vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
ix
LIST OF FIGURES
x
LIST OF ABBREVIATIONS
xiii
LIST OF SYMBOLS
xiv
INTRODUCTION
1
1.1 Background
1
1.2 Project Objectives
4
1.3 Problem statement
4
1.4 Project Scope
4
1.5 Outline of the project report
5
LITERATURE REVIEW
6
2.1 introduction
6
2.2 The concept of ATC and related terms
6
2.2.1 Classification of ATC
7
2.2.2 ATC and related terms
7
2.2.3 Total transfer capability
7
2.3 Conditions for the operation of a power system
8
2.3.1 The concept power system operating limits
8
2.3.2 Definitions and Classification of PS Stability
9
2.3.3 Small angle disturbance concept
9
2.4 The concept of transient stability
10
viii
2.4.1 Power-angle relationship
11
2.4.2 Rotor Dynamics and the Swing Equation
13
2.4.3 The Practical Concept of Equal area criterion
14
2.5 Power system models
2.5.1 Generator model
15
16
2.6 The optimal power flow concept
18
2.7 Performance indices for transient stability analysis
19
2.7.1 Transient stability margin
20
2.8 Previous work on ATC computation
22
2.8.1 Stochastic Parallel Algorithm Based Evaluation
3
of ATC
22
2.8.2 Assessment on the technique
24
2.8.3 Analysis of ATC Determination by PTDF
25
2.9 Summary
29
METHODOLOGY
30
3.1 Introduction
30
3.2 Modification of Fast Decouple Power Flow for SATC 31
4
3.2.1 Implementation of SATC Algorithm
33
3.3 Proposed approach to transient stability analysis
34
3.3.1 The concept for Transient stability Analysis
34
3.3.2 Procedure for determining stability
34
3.3.3 Implementation of TSA in Matlab
37
3.4 Algorithm and code for computation of DATC
38
3.5 Summary
38
RESULT AND ANALYSIS
39
4.1 Introduction
39
4.2 Power flow results
39
4.3 Static ATC results
40
4.3.1 Analysis of Bilateral transactions
4.4 Transient stability test results
42
43
4.4.1 Case when a fault applied to bus 7
44
4.4.2 Case when a fault applied to bus 2
46
4.4.3 Discussion of results for TSA
51
4.5 Dynamic ATC results
50
ix
4.6 Validation of results
5
52
4.6.1 Validation of SATC
52
4.6.2 Validation DATC results
53
4.7 Summary
59
CONCLUSIONS AND FUTURE WORK
57
5.1 Conclusions
57
5.2 Future work
58
REFERENCES
Appendices A - K
59
62
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
2.1.
Statistical indices OF ATC
25
2.2
ATC (MW) - IEEE 30 bus system
28
2.3.
28
3.1
Execution time in seconds for ATC determination
of three test systems
The generator data matrix for ‘trstab’ program
4.1
SATC results with seller bus 2 and buyer bus 4
40
4.2
SATC result with seller bus 2 and buyer bus 28
41
4.3
SATC Transactions from Area 1 to Area 2
42
4.4
SATC Transactions from Area 1 to Area 3
42
4.5
Generator data results of the trstab function
44
4.6
Selected stability points against the generator phase
angles (δ)
48
4.8
DATC transactions from Area 1 to Area 2
50
4.8
DATC transactions from Area 1 to Area 3
51
4.9
The four selected SATC methods for comparison
52
37
xi
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
2.1
Classification of power system stability
9
2.2
Examples of the generator swing curves
11
2.3
Power-angle relationship
12
2.4
Power-angle relationship with one circuit out of
12
service
2.5
Power-angle characteristics of a single machine
14
2.6
The generator connected to turbine
16
2.7
The generator model
18
2.8
The accelerating and decelerating areas
20
2.9
Flowchart of ATC assessment by parallel
computing
23
2.10
Divided areas of IEEE 30-bus system
24
2.11
The flow chart for the analysed technique
27
3.1
Flow Chart of the methodology
31
3.2
Simple harmonic motion of the generator due to
change in rotor angle
36
4.1
Comparison of SATC between transacting areas
43
4.2a
Angle differences do not increase: Stable
45
4.2b
Some of angle differences increases indefinitely;
46
xii
Unstable
4.3a
Fault at bus 2, angle differences do not increase;
stable
47
4.3b
All angle differences increase indefinitely; unstable
47
4.4
Fault at 3, 3-4 removed
49
4.5
Comparison of DATC between regional
transactions
51
4.6
Percentage deviation of other methods with respect
to power world
53
4.7
ATC for 39-bus New England system for constant
impedance load models
54
4.8
ATC for 246-bus NREB system for constant
54
impedance loads
4.9
Comparison of SATC and DATC from Fast
decouple method
55
xiii
LIST OF ABBREVIATIONS
ACPTDF
ATC
−
−
AC Power Transfer Distribution Factor
Available Transfer Capability
CEED −
Combined economic emission dispatch
CIGRE−
Conseil International des Grands Reseux Electriques
COI
−
Center of inertia
DATC −
Dynamic Available Transfer Capability
DC PTDF−
DC Power Transfer Distribution Factor
IEEE −
Institute of Electrical and Electronics Engineers
MVA −
Mega volt ampere
MW
−
Mega watt
NERC −
North American Electric Reliability Council
NRLF −
Newton Raphson Load Flow method
SATC −
Static Available Transfer Capability
SO
−
System Operator
TDS
−
Time domain simulation
TRM −
TSA
−
Transmission Reliability Margin
Transient Stability Analysis
TSM −
Transient stability margin
−
Total Transfer Capability
TTC
xiv
LIST OF SYMBOLS
Pe∆
−
Change in electrical load
δ∆
−
Change in the rotor angle
Pe
−
Electrical Power
Pm
−
Mechanical Power
ωo
−
Angular velocity
Telect
−
Electric torque
Tmech −
mechanical torque
Tnet
−
Net torque
Δδ
−
Phase angle deviation
Δω
−
Deviations of the angular speed
Pl
−
The transmission line loss
Pi
−
The active power injection at bus i
Pgi
−
The active power generation, and
Ploadi
−
Active load at bus i
NG
−
Total number of generator buses (or PV buses)
N
−
Total number of buses
|Vi|
−
Voltage magnitude of the i-th bus
|Vk|
−
Voltage magnitude of the k-th bus
δi
−
Voltage angle of the i-th bus and
xv
δk
−
Voltage angle of the k-th bus (bus number 1 is the slack bus)
Hi
−
Inertia constant of each generator
Ht
−
Total inertia constant of the generators
θi
−
Rotor angle with respect to COI
θicl
−
Rotor angle of i-th generator at fault clearing
tcl
−
Time of clearing the fault
T
−
Short period after fault clearing
Ybus −
E
−
bus dmittance matrix
Generator excitation voltage
Δmin −
Minimum allowable generator angle
Δmax −
Maximum allowable generator angle
tcr
−
Critical clearing time