Prototype Of Fuzzy PID Controller For Load Frequency Control

Based On Hybrid Optimization Algorithm

Avula Vijay Kumar

, G. Pandu Ranga Reddy

Department of Electrical and Electronics Enineering, G. Pulliah College of Engineering. & Technology, Kurnool, Andhra

Pradesh, India

Keywords: Firefly algorithm (FA), Pattern Search, Area Control Error (ACE), Load Frequency Control (LFC), and the

Integral of Time multiplied Absolute Error (ITAE) Algorithm (PSA).

Abstract: Power system consists of large networks linked together which seem to be large and complex in structure. In

connection with the component some factor affects the performance of operation as well stability, the Prime

aim of power system is to meet out requirement of the load demand. For reliable, secure, economic and stable

operation of a power system requires certain control strategies. The Evolution of Artificial Intelligence of

cognitive behaviour paved the way to obtain optimal solution for problems involving imprecise data of nature.

Soft computing algorithms resembling Genetic Algorithm, particle swarm optimization, artificial neural

network, were used for the optimization process. In this proposed work, the pattern search algorithm (PSA)

and firefly algorithm (FA) were used to maintain the operation frequency near the standard desired value. The

controller used in this proposed work is comparing the results with some existing technique. Then the

sensitivity analysis is performed for various load conditions from its nominal value. The proposed work

provides the better solution for handling the nonlinearity systems.

1 INTRODUCTION

In power system network the utility of Load

Frequency Control is to adjust generator output power

within a specify limits with respect to change in

system frequency and tie-line loading. In an inter

connected system with more than regions that are

separately regulated in addition to frequency control,

to maintain the scheduled power interchange, the

generation within each area has to be control. The

control of generation in accordance with variation in

frequency is termed as Load Frequency Control.

Since a power grid requires Monitoring of

Generation matching load demand from time to time.

It is mandatory to regulate and adjust the output of

generators. This power balance match is determined

by measuring the system frequency. The power

generation must be maintained near the sum of load

demand and related losses (Elgerd, 2000). When load

demand is less than generated power the frequency

will increase. In contrast, when the generated power

https://orcid.org/0009-0000-9689-9222

https://orcid.org/0000-0001-9384-0081

is less than load demand the frequency decreases. The

main target is to maintain the frequency as constant

in the predefined value in the Load Frequency

Control (Santhan Kumar Ch, 2022).

Based on the operation of generating units in

response to command inputs (control signals) the

LFC performance is mainly dependent. The operating

characteristics of generating unit depend on operating

point, type of unit, fuel, and control strategy. The

Area Control Error (ACE) (Ibraheem, 2005) is

defined as the control signal is the power variation of

the tie line which is summed up with the frequency

deviation with the inclusion of the bias factor.

Through supplementary feedback to the dynamic

controller, tie-line flow and frequency deviation are

also combined (Vijayan M, 2022). Significant

changes have seen in the designs of LFC to handle

with uncertainties, different load characteristics,

structure change and new systems integration

(Parmar KPS, 2012). In LFC synthesis the most

recent progress is to deal with the using of complex,

nonlinear power system models or application of

Vijay Kumar, A. and Ranga Reddy, G.

Prototype Of Fuzzy PID Controller For Load Frequency Control Based On Hybrid Optimization Algorithm.

DOI: 10.5220/0012506000003808

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 1st International Conference on Intelligent and Sustainable Power and Energy Systems (ISPES 2023), pages 38-44

ISBN: 978-989-758-689-7

modern concepts to the system such as Neural

networks, Fuzzy logic, Multi agent systems, and

evolutionary and Heuristic Optimization techniques

(Ghoshal SP, 2004).

In literature survey, many researchers have done

their works on Load Frequency controller, by using

optimization techniques and tools such as, Genetic

algorithm (GA), Particle Swarm optimization

technique and Artificial Neural Network (ANN) etc.

Each algorithm performs well for controlling the

frequency (Gozde H, 2011). However every new

arrived approach gives improved results than the

existing methodology. Here the proposed work

presents fuzzy PID controller based on the firefly

algorithm and pattern search algorithm. In DE based

PID controller, the DE algorithm determines the gain

of PID controller whereas the PID controller performs

the tuning process for controlling the load frequency

(Sahu RK, 2013). Fuzzy logic controllers have the

ability to analyze the non-linear systems, However it

does not have any specific mathematical formulation

for considering the parameters and selecting the

input, output (C. N. Sai Kalyan, 2022).

The operation of the power grid is dependent on

optimization methods, the controller's structure

objective too. Hence it custom to aid on high

performable heuristic algorithm intend to solve the

real time problems obtaining optimal solutions. The

Firefly algorithm is a type under the heuristic

algorithms and a biologically stimulate Meta heuristic

algorithm proposed by Yang. Firefly algorithm works

on population search and it was stimulate by the

flashing behavior of Fireflies. Firefly algorithm can

solve non-linear Optimization problems in successful

and efficient manner.

In the search process of firefly algorithm a

balance is maintained between the exploitation and

the exploration. Pattern search algorithm is being

integrated along with the firefly algorithm for

achieving good performance. Due to fact that firefly

algorithm explore in search space may not obtain the

better solution because of exploitation. The pattern

search algorithm can exploit in local area search

space may yield better result than firefly algorithm.

Combining the features of two algorithms the best

solution for the system’s objective function has been

arrived. In this paper, the Load Frequency Control is

applicable to multi area power systems and for tuning

the input and output to the PID controller the Firefly

algorithm and the Pattern search algorithm were used.

2 FUZZY PID CONTROLLER

A PID controller calculated the error (a measured

variable's deviation from the expected set point

present on the system). The error can be reduced by

the controller by rearranging the process through

manipulated variable. The parameters involve in the

PID controller and sometimes called three-term-

control is Proportional Gain (Kp), Integral Gain (Ki)

and Derivative Gain (Kd).

Figure 1: TF model for two area system

These parameters are defined in terms of time:

P rely on the present error, I rely on the past error

collection and D is the future error forecast based on

the existing rate of deviation. The process can be

adjusted by weighted sum of these sections through a

control element like damper and the position of a

control valve.

1. Proportional gain can minimize the rise time

and no effect in the steady state error.

2. Integral gain can minimize steady state error but

it weakens the transient response.

3. Derivative gain will increase the system

stability, reduce the overshoot and improve the

transient response.

3 SYSTEM STUDY AND

PROPOSED CONTROLLER

For the design and analysis purpose an interconnected

two area system has taken. The rating of each thermal

plant is 2000MW. Frequency bias parameters are

denoted as B

and B

. Area control errors for both two

systems are denoted as ACE

and ACE

. The

controller output for system1 denoted as u

and u

for

system 2. The speed regulation of governor was

denoted asR

and R

in pu Hz. Time variables are

denoted called TG

and TG

. Time constants for

turbines are denoted asTT

and TT

in sec. Change of

the turbine outputis representing as DPT

and DPT

Change in load demand is representing as DPD

and

DPD

. The change in the tie-line power is represented

Prototype Of Fuzzy PID Controller For Load Frequency Control Based On Hybrid Optimization Algorithm

as DPTie (Saikia LC, 2011). Power system gain and

time constant are denoted as KP

, KP

andTP

, TP

Figure 2: Structure of proposed LFC.

The speed governor dead band is a term used in

speed governor, and it is very small. The non-linearity

of the speed governor is solved by the speed governor

dead band. Generally mechanical frictions, valve

overlaps in relay are some of the factors contributing

governor dead band. This dead band increases the non

linearity of the system and makes the optimization

problem as more complex. The proposed work

mitigates the dead band’s effect on power system and

also improves the performance of system under

consideration.

For controlling the frequency near the operating

point, fuzzy PID controller has used in each area. The

structure is shown in the following figure 2,

The area control error (ACE) induced by the

specific error signal in each area is calculated and fed

as the input.

E1(t) = B1* + ACE1(Change in frequency

1) + Change in Tie Line Power 1

(1)

E2(t) = ACE2+B2*(Change in frequency2)

+ Change in tie line power2

(2)

At this point, the error (E) and the first derivative of

error are fed as the input signal. The fuzzy PID

controller output signals are given as input signal to

the power systems. Tunable parameters (K

)are

input scaling factors. K

, K

are the Proportional

gain, Integral gain and Derivative gain. The

membership function is used with three fuzzy

parameters N(negative), P(positive) and Z(zero), both

the input and the output are used for these. The Fuzzy

Logic Controller (FLC) output is defuzzed using the

Centre of Gravity approach. The rule base for Error,

Derivative Error, and FLC Output is displayed in the

table 1.

Table 1: Rule table for LFC.

Example E’’

4 OBJECTIVE FUNCTION

Based on the concept of recent Heuristic optimization

technique we can design a controller based on this

work. Integral of Time multiplied Absolute Error

(ITAE), Integral of Squared Error (ISE), and Integral

of Time multiplied Squared Error (ITSE) and Integral

of Absolute Error (IAE) are the various performance

criteria for designing a controller. By using the ITAE

criterion we can reduced the settling time and the peak

overshoot. ITSE base controller gives larger controller

output with an unexpected change in the set point

occurs. However the ITAE base controller suits as the

better method for Load Frequency Control,

accordingly ITAE is used as the objective function for

this work, for optimizing the scaling factors, K

, K

and K



    































(3)

The frequency change and the incremental change

in the tie-line power were represented in this objective

function can be given as,

Minimize F

Subject to,





 



 



(4)





 



 



(5)





 



 



(6)

This is the objective function for the proposed

work. K

, K

and K

are the Proportional, Integral and

Derivative gain.

5 FIREFLY ALGORITHM

Firefly algorithm is a Heuristic mathematical

optimization for solving the optimization problems.

The algorithm works on the flashing behavior of the

Fireflies. The scientific reason behind the flashing

behavior of the Firefly is that it contains some organic

compounds named as lucifer in. Whenever the air

enters into the abdomen, it reacts with the luciferin and

emits light. This luciferin is a chemical compound

which emits the light. Based on this flashing behavior

and with the following assumptions the firefly

algorithm has derived. The assumptions are,

1. All fireflies are unisexual; they attract others

and get attracted by others.

2. The brightness defines the degree of

attractiveness. The brightness and distance

are directly proportional to each other. The

firefly is attracted by another one which has

more brightness that means a nearby firefly.

ISPES 2023 - International Conference on Intelligent and Sustainable Power and Energy Systems

3. If no other firefly has more brightness than

the given one, in the search space it will

move randomly.

Two factors are defined for the optimization using

firefly algorithm and they are the light intensity

variation and attractiveness. Attractiveness is

determined using the objective function's

measurement of the firefly's brightness. Brightness is

the problem's objective function right now.

The light intensity is given as,









 







(7)

Where,

I(r) represent the light intensity at distance r.

 is a light absorption co efficient

The attractiveness of the firefly can be given as,

  









(8)

Where 



the attractiveness at the distance r=0.

Euclidean Distance is defined as the distance between

two fireflies. The search space possesses ‘n’ no of

fireflies. Every firefly participates in the optimization

problem. At any instant of time, the ith firefly is

attracted by jth firefly and the distance can be

calculated as,





 



 





(9)

rij= distance between the ith and jth firefly.

The ith firefly is in search of the jth firefly to

attract it. The ith firefly moves randomly to the firefly

sj which has more brightness. This searching process

is done by random selection at particular time

intervals. From this time it achieves the maximum no

of iterations, and the best solution will be obtained by

the objective function whether maximum or

minimum.

The moment speed can be written as,























 



  



(10)

Where,  is the randomization parameter,





is the random generated number.

Various steps involved in the FA algorithm is,

Step1: Generation of initial population of the

fireflies.

Step2: Evaluation of fitness for all fireflies from

the objective function.

Step3: Update the fitness value of firefly.

Step4: Rank and update the firefly and its position.

Step5: Check for maximum no of iteration.

Step6: Optimal result for the objective function.

6 PATTERN SEARCH

ALGORITHM:

This algorithm is very Lucid and derivative-free

optimization algorithm used for solving a variety of

optimization problems. In some cases, it performs

better than the standard optimization algorithms. The

algorithm is initiated with the initial point or position.

And it adds the nearby points to it to form a mesh. The

initial points are added to it by the constraints. Then

this current point adds the scalar multiple of a set of

the vector, which is called as the pattern. The point in

the mesh, which has the improved objective function,

then it is marked and used as the recent point for the

next iteration (Ali ES, 2011).

Initially, it chooses a point from the search space

and set it as the optimum solution. Then it moves right,

left, up and bottom to search the points. If the objective

function is applicable for minimization problem it

chooses the point which has the minimum value. Then

again it searches the points around it and compares

with the current optimum point. The solution obtained

is less than the current point, then it moves to it and

fixes it as the optimum point. This process will

continue till the surround points are greater than the

current optimum point. The process repeats till we turn

up the optimum best solution. The initial point is set

as the X and it assumed as the current optimum point.

It takes the points around it and form a mesh. Then it

measures the value of every point in the mesh. As

shown in figure it goes for the position like, X[1,0],

X[-1,0],X[0,1] and X[0,-1]. These points possesses

some values belongs to it. Based on the objective

function, the new optimum point has been selected. If

the objective function is maximization, then the point

which has the maximum value on the mesh will be

taken as the new optimum point for the next iteration.

If the objective function is minimization, the

minimum value will be selected. This process will be

repeated till get the global optimum solution.

Figure 3: Pattern search algorithm.

Prototype Of Fuzzy PID Controller For Load Frequency Control Based On Hybrid Optimization Algorithm

7 HYBRIDIZATION OF FA AND

PS ALGORITHM

The objective function is to minimize F (i.e. Integral

of Time multiplied Absolute Error, ITAE).

The firefly algorithm is used for obtaining the

initial point for Pattern Search algorithm. This current

point is denoted as N. The size of mesh is 1 for the first

iteration, and the pattern has formed as [1, 0], [-1, 0],

[0, 1] and [0,-1]. For calculating the mesh points like,

N0+[1,0], N0+[-1,0], N0+[0,1], and N0+[0,-1] for the

current point these vectors are added. After computing

the mesh points, the algorithm find out the objective

function values. When the objective function value of

N0 is greater than mesh point the iteration is

successful and the new objective function is set on the.

Figure 4: Flow chart of proposed algorithm.

small mesh point and named it as N1. After this first

iteration the process will continue for the second

iteration and the mesh size is increased to 2 and called

as the expansion factor. The values of the mesh points

in iteration 2 are N1+2*[1, 0], N1+2*[-1, 0], N1+2*[0,

1], and N1+2*[0, -1]. This process will be repeated

until achieve the global optimum point

8 SIMULATION:

The transfer function of each area is represented as the

Simulink model in the MATLAB. The fuzzy logic

PID controller has designed by using the firefly

algorithm and the pattern search algorithm. Fuzzy

controllers are designed for each area. When applying

1% load change in the area 1 then the frequency

associated with this area will disturb. The FA

algorithm works on it and brings that back to its

standard value. The curve has plotted for this using FA

and compares with the DE and PSO fuzzy controllers’

waveform. The MATLAB Simulink model is shown

in figure 5.

For the optimum solution with the minimum no of

iteration, the no of fireflies and maximum generation

must be defined exactly. The no of iteration is directly

proportional to the no of fireflies. The effect of firefly

algorithm, hybrid firefly algorithm and pattern search

algorithm were compared with no of iterations and the

hybrid algorithm takes less no of iterations to achieve

the best solution. This shows in following figures 6-9.

Table 1: PERFORMANCE COMPARISON FOR

VARIOUS TECHNIQUES

Various

Optimizatio

Techniques

Errors

Settling Time

deviations

ISE

ITSE

IAE









1. .

PSO

algorithm

based FLC

4.38

x10

7.983

x103

.57

.207

9.6

10.

13.1

optimizatio

n algorithm

based FLC

0.13

x10

0.079

x10

.05

.027

5.1

5.5

8.67

algorithm

based FLC

0.35

x10

0.279

x10

.03

.016

4.1

5.6

4.23

New

Hybrid FA

& PS

algorithm

based FLC

0.28

x10

0.134

x10

.01

.012

2.2

3.8

3.00

ISPES 2023 - International Conference on Intelligent and Sustainable Power and Energy Systems

Figure 5: Simulation Model for three area system

Figure 6: Convergence of FA and proposed Method

Figure 7: Frequency deviation for 1% change in area-1

Figure 8: Frequency deviation for 1% change in area-2

Figure 9: Tieline power deviation for 1%change area-1

9 RESULT

The performance for this submitted work is

compared with the recent optimization techniques

such as, Differential Evolution (DE) algorithm and

Particle Swarm Optimisation (PSO) algorithm. The

Firefly algorithm obtains the minimum errors for the

interconnected system as compared to other

techniques. The hybridization of firefly and pattern

search algorithms further reduces the errors as

compared to Firefly algorithm. The proposed work

performs better in terms of minimum setting time,

power deviations, and accuracy.

10 CONCLUSION

By integrating two optimisation algorithms, a novel

optimisation technique has been suggested. The

firefly and pattern search methods are both quite

straightforward and successfully used. The global

exploration and pattern search capabilities of the

Firefly algorithm are superior for greater local

exploitation. Due to reality if they are operated alone

firefly algorithm is poor in local exploitation and

pattern search is poor in global exploration.

Incorporating the prominent attribute from these two

algorithms satisfactory methodology has been

obtained for best optimal solution. In this paper the

comparison is made between individual FA

algorithm, Particle Swarm optimization algorithm,

Differential Evolution Optimization technique and

hybrid FA and PS algorithm and represented. Amid

this all performance the proposed hybrid approach

achieves the best optimization solution.

Prototype Of Fuzzy PID Controller For Load Frequency Control Based On Hybrid Optimization Algorithm

REFERENCES

Elgerd OI. Electric energy systems theory – an introduction.

2nd ed. New Delhi: Tata McGraw Hill; 2000.

Santhan Kumar Ch, N. Karuppiah, B. Praveen Kumar, S.

Shitharth, B. Dasu, "Improvement of the Resilience of

a Microgrid Using Fragility Modeling and

Simulation", Journal of Electrical and Computer

Engineering, vol. 2022, Article ID 3074298, 12 pages,

2022. https://doi.org/10.1155/2022/3074298.

Ibraheem, Kumar P, Kothari DP. Recent philosophies of

automatic generation control strategies in power

systems. IEEE Trans Power Syst 2005;20:346–57.

Vijayan M, Udumula RR, Mahto T, Lokeshgupta B, Goud

BS, Kalyan CNS, Balachandran PK, C D, Padmanaban

S, Twala B. Optimal PI-Controller-Based Hybrid

Energy Storage System in DC

Microgrid. Sustainability. 2022; 14(22):14666.

https://doi.org/10.3390/su142214666.

Parmar KPS, Majhi S, Kothari DP. Load frequency control

of a realistic power system with multi-source power

generation. Int J Elect Power Energy Syst2012;42:426–

33.

Ghoshal SP. Application of GA/GA–SA based fuzzy

automatic generation control of a multi area thermal

generating system. ElectrPower Syst Res 2004;70:115–

27.

Gozde H, Taplamacioglu MC. Automatic generation

control application with craziness based particle swarm

optimization in a thermal power system. IntJ Elect

Power Energy Syst 2011;33:8–16.

Sahu RK, Panda S, Rout UK. DE optimized parallel 2-DOF

PID controller for load frequency control of power

system with governor dead-band nonlinearity. IntJ

Elect Power Energy Syst 2013;49:19–33.

C. N. Sai Kalyan, B. Srikanth Goud, H. Kishan, P.

Ramineni, B. P. Kumar and T. Anil Kumar, "Donkey

and Smuggler Optimization Algorithm-based Degree of

Freedom Controller for Stability of Two Area Power

System with AC-DC Links," 2022 IEEE 7th

International Conference on Recent Advances and

Innovations in Engineering (ICRAIE), MANGALORE,

India, 2022, pp. 461-466, doi:

10.1109/ICRAIE56454.2022.10054318.

Saikia LC, Mishra S, Sinha N, Nanda J. Automatic

generation control of a multi area hydrothermal system

using reinforced learning neural network controller. Int

J Elect Power Energy Syst 2011;33(4):1101–8.

Ali ES, Abd-Elazim SM. Bacteria foraging optimization

algorithm based load frequency controller for

interconnected power system. Int J Electr Power.

ISPES 2023 - International Conference on Intelligent and Sustainable Power and Energy Systems