Design and Analysis of Hybrid PSO-GA-FA Technique for Load ... · mentioned methods over PSO, GA...

Vol. 9(33), Jul. 2019, PP. 4287-4301

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Article History: Received Date: Jan. 09, 2018 Accepted Date: May. 16, 2019 Available Online: Jul. 01, 2019

Design and Analysis of Hybrid PSO-GA-FA Technique for Load Frequency

Control of Two-Area Power System

Hatef Farshi

Department of Electrical Engineering, Mohaghegh Ardabili University, Ardabil, Iran

Phone Number: +98-4532526170

*Corresponding Author's E-mail: [email protected]

Abstract

he Load Frequency Control (LFC) or Automatic Generation Control (AGC) is one of the

substantial parts in power system design, automation, operation and stability. In this paper, the

new hybrid technique are proposed in which Particle Swarm Optimization, Genetic Algorithm

and Firefly Algorithm (named hPSO-GA-FA) are combined to obtain the parameters of Two Degree of

Freedom PID (2DOF-PID) controllers for LFC problem of two-area hydrothermal power system. The

objective function used in this paper is combination of IAE, ISE, ITAE and ITSE. The responses of

mentioned approach are compared with Teaching-Learning-Based Optimization (TLBO) based 2DOF-

PID and Artificial Neural Network (ANN) Controllers. The simulation results in some scenarios show

that proposed hPSO-GA-FA based 2DOF-PID controller achieves better responses in comparison with

TLBO and ANN.

Keywords: Load Frequency Control, 2DOF-PID Controller, Hybrid PSO-GA-FA, Teaching-Learning-

Based Optimization, Artificial Neural Network

1. Introduction

The successful operation of interconnected power systems needs matching the total generation

with the total load demand and with the associated system losses. By passing time, the operating point

of a power system may face some changes, and hence, systems may experience deviations in system's

nominal frequency and scheduled power exchanges to other interconnected areas, which may yield

undesirable impacts on power system [10]. Therefore, the control strategy is needed to overcome

these kinds of problems. LFC is one of the most important issues in electric power system design,

stability, automation and operation for supplying sufficient and reliable electric power with good

quality. The main purposes of LFC for a power system are generally as follows:

Maintaining frequency in its nominal value or within predetermined limits.

Maintaining the transferred power between the areas at prescribed levels.

Maintaining each unit generation in the best possible economic value.

Obtaining acceptable overshoot, undershoot and settling time on the frequency and tie line

power deviations [10],[8].

The researchers all over the world are trying to introduce several control strategies for LFC of power

systems in order to restore the system frequency and tie line power to their scheduled values or close

T

mailto:[email protected]

Hatef Farshi / Vol. 9(33), Jul. 2019, PP. 4287-4301

4288

International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)

Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543

to them in the fastest possible time during load perturbations. Some state-of-the-art survey and review

articles on the LFC of power systems has been presented in [10], [18] where various control strategies

concerning LFC problem have been studied. Moreover, there are many research articles attempting to

propose better control methods for LFC systems based on Artificial Neural Network (ANN) [9], [7], fuzzy

logic theory [2], reinforcement learning [13] and Adaptive Neuro-Fuzzy Inference System (ANFIS)

approach [20].

Various Artificial Intelligence (AI) techniques have been proposed for LFC problem to improve the

performance of a power system. Some of these approaches include Imperialist Competitive Algorithm

(ICA) [8], Firefly Algorithm (FA) [12], Differential Evolution (DE) [1], Artificial Bee Colony (ABC) [6],

Quasi-Oppositional Grey Wolf Optimization Algorithm (QOGWOA) [3], Teaching Learning Based

Optimization Algorithm (TLBO) [17], Cuckoo Search Algorithm (CSA) [15], Elephant Herding

Optimization (EHO) [4] and so on.

In addition to the above examples, there are also hybrid algorithms used to LFC problem such as

[16], in which hybrid Firefly Algorithm and Pattern Search (hFA-PS) technique is used to optimize PID

parameters for AGC of multi-area interconnected power systems and the results prove that the

proposed hFA–PS algorithm provide better performance compared to some techniques such as BFOA

and GA for the same interconnected power system. Also, in [19], hybrid Bacteria Foraging Optimization

Algorithm-Particle Swarm Optimization (hBFOA–PSO) method is applied to obtain the PI controller

parameters of a two-area interconnected power system and the results indicate the superiority of

mentioned methods over PSO, GA and BFOA.

As mentioned, there are many articles in the area of LFC problems using AI algorithms specially

tuning of PID controller parameters but it is better to use the advantages and features of several

algorithms, by combining them, instead of just one algorithm. So, the hybrid PSO-GA-FA algorithm is

used to optimize the 2DOF-PID controllers' parameters for two-area interconnected power system in

this paper. The mentioned method is applied for this controller by the objective function, which is the

sum of IAE, ISE, ITAE and ITSE (it will be explained in section 3.2), and their results are compared with

TLBO based 2DOF-PID and Multi-Layer Perceptron ANN (MLP-ANN) controllers.

2. Investigated LFC model

Generally, power system consists of number of subsystems interconnected through tie lines. The

investigated LFC system, in this paper, consists of two hydro-thermal areas. Area 1 is a thermal unit

and area 2 is a hydro unit. The thermal unit of investigated power system consists of governor and

steam turbine with reheater. Hydro area includes electric governor and hydro turbine. The dynamic

model of two-area interconnected power system is shown in Figure 1.

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Figure 1: Two-area hydrothermal power system.

3. Control System

3.1. 2DOF-PID controller

The number of closed loop transfer functions that can be adjusted independently is defined as the

degree of freedom for a control system. The 2DOF-PID controller provides an output signal based on

the difference between a reference signal and a measured output of the system. This controller

computes a weighted difference signal for each of the proportional, integral, and derivative actions

according to the certain set point weights. The output of the controller is sum of the proportional,

integral, and derivative actions. Each action is weighted according to the selected gain parameters. A

derivative filter is used to improve performance when there is random error or noise in the measured

process variables. The derivative filter is employed to limit the large controller output shifts that

derivative action causes as a result of measurement noise.

Also, derivative filter can help to decrease the constant controller output fluctuations which can

lead to wear in the final control element. Obviously the above reasons show that two degree of

freedom control system has advantages over conventional single degree of freedom control system

[15]. The control system of a parallel 2DOF-PID controller is shown in Figure 2 where R(s), Y(s) and U(s)

are reference signal, feedback from measured output of the system and output signal, respectively.

For a 2DOF-PID controller, C(s) and F(s) are given by Equations (4) and (5) respectively.

Figure 2: 2DOF-PID controller model.



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(1)

(2)

where kp, ki, kd, b, c and N are the proportional gain, integral gain, derivative gain, proportional set

point weight, derivative set point weight and derivative filter coefficient respectively. The structure

of a parallel 2DOF-PID controller is shown in Figure 3.

Figure 3: Structure of a parallel 2DOF-PID controller.

3.2. Objective function

In this paper, the objective function (J) is sum of Integral Absolute Error (IAE), Integral Square Error

(ISE), Integral Time Absolute Error (ITAE) and Integral Time Square Error (ITSE). The mentioned

objective function is given as follows:



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ΔP, Δf and ACE are tie-line power deviation, frequency deviation and area control error.

3.3. hPSO-GA-FA based 2DOF-PID controller

PSO is a population based optimization technique based on intelligent scheme, proposed and

developed by Kennedy and Eberhart in 1995, inspired by the social behaviour of bird flocking or fish

schooling. In this algorithm, there are a number of birds called particles. PSO is initialized with a group

of random particles and then searches for optimal value by updating each generation. All particles

have not only fitness values which are evaluated by the objective function to be optimized, but also

velocities which direct the flying of the particles. The particles fly through the search space by following

the particles with the best solutions ever found [11].

GA is a global search technique for solving optimization problems, which is based on the theory of

natural selection, proposed by Holland in 1975. It is a repetitive search procedure that operates on a

set of strings called chromosomes. The implementation of this algorithm is briefly listed in the

following process [11]:

Initialize the chromosome strings of population.

Decode the strings and assess them.

Choose the best strings.



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Copy the best strings and paste them on the non-selected strings.

Combine and develop it to generate off strings.

Update the genetic cycle and stop the process.

FA is a population-based algorithm developed by Yang in 2008. In this algorithm, fireflies are

characterized by their flashing light which produced by their body's biochemical process. The flashing

light may serve as the main courtship signals for mating. It is based on the following three idealized

behaviours of the fireflies flashing characteristics [14]:

All fireflies are unisex and attracted to other fireflies regardless of their gender.

The firefly's degree of attractiveness is proportional to its brightness (light intensity). So, for any

two flashing fireflies, less bright firefly moves toward the brighter one. More brightness means

less distance between two fireflies because brightness is proportional to distance. If any two

flashing fireflies have the same brightness, then they move randomly.

The brightness of a firefly is determined by the objective function.

For proper design of FA, two important issues need to be defined: the variation of light intensity (I)

and the formulation of attractiveness ( ). The attractiveness of a firefly is determined by its light

intensity or brightness and the brightness is associated with the objective function. The light intensity

I(r) varies with the distance (r) monotonically and exponentially as:

(14)

where I0 is the original light intensity and is the light absorption coefficient. Because the firefly’s

attractiveness is proportional to the light intensity, the attractiveness (β) of a firefly is defined as:

(15)

where is the attractiveness at r=0.

The distance between two fireflies (si and sj) is expressed as:

(16)

where n denotes the dimensionality of the problem.

The movement of fireflies is expressed as below:

(17)

This equation consists of three parts: the current position of ith firefly (Si), attraction to another more

attractive firefly , and a random walk (αεi) which consists of a randomization parameter

(α) and the random generated number (ε). It should be noted that , β and ϒ are generally chosen in the

range 0–1. In summary, FA is controlled by these three parameters: α, β, and γ. According to the

parameter setting, each implementation of FA distinguishes two asymptotic behaviours. First, if γ→0,

the attractiveness becomes β=β0. So, within the search space the attractiveness is constant. Second,

if γ→∞, falls out from Equation (17), and the firefly movement becomes a random

walk [16], [19]. Generally, the random nature of GA operators makes this algorithm sensitive to initial



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population. This dependence to initial population is the reason that GA may not converge properly if

the initial population is not well chosen. On the other hand, PSO is not as sensitive as GA to initial

population and it has been indicated that PSO converge rapidly during the initial stages of a global

search, but around global optimum, the search process will become very slow. One of the features of

PSO is its fast convergence towards global optima in the early stage of the search and its slow

convergence near the global optima [11].

FA can find the global optima as well as all the local optima simultaneously in a very effective

manner. A further advantage of FA is that different fireflies will work almost independently; it is thus

particularly suitable for parallel implementation. Furthermore, fireflies aggregate more closely around

each optimum and the interactions between different sub-regions are minimal in parallel

implementations.

Therefore, FA can overcome both GA and PSO deficiencies [12], [14]. In this paper, the idea is the

combination of FA, PSO and GA, to overcome the mentioned algorithms' problems and obtain better

dynamic responses. It could be noted that the hPSO-GAFA results are obtained in lower iteration than

FA, PSO and GA and, thus, this hybrid algorithm could be used for many optimization problems.

In the first step of solving the optimization problem, objective function, variables and each

algorithm's parameters are defined. The objective function values are evaluated in MATLAB/SIMULINK

model and moved to main PSO program through workspace. Then PSO algorithm will create an initial

population and particles value is determined by objective function and rank of particles as well as best

one is recorded.

This process searches for optima by updating generation, velocity and position until the stopping

criteria is met or iteration finished. When the evaluation and iteration of PSO finished, the GA starts

to work and continues to solve the optimization problem step by step; population selection, crossover

and mutation. Afterwards, FA begins its process by evaluation of fireflies' light intensities and update

them till the iteration finished.

The hPSO-GA-FA flowchart is shown in Figure 4. The values of hPSO-GA-FA parameters are set

accordingly; Population size=100, hPSO-GA-FA Iteration=100, PSO sub-iteration=10, GA sub-

iteration=10, FA sub-iteration=10, Parents (off springs) Ratio=0.7, Mutants Population size Ratio=0.2,

PSO parameter (C1 and C2)=1.5, PSO momentum or inertia=0.73, α=0.5, β=0.2, γ=0.5. The proposed

hPSO-GA-FA will optimize the parameters of 2DOF-PID controllers with the mentioned objective

functions.



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Figure 4: hPSO-GA-FA flowchart.

3.4. TLBO based 2DOF-PID controller

The TLBO algorithm is an algorithm proposed by Rao and et al. (2011, 2012) based on the effect of

influence of a teacher on the output of learners in a class. The algorithm describes two basic modes of

the learning [17]:

through teacher (known as teacher phase)

through interaction with the other learners (known as learner phase)

In this optimization algorithm, a group of learners is considered as population and different subjects

offered to the learners are considered as different design variables of the optimization problem. The

best solution in the entire population is considered as the teacher. The design variables are actually

the parameters involved in the objective function of the given optimization problem and the best

solution is the best value of the objective function.

As mentioned, TLBO is divided into two parts; teacher phase and learner phase.

In teacher phase, it is assumed that a good teacher brings his or her learners up to his or her level in

terms of knowledge. But this is impossible, in practice, and a teacher can only move the mean of a

class up depending on the potency of the class.



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In learner phase, learners increase their knowledge by two different means; through input from the teacher and through interaction between themselves. A learner interacts randomly with other learners by discussions, presentations, formal

communications, etc. A learner learns something new if the other learner has more knowledge

optimize the parameters of 2DOF-PID with the objective functions expressed in Equation (13). Unlike

other optimization techniques, TLBO does not require any algorithm parameters to be tuned, thus

making its implementation simpler.

3.5. ANN controller

The ability of human brain to control complex systems has encouraged researchers to model the

human nervous system. So, artificial neural networks are used in various scientific and industrial

branches, especially the design of controllers due to their unique capability to learn any type of

nonlinear system. An ANN consists of a number of nonlinear elements which are arranged in three

layers; Input layer, Hidden layer and Output Layer. Each layer usually contains several neurons and the

output of each neuron is usually the inputs of the next layer neurons. The input layer receives the input

signals, and then these signals propagate layer-to-layer through the network in order to apply the

investigated system.

Figure 5: TLBO flowchart.



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The mathematical model of the neuron that represents the basic elements of an ANN is shown in

Figure 6. It consists of three fundamental elements; weight (W), bias factor (θ) and activation

function (f). The neural network output (y) is given below [5]:

Figure 6: The mathematical model of a neuron.

In this paper, the multi-layer perceptron artificial neural network (MLP-ANN) controller is also used

for the investigated two-area power system. Since the purposes of LFC controller design in an

interconnected power system are damping of the frequency and tie-line power deviations in such a

way to minimize transient oscillation under the different load conditions [9]. Thus, frequency

deviations (Δf) and area control error (ACE) are chosen as the MLP-ANN inputs. The outputs of the

neural network are the control signals, which are applied to the governors in each area. Figure 7 shows

the block diagram of the MLP-ANN controller in each area. It means that an ANN controller is placed

in each area of the system. As seen in the Figure 7, ACE and ΔF of each area are entered into the MLP-

ANN, and then, by performing the neural network process, the control signal u is exited from the

controller and applied to the system.

Figure 7: The block diagram of MLP-ANN controller in each area.

Mentioned MLP-ANN is a three-layer perceptron with two inputs, 11 neurons in the hidden layer, and

one output. The activation functions used in hidden and output layers are tansig and purelin,

respectively. The proposed network has been trained by using Levenberg-Marquardt algorithm. The

root mean square (RMS) error criterion is being used to evaluate the learning performance. Learning

algorithms cause the adjustment of the weights so that the controlled system gives the desired

response [9]. The schematic of this three-layer perceptron neural network with a hidden layer is shown

in Figure 8.



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Figure 8: The schematic of 3-layer perceptron neural network.

4. Results and analysis

In this paper, three controllers are applied to LFC problem of two-area interconnected hydrothermal

power system; hPSO-GA-FA based 2DOF-PID, TLBO based 2DOF-PID and MLP-ANN controllers. The

controllers used in each area are similar. Two scenarios are used as follows:

first scenario: 1% step load perturbation (SLP) in both thermal and hydro area

second scenario: 10% SLP in thermal area and 15% SLP in hydro area

The dynamic responses of frequency and tie-line power deviation by these three controllers for

two mentioned scenarios are shown in Figures 9, 10, 11, 12, 13 and 14 and they are compared with

each other. Also, 2DOF-PID parameters obtained by hPSO-GA-FA and TLBO are shown in Table 1and

detailed information for frequency and tie-line power deviation is shown in Table 2.

Figure 9: Δf1 in first scenario

Figure 10: Δf2 in first scenario.



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Figure 11: ΔP12 in first scenario

Figure 12: Δf1 in second scenario.

Figure 13: Δf2 in second scenario.

Figure 14: ΔP12 in second scenario.



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Table 1: 2DOF-PID controllers' parameters.

Table 2: Detailed information for three controllers.

The above table shows the settling time improvement (by percent) for frequency and tie-line power

deviation of hPSO-GA-FA based 2DOF-PID in comparison with two other controllers. So, it could be

concluded that the proposed hybrid algorithm performs better than TLBO based 2DOF-PID and ANN

controllers.

Conclusion

In this paper, 2DOF-PID and ANN controllers have employed for LFC of two-area interconnected

hydro-thermal power system. Accordingly, LFC model has first simulated in MATLAB/SIMULINK and

the parameters of 2DOF-PID controller have determined by two metaheuristic algorithms; hPSO-GAFA

and TLBO. Then, MLP-ANN controller has also applied in this system. Finally, the three controllers'

results with two different SLP scenarios have compared with each other. Consequently, it has shown

in results and analysis section that hPSO-GA-FA based 2DOF-PID controller has superiority in

comparison with TLBO based 2DOF-PID and MLP-ANN controllers.



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Appendix f=Nominal system frequency=60Hz, R=Governor speed regulation parameter=2.4Hz/p.u. MW,

Tg=Steam governor time constant=0.08s, Kr=Steam turbine reheat constant=0.5, Tr=Steam turbine

reheat time constant=10s, Tt=Steam turbine time constant=0.3s, B= Frequency bias factor=0.424,

TP=Power system time constant=20s, Tw=Water starting time=1s, KP=Power system gain=120Hz/p.u.

MW, Kd=Electric governor derivative gain=4, Kp=Electric governor proportional gain=1, Ki=Electric

governor integral gain=5, a12=Ratio between the base values of two area=-1, T12=Synchronizing

coefficient=0.086p.u. MW/radians.

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Author

Hatef Farshi was born in Meshkin Shahr, Iran, 1990. He received the B.Sc. of electrical engineering from Islamic Azad University-Ardabil Branch in 2013 and M.Sc. degree of electrical engineering from Mohaghegh Ardabili University in 2016. His research interests include application of artificial intelligence in power systems, power system dynamics, renewable energy and distributed generation.

Email: [email protected] Phone Number: +98-4532526170


mailto:[email protected]

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