14bus Matlab Code

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UNIVERSITI

EKNOLOGIALAYSIA

NOTES

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Dote :

t l

MAY2Ol

LING

INGYI

23RD

EPTEMBER

988

VOTTAGE ECURITY

NALYSIS

UTITIZING

OLTAGE

COLTAPSE

PROXIMITY

NDICATORN POWER

YSTEM

20r0/201

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ASSOC.

PROF. DR

AZHAR KIIAIRUDIN

NAMEOFSUPERVISOR

Dote

l2

MAY2ot

Certi f ied y:


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I

hereby

declare that I

have read this thesis

and

in my

opinion

this thesis

is sufficient

in terms of

quality

and

scope

for the award

of the

degreeof

Bachelor of Engineering

(Electrical)

Signature

Supervisor

Date

ASSOC.

PROF.

DR AZHAR

KHAIRUDIN

\2MAY

2011


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VOLTAGE SECURITY ANALYSIS UTILIZING VOLTAGE COLLAPSE

PROXIMITY INDICATOR IN POWER SYSTEM

LING TING YI

This thesis is submitted in fulfillment for the

requirement for the award of the degree of

Bachelor of Engineering (Electrical)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

MAY 2011


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DECLARATION

It

is hereby declared that all

the materials

in

this thesis are the effort of my own work

and idea except for works

that have been

cited clearly in

the

references. The thesis

has

not been accepted or any

degree and

is

not

concurrently

subrnitted

in

candidature ofany

degree.

Name of

Author :

LING

TING YI

Date

,

lf,

MAY2oll


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To my parents, Ling Yoke Hook and Chew Chui Har;

younger sister, Ling Zhi Han;

younger brothers, Ling Ting Yan and Ling Ting Rui;

all my friends and those great people who appear in my life

that makes me who I am today


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ACKNOWLEDGMENT

First of all, I would like to express my heartiest gratitude to Assoc. Prof. Dr

Azhar Khairudin for his comments, guidance and advice in the preparation of this

research from scratch to successfully accomplish. Besides, I would like to thank Assoc.

Prof. Dr. Mohd. Wazir Mustafa for his lectures and guidance on Power System Analysis

course which enhance my knowledge to complete the research. My deepest appreciation

goes to my family, friends and colleagues as well for their patience and cooperation

during the entire research process. Finally, I was also greatly indebted to who helped our

research very much directly and indirectly.


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ABSTRACT

Voltage instability leading to voltage collapse phenomenon is mostly due to the

inability of power system to meet the demand for reactive power at certain critical load

buses. The primary purpose of identifying weak load buses is to maintain control of

voltage at those buses, in particular to prevent voltage collapse. This research was

carried out for voltage security analysis utilizing voltage collapse proximity indicator for

contingency screening and ranking process, as part of the voltage stability assessment.

Two benchmark results were adopted which were relative voltage change index (VC)

and continuation power flow (CPF) to be compared to the proposed voltage collapse

proximity indicator (VCPI). MATPOWER and MATLAB were used as the primary

software to carry out load flow analysis required to generate the data for the indices.

IEEE 14-bus and 30-bus test system were the power system network used to implement

the indices. The overall findings indicated that proposed VCPI was satisfactory in terms

of accuracy, but has longer computation time compared to VC. While for comparison

with CPF, their results deviated much due to the assumption of critical loading condition

on VCPI index calculation, and VCPI was superior to CPF from the perspective of

computation time. In conclusion, some suggestions have been made to enhance the

efficiency of the VCPI and recommendations for future research have also been included

in the final part of the report.


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ABSTRAK

Fenomena ketidakstabilan voltan yang menyebabkan voltan runtuh sebahagian

besar adalah disebabkan oleh ketidakmampuan sistem tenaga untuk memenuhi

keperluan kuasa reaktif pada bus beban kritikal tertentu. Tujuan utama untuk

mengenalpasti bas beban lemah adalah untuk mempertahankan kawalan voltan terhadap

bus tersebut, khususnya untuk mencegah runtuh voltan. Penyelidikan ini dilakukan

untuk analisis keselamatan voltan dengan menggunakan penunjuk jarak runtuh voltan

(VCPI) untuk penapisan kontingensi dan proses peringkat, sebagai sebahagian daripada

penilaian kestabilan voltan. Dua keputusan benchmark, indeks relatif penukaran voltan

(VC) dan kelanjutan aliran kuasa (CPF) akan dibandingkan dengan VCPI yang

dicadangkan. MATPOWER dan MATLAB digunakan sebagai perisian utama untuk

melakukan analisis aliran beban yang diperlukan untuk menghasilkan data untuk

indeks. IEEE 14-bus dan 30-bus adalah sistem tenaga rangkaian yang digunakan untuk

pelaksanaan indeks. Penemuan keseluruhan menunjukkan bahawa VCPI dicadangkan

adalah memuaskan dari aspek kejituan, namun ia mempunyai masa pengiraan yang lebih

lama dibandingkan dengan VC. Sedangkan untuk perbandingan dengan CPF, keputusan

CPF menyimpang jauh disebabkan andaian keadaan pembebanan kritikal pada

perhitungan indeks VCPI. Walau bagaimanapun VCPI lebih unggul daripada CPF dari

perspektif masa pengiraan. Sebagai kesimpulan, beberapa cadangan telah dibentang

untuk meningkatkan kecekapan VCPI dan cadangan untuk kajian akan datang juga

telah disertakan di bahagian akhir laporan.


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TABLE OF CONTENTS

CHAPTER TITLE PAGE

THESIS STATUS CONFIRMATION FORM

SUPERVISOR CONFIRMATION

TITLE COVER i

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xii

LIST OF SYMBOLS xiii

LIST OF APPENDICES xiv

1 INTRODUCTION 1

1.1 Introduction 1

1.2 Background of the Study 1

1.3 Problem Statement 2

1.4 Objectives of the Study 3

1.5 Scope of the Study 3

1.6 Significance of the Study 4

1.7 Thesis Organization 4


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2 LITERATURE REVIEW 6

2.1 Introduction 6

2.2 Power System Security 6

2.3 Voltage Security Assessment 8

2.4 Relative Voltage-Change Method (VC) 10

2.4 Continuation Power Flow (CPF) 11

2.4 Voltage Collapse Proximity Indicator (VCPI) 12

2.4 Summary 14

3 RESEARCH METHODOLOGY 15

3.1 Introduction 15

3.2 Research Procedure 15

3.2.1 Critical Loading Condition 16

3.2.2 Relative Voltage-Change Method 17

3.2.3 Continuation Power Flow 18

3.2.4 Voltage Collapse Proximity Indicator 19

3.3 Research Instruments 20

3.3.1 MATPOWER Software 21

3.4 Data Analysis 27

3.4.1 PV Curve 27

3.4.2 Microsoft® Office Excel 2007 SP2 27

3.5 Summary 28

4 RESULTS AND DISCUSSION 29

4.1 Introduction 29

4.2 Results and Discussion 29


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4.2.1 IEEE 14-Bus Test System 30

4.2.1.1 Benchmark Results 31

4.2.1.1.1 VC 31

4.2.1.1.2 CPF 33

4.2.1.2 Critical Bus Ranking by VCPI 34

4.2.1.3 Discussion 36

4.2.2 IEEE 30-Bus Test System 36

4.2.1.1 Benchmark Results 38

4.2.1.1.1 VC 38

4.2.1.1.2 CPF 40

4.2.1.2 Critical Bus Ranking by VCPI 42

4.2.1.3 Discussion 45

4.3 Summary 48

5 CONCLUSIONS AND RECOMMENDATIONS 49

5.1 Introduction 49

5.2 Conclusions 49

5.3 Recommendations 50

5.4 Future Research Work 51

REFERENCES 52

APPENDICES A – E 55-70


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LIST OF TABLES

TABLE NO TITLE PAGE

4.1 Determination of critical loading condition for IEEE

14-bus system

31

4.2 Calculation of VCi on heavy load state (IEEE 14-bus

system)

32

4.3 Critical load bus ranking of IEEE 14-bus system using

VCi

33


VCi

33


voltage collapse point from PV curve

34

4.6 Calculation of VCPI on heavy load state (IEEE 14-bus

system)

35


VCPI

35

4.8 Comparison of 3 proximity measures for contingency

ranking of IEEE 14-bus system

36

4.9 Determination of critical loading condition for IEEE

30-bus system

38

4.10 Calculation of VCi on heavy load state (IEEE 30-bus

system)

39


VCi

40

4.12 Real power and voltage magnitude of P-Q bus at 41


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voltage collapse point from PV curve (IEEE 30-bus

system)


voltage collapse point from PV curve

42

4.14 Calculation of VCPI on heavy load state (IEEE 30-bus

system)

43


VCPI

44

4.16 Comparison of 3 proximity measures for contingency

ranking of IEEE 30-bus system

45

4.17 Comparison of 3 proximity measures in terms of

computation time per load flow for both test systems

47

4.18 Comparison of 3 proximity measures in terms of

overall computation time for both test systems

47


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LIST OF FIGURES

FIGURE

NO.

TITLE PAGE

2.1 Voltage Stability Assessment Flowchart 9

2.2 PV curve of a load bus 12

3.1 Flowchart for methodology of critical loading condition 17

3.2 Flowchart for methodology of critical bus ranking utilizing

VC

18


CPF

19


VCPI

20

3.5 System summary of runpf command 22

3.6 Bus data of runpf command 23

3.7 Branch data of runpf command 23

3.8 PV curve of IEEE 14-bus system, bus 4 26

4.1 IEEE 14-bus system 30

4.2 IEEE 30-bus system 37


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LIST OF ABBREVIATIONS

CPF - Continuation Power Flow

GUI - Graphic User Interface

IEEE - Institute of Electrical and Electronics Engineering

PD - Real Power Demand

QD - Reactive Power Demand

SCADA - Supervisory Control and Data Acquisition

SNB - Saddle Node Bifurcation

TNB - Tenaga Nasional Berhad

VC - Relative Voltage-Change Index

VCPI - Voltage Collapse Proximity Indicator

VSA - Voltage Stability Assessment


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LIST OF APPENDICES

APPENDIX TITLE PAGE

A1 IEEE 14-bus system MATLAB M-file 55

A2 IEEE 30-bus system MATLAB M-file 58

B test_cpf MATLAB M-file 62

C PV curves for each load bus in IEEE 14-bus system 64

D PV curves for each load bus in IEEE 30-bus system 66

E MATLAB command for constant power factor load

increment69

F MATLAB M-file for command computation time 70


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CHAPTER 1

INTRODUCTION

1.1 Introduction

This project proposes Voltage Security Analysis utilizing Voltage Collapse

Proximity Indicator in power system. This analysis is very important in contingency

screening and ranking as part of the voltage security assessment.

In this chapter, background of the study, problem statement, objectives of the

study, scope of the study, significance of the study, and thesis organization are to be

presented.

1.2 Background of the Study

Up to year 2009, industrial sector is the second largest consumer of energy in

Malaysia, followed closely by transport sector [1]. Electrical energy is the major energy

supply for the industries, and the result of the energy audit in 2008 shows that the

highest energy consuming equipment is electric motor followed by liquid pumps and air

compressors which are used most in industry sectors [1].


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Thus the power system is expected to be more heavily loaded from day to day.

However, many environmental and economic constraints preventing the constructions of

new or upgrading power system. The power producing utilities such as Tenaga Nasional

Berhad (TNB) shows reluctance to expand their generation and transmission capabilities

due to social pressure, such as the public concerns about the effect of electric and

magnetic field around the housing area near to transmission lines.

All the constraints lead the current power system to operate closely to stability

limits, causing loss of control of the voltage levels in a power system. Usually the

voltage decay is gradual that makes system operators unaware that it is the symptom of

voltage collapse which will lead to complete blackout. Therefore, constant attention is

required to ensure the systems are operated above desired level of voltage stability

margin.

Voltage Stability Assessment (VSA) is the process to ensure the voltage security

in power system. There are two main scope of the assessment, which is static security

and dynamic security of system. One of the various steps of carrying out the assessment

is contingency screening and ranking of weak load buses. Numerous ways were

developed by researchers and industries to indicate the weakest bus in the power system.

This step is vital to make preventive maintenance before the voltage collapse happen.

1.3 Problem statement

The problem statements of this project are:

i. Most of authors realized voltage collapse in power system as a static

phenomenon;


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ii. Static study is appropriate for bulk power system study, which involves

enormous number of buses and generators;

iii. Static voltage instability is most affected by reactive power imbalance.

1.4 Objectives of the Study

The objectives of this project are:

i. To develop an indicator to perform contingency screening and ranking as part of

the voltage security assessment on standard IEEE test system using MATLAB

language;

ii. To compare the results obtained from the proposed VCPI to two benchmark

results.

1.5 Scope of the study

The scope of this project is:

i. Contingency screening and ranking of Voltage Security Assessment;

ii. Static power system analysis;

iii. Analysis applied to offline system;

iv. Weak load buses and critical lines identification in power system.

The assumptions made in the project are:


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i. The PQ-buses with zero loads are assumed to be of zero loads throughout the

analysis;

ii. The parameters of the PV-buses, i.e. bus voltage magnitude and injected power,

P are assumed to be constant throughout the analysis;

iii.

The slack bus is capable to absorb the losses in the system.

There is limitation in the project. Only load with sufficient reactive power will be

considered as the proposed VCPI is considering reactive power solely.

1.6 Significance of the study

Although there are various ways of contingency screening and ranking in the

research field, the findings of this study are important as part of Voltage Security

Assessment. Critical load bus identification is vital to ensure the priority of preventive

and correction action is given to the most critical load bus in the power system.

Through this research, a simplified implementation of VCPI that was proposed

by Chen is presented [2], thus ease the researchers from similar field as well as the

power utility industries who implement it.

1.7 Thesis Organization

This thesis consists of 5 chapters.

Chapter 2 presents literature review on the project, namely the background of

Power System Security, Voltage Security Assessment, and the available voltage collapse

proximity indicators and indexes to perform the analysis.


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Chapter 3 discusses the methodology used in the project, including methodology

to perform continuation power flow analysis, critical loading condition, voltage change

index analysis and VCPI analysis.

Chapter 4 presents the findings and results obtained from the project. The data

are analyzed and the three critical bus rankings are compared and discussed.

Chapter 5 discusses the conclusion of the project, and suggestions for further

extension on the current work.


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CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

In this chapter, literature review starts with screening the concept of power

system security, which is the big picture of the research. The research is part of the effort

to ensure power system to operate without interruption of supply to the consumers in the

same time it can withstand credible contingencies. Next the voltage stability analysis

procedure is examined and the scope steep down to static security assessment. Finally

two benchmark methods and the proposed method are reviewed from the original

authors, and the reviews of some other methods are presented as well.

2.2 Power System Security

Voltage stability problems normally occur in heavily stressed systems. A system

enters a state of voltage instability when a disturbance, increase in load demand, or

change in system condition causes a progressive and uncontrollable drop in voltage. The

main factor causing instability is the inability of the power system to meet the reactive

power demand. The heart of the problem is usually the voltage drop that occurs when

active power and reactive power flow through inductive reactance associated with the

transmission network. Moreover, a criterion for voltage stability is at a given operation


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condition for every bus in the system, the bus voltage magnitude increases as the

reactive power injection at the same bus is increased. A system is voltage unstable if, for

at least one bus in the system, the bus voltage magnitude (V) decreases as the reactive

power injection (Q) at the same bus is increased. [3]

The phenomenon of voltage collapse on a transmission system, due to operation

near the maximum transmissible power, is characterized by a fall in voltage, which is at

first gradual and then rapid. The theoretical relationship between power transferred

across a system and the receiving-end voltage follows an approximately parabolic shape.

The gradient of the curve becomes steeper as the apogee of the parabola is approached,

and a small increase in power demand at the receiving end can cause its voltage to

collapse to an unacceptably low level, rather than to continue declining in a controlled

and predictable manner. [4] The curve is also known as PV curve.

Since it is impossible to eliminate completely random faults and failures,

measures must be taken to reduce the likelihood that disturbances degenerate into major

incidents involving the disconnection of consumers. We will therefore define power

system security as the ability of the system to withstand unexpected failures and

continue operating without interruption of supply to the consumers. [5]

A power system can never be totally secure. It is always possible to devise a

sequence of events that will lead to a total or partial collapse of the system. The

probability of such a sequence of events may be very small but it will never be zero. At

the other extreme, a power system operating on its stability limit has zero security

because any deterioration in its condition (such as the outage of a component or a small

increase in load) will result in the disconnection of at least some consumers. [5]

There are some other important terms to understand for this research, which is

defined in [6]:


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i. Voltage stability - the ability of a system to maintain voltage magnitude at all the

buses in the system after disturbance;

ii. Voltage collapse - a process by which voltage instability leads to a very low

voltage;

iii. Voltage security - the ability of a system not only to operate stably but also to

remain stable following credible contingencies or adverse system changes.

2.3 Voltage Stability Assessment

Voltage stability security assessment should indicate with:

a. Where the voltage collapse occurs for any equipment outage or operating

change,

b. All contingencies and operating changes that cause voltage collapse in that

location (a specific sub region in the transmission, sub transmission, or

distribution network),

c. The cause of the voltage collapse in terms of

i. lack of reactive supply on specific reactive sources or

ii. an inability to deliver reactive to the specific region experiencing voltage

collapse,

d.

What operating changes could be made in anticipation to prevent the voltageinstability from occurring when a specific contingency and operating change

combination predicted to cause voltage instability occurs. [7]


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Figure 2.1 is the modified flowchart from [8] which represents the voltage

stability assessment. The VSA environment receives its input from a real time database.

Voltage stability assessment of the current operating point is necessary to enable the

system engineer know the voltage stability status of the system. The outcome of this

assessment determines the next line of action. If the result of the assessment is positive,

i.e. the system is secured at the present operating point, the next step would be to initiate

some credible contingencies, such as line outages and critical loading conditions, which

would be analyzed further. The large list of contingencies is screened and ranked with

respect to their margins to voltage collapse, using any fast and accurate ranking

algorithm available. Finally, the contingencies flagged as potentially harmful to the

system‟s stability are investigated further using tools like continuation power flow (CPF)

and consequently develop some control schemes to be executed in either a pre-

contingency or post-contingency mode. [9]

Figure 2.1: Voltage Stability Assessment Flowchart


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In this research, the focus is on the dotted box in the flowchart, which is

contingency selection, screening and ranking of potential harmful load bus in power

system.

System dynamics influencing voltage stability are usually slow. Therefore many

aspects of the problem can be effectively analyzed by static methods, which examine the

viability of the equilibrium point represented by a specified operating condition of the

power system. The static analysis techniques allow examination of a wide range of

system conditions and, if appropriately used, can provide much insight into the nature of

the problem and identify the key contributing factors. Dynamic analysis, on the other

hand, is useful for detailed study of specific voltage collapse situations, coordination of

protection and controls, and testing of remedial measures. Dynamic simulations also

examine whether and how the steady state equilibrium point will be reached. [3]

2.4 Relative Voltage-Change Method (VC)

Introduced by [10] and adopted by [2], the first benchmark method is based on

the relative change in the bus voltages going from the initial operating point to the

voltage stability limit.

Let and be the voltage magnitudes at bus i at the initial operatingstate and the voltage stability limit, respectively. A voltage change index is defined for

each load bus as,

(2.1)

As mentioned previously, the „weak‟ or critical bus in the network is the most

(electrically) remote bus from the point of constant or controllable voltage. It is expected

that the critical bus would be the worst affected (voltage wise) because of a shortage of


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local VARs or VARs transferred from a remote source. [10] It is anticipated that for a

specified operating regime, going from an initial operating point to the voltage stability

limit, the weakest bus would experience the largest voltage change (or drop), i.e., the

largest index VC, defined by eqn. 14. Therefore if bus k is the weakest bus,

}{max i J i

k VC VC L

(2.2)

Based on the index VCi, the system buses may be arranged in order of weakness,

the weakest bus corresponding to that with the largest index.

2.5 Continuation Power Flow (CPF)

First introduced by [11], CPF employs predictor-corrector scheme to find

solution path that have been reformulated to include load parameter. It belongs to a

general class of methods for solving nonlinear algebraic equations known as path-

following methods. [3]

In the research, a MATLAB M-file which was programmed in MATPOWER by

[12] to plot PV curve was adopted. The PV curves are the most used method of

predicting voltage security. They are used to determine the loading margin of a power

system. The power system load is gradually increased and, at each increment, is

necessary recomputed power flows until the nose of the PV curve is reached. The

margin between the voltage collapse point and the current operating point is used as

voltage stability criterion. [13]

Fig. 2.1 presents the PV curves of the power flow solution when generator limits

are neglected. Any attempt to increase PR (QR ) beyond point A in the figure would result

in a system voltage collapse. The maximum loading points are depicted in the figure


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with A and C. Different PV and QV curves can be computed based on the system

parameters chosen to do so. Each curve shows the maximum power that can be

transferred at a particular power factor. [9]

Figure 2.1: PV curve of a load bus

2.6 Voltage Collapse Proximity Indicator (VCPI)

A variety of analysis like the PV curve, QV curve, minimum eigenvaule/singular

value, right eigenvector, family of test functions, tangent vector, reduced Jacobian,

sensitivity analysis and energy based methods have been proposed [11, 14, 15, 16].

These methods usually use simple generator and load models (e.g. constant power loads

at high voltage buses).

Greene [17] proposed sensitivity analysis of the pre-contingency conditions to

avoid voltage collapse on the system. Also, Yorino et al [18] used a fast computation

method to evaluate the load power margin with respect to saddle node bifurcation. Also,

the use of the reactive power reserves was proposed as an index for evaluation of the

voltage stability of post-contingency system [19]. In [20], the improved voltage stability


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index L1 was adopted as a fast and accurate tool to trace the SNB point, regardless of

the type of load model. This takes care of the limitations of the index-L proposed by

Kessel [21] that is only suitable for constant power type of load. Fast curve fitting

method was proposed by Ejebe et al [8] to calculate the limit of the nose curve.

This project adopted voltage collapse proximity indicator (VCPI) method

proposed by Chen et al [2], to carry out the screening and ranking of the test system

buses. The critical lines are determined by linearly increasing the loads. VCPI proposed

by Chen [2] is used to identify weak load buses and areas in the power network. The

rationale behind this definition in is that voltage is the most affected by reactive power.

For a voltage stability system, all VCPIQ will have a value greater than but close to unity,

whereas a system close to voltage collapse would have at least one VCPIQ which is large,

approaching infinity at the point of collapse. In other words, the weakest bus in the

network would have the maximum value of VCPI.

VCPI for i load bus is defined as:

(2.3)

Therefore if bus k is the weakest bus,

}{max ii

Qk VCPI VCPI L

(2.4)


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Based on the index VCi, the system buses may be arranged in order of weakness,

the weakest bus corresponding to that with the largest index.

2.8 Summary

This chapter has presented the related knowledge of the research and numerous

of past works which were developed by other researchers. It starts from power system

security concept, and go deep to voltage stability assessment overview, until the

benchmark methods and proposed method as well as other methods of developing VCPI.


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CHAPTER 3

RESEARCH METHODOLOGY

3.1 Introduction

This section discusses the methodology used to archive the objective of the

research. Three procedures of implementing the indices were explained, namely VC,

CPF and VCPI. Before that another additional procedure is the pre-requisite of acquiring

VC and VCPI ranking, which is obtaining the critical loading condition. The main

research software, MATPOWER and Microsoft® Office Excel 2007 SP2 were discussed.

Finally data analysis was done utilizing PV curve.

3.2 Research Procedure

Two benchmark results produced from different method is adopted to be

compared to a proposed VCPI, which is simplified from the original version. All

procedures of the indices are presented, plus an additional procedure which is a pre-

requisite for two of the three critical load bus ranking methods.


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3.2.1 Critical Loading Condition

Before the indices VC and VCPI could be calculated, critical loading condition

must be obtained to ensure the weakest load bus was exposed for identification. Whenthe power system is stressed to heavy load state, the voltage magnitude will drop and

reactive power shortage will appear. In this research, ±10% margin is adopted as one of

the test systems exceeds 5% tolerance at basecase. Undervoltage will cause voltage

instability and malfunction of electrical equipments, inducing economic losses

especially for heavy industries.

To obtain the critical loading condition for a power system, firstly a load flow

analysis is ran at basecase, and the voltage magnitude on each load bus is recorded. Next,

the load of the power system is increased linearly at constant power factor, on a step of

10%. Constant power factor load increment is done by increasing both real and reactive

power at the same time with same step size. To obtain more precise of critical loading

condition, a smaller step size such as 5% or 1% can be adopted. The increment is

continued with the record of load bus voltage magnitudes until the magnitudes exceeded

the specified range of voltage margin, which is 0.9 p.u. to 1.1 p.u. in this research.

Therefore the last increment of the load before the voltage magnitude exceeded the limit

will be the critical loading condition of the power system. Figure 3.1 shows the

procedure of obtaining critical loading condition for this research in flowchart.


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Figure 3.1: Flowchart for methodology of critical loading condition

3.2.2 Relative Voltage-Change Index (VC)

VC is calculated based on the relative voltage change during initial and critical

loading condition of the power system. The weakest bus will be experiencing largest

voltage drop; hence will produce the largest index. Firstly the critical loading condition

is obtained for the power system. Next, from the load flow results of basecase and

critical loading condition, the voltage magnitude for each load bus is tabulated. After

that, VC index is calculated according to the formula in Chapter 2. When all the indices

are obtained for each load bus, they are ranked from highest to lowest value, indicating

the weakest to strongest bus in the system. Figure 3.2 shows the procedure of obtainingcritical bus ranking utilizing VC for this research in flowchart.

STARTRun a load flow at

basecase, record the

load bus voltagemagnitude

Increase load of IEEE 14-

bus test system linearly

at constant power factoron a step of 10%

Stop the iteration when

load bus voltage

magnitude is dropped

out of specified range(0.9


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Figure 3.2: Flowchart for methodology of critical bus ranking utilizing VC

3.2.3 Continuation Power Flow (CPF)

CPF method is a graphical method, plotting the PV curve and acquires the data

from the voltage collapse point. Firstly, PV curve is plotted for each load bus using

MATPOWER, the primary research software which will be discussed in the latter

section. Next, values for the voltage and real power magnitude at the voltage collapse

point are tabulated. The ranking is done by examine the real power value from lowest to

highest, indicating the lowest power handling bus as the weakest bus. Higher the value

of real power at voltage collapse point, stronger the load bus. Figure 3.3 shows the

procedure of obtaining critical bus ranking utilizing CPF for this research in flowchart.

STARTObtain critical

loading condition forIEEE 14-bus test

system

Tabulate data of the

voltage magnitude atinitial state and

critical state

Calculate the VC

index for each loadbus

Rank the load buses

from the highest to

lowest value of VCindex

Repeat the procedure

for IEEE 30-bus testsystem

END


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Figure 3.3: Flowchart for methodology of critical bus ranking utilizing CPF

3.2.4 Voltage Collapse Proximity Indicator (VCPI)

VCPI is based on the reactive power compensation of the power system. When a

load bus is having small increment of reactive power, other generation buses will

compensate the load increment by generating more reactive power. The load bus that

needs more reactive power compensation from the generation will be indicated as the

weakest bus as it will cause reactive power shortage in the system more likely than other

buses with the same increment of reactive power loading. Therefore the weakest bus will

be taking largest reactive power compensation; hence will produce the largest index.

Critical loading condition is implemented to ensure the system was critically stressed

and this will amplify the effect of reactive power shortage, giving larger value of VCPIindex.

Firstly the critical loading condition is obtained for the power system, same as

the methodology for VC. Next, the reactive power for specific load bus is increased by a

STARTPlot PV curve for each

load bus of IEEE 14-bustest system

Tabulate data of thevoltage magnitude andreal power magnitude

at voltage collapse point

Rank the load busesfrom the lowest to

highest value of realpower


for IEEE 30-bus testsystem

END


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small increment, in this research it is simplified by value one (1). The load flow is rerun

after the increment to monitor the additional reactive power generated by the generation

buses. The increment of reactive power of each generation bus is summed up as one of

the parameter for the calculation of VCPI. Then VCPI index is calculated according to

the formula mentioned in Chapter 2. When all the indices are obtained for each load bus,

they are ranked from highest to lowest value, indicating the weakest to strongest bus in

the system. Figure 3.4 shows the procedure of obtaining critical bus ranking utilizing

VCPI for this research in flowchart.

Figure 3.4: Flowchart for methodology of critical bus ranking utilizing VCPI

3.3 Research Instruments

The main research software used in the research was MATPOWER. It is a third

party freeware MATLAB power system simulation package, including several M-files

for solving power flow and optimal power flow problems. The latest version for

MATPOWER is Version 4.0b4, 21-May-2010. Data analysis was done using

STARTObtain critical

loading condition forIEEE 14-bus test

system

Increase reactive

power of specificload bus by ΔQi and

rerun the load flow

Obtain the sum of

increment of reactive

power of eachgeneration bus, ΔQGj

Calculate VCPI for the

specific load bus


for remaining loadbuses

Rank the load buses

from the highest to

lowest value of VCPI


for IEEE 30-bus test

systemEND


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conventional spreadsheet software, Microsoft® Office Excel 2007 spreadsheet. The

research was implemented on IEEE 14-bus test system and IEEE 30-bus test system.

After the data was extracted from MATPOWER load flow solution, it was analyzed

using Microsoft® Office Excel 2007 SP2.

3.3.1 MATPOWER

MATPOWER is a package of MATLAB® M-files for solving power flow and

optimal power flow problems. It is intended as a simulation tool for researchers and

educators that are easy to use and modify. MATPOWER is designed to give the best

performance possible while keeping the code simple to understand and modify. [12]

The primary functionality of MATPOWER is to solve power flow and optimal

power flow (OPF) problems. This involves (1) preparing the input data defining the all

of the relevant power system parameters, (2) invoking the function to run the simulation

and (3) viewing and accessing the results that are printed to the screen and/or saved in

output data structures or files. [12]

The input data for the case to be simulated are specified in a set of data matrices

packaged as the fields of a MATLAB struct, referred to as a “MATPOWER case” struct

and conventionally denoted by the variable mpc. This struct is typically defined in a case

file, either a function M-file whose return value is the mpc struct or a MAT-file that

defines a variable named mpc when loaded. The main simulation routines, whose names

begin with run (e.g. runpf , runopf ), accept either a file name or a MATPOWER casestruct as an input. Use loadcase to load the data from a case file into a struct if

modifications need to be made to the data before passing it to the simulation. [12]


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loadcase is used to load the data from a case file into a struct if modifications

need to be made to the data before passing it to the simulation. To load the IEEE 14-bus

test system, defined in case14.m M-file into the mpc variable, the following function can

be entered:

>> mpc=loadcase (‘case14’);

The solver is invoked by calling one of the main simulation functions, such as

runpf , passing in a case file name or a case struct as the first argument [12]. To run a

Newton power flow with default options on the 14-bus system, the following function

can be entered at the MATLAB prompt:

>> runpf (‘case14’);

Figure 3.5 to 3.7 shows the results of AC power flow results when command

runpf(‘case14’) was entered in MATPOWER:

Figure 3.5: System summary of runpf command


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Figure 3.6: Bus data of runpf command

Figure 3.7: Branch data of runpf command


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System summary, bus data, and branch data are displayed. The bus data includes

the voltage, angle and total generation and load at each bus. The branch data shows the

flows and losses in each branch. From the minimum and maximum voltage magnitude

printed in Figure 3.1, it is used in the research for determination of critical loading

condition while bus voltage magnitude in Figure 3.2 is used for VC computation.

On the other hand, real and reactive power demand can be modified to suit the

research need. To load the IEEE 30-bus test system data denoted from case30.m,

increase its real power demand at bus 2 to 30 MW, then run a Newton power flow with

default options, this could be accomplished as follows:

>> define_constants;

>> mpc = loadcase('case30');

>> mpc.bus(2, PD) = 30;

>> runpf(mpc);

The define constants in the first line is simply a convenience script that defines a

number of variables to serve as named column indices for the data matrices. In this

example, it allows us to access the “real power demand” column of the bus matrix using

the name PD without having to remember that it is the 3rd column [12]. Another

variable used in the research is reactive power demand, which is denoted as QD.

For realization of CPF, continuation power flow code contributed by Rui Bo and

implemented in MATPOWER is used. Implementation of continuous power flow solver

allows the plot of PV curve as well as the prediction-correction trajectory [12]. A

MATLAB M-file test_cpf as the test program for CPF is a PV curve plotter for IEEE 30-

bus test system with respect to load at bus 7. The program can be simply run by typing

test_cpf in the command window. The full code can be obtained in Appendix B.


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To suit the research need, the program is modified in order to change the case

file to be analyzed. To analyze 14-bus system, line 34 is modified:

>>casename=(‘case14’);

30-bus test system can be implemented by changing case14 into case30 that

represented 30-Bus data. Currently, continuous power flow with respect to demand

being provided to one bus only. So, only one graph for one bus can be drawn at a time.

The number of bus to be analyzed can be simply done by changing the next line:

>>loadvarloc=4

In order to change to other bus, it can be done by changing number 4 to number

10 in order to analyze Bus 10.

Figure 3.8 shows the PV curve for 14-bus system, with respect to bus 4. It is

significant to ensure which buses are critical in this project. PV curves were used to

determine system load handling capability. System performance can be shown for

various types of contingencies. In addition, the curves reflects how much load can be

served at minimum operating voltage level and the contingencies combination that lead

to system voltage collapse. The voltage and power limit for the specific bus can be

determined. For this research, CPF serves as a graphical method to obtain critical bus

ranking for the test power system.


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Figure 3.8: PV curve of IEEE 14-bus system, bus 4

To record the pure CPU calculation time of a MATLAB programme for

computation time performance analysis, tic and toc function is used. They are the

internal stopwatch timer in MATLAB, where tic starts the timer while toc prints the

elapsed time since tic was used. For example, to measure the computation time of a

power flow of IEEE 14-bus test system, the following MATLAB code can be entered:

>>tic

>>runpf('case14');

>>toc

After the code is entered, the following result will be shown:

Elapsed time is 0.038411seconds.


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3.4 Data Analysis

To analyze the data, various ways are adopted including graphical method and

tables.

The data from the power flow results are transcribed and analyzed and tabulated

in tables using spreadsheet software. The results present through tables. Table is the best

way to show the ranking of a series of data. In this research, the main purpose is to

produce weak bus ranking in power system network, thus table is the most effective way.

Ranking is done by arranging the indices ascending. Comparison table is tabulated for

clearer judgement in terms of accuracy and deviation of results.

3.4.1 PV Curve

PV curve is adopted as a graphical method to obtain the critical bus ranking in

power system. From the PV curve shown in Figure 3.4, data cursor is placed at the

voltage collapse point (also known as nose point or knee point) to acquire the real power

and voltage magnitude at critical point. After that all the data is tabulated and ranking is

made from the data as mentioned in section 3.2.3.

3.4.2 Microsoft® Office Excel 2007 SP2

Good spreadsheet computer software is crucial to analyze numerous data, and it

is vital especially for power system analysis research. Microsoft® Office Excel 2007

SP2 is used in the research to simplify the load increment for the power test system used,

computation of VC, critical loading condition computation and computation time and

many more. The ability of Excel to key in formulae in tables and solve numerous data in


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short time is very helpful in the research. The implementation can be referred from the

attached CD to the thesis.

3.5 Summary

This research proposes two benchmarks, which are VC and CPF, and one

simplified VCPI to examine the ranking of critical bus in power system. As mention

earlier in the introduction, the purpose of this study is to develop an indicator to perform

contingency screening and ranking as part of the voltage security assessment on standard

IEEE test system using MATLAB language, as well as compare the results obtained

from the proposed VCPI to two benchmark results. The research instruments that the

researchers are going to use are MATPOWER and Microsoft® Office Excel 2007 SP2.

Then, researcher performs a data analysis base on the results in the form of table and PV

curve.


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CHAPTER 4

RESULTS AND DISCUSSION

4.1 Introduction

This section presents the results of critical bus ranking tested on IEEE 14-bus test

system and IEEE 30-bus test system. Two benchmark results has been adopted, which

are relative voltage-change method (VC) and continuation power flow (CPF). For CPF,

the results are tabulated using data obtained from PV curves plotted on each load bus in

test systems while for VC, the relative change of bus voltage magnitude between initial

state and critical state are recorded. The actual results are computed by proposed VCPI

utilizing the reactive power compensation for small increase on each load bus. Both

results are compared in terms of accuracy and computation time.

4.2 Results and Discussion

Results for the benchmark results, VC and CPF as well as the proposed method,

VCPI are presented, and analysis is done in terms of accuracy and computation time.


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4.2.1 IEEE 14-bus test system

This project adopts IEEE 14-bus system which is part of American Electric

Power System at February 1962 as shown in Figure 4.1. This power system network

consists of 14 buses with five machines and 11 loads. There is no line limit for 14-bus

system, but it has low base voltages and an overabundance of voltage control capability.

Full data of the test system can be referred at Appendix A section.

Figure 4.1: IEEE 14-bus system

Before the computation of VC and VCPI, critical loading condition is obtained

for the test system. As shown in Table 4.1, heavy load state happens when the load is

increased 180% from basecase, at the same time maintaining 0.9 p.u. to 1.1 p.u. of

voltage magnitude on the load bus, which is 10% tolerance of the normal value. It

appears when the minimum voltage magnitude is stressed to 0.909 p.u. for bus 14 and

maximum voltage magnitude is 1.090 p.u. for bus 8.


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Table 4.1: Determination of critical loading condition for IEEE 14-bus system

% of increment 0% 10% 20% … 170% 180% 190%

Minimum

voltagemagnitude

1.010

p.u. @ bus 3

1.010

p.u. @ bus 3

1.010

p.u. @ bus 3 …

0.918

p.u. @ bus 14

0.909

p.u. @bus 14

0.899

p.u. @ bus 14

Maximum

voltage

magnitude

1.090 p.u. @ bus 8

1.090 p.u. @ bus 8

1.090 p.u. @ bus 8 …

1.090 p.u. @ bus 8

1.090

p.u. @

bus 8

1.090 p.u. @ bus 8

4.2.1.1 Benchmark results

Benchmark results consist of VC and CPF. The calculation of the indices and the

critical bus ranking are shown.

4.2.1.1.1 Relative Voltage-Change Method

Table 4.2 shows the calculation of VC on IEEE 14-bus system during critical

loading condition. For load bus 1, 2, 3, 6, 8, the VC index appears as nil due to their

generation bus or P-V bus characteristics, which will maintain their voltage magnitude

in spite of load change. Bus 7 is not considered for the ranking as it is not a load bus,

containing no load data for active and reactive power.


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Table 4.2: Calculation of VCi on heavy load state (IEEE 14-bus system)

Load bus

1 1.060 1.060 0

2 1.045 1.045 03 1.010 1.010 0

4 1.018 0.933 0.091104

5 1.020 0.934 0.092077

6 1.070 1.070 0

7* 1.062 0.984 0.079268

8 1.090 1.090 0

9 1.056 0.944 0.118644

10 1.051 0.943 0.114528

11 1.057 0.995 0.062312

12 1.055 1.019 0.035329

13 1.050 0.998 0.05210414 1.036 0.909 0.139714

* Bus 7 was neglected from ranking as it is not a P-Q bus

Table 4.3 shows the critical bus ranking using VC index. Eight rankings are

produced as there are 8 load buses out of 14 buses available for the use this research.

Load buses are ranked ascending from weak to strong from the calculated VC index

above. Bus 14 appears as the weakest bus according to the index; follow by bus 9, 10, 5,

4, 11, 13 and finally bus 12 as the strongest bus.


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Table 4.3: Critical load bus ranking of IEEE 14-bus system using VCi

Critical bus

ranking (weak to

strong)

Load bus

1 14

2 93 10

4 5

5 4

6 11

7 13

8 12

4.2.1.1.2 Continuation Power Flow (CPF) Based Method

Table 4.4 shows the tabulated real power and voltage magnitude from CPF on

IEEE 14-bus system. Only pure load bus is considered for the plotting of CPF, therefore

there is no data for bus 1, 2, 3, 6, 7, and 8.

Table 4.4: Real power and voltage magnitude of P-Q bus at voltage collapse point from

PV curve (IEEE 14-bus system)

Load bus P (p.u.) V (p.u.)

4 7.266 0.6824

5 6.055 0.6249

9 2.536 0.5905

10 1.695 0.5870

11 1.871 0.5781

12 1.826 0.5705

13 2.690 0.5878

14 1.354 0.6008

Table 4.5 shows the critical bus ranking using CPF. Eight rankings are produced

from the tabulated data above and load buses are ranked ascending from weak to strong.

Bus 14 appears as the weakest bus according to the index; follow by bus 10, 12, 11, 9,

13, 5 and finally bus 4 as the strongest bus.


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Table 4.5: Critical load bus ranking of IEEE 14-bus system using voltage collapse point

from PV curve

Critical bus

ranking (weak tostrong)

Load bus

1 14

2 10

3 12

4 11

5 9

6 13

7 5

8 4

4.2.1.2 Critical bus ranking by VCPI

Table 4.6 shows the calculation of VCPI on IEEE 14-bus system during critical

loading condition. For load bus 1, 2, 3, 6, 7, and 8, there were no VCPI index appears

due to their generation bus or P-V bus characteristics. As shown in column 3, proposed

VCPI is simplified by stating small change in load reactive power to one (1), compared

to the original VCPI introduced by Chen [2].


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Table 4.6: Calculation of VCPI on heavy load state (IEEE 14-bus system)

Load bus

1 - - -

2 - - -

3 - - -

4 1.31 1 1.31

5 1.41 1 1.41

6 - - -

7 - - -

8 - - -

9 1.56 1 1.56

10 1.54 1 1.54

11 1.29 1 1.29

12 1.13 1 1.13

13 1.21 1 1.2114 1.59 1 1.59

Table 4.7 shows the critical bus ranking using VCPI index. Eight rankings are

produced from the tabulated data above and load buses are ranked ascending from weak

to strong. Load buses are ranked ascending from weak to strong from the calculated

VCPI index above. Bus 14 appears as the weakest bus according to the index; follow by

bus 9, 10, 5, 4, 11, 13 and finally bus 12 as the strongest bus.

Table 4.7: Critical load bus ranking of IEEE 14-bus system using VCPI

Critical bus

ranking

(weak to strong)

Load bus

1 14

2 9

3 10

4 5

5 46 11

7 13

8 12


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4.2.1.3 Discussion

Table 4.8: Comparison of 3 proximity measures for contingency ranking of IEEE 14-

bus system Rank (weakest to

strongest)

Proximity measures

CPF VC VCPI

1 14 14 14

2 10 9 9

3 12 10 10

4 11 5 5

5 9 4 4

6 13 11 11

7 5 13 13

8 4 12 12

Table 4.8 shows the load buses of IEEE 14-bus test system ordered from the

weakest to strongest using continuous power flow (CPF) and relative voltage change

index (VC), compared to voltage collapse proximity indicator (VCPI). All three

indicator noted bus 14 as the weakest bus. For VC and VCPI, both of them produce the

same rank of weak load buses, it is evidenced by their same choice of strongest bus in

system, which is bus 12, followed by bus 13, bus 11, bus 4, bus 5, bus 10, bus 9 and

finally bus 14. Besides the weakest bus, CPF screens different results compared to

another two indices. Except ranking of bus 10 and bus 13 are similar to those shown by

others, the remaining rank of buses deviate much, as it can be seen that CPF ranked bus

4 as the strongest bus while others ranked it as the fifth of weakest.

4.2.2 IEEE 30-bus test system

While for IEEE 30-bus system, it consists of 30 buses, 6 generators and 20 loads.

The test system data can be viewed in Appendix A.


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Figure 4.2: IEEE 30-bus system

Before the computation of VC and VCPI, critical loading condition is obtained

for the test system, same as done for IEEE 14-bus test system. As shown in Table 4.9,

heavy load state happens when the load is increased 80% from basecase, at the same

time maintaining 0.9 p.u. to 1.1 p.u. of voltage magnitude on the load bus, which is 10%

tolerance of the normal value. It appears when the minimum voltage magnitude is

stressed to 0.907 p.u. for bus 8 is and maximum voltage magnitude is 1.000 p.u. for bus

1.


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Table 4.9: Determination of critical loading condition for IEEE 30-bus system

% of

increment 0% 10% 20% … 70% 80% 90%

Minimum

voltage

magnitude

0.961 p.u. @

bus 8

0.955 p.u. @

bus 8

0.949 p.u. @

bus 8 …

0.915 p.u. @

bus 8

0.907

p.u. @

bus 8

0.899 p.u. @

bus 8Maximumvoltage

magnitude

1.000 p.u. @ bus 1

1.000 p.u. @ bus 1

1.000 p.u. @ bus 1 …

1.000 p.u. @ bus 1

1.000

p.u. @

bus 1

1.000 p.u. @ bus 1

4.2.2.1 Benchmark results

Benchmark results consist of VC and CPF. The calculation of the indices and the

critical bus ranking are shown.

4.2.2.1.1 Relative Voltage-Change Method

Table 4.10 shows the calculation of VC on IEEE 30-bus system during criticalloading condition. For load bus 1, 2, 13, 22, 23 and 27, the VC index appears as nil due

to their generation bus or P-V bus characteristics, which will maintain their voltage

magnitude in spite of load change. Bus 5, 6, 9, 11, 25 and 28 are not considered for the

ranking as it is not a load bus, containing no load data for active and reactive power.


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Table 4.10: Calculation of VCi on heavy load state (IEEE 30-bus system)

Load bus

1 1 1 0

2 1 1 03 0.983 0.952 0.032563

4 0.98 0.946 0.035941

5* 0.982 0.956 0.027197

6* 0.973 0.932 0.043991

7 0.967 0.923 0.047671

8 0.961 0.907 0.059537

9* 0.981 0.957 0.025078

10 0.984 0.972 0.012346

11* 0.981 0.957 0.025078

12 0.985 0.97 0.015464

13 1 1 014 0.977 0.955 0.023037

15 0.98 0.961 0.019771

16 0.977 0.957 0.020899

17 0.977 0.957 0.020899

18 0.968 0.94 0.029787

19 0.965 0.935 0.032086

20 0.969 0.942 0.028662

21 0.993 0.988 0.005061

22 1 1 0

23 1 1 0

24 0.989 0.978 0.01124725* 0.99 0.981 0.009174

26 0.972 0.948 0.025316

27 1 1 0

28* 0.975 0.932 0.046137

29 0.98 0.961 0.019771

30 0.968 0.939 0.030884

* Bus 5, 6, 9, 11, 25 and 28 were neglected from ranking as it is not a P-Q bus

Table 4.11 shows the critical bus ranking using VC index. Eighteen rankings are


to strong. The top three weakest buses appear as bus 8, 7 and 4, while the top three

strongest buses are bus 21, 24 and 10.


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Table 4.11: Critical load bus ranking of IEEE 30-bus system using VCi

Critical bus

ranking (weak to

strong)

Load bus

1 8

2 7

3 4

4 3

5 19

6 30

7 18

8 20

9 26

10 14

11 16

12 17

13 15

14 29

15 12

16 10

17 24

18 21

4.2.2.1.2 Continuation Power Flow (CPF) Based Method

Table 4.12 shows the tabulated real power and voltage magnitude from CPF on

IEEE 30-bus system. Only pure load bus is considered for the plotting of CPF, therefore

there is no data for bus 1, 2, 5, 6, 9, 11, 13, 22, 23, 25, 27 and 28.


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Table 4.12: Real power and voltage magnitude of P-Q bus at voltage collapse point

from PV curve (IEEE 30-bus system)

Load bus P (p.u.) V (p.u.)

3 3.702 0.5237

4 5.676 0.5995

7 2.586 0.51668 2.254 0.4937

10 3.307 0.7693

12 2.850 0.6237

14 1.337 0.5350

15 2.544 0.5963

16 1.523 0.5495

17 2.048 0.5601

18 1.297 0.5229

19 1.277 0.5208

20 1.400 0.5366

21* 2.600 0.938824 1.930 0.5212

26 0.352 0.4964

29 0.754 0.5364

30 0.748 0.5463

Table 4.13 shows the critical bus ranking using CPF. Eighteen rankings are


to strong. The top three weakest buses appear as bus 26, 30 and 29, while the top three

strongest buses are bus 4, 3 and 10. PV curve for bus 21 is not plotted accurately as it

does not showed a full swing curve as others, thus the lowest point of the curve is

adopted for the research.


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Table 4.13: Critical load bus ranking of IEEE 30-bus system using voltage collapse

point from PV curve

Critical bus

ranking (weak to

strong)

Load bus

1 262 30

3 29

4 19

5 18

6 14

7 20

8 16

9 24

10 17

11 8

12 1513 7

14 21*

15 12

16 10

17 3

18 4

*PV curve for bus 21 was not plotted accurately

4.2.2.2 Critical bus ranking by VCPI

Table 4.14 shows the calculation of VCPI on IEEE 30-bus system during critical

loading condition. For load bus 1, 2, 5, 6, 9, 11, 13, 22, 23, 25, 27 and 28, there are no

VCPI index appeared due to their generation bus or P-V bus characteristics. As shown in

column 3, proposed VCPI is simplified by stating small change in load reactive power to

one (1), compared to the original VCPI introduced by Chen [2].


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Table 4.14: Calculation of VCPI on heavy load state (IEEE 30-bus system)

Load bus

1 - - -

2 1.00 1 1.00

3 1.10 1 1.10

4 1.11 1 1.11

5 - - -

6 - - -

7 1.15 1 1.15

8 1.19 1 1.19

9 - - -

10 1.07 1 1.07

11 - - -

12 1.09 1 1.09

13 - - -14 1.10 1 1.10

15 1.08 1 1.08

16 1.10 1 1.10

17 1.10 1 1.10

18 1.11 1 1.11

19 1.12 1 1.12

20 1.11 1 1.11

21 1.02 1 1.02

22 - 1 -

23 1.00 1 1.00

24 1.04 1 1.0425 - 1 -

26 1.09 1 1.09

27 - 1 -

28 - 1 -

29 1.04 1 1.04

30 1.06 1 1.06

Table 4.15 shows the critical bus ranking using VCPI index. Twenty rankings are

produced from the tabulated data above and load buses are ranked ascending from weakto strong. Load buses are ranked ascending from weak to strong from the calculated

VCPI index above. The top three weakest buses appear as bus 8, 7 and 19, while the top

three strongest buses are bus 23, 2 and 21.


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Table 4.15: Critical load bus ranking of IEEE 30-bus system using VCPI

Critical bus

ranking (weak to

strong)

Load bus

1 8

2 73 19

4 4

4 18

4 20

7 3

7 14

7 16

7 17

11 12

11 26

13 15

14 10

15 30

16 24

16 29

18 21

19 2

19 23


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4.2.2.3 Discussion

Table 4.16: Comparison of 3 proximity measures for contingency ranking of IEEE 30-

bus system

Rank (weakest to

strongest)

Proximity measures

CPF VC VCPI

1 26 8 8

2 30 7 7

3 29 4 19

4 19 3 4

5 18 19 18

6 14 30 20

7 20 18 3

8 16 20 14

9 24 26 1610 17 14 17

11 8 16 12

12 15 17 26

13 7 15 15

14 21* 29 10

15 12 12 30

16 10 10 24

17 3 24 29

18 4 21 21

19 - - 2

20 - - 23

Table 4.16 shows the load buses of IEEE 30-bus test system ordered from the

weakest to strongest using continuous power flow (CPF) and relative voltage change

index (VC), compared to voltage collapse proximity indicator (VCPI). In overall, VC

and VCPI produce similar ranking of weak load buses while CPF shows an irrelevant

ranking compared to others. VC and VCPI indicate bus 8 as the weakest bus while CPF

votes for bus 26. For the strongest bus, both of them choose bus 12 but CPF goes for bus4. When zooming into the difference of results by both VC and VCPI indices, their

ranking of load buses deviate not more than three (3) position of rank. For CPF, the

ranking is better at the middle rank. It is proofed that rank 5 and 10 for CPF is exactly

same as VCPI and ranking for bus 19, 14, 20, 16, 15, 12 and 10 are similar to what VC

and VCPI have ranked.


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The deviation of results produced by CPF is explained by the critical loading

condition set for VC and VCPI. Results of VC and VCPI are influenced by the

assumption of heavy load state, where their voltage magnitude of all load buses has tolie between 0.9 p.u. to 1.1 p.u.. The increment of load with constant power factor stops

at 80% from basecase. For CPF, the results are obtained from PV curve plotted using

Continuation Power Flow program included in MATPOWER software package. It can

be seen from the PV curves that the system is stressed to the condition where the bus

voltage magnitudes are suppressed down to 0.57 p.u. in 14-bus system, even 0.49 p.u. in

30-bus system.

In terms of computation time, CPF and VCPI require one complete load flow

solution per load bus. CPF method need to plot the PV curve per load bus and obtain the

voltage collapse point, while it is vital for VCPI to obtain small increase in generation

and load reactive power. For VC, it requires two complete power flow solutions to

obtain the load bus voltage magnitude for initial and critical state. Table 4.17 shows the

computation time per power flow and table shows the overall computation time of all

indices. Stopwatch time function in MATLAB utilizing “tic and toc” code is used in the

analysis.


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Table 4.17: Comparison of 3 proximity measures in terms of computation time per load

flow for both test systems

Test system Run

attempt

Computation time per load flow (second)

CPF (on bus 4) VC VCPI

IEEE 14-bus 1 0.381236 0.018805 0.0188052 0.384566 0.018985 0.018985

3 0.385031 0.018978 0.018978

4 0.391615 0.017533 0.017533

5 0.385207 0.018658 0.018658

Average 0.385531 0.018592 0.018592

IEEE 30-bus 1 0.412958 0.029133 0.029133

2 0.417074 0.028265 0.028265

3 0.421429 0.026094 0.026094

4 0.411697 0.025931 0.025931

5 0.409544 0.027766 0.027766Average 0.41454 0.027438 0.027438

From Table 4.18, it can be seen that CPF has the longest computation time

compared to another two indices, and VC appears to be the fastest indices to compute.

For IEEE 14-bus test system, VCPI is seven (7) times slower than VC while twenty (20)

times faster than CPF. For IEEE 30-bus test system, VCPI is seven (7) times slower than

VC while fifteen (15) times faster than CPF. The assumption made for the analysis is the

power flow is attempted on bus 4 solely for CPF, and the power flow process for VC

and VCPI is the same. All the computation time tabulated is based on pure CPU

calculation time, neglecting time delay by user interaction. In comparison, VC has the

shortest computation time compared to another two indices.

Table 4.18: Comparison of 3 proximity measures in terms of overall computation time

for both test systems

Test system Overall computation time

CPF (on bus 4) VC VCPI

IEEE 14-bus 5.38743 0.037184 0.260288

IEEE 30-bus 5.80356 0.054876 0.384132


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For the overall performance of proposed VCPI, it can be rated as satisfactory as

the result produced in both 14-bus and 30-bus test system are similar. The drawback is it

has longer computation time than VC. With the advancement of computer technology

nowadays, solution for a power flow by computer is less than one second and the

problem is minimized.

4.3 Summary

This chapter has discussed the comparison of three indices to indicate weak load

buses in the power system, tested on IEEE 14-bus test system and 30-bus test system.

Two benchmark methods are adopted which were VC and CPF. The proposed VCPI is

rated as satisfactory in terms of accuracy, but has longer computation time compared to

performance of VC. While for comparison with CPF, their ranking results deviate much

due to the assumption of critical loading condition on VCPI index calculation, and VCPI

is superior to CPF from the perspective of computation time.


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CHAPTER 5

CONCLUSIONS & RECOMMENDATIONS

5.1 Introduction

In this chapter, conclusions are presented to address the stated objectives,

implication of the findings, and limitations related to the proposed approach.

Recommendations and future research work related to the current method are also

highlighted.

5.2 Conclusions

This research has presented a comparative study and analysis of the performance

of some static voltage collapse indices. The objectives for the research are archived: to

develop an indicator to perform contingency screening and ranking – part of Voltage

Security Assessment on standard IEEE test system using MATLAB language and to

compare the results obtained from the VCPI to two benchmark results, which are VC

and CPF. The software used to analysis primary data included Matpower and Matlab.

Data collected is then analyzed by spreadsheet software Microsoft® Office Excel.

For the results, all the indices VC, CPF and VCPI point bus 14 as the weakest

bus in the system for IEEE 14-bus test system, and VC and VCPI produce the exact


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ranking from each other. While for IEEE 30-bus test system, VC and VCPI produce

similar ranking as well, rate bus 8 as the weakest bus but ranking of CPF deviates much,

it rates bus 26 which is ranked 12 by VCPI. The researcher believes that the deviation is

due to the critical loading condition assumption for calculation of VC and VCPI. In

terms of computation time, VC is the best among three indices, followed by VCPI and

CPF.

The results of this study indicate that the proposed VCPI is rated as satisfactory

in terms of accuracy, but has longer computation time compared to performance of VC.

While for comparison with CPF, their ranking results deviate much due to the

assumption of critical loading condition, and VCPI is superior to CPF from the

perspective of computation time. Compared to the original VCPI by Chen [2], proposed

VCPI is simplified by stating the small increase of load reactive power, ΔQi to one (1).

However, these findings are only applicable to contingency screening and

ranking process as the part of Voltage Stability Assessment (VSA) discussed in Chapter

2. The research utilized static voltage collapse indices, and only applicable to offline

power system.

5.3 Recommendations

Based on the findings and conclusion of the study, here are several

recommendations to be considered:

1. User Interface – development of VCPI to Matlab program or incorporating

Graphic User Interface (GUI). This will ease the user on the analysis. By calling

certain function in Matlab, critical loading condition could be obtained and CPF,

VC and VCPI could be tabulated nicely on the screen.


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2. Complex power VCPI – proposed VCPI is applicable for load with sufficient

reactive power, obviously it would produce inaccurate index for unity power

factor loads. Therefore a complex power index will be a better indicator. Further

development of the index could refer to [22].

3.

Precision on critical loading condition – to obtain more precise of critical loading

condition, a smaller step size such as 5% or 1% can be adopted instead of 10%

that was used in this research.

5.4 Future Research Work

This study should be conducted with large buses test system such as 57-bus or

118-bus to increase the validity of the research. Researchers should do more reading on

the topic of voltage security assessment and previous methods of voltage collapse

proximity indicators and indices to identify weak load buses in power system.

Source of the information should not depend solely on internet articles. Journals

and newspaper archive should also be taken into consideration. Methods of analyzing

data collected should not be restricted on reactive power and voltage magnitude, but

from more complex method such as right singular vector by Chen [2].

More advanced method should be implemented in order to increase the validity

of the research, such as utilizing software like PowerWorld, Power System Analysis

Toolbox (PSAT), Voltage Stability Toolbox (VST) and many more.


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REFERENCES

1. R, Saidura and H.H, Masjukia and S, Mekhilef and H.W, Ping and Rahim,

N.A and Jahirul, M.I (2008) Energy Audit And Consumption Study Of Malaysian

Industrial Sector. In: The 2nd Industrial Applications Of Energy Systems

Conference, April 1-2, 2008, Oman.

2.

Y. L. Chen, C. W. Chang, and C. C. Liu, "Efficient methods for identifying weak

nodes in electrical powernetworks," IEE Proceedings-Generation, Transmission

and Distribution, vol. 142, pp. 317-322, 1995.

3. P. Kundur. (1994). Power System Stability and Control : McGraw Hill, Inc.

4. A. M. Chebbo , M. R. Irving and M. J. H. Sterling “Voltage collapse proximity

indicator: Behavior and implications”, Proc. Inst. Elect. Eng., C , vol. 139, pp.

241 1992.

5. D S Kirschen, “Power System Security”, IEE Power Engineering Journal, Vol.

16, No. 5, pp.241-248, October 2002.

6. Hadi Saadat (1999), Power System Analysis, Boston: McGraw-Hill.

7. R. A. Schlueter, "A voltage stability security assessment method", IEEE Trans.

Power Syst., vol. 13, no. 4, pp. 1423 - 1438, 1998.

8. G. C. Ejebe, G. D. Irisarri, S. Mokhtari, O. Obadina, P. Ristanovic, and J. Tong,

"Methods for contingency screening and ranking for voltage stability analysis of

power systems," 1995.

9.

Akorede, M.F.; Hizam, H.; Aris, I.; Kadir, M.Z.A.; , "Contingency evaluation for

voltage security assessment of power systems," Research and Development

(SCOReD), 2009 IEEE Student Conference on , vol., no., pp.345-348, 16-18 Nov.

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10. Obadina, O.O.; Berg, G.J.; , "Identifying electrically weak and strong segments

of a power system from a voltage stability viewpoint," Generation, Transmission

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11.

H. Song, S. Kim, B. Lee, S.H. Kwon, V. Ajjarapu, “Determination of interface

flow margin using the modified continuation power flow in voltage stability

analysis”, IEE Proc. Gen. Transm. Distrib. 148 (2) (2001) 128– 132.

12. R. D. Zimmerman, C. E. Murillo-Sanchez, and R. J. Thomas, “Matpower's

Extensible Optimal Power Flow Architecture,” Power and Energy Society

General Meeting, 2009 IEEE, pp. 1-7, July 26-30 2009.

13. Reis, C.; Andrade, A.; Maciel, F.P.; , "Voltage stability analysis of electrical

power system," Power Engineering, Energy and Electrical Drives, 2009.

POWERENG '09. International Conference on , vol., no., pp.244-248, 18-20

March 2009

14. A.C. Zambroni, “Identifying a vanishing eigenvalue in voltage collapse analysis

with consideration of limits”. IEE Proc. Gen. Transm. Distrib. 148 2 (2001), pp.

263 – 267.

15. A.A. El-Keib, X. Ma, “Application of artificial neural networks in voltage

stability assessment”, IEEE Trans. Power Syst. 10 (4) (1995) 1890– 1896.

16. A.C.Z. de Souza, C.A. Canizares and V.H. Quintana, “New techniques to speed

up voltage collapse computations using tangent vectors”. IEEE Trans. Power

Syst. 12 3 (1997), pp. 1380 – 1387

17. S. Greene, I. Dobson, and F. L. Alvarado, "Contingency ranking for voltage

collapse via sensitivities from a single nose curve," IEEE Transactions on Power

Systems, vol. 14, pp. 232-240, 1999.

18. N. Yorino, H. Q. Li, S. Harada, A. Ohta, and H. Sasaki, "A method of voltage

stability evaluation for branch and generator outage contingencies," IEEE

Transactions on Power Systems, vol. 19, pp. 252-259, 2004.

19. T. Van Cutsem, C. Moisse, and R. Mailhot, "Determination of secure operating

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20. J. Hongjie, Y. Xiaodan, and Y. Yixin, "An improved voltage stability index and

its application," International Journal of Electrical Power and Energy Systems,

vol. 27, pp. 567-574, 2005.

21.

P. Kessel and H. Glavitsch, "Estimating the voltage stability of a power system,"

IEEE Transactions on Power Delivery, vol. 1, pp. 346-354, 1986.


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Appendix A1

IEEE 14-bus system MATLAB M-file

function mpc = case14%CASE14 Power flow data for IEEE 14 bus test case.

% Please see CASEFORMAT for details on the case file format.% This data was converted from IEEE Common Data Format% (ieee14cdf.txt) on 20-Sep-2004 by cdf2matp, rev. 1.11% See end of file for warnings generated during conversion.%% Converted from IEEE CDF file from:% http://www.ee.washington.edu/research/pstca/%% 08/19/93 UW ARCHIVE 100.0 1962 W IEEE 14 Bus Test Case

% MATPOWER% $Id: case14.m,v 1.11 2010/03/10 18:08:15 ray Exp $

%% MATPOWER Case Format : Version 2mpc.version = '2';

%%----- Power Flow Data -----%%%% system MVA basempc.baseMVA = 100;

%% bus data% bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax Vminmpc.bus = [

1 3 0 0 0 0 1 1.06 0 0 1 1.06 0.94;2 2 21.7 12.7 0 0 1 1.045 -4.98 0 1 1.06 0.94;3 2 94.2 19 0 0 1 1.01 -12.72 0 1 1.06 0.94;4 1 47.8 -3.9 0 0 1 1.019 -10.33 0 1 1.06 0.94;5 1 7.6 1.6 0 0 1 1.02 -8.78 0 1 1.06 0.94;6 2 11.2 7.5 0 0 1 1.07 -14.22 0 1 1.06 0.94;7 1 0 0 0 0 1 1.062 -13.37 0 1 1.06 0.94;8 2 0 0 0 0 1 1.09 -13.36 0 1 1.06 0.94;9 1 29.5 16.6 0 19 1 1.056 -14.94 0 1 1.06 0.94;10 1 9 5.8 0 0 1 1.051 -15.1 0 1 1.06 0.94;11 1 3.5 1.8 0 0 1 1.057 -14.79 0 1 1.06 0.94;12 1 6.1 1.6 0 0 1 1.055 -15.07 0 1 1.06 0.94;13 1 13.5 5.8 0 0 1 1.05 -15.16 0 1 1.06 0.94;14 1 14.9 5 0 0 1 1.036 -16.04 0 1 1.06 0.94;

];

%% generator data% bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin Pc1 Pc2 Qc1minQc1max Qc2min Qc2max ramp_agc ramp_10 ramp_30 ramp_q apf


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mpc.gen = [1 232.4 -16.9 10 0 1.06 100 1 332.4 0 0 0 0 0 0 0 0 0 0 0 0;2 40 42.4 50 -40 1.045 100 1 140 0 0 0 0 0 0 0 0 0 0 0 0;3 0 23.4 40 0 1.01 100 1 100 0 0 0 0 0 0 0 0 0 0 0 0;6 0 12.2 24 -6 1.07 100 1 100 0 0 0 0 0 0 0 0 0 0 0 0;

8 0 17.4 24 -6 1.09 100 1 100 0 0 0 0 0 0 0 0 0 0 0 0;];

%% branch data% fbus tbus r x b rateA rateB rateC ratio angle status angmin angmaxmpc.branch = [

1 2 0.01938 0.05917 0.0528 9900 0 0 0 0 1 -360 360;1 5 0.05403 0.22304 0.0492 9900 0 0 0 0 1 -360 360;2 3 0.04699 0.19797 0.0438 9900 0 0 0 0 1 -360 360;2 4 0.05811 0.17632 0.034 9900 0 0 0 0 1 -360 360;2 5 0.05695 0.17388 0.0346 9900 0 0 0 0 1 -360 360;3 4 0.06701 0.17103 0.0128 9900 0 0 0 0 1 -360 360;4 5 0.01335 0.04211 0 9900 0 0 0 0 1 -360 360;4 7 0 0.20912 0 9900 0 0 0.978 0 1 -360 360;4 9 0 0.55618 0 9900 0 0 0.969 0 1 -360 360;5 6 0 0.25202 0 9900 0 0 0.932 0 1 -360 360;6 11 0.09498 0.1989 0 9900 0 0 0 0 1 -360 360;6 12 0.12291 0.25581 0 9900 0 0 0 0 1 -360 360;6 13 0.06615 0.13027 0 9900 0 0 0 0 1 -360 360;7 8 0 0.17615 0 9900 0 0 0 0 1 -360 360;7 9 0 0.11001 0 9900 0 0 0 0 1 -360 360;9 10 0.03181 0.0845 0 9900 0 0 0 0 1 -360 360;9 14 0.12711 0.27038 0 9900 0 0 0 0 1 -360 360;10 11 0.08205 0.19207 0 9900 0 0 0 0 1 -360 360;12 13 0.22092 0.19988 0 9900 0 0 0 0 1 -360 360;13 14 0.17093 0.34802 0 9900 0 0 0 0 1 -360 360;

];

%%----- OPF Data -----%%%% generator cost data% 1 startup shutdown n x1 y1 ... xn yn% 2 startup shutdown n c(n-1) ... c0mpc.gencost = [

2 0 0 3 0.0430293 20 0;2 0 0 3 0.25 20 0;2 0 0 3 0.01 40 0;2 0 0 3 0.01 40 0;2 0 0 3 0.01 40 0;

];

% Warnings from cdf2matp conversion:%


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% ***** Qmax = Qmin at generator at bus 1 (Qmax set to Qmin + 10)% ***** area data conversion not yet implemented (creating dummy area data)% ***** MVA limit of branch 1 - 2 not given, set to 9900% ***** MVA limit of branch 1 - 5 not given, set to 9900% ***** MVA limit of branch 2 - 3 not given, set to 9900

% ***** MVA limit of branch 2 - 4 not given, set to 9900% ***** MVA limit of branch 2 - 5 not given, set to 9900% ***** MVA limit of branch 3 - 4 not given, set to 9900% ***** MVA limit of branch 4 - 5 not given, set to 9900% ***** MVA limit of branch 4 - 7 not given, set to 9900% ***** MVA limit of branch 4 - 9 not given, set to 9900% ***** MVA limit of branch 5 - 6 not given, set to 9900% ***** MVA limit of branch 6 - 11 not given, set to 9900% ***** MVA limit of branch 6 - 12 not given, set to 9900% ***** MVA limit of branch 6 - 13 not given, set to 9900% ***** MVA limit of branch 7 - 8 not given, set to 9900% ***** MVA limit of branch 7 - 9 not given, set to 9900% ***** MVA limit of branch 9 - 10 not given, set to 9900% ***** MVA limit of branch 9 - 14 not given, set to 9900% ***** MVA limit of branch 10 - 11 not given, set to 9900% ***** MVA limit of branch 12 - 13 not given, set to 9900% ***** MVA limit of branch 13 - 14 not given, set to 9900


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Appendix A2

IEEE 30-bus system MATLAB M-file

function mpc = case30%CASE30 Power flow data for 30 bus, 6 generator case.

% Please see CASEFORMAT for details on the case file format.%% Based on data from ...% Alsac, O. & Stott, B., "Optimal Load Flow with Steady State Security",% IEEE Transactions on Power Apparatus and Systems, Vol. PAS 93, No. 3,% 1974, pp. 745-751.% ... with branch parameters rounded to nearest 0.01, shunt values divided% by 100 and shunt on bus 10 moved to bus 5, load at bus 5 zeroed out.% Generator locations, costs and limits and bus areas were taken from ...% Ferrero, R.W., Shahidehpour, S.M., Ramesh, V.C., "Transaction analysis% in deregulated power systems using game theory", IEEE Transactions on% Power Systems, Vol. 12, No. 3, Aug 1997, pp. 1340-1347.% Generator Q limits were derived from Alsac & Stott, using their Pmax% capacities. V limits and line |S| limits taken from Alsac & Stott.

% MATPOWER% $Id: case30.m,v 1.12 2010/03/10 18:08:13 ray Exp $

%% MATPOWER Case Format : Version 2mpc.version = '2';

%%----- Power Flow Data -----%%%% system MVA basempc.baseMVA = 100;

%% bus data% bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax Vminmpc.bus = [

1 3 0 0 0 0 1 1 0 135 1 1.05 0.95;2 2 21.7 12.7 0 0 1 1 0 135 1 1.1 0.95;3 1 2.4 1.2 0 0 1 1 0 135 1 1.05 0.95;4 1 7.6 1.6 0 0 1 1 0 135 1 1.05 0.95;5 1 0 0 0 0.19 1 1 0 135 1 1.05 0.95;6 1 0 0 0 0 1 1 0 135 1 1.05 0.95;7 1 22.8 10.9 0 0 1 1 0 135 1 1.05 0.95;8 1 30 30 0 0 1 1 0 135 1 1.05 0.95;9 1 0 0 0 0 1 1 0 135

Documents

14bus Matlab Code