, Power and Computing Technologies [ICCPCT]
[9] R.Mohamid Idris, A.Khairuddin, M.W.Mustafa, “Optimal allocation of FACTS devices for ATC enhancement using Bees algorithm,” World Academy of science Engineering and Technology, no.30, pp.313-320, 2009. [10] M.Tripathy and S.Mishra, “Bacteria foraging based solution to optimize both real power loss and voltage stability limit,”IEEE Trans. on Power Syst., vol.22, no 1, pp.240-248, 2007. [11] Taher Niknam, Rasoul Azizipanah-Abarghooee, and Alireza Roosta, “Reserve Constrained Dynamic Economic Dispatch: A New Fast Self-Adaptive Modified Firefly Algorithm”, IEEE System Journal, vol.6, no 4, pp.635-646, 2012. [12] X.S. Yang, S.S. Hosseini, and A.H. Gandomi, “Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect,” Applied Soft Computing, vol. 12, Issue 3, pp.180- 1186, Mar. 2012. [13] K Chandrasekaran, and S. P. Simon, “Network and reliability constrained unit commitment problem using binary real coded firefly algorithm,” International Journal of Electrical Power & Energy Systems, vol.43, no.1, pp. 921–932, Dec. 2012. [14] R Selvarasu and C Christober Asir Rajan, “Self Adaptive Firefly algorithm based transmission loss minimization using TCSC,” in proc. International Conference on Advanced Nonmaterial’s and Emerging Engineering Technologies, Jul.2013, pp.683-688. [15] R Selvarasu and M Surya Kalavathi, “Optimal placement of UPFC for voltage constrained loss minimization using self adaptive Firefly algorithm,” International Review of Electrical Engineering, vol.8, no.4, pp.1296-1301, Aug.2013. [16] Power Systems Test Case, The University of Washington Archive, [Online].Available: http://www.ee.washington.edu/research/pstca/
locations 24, 29, 9, 35 and 4 respectively. For IEEE 57 bus system two SVC, two TCSC and two UPFC is required at line locations 67, 49, 54, 60, 53 and 14 respectively It is very clear from the above discussions that the proposed SAFA based strategy is able to reduce to the loss to the lowest possible value than those of other strategies. In addition the self adaptive nature of the algorithm avoids repeated runs for fixing the optimal FA parameters through a trial and error procedure and provides the best possible parameters values. VI. CONCLUSION In this paper a new Self Adaptive Firefly Algorithm has been proposed to identify the most appropriate type of FACTS devices, their best possible locations and their optimal parameters with a view of minimizing the transmission loss. Simulations results in terms of the type, the locations, their parameters and the resulting loss have been presented for three IEEE test systems. It has been found that the proposed strategy is able to reduce the loss to the lowest possible value and suitable for practical applications to improve the performance of the power system. REFERENCES [1] N. G. Hingorani and I.Gyugyi,“Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems,”New York:IEEE Press,2000. [2] R.M.Mathur and R.K.Varma, “Thyristor-based FACTS controllers for e lectrical t ransmission systems,”Piscataway: IEEE Press,2002. [3] H.Ambriz-perez,E.Achaand,C.R.FuerteEsquivel.“Advanced SVC models for Newton Raphson load flow and Newton optimal power flow studies,” IEEE Trans. on Power Syst.,Vol.15.pp.129136,2000. [4] E.V.Larsen,K.Clark,S.A.Miske,Jr.,andJ.Urbanek,“Ch aracteristic and rating considerations of thyristor controlled series compensation,” IEEE Transaction Power Delivery.,vol.9,pp.992-1000,1994. [5] L.Gyugyi, “Unified power flow controler concept for flexible AC transmission system,”in IEE proceedings, vol.139,no.4.pp.323-331, July, 1992. [6] X. S. Yang, Nature-Inspired Meta-Heuristic Algorithms, 2nd ed., Beckington, Luniver Press,2010. [7] S.Gerbex, R.Cherkaom, and A.J.Germond, “Optimal location of multi type FACTS devices in a power systems by means of genetic algorithms,” IEEE Transaction on Power Systems.vol.16, no 3, pp.537544, 2001 [8] M. Saravanan, S. M. R. Slochanal, P. Venkatesh, and J. P. S. Abraham, “Application of particle swarm optimization technique for optimal location of FACTS devices considering cost of installation and system loadability,” Electrical Power System Research, vol.77, pp. 276-283, 2007.
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