Journal of Power and Energy Engineering, 2014, 2, 639-646
Published Online April 2014 in SciRes.
How to cite this paper: Ravi, K., Shilaja, C., Babu, B.C. and Kothari, D.P. (2014) Solving Optimal Power Flow Using Modified
Bacterial Foraging Algorithm Considering FACTS Devices. Journal of Power and Energy Engineering, 2, 639-646.
Solving Optimal Power Flow Using Modified
Bacterial Foraging Algorithm Considering
FACTS Devices
K. Ravi1, C. Shilaja1, B. Chitti Babu2, D. P. Kothari3
1School of Electrical Engineering, VIT University, Vellore, India
2NIT, Rourkela, India
3Former IIT Director, Delhi, India
Received February 2014
In this paper, a new Modified Bacterial Foraging Algorithm (MBFA) method is developed to incor-
porate FACTS devices in optimal power flow (OPF) problem. This method can provide an enhanced
economic solution with the use of controllable FACTS devices. Two types of FACTS devices, thyris-
tor controlled series compensators (TCSC) and Static VAR Compensator (SVC) are considered in
this method. The basic bacterial foraging algorithm (BFA) is an evolutionary optimization tech-
nique inspired by the foraging behavior of the E. coli bacteria. The strategy of the OPF problem is
decomposed in two sub-problems, the first sub-problem related to active power planning to mi-
nimize the fuel cost function, and the second sub-problem designed to make corrections to the
voltage deviation and reactive power violation based in an efficient reactive power planning of
multi Static VAR Compensator (SVC). The specified power flow control constraints due to the use
of FACTS devices are included in the OPF problem. The proposed method decomposes the solution
of such modified OPF problem into two sub problemsiteration. The first sub problem is a power
flow control problem and the second sub problem is a modified Bacterial foraging algorithm
(MBFA) OPF problem. The two sub problems are solved iteratively until convergence. Case studies
are presented to show the effectiveness of the proposed method.
Flexible AC Transmission System (FACTS); Modified Bacterial Foraging Algorithm (MBFA);
Optimal Power Flow (OPF); TCSC; SVC
1. Introduction
The solution of an OPF problem determines the optimal settings for control variables in a power network ob-
serving various constraints. In the last 30 yearsdevelopment, many different solution approaches have been
proposed to solve the OPF problems [1]. Recent developments in power electronics have opened a new world in
power systems control. Several control devices are being developed under this new concept, known as FACTS
K. Ravi et al.
(Flexible AC Transmission System) [2]. These FACTS devices can make the power systems operating in a more
flexible, more secure and economic way. However, these FACTS devices also make the power system operating
in a more complicated way. In [3], the Benders decomposition method was first proposed to solve the optimal
active power flow dispatch problem incorporating FACTS devices. This method can deal with the representation
of series compensators and phase shifters, but this method did not consider the specified line flow constraints. In
[4], a method for solving the power flow control problem incorporating FACTS devices was proposed based on
decomposition. However, this method did not combine tilt OPF problem with the power flow control problem,
hence the solution probably may not be the overall optimal solution. In [5] author presented the solution of op-
timal power flow using linear programming method for power system network security application. Gotham
and Heydt [6] have presented the modeling of FACTS devices for power flow studies and the role of that mod-
eling in the study of FACTS devices. The presence of discrete control variables, such as switch able shunt de-
vices, transformer tap positions, and phase shifters, further complicates the problem solution [7,8]. The global
optimization techniques known as genetic algorithms (GA) [9], simulated annealing (SA), tabu search (TS) [10],
evolutionary programming (EP), improved particle swarm optimization (IPSO) [11], a novel crazy swarm optimi-
zation (NCSO) [12] and a hybrid genetic algorithm approach based on differential evolution (IGA-DE) [6], in [13]
the authors proposed a simple genetic algorithm fuzzy system and evolutionary programming applied to the OPF
problem in large-scale power systems. Author in [14] presents a particle swarm optimization (PSO) to solve the
economic dispatch with consideration of many nonlinear characteristics of the generator, such as ramp rate limits,
prohibited operating zones, and non smooth cost functions. In [15] authors present a novel string structure for
solving the economic dispatch through genetic algorithm (GA) with consideration of practical generators con-
straints. In [16] authors proposed optimal power dispatch for large scale power system using stochastic search al-
gorithms. To accelerate the search process authors in [10] proposed a multiple tabu search algorithm. To overcome
the drawbacks of the conventional methods related to the form of the cost function, and to reduce the computa-
tional time related to the large space search required by GA, this paper presents a modified BFA for the solution
of large-scale OPF with practical generators constraints and with consideration shunt FACTS devices.
This paper is organized as follows: Modeling of FACTS device is given in Section 2; Problem Formulation is
given in Section 3. Modified Bacterial Foraging algorithm for proposed method is given in Section 4. Results
and discussion are given in Section 5, the conclusion is drawn in Section 6 and references are given in Section 7
2. Modeling of Fact Device
2.1. Thyristor Controlled Series Compensator (TCSC)
When the DC network model is used, the model of the transmission line with TCSC is shown in s. The total
susceptance of the transmission line can be formulated as:
( )
ijij i
= −
Which is directly used as the control variable to be implemented in the bus susceptance matrices (Figure 1).
The power flow equations of the branch can be formulated as follows:
ijij ij
2.2. Static VAR Compensator (SVC)
The steady-state proposed model is used to incorporate the SVC on power flow problems. This model is based
on representing the controller as a variable impedance, assuming an SVC configuration with a fixed capacitor
(FC) and Thyristor-controlled reactor (TCR) as depicted in Figure 2. Applying simultaneously a gate pulse to
Figure 1. Equivalent circuit of TCSC.
K. Ravi et al.
Figure 2. SVC steady state circuit representation.
all thyristor of a thyristor valve brings the valve into conduction. The valve will block approximately at the zero
crossing of the ac current, in the absence of firing signals. Thus, the controlling element is the Thyristor valve.
The thyristors are fired symmetrically, in an angle control range of 90 - 180 with respect to the capacitor (in-
ductor) voltage.
ref sl
VV X= +
Xsl are in the range of 0.02 - 0.05 p.u. with respect to the SVC base. The slope is needed to avoid hitting limits.
At the voltage limits the SVC is transformed into a fixed reactance. The total equivalent impedance Xe of SVC
may be represented by
sin 22(21/)
eC x
XX k
α απ
=−+ −
x CL
k XX
3. Problem Formulation
In this paper, as our attention is focused on the optimal active power flow problem, the liberalized (DC) power
flow model is used. When the n 1 security constraints were considered, the OPF problem can be formulated as
To minimize CP,
P PP≤≤
(0)F FF≤≤
whe r e ,
C: is the generation cost vector
P: is the vector of active bus generation
s': is the transpose of bus-branch incidence matrix
: is the diagonal matrix of circuit susceptance
: is the vector of angle across branch
F (0) is the vector of base state active power flour in lines
F (/) is the vector of active power flow in lines when branch I is break out
: Is the active power loss in the system
L: is the vector of active bus loads
F and
is the circuit flow limits
P and
are the generation limits
This conventional optimization problem can be solved by the LP-based algorithm efficiently [5,17]. Next, two
additional control variables and a set of power flow control equality constraints will be introduced into this op-
K. Ravi et al.
Because the FACTS devices parameters can be controlled in very small steps, the new additional control va-
riables can be seen as continuous and limited by lower and upper bounds. The modified optimal active power
flow problem can be formulated as follows:
0F S
( )
sp c
W cs
= +Ψ
P PP≤≤
(0)F FF≤≤
()F FFl≤≤
whe r e ,
is the diagonal matrix of controlled line susceptance and sc is the bus-branch incidence matrix re-
lated to controlled line. While
is the vector of controlled line phase shifter angle and
is a vector of
specified line flows.
is the vector of bus generation including the compensation injection power of phase
shifter. It can be seen that this OPF problem is no longer a linear optimization problem due to the new control
and the specified power flow equality constraints. Thus, it is not possible to use conventional LP
technique [5,17] directly, and it becomes necessary to develop a new method to solve this optimization problem.
4. The Proposed Mbfa
4.1. Bacterial Foraging Algorithm
BFA is an optimization technique motivated by the foraging behavior of the E coli. Bacteria. The biological as-
pects of the bacterial foraging strategies and their motile behavior as well as their decision making mechanisms
can be found in [9]. BFA is designed to solve non-gradient optimization problems and to handle complex and
non-differentiable objective functions. Searching the hyperspace is performed through three main operations,
namely; chemotaxis, reproduction and elimination dispersal activities [18]. The chemotaxis process is performed
through swimming and tumbling. The bacterium spends its life alternating between these two modes of motion.
In the BFA, a tumble is represented by a unit length in a random direction, Ф(j), which specifies the direction of
movement after a tumble. The size of the step taken in the random direction is represented by the constant
run-length unit, C(i). For a population of bacteria, the location of the ith bacterium at the jth chemotactic step, kth
reproduction step and lth elimination/dispersal event is represented by
(, ,).
At this location the cost function is denoted by
( 1,,)(,,)(,)()
jkljkl Cijj
θθ φ
+= +
(1,, )
j kl
the cost function J (i, j + 1, k, l) better (lower) than J(i ,j k, l), another step of size C(i, j)
in the same direction is taken. This swimming operation is repeated as long as a lower cost is obtained until a
maximum preset number of steps, Ns, is reached. The cost function of each bacterium in the population is af-
fected by a kind of swarming that is performed by the cell-to-cell signaling released by the bacteria groups to
form swarm patterns. This swarming is expressed as follows:
( )
11 1
exp( )
ss P
ii i
attract attractm
ii m
repellent repellentm
JPjkljj kld
θθθωθ θ
ω θθ
∞∞ ∞
= ==
= =
==−− −
=−− −
∑∑ ∑
where dattract,
attract, hrepellant and
repellant are coefficients that represent the characteristics of the
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attractant and repellant signals released by the cell and
is the mth component of ith bacterium position
(, ,)
P jkl
is the position of each member of the population of the S bacteria and defined as:
{ }
(,, )(,, )1,2,......,
P jkljkliS
= =
where S is the size of the bacteria population. The function (9) which represents the cell-to-cell signaling effect
is added to the cost function
(,, ,)(,)
Ji jklJP
A reproduction process is performed after taking a maximum number of chemotactic steps, Nc. The popula-
tion is halved so that the least healthy half dies and each bacterium in the other healthiest one splits into two
bacteria which takes the same position.
After Nre reproduction steps an elimination/dispersal event takes place for Ned number of excisions. In this
operation each bacterium could be moved to explore other parts of the search space. The probability for each
bacterium to experience the elimination/dispersal event is determined by a predefined fraction Ped.
4.2. Modified Bacterial Foraging Algorithm
The unit step length of the basic BFA is constant which may guarantee good searching results for all optimiza-
tion problems. However, when applied to complex problems with high dimensionality it shows poor perfor-
mance. The run length parameter is the key factor for controlling the local and global search ability of the BFA.
From this perspective, balancing the exploration and exploitation of the search could be achieved by adjusting
the run-length unit. In this paper we propose a nonlinear decreasing dynamic function to perform the swim walk
instead of the constant step. This function is expressed as:
(, )()
( ,1)()
Ci jCN
Ci jNj
+= −
(15 )
where j is the chemotactic step and Nc is the maximum number of chemotactic steps while C(Nc) is a predefined
parameter. Control parameters of the MBFA are given in Table 1.
The algorithm of the proposed technique is as follows:
Step 1: Initialization of the following parameters:
p: Dimension of the search space
S: The number of bacteria in the population
Nc: Number of chemotactic steps
Ns: The length of a swim when it is on a gradient
Nre: The number of reproduction steps
Ned: The number of elimination-dispersal events
ped: The probability that each bacterium will be eliminated/dispersed
C(i, j)|j = 1: Initial run-length unit
C(Nc): The run-length unit at the end of the
Table 1. Control Parameter of the MBFA.
1 Number of bacteria’s 4
2 Maximum number of steps, Ns 4
3 Number of chemotactic steps, Nc 5
4 Number of reproduction steps, Nre 4
5 Number of eliminationdisperse steps, Ned 2
6 Probability, Ned 0.2
7 Size of the step, C(i) 0.1
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chemotactic steps (j = Nc).
: The initial random location of each bacterium
Step 2: Elimination/dispersal loop, l = l + 1
Step 3: Reproduction loop, k = k + 1
Step 4: Chemotaxis loop, j = j + 1
For i = 1, 2, …, S, execute the chemotactic step
for each bacterium as follows:
- Evaluate the cost function J(i, j, k, l) using (9) and (11).
- Let Jlast= J (i, j, k, l) so that a lower cost could be found.
- Tumble: generate a random vector
∆ ∈ℜ
( ),1,2,......,
mim p∆=
is a random number in the range [1, 1].
- Compute
() () ()
- Move using (8)
- Compute
( ,1,,)Jij kl+
and use (9) to Compute
,(1,, )JPj kl
then use (11) to find the new
( ,1,,)
Jij kl+
-Swim: let m=0 (counter for swim length)
While m< Ns (no climbing down too long)
Let m=m+1.
( ,1,,)
Jijkl J+<
( ,1,,)
JJij kl= +
then take another step in the same direction and compute
the new
( ,1,,)lost
Jij kl+
- Go to the next bacterium (i = i + 1 if i ≠ S).
- Update the run length unit using (15).
Step 5: If j < Nc go to step 4 (j = j + 1).
Step 6: Reproduction:
For the given k, l, evaluate the health of each bacterium i as follows:
(, , ,)
health j
health of the bacterium i measures how many nutrient it got over its lifetime.
Sort bacteria according to their health
in ascending order.
The bacteria with the highest
values, computed by (16) die while the other Sr with the lowest values
split and take the same location of their parents.
Step 7: if k < Nre, go to step 3 (k = k + 1)
Step 8: Elimination/ dispersal
With probability ped, randomly eliminate and dispersal each bacterium i, keeping the size of the population
const ant.
Step 9: if l < N, go to step 2 (l = l + 1), otherwise end
5. Simulation Results
The proposed algorithm is developed in the Matlab programming language using 7.5 versions. The proposed
MBFA is tested using modified IEEE 30-Bus system. The test example has been run on a 2.6-Ghz Pentium-IV PC.
Case Studies on the IEEE 30-Bus System
IEEE 30-Bus, 41-branch system is tested, for the voltage constraint the lower and upper limits are 0.9 p.u and
1.06 p.u., respectively, (expect for PV buses where Vmax = 1:1 p.u).
The efficiency of the proposed approach, we made a comparison of our algorithm with others competing OPF
algorithm. In [9 ], they presented a standard GA, in [19], the authors presented an enhanced GA, and then in [20],
they proposed an Ant colony optimization (ACO).
In [13] they presented an optimal power flow solution using GA-fuzzy system approach. In [21], they pre-
sented an efficient parallel GA (EPGA). The operating cost in our proposed approach is 800.1585 and the power
loss is 8.4625 which are better than other methods reported in the literature. Results in Table 2 show clearly that
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Table 2. Results of minimum cost and power generation with SGA, EGA, ACO, FGA and EPGA for IEEE
30 bus.
Variable SGA [9] EGA [19] ACO [20 ] FGA [13] E PGA [21] Proposed method (MBFA)
P1 (MW) 179.367 176.20 181.945 175.137 180.12 164.501
P2 (MW) 44. 24 4 8. 75 47.001 0 5 0. 353 44.18 3 2. 423
P5 (MW) 24. 61 2 1. 44 20.553 0 2 1. 451 19.64 2 1. 459
P8 (MW) 19. 90 2 1. 95 21.146 0 2 1. 176 20.96 1 1. 130
P11 (MW) 1 0. 71 12.42 1 0. 433 0 12.667 1 4. 90 2 3. 872
P13 (MW) 1 4. 09 12.02 1 2. 173 0 12.11 1 2. 72 3 8. 470
Q1 (MVAR) 3.156 - - 6.562 4.50 3.609
Q2 (MVAR) 42.543 - - 22.356 30.71 3 7. 423
Q5 (MVAR) 26. 292 - - 30.372 22.59 24.985
Q8 (MVAR) 22. 768 - - 18.89 3 7. 85 19.530
Q11 (MVAR) 29. 923 - - 21.737 2.52 15.821
Q13 (MVAR) 32. 346 - - 22.635 13.08 7.598
θ1 (deg) 0.000 - - 0.00 0.00 0.00
θ2 (deg) 3.674 - - 3.608 3.448 3.375
θ5 (deg) 1 0. 14 - - 10.509 9.858 9.596
θ8 (deg) 1 0. 00 - - 8.154 7.638 7.012
θ11 (deg) 8.851 - - 8.783 7.507 4.789
θ13 (deg) 10. 13 - - 10.228 9.102 4.584
Ploss (MW) 9 .5 177 9 .3 900 9.8520 9.494 9.120 8.4625
Cost ($/h) 803.699 802.06 802.578 802.00 03 801.34 45 800.15 85
the proposed approach gives better results and the best solution of shunt compensation obtained at the standard
load demand (Pd = 283.4 MW) using reactive power planning [18,22], line flows obtained are well under secu-
rity limits compared to other algorithm such as FGA, SGA, ACO and other algorithms.
First of all, the total real power loss of the system is calculated with shunt FACTS device and the result is
8.4625 MW. And to improve the performance of reactive power planning of the system shunt FACTS device in-
cluded at different locations. The power loss is optimized by the MBFA with the combination of improving the
bus voltage profile and generator reactive power
6. Conclusion
A modified bacterial foraging algorithm (MBFA) for solving large scale OPF Problem has been demonstrated in
this paper. Simulation results have demonstrated the effectiveness of the proposed algorithm and Comparison
with other computational methods has shown that the MBFA achieved better results. A new method to incorp o-
rating FACTS devised in OPF problem has been presented in this paper. The proposed method separates the
modified optimization problem into problems’ iteration. The power flow control problem while the sub problem
is a conventional OPF problem. The method incorporates the power flow control needs due to FACTS devices
into the OPF Problem, and the optimization results can satisfy the power flow control needs and the economic
operation at the same time. The case studies of an adapted IEEE 30-bus system have been presented to show the
efficiency of the proposed method.
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