Design of pss using bees colony intelligence

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976
– 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 5, July – August (2013), © IAEME
24
DESIGN OF PSS USING BEES COLONY INTELLIGENCE
R.sheeba a*
, Dr.M.Jayaraju a
, Dr. K. Sundareswaran b
a
Department of Electrical & Electronics engineering, T.K.M.college of Engineering, Kollam,
Kerala, India
b
Department of Electrical & Electronics engineering, National Institute of Technology,
Thiruchirapalli, India
ABSTRACT
This paper report the development of a new optimization technique based on the biological
behaviour of a colony of honey bees. The optimization method is prepared by closely imitating the
foraging pattern of bees. The development of the algorithm and their validation is well documented
in this work. The optimization scheme is then applied for a classical problem of design of Power
System Stabilizer (PSS). Simulation results are carried out to validate the proposed algorithm.
Key words— Optimization, Bees, Power System Stabilizer.
I. INTRODUCTION
The stable operations of a synchronous machine, its ability to maintain the quality of
electrical power delivered to the consumers and the economy in the generation cost with maximum
possible power transfer are some of the requirements to be considered in the design of electrical
power system. One of the effective means of achieving the above requirements is by providing an
efficient excitation controller for synchronous machine. The realization of power system stabilizer
(PSS) is based on the idea that the use of supplementary control signal in the excitation system of
the generating unit can provide extra damping for the system and thus improve the machine dynamic
performance [1]. This is the easy, economical and flexible way to improve power system stability.
Over the past few decades, many types of PSSs have been extensively studied and some of them
have been successfully used in the field.
The conventional PSS was based on a linear model of the power system at some operating
point and classic control theory was employed as the design tool [2]. With the increasing demand for
quality power, modern control techniques like optimal control theory [3] and high-gain control
theory [4] have been proposed for supplementary excitation controllers. Power systems are dynamic
systems and the operating point of the system will change with varying system load.
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN
ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 4, Issue 5, July – August 2013, pp. 24-34
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25
To improve the damping characteristics of a power system over wide operating points,
adaptive stabilizers or self-tuning controllers have been proposed [5-8]. In these controllers the
system model is first identified in real time using the measured system input and output variables.
The gain settings are then computed based on the model and the adaptation law. Even though better
dynamic response can be achieved by self-tuning controllers, the major hurdle is the need to identify
system model in real time, which is very time consuming.
Recently artificial neural networks (ANN) [9] and fuzzy logic principles [10] are applied for
the realization of adaptive PSS. It is shown that ANN based PSS can provide good damping of the
power system over a wide operating range and significantly improve the dynamic performance of the
power system. Fuzzy excitation controller also improves the dynamic response of the power system
at different operating points. In addition, fuzzy controller does not require model identification and
thus can be easily implemented on a microcomputer.
The contribution of this paper lies in the development of a new optimization algorithm
developed by the authors which closely mimic the behavior of honey bees [11]. Literature survey
shows that attempts have been made recently by the researchers to utilize the behavior of honey bees
for a few applications [12-18]. The foraging behavior of honey bees is also used for optimization
algorithms for various applications such as training of learning vector quantization networks [15],
job scheduling [16], optimizing neural networks [17] etc.
In this work, we have developed a algorithm which fundamentally imitate natural behavior of
a colony of honey bees in nectar collection and reproduction. The first proposal mimics the foraging
behavior of honey bees. The randomly generated worker bees are forced to move in the direction of
the elite bee, which locates the best possible solution. The movement is made based on a
probabilistic approach and the step distance of flight of bees is made as a variable parameter in the
algorithm [19-25].
The algorithm is used for the design of PSS for a single machine connected to infinite bus
system and the results are discussed. It is shown that the newly proposed scheme is derivative-free,
efficient in locating the global optima with reduced number of iterations, independent of initial
values, and are robust in their convergence characteristics.
II. BRIEF DESCRIPTION ABOUT THE BIOLOGY OF HONEY BEES [11]
The honey bees are believed to be originated in Tropical Africa and spread from South Africa
to Northern Europe and East in to India and China. A typical small hive contains approximately
20,000 bees and the bees in a hive are divided in to three different types: Queen, Drone and Worker.
The functions, sex, life span and physical size of these three categories are largely different. The sole
function of the queen is re-production; it is female, and can live up to two years. The queen is the
mother of all bees in the hive. The size of queen is larger with its abdomen noticeably longer than the
other bees. Drone is a male bee which survives about 21-32 days in spring or 90 days in summer.
Drones are medium in size and are designated for mating only. Drone’s eyes and antennae are
specially designed for seeing, following and mating with a queen. They can fly fast to catch up with
a queen. Queens and drones do not have effective body parts for harvesting honey or pollen for self
feeding. Worker bees are sterile females and they have numerous functions. Worker bees make
comb, clean and defend hive, gather honey and pollen, and tend queen and young drones. They are
small in size and survive up to 20-40 days in summer and 140 days in winter.
II. 1. Foraging behavior of honey bees
The foraging behavior of honey bees is quite interesting and it is found that bees are fairly
adept at effective communication of food sources. In the hive, the worker bees are responsible for
food collection. A few worker bees are sent to different random directions and a single bee visits
many different flowers in the morning. If there is sufficiently large food, the bee makes many transits

26
between the flowers and its hive. The floral findings are communicated to other worker bees in the
hive through a “dancing”. A bee which returns from an area which has many flowers producing
much honey/pollen performs a dance on the comb. The orientation of her movements together with
frequency of vibrations indicates the direction and distance of flowers from the hive. This dance
serves as an effective way of communication among worker bees. The other worker bees waiting in
the hive will observe this dance and will come to know the location and quantity of food source. All
the worker bees, who had found flowers, will perform dances; but majority of worker bees will
follow the “elite” bee- the bee which had located better and nearer food source than the remaining.
This mechanism helps the colony to gather food quickly and efficiently.
II. 2. Development of optimization algorithm based on foraging behavior
As can bee in the previous section, worker bees perform the task of food collection in an
optimized manner. This makes it possible to build an optimization algorithm. The bees can be placed
initially at random locations in the solution space; the bee at the “best” location- the location where
the objective function is minimum- can be treated as “elite” bee. In nature, majority of worker bees
follow the elite bee, while remaining bees fly to other less attractive locations. This can be perceived
as a probabilistic approach. Thus, it can be assumed that, based on a probability, some fly towards
the location of the elite bee and the left out bees to other locations. The complete algorithm
developed by the authors is given in the following steps:
Let the optimization task is defined as follows:
Minimize: )(xF (1)
subject to,
ul xxx ≤≤ . (2)
In the above, )(xF is a scalar valued objective function and lx and ux are the lower and upper
bounds of the variable.
Step 1: Deploying bees initially at random locations
The initial step involved is deploying the bees in a feasible solution space subject to the constraints
imposed on the solution variables. Here, position of a bee refers to one complete solution set to the
problem. For generality, let the bees be described as ni BBBB .............,......., 21 where n is the number
of bees and can be termed as population size. For ,4=n initial random position of bees is shown in
figure 1(a).
(a) (b)

27
(c) (d)
(e) (f)
Figure 1. Bee movement. (a) Initial poison of bees. (b) Indication of duration of dance.
(c) Probability of movement. (d) Bee flight for ti pp ≥ . (e) Bee flight for ti pp < . (f) Final position
of bees
ti pp ≥
ti pp <
ti pp ≥
ti pp <
ti pp ≥
ti pp <

28
Step 2: Evaluation of objective function value
The objective function value, ( )φF at each bee position is evaluated using equation 1.
Step 3: Computation of duration of dance of each bee
In this step, depending on the floral findings, each worker bee performs dance on the comb. The
duration of dance is a measure of quantum of food and let dD represent the duration of dance. The
duration of dance of the i -th bee in the j -th location at t -th iteration is given in equation 3.
1)(
1
)(
)(
)(
+
=
φji
jdi
F
tD (3)
The duration dance of bees is indicated in circles and the size of the circle is used to measure dD .
This is illustrated in figure 1(b).
Step 4: Identification of elite bee.
The bee, whose location gives maximum value for dD is designated as elite bee. Thus elite bee, eB
in the t -th iteration is given by equation (4).
( ))()( )(
,
tDtB jdi
ji
e Max= (4)
In figure 1(c), 4B is the identified as the elite bee.
Step 5: Movement of bees
Majority of bees follow the elite bee; however, few bees may fly to other flower patches too. Hence
the movement of bees can be thought of based on a probability. This will make the search more
probabilistic and may yield better results. A term named as threshold probability is therefore
introduced and is denoted as tp . The value of tp is fixed at a suitable value between 0 and 1.
In order to find the direction of flight of a particular bee, a random number between 0 and 1 is
generated denoted as ip and is compared with tp .
For ti pp ≥ , then the bee flies a distance of 1R towards the elite bee. The distance of flight, denoted
as 1R is a variable in the problem and is to be judicially chosen.
In figure 1(c), for bees 1B and 2B , ti pp ≥ and hence will move towards the elite bee. The flight of
1B and 2B is shown in figure 1(d) where 1B flies a distance of 1R towards the elite bee, 4B and
reaches the point, Y. Similarly, bee 2B flies a distance of 1R towards 4B and reaches the point, X.
For ip < tp , then that bee flies a distance of 1R towards any other bee location, which is randomly
decided between 1 and n . This is demonstrated in figure 1(e). The bee, 3B falls in the category of
ip < tp and hence flies a distance of 1R towards any other bee location. For this, a random number
between 1 and n is generated. Let the number be 1 so that 3B moves towards the past location of 1B .
Thus, 3B reaches point Z. When all bees make a flight of distance 1R , one iteration is completed. The
final position of all bees after one iteration is shown in figure 1(f).
Step 6: End the program, if termination criterion is reached; else go to step 2.

29
III. APPLICATION OF THE ALGORITHMS FOR PSS DESIGN
III. 1. Single machine infinite bus system model
For developing dynamic model, a single machine synchronous generator connected to infinite
busbar is considered [1] and is shown in figure 3(a).
Figure 3. Component of torque produced by voltage regulator action in response to a speed-derived
signal
Figure 3 shows the effect of speed through the stabilizing function G(s) through the voltage
regulator loops affecting
'
qE∆ , which produces component of torque T∆ . In figure 3 (b) speed
deviations ω∆ is given as input of PSS. It produces an output, which is a voltage signal sV∆ . The
output from the PSS is given to AVR, which produces a corresponding change in torque. In other
words stabilizing signal derived from machine speed is processed through a device called the power
system stabilizer (PSS) with a transfer function G(S) and its output connected to an input of the
exciter. Contribution of PSS to the torque–angle loop [1] is given by
( )
( ) addaa
a
TTsTKTsKKK
KKsG
s
sT
'
0
2'
0363
2
)/()/1(
)(
++++
=
∆
∆
ω
(6)
For the usual range of constants, this function can be approximated by
( )
( ) )1)](/(1)[/1(
)(
6
'
063
2
aada
a
sTKKTsKKK
KKsG
s
sT
+++
≈
∆
∆
ω
(7)
For large values of aK it can be further approximated by
( )
( ) )1)](/(1[
)(
6
'
06
2
aad sTKKTs
sG
K
K
s
sT
++
=
∆
∆
ω
(8)
( )
( )
)()(
)1)](/(1[
)(
6
'
06
2
sGEPsG
sTKKTs
sG
K
K
s
sT
aad
=
++
=
∆
∆
ω
(9)
The transfer function of a PID controller is
G(s) = ( d
i
p sK
s
K
K ++ ).
fdE∆
'
qE∆

30
III. 2. SIMULATION RESULTS
A generalized controller structure is considered for the PSS with the objective of achieving
the best dynamic response at all operating points. Let the controller structure be
( ) ∑−
=
n
n
n
n sKsG (10)
In the above equation Kn represents the controller parameters and n decides the order of the
controller. For simplicity a PID controller is chosen, i.e., n =1. The task is to identify the parameters
of the controller so as to obtain optimum performance at all operating points using the above
mentioned method.
Thus the problem is formulated as follows:
Find ( )φF such that
Minimize
( ) srp tF +∆= ωφ (11)
Subject to maxmin φφφ ≤≤
Where ( )φF is the objective function, rpω∆ and st denotes the peak overshoot and settling time
respectively.
φ is a set of controller parameters to be determined and is denoted as [ D
KKK IP ,, ], the subscripts
min and max represent the lower and upper bounds of the variables.
The minimization of the objective function in equation (11) is now carried out using the two
new optimization method described in the previous section. For this, a typical operating point given
in table 1 is considered.
Table-1. Parameters of single machine system
Table-2. Parameters of bee food foraging approach
Bee population size 15
Threshold probability 0.7
Step size of movement of bees, 1R 8.2
Machine
Data(p.u)
Transmission
line(p.u)
Exciter
Operating
Point
Xd=0.973
X'd=0.19
Xq=0.55 Re=0.0 KA=50 Vto=1.0
T'do=7.765s Xe=0.997 TA=0.05 Po= 0.8 p.u
D=0.0 Qo=0.4 p.u
H=4.62 0δ =72.83830

31
Dedicated software Matlab is developed for the optimal design of the PSS at the above
mentioned operating point using the bees algorithm. The computed results are delineated in figure 4.
The parameters employed in each algorithm are tabulated through tables 2 and 3. All the parameters
are obtained by trial and error and no attempt has been made to optimize them. Figure 4(a) shows the
variation of objective function at each iterative step of the two novel optimization algorithms. This
figure also shows objective function variation employing GA which is included for comparison. It is
important to mention that for fairness of comparison the initial population is taken as same for all the
three optimization methods to commence with.
Table- 3. Parameters of genetic algorithm approach
population size 15
Crossover probability 0.8
Mutation probability 0.06
Figure 4. Convergence characteristics
Figure 5 illustrates the convergence characteristics of two novel optimization methods. The
variation of objective function of each bee against iterative step as shown in figure 5(a) is a clear
indication of effective communication through “waggle dance”. While each bee starts at random
location they all converge coherently to the best position of high quality flower batches. However
such a mechanism is absent in the reproduction algorithm and this scheme relies on the survival of
the fittest mechanism. For completeness, the variation of controller constants with each iterative step
is also included in figure 5. At the end of iteration the optimal PSS structure identified and is given in
table 4.
Table-4. Optimum PSS structure
PK IK DK
OBF 22.72 1.11 4.12
GA 22.12 1.782 3.21
The dynamic response of single machine connected to infinite busbar with optimized PSS is now
studied and is available in figure 6. Figure 6 (a) shows the variation ω∆ of the machine, when
subjected to 0.05 p.u. step disturbance in mT∆ at rated operating conditions. From this dynamic
response the peak value is limited to 0.0006 and settling time is 1.6 seconds. Figure 6(b) shows the
variation of terminal voltage of the generator delivering rated load when subjected to a dip in mT∆ of
amplitude 0.05 p.u. step.

32
(a) (b)
(c) (d)
Figure 5. Colony behaviour of bees. Variation of controller parameters (a) PK , (b) IK (c) DK and
(d) Convergence characteristics.
The response shows that the proposed controller effectively stabilizes the machine terminal
voltage with a settling time of 1.4 seconds. Also the maximum dip in machine voltage is as low as
0.06 p.u. It is evident that the proposed schemes are on a par with that of GA.
(a) (b)
Figure 6 (a) Variation ω∆ of the machine, when subjected to 0.05 p.u. step disturbance in mT∆ at
rated operating conditions. (b) Variation of terminal voltage of the generator delivering rated load
when subjected to a dip in mT∆ of amplitude 0.05 p.u.
0
5
10
15
20
25
30
35
1 101 201 301
No of iterations
Kp
0
1
2
3
4
5
6
1 101 201 301
No of iterations
Ki
0
2
4
6
8
10
12
1 101 201 301
No of iterations
Kd
0
1
2
3
4
5
6
7
8
9
1 51 101 151 201 251 301
No of iterations
Objectivefunction

33
V. CONCLUSION
The prospective method based on honey bees presented in this paper supplements the present
wealth of recently developed optimization techniques and knowledge. The novel concept promise
confirmed convergence with random initial guess, simple computational steps, derivative-free
operation etc. Results obtained from computer simulations of a single machine connected to infinite
busbar indicate that the bee tuned excitation controller can yield good damping characteristics over a
wide range of operating conditions.
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