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CHAPTER 5
PSO AND ACO BASED PID CONTROLLER
5.1 INTRODUCTION
The quality and stability of the power supply are the important
factors for the generating system. To optimize the performance of electrical
equipment, it is important to ensure the quality of the electric power. During
the transportation, both the active power balance and the reactive power
balance must be maintained between the generation and utilization of AC
power. These two balances correspond to two equilibrium points: frequency
and voltage. When either of the two balances is broken and reset at a new
level, the equilibrium points will float. A good quality of the electric power
system requires both the frequency and voltage to remain at standard values
during operation. Control system plays an important role in maintaining these
power system parameters. The first attempt in the area of AGC has been to
control the frequency of a power system via the fly wheel governor of the
synchronous machine. The turbine-governor technique was subsequently
insufficient and a supplementary control was included to the governor with
the help of a signal directly proportional to the frequency deviation. Based on
the experiences with actual implementation of AGC schemes, modifications
to the definition of Area Control Error (ACE) are suggested from time to time
to cope with the change in a power system environment. The daily load cycle
changes significantly and hence fixed gain controllers will fail to provide best
performance under a wide range of operating conditions. Power systems are
subject to constant changes due to loading conditions, disturbances or
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structural changes. Controllers are designed to stabilize or enhance the
stability of the system under these conditions. However, in general, each
controller is designed for a specific situation or scenario and is effective under
these particular conditions. Hence, it is desirable to increase the capability of
PID controllers to suit the needs of present day applications.
A PID controller improves the transient response of a system by
reducing the overshoot and settling time of a system. The main reason to
develop better methods to design PID controllers is because of the significant
impact on the performance improvement. The performance index adopted for
problem formulation is settling time, overshoot and oscillations. The primary
design goal is to obtain a good load disturbance response by optimally
selecting the PID controller parameters. Traditionally, the control parameters
have been obtained by trial and error approach, which consumes more
amounts of time in optimizing the choice of gains. To reduce the complexity
in tuning PID parameters, Evolutionary computation techniques can be used
to solve a wide range of practical problems including optimization and design
of PID gains. It can obtain suboptimal solutions for very difficult problems
which conventional methods fail to produce in reasonable time. Evolutionary
algorithms can be a useful paradigm and provide promising results for solving
complex optimization functions. Evolutionary computation refers to the study
of computational systems that use ideas to draw inspirations from natural
evolution. Evolutionary algorithms like Genetic Algorithm (GA), Simulated
Annealing (SA), and Particle Swarm Optimization (PSO), Ant Colony
Optimization (ACO) has been employed in control applications to efficiently
search global optimum solutions.
Zwe-Lee Gaing(2004) have presented PSO for optimum design of
PID controller in AVR system. The simulation results proved the proposed
method was indeed more efficient and robust in improving the step response
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of an AVR system. Yoshida et al (1999) proposed PSO for reactive power and
voltage control considering voltage stability. The results reveal that the
proposed method generates a solution very near to the global optimum
solution. Miranda and Fonseca (2002) developed new Evolutionary PSO for
voltage/AVR control. The simulation results obtained indicate that it can
obtain high quality solutions with shorter calculation time. Chatterjee et al
(2006) incorporated PSO for intelligent control of AVR system. It has been
revealed that PSO exhibits better transient performance and can be
successfully applied to obtain on-line responses. Wong et al (2009) proposed
PSO-PID controller design for AVR system with new fitness function. From
simulation and comparison results, it can be seen that the proposed PSO
algorithm finds high quality solutions and demonstrates better control
performance. Yousuf et al (2009) developed PSO based predictive non-linear
single area automatic generation control. The simulation results show
improvement over the response characteristics and signify the strengths of the
proposed scheme. Rohit Kumar (2003) presented PSO based approach to
solve the economic load dispatch with line flows and voltage constraints, and
concluded that the proposed approach is computationally faster than GA.
Zhao et al (2005) proposed PSO approach based on the multi-agent system to
solve reactive power dispatch problem. The results indicate the possibility of
PSO as a practical tool for various optimization problems in the power
system.
Another meta-heuristic technique used for combinatorial
optimization problems is the Ant Colony Optimization (ACO) algorithm that
has been inspired by the foraging behaviour of real ants. Ying-Tung Hsiao
(2004) proposed an optimum approach for designing of PID controllers using
ACO to minimize the integral absolute control error. The experiment results
demonstrate that better control performance can be achieved in comparison
with conventional PID method. Duan Hai-bin (2006) presented a novel
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parameter optimization strategy for PID controller using ACO Algorithm. The
algorithm has been applied to the combinatorial optimization problem, and
the results indicate high precision of control and quick response. Shyh-Jier
Huang (2001) proposed ACO based optimization approach for enhancing
hydroelectric generation scheduling. Test results demonstrated the feasibility
and effectiveness of the method for the application considered. Boubertakh
et al (2009) developed ACO for tuning PID controllers and illustrated the
efficiency of the proposed method by simulation examples. Hong He et al
(2009) designed ACO based PID parameter optimization to increase the
search speed for PID parameter optimization. Simulation results show the
validity of this algorithm, and the methodology adapted to overcome the
drawbacks of traditional PID parameter optimization. Girirajkumar (2009)
presented the application of ACO algorithm to optimize the PID parameters in
the design of PID controller. The results presented prove the improvement of
ACO-PID controller and its stability over different operating conditions.
In this research, an efficient optimization algorithm is proposed
using PSO and ACO for tuning the optimal gains of PID controllers used for
LFC and AVR of Power generating systems. The primary aim of the
controller is to maintain the frequency and voltage at an optimal level under
varying operating conditions. The transient response of LFC and AVR is
very important, because both the amplitude and time duration of the response
must be within the prescribed limits. The performance of two area system
with PSO and ACO tuned PID controllers is analysed for its validity and
application worthiness. The proposed method has better adaptability towards
changes in load than the conventional PID, Fuzzy, and Genetic Algorithm
based controllers, thereby providing improved performance with respect to
overshoot, settling time and oscillations.
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The chapter is organized as follows: Section 5.2 describes the
evolutionary algorithms for power system control. Section 5.3 demonstrates
the basic concepts of ACO algorithm, Section 5.4 explains the concepts of
PSO algorithm, Section 5.5 deals with Simulink models of proposed
controllers, Simulation results are presented in Section 5.6, Comparative
analysis is briefed in section 5.7 and conclusion is derived in Section 5.8.
5.2 EVOLUTIONARY ALGORITHMS FOR POWER SYSTEM
CONTROL
In general, an electric power network is a large and complex system
consists of synchronous generators, transformers, transmission lines, relays
and switches, etc... Various control objectives such as operating conditions,
actions, and design decisions requires solving one or more linear or non-linear
optimization problems. Evolutionary Algorithm (EA) is considered as a useful
promising technique for deriving the global optimization solution for complex
problems. Since the loads are switched on and off, the power system is prone
to sudden changes to its configuration. Under these circumstances, keeping
voltage and frequency within the allowable range is one of the important tasks
for power system control. An online control strategy to achieve this is referred
to as real and reactive power control, using LFC and AVR. Essentially, LFC
takes care of frequency, and AVR ensures voltage of the generating system.
The PID control system with plant indicating LFC/AVR and EA
based PID is shown in Figure 5.1. The Kp, Ki and Kd are respectively the
proportional, integral and derivative gains of the PID controller that are tuned
by EA. In the proposed system, PSO and ACO algorithms are used to
optimize set of PID parameters in the system to achieve desired output ‘yd’.
The control output ‘u’ from EA-PID is based on the error signal ‘e’, which is
the difference between actual output ‘y’ and the desired output ‘yd’. The
objective on the PSO and ACO based optimization is to seek a set of PID
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parameters such that the feedback control system has a minimum performance
index. A set of optimal PID parameters can yield good frequency and voltage
characteristics of LFC and AVR. EA is considered as a useful and promising
technique for deriving the global optimum solution of complex functions.
Hence, application of these algorithms yields improved performance
characteristics in terms of settling time, oscillations and frequency.
Figure 5.1 PID Control System with Evolutionary Algorithm
The LFC/AVR is subjected to different operating characteristics
like, varying load and regulation parameters to verify the validity of the
proposed algorithm. Stochastic techniques like Particle Swarm Optimization
(PSO) and Ant Colony Optimization (ACO) are applied to tune the controller
gains to ensure optimal performance at nominal operating conditions. PSO
and ACO are used in offline to tune the gain parameters and applied to PID
controller in the secondary control loop of the plant.
5.3 BASIC CONCEPTS OF ACO ALGORITHM
Ant Colony Optimization (ACO) was introduced around 1991-1992
by M. Dorigo and colleagues as a novel nature-inspired meta-heuristic for the
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solution of hard combinatorial optimization problems (Dorigo and Blum
2005), (Dorigo et al 1999). In this algorithm, computational resources are
allocated to a set of relatively simple agents that exploit a form of indirect
communication mediated by the environment to find the shortest path from
the ant nest to a set target. While walking, Ants can follow through to a food
source because, they deposit pheromone on the ground, and they have a
probabilistic preference for paths with a larger amount of pheromone.
Figure 5.2 Behavior of Real Ants in Finding Shortest Path
As shown in Figure 5.2, ants arrive at a point where they have to
decide whether to turn left or right. Since they have no clue of which is the
better choice, they choose randomly. It can be expected that, on an average,
half of the ants decide to turn left and the other half to turn right. This
happens both to ants moving from left to right and to those moving from right
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to left Figure 5.2(a) and (c) show what happens in the immediate instants,
supposing all ants walk at approximately the same speed.
The number of lines is roughly proportional to the amount of
pheromone that the ants have deposited. Since the lower path is shorter than
the upper one, more ants will visit it on average, and therefore, pheromone
accumulates faster. After a short period, the difference in the amount of
pheromone on the two paths is large enough to influence the decision of new
ants coming into the system (Figure 5.2(d)), from this point on, new ants will
prefer the lower path, since at the decision point they perceive a greater
amount of pheromone on this lower path. In turn, this increases the positive
feedback and the numbers of ants are choosing the lower and shorter path.
Very soon all ants will use the shorter path. This process is thus characterized
by a positive feedback loop, where the probability with which an ant chooses
a path increases with the number of ants that previously chose the same path.
This behavior inspired the ACO algorithm in which a set of artificial ants
cooperate in the solution of a problem by exchanging information via
pheromone deposited on graph edges.
The ACO algorithm is developed using artificial ants, which are
designed based on the behaviour of real ants. The artificial ants walk through
this graph, looking for food paths; each ant has a rather simple behaviour so
that it will typically only find rather poor-quality paths on its own. Better
paths are found as the emergent result of the global cooperation among ants in
the colony. The behaviour of artificial ants is inspired from real ants. They lay
pheromone trails on the graph edges and chooses their path with respect to
probabilities that depend on pheromone trails and this pheromone trails
progressively decrease by evaporation.
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Ants prefer to move to nodes, which are connected by short
edges with a high mount of pheromone. In addition, artificial ants have some
extra features that do not find in their counterpart, real ants. In particular, they
live in a discrete world, and their moves consist of transitions from nodes to
nodes. Furthermore, they are usually associated with data structures that
contain the memory of their previous action. Finally, the probability for an
artificial ant to choose an edge often depends not only on pheromone,
but also on some problem-specific local heuristics. The variables which
are used in ACO algorithm and their definitions are tabulated in Table 5.1.
Table 5.1 Variables and their Definitions used in ACO Algorithm
Variable Definition
ij Heuristic factor
ij Pheromone factor
Pij Transition probability
and Constants greater than 0
Coefficient of the persistence of the trail
At each generation, each ant generates a complete tour by choosing
the nodes according to a probabilistic state transition rule. Every ant selects
the nodes in the order in which they will appear in the permutation. For the
selection of a node, an ant uses a heuristic factor as well as a pheromone
factor. The heuristic factor, denoted by ij, and the pheromone factor, denoted
by i, are indicators of how good it seems to have node j at node i of the
permutation.
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The heuristic value is generated by the problem dependent
heuristics, whereas the pheromone factor stems from former ants that have
found good solution. The next node is chosen by an ant according to the
Pseudo Random Proportional Action Choice rule. With Probability q0, (where
0 q0 < 1) the ant chooses a node from the set of nodes (s) that have not been
selected and which maximizes the Equation (5.1).
[ ij] [ ij] (5.1)
where 0 and 0 are constants that determine the relative influence of
pheromone values and heuristic values on the decision of ant. With
probability (1 – q0) the next node is chosen from the set S according to the
probability distribution that is determined by
ijij
ijij
ijSh
P (5.2)
Therefore, the transition probability is a trade-off between the
heuristic and pheromone factor. For the heuristic factor, the close nodes (low
cost of path) should be chosen with high probability, thus implementing
greedy constructive heuristic. As the pheromone factor is on an edge (i, j)
there has been a lot of traffic then it is highly desirable to implement the
autocatalytic process. The heuristic factor ij j is computed according to the
rule,
Sj),X(F
1
j
ij (5.3)
where, F(X) represents the cost function of X. It is in favour that the choice of
edges, which are shorter (with low cost) and, which have a greater amount of
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pheromone. The ant lays a trial substance along the path from i to j as
mentioned in Equation (5.4),
Lk
Qk
ij (5.4)
if Kth ant uses edge (I,j) in its tour then,k
ij = 0.
where Q is a constant related to the quality of pheromone trails laid by ants
and LK is the cost of the tour performed by the kth ant. In other words,
pheromone updating is intended to allocate a greater amount of pheromone
with low cost (shorter tours). This value is evaluated when the ant has
completed a tour and consisting of a cycle of n iterations (generations). It is
used to update the amount of substance previously laid on the trail, on the
following rules
ij(t+n)= . ij(t)+ ij(t) (5.5)
m
1k ijij )t()t( (5.6)
where, m denotes the number of ants, , (0,1) is a coefficient of persistence
of the trial during a cycle such that (1- )represents the evaporation of the trail
between generation ng and ng+1. The pheromone updating rule was meant to
simulate the change in the amount of pheromone due to both the addition of
new pheromone deposited by ants on the visited edges and to pheromone
evaporation. The algorithm stops iterating either when an ant found a solution
or when a maximum number of generations has been performed.
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5.3.1 ACO-PID Controller Design
The Conventional fixed gain PID controller is well known
technique for industrial control process. The design of this controller requires
the three main parameters, Proportional gain (Kp), Integral time constant (Ki)
and derivative time constant (Kd). The gains of the controller are tuned by
trial and error method based on the experience and plant behaviour. This
process will consume more time and will be suitable only for particular
operating condition. In this research, ACO algorithm is used to optimize the
gains, and the values are transferred to the PID controller of the plant
representing LFC and AVR of the power generating system as shown in
Figure 5.3.
Figure 5.3 ACO-PID Controller
The proportional gain makes the controller respond to the error
while the integral gain help to eliminate steady state error and derivative gain
to prevent overshoot. The plant is replaced by LFC and AVR models
developed using simulink in MATLAB. With the optimum gains generated by
the proposed algorithm the models are simulated for various operating
conditions to validate the performance. The flowchart for ACO based PID
controller is shown in Figure 5.4.
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Figure 5.4 Flow Chart of ACO Algorithm
The design steps of ACO based PID controller for AVR is as follows.
1. Initialize the algorithm parameters like number of iterations,
number of ants, strength of pheromone and decay rate.
2. Initialize the ranges of PID controller gain values.
3. For each ant the transition probability is calculated using the
Equation (5.2).
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4. Incrementally builds a solution and local pheromone updating
is done by using the Equation (5.5).
5. Record the best solution found so far.
6. A global pheromone update is done by using the Equation (5.6).
7. Repeat the steps 3 to 6 until the maximum iteration is reached.
The algorithm is tested for different values of parameters by
simulating the model for different operating conditions. According to the
trials, the optimum parameters used for verifying the performance of the
ACO-PID controller is listed in Table 5.2.
Table 5.2 ACO Parameters
Parameters LFC AVR
Number of ants 500 400
Number of nodes 120 130
Number of generations 10 25
Pheromone strength 0.01 0.02
Decay rate 0.99 0.84
The ACO algorithm design steps for LFC is
1. Initialize the population size, the initial search steps of all
variables and number of ants, t = 0, and count t = 0.
2. Initialize the PID parameters.
3. For each ant (j = 1,2,……n), select the jth
solution component
with a probability Pij.
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4. Evaluate the candidate solution and get the best individual ant
and the path.
5. Update the trial matrix as in Equation (5.4). Evaluate the local
and global pheromone using Equations (5.5) and (5.6). If no
improvement occurs, adjust the current searching step scheme
according to the path.
6. Repeat the process until the best searching step is reached or
the maximum iteration is performed.
Since the model parameters of LFC are identical, the optimized
parameters are used in the PID controller for single and two area
interconnected LFC system. The system is stable and the control task is to
minimize the system frequency deviation f1 in area 1, f2 in area2 and tie-
line power deviation Ptie. The performance of the system can be tested by
applying load disturbance PD1 to system and observing the change in
frequency in both areas. To assess the effectiveness of the optimized
parameters, the models are tested for different load and regulation parameters.
5.4 OVERVIEW OF PSO ALGORITHM
In PSO algorithm, each particle in the swarm represents a solution
to the problem, and it is defined with its position and velocity. PSO is
initialized with a group of random particles (solutions) and then searches for
optima by updating the particles in each generation. In every iteration, each
particle is updated by two "best" values. The first one is the best solution
(fitness) achieved so far (the fitness value is also stored) called pbest. Another
"best" value that is tracked by the particle swarm optimizer is the best value,
obtained so far by any particle in the population. This best value is a global
best and called gbest. After finding the two best values, the particle updates
its velocity and positions. The above mentioned overview of PSO is depicted
as shown in Figure 5.5.
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Figure 5.5 Representation of PSO
The variables which are used in PSO algorithm and their definitions
are given in Table 5.3.
Table 5.3 Variables and their Definitions used in PSO Algorithm
Variable Definition
itermax Maximum number of iterations
X Position of the particle
Xi Position of ith
particle
V Velocity of the particle
Vi Velocity of ith
particle
P Best position of the particle
Pi Best position previously visited
by ith
particle
Pg Best position visited by a particle
W Inertia weight
Wmax Maximum value of inertia weight
Wmin Minimum value of inertia weight
C1 Cognitive coefficient
C2 Social coefficient
R and r Random number between 0 and 1
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In D-dimensional search space, the position of the ith particle can
be represented by a D-dimensional vector, Xi = (Xi1,…, Xid, …, XiD). The
velocity of the particle vi can be represented by another D-dimensional vector
Vi = (Vi1,…, Vid, …, ViD). The best position visited by the ith particle is
denoted as Pi=(Pi1,…,Pid,…,PiD), and Pg as the index of the particle visited the
best position in the swarm, then Pg becomes the best solution found so far,
and the velocity of the particle and its new position will be determined
according to the Equations (5.6) and (5.7).
Vid=WVid+C1R (Pid-Xid) + C2R (Pgd –Xid) (5.6)
Xid=Xid + Vid (5.7)
The parameter ‘W’ in Equation (5.6) is inertia weight that increases
the overall performance of PSO. It is reported that a larger value of ‘W’ can
favour higher ability for global search while lower value of W implies a
higher ability for local re-search. To achieve a higher performance, we
linearly decrease the value of inertia weight W over the generations to favour
global re-search in initial generations and local re-search in the later
generations. The linearly decreasing value of inertia is expressed in
Equation (5.8).
max
minmin
maxiter
WW*iterWW (5.8)
wheremax
iter is the maximum of iteration in evolution process, Wmax is
maximum value of inertia weight,min
W is the minimum value of inertia
weight, and iter is current value of iteration.
5.4.1 PSO-PID Controller Design
With the advancement of computational methods in the recent
times, optimization techniques are often proposed to tune the control
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parameters. Stochastic Algorithm can be applied for tuning of PID controller
gains to ensure optimal control performance at nominal operating conditions.
In Conventional PID controller, the gains are randomly selected and the
results are verified for every set of random gain values. PSO algorithm finds
the Proportional, Integral and Derivative gains of the PID controller and the
values are passed to the PID controller of single area LFC and AVR as shown
in Figure 5.6. The gain values are tested for two area LFC to optimize the
change in frequency in both areas.
Figure 5.6 PSO Algorithm Based PID Controller
The design steps of PSO based PID controller for LFC of a power
generating system is
1. Initialize the algorithm parameters like number of generations,
population, inertia weight, cognitive and social coefficients.
2. Initialize the values of the parameters KP, Ki and KD
randomly.
3. Calculate the fitness function of each particle in each
generation.
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4. Calculate the local best of each particle and the global best of
the particles.
5. Update the position, velocity, local best and global best in
each generation.
6. Repeat the steps 3 to 5 until the maximum iteration reached or
the best solution is found.
The objective function represents the function that measures the
performance of the system. The fitness function (objective) function for PSO
is defined as the Integral of Time multiplied by the Absolute value of Error
(ITAE) of the corresponding system. Therefore, it becomes an unconstrained
optimization problem to find a set of decision variables by minimizing the
objective function. The AGC performance of a two area test system has been
tested with a PSO tuned optimal PID controller. The main objectives of the
AGC in multi-area power system are maintaining zero steady state errors for
frequency deviation and accurate tracking of load demands. Hence, the
optimal parameters obtained by the proposed algorithm, guarantee both
stability and desired performance in both areas of interconnected system.
Each area consists of three first-order transfer functions, modelling the
turbine, governor and power system. In addition, all generators in each area
are assumed to form a coherent group. For PID controller, the objective
function is defined as
N
1j
N
1i0
j
idtftf
where, N is the number of areas in the power system and j
if is the frequency
deviation in area i for step load changes in area j. The flowchart for PSO
based PID controller is shown in Figure 5.7. To design the LFC for two area,
the change in load in both areas must be taken into account along with the
parameters of the governor, turbine, and load. Two identical areas with non-
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reheat type turbine with similar parameters are considered for
implementation. Furthermore, the generators tend to have the same response
characteristics are said to be coherent. Then it is possible to let the LFC loop
represent the whole system, which is referred to as a common area. The prime
mover control must have drooping characteristics to ensure proper division of
load, when generators are operating in parallel. In many cases, a group of
generators are closely coupled internally and swing in unison. The Automatic
Generation Control (AGC) of a multi area system can be realized by
analyzing AGC for a two area system. Tie line power appears as a load
increase in one area and a load decrease in the other area, depending on the
direction of the flow. The optimum values used for various parameters in PSO
implementation are listed in Table 5.4.
Figure 5.7 PSO Algorithm for PID Controller
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Table 5.4 PSO Parameters
Parameters LFC AVR
Population size 5 50
Number of generations 10 50
Inertia weight 0.8 0.9
cognitive coefficient 2.05 2.0
social coefficient 2.05 2.0
The following procedure is used for implementing the PSO algorithm
for AVR.
1. Initialize the swarm by assigning a random position in the
problem hyperspace to each particle.
2. Evaluate the fitness function for each particle.
3. For each individual particle, compare the particle’s fitness
value with its Pbest. If the current value is better than the
Pbest value, then set this value as the Pbest and the current
particle’s position, xi and pi.
4. Identify the particle that has the best fitness value. The value
of its fitness function is identified as gbest and its best
position as pg.
5. Update the velocities and positions of all the particles using
Equations (5.6) and (5.7).
6. Repeat steps 2–5 until the stopping criteria is reached.
Maximum iterations or when the optimum solution is reached.
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5.5 SIMULINK MODEL OF ACO AND PSO BASED PID
CONTROLLER
5.5.1 Simulink Model of an AVR
The AVR model consists of a step input, PID controller based on
PSO, an amplifier that amplifies the signal to the exciter which in turn
controls the voltage of the generator and a scope to display the terminal
voltage. It also contains a sensor that senses the voltage rise or fall due to the
difference between load demand and power generated and feeds it to the
controller based on the load changes. The AVR model shown in Figure 5.8 is
simulated with system parameter values indicated in Table 5.5.
Figure 5.8 Simulink Model of Automatic Voltage Regulator with PID
Controller
Table 5.5 Values for constants in AVR model
Symbol Parameters Optimum Values
Ka Amplifier gain 10
a Amplifier time constant 0.1
Kg Generator gain 1
g Generator time constant 1
Kr Sensor gain 1
r Sensor time constant 0.05
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5.5.2 Simulation Model for LFC
PID controllers are parametric controllers that affect the behaviour
of the LFC system, if the parameters are not optimized. Designing an
optimum controller ensures improved performance by minimizing the
performance index. To illustrate the importance of proposed PSO and ACO
algorithms, the LFC model designed using simulink in MATLAB is
considered. It consists of a step input, PID controller based on PSO, a
governor that controls the speed of the turbine that drives the generator and
the scope that shows the frequency deviation. The optimum parameters used
in LFC model in Figure 5.9 are indicated in Table 5.6.
Figure 5.9 Simulink Model of LFC with PID Controller
Table 5.6 Values for constants in LFC model
Symbol ParametersOptimum
Values
g Governor time constant 0.2
t turbine time constant 0.5
R Regulation parameter 20, 30
H and D Inertia constants of the load 10 and 0.8
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5.5.3 Simulation model for LFC in a Two Area Power System
The normal operation of the multi-area interconnected power
system requires that each area maintain the load and generation balance. This
system experiences deviations in nominal system frequency and schedules
power exchanges to other areas with change in load. AGC tries to achieve this
balance by maintaining the system frequency and the tie line flows at their
scheduled values. The AGC action is guided by the Area Control Error
(ACE), which is a function of system frequency and tie line flows. The ACE
represents a mismatch between area load and generation taking into account
any interchange agreement with the neighboring areas (Ibraheem et al 2005),
(Kothari and Nagrath 2007). Since both areas are connected together, a load
perturbation in one area affects the output frequencies of both areas. The
controller employed in each area needs the status about the transient behavior
of both areas in order to maintain the frequency to optimal value.
The tie-line power fluctuations and frequency fluctuations is
sensed, and the signal is fed back into both areas (Ertugrul and Kocaarslan
2005) (Yesil and Eksin 2004). The primary speed controller employed makes
initial course of adjustment, but it is limited by the time lags of the turbine
and the system. Hence, an intelligent and efficient secondary controller is
required to adjust the system frequency by reducing the error. The model of
LFC for two areas interconnected system is represented in Figure 5.10 with
PSO and ACO based PID controller. This model depicts the interconnection
of two power systems with LFC, and the results are analysed from the scope
that displays the combined output of the frequencies of the two systems.
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Figure 5.10 Simulink Model of LFC for a Two Area Power System with
PID Controller
5.6 SIMULATION RESULTS
The main purpose of the simulations under the normal conditions is
to evaluate the performance of the LFC/AVR and to achieve improvements
in the performance in the transient response of the system. To view a
complete picture about the performance of the proposed controller a set of
simulations are conducted to assure the robustness of the LFC/AVR under
different disturbance magnitude. Load disturbances of 0.1, 0.2, 0.5, 0.6pu are
applied to area 1 each at a time. For robustness, regulation constant is tuned
according to load and system changes. The overshoot, oscillations, settling
time are adapted as a standard set of performance indices to compare the time
response of f1, f2 of the controllers. As it is observed from the results, the
controllers will learn to bring the system to a stable operating point and the
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transient oscillations are finally converged close to zero. The PID controller is
conFigure ured with the auto-tuned parameters KP, KI, KD and the transient
response of LFC and AVR are presented in this section.
5.6.1 PSO Based PID Controller
The model for LFC and AVR with PSO based PID controller is
designed in the simulink. The Kp, KI and Kd values for the PID controller
were obtained by running the M-file. The simulation was performed for
different regulations and loads to validate the robustness of the proposed
controller. The terminal voltage response for a change in load of 0.1 p.u and
regulation of 10 is shown in Figure 5.11.
Figure 5.11 AVR with PSO Based PID Controller for PL=0.1 p.u
From Figure 5.11, it is observed that the settling time of AVR with
PSO based PID controller is 9.03 seconds and there is no transient peak
overshoot.
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Figure 5.12 LFC with PSO Based PID Controller for R=10 and PL = 0.1 p.u
From Figure 5.12, it is inferred that the settling time of LFC with
PSO based PID controller is 8.2 seconds, and the peak overshoot is -0.0114.
The simulation results for AVR and LFC with PSO based PID controller
under various load changes and regulations are tabulated in Table 5.7 and
Table 5.8, respectively. These results show that the proposed algorithm can
search optimal PID controller parameters quickly and efficiently. The PSO
method does not perform the selection and crossover operation in
evolutionary processes; the computation time is reduced by 47% when
compared with GA method.
Table 5.7 Performance Analysis of PSO Based PID Controller for AVR
Change in LoadParameters
PL=0.2 PL=0.4 PL=0.6 PL=0.8
Computational
time (sec)26.8 27.2 28.4 29
Settling Time(sec) 9.03 10.2 11.2 11.8
Overshoot (V) 0 0.22 0 0.204
Oscillation (V) 0 to 0.1 0 to 0.22 0 to 0.1 0 to 0.204
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Table 5.8 Performance Analysis of PSO Based PID Controller for LFC
R1=10 R2=20Parameters
PL=0.2 PL=0.7 PL=0.2 PL=0.7
Computational time (sec) 26.8 27.2 28.4 29
Settling Time(sec) 8.2 8.34 10.3 10.42
Overshoot(Hz) -0.0014 -0.0213 -0.0147 -0.0076
Oscillation(Hz) 0 to 0.0014 0 to 0.0213 0 to -0.0147 0 to 0.0076
It is observed from the results that, when compared to the
conventional controller the settling time, peak overshoots and oscillations of
LFC are reduced by 73%, 77% and 77%, respectively. The settling time of
AVR is reduced by 66% as compared to the conventional controller for a
change in load of 20%. The objective function (ITAE) used for the PSO
algorithm is same for AVR and LFC, hence the computational time is similar
as mentioned in Table 5.7.
5.6.2 ACO Based PID Controller
The simulink model for LFC and AVR with ACO based PID controller
was simulated. The optimum gain values obtained by the M-file are
transferred to the simulink model and tested for different loads and regulation
parameters. The frequency deviation and terminal voltage response for a
change in load of 0.1 p.u and regulation of 10 is shown in Figures 5.13 and
5.14, respectively.
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Figure 5.13 LFC with ACO-PID controller for R=10 and PL = 0.1 p.u
From Figure 5.13, it is observed that the frequency deviation and
the peak overshoot is minimum. The settling time for frequency deviation is 9
seconds, and the oscillation varies between -0.0080 to +0.0030, which is very
less compared to PID controllers.
Figure 5.14 AVR with ACO-PID Controller for PL = 0.1 p.u
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From Figure 5.14, it is found that the settling time of AVR with
ACO based Integral controller is 5.2 seconds and there is a transient
overshoot of about 0.16. The LFC and AVR models are simulated for
different load conditions in order to replicate the daily load curve of the
power system. The computational time taken by the proposed algorithm in
generating the optimum values of PID gains is obtained and tabulated. To
show the effectiveness of the proposed algorithm, the settling time for
different operating conditions of LFC is presented in Table 5.9. As witnessed
from the table, the merits of ACO are the response characteristics and
computational efficiency. The computational time is reduced by 21.6% when
compared to GA based PID controller. Since the population of ants is
operated simultaneously, the computational efficiency is improved. It is
achieved because of the parallel search and optimization capabilities inspired
by the behaviour of ant colonies.
Table 5.9 Performance Analysis of ACO Based PID Controller for LFC
R1=10 R2=20Parameters
PL=0.2 PL=0.7 PL=0.2 PL=0.7
Computational
time (sec)42 44.5 41.8 44.2
Settling time(sec) 9 8.6 10.3 9.8
Overshoot(Hz) 0.0030 0.0053 -0.00058 -0.00034
Oscillation(Hz)-0.0080 to
+0.0030
-0.018 to
+0.0053
-0.0071 to -
0.00058
-0.138
to -0.00034
Owing to the randomness of heuristic algorithms, their performance
cannot be judged by a single run. Many trials with different initialization
should be made to acquire useful conclusion about the performance. An
algorithm is robust, if it gives a consistent result during all the trials. The
simulation results for LFC and AVR with ACO based PID controller under
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various load changes and regulations are tabulated in Table 5.9 and Table
5.10, respectively. From the Tables, it is observed that the settling time, peak
overshoots and oscillations of LFC are reduced by 37%, 21% and 50%,
respectively. The settling time of AVR is reduced by 53% when compared to
the conventional controller for a sudden increase in load of 0.2p.u. The fitness
function of the algorithm to generate optimum gain value is same; hence the
execution time for LFC and AVR is similar as tabulated. From the results, it is
revealed that ACO method is a potential alternative to be developed in solving
LFC and AVR problems.
Table 5.10 Performance Analysis of ACO based PID Controller for AVR
Change in Load
PL=0.2 PL=0.4 PL=0.6 PL=0.8
Computational time (sec) 42 44.5 41.8 44.2
Settling Time(sec) 5.2 5.5 5.86 6.6
Overshoot (V) 0.15 0.301 0.142 0.28
Oscillation (V) 0 to 0.15 0 to 0.301 0 to 0.142 0 to 0.28
5.6.3 Two Area Interconnected System
In order to emphasize the advantages of the proposed controller, the
two area LFC has been implemented and compared with conventional
controllers. In multi area power networks the active power generation within
each area should be controlled to maintain scheduled power interchanges.
Control and balance of power flows at tie line are required for supplementary
frequency control. For successful control of frequency and active power
generation, the damping of oscillation at tie-line is important. The simulation
result is plotted in Figure 5.15 for a change in load of 20% in area1 and 60%
in area2.
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Figure 5.15 PSO-PID based LFC for Area 1 Loaded by 0.2p.u and Area
2 Loaded by 0.6p.u
It can be shown from the Figure 5.15 that, the proposed secondary
controller damps the frequency oscillations in both areas by achieving power
balance between them and increasing the tie-line power flow. Initial
oscillation is due to time delay in governor control but then the proposed
secondary controller starts acting and decreases the oscillations. The deviation
in frequency is further investigated due to change in load from 20% to 80% in
both areas and the results are tabulated in Table 5.11. For comparing the
performance of the algorithm, the computational time for different operating
conditions is specified in Table 5.11. This approach can be a useful alternative
when compared to GA, since the computational time taken for convergence of
particles is reduced by 46.5%.
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Table 5.11 Performance Analysis of PSO-PID for Two Area LFC
R1=20, R2=15
Computational
time = 29.6 sec
Computational
time = 30.4 sec
Computational
time = 31 sec
PL1=0.2 PL2=0.6 PL1=0.3 PL2=0.7 PL1=0.4 PL2=0.8
Parameters
Area1 Area2 Area1 Area2 Area1 Area2
Settling
Time (s)12.5 13.1 12.8 13.5
13.014.0
Overshoot
(Hz)-0.0089 -0.026 -0.008 -0.029 -0.0045 -0.035
Oscillation
(Hz)
0 to
0.0089
0 to
0.026
0 to
0.008
0 to
0.029
0 to
0.0045
0 to
0.035
As can be seen from the simulation result, the PSO method has
prompt convergence and good evaluation value. The results indicate that the
PSO-PID controller is efficient in arresting the frequency oscillation of both
areas. The settling time, oscillations and overshoot are reduced by 76%,
70.8%, and 63.6 % respectively when compared to conventional PID
controller for change in load of 0.2 and 0.6 p.u.
In the application of ACO algorithm for two areas LFC system, the
initial population of the colony is randomly generated within the search space.
Then, the fitness of ants is individually assessed based on their corresponding
objective function. In order to examine the dynamic behaviour and
convergence characteristics of the proposed method, simulation is carried out
for the different load and regulation parameters. Figure 5.16 shows the
frequency response of the two area interconnected system for change in load
of 20% in area1 and 40% in area2.
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Figure 5.16 ACO-PID based LFC for Area 1 Loaded by 0.2p.u and Area2
Loaded by 0.4p.u
The low frequency oscillations if not damped immediately after a
sudden load in a power system, will drive the system to instability. Hence the
secondary controller employed in LFC has to manage efficiently for the
increase in load and act dynamically to reduce the frequency oscillations.
Table 5.12 shows the simulation results of a two area system for loads varying
from 0.02 to 0.08p.u with R value of 20 and 15. The effectiveness of the
algorithm is evaluated by comparing it with conventional PID and found that
settling time, oscillations and overshoot are reduced by 75%, 82.9% and
61.8% respectively for change in load of 0.2 and 0.4 in both areas. The
computational efficiency of the proposed ACO-PID controller is found to be
improved since the execution time is reduced by 20.8% when compared to
GA-PID controller. The computational time taken by the algorithm in
generating optimum gain values are indicated in Table 5.12 for different load
and regulation parameters.
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Table 5.12 Performance Analysis of ACO-PID for Two Area LFC
R1=20, R2=15
Computational
time =43.6 sec
Computational
time = 44.9sec
Computational
time = 45.2 sec
PL1=0.2 PL2=0.4 PL1=0.3 PL2=0.6 PL1=0.2 PL2=0.8
Parameters
Area1 Area2 Area1 Area2 Area1 Area2
Settling
Time (s)13.1 14.8 13.8 14.1 13.2 15.1
Overshoot
(Hz)-0.011 -0.023 -0.014 -0.028 -0.015 -0.03
Oscillation
(Hz)
0 to
0.011
0 to
0.023
0 to
0.014
0 to
0.028
0 to
0.015
0 to
0.03
5.7 COMPARATIVE ANALYSIS
A statistical analysis is performed to show that the proposed PSO
and ACO algorithms allow the search process to be more efficient in finding
feasible solutions and global minimum as compared with the conventional
PID, fuzzy, and GA based controllers. This section deals with the
performance evaluation of Conventional and EC based controllers for LFC
and AVR of the generating system. The settling time, oscillations and
overshoot are compared for a change in load of 0.10 and regulation of 10 for
all types of controllers.
5.7.1 Performance Analysis of PSO Based Controller
Table 5.13 Performance Comparison of PSO Based AVR
Fixed Parameters: Ka= 10, a= 0.1 ,
Ke= 1, e = 0.1, kg= 1 , g= 1, Kr= 1 , 6 = 0.05
Methods Settling Time (sec) Overshoot (V) Oscillations (V)
Conventional PID 37.5 0 0 to 0.1
Fuzzy Controller 16 0 0 to 0.1
GA-PID 11.38 0 0 to 0.1
PSO-PID 8.82 0 0 to 0.1
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Table 5.14 Performance Comparison of PSO Based LFC
Fixed Parameters: g = 0.2 , T =0.5 ,kg=1 ,
H = 5,D=0.8
MethodsSettling Time
(sec)
Overshoot
(Hz)
Oscillations
(Hz)
Conventional PID 51 -0.0083 0 to 0.0083
Fuzzy Controller 20 -0.0052 0 to -0.0052
GA-PID10.25
-0.00261.5919e006 to
-0.0026
PSO-PID 8.1 -0.0013 0 to-0.0013
The results in comparison table shows that, for a load of 0.1 p.u
and regulation of 10 the settling time of LFC is reduced by a factor of 59.5%,
the oscillations are decreased by 75%, reduction of 75% in overshoot and the
settling time of AVR is reduced by 44.87% as compared to fuzzy controllers.
When compared GA based controller the settling time of LFC is reduced by
20.9%, the oscillations are decreased by 50%, reduction of 50% in the
overshoots and the settling time of AVR is reduced by a factor of 22.49%. It
is clear from the results that the proposed PSO method can avoid the
drawback of the premature convergence problem in GA and obtain a high
reliable solution with reduced computational time. The bar chart in the Figure
5.17 shows the comparative analysis of LFC and AVR with conventional
controllers and PSO based controller.
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Figure 5.17 Comparative Analysis of Conventional Controllers with
PSO Based Controller for LFC and AVR
5.7.2 Performance Analysis of ACO Based Controller
To assess the effectiveness of the ACO-PID controller, the
simulation results are compared with the conventional PID, fuzzy and GA
based controllers in Tables 5.15 and 5.16. The settling time of ACO based
AVR is reduced by 54.3% when compared to GA-PID and 67.5% when
compared to the fuzzy controller. The simulation results demonstrate the
adaptability of ACO algorithm and its advantage in solving power system
optimization problem.
Table 5.15 Performance Comparison of ACO based AVR
Fixed Parameters: Ka= 10 , a = 0.1 ,
Ke= 1, e = 0.1, kg= 1 , g = 1, Kr= 1 , r = 0.05
Methods Settling Time (sec) Overshoot(V) Oscillations(V)
Conventional PID 37.5 0.1 0 to 0.1
Fuzzy Controller 16 0.1 0 to 0.1
GA-PID 11.38 0.1 0 to 0.1
ACO-PID 5.2 0.15 0 to 0.15
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Table 5.16 Performance Comparison of ACO based LFC
Fixed Parameters: g = 0.2 , T =0.5 ,
kg=1, H = 5, D=0.8
Methods Settling Time (sec) Overshoot(Hz) Oscillations(Hz)
Conventional PID 51 -0.0083 0 to 0.0083
Fuzzy Controller 20 -0.0052 0 to -0.0052
GA-PID 10.25 -0.0026 0 to -0.0026
ACO-PID 8.6 0.003 0 to 0.005
The settling time, oscillations and overshoot of proposed LFC with
ACO based controller is reduced by 63.6%, 88.9% and 66.3%, respectively
when compared to conventional PID controller. The settling time of AVR
with ACO based controller is decreased by a factor of 86.2%. Hence, ACO
based controller gives improved performance characteristics when compared
to the conventional controllers. When compared to the fuzzy controller, the
proposed ACO-PID controller is reduced by 57%, 42.3%, and 3.8% with
respect to settling time, overshoot and oscillations respectively. When
compared GA based controller the settling time of LFC and AVR is reduced
by 16% and 54.3% respectively. With respect to oscillations and overshoot,
the performance of ACO based controller is found to be very close with GA-
PID controller and can be varied by optimum tuning of regulation. The bar
chart in Figure 5.18 can be used to visually analyse the impact of ACO based
controller for LFC and AVR applications.
166
Figure 5.18 Comparative Analysis of Conventional Controllers with
ACO Based Controller for LFC and AVR
In standard numerical engineering analysis, the CPU time is less
important than the effort of the engineer preparing the data. Therefore, the
contemporary commercial finite element systems do not attach primary
importance to the decrease of the computational time. In optimization
algorithms, it is entirely different, since then the gradually modified solution
must here be repeated even thousand times in the optimization loops. Hence,
the time complexity of different evolutionary algorithms used in the
optimization of PID gains are analyzed. To show the effectiveness of the
ACO and PSO algorithms the mean CPU time taken to generate optimum
parameters for a uniform load of 0.2pu and regulation value of 100 is
considered. The comparison of average computation time or time complexity
of GA, ACO and PSO are shown in Figure 5.19. As it can be seen from the
bar chart, since the PSO does not perform selection and crossover operation it
can save some computation time when compared to GA and ACO.
167
Figure 5.19 Comparative Analysis of Execution Time for Different
Evolutionary Algorithms
5.8 SUMMARY
An efficient and intelligent computation based techniques such as
PSO, and ACO is designed for determining the PID controller parameters for
efficient control of frequency and voltage of the power generating system.
The proposed method is effectively applied to the different optimization
problem of the power system and can converge to produce an optimal
solutions. The premature convergence problems of conventional controllers
are avoided and hence obtain a high quality solution with better
computational efficiency.
The LFC and AVR models with PSO and ACO based controllers
were simulated for different load changes and regulations to validate the
efficiency of the proposed algorithms. From the simulation results it can be
found that the EA based controllers can produce relatively better results with
faster convergence rate and higher precision. As evident from the graphs and
168
empirical results, the suggested algorithms performed well under changing
loads and regulations.
The proposed algorithm attempts to make a judicious use of
exploration and exploitation abilities of the search space and therefore likely
to avoid false and premature convergence. Hence application of these
evolutionary algorithms will lead to the satisfactory performance of the power
generating system. The work can be extended in future by incorporating
advanced hybrid evolutionary algorithms like, Hybrid GA, GA-PSO, Fuzzy
PSO, etc., to optimize the PID gains.
