A Thesis entitled Nature Inspired Discrete Integer Cuckoo Search Algorithm for Optimal Planned Generator Maintenance Scheduling by Srinivasan Lakshminarayanan Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Engineering _________________________________________ Dr. Devinder Kaur, Committee Chair _________________________________________ Dr. Mansoor Alam, Committee Member _________________________________________ Dr. Srinivasa Vemuru, Committee Member _________________________________________ Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo August 2015 Copyright 2015, Srinivasan Lakshminarayanan This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of Nature Inspired Discrete Integer Cuckoo Search Algorithm for Optimal Planned Generator Maintenance Scheduling by Srinivasan Lakshminarayanan Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Engineering The University of Toledo August 2015 In this thesis, Discrete Integer Cuckoo Search Optimization Algorithm (DICS) is proposed for generating an Optimal Maintenance Schedule for power utility with multiple generator units and complex constraints of Man Power Availability, Load Demand and strict Maintenance Window. The objective is to maximize the levelness of the Reserve Power over the entire planning period while satisfying the multiple constraints. This is an NP hard problem and there is no unique solution available for it. Nature inspired Cuckoo Search algorithm has been chosen to address this problem. Cuckoo search algorithm is a metaheuristic algorithm based on the obligate brood parasitism of cuckoo bird species, where cuckoo tries to find the best nest of other birds whose eggs resemble her own to lay her eggs to be hatched by other birds. Therefore the problem is formulated to find the best host nest. The host nest is defined according to the constraints of the power utility. The algorithm was tested on two test systems, one with 21 generator units and the other with 9 generator units which is called IEEE RTS test system. The results obtained with the DICS on the 21 generator power utility system are compared with the work of iii previous researchers using the same test system and using the five traditional algorithms namely the Genetic Algorithm with Binary Representation (GABR), Genetic Algorithm with Integer Representation (GAIR), Discrete Particle Swarm Optimization (DPSO), Modified Discrete Particle Swarm Optimization (MDPSO) and Hybrid Scatter Genetic Algorithm (HSGA). The results obtained by applying DICS on the IEEE RTS test system are compared with HSGA algorithm. The results show that DICS outperformed all the other algorithms in the two test systems. iv Dedicated to Shree Mahaperiyava! Acknowledgements I offer my reverence to the Almighty for showering his abundant grace on me which made all things possible. I would like to offer my sincere and special thanks to my advisor Dr. Devinder Kaur for her encouragement, wise, patient and thorough guidance and support. It was a great experience to work under her. I would like to thank Dr. Mansoor Alam for his kind and wise guidance throughout my Master's Program. I thank Dr. Srinivasa Vemuru for his gracious support and encouragement. I would also like to thank Dr. Devinder Kaur, Dr. Mansoor Alam, Mr. William McCreary and EECS Department for the financial support. I thank my parents, grandmother, sister, twin brother and friends for their love, support and encouragement in all my endeavors. I would like to specially thank my twin brother for being my constant companion and inspiring me always. v Table of Contents Abstract .............................................................................................................................. iii Acknowledgements ..............................................................................................................v Table of Contents ............................................................................................................... vi List of Tables .................................................................................................................. viii List of Figures ......................................................................................................................x List of Abbreviations ........................................................................................................ xii 1 Introduction ............ ................................................................................................1 2 Problem Formulation and Test Systems ..................................................................5 2.1 Problem Formulation .......................................................................................5 2.2 21-Generator Power Utility Test System ........................................................11 2.3 IEEE RTS Test System ...................................................................................13 3 Cuckoo Search ........................................................................................................16 4 Problem Encoding and Algorithm Steps of DICS ..................................................18 4.1 Initialization of Population ...........................................................................19 4.2 Computation of Fitness ...................................................................................20 4.3 Discrete Lévy/Global Random Flight .............................................................21 4.4 Revert Flight ...................................................................................................24 4.5 Discrete Local Walk ......................................................................................24 4.6 Special Cases of the Local Flight....................................................................26 vi 5 Results and Discussion………………………… ...................................................28 5.1 21 generator power utility test system……… ...................…………………28 5.1.1 Results ................................................................................................28 5.1.2 Comparison ........................................................................................33 5.2 IEEE RTS test system ...................................................................................41 5.2.1 Results. ................................................................................................41 5.2.2 Comparison ..........................................................................................46 6 Conclusion and Future Work ...................................................................................49 References ........................................................................................................51 vii List of Tables 2.1 The Weight Coefficients ........................................................................................10 2.2 The 21-Generator Power Utility Test Dataset .......................................................11 2.3 The IEEE RTS Test System Test Dataset ..............................................................13 2.4 Weekly Load Demand on the IEEE RTS Test System ..........................................14 5.1 Generators in maintenance during each week for the fittest host nest for 21 generator system. ..........................................................29 5.2 Power Generated, Reserve Power and Man Power Required during weeks (1-26) for the fittest host for 21 generator system. .....................................30 5.3 Power Generated, Reserve Power and Man Power Required during weeks (27-52) for the fittest host for 21 generator system ....................................31 5.4 The Maintenance Schedule arrays from the six algorithms. ..................................34 5.5 Pgenerated (t) during weeks (1-26) for the six algorithms for 21 generator system……………………………………………………………………………35 5.6 Pgenerated (t) during weeks (27-52) for the six algorithms for 21 generator system……………………………………………………………………………36 5.7 TMPRt during weeks (1-26) for the six algorithms for 21 generator system……………………………………………………………………………38 5.8 TMPRt during weeks (27-52) for the six algorithms for 21 generator system……………………………………………………………………………39 viii 5.9 Comparison of the result of the six algorithms for 21generator system ....................................................................................................................41 5.10 Generators in maintenance during each week for the fittest host for IEEE RTS system .................................................................... 42 5.10 Pgenerated (t) during each week for the fittest host nest for IEEE RTS system ........43 5.11 Reserve (surplus) power during each week for the fittest host nest for IEEE RTS system....................................................................44 5.12 Maintenance Schedule Arrays from HSGA and DICS algorithms for the IEEE RTS test system.. ..............................................................................46 5.13 Comparison of SSR for the Schedules from HSGA and DICS algorithms for the IEEE RTS test system. ...............................................................................47 ix List of Figures 2-1 Maintenance Schedule Array ...................................................................................6