exciter effect on transient stability of multi-machine...

AIN SHAMS UNIVERSITY FACULTY OF ENGINEERING

ELECTRICAL POWER AND MACHINES DEPARTMENT

EXCITER EFFECT ON TRANSIENT STABILITY OF MULTI-MACHINE POWER SYSTEMS USING SPARSE FORMULATION OF TRANSIENT ENERGY FUNCTION

A Thesis submitted for the partial fulfillment of the Degree of Master of Science

Tn

Electrical Engineering (Power and Machines)

Presented by

Eng. Noha lIany Yosscry Ali EI-Amary

B. Sc. In Elect. Eng., Ain Shams University

Supervised by

Prof. Dr. Mohammed Abd EI-Latif Badr

Dr. Moneer M. Abu-Elnaga

Dr. Yasser Galal Mostafa (Arab Academy)

Electrical Power and Machines Department Faculty of Engineering Ain Shams University

Cairo-Egypt

2004

EXAMINERS COMMITTEE

EXCITER EFFECT ON TRANSIENT STABILITY OF MULTIMACHINE POWER SYSTEMS USING SPARSE FORMULATION OF

TRANSIENT ENERGY FUNCTION

A Thesis submitted for the partial fulfillment of the Degree of Master of Science

In

Electrical Engineering (power and Machines)

Presented by

Eng. Noha Hany Yossery Ali EI-Amary

B. Sc. In Elect. Eng., Ain Shams University

Approved by

Name

1. Prof. Dr. Mohammed A. Hassan EI-Sayed

Faculty of Engineering, Cairo University Cairo, Egypt.

2. Prof. Dr. Mohammed Abd EI-Rehim Badr

Faculty of Engineering, Ain Shams University Cairo, Egypt.

Signature

3. Prof. Dr. Mohammed Abd EI-Latif Badr


;1.;4. L.

4. Dr. Moneer M. Abu-Elnaga


II

STATEMENT

This thesis is submitted to Ain Shams University in partial fulfillment

of Master of Science in Electrical Engineering (Power and Machines).

The work included in this thesis was carried out by the author at the

Electrical Power and Machines Department, Ain Shams University. No part

of this thesis has been submitted for a degree or a qualification at any other

university or institute.

Name

Signature

Date

Noha Hany Yossery Ali El-Amary

2004

III

Dedicated to the soul of my father, my mother" the

greatest mother on the earth" and my lovely brother

Ahmed

Also, dedicated to everyone tried to help me, all my

teachers, professors, my friends, ...

IV

ACKNOWLEDGMENT

ACKNOWLEDGMENT

There isn't any great word can express my deepest appreciation and

sincere to my soul father, Prof. Dr. Mohammed Abd EI-Latif Badr for his

continuous help, support and caring.

My deep gratitude is, also, dedicated to Dr. Moneer M. Abu-Elnaga,

my direct supervisor, for his great effort to achieve this work.

I am greatly indebted to Dr. Vasser Galal for his great support and help.

v

ABSTRACT

ABSTRACT

Transient stability of power systems is one of the most important fields

m the electrical power studies. The methods of analyzing the transient

stability can be divided into two main categories: time domain simulation,

and the direct methods.

The main advantage of time domain simulation (TDS) is that system

components can be modeled in more details. On the other hand, this method

reqUIres considerable computational effort, especially for large-scale

systems. Also, swing curves, usually associated with this method, need

interpretation that depends on human experience for deciding about the

stability of the system. Moreover, this method yields Yes-or-No type of

answer, i.e. it tells whether or not stability is maintained and it does not give

any qualitative measure for system stability.

In direct methods, system differential equations are not solved in the

time domain, therefore, the computational time is saved tremendously. In

addition, these methods give a qualitative measure for system stability. The

simplest example of the direct methods is the well-known Equal Area

Criterion (EAC). Unfortunately, this technique is applicable only for one

machine-infinite bus system or two-machine system at most. Transient

Energy Function (TEF) technique, considered as a generalized form of EAC,

represents a powerful method to analyze the transient stability of multi

machine power systems. This method is based on Lyapunov stability theory.

The Sparse Network Formulation (SNF) of this method retains the original

structure of the system network and avoids network reduction. This

formulation has many advantages as compared with the Reduced Network

VI

A13STRACT

Fonnulation (RNF). The time consummg network reduction is avoided

completely. All matrices used in calculating the Stable Equilibrium Point

(SEP) and Unstable Equilibrium Point (UEP), which represent the main step

for stability assessment, are very sparse. Therefore, the computational time is

reduced signiticantly. Also, SNF permits the system loads to be modeled as

they exist in practical life. In the current applications of SNF, the classical

model of the synchronous generator is used, i.e. the generator internal emf is

considered constant.

This research introduces the exciter effect to the TEF technique. The

system equations are modified to include the exciter model, and the current

computer package is updated accordingly. The computer program is

implemented for general application to large-scale power systems with

international PTI data input and dynamic data sizing.

The moditied technique is applied to two different power systems; 4-

generator, I I-bus test system, and II-generator, 55-bus real system of

Ontario-Hydro (Canada) [5]. The second system includes the state of Ontario

(Canada) and upper New York area (USA).

The effect of the exciter gain (Ka) and reference voltage (Vref) on the

system perfonnance (energy margin and critical clearing time) is studied. The

inclusion of the exciter effect gives a wider view of the system

performance.

Increasing the exciter gam mcreases the tendency of the sy~tem

towards more stable operation and increases the critical clearing times as

compared with those estimated without exciters effect. Also, increasing the

rcference voltage increases the critical clearing time.

VII

LIST OF CONTENTS

LIST OF CONTENTS

LIST OF ABBREVIATIONS

LIST OF SYMBOLS

LIST OF FIGURES

LIST OF TABLES

CHAPTER (1): INTRODUCTION

1.1 GENERAL

1.2 CLASSIFICATION OF POWER SYSTEM STUDIES

1.2.1 Power system operation

1.2.1.1 Load Flow

1.2.1.2 Short Circuit Studies

i .2.1.3 Power System Stability

1.3 TRANSIENT STABILITY ANALYSIS

i .3. i Time Domain Simulation Method

1.3.2 Direct Methods

1.3.2.1 Equal Area Criterion

i.3.2.2 Energy Function Technique

1.4 LITERATURE SURVEY

1.4.1 Energy Function Technique

1.4.2 Applications and Artificial InteHigence Techniques

1.5 RESEARCH OBJECTIVE AND THESIS OUTLINES

VIII

XU

XIV

XVII

XXI

1

2

2

2

3

3

4

4

5

6

7

8

10

11

11

LIST OF CONTENTS

CHAPTER (2): SYSTEM MODEL WITHOUT EXCITATION

CONTROL

2.1 INTRODUCTION

2.2 S YSTElVl EQUATIONS

2.3 TRANSIENT ENERGY MARGIN

2.3.1 Practical Considerations

2.4 ALGORITHM

13

14

18

19

21

CHAPTER (3): EXCITATION CONTROL SYSTEM MODEL

3. i INTRODUCTION

3.2 CALCULA nONS OF INITIAL EMF

3.3 SYSTEM EQUATIONS

3.4 JACOBIAN CALCULATIONS

3.5 ENERGY lVIARGIN

3.6 PRACTICLE ASSUMPTIONS

3.6.1 Exciter Limiter

3.7 ALGORITHM

CHAPTER (4): SYSTEM DA T A

4.1 INTRODUCTION

4.2 LOAD FLOW DATA FILE

(a) Bus Data

(b) Generator Data

IX

25

25

28

30

30

32

32

33

34

34

34

36

LIST OF CONTENTS

( c) Branch Data

4.3 DYNAMIC DATA FILE

(a) Fault Description

(b) Fault Clearing

( c) Generator Inertia

(d) Mode Of Disturbance (MOO)

4.4 DATA FILE SAMPLE·

4.4.1 Load Flow Data File

4.4.2 Dynamic Data File

CHAPTER (5): APPLICATIONS AND RESULTS

5.1 INTRODUCTION

5.2 SYSTEMS WITHOUT EXICTA nON CONTROL

5.2.1 4 Generator - 11 Bus System

5.2.2 I i Generator - 55 Bus System

5.3 SYSTEMS WITH EXICTATION CONTROL


5.3.1.1 Thermal Generator System

5.3.1.2 Hydro - Generator System


5.3.2.1 Thermal Generator System

5.3.2.2 Hydro - Generator System

CHAPTER (6): CONCLUSIONS AND FUTURE WORK

x

38

40

40

41

41

42

42

42

45

46

46

46

48

48

48

48

59

67

67

79

LIST OF CONTENTS

FUTURE WORK

REFERENCES

APPENDIX (A)

APPENDIX (B)

XI

92

93

A-I

B-1



TDS Time Domain Simulation.

EAC Equal Area Criterion.

TEF Transient Energy Function.

SN.F Sparse Network Formulation.

RNF Reduced Network Formulation.

SEP Stable Equilibrium Point.

UEP Unstable Equilibrium Point.

Ka Exciter gain.

V ref Reference voltage of the exciter.

SC Short Circuit.

EM Energy Margin.

PEBS Potential Energy Boundary Surface.

EEAC Extended Equal Area Criterion.

ReV Boundary Controlling Unstable.

PM Plant Mode.

IAlVI Inter-Area Mode.

MOD Mode Of Disturbance.

LFD Load Flow Data.

DYN Dynamic Data.

COA Center Of Angle.

NR Newton-Raphson.

KE Kinetic Energy.

NEM Normalized Energy Margin.

PTI Power Technology Institute.

xu

LIST OF A1313REVIATIONS

IEEE

MDE

eKE PE

TE

Institute of Electrical and Electronics Engineers.

Magnetic and Dissipation Energy.

Corrected Kinetic Energy.

Positional Energy.

Total Energy.

Exciter EMF.

Clearing Time.

XIII

LIST OF SYMBOLS

g

({Jj

LIST OF SYMBOLS

is the inertia constant of generator g.

is the internal voltage angle of generator g in the synchronous frame of reference.

is the number of generators.

is total number of buses.

is total number of load buses.

is total number of generator buses.

is an index for the load buses: 1,2, ..... , N f .

is an index for the generator buses: 1,2, ..... ,Ng•

is the magnitude of bus voltage.

is the angle of bus voltage in eGA frame.

is the angle of the generator terminal voltage in eGA.

is the magnitude or the element ij of the bus admittance matrix.

is the angle of the element ij of the bus admittance matrix.

is the real load power injected at bus i.

is the imajinary load power injected at bus i.

is the electrical output power of generator g.

is the mechanical input power of generator g.

is the direct-axis transient reactance of generator g.

is the reciprocal of Xdg.

is the Jacobian matrix.

XIV

LIST OF SYMBOLS

8

cl

cr

g

OCg

is the mismatch vector.

is the machine angle in general case.

is the post-fault SEP.

is the rotor speed in e~A.

is the clearing values.

is the critical values.

is the unstable equilibrium point.

is an index for the generator buses: 1,2, ..... ,Ns.

is the bus voltage of generator g.

is the q-axis component of internal voltage of generator g.

is the angle of the q-axis of generator g w.r.t. the system reference.

is the transient internal voltage of generator g.

is the angle of the generator terminal voltage w.r.t. the system reference.

is the q-axis component of the transient internal voltage of generator g.

is the d-axis component of the transient internal voltage of generator g.

is the current of generator g.

is the angle of the generator current w.r.t. the system reference.

is the q-axis component of the current of generator g.

is the d-axis component current of generator g.

xv

LIST Of SYMBOLS

EFDg

is the direct-axis transient reactance of generator g.

is the quadrature-axis transient reactance of generator g.

is the quadrature-axis reactance of generator g.

is the magnitude of terminal bus voltage of generator g E

MOD.

is the reference voltage of the exciter of generator g E MOD.

is the excitation voltage of the exciter of generator g E MOD.

is the direct-axis reactance of generator g E MOD.

is the gain of the exciter of generator g E MOD.

XVI

LIST OF FIGURES

LIST OF FIGURES

Figure 1.1 A general application ofEAC. 6

Figure 2.1 A tableau form of equation (2.11). 17

Figure 3.1 Voltage phasor diagram ofa synchronous generator. 26

Figure 3.2 Excitation control system block diagram. 28

Figure 3.3 A tableau form of Equation (2.11) for the modified system. 31

Figure 5.1 Single line diagram for 4 generator - II bus system. 47

Figure 5.2 SEP for the advanced machine (thermal). 50

Figure 5.3 UEP for the advanced machine (thermal). 50

Figure 5.4 Magnetic and dissipation energy for 4 generator - 11 bus 51 thermal system.

Figure 5.5 Positional energy tor 4 generator - II bus thermal system. 51

Figure 5.6 Total energy for 4 generator - I I bus thermal system. 52

Figure 5.7 Energy margin for 4 generator - II bus thermal system. 52

Figure 5.8 Normalized energy margin for 4 generator - 11 bus thermal 54 system.

Figure 5.9 Em for 4 generator - I I bus thermal system. 54

Figure 5.10 Energy margin versus clearing time for 4 generator - 11 bus 55 thermal system (no exciter limit).

Figure 5.11 Effect of EFD on Ka for 4 generator - 11 bus thermal system 56 (EFD = 6.1 p.u.).

Figure 5.12 Energy margin versus clearing time for 4 generator - 11 bus 57 thermal system (with exciter limit = 6.1 p.u.).

Figure 5.13 Effect of EFD on Ka for 4 generator - 11 bus thermal system 58 (EFD = 5.4 p.u.).

Figure 5.14 Energy margin versus clearing time for 4 generator - 11 bus 58 thermal system (with exciter limit = 5.4 p.u.).

XVII

LIST OF FIGURES

Figure 5.15 SEP for the advanced machine (hydro). 59

Figure 5.16 UEP for the advanced machine (hydro). 60

Figure 5.17 Magnetic and dissipation energy for 4 generator - 11 bus 60 hydro-system.

Figure 5.18 Positional energy for 4 generator - 11 bus hydro-system. 61

Figure 5.19 Total energy for 4 generator - 11 bus hydro-system. 61

Figure 5.20 Energy margin for 4 generator - 1 1 bus hydro-system. 62

Figure 5.21 Normalized energy margin for 4 generator - 11 bus hydro- 62 system.

F' 5 "'? 19ure ._- Energy margin versus clearing time for 4 generator - 11 bus 63 hydro-system (no exciter limit).

Figure 5.23 Effect of EFD on Ka for 4 generator - 11 bus hydro-system 64 (EFD = 4.5 p.u.).

Figure 5.24 Energy margin versus clearing time for 4 generator - 11 bus 65 hydro-system (with exciter limit = 4.5 p.u.).

Figure 5.25 Effect of EFD on Ka for 4 generator - 11 bus hydro-system 66 (EFD = 3.9 p.u.).

Figure 5.26 Energy margin versus clearing time for 4 generator - 1 1 bus 66 hydro-system (with exciter limit = 3.9 p.u.).

Figure 5.27 SEP for the advanced generator 975 (thermal). 68

Figure 5.28 UEP for the advanced generator 975 (thermal). 68





Figure 5.33 Magnetic and dissipation energy for 11 generator - 55 bus 71 thermal system.

Figure 5.34 Positional energy for 11 generator - 55 bus thermal system. 71

Figure 5.35 Total energy for 11 generator - 55 bus thermal system. 72

XVIII

LIST OF FIGURES

Figure 5.36 Energy margin for 11 generator - 55 bus thermal system. 72

Figure 5.37 Normalized energy margin for 11 generator - 55 bus thermal 73 system.

Figure 5.38 Ern for the advanced generator 975 (thermal). 74

Figure 5.39 EFD for the advanced generator 991 (thermal). 74

Figure 5.40 EFD for the advanced generator 1001 (thennal). 75

Figure 5.41 Energy margin versus clearing time for II generator - 55 bus 75 thermal system (no exciter limit).

Figure 5.42 Effect of EFD on Ka for 11 generator - 55 bus thermal system 76 (EFD = 6 p.u.).

Figure 5.43 Energy margin versus clearing time for 11 generator - 55 bus 77 thermal system (with exciter limit = 6 p. u.).

Figure 5.44 Effect ofEFD on Ka for II generator - 55 bus thermal system 78 (EFD = 4.4 p.u.).

Figure 5.45 Energy margin versus clearing time for II generator - 55 bus 78 thermal system (with exciter limit = 4.4 p.u.).

Figure 5.46 SEP for the advanced generator 975 (hydro). 80

Figure 5.47 UEP for the advanced generator 975 (hydro). 80





Figure 5.52 Magnetic and dissipation energy for I 1 generator - 55 bus 83 hydro-system.

Figure 5.53 Positional energy for 11 generator - 55 bus hydro-system. 83

Figure 5.54 Total energy for 11 generator - 55 bus hydro-system. 84

Figure 5.55 Energy margin for II generator - 55 bus hydro-system. 84

Figure 5.56 Normalized energy margin for II generator - 55 bus hydro- 85 system.

XIX

LIST OF FIGURES

Figure 5.57 EFD for the advanced generator 975 (hydro). 85



Figure 5.60 Energy margin versus clearing time for 11 generator - 55 87 bus hydro-system (no exciter limit).

Figure 5.61 Energy margin versus clearing time for 11 generator - 55 88 bus hydro-system (with exciter limit = 5 p.u.).

Figure 5.62 Effect ofEFD on Ka for 11 generator- 55 bus hydro-system 89 (EFD = 4.5 p.u.).

Figure 5.63 Energy margin versus clearing time for 11 generator - 55 89 bus hydro-system (with exciter limit = 4.5 p.u.).

xx

LIST OF TABLES

LIST OF TABLES

Table 4.1 Load flow data file of 4-Gen, II-Bus system. 43

Table 4.2 Dynamic data file of 4-Gen, II-Bus system. 45

Table 5.1 Results of the 4 generator - 1 ] bus system. 47

Table 5.2 Results of the II generator - 55 bus system. 48

Table 5.3 Minimum values of Ka for the 4 generator - I 1 bus thermal 53 system.

Table 5.4 Critical clearing time for the 4 generator - 11 bus thermal 55 system (no exciter limit).

Table 5.5 Critical clearing time for the 4 generator - 11 bus thermal 57 system (with exciter limit = 6.1 p.u.).

Table 5.6 Critical clearing time for the 4 generator - II bus thermal 59 system (with exciter limit = 5.4 p.u.).

Table 5.7 Minimum values of Ka for the 4 generator - 11 bus hydro- 63 system.

Table 5.8 Critical clearing time for the 4 generator - 11 bus hydro- 64 system (no exciter limit).

Table 5.9 Critical clearing time for the 4 generator - II bus hydro- 65 system (with exciter limit = 4.5 p.u.).

Table 5.10 Critical clearing time for the 4 generator - 11 bus hydro- 67 system (with exciter limit = 3.9 p.u.).

Table 5.11 Critical clearing time for the 11 generator - 55 bus thermal 76 system (no exciter limit).

Table 5.12 Critical clearing time for the 11 generator - 55 bus thermal 77 system (with exciter limit = 6 p.u.).

Table 5.13 Critical clearing time for the 11 generator - 55 bus thermal 79 system (with exciter limit = 4.4 p.u.).

Table 5.14 Critical clearing time for the 11 generator - 55 bus hydro- 87 system (no exciter limit).

XXI

LIST OF TABLES

Table 5.15 Critical clearing time for the 11 generator - 55 bus hydro- 88 system (with exciter limit = 5 p.u.).

Table 5.16 Critical clearing time for the 11 generator - 55 bus hydro- 90 system (with exciter limit = 4.5 p.u.).

XXII

exciter effect on transient stability of multi-machine...

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