Bio Inspired Algorithms in PID Controller Optimization pdf pdf

  

Bio-Inspired

Algorithms in

PID Controller

Optimization

  

Intelligent Signal Processing

and Data Analysis

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Nilanjan Dey

  Department of Information Technology Techno India College of Technology

  Kolkata, India

  

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Bio-Inspired Algorithms in PID Controller Optimization

Jagatheesan Kaliannan, Anand Baskaran,

  

Nilanjan Dey and Amira S. Ashour

  

Bio-Inspired

Algorithms in

PID Controller

Optimization

  

Jagatheesan Kaliannan

Anand Baskaran

Nilanjan Dey

Amira S. Ashour

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Library of Congress Cataloging-in-Publication Data

Names: Kaliannan, Jagatheesan, author. | Baskaran, Anand, author. | Dey, Nilanjan, 1984- author. | Ashour, Amira, 1975- author. Title: Bio-inspired algorithms in PID controller optimization / Jagatheesan Kaliannan, Anand Baskaran, Nilanjan Dey, and Amira S. Ashour. Description: First edition. | Boca Raton, FL : CRC/Taylor & Francis Group, 2018. | Series: Intelligent signal processing and data analysis | “A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc.” | Includes bibliographical references and index.

Identifiers: LCCN 2018014060| ISBN 9781138598164 (hardback : acid-free paper)

| ISBN 9780429486579 (ebook) Subjects: LCSH: Interconnected electric utility systems--Automation. | Electric power systems--Load dispatching--Mathematics. | Mathematical optimization. | Nature-inspired algorithms. | Cogeneration of electric power and heat. | PID controllers. Classification: LCC TK1007 .K35 2018 | DDC 621.319/1--dc23 LC record available a

  v Contents Preface, vii Book Objectives, ix Authors, xi C HAPTER

  2.1 INVESTIGATED THERMAL POWER SYSTEM

  2.4.1 Response of System with and without Load Demand

  17

  2.4 RESULTS AND ANALYSIS

  2.3 BIOGEOGRAPHY-BASED OPTIMIZATION TECHNIQUE 15

  2.2 CONTROLLER DESIGN AND OBJECTIVE FUNCTION 14

  12

  2 _◾ Load Frequency Control of Single Area Thermal Power System with Biogeography-Based Optimization Technique 11

  1 _◾ Introduction 1

  6 C HAPTER

  1.3 LITERATURE SURVEY

  4

  1.2 BIO-INSPIRED OPTIMIZATION ALGORITHMS

  3

  1.1 LOAD FREQUENCY CONTROL AND AUTOMATIC GENERATION CONTROL

  18

  2.4.2 System Response with Different BIAs Tuned PID Controller

  19 _HAPTER

  2.5 CONCLUSION

  21 C

  3 _◾

Automatic Generation Control

with Superconducting Magnetic

Energy Storage Unit and Ant Colony Optimization-PID Controller in Multiarea Interconnected Thermal Power System

  23

  3.1 SYSTEM UNDER STUDY

  24

  3.2 SUPERCONDUCTING MAGNETIC ENERGY STORAGE (SMES) UNIT

  26

  3.3 PID CONTROLLER DESIGN

  28

  3.4 ANT COLONY OPTIMIZATION

  30

  3.5 SIMULATION RESULTS AND DISCUSSION

  31 _HAPTER

  3.6 CONCLUSION

  38 C

  4 _◾ Flower Pollination Algorithm Optimized

PID Controller for Performance

Improvement of Multiarea Interconnected Thermal Power System with Nonlinearities 41

  4.1 SYSTEM INVESTIGATED

  42

  4.2 CONTROLLER DESIGN AND OBJECTIVE FUNCTION 43

  4.3 FLOWER POLLINATION ALGORITHM (FPA)

  46

  4.4 SIMULATION RESULT AND ANALYSIS

  48 _HAPTER

  4.5 CONCLUSION

  56 C

  57 REFERENCES, 59

  5 _◾ Challenges and Future Perspectives

  INDEX, 71

  Preface

  Nowadays, interconnection of different power-generating systems has increased due to the enormous amount of technical growth, industrial development, and modern technologies to satisfy load demand. The automatic generation control (AGC) in power sys- tems handles the sudden load demand and the delivering of stipu- lated power with good quality in a sudden and continuously varied load period. Stability of standalone power systems and the power quality are affected during the sudden load disturbance. In order to overcome these issues, proper design of power systems and suitable controller modeling is crucial when nonlinearities and boiler dynamics component effects are incorporated in the sys- tem. Load frequency control (LFC) has a substantial role in elec- tric power systems with interconnected areas. Reliable maneuver of the power system necessitates the power balance between the system-associated losses and the total load demand of the power generation. Thus, the LFC is used in the power system to keep the frequency and tie-line power flow of the system within the limit during sudden load disturbance.

  The main problem in the interconnected power system is reduc- ing the damping oscillations in the system frequency; thus, the tie-line power flow deviations should be kept within the limit dur- ing sudden load demand. When damping oscillations exist in the system response for a long period of time without any adequate controller, it affects the system operation and quality of delivered power supply. To provide good quality power and stable power

  vii system operation, extensive research work has been carried out and proposed in the last few decades. Due to the massive devel- opment in industries and technology, the load demand value is changeable and cannot be predicted as it varies randomly.

  Several efforts are carried out based on effective optimization methods to realize numerous benefits and purposes for a power system’s operation control. Researchers have conducted differ- ent studies to solve the optimization problems to optimize the power system secondary controller parameters. Differential evo- lution (DE), particle swarm optimization (PSO), firefly algorithm (FA), genetic algorithm (GA), and ant colony optimization (ACO) are examples of optimization algorithms that can be included to design PID controller parameters for effective operation of a thermal power system. In the power systems, the proportional– integral (PI) and proportional–integral–derivative (PID) control- lers are used as secondary controllers. Consequently, this book includes different applications of the optimization techniques to design the PID controller for LFC of single area as well as multi- area interconnected thermal power systems with and without incorporating nonlinearities and boiler dynamics effects.

  Jagatheesan Kaliannan, PhD Anand Baskaran, PhD Nilanjan Dey, PhD Amira S. Ashour, PhD Book Objectives

  Single area and multiarea power generating system responses are affected during emergency load disturbance conditions, and the power system has more nonlinear components, such as the governor dead band (GDB) and generation rate constraint (GRC) nonlinearities. In order to get desired performance in the power system, all nonlinear component effects are incorporated during optimization of the controller gain values. Therefore, optimiza- tion techniques based on bio-inspired algorithms (BIAs) are implemented to tune PID controller gain values and it is consid- ered as secondary controller during emergency load conditions in the power system. The primary objectives of this book are as follows: _®

• To propose the clear Simulink model of the single area and multiarea interconnected thermal power system by consid- ering nonlinearities and boiler dynamics effects in power systems.
• To discuss and propose a bio-inspired algorithm–based optimization technique to tune the gain value of the PID controller in single area as well as multiarea interconnected thermal power systems.
• To evaluate the performance of the proposed BIA’s tuned controller by comparing other optimization techniques’ optimized controller performance in the same system.

  ix

   Authors

Jagatheesan Kaliannan, PhD, is currently associated with the

  Department of Electrical and Electronics Engineering, Paavai Engineering College, Namakkal, India. He received his BE degree in electrical and electronics engineering in 2009 from Hindusthan College of Engineering and Technology, Coimbatore, Tamil Nadu, India, and his ME degree in applied electronics in 2012 from Paavai College of Engineering, Namakkal, Tamil Nadu, India. He completed his PhD in information and communica- tion engineering in 2017 from Anna University Chennai, India.

  His research interests include optimization techniques, advanced control systems, electrical machines, and power system modeling and control. He has published more than 35 papers in national and international journals and conference proceedings, and more than 5 book chapters in reputed books. He is an associate member of UACEE; member of SCIEI, IACSIT, IAENG, and ISRD; and graduate student member of IEEE.

  

Anand Baskaran, PhD, received his BE in electrical and electron-

  ics engineering in 2001 from Government College of Engineering, Tirunelveli, India; ME in power systems engineering from Annamalai University in 2002; and PhD in electrical engineer- ing from Anna University, Chennai, India, in 2011. Since 2003, he has been with the Department of Electrical and Electronics Engineering, Hindusthan College of Engineering and Technology, Coimbatore, Tamil Nadu, India, where he is currently working

  xi as an associate professor. His research interests are power system control, optimization, and application of computational intel- ligence to power system problems. He has published more than 85 papers in national and international journals and conference proceedings. He is a member of IEEE, SSI, and ISTE.

  

Nilanjan Dey, PhD, is currently associated with the Department

  of Information Technology, Techno India College of Technology, Kolkata, West Bengal, India. He holds an honorary position of vis- iting scientist at Global Biomedical Technologies Inc. (California); and research scientist of laboratory of applied mathematical mod- eling in human physiology, Territorial Organization of Scientific and Engineering Unions, Bulgaria. He is an associate researcher at Laboratoire RIADI, University of Manouba, Tunisia. He is an associated member of the Wearable Computing Research Lab, University of Reading, London. His research topics include medi- cal imaging, soft computing, data mining, machine learning, rough sets, computer-aided diagnosis, and atherosclerosis. He has published 25 books, and 300 international conference and journal papers. He is the editor in chief of the International Journal of Ambient Computing and Intelligence and International Journal of Rough Sets and Data Analysis; co-editor in chief of International Journal of Synthetic Emotions (IJSE) and International Journal of Natural Computing Research; series editor of Advances in Geospatial Technologies and Advances in Ubiquitous Sensing Applications for Healthcare (AUSAH), Elsevier; executive edi- tor of International Journal of Image Mining (IJIM); and associ- ated editor of IEEE Access and the International Journal of Service Science, Management, Engineering and Technology. He is a life member of IE, UACEE, and ISOC. He is also been the chairman of numerous international conferences, including ITITS 2017, WS4 2017, and INDIA 2017.

  

Amira S. Ashour, PhD , is an assistant professor and head of

  the Department of Electronics and Electrical Communications Engineering, Faculty of Engineering, Tanta University, Egypt. She received her masters degree in electrical engineering in 2001 and PhD in smart antenna in 2005 from the Department of Electronics and Electrical Communications Engineering, Faculty of Engineering, Tanta University, Egypt. She was the vice chair of the Computer Science Department, Computers and Information Technology College, Taif University, Saudi Arabia, from 2009 to 2015. She was the vice chair of the Computer Engineering Department, Computers and Information Technology College, Taif University, Saudi Arabia, for one year in 2015. Her research topics of interest include smart antennas, direction of arrival estimation, target tracking, image processing, medical imaging, machine learning, soft computing, and image analysis. She has been published in 7 books and 105 international conference and journal papers. Ashour is an editor in chief for the International Journal of Synthetic Emotions (IJSE). She is coeditor of the book series Advances in Ubiquitous Sensing Applications for Healthcare (AUSAH). She is an associate editor for the International Journal of Rough Sets and Data Analysis, as well as the International Journal of Ambient Computing and Intelligence. She is an editorial board member of the International Journal of Image Mining (IJIM).

  

  C H A P T E R

  1 Introduction

  ontinuing development in technology has raised the dependence on electrical power availability. Commercial

  C

  power resources enable the modern world to operate even with all the required demands. The electric power system has a significant role in several applications including the storage, transfer, and use of electric power. The electric power system is an electrical net- work of components organized to convert one form of energy into a useful form of electrical power. The operation and performance of electrical equipment is mainly based on the quality of power supply. With the emergence of sophisticated technology, intelli- gent technology demands power that is free of disturbance and interruption.

  The mismatch between power generation and load disturbance affects generating voltage and frequency of the standalone sys- tem. In order to overcome this concern, a power-generating unit becomes an essential part of regulating the frequency of the sys- tem, tie-line power flow between connected areas, voltage value, and load flow conditions within the desired value. Nonetheless, nowadays, the electric energy demand is rapidly increasing due to the enormous development in technology. Consequently, large- scale power systems are created to balance energy demand with

  1

  ◾ Bio-Inspired Algorithms in PID Controller Optimization

  generation. When load demand is increased in any one of the power systems, the remaining connected areas share the power between them to maintain the system in stable condition. The size and complexity of systems are increasing with large interconnec- tions of control areas. The complexity of systems is reduced with the help of recently developed modern control theory.

  The power balance among the generating power and the total load demand provides good quality power and reliable power supply to all consumers. During the nominal loading conditions, each power-generating unit takes care of its stability and operat- ing point. Whenever sudden load disturbance occurs in any of the generating units, it disturbs the frequency of the system and tie-line power flow within the interconnected power systems. In addition, the tie-line power flow deviations between the intercon- nected power plant and damping oscillations that occur in the system response affect the stability of the power system. In order to guarantee power system stability, a speed governor can be used to act as a primary control loop; in addition, a secondary control- ler can also be introduced to retain the system parameters within the quantified value. The frequency regulation and active power control is called load frequency control (LFC). Furthermore, the voltage control and reactive power are referred to as automatic voltage regulation (AVR). The main aim of LFC is to preserve the frequency with a constant value even with the continuous change of the active power demand, which is related to the loads, and it regulates the tie-line power exchange between the interconnected areas.

  The electrical grid of interconnected networks is used to deliver the electrical supply from the generating unit to power consum- ers. The grid contains power-generating stations to generate the electrical power supply. The high voltage transmission line carries the generated power from the sources to load centers, where the distribution centers connect individual customers and where the power-generating stations are positioned near the fuel source.

  Introduction ◾

  1.1 LOAD FREQUENCY CONTROL AND AUTOMATIC GENERATION CONTROL

  The automatic generation control (AGC) as well as the LFC play the foremost role in the power system process and the control of any type of power plant unit. For generating and power deliv- ery, suitable analysis of the power supply quality and regularity become essential during emergency situations. In this situation, power-generating units are interconnected via tie-lines to obtain good quality of power supply. The interconnected power system comprises hydro, nuclear, wind, solar, gas, and thermal power plants. Thus, the system response yields damping oscillations in the frequency and tie-line power flow deviations during the load demand condition. To deliver good quality power supply to con- sumers, the secondary controller gain values should change uni- formly. During the higher-load demand condition, controller gain values change maximally and this repeating process maintains the quality of generated power by keeping error values equal to zero.

  Typically, the PID controller consists of three basic terms: pro- portional controller (P), integral controller (I), and derivative con- troller (D). The proportional controller reduces the peak overshoot in the system responses, the integral controller reduces the steady- state error to zero, and the stability of the system is increased by using the derivative controller. The input of PID controller is the area control error (ACE) and the output of the controller is the con- trol signal (delP ). The output of controller is given into the power

  ref system as a reference signal.

  The PID controller design in the literature review included sev- eral methods for optimization of controller gain values with dif- ferent cost functions. Such functions include the integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE), and integral time absolute error (ITAE) cost func- tions. In this book, the PID controller is considered a feedback controller, which gives the appropriate control signal for control- ling the power plant during abnormal conditions. The value of the

  ◾ Bio-Inspired Algorithms in PID Controller Optimization

  control signal generated by the controller for each area is given in the following expression:

  K d i

  = = − − − u t ( ) K ACE . ACE K T ACE (1.1) ∆P ref p d d

  ∫ T dt i

  Δ P , or u(t), represents the control signal generated by the

  ref

  controller. In addition, K , K , and K represent the proportional,

  p i d

  integral, and derivative controller gain values, respectively. ACE indicates the area control error. Based on the IEEE standards, ACE is defined as linear combinations of change in frequency and tie-line power flow deviations between connected areas. So, proper control of the ACE within the tolerance value keeps the system parameters within the nominal value during sudden load disturbance. The deviations in frequency and tie-line power flow deviations will be zero when the value of ACE is zero. The value of ACE is given in the following expression:

  

= +

ACE F B . P (1.2) ∆ ∆ − i i i tiei j

  where B represents frequency bias constant. The subscripts i, j indicate area, that is, i, j = 1, 2, and 3. In these conditions, opti- mization techniques based on bio-inspired algorithms (BIAs) are implemented to tune controller gain values for providing adequate and suitable control signals by optimizing controller gain values. Recently, different controllers have been designed based on bio- inspired algorithms optimization techniques to tune the control- ler gain values for powerful implementation of the LFC and AGC of the power system.

1.2 BIO-INSPIRED OPTIMIZATION ALGORITHMS

  Bio-inspired algorithm–based optimization techniques are imple- mented based on the behavior of natural living beings. These algo-

  Introduction ◾

  phenomena are observed by grouping these algorithms, which are used to solve issues related the mathematics. The computational algorithm–based techniques are designed and optimized based on the inputs from the natural behavior of biological systems, such as the bee or ant colonies.

  The implementation of suitable secondary controllers is more essential for getting superior, controlled dynamic performance in the interconnected power system during sudden load demand situations. In this book, a PID controller is considered a second- ary controller. The major aim of implementing a secondary PID controller is to regulate the power system response by eliminat- ing or reducing the time-domain specification parameters, such as steady-state error, minimum damping oscillations, peak fre- quency, and the tie-power flow during sudden load demand in any interconnected power system.

  The tuning of optimal gain values of proportional, integral, and derivative gain values, K , K , and K , respectively, are crucial.

  

p i d

  First, find the integral controller gain value by keeping K con-

  i

  stant, and tuning the K gain value. Similarly, by keeping K and

  p i

  K constant, one can then tune the derivative controller gain value

  p K . This type of tuning method is called a trial-and-error method. d

  The system response yields more damping oscillations in the fre- quency and tie-line power flow deviations during sudden load demand period. To deliver a good quality control signal to the power system, the controller gain values should change equally. During the higher-error value condition, the controller gain value should change maximally and this process repeats until the error value is zero. In this condition, BIA-based optimization tech- niques are implemented to tune controller gain values to provide adequate and suitable control signals by optimizing controller gain values.

  In a system, groups of components are connected together to perform some specific operation or function. The output of a system is controlled by varying input quantity of the system is

  ◾ Bio-Inspired Algorithms in PID Controller Optimization

  variable and input of the system is the command signal. Generally, the system can be classified into two types, namely, open-loop system and closed-loop system. In the open-loop system, the sys- tem output is affected by the input signal. However, in the case of a closed-loop system, the output of the system is determined by the input of the system. For regulating the output of the system, a controller device is introduced to the system. The controller modi- fies the error signal by generating an appropriate control signal to the system. The basic control signals that are commonly available in the two-position analog controller are proportional, integral, derivative, proportional–derivative, and proportional–integral– derivative control actions. In this research work, the PID controller is introduced as a secondary controller. The parameters of the PID controller are optimized by using BIA-based optimization tech- niques for superior system performance.

1.3 LITERATURE SURVEY

  The gain values of the fuzzy PID controller are optimized using teaching-learning based optimization (TLBO) that B. K. Sahu et al. [1] proposed for tuning of fuzzy PID controllers for the AGC of a two unequal-area thermal power systems. A hybrid particle swarm optimization–pattern search (hPSO-PS) procedure is applied in the AGC for optimizing the fuzzy PI controller gain values in a multiarea interconnected power system [2]. R. K. Sahu et al. [3] obtained the PI controller gain values using the minority charge carrier inspired (MCI) algorithm in an AGC of an inter- connected hydrothermal power system. The bat-inspired algo- rithm has been applied to optimize the PI controller gain values for a multiarea interconnected power-generating system to solve LFC issues such as frequency deviations and tie-line power flow deviations and stability of the power system [4]. A fractional order PID (FOPID) controller has been designed for the LFC of an interconnected power generating system, where the controller gain values were optimized using a multiobjective optimization

  Introduction ◾

  Dash et al. [6] used the cuckoo search (CS) algorithm to tune two degrees of freedom (2-DOF) controllers for solving the AGC issue (frequency deviations and tie-line power flow deviations within interconnected power systems) in a multiarea interconnected power system with several flexible alternating current transmis- sion systems. A PD-PID cascade controller has been designed for solving the AGC issue in multiarea interconnected thermal power systems by considering the generation rate constraint nonlinear- ity effect [7]. A hybrid firefly algorithm–pattern search (hFA-PS) method designed controller has been applied for solving the AGC issue in multiarea interconnected power systems by considering the integral time absolute error objective function [8]. Sahu et al. [9] implemented a hybrid local unimodal sampling (LUS) and TLBO technique tuned fuzzy PID controller into the LFC of inter- connected multisource power systems.

  Shankar and Mukherjee [10] applied the quasi oppositional har- mony search technique to optimized classical controller gain values into the LFC of multiarea, multisource power generating-systems. Vukarasu and Chidmbaram [11] used the bacterial foraging opti- mization (BFO) algorithm to optimize the proportional–double

  2

  integral (PI ) controller in the AGC of interconnected power sys- tems under deregulated environments. The fuzzy PID controller parameters are optimized using the firefly algorithm, which have been applied into the AGC of multiarea, multisource power systems with a unified power flow controller (UPFC) and superconducting magnetic energy storage unit by Pradhan et al. [12]. Sharma and Saikia [13] used the grey wolf optimizer algorithm–based classical controller in a multiarea solar thermal–thermal power system as a secondary controller.

  Francis and Chidambaram [14] proposed a teaching–learning- based optimization technique for tuning of PI controller gain val- ues and PI+ controller gain values. Shivaie et al. [15] proposed a modified harmony search algorithm–tuned PID controller for the LFC of interconnected nonlinear hydrothermal power systems.

  ◾ Bio-Inspired Algorithms in PID Controller Optimization

  firefly algorithm in the LFC of multiarea interconnected thermal power systems. The proposed optimization technique’s tuned con- troller performance has been compared to the genetic algorithm, bacteria foraging optimization technique, differential evolution optimization algorithm, particle swarm optimization technique, and Ziegler-Nichols technique–based controller performance of the investigated power generating system [16]. Prakash and Sinha [17] presented a neuro-fuzzy hybrid intelligent PI controller for the LFC of a four-area interconnected power system. Farhangi et al. [18] applied an emotional learning–based intelligent control- ler for the LFC of an interconnected power system by consider- ing the generation rate constraint nonlinearity effect. Farook and Raju [19] proposed a hybrid genetic algorithm–firefly algorithm in the AGC of an interconnected three-area deregulated power sys- tem. Moreover, a self-adaptive modified bat algorithm has been implemented for optimization of controller gain values in a four- area interconnected power generating system [20].

  The AGC of an equal three-area thermal–thermal–hydro power system has been investigated with different classical con- trollers [21]. The performance is compared to the fuzzy integral double derivative (IDD) controller. The controller gain values are optimized by implementing the BFO technique. The results estab- lished that this technique is superior to existing methods. The imperialist competitive algorithm (ICA) has been implemented for the LFC of a three-area power system with different generating units and a fractional order PID (FOPID) controller [22]. The sim- ulation result proved the superiority of the system performance with ICA-based controller compared to the existing controller.

  Some other types of controllers and optimization techniques used in the LFC of power systems include the fuzzy logic control- ler [23], genetic algorithm (GA) [24], artificial neural network (ANN) [25,26], variable structure control (VSC) [27], Lyapunov technique [28], continuous and discrete mode optimization [29], adaptive controller [30], parameter-plane technique [31], optimal control

  Introduction ◾

  ant  colony  optimization (ACO) [35–37], bacteria foraging opti- mization (BFO) [38,39] artificial bee colony (ABC) [40], particle swarm optimization (PSO) technique [41], stochastic particle swarm optimization (SPSO) [42], bacterial foraging optimization algorithm (BFOA) [43], bacterial foraging (BF) technique [44], bat- inspired algorithm [45], beta wavelet neural network (BWNN) [46], and cuckoo search (CS) [47,48].

  From the aforementioned studies, it is clear that in recent years several optimization techniques and optimized controller gain values-based controllers are considered for improvement of power system performances during sudden load demands.

  

  C H A P T E R

  2 Load Frequency Control of Single Area Thermal Power System with Biogeography- Based Optimization Technique

  his chapter considers a load frequency controller for a single area thermal power-generating unit by considering dif-

  T

  ferent bio-inspired algorithm (BIA)–based optimization techniques for tuning PID (proportional–integral–derivative) controller per- formance with 1% step load perturbation (SLP). The PID controller

  11

  ◾ Bio-Inspired Algorithms in PID Controller Optimization

  is presented as a secondary controller to control the parameters of the system within the specified value during the sudden load disturbance. The gain values of the implemented controller are tuned by using various bio-inspired algorithms, such as simulated annealing, genetic algorithm, particle swarm optimization, and biogeography-based optimization techniques.

  The structure of this chapter is as follows. The first section, _® “Investigated Thermal Power System,” presents the Simulink model of the investigated single-area thermal power system.

  Controller Design and Objective Function,” pres- ents the details of the proposed controller and the necessary cost function for tuning of controller gain values. The subsequent sec- tion, “Biogeography-Based Optimization Technique,” delivers the proposed optimization technique details, and the “Results and Analysis” section demonstrates the effectiveness of the proposed technique. The “Conclusion” describes the performance of differ- ent BIA-based optimization techniques over the proposed opti- mization technique.

2.1 INVESTIGATED THERMAL POWER SYSTEM

  In order to model the investigated power system with the pro- _{® ®} posed optimization based controller, a MATLAB Simulink model of the single-area thermal power system is illustrated in

Figure 2.1. A thermal power-generating system comprises a tur- bine with a reheater, speed governor, generator unit, and PID

  controller. A 1% SLP is applied into the power for the analysis of power system with and without any load demand. The nom- inal parameters of the investigated thermal power system are as follows: Tg, governor time constant = 0.2 s; Kr, steam tur- bine reheat coefficient = 0.333; Tr, steam turbine reheat time constant  = 10 s; Tt, steam turbine time constant = 0.3 s; Kp,

• –1

  power system constant  = 120 Hz pu MW; Tp, power system

• –1 time constant = 20 s; and R, speed regulation = 2.4 Hz pu MW.

  LF C o f S

  1 Kp Kr.Tr.s+1

  1

• PID
• −

  in Tg.s+1 Tp.s+1

Tr.s+1 Tt.s+1

  − PID controller Governer Turbine Generator Reheater gle Ar

  SLP 1/R Speed Thermal power system regulator ea T h erm al P

  ACE = delF U 1 delXE Kr.Tr.s+1 delPg Kp delF

  1

• PID
• −

  o Tg.s+1 Tr.s+1 Tt.s+1 Tp.s+1

  − w

  PID controller Governer Turbine Generator Reheater

  SLP er S

  1/R Speed regulator yst

  Thermal power system em w ith 

• GDB Governor Boiler dynamics Reheater GRC

  PID controller

  Turbine Generator B

• −

  − B O T SLP

  Speed 1/R ec regulator h n iq u e

  FIGURE 2.1 ◾ Simulink model of single-area thermal power system.

  13

  ◾ Bio-Inspired Algorithms in PID Controller Optimization

  The area control error (ACE), which is the input of the investi- gated power system, is specified as follows:

  ACE f (2.1) = ∆

  where Δf is the change in frequency deviation of the investigated power systemllustrates the MATLAB Simulink of a single-area thermal power system model.

  The secondary PID controller is equipped for regulating power system parameters during a sudden load demand condition. The thermal power system incorporates the governor, reheater, tur- bine, speed regulator, and generator units. When a load distur- bance occurs in the open-loop power system, system parameters are affected and yield more damping oscillations with steady error. In order to overcome this issue, secondary controllers are introduced to regulate power system parameters.

  2.2 CONTROLLER DESIGN AND OBJECTIVE FUNCTION

  Generally, the PID controller consists of a proportional control- ler, integral controller, and derivative controller. The proportional controller steadies the gain, yet it yields a steady-state error. The integral controller eliminates the steady-state error and the deriv- ative controller reduces change of error rate. The structure of the PID controller under concern is shown i

  The PID controller input is the ACE and the output is the con- trol signal (U), where the output is given as follows:

  K d

_i

= = − U K ⋅ ACE − ACE K T − ACE ∆P ef P d d (2.2) r

  ∫ T dt

_i

  where ΔP = U is the output control signal, K is the integral

  ref i

  controller gain, K is the proportional controller gain, K is the

  p d

  derivative controller gain, T is the integral time constant, T is the

  i d derivative time constant, and ACE is the area control error. LFC of Single Area Thermal Power System with BBO Technique ◾ Kp Proportional gain

• 1

• ACE Ki delPref

  s
• Integral grain Integrator Kd du/dt Derivative Derivative gain FIGURE 2.2 Arrangement of the PID controller.

  The objective function is defined based on the preferred specifi- cation and constraint for design of modern BIA-tuned controllers. In this work, the integral time absolute error objective function is considered, which is stated by

  T = J t f dt (2.3)

  

. ∆

∫ o

  where t is the simulation time. The controller gain values of inte- gral (K ), proportional (K ), and derivative (K ) are optimized by

  i p d using any of the BIAs.

  2.3 BIOGEOGRAPHY-BASED OPTIMIZATION TECHNIQUE

  In this research work, the biogeography-based optimization (BBO) technique is proposed for the optimization of gain val- ues in load frequency control (LFC) of a single-area thermal power system. The BBO technique is a population-based opti- mization technique [49,50]. The human reproduction process

  ◾ Bio-Inspired Algorithms in PID Controller Optimization

  is not involved in this optimization algorithm. The BBO opti- mization technique differs from other population-based opti- mization techniques. For example, the ant colony optimization technique generates a new solution for each iteration during the optimization process [51,52], whereas the BBO technique keeps the solution set from one iteration to the next iteration. The BBO strategies are common with the particle swarm [53] and differ- ential evolution techniques [54,55]. In these technique-based algorithms, tuned gain values are retained one iteration to the next. Each generated solution has the capability to learn from its neighbor and can adjust itself for tuning the technique process. Particle swarm optimization refers to the corresponding solution as a point in space. It indicates the change over time of each solu- tion of the velocity vector. The selection of differential evolution algorithm parameters can have a great role in performance of the optimization. The choice and selection of DE optimization parameters yield better performance, so it has been the topic of a great deal research.

  The biogeography-based optimization technique is an evo- lutionary algorithm (EA). The optimization technique is imple- mented for tuning of controller gain values that optimize a cost function by stochastically and iteratively improving the solutions to a given measure of cost function or superiority. The BBO algo- rithm steps are as follows [49]:

  Step 1—Initialize the parameters. In this step, the driving methods are indicated for mapping issues including the suitability index variable (SIV) and habitats. In addition, the maximum species count S , maximum mutation rate

  max

  m , maximum migration rate, and an elitism parameter

  max are initialized.

  Step 2—Initialize a random set of habitats to represent imple- mentation of the operator.

   LFC of Single Area Thermal Power System with BBO Technique ◾

  Step 3—Each habitat maps the Habitat Suitability Index (HSI) to the number of species S, emigration rate μ, and immigra- tion rate λ. Step 4—Probabilistically use the emigration rate and immi- gration rate to change each nonelite habitat and recompute every HSI. Step 5—For every habitat, update its probability of species count by applying initialization of a random set of habitats.

  Afterward, based on the probability, mutate each nonelite habitat and recompute HSI. Step 6—Go to step 3 for the next iteration. After a predeter- mined number of iterations, this loop can be terminated.

  This is the implementation of the T operator.

2.4 RESULTS AND ANALYSIS

  Different BIA-based optimization techniques tuned to PID con- troller performance are compared by considering 1% step load perturbation in the investigated thermal power system under MATLAB Simulink environment for the simulation period time of 120 s. The effectiveness of the proposed tuning algorithm is analyzed by comparing the frequency deviations and area control error deviations with other techniques for controller tuning per- formance. By using this proposed algorithm with the ITAE cost function, the PID controller gain values are optimized. The opti- mal PID controller gain values of different BIA-tuned values are tabulated i. The table reports the PID controller gain values of simulated annealing, genetic algorithm, particle swarm optimization, and BBO technique-optimized controller gain val- ues by considering 120 s as a simulation time period. It is clearly evident that the proposed BBO optimization technique yielded minimum performance index compared to other optimiza- tion techniques. The comparisons of simulation results based on

  ◾ Bio-Inspired Algorithms in PID Controller Optimization

TABLE 2.1 Optimal Gain Values of PID Controllers Obtained by Using Different BIAs

  Performance BIA Algorithm K K K Index _{P I D} Simulated annealing 0.93245254 0.63703068 0.0213324 0.16754546

  (SA) Genetic algorithm 0.85542643 0.89133524 0.13190307 0.14811123 (GA)

  Particle swarm 0.96310035 0.9929861 0.08711779 0.13001764 optimization (PSO) Biogeography-based

  0.99999989 0.99999917 0.00099059 0.12606583 optimization (BBO)

  different BIA-based optimization techniques are given for a clear understanding.

  2.4.1 Response of System with and without Load Demand The system response does not yield any damping oscillations and steady-state error values. However, when a load disturbance occurs in a power system, the responses yield more damping oscillations with steady-state error. Also the system takes more time to settle with particular error valueshows the open loop per- formance comparisons of a proposed power system with and with- out any load demand. The solid line shows the open-loop response of a system without any load demand. The dashed line shows the response of system with 1% SLP in the investigated power system.

Figure 2.3 establishes that the comparisons of open-loop per- formance of the system response do not yield any oscillations,

  peak overshoot and undershoot, and steady-state error for zero load demand (peak undershoot = 0 Hz and steady-state error = 0  Hz). However, when load demand exists, the response yields more damping oscillations (peak undershoot = –0.058 Hz and steady-state error = 0.026 Hz). In order to overcome this issue, a controller is introduced to get good quality power.

  LFC of Single Area Thermal Power System with BBO Technique ◾

  0.02

  0.00

• –0.02

  delF (Hz) –0.04

• –0.06 Response with zero load demand Response with 1% SLP demand
• –0.08

  20

  40

  60 80 100 120 Time (s) FIGURE 2.3

  Dynamic response of system with and without consider- ing load demand.

  2.4.2 System Response with Different BIAs Tuned PID Controller

  The frequency deviations of PID controller responses to differ- ent BIA-based optimization techniques are illustrated in