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  • POWER SYSTEM TRANSIENT STABILITY ANALYSIS USING MATLAB

    SOFTWARE

    NUR AQILAH BINTI MOHAMAD AMIN

    This project report is submitted as partial fulfilment

    of the requirements for the award of a

    Degree of Master of Electrical Engineering

    Faculty of Electric and Electronic Engineering

    Universiti Tun Hussein Onn Malaysia

    DECEMBER 2013

  • v

    ABSTRACT

    The electric market liberalization increases its importance, as economical pressure and

    intensified transactions tend to operate electric power systems much closer to their

    security limits than ever before. The trend to merge existing systems into much larger

    entities and to monitor them in shorter and shorter time horizons creates more

    difficulties. This holds true for analysis aspects and even more for control, in as much

    as, today; control actions must cope with considerably more stringent market

    requirements than in the past. The difficulties increase further when it comes to transient

    stability phenomena. This thesis has discussed some theory related to transient stability

    such as the swing equation, transfer reactance, power angle curve and equal area

    criterion. In this thesis two possible methods of transient stability have been discussed

    and they are step by step solution for swing curve and equal area criterion. Some

    MATLAB programs have been developed to study the transient stability cases by using

    these two methods. For first method, the transient studies are conducted in two cases.

    For case 1, the fault cleared at time t = 0.2 second and the second case 2 where the fault

    cleared at time t =0.4 second. For second method of equal area criterion has three case

    studies. All the input are same accept for sudden increase in power generator which for

    case 3 is 0.9 p.u, case 4 is 1.099 p.u and case 5 is 1.1 p.u. Lastly for case 6 and 7 the

    application of equal area criterion to three phase fault were investigate the fault at the

    sending end of the line and fault at some distance away from the sending end. These

    programs are helpful in determining critical power angle, critical clearing times for

    circuit breaker, voltage level of systems and transfer capability between systems. Thus,

    a better relay setting can be proposed.

  • vi

    ABSTRAK

    Pasaran terhadap elektrik kini menjadi sangat penting disebabkan oleh tekanan ekonomi

    dan keperluan secara mendalam untuk menjana kuasa elektrik sesuatu sistem supaya

    sistem berkenaan berada dalam keadaan selamat. Pada masa yang sama, beberapa

    masalah turut timbul disebabkan oleh penggabungan sistem yang sedia ada kepada entiti

    yang lebih meluas dan mengawas sistem berkenaan dalam masa yang singkat. Perkara

    ini akan menimbulkan kepentingan untuk menganalisis beberapa aspek dan yang lebih

    penting adalah menganalisa pengawalan di mana kaedah pengawalan mesti menyaingi

    keperluan pasaran yang lebih luas pada masa sekarang daripada sebelum ini. Masalah

    ini lebih membebankan apabila wujudnya fenomena kestabilan fana (transient stability).

    Dalam tesis ini, beberapa teori seperti persamaan buai (swing equation), regangan

    pindah (transfer reactance), sudut kelengkungan kuasa (power angle curve), dan

    kriterion sama luas (equal area criterion) diaplikasikan. Dalam tesis ini, dua kaedah

    penyelesaian kestabilan fana telah dibincangkan iaitu penyelesaian peringkat demi

    peringkat bagi lengkungan buai dan kriterion sama luas. Beberapa program MATLAB

    telah direka untuk mengkaji kes kestabilan fana menggunakan dua kaedah tersebut. Bagi

    kaedah pertama, kestabilan fana dibahagikan kepada dua kes. Bagi kes 1, kerosakan

    berlaku pada masa t = 0.2 saat dan kes 2 di mana kerosakan berlaku pada masa t = 0.4

    saat. Bagi kaedah kedua iaitu kriterion sama luas dijalankan dalam tiga kajian kes.

    Semua input adalah sama kecuali bagi peningkatan mendadak dalam penjana kuasa iaitu

    pada kes 3, 0.9 p.u, kes 4, 1.099 p.u, dan kes 5, 1.1 p.u. Akhir sekali untuk kes 6 dan 7

    bagi aplikasi kriteria sama luas dengan tiga fasa adalah untuk menyiasat kerosakan pada

    akhir penghantaran garisan dan kerosakan yang agak jauh dari hujung hantaran.

    Program ini membantu menentukan masa geganti semulajadi, masa melengah genting

    untuk pemutus litar, paras voltan sesuatu sistem dan kebolehan pemindahan di antara

    system. Dengan demikian, satu tatacara relay yang lebih baik akan dicadangkan.

  • vii

    TABLE OF CONTENTS

    CONTENTS PAGES

    Title i

    Declaration ii

    Dedication iii

    Acknowledgements iv

    Abstract v

    Abstrak vi

    Table of contents vii

    List of Table x

    List of Figure xi

    CHAPTER 1 INTRODUCTION 1.

    1.1 Stability in Power System 1

    1.1.1 Steady State Stability Studies 3

    1.1.2 Dynamic Stability Studies 4

    1.1.3 Transient Stability Studies 4

    1.2 Problem Statement 6

    1.3 Objectives 7

    1.4 Project Scope 7

    1.5 Thesis Outline 8

  • viii

    CHAPTER 2 LITERATURE REVIEW 9

    2.1 Theory Related to Transient Stability Studies 9

    2.1.1 Transient Stability 9

    2.1.2 Swing Equation 12

    2.1.3 Power Angle Curve 15

    2.1.4 Transfer Reactance 16

    2.1.5 Equal Area Criterion 19

    2.2 Review on the Stability of Power System 22

    CHAPTER 3 METHODOLOGY 27

    3.1 Overall Methodology Process 28

    3.1.1 Case Study on step by step solution of the swing curve 29

    3.1.2 Case study on application of equal area criterion on sudden increases

    in power input 30

    3.1.3 Case study on application of equal area criterion for a three phase 31

    3.2 Step by Step Solution of Obtaining Swing Curves 31

    3.3 Application of Equal Area Criterion on Sudden Increase in Power Input 38

    3.3.1 Example calculation for the application of the equal area criterion 39

    3.4 Application of Equal Area Criterion to Three-Phase Fault 42

    3.4.1 Fault at the Sending End of a Line 42

    3.4.2 Fault at Some Distance away from Sending End 44

    CHAPTER 4 RESULT AND DISCUSSION 47

    4.1 Case Study on Step by Step Solution of the Swing Curve 47

    4.1.1 Case 1: fault cleared at time, t = 0.2 second 48

    4.1.2 Case 2: fault cleared at time, t = 0.4 second 50

    4.2 Case Study on Application of Equal Area Criterion on Sudden Increases in

    Power Input 51

    4.2.1 Case 3: sudden increase in input power, Pil = 0.9 53

  • ix

    4.2.2 Case 4: sudden increase in input power, Pil = 1.099 54

    4.2.3 Case 5: sudden increase in input power, Pil = 1.1 55

    4.3 Case Study on Application of Equal Area Criterion for a Three Phase Fault 56

    4.3.1 Case 6: fault occurs at the sending end of the line 2 of a one single

    machine 57

    4.3.2 Case 7: fault occurs at the center of the line 2 of a one single machine 58

    4.4 Discussion of the Overall Performance Result 59

    CHAPTER 5 CONCLUSION AND RECOMMENDATIONS 61

    5.1 Conclusion 61

    5.2 Recommendations 62

    REFERENCES 64

  • x

    LIST OF TABLE

    Table Title Pages

    2.1 Publications and patents related to the development of implantable

    microbial fuel cells 26

    3.1 Subsequent calculations 37

    3.2 Power per-unit value with different value of 41

    4.1 Input for step by step method of one single machine 48

    4.2 Computations of swing curve for case 1 48

    4.3 Computations of swing curve for case 2 50

    4.4 Input for sudden increases in power input 52

    4.5 Output for sudden increases in power input 52

    4.6 Input for application of equal area criterion on three phase fault 56

    4.7 Output for application of equal area criterion on three phase fault 56

  • xi

    LIST OF FIGURE

    Figure Title Pages

    1.1 Power system stability 2

    2.1 Transient stability illustration 10

    2.2 Effect of fault clearing time 11

    2.3 The flow of mechanical and electrical power in a generator and

    motor 13

    2.4 Swing curve 15

    2.5 One machine infinite bus 15

    2.6 Diagram of one machine infinite bus where fault happen at the middle

    of the line 17

    2.7 Equal area criterion - sudden change of load 21

    3.1 Flow Chart of the overall project 28

    3.2

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