POWER FLOW ANALYSIS FOR INTERCONNECTED POWER SYSTEM USING MATLAB

Document Sample
POWER FLOW ANALYSIS FOR INTERCONNECTED POWER SYSTEM USING MATLAB Powered By Docstoc
					                                                                              PSZl9:16 (Ptnd.l/07)

                                            TI,IAIAYSIA
                                    TEKNOLOGI
                            UNIVERSITI
                                           AI{D COFYRIGHI
                                       PAPER
                                 PROJECT
  DECTARAIIOT{ THESISUNDERGRADI'ATI
            OI      /


                           MOMFARIIAN           BIN ABDI'L RAIIIM
         full
  Author's nome
                           30MAY 1986
  Dote of birth

  Iitle                    FOWER FTI)W ANALYS TOR IhITERCOI{NECIEI)

                           FOWER SYSTEMUSING MATI"AB


                           20(nr:lfr)!l
  Acodemic Session:

  ldeclore thot thisthesis clossified :
                         is         os

    n           coNFrDENnAt
                          {Contoinsconfidenliol informotionunder the Otficiol Secret
                                          Act 1?721*

    |-]         Rs$rilcrtD                {Contoinsrestdctedinformotion specifiedby ihe
                                                                       os
                                                     where reseorch
                                          orgonisotion              wos done)*

    E              AccEs:t
                oPEN                      I ogreethot my thesis be published onlineopen occess
                                                              to           os
                                          {fulltexi)
                                       Moloysio
   I ocknowledgedthoi UniversitiTeknologi      reseryes right os follows:
                                                      the

          l. Thethesis the properlyof UniversitiTeknologi
                      is                               Moloysio.
                       of
          2. TheLibrory UnivenitiTeknologiMoloyaio lhe right to moke copiesfor the purpose
                                                   hos
             of reseorchonly.
          3. TheLibrory the rightto moke copiesof the ihesis ocodemic exchonge.
                       hos                                  for




                    SIGNATURE                                        I{-ATUNE SUFERVISOR
                                                                            OF

                    86053&,29-5249
            (NEW NO./PASSPOnT
                rC         NO.)                                     NAIAEOF SUPERVISOR


          Do te:1MA Y 200!|                                         Dote: 5 MAY 20S)




NOTES:          *       lf the thesis CONFIDENTIAL
                                    is                         pleose
                                                  or RESTRICTED, ottoch with the lefter from
                        lhe orgonisotionwith pedod ond reosons confidentiolity restriction.
                                                             for              or
           "I hereby declare that I have read this thesis and in my

     opinion this thesis is sufficient in terms of scope and quality for the
         award of the degree of Bachelor of Electrical Engineering"




                   Signature
                   Nameof Supervisor : ALIAS B. MOHD YUSOF
                   Date                   : 5 MAY 2009




fi
I
POWER FLOW ANALYSIS FOR INTERCONNECTED POWER SYSTEM
                        USING MATLAB




            MOHD FARHAN BIN ABDUL RAHIM




          A thesis submitted in partial fulfillment of the
           requirements for the award of the degree of
               Bachelor of Electrical Engineering




                Faculty of Electrical Engineering
                 Universiti Teknologi Malaysia




                           MAY 2009
                                  uPotserFlow Analysisfor Interconnected
                                                                       Power
I declarethat this thesisentitled
 System                                             exceptascitied in the
       UsingIIATIaIR'is the resultsof my own research
references. thesishasnot beenaccepted any degreeand is not concurrently
          The                       for
                                   of
                          candidate any degree.




         Author's nam€ : MOHD FARHAN BIN ABDUL RAHIM
          Date            :1May2009
                                             iii




          To my beloved father
     Abdul Rahim Bin Abdul Rahim




         To my beloved mother
          Narini Binti Zakaria




         To my beloved brother
      Mohd Faiz Bin Abdul Rahim




For your love, perseverance and sacrifices
           Thank you so much
                                                                                   iv




                            ACKNOWLEDGEMENT




       The author would like to express his gratitude and thanks to his project
supervisor, En. Alias B. Mohd Yusof. Thanks for his invaluable guidance and advice
towards completing this project. En. Alias B. Mohd Yusof had always been there to
explain and answer most of the doubts regarding this project. He had been very
supporting and understanding throughout the course of this project.



       The author’s gratitude also goes to all those who contributed directly or
indirectly towards the successful of this project. The author also thanks Ganesan A/L
Kalianan who writes the thesis that is became major guidance for completed this
project.



       Last but not the least; the author would like to thank his beloved family
members, who gave their full support, financial backings and motivation when he
needed it most.
                                                                                    v




                                     ABSTRACT




       Power flow solutions are needed in both for planning and operation studies.
Power flow studies for three phases balanced power system can be carried out using
very efficient methods. Power flow analysis for certain type of power system
network can be carried on by using several software that already been develop
without manual calculation on this time. One of the software is MATLAB with its
toolbox: Power System Analysis Toolbox. This software also uses numerical
methods to do power flow analysis like Newton-Raphson and its modified form, Fast
Decoupled Method. This thesis reports on performances of each numerical method
for power flow studies in term of convergence, CPU times for MATLAB calculation
and power mismatch. Numerical methods that discussed in this thesis are Newton-
Raphson, XB Fast Decoupled and BX Fast Decoupled. The test system that was used
is 9, 14, 30 and 57 bus. The thesis is organized such that the requirement and
specifications for power flow are first introduced. These relate both to the power
system modelling as well as the operational for each method that need to be
accounted for during the solution. The results and detail of the implementation of the
MATLAB are presented successfully. Simulation results are included and followed
by the conclusions that will end the report.
                                                                                   vi




                                    ABSTRAK




       Analisis aliran beban untuk sistem kuasa tiga fasa seimbang diperlukan pada
ketika tahap perancangan serta pembangunan sesuatu rangkaian sistem kuasa.
Analisis aliran beban sistem stabil merupakan kaedah yang digunakan secara meluas.
Pada zaman kini, kiraan secara manual untuk menganalisis aliran beban secara
manual tidak diperlukan lagi kerana terdapat pelbagai peisian untuk analisis sistem
kuasa. Salah satu daripadanya adalah perisian MATLAB bersama Power System
Analysis Toolbox. Perisian ini menggunakan kaedah berangka untuk menyelesaikan
analisis aliran beban seperti kaedah Newton-Raphson dan kaedah terubahsuainya
iaitu kaedah Fast Decoupled. Tesis ini memperkenalkan setiap kaedah berangka iaitu
Newton-Raphson, XB Fast Decoupled dan BX Fast Decoupled dari segi pencapahan,
masa diambil oleh MATLAB untuk kiraan dan selisihan kuasa. Rangkaian sistem
kuasa yang digunakan adalah terdiri daripada 9, 14, 30 dan 57 bus. Tesis ini disusun
supaya spesifikasi yang diperlukan untuk analisis aliran beban dapat ditonjolkan. Ini
termasuklah perkaitan di antara permodelan sistem kuasa dan bagaimana setiap
kaedah beroperasi untuk menyelesaikan analisis aliran beban. Keputusan dan
implikasi perisian MATLAB ditonjolkan dengan jayanya. Keputusan simulasi aliran
beban setiap rangkaian sistem kuasa dipersembahkan diikuti dengan rumusan yang
mengakhiri laporan tesis ini.
                                                                      vii




                      TABLE OF CONTENTS




CHAPTER                          TITLE                        PAGE


          DECLARATION                                          ii
          DEDICATION                                           iii
          ACKNOWLEDGEMENT                                      iv
          ABSTRACT                                             v
          ABSTRAK                                              vi
          TABLE OF CONTENTS                                    vii
          LIST OF TABLES                                       x
          LIST OF FIGURES                                      xi
          LIST OF ABBREVIATIONS                                xiii
          LIST OF SYMBOLS                                      xiv
          LIST OF APPENDICES                                   xv


 1        INTRODUCTION                                         1
          1.0   Overview                                       1
          1.1   Background of Problem                          2
          1.2   Objective                                      2
          1.3   Scope of Project                               3
          1.4   Methodology                                    3
          1.5   Thesis Outline                                 4



 2        LITERATURE REVIEW                                    6
          2.0   Introduction                                   6
          2.1   Three Phase System                             6
                2.1.1 Requirement of a Balanced Three Phase    6
                       System
                                                          viii




    2.2   Interconnected Power System                 8
    2.3   Power Flow Analysis                         8
    2.4   Power Flow Problem Formulation             10
    2.5   Solution Technique                         11
          2.5.1 Newton-Raphson                       12
          2.5.2 Fast Decoupled                       13


3   INTRODUCTION TO MATLAB AND PSAT                  15
    3.0   Introduction                               15
    3.1   MATLAB Software                            15
    3.2   Power System Analysis Toolbox              16



4   MODELLING AND SIMULATION                         18
    4.0   Introduction                               18
    4.1   Modelling of Bus Test System               18
    4.2   Simulation of Test System                  23



5   RESULTS AND ANALYSIS                             26
    5.0   Introduction                               26
    5.1   Normal kW Loads                            26
          5.1.1 Effect of Different Convergence      27
                 Tolerance
          5.1.2 CPU Times in Seconds                 28
          5.1.3 Maximum Power Mismatch               29
    5.2   Different kW Loads                         30
          5.2.1 Effect of Different kW Loads to      30
                 Number of Iterations
          5.2.2 CPU Times in Seconds for Different   31
                 kW Loads
                                                      ix


  6         CONCLUSION AND RECOMMENDATION       33
            6.0   Introduction                  33
            6.1   Conclusion                    33
            6.2   Recommendation                35



REFERENCES                                      36
Appendices A-B                              37 - 50
                                                                               x




                             LIST OF TABLES




TABLE NO.                         TITLE                                 PAGE

5.1         Number of iterations with different convergence tolerance
            For normal kW Loads                                       27

5.2         CPU times in seconds (total and per iteration) for normal
            kW Loads                                                    28

5.3         Maximum power mismatch for normal kW Loads                  29

5.4         Number of iterations with different kW Loads                30

5.5         CPU times in seconds (total and per iteration) for
            different kW Loads                                          31

5.6         Maximum power mismatch for different kW Loads               32
                                                                             xi




                              LIST OF FIGURES




FIGURE NO.                          TITLE                             PAGE

1.1          The methodology structure                                 4

2.1          Balanced three phase variables in time domain             7

2.2          Balanced three phase phasors                              8

2.3          Power system network                                      8
             (a) Radial distribution network
             (b) Interconnected power system

4.1          Graphical user interface of PSAT                          19

4.2          Icon of PSAT Simulink. Modelling of bus test system
             can be done by clicking that icon                         19

4.3          Library of PSAT Simlink                                   20

4.4          Figured showed where the place for modelling bus test
             system in PSAT                                            20

4.5          9 bus test system                                         21

4.6          14 IEEE bus test system                                   21

4.7          30 IEEE bus test system                                   22

4.8          57 IEEE bus test system                                   22

4.9          Figured showed the setting of PSAT                        23

4.10         Figured showed the general setting of PSAT                24

4.11         Simulation of power flow will be done by clicking this
             icon                                                      24

4.12         CPU for total iterations in times (s)                     25
                                                                    xii



4.13   Number of iteration that needed to complete the power
       Flow analysis appeared in command history               25

A.1    Slack bus                                               37

A.2    PV Generator                                            37

A.3    Load buses                                              38

A.4    Transmission line                                       38

A.5    (a) Transformer                                         39
       (b) Tap ratio transformer

A.6    Shunt admittance                                        39

A.7    Static compensator                                      40

A.8    Synchronous generator                                   40

A.9    Automatic Voltage Regulator                             41
                                         xiii




             LIST OF ABBREVIATIONS




PSAT     Power System Analysis Toolbox
MATLAB   Matrix Laboratory
CPU      Central Processing Unit
NR       Newton-Raphson
XB       XB Fast Decoupled
BX       BX Fast Decoupled
                                               xiv




                             LIST OF SYMBOLS




P      -   Real power
Q      -   Reactive power
V      -   Voltage
I      -   Current
       -   Nod voltage
A      -   Ampere
V      -   Volt
AC     -   Alternate current
kW     -   Kilowatt
p.u.   -   Per unit
       -   Degree
J      -   Jacobian matrix
                                                     xv




                 LIST OF APPENDICES




APPENDIX                 TITLE                PAGE


A          Description of related component   37

B          Result of power flow analysis      42
                                     CHAPTER 1




                                  INTRODUCTION




1.0    Overview


       Three main sections of power systems consist of namely the generation, the
transmission and the distribution. All three sections in the power systems play an
important role in the electricity industry. Though, today the electricity industry has
developed remarkably, due to technological innovations, weaknesses are still to be
found. For instance, in the power analysis, analyzing the three phase interconnected
power system poses problem.



       The problem lies when there are new of a load that want to connect with
national grid system like a new customer intends to open an industrial that required
100MW load and the location of this plant on the outskirt of the city. So the
problems are:



           •    Will there be enough power-handling capacity for this load?
           •    Will the additional load cause some components to be overloaded?
           •    Will it necessary to built new transmission lines?



       Power flow study commonly known as load flow is the backbone of power
system analysis. They are necessary for planning, operation, economic scheduling
and exchange of power system utilities. In addition, power flow analysis is required
for many other analyses such as transient stability and fault analysis [1].
                                                                                     2


1.1    Background of Problem


       In recent years, every engineering felt the impact of computer-aided analysis
and design. The area of power engineering was no exception to feeling the impact of
digital computers and problems faced were no less challenging. Indeed, they were
more complex both in terms of dimension (physically and mathematically) and also
for power flow analysis, it needs numerical methods to solve the problem. Many
numerical methods can solve the problem of power flow analysis but manual
calculations for it take too long time. Also the sizes of power systems had grown
steadily and the need for interconnected power system for economic operation raised
in its wake a host of other problems. The solution to many of these problems, which
had generally evolved hitherto on an approximate and sometimes heuristic basis,
now needed an integrated approach [2].




       MATLAB with Power System Analysis Toolbox (PSAT) is one of computer-
aided analysis for power flow study. By using numerical method (Newton-Raphson,
XB Fast Decoupled and BX Fast Decoupled), PSAT will do the power flow analysis.
But different numerical methods it will use, different performance of these methods
to power flow analysis results in term of convergence (related to iteration that needed
to complete analysis). This project will focus on using MATLAB via PSAT do
power flow analysis for interconnected power system by using different numerical
methods to test which one is the best method for power flow study without manual
calculations. So because of that the title for this project’s will be: “POWER FLOW
ANALYSIS FOR INTERCONNECTED POWER SYSTEM USING MATLAB”.




1.2    Objective


       In power engineering, the power flow study is an important tool involving
numerical analysis applied to a power system. Unlike traditional circuit analysis, a
power flow study usually uses simplified notation such as a one-line diagram and
per-unit system, and focuses on various forms of AC power rather than voltage and
                                                                                     3


current. It analyses the power systems in normal steady state operation. There exist a
number of software implementations of power flow studies including MATLAB
software [3]. So for this project’s objective is to show the performance of different
power flow analysis numerical methods or analysis for interconnected power system
especially Newton-Raphson, XB Fast Decoupled and BX Fast Decoupled by using
MATLAB software via PSAT. The performances of all these methods that like to
know from this project are number of iteration to complete power flow analysis,
effect of power flow tolerance to convergence value, CPU times need for PSAT to
complete power flow, power mismatch for each method and effect to performances
of all methods regarding suddenly increased demand from loads in term of AC power
(real and reactive power).




1.3    Scope of Project


       Scopes are the extent of the area or subject matter that will be covered in a
project. The scope of this project is to model an interconnected power system with
several buses (3 phases balanced – 9, 14, 30, and 57 buses) by using MATLAB via
PSAT to do power flow analysis (simulation) by different numerical methods to look
the effect of numerical method to the power flow analysis by changing power flow
tolerance, added new demand by increasing power of loads in the bus test system,
power mismatch for each method and CPU times for each method to convergence
toward the power flow tolerance value. After all 3 methods of numerical analysis
were testing by using PSAT (simulation), all the result obtained will gather and the
performance of each method will study.




1.4    Methodology


       The methodology for this project was following the structure shown in Figure
1.1. Start with gather data for modelling the bus test system and at the end of project
                                                                                4


was to analyze the result of power flow analysis obtained regarding different
             hods
numerical methods that was used.




                     Figure 1.1    The methodology structure




1.5    Thesis Outline


       This thesis divided into six main chapters. Chapter 1 enlighten the readers
about the project overview, background of problem, objective, scope and
methodology of project.



       Chapter 2 enlighten the readers about corresponding literature review that
suits the project. Various sources have been reviewed and all of the sources are
summarized and accordingly in this chapter.



       Chapter 3 gives the readers’ information on the software MATLAB and it
toolbox for power system called Power System Analysis Toolbox (PSAT). This
                                                                                   5


chapter also discusses role played by MATLAB and PSAT in developing power
system analysis for interconnected power system.



       Chapter 4 gives the readers about modelling and simulation. It starts from
modelling bus test system to simulation of all bus test system by doing power flow
analysis.



       Chapter 5 discussed about the result gathered from analysis and form it in
table for easy to read and understand. Also some discussion after analyze the data
gathered.



       Chapter 6 is final chapter for this thesis is to conclude all summary findings
from beginning until to the end of this project. Some recommend for future work or
upgrade this project also given in detailed.
                                    CHAPTER 2




                             LITERATURE REVIEW




2.0    Introduction


       This chapter describes manifestly the background theory of interconnected
power system and power flow analysis. Beside that all journal and FYPs that have
been done on areas related to this study will be discussed and contribution of this
thesis to the existing wealth of knowledge on this field will be explained.




2.1    Three Phase System




three conductors carrying voltage waveforms that are 2 /3 radians (120˚, 1/3 of a
       In electrical engineering, three phase electric power systems have at least


cycle) offset in time.




2.1.1 Requirement of a Balanced Three Phase System


       Following are the requirement that must be satisfied in order for a set of three
sinusoidal variables (usually voltages or currents) to be a ‘balanced three phase set’



           •   All three variables have the same amplitude
           •   All three variables have the same frequency
                                                                                    7


           •   All three variables are 120⁰ in phase.


        In terms of the time domain, a set of balance three phase voltages has the
following general form.



   = √2      cos    +∅                                                      (2.1)
   = √2      cos    + ∅ − 120˚                                              (2.2)
  = √2      cos     + ∅ − 240˚                                              (2.3)



        Figure 2.1 below illustrates the balanced three phase voltages in time domain




             Figure 2.1     Balanced three phase variables in time domain



   =    ∠∅                                                                  (2.4)
   =     ∠∅ − 120°                                                          (2.5)
  =     ∠∅ − 240°                                                           (2.6)



Thus,


   =      1∠ − 120° , and     =     1∠ + 120°                               (2.7)


Figure 2.2 illustrates the balanced three phase phasors graphically [1],
                                                                                  8




                   Figure 2.2       Balanced three phase phasors




2.2    Interconnected Power System


                                                                     project,
       Figure 2.3 below showed typical power system network. In this project it
only focused on interconnected power system for power flow analysis.




                          (a)                                      (b)


                       Figure 2.3      Power system network
          (a) Radial distribution network   , (b) Interconnected power system




2.3    Power Flow Analysis


                                            ower
       From Hadi Saadat (1999) review that power flow is the analysis to determine
           state
the steady-state complex voltages at all buses of the network and also the real and
                                           line.
reactive power flows in every transmission line These is the routine power network
                                                                                    9


calculations, which can used in power system planning, operational planning, and
operation or control. Types of methods to analysis power flow for examples
impedance matrix methods, Newton- Raphson methods, and Decoupled Newton
power flow methods [4].



       Power flow analysis is a basic tool and very important for the analysis of any
power system as it is used in the planning and design stages as well as during the
operational stages. Some applications need repeated fast power flow solutions
especially in the fields of optimizations of power system and distribution automation.
It is imperative in these applications that the power flow analysis is solved as
efficiently as possible. Power flow solutions are needed for the system under the
following conditions.



           •   With certain equipment out aged
           •   Addition of new generators
           •   Addition of new transmission lines or cables
           •   Interconnection with other systems
           •   Load growth studies
           •   Loss of line evaluation



       With the widespread and invention use of digital computers in 1950s, many
methods for solving the power flow problem have been developed such as indirect
Gauss-Seidel Load Flow (bus admittance matrix), direct Gauss-Seidel Load Flow
(bus impedance matrix), Newton-Raphson Load Flow and its Fast Decoupled Load
Flow versions. Voltage solution in all these methods is initially assumed and the
improved upon using some iterative process until convergence is reached.



       The first method Gauss-Seidel Load Flow is a simple method to program but
the voltage solution is updated only node by node and hence the convergence rate is
poor. Newton-Raphson Load Flow and Fat Decoupled Load Flow methods update
the voltage solution of all the buses simultaneously in each of iteration and hence
have faster convergence rate [1].
                                                                                    10


2.4    Power Flow Problem Formulation


       Power flow study is to obtain complete voltage angle and magnitude
information for each bus in a power system for specified load and generator real
power and voltage conditions. When information is known, real and reactive power
flow on each branch as well as generator reactive power output can be analytically
determined. For nonlinear nature of this problem, numerical methods are employed
to obtain a solution that is within an acceptable tolerance.



       Power flow problem solution begins with identifying the known and
unknown variables in the system. All known and unknown variables are dependent
on the type of bus. Load Bus is a bus without any generators connected to it. With
one exception, Generator Bus is a bus with at least one generator connected to it. The
exception is one arbitrarily-selected bus that has a generator. This bus is referred to
as the Slack Bus.



       It is assumed that in the power flow problem, the real power PD and reactive
power QD at each Load Bus are known. Load Buses are also known as PQ Buses. For
Generator Buses, it is assumed that the real power generated PG and the voltage
magnitude |V| is known. For the Slack Bus, it is assumed that the voltage magnitude
|V| and voltage phase Θ are known. Therefore, for each Load Bus, the voltage
magnitude and angle are unknown and must be solved for; for each Generator Bus,
the voltage angle must be solved for; there are no variables that must be solved for
the Slack Bus. In a system with N buses and R generators, there are then 2(N − 1) −
(R − 1) unknowns.



       In order to solve for the 2(N − 1) − (R − 1) unknowns, there must be 2(N − 1)
− (R − 1) equations that do not introduce any new unknown variables. The possible
equations to use are power balance equations, which can be written for real and
reactive power for each bus. The real power balance equation is:
                                                                                    11



0=−      +                  cos     +     sin                                2.8




where Pi is the net power injected at bus i, Gik is the real part of the element in the
Ybus corresponding to the ith row and kth column, Bik is the imaginary part of the
element in the Ybus corresponding to the ith row and kth column and θik is the
difference in voltage angle between the ith and kth buses. The reactive power balance
equation is:




0=−      +                  sin     −     cos                                2.9




where Qi is the net reactive power injected at bus i.


       Equations included are the real and reactive power balance equations for each
Load Bus and the real power balance equation for each Generator Bus. Only the real
power balance equation is written for a Generator Bus because the net reactive power
injected is not assumed to be known and therefore including the reactive power
balance equation would result in an additional unknown variable. For similar
reasons, there are no equations written for the Slack Bus [3].




2.5    Solution Technique


       Power flow analysis was design by using numerical analysis or methods to
solve the problem for interconnected power system. For this project all simulation
had done actually using numerical analysis to do power flow analysis for bus test
system. MATLAB via PSAT also had no exception to do power flow analysis by
using several type of numerical analysis or methods. There are several different
methods of solving the resulting nonlinear system of equations. The most popular is
known as the Newton-Raphson Method. There are other 2 methods that will discuss
                                                                                     12


in this project. There are XB Fast Decoupled and BX Fast Decoupled. This two
actually modified from Newton-Raphson methods of numerical analysis for power
flow analysis to increase the rate of convergence and faster for technique solution in
term of CPU (central processing unit) time of calculation. For distribution network,
BX Fast Decoupled is faster in term of convergence to get solution for power flow
results and had minimal iterations compared to Newton-Raphson and XB Fast
Decoupled.




2.5.1 Newton-Raphson


       Newton-Raphson method begins with initial guesses of all unknown variables
(voltage magnitude and angles at Load Buses and voltage angles at Generator
Buses). Next, a Taylor Series is written, with the higher order terms ignored, for each
of the power balance equations included in the system of equations. The result is a
linear system of equations that can be expressed as:


∆                  ∆
     =
∆                 ∆
                                                                            (2.10)


where ∆P and ∆Q are called the mismatch equations:



∆   =−     +                  cos     +     sin                             2.11




∆   =−       +                sin     −     cos                              2.12




and J is a matrix of partial derivatives known as a Jacobian:
                                                                                     13


           ∆           ∆

 =                                                                           2.13
           ∆           ∆




The linearized system of equations is solved to determine the next guess (m + 1) of
voltage magnitude and angles based on:



           =       ∆                                                         2.14


           =           ∆                                                    (2.15)



The process continues until a stopping condition is met. A common stopping
condition is to terminate if the norm of the mismatch equations are below a specified
tolerance [3].




2.5.2 Fast Decoupled


           Fast Decoupled is the improvement of Newton-Raphson method. 2 version of
Fast Decoupled are XB Fast Decoupled and BX Fast Decoupled. For Fast Decoupled
method because it’s origin from Newton-Raphson method, then its equation was set
     and       of the Jacobian matrix to zero. Thus equation of Newton Raphson method
becomes:


 ∆                     0    ∆
       =                                                                     2.16
 ∆             0           ∆


X from XB Fast Decoupled or BX Fast Decoupled indicates that resistances were
neglected when calculating the susceptance matrix and the B indicates that they were
not neglected. The first letter refers to the coefficient matrix of the power angle
equations and the second letter refers to that of the reactive power-voltage equations.
                                                                              14


Thus, version XB is the Stott-Alsac method, and version BX was introduced for the


                                                                               ≥
first time by Van Amerongen. BX Fast Decoupled method is more suitable for
systems with large r/x ratios. For heavily loaded systems, with a range of
20°, the XB Fast Decoupled method is more reliable [5].
                                   CHAPTER 3




                   INTRODUCTION TO MATLAB AND PSAT




3.0      Introduction


         Several type of Bus Test System including 3 IEEE Bus Test System was used
for power flow analysis by different method (Newton-Raphson, XB Fast Decoupled
and BX Fast Decoupled). To know the performance for each method, 9 Bus Test
System, 14 IEEE Bus Test System, 30 IEEE Bus Test System and 57 IEEE Bus Test
System were used for this project. All of the process from modelling to simulation
for each bus test was using MATLAB software with Power System Analysis
Toolbox (PSAT). This chapter is purposely to explain the application of MATLAB
and PSAT package in this work. PSAT is the MATLAB toolboxes for power system
analysis. Furthermore the test system was modelling with PSAT.




3.1      MATLAB Software


         Power flow analysis for interconnected power system is developed with the
aid of MATLAB program. MATLAB stands for Matrix Laboratory. MATLAB is a
high performance language for technical computing. It integrates computation,
visualization, and programming in an easy use-to-use environmental where problems
and solutions are expressed in familiar mathematical notation. Typical uses include
modelling, simulation and prototyping. The MATLAB systems consist of five main
parts:
                                                                                  16




       •   Desktop Tools and Development Environment
       •   The MATLAB Mathematical Function Library
       •   The MATLAB Language
       •   Graphics
       •   The MATLAB External Interfaces/API



       These outstanding and dynamic software packages is for scientific and
engineering computations and are used in educational institutions and in industries
including automotive, aerospace, electrics and electronics, telecommunications, and
environmental applications. MATLAB enables us to solve many advanced numerical
problems fast, practically and efficiently. Simulink is a block diagram tool used for
modelling and simulating dynamic systems such as signal processing and
communications [1].




3.2    Power System Analysis Toolbox (PSAT)


       PSAT is a MATLAB toolbox for electric power system analysis and control.
PSAT stands for Power System Analysis Toolbox. The command line version of
PSAT is also GNU Octave compatible. PSAT includes power flow, continuation
power flow, optimal power flow, and small signal stability analysis and time domain
simulation. All operations can be assessed by means of graphical user interfaces
(GUIs) and a Simulink-based library provides a user friendly tool for network design.



       PSAT core is the power flow routine, which also takes care of state variable
initialization. Once the power flow has been solved, further static and/or dynamic
analysis can be performed. These routines are:



           •   Continuation power flow
           •   Optimal power flow
                                                                               17


            •   Small signal stability analysis
            •   Time domain simulations
            •   Phasor measurement unit (PMU) placement



       In order to perform accurate power system analysis, PSAT supports a variety
of static and dynamic component models. Besides mathematical routines and models,
PSAT includes a variety of utilities, as follows:



            •   One-line network diagram editor (Simulink library)
            •   GUIs for settings system and routine parameters
            •   User defined model construction and installation
            •   GUI for plotting results
            •   Filters for converting data to and from other formats
            •   Command logs.



       Finally, PSAT includes bridges to GAMS and UWPFLOW programs, which
highly extend PSAT ability of performing optimization and continuation power flow
analysis. PSAT suitable for simulation results of several buses of interconnected
power system to know the performance for each method to do the power flow
analysis.
                                    CHAPTER 4




                       MODELLING AND SIMULATION




4.0    Introduction


       For this project, modelling and simulation of each bus test system is needed
for power flow analysis to know the performances of all methods like Newton-
Raphson, XB Fast Decoupled and BX Fast Decoupled. This chapter is purposely to
give details how the application of Power System Analysis Toolbox (PSAT)
interfaced via MATLAB for power flow analysis in this project. PSAT is the
MATLAB toolboxes for power system analysis. Description of related component in
this project is as in Appendix A. Furthermore all of test system construction will
developed by using PSAT. For this project there are several test systems will be used
for the purpose of analysis. They are 9, 14, 30 and 57 bus test systems.




4.1    Modelling of Bus Test System


       For these projects, 9, 14, 30, 57 bus test system were modelling using PSAT
simulink. First thing to do is to open PSAT Graphical User Interface by typing the
word ‘psat’ in command window of MATLAB Software. After that there are so
many steps that must be done before modelling the bus test system. Figure 4.1
showed Graphical User Interface of PSAT and Figure 4.2 showed icon of PSAT
Simulink. Figure 4.3 showed library of PSAT Simulink and Figure 4.4 showed the
place for modelling bus test system in PSAT menu.
                                                                                19




                  Figure 4.1    Graphical User Interface of PSAT


After Graphical User Interface of PSAT was opened, the next step to do is modelling
bus test systems by using PSAT Simulink. Below is where the icon of PSAT
Simulink. PSAT Simulink is where the place for modelling all buses tests systems
before runs the simulation by clicking power flow icon.




                                           Icon of PSAT
                                           Simulink




Figure 4.2     Icon of PSAT Simulink. Modelling of bus test system can be done by
                               clicking that icon.
                                                                                    20




                     Figure 4.3     Library of PSAT Simulink




  Figure 4.4     Figure showed where the place for modelling bus tests system in
                                       PSAT.

Figures 4.5, 4.6, 4.7 and 4.8 showed all bus test system after modelling was done
completely.
                                                                                                                        21

                             Bus 7                                                 Bus 9




          Bus 2                                                                                       Bus 3



                         Bus 5                                                          Bus 6

                                                 Bus 8




                                                                          Bus 4




                                                                              Bus 1


                                  Figure 4.5                9 bus test system




                                                            Bus10
                                                                                                        Bus14




        Bus08


                                 Bus07                      Bus09



                                  Tap 4-7
                                                                         Tap 4-9




                Bus03
                                         Bus04



                                                                              Bus11           Bus12             Bus13




                 Bus02
                                            Bus05



Bus01                                                               Tap 5-6



                                                                                      Bus06




                            Figure 4.6                   14 bus IEEE test system
                                                                                                                                                                                                                                                                                        22



                        Bus21
                                                                                                             28 -27                              Bus11
                                                                                                                                                                                                                                                                  Bus19
                                                                              Bus08
                                             Bus07                                                                     Bus28
                                                                                                                                                                                                                                  Bus18

                                                 Bus22                                                                                                                                     Bus10

                                                                                                                                             Bus09

                                                                                                                                                                                                                                                                                      Bus20
                                                                                                                         6-9

                                                                                        Bus06                                                      6-10
                                                                                                                                                                                       Bus14
                                                                                                                                                                                                                         Bus15
                                                 Bus24
                                                                                                                                                                                                                                            Bus23


                                                                                                                                 Bus13

                                                                   Bus05
                                                                                                                 Bus04
                                                                                                                                                                              Bus12
                        Bus25
                                                                                                                                                                                                                         Bus16


                                                                                                                                                                              4-12


                                                                                                                                                                                                                                                  Bus17

                                                         Bus27                                       Bus02
        Bus26
                                                                                                                                                 Bus03


                                                                                                 Bus30




                                                         Bus29                                           Bus01



                                                                                                                                 Slack




                                                                                  Figure 4.7                                                30 IEEE bus test system




                                                          Bus02


                                                                                                                                                                                                                                                  Bus01


                                 Bus03



                                                                  Bus19

                                                                                                                                                                                                                           Bus14
                                                                                                                                                                  Bus15                                                                                           Bus17

                                                                                                                                                                                                                                                                              Bus16
                         Bus04




                                                                  Bus20                                                                                                                                                                   Bus13
                                                                                                             Bus44
                                                                                                                                                                                         Bus46

                                 Bus18                                                                                                                    Bus45

                                                                                                                                                                                                                 Bus50

Bus05                                                                                                                                                                                                    Bus47

                                                                  Bus21
                                                                                                                                                                                                                              Bus51


                                                                                                                                                                                                                                                                          Bus12


                                                                                                                                                                                                                 Bus49
                                         Bus26
                                                                                                                                                                                                         Bus48
                                                                  Bus22

                                                                                             Bus38




                                                                                                                                         Bus39                Bus57

                                         Bus27



                                                                          Bus23



                                                                                                                                                                                                                          Bus42




                                                                                                               Bus37                                                  Bus56
                                                                                                                                                  Bus40
                                         Bus28
                                                                             Bus24                                                                                                                                        Bus43



                                                                                                                                                                                                 Bus41




                Bus06
                                                                                                                         Bus36
                                                                             Bus25

                                                     Bus29


                                                                                                 Bus33                                                                         Bus11                                                                      Bus10



                                                                             Bus30                                               Bus35



                                 Bus07



                                                                                         Bus32

                                                                             Bus31
                                                                                                                                 Bus34
                                                                                                                                                                                   Bus09

                                             Bus08




                                            Bus52                                    Bus53                              Bus54                                                           Bus55




                                                                                  Figure 4.8                                                57 IEEE bus test system
                                                                                     23


4.2     Simulation of Test System


        For this project, all the setting like power flow tolerance, max power flow
iteration and frequency was set up first. All bus test system in this project based on
real interconnected power system in America. So frequency is set up at constant
value at 60 Hz regardless what type of test will be done in this project like increasing
reactive power and real power of the load. Figure 4.9 showed the setting icon of
PSAT.




       Frequency was
       set up at
       constant value
       of 60 Hz




  Power Flow
  Tolerance


      Max Power Flow
      Tolerance
      Iteration




                   Figure 4.9    Figure showed the setting of PSAT


The performance for each method will know by adjust the method that will use each
time doing simulation of bus test system. In this project each methods of power flow
analysis has own unique characteristics regarding certain factor like power flow
tolerance, the load power (real power and reactive power) sudden increased in same
bus test systems and other else but all of this will result in different performances
characteristics. Figure 4.10 showed the general setting in PSAT that can set what
type of method that will use in power flow analysis (by clicking setting icon in PSAT
Graphical User Interface).
                                                                                     24




                                                                   Power
                                                                   Flow
                                                                   Solver




               Figure 4.10   Figured showed the general setting of PSAT




After all setting was done, next to do is to run power flow analysis by clicking icon
Power Flow in PSAT Graphical User Interface. Results of power flow analysis for all
bus test system with normal kW and power flow tolerance = 0.00001 appeared in
Appendix B. Figure 4.11 showed the Power Flow Analysis icon. CPU times (time to
complete power flow analysis) and number of iterations for all methods also
appeared in PSAT Graphical User Interface like showed in Figure 4.12 and Figure
4.13.




    Power
    Flow icon


        Figure 4.11   Simulation of power flow will be done by clicking this icon.
                                                                              25




              Figure 4.12    CPU for total iterations in times (s).




Figure 4.13 Number of iteration that needed to complete the power flow analysis
                        appeared in command history.
                                   CHAPTER 5




                           RESULTS AND ANALYSIS




5.0    Introduction


       In this chapter, all the results obtained after power flow simulation were
showed depends on what type of testing including power flow tolerance, CPU times,
power mismatch, and by different kW loads on the test system. All of this to show
that by different methods of numerical analysis used will lead to difference approach
on getting the results of power flow analysis. So this chapter will divided into two
sub-main chapters. First is by testing on normal kW loads and the other one is on
different kW loads. Power flow results of normal kW loads for each bus test system
(power flow tolerance = 0.00001, Newton-Raphson method) showed in Appendix B.




5.1    Normal kW loads


       First thing to do was set up all buses test system (9, 14, 30 and 57) with
normal kW loads, 1*P (100% of real power and reactive power of all loads) by adjust
the demand power of all loads. For example, all loads power (reactive power, Q and
real power, P) in 30 IEEE bus test systems was set up in normal condition. For this
case , the assumptions that made is all loads the system has normal kW loads
although in normal situation (practical) not all loads was connect to the power system
in same time. After that, by using different numerical methods for power flow
analysis will lead to different approach performance to get power flow results.
Instead different methods was used, it also was used different power flow tolerances.
                                                                                    27


5.1.1 Effect of Different Convergence Tolerances



 Table 5.1: Number of iterations with different convergence tolerances for normal
                                      kW loads
    Test System         Tolerance
                                             NR              XB             BX
      (Buses)            In p.u.
                           0.01               3               3              2
                          0.001               3               3              3
          9
                         0.0005               3               4              4
                         0.00001              4               5              5

                           0.01               2               4              4
                          0.001               3               5              5
          14
                         0.0005               3               6              6
                         0.00001              4               8              9

                           0.01               2               3              2
                          0.001               3               4              4
          30
                         0.0005               3               4              4
                         0.00001              4               6              6

                           0.01               3               5              5
                          0.001               4               6              7
          57
                         0.0005               4               6              7
                         0.00001              4               9             11



       Table 5.1 showed number of iterations with different convergence tolerances
for normal kW loads in all bus test systems. It seems that the more buses on one
interconnected power system, the more number of iterations that needed for one
methods to solve the problem of power flow analysis. Different power flow
convergence tolerance (p.u.) will lead different performances of all methods toward
number of iterations they need to use for power flow analysis until it satisfied that
maximum convergence error was below power flow tolerance. Newton-Raphson was
the faster in term of convergence compare with other methods and BX Fast
Decoupled showed that its method was the slower in term of convergence. Numerical
methods that called as faster convergence in this case referred to the smallest number
of iterations it’s calculation to get power flow analysis results for the same bus test
system and power flow tolerance (same condition) compared with other methods.
                                                                                     28


5.1.2 CPU Times in Seconds


   Table 5.2: CPU times in seconds (total and per iteration) for normal kW loads
  Test                           NR                   XB                   BX
 System     Tolerance    CPU                  CPU                  CPU
                                  CPU/iter             CPU/iter            CPU/iter
 (Buses)     In p.u.     total                total                total
                                    (s)                  (s)                 (s)
                          (s)                  (s)                  (s)
               0.01     0.0259     0.0086    0.0200     0.0067    0.0170    0.0085
               0.001    0.0500     0.0167    0.0460     0.0153    0.0300    0.0100
    9
              0.0005    0.0586     0.0195    0.0500     0.0125    0.0422    0.0106
             0.00001    0.0600     0.0150    0.0540     0.0108    0.0480    0.0096

               0.01     0.0360     0.0180    0.0300     0.0075    0.0249    0.0062
               0.001    0.0531     0.0177    0.0510     0.0102    0.0330    0.0066
   14
              0.0005    0.0540     0.0180    0.0511     0.0085    0.0433    0.0072
             0.00001    0.0612     0.0153    0.0560     0.0070    0.0487    0.0054

               0.01     0.0450     0.0225    0.0400     0.0133    0.0299    0.0150
               0.001    0.0561     0.0187    0.0456     0.0114    0.0378    0.0095
   30
              0.0005    0.0630     0.0210    0.0512     0.0128    0.0437    0.0109
             0.00001    0.0792     0.0198    0.0612     0.0102    0.0512    0.0085

               0.01     0.0609     0.0203    0.0567     0.0113    0.0467    0.0093
               0.001    0.0640     0.0160    0.0570     0.0095    0.0412    0.0059
   57
              0.0005    0.0732     0.0183    0.0680     0.0113    0.0501    0.0072
             0.00001    0.0800     0.0200    0.0722     0.0080    0.0613    0.0056



        Table 5.2 showed CPU total times and CPU times per iteration of power flow
analysis in seconds for normal kW loads in all bus test systems. It seems that the
more buses on interconnected power system, the more CPU total times that needed
for one method to solve the problem of power flow analysis. Different power flow
convergence tolerance (p.u.) will lead to different duration of times that MATLAB
via PSAT taken to solve the problem. BX Fast Decoupled method showed that its
method was the faster in term of time taken for converges. In this case it seems that
although Newton-Raphson method is slower than in term of CPU times taken for
converge but in term number of iterations needed to complete solve power flow
problem, it is smaller. For this analysis, BX Fast Decoupled is the faster in term of
MATLAB via PSAT (computerize calculation) for power flow analysis but lacking
in term of convergence (need more iteration to complete solve power flow problem).
                                                                                   29


5.1.3 Maximum Power Mismatch


             Table 5.3: Maximum power mismatch for normal kW loads
                                  NR                  XB               BX
    Test
              Tolerance    Real    Reactive    Real    Reactive    Real Reactive
   System
               In p.u     Power     Power     Power     Power     Power Power
   (Buses)
                          (KW)     (KVAR)     (KW)     (KVAR)     (KW) (KVAR)
                 0.01       0         0         0         0         0      0
                 0.001      0         0         0         0         0      0
      9
                0.0005      0         0         0         0         0      0
               0.00001      0         0         0         0         0      0

                 0.01       0         0         0         0         0       0
                 0.001      0         0         0         0        100      0
      14
                0.0005      0         0         0         0         0       0
               0.00001      0         0         0         0         0       0

                 0.01       0         0         0         0        100      0
                 0.001      0         0         0         0         0       0
      30
                0.0005      0         0         0         0         0       0
               0.00001      0         0         0         0         0       0

                 0.01       0         0         0         0         0       0
                 0.001      0         0         0         0         0       0
      57
                0.0005      0         0         0         0         0      50
               0.00001      0         0         0         0         0       0


       Table 5.3 showed maximum power mismatch for each methods for all bus
test system after completed solve the problem of power flow using MATLAB
software. For this case only BX Fast Decoupled only had power mismatch in term of
real power (kW) or reactive power (kvar).
                                                                                  30



5.2    Different kW Loads


       First thing to do was set up all buses test system (9, 14, 30 and 57) with
different kW loads, (increase the loads power by 1.4*P, 1.6*P, 1.8*P and 2.0*P) by
adjust the demand power that needed for all loads. By using different numerical
methods of power flow analysis, it will lead to different performance approach to get
power flow results. Instead different methods was used, it also used different power
flow tolerances. Maximum number of iteration MATLAB via PSAT calculation for
power flow analysis was set up to 20 iterations. More than that, MATLAB will
conclude that it already diverges.




5.2.1 Effect of Different kW Loads to Number of Iterations


              Table 5.4: Number of iterations with different kW loads
       Test System
                            Load          NR             XB             BX
         (Buses)
                           1.4*P           4             5              6
                           1.6*P           4             7              7
             9
                           1.8*P           5             10             10
                           2.0*P           5             13             13

                           1.4*P           4              8             8
                           1.6*P           4              7             8
             14
                           1.8*P           4              7             8
                           2.0*P           4              7             7

                           1.4*P           4              6             6
                           1.6*P           4              7             6
             30
                           1.8*P           4              8             7
                           2.0*P           5              9             8

                           1.4*P          5            12              11
                           1.6*P          6            20              19
             57
                           1.8*P       diverge       diverge         diverge
                           2.0*P       diverge       diverge         diverge
                             *Tolerance = 0.00001p.u.
                                                                                      31


        Table 5.4 showed the number of iterations with different kW loads in all bus
test systems. In this case, power flow tolerance was set up as a constant value =
0.00001 p.u. Also with different power flow convergence tolerance (p.u.) was set up,
it will lead to different performances of all methods toward the number of iterations
they need to use for power flow analysis until it satisfied that maximum convergence
error was below power flow tolerance. Newton-Raphson method was the faster in
term of convergence compared with other methods. BX Fast Decoupled showed that
its method was the slower in term of convergence. For 57 bus test system, it showed
all methods did not solve the problem of power flow when all loads in that bus test
system was increased to 1.8*P and 2.0*P after 20 iterations. For that level of loads
power demand, it need other numerical method that will compute all power flow
analysis for more faster in term of convergence properties.




5.2.2 CPU Times in Seconds for Different kW Loads


  Table 5.5: CPU times in seconds (total and per iteration) for different kW loads
                              NR                     XB                     BX
  Test
                      CPU                    CPU                    CPU
 System    Loads                CPU/iter              CPU/iter              CPU/iter
                      total                  total                  total
 (Buses)                          (s)                   (s)                   (s)
                       (s)                    (s)                    (s)
            1.4*P    0.0772        0.0181   0.0620        0.0124   0.0521    0.0087
            1.6*P    0.0854        0.0214   0.0801        0.0114   0.0621    0.0089
    9
            1.8*P    0.0932        0.0187   0.0845        0.0085   0.0790    0.0079
            2.0*P    0.1002        0.0200   0.0921        0.0071   0.0823    0.0063

            1.4*P    0.0799        0.0200   0.0673        0.0084   0.0570    0.0071
            1.6*P    0.0870        0.0218   0.0810        0.0116   0.0721    0.0090
   14
            1.8*P    0.0942        0.0234   0.0870        0.0124   0.0788    0.0099
            2.0*P    0.1012        0.0253   0.0912        0.0130   0.0857    0.0122

            1.4*P    0.0821        0.0205   0.0701        0.0117   0.0640    0.0107
            1.6*P    0.0900        0.0225   0.0812        0.0116   0.0721    0.0120
   30
            1.8*P    0.1052        0.0263   0.0900        0.0113   0.0865    0.0124
            2.0*P    0.1100        0.0220   0.0924        0.0103   0.0888    0.0111

            1.4*P    0.0850        0.0170   0.0721        0.0060   0.0687    0.0062
            1.6*P    0.1042        0.0174   0.0943        0.0047   0.0840    0.0044
   57
            1.8*P       -             -        -             -        -         -
            2.0*P       -             -        -             -        -         -
                              *Tolerance = 0.00001p.u.
                                                                                  32


       Table 5.5 showed that CPU (total) times in seconds that needed for
MATLAB to compute all power flow analysis calculation by using different
numerical methods with constant value of power flow tolerance = 0.00001 p.u. It
showed that, the higher load power demand increased, the higher CPU times need to
take for power flow analysis by computerized calculation using MATLAB. It also
showed that BX Fast Decoupled is the faster in CPU total times for MATLAB to
solved power flow problem. BX Fast Decoupled is the faster in CPU per iteration
times to solve power flow problem but for converge it take more number of iterations
compared to Newton-Raphson method.



             Table 5.6: Maximum power mismatch for different kW loads
                              NR                  XB                  BX
    Test
                       Real    Reactive    Real    Reactive    Real    Reactive
   System     Loads
                      Power     Power     Power     Power     Power     Power
   (Buses)
                      (KW)     (KVAR)     (KW)     (KVAR)     (KW)     (KVAR)
              1.4*P     0         0          0        0         0         0
              1.6*P     0         0          0        0         0         0
      9
              1.8*P     0         0          0        0         0         0
              2.0*P     0         0         10        0         10        0

              1.4*P      0         0         0           0      10         0
              1.6*P      0         0         0           0      0          0
     14
              1.8*P      0         0         0           0      0          0
              2.0*P      0         0        10           0      10         0

              1.4*P      0         0         0           0      0          0
              1.6*P      0         0         0           0      10         0
     30
              1.8*P      0         0         0           0      0          0
              2.0*P      0         0         0           0      0          0

              1.4*P      0         0        10           0      0          0
              1.6*P      0         0        10           0      10         10
     57
              1.8*P      0         0         0           0      0          0
              2.0*P      0         0         0           0      0          0
                              *Tolerance = 0.00001p.u.


       Table 5.6 showed that CPU times in seconds that need for MATLAB to
compute all power flow analysis calculation by using different numerical methods
with constant value of power flow tolerance = 0.00001 p.u. For this case, Newton-
Raphson didn’t have any power mismatch (real power and reactive power) for all bus
test system. Only at 1.6*P for 57 bus test system, the table showed that BX Fast
Decoupled had power mismatch for both real power and reactive power.
                                      CHAPTER 6




                    CONCLUSION AND RECOMMENDATION




6.0       Introduction


          The stated objective is fulfilled in this project. All modelling and power flow
simulation was done using MATLAB via PSAT software. All performances of all
numerical methods, Newton-Raphson, XB Fast Decoupled and BX Fast Decoupled
was obtained and also an analysis regarding power flow already done. Analysis that
was done in this project was to determined the good performance of all numerical
methods that will use in power flow analysis regarding number of busses in
interconnected power system by using MATLAB software without manual
calculation. The specifications that was determined in this project including effect of
increasing power demand by loads to maximum convergence error and number of
iterations for each method. Other than that, CPU times taken for MATLAB to
complete power flow analysis and power flow tolerance effect also determined in
detail.




6.1       Conclusion


          Three different methods of power flow for three phase interconnected power
system have been performed on different condition. In term of convergence, Newton-
Raphson is the good one because it only needs a little number of iterations to
complete power flow analysis compared to Decoupling method. Decoupling method
take less time for CPU times (MATLAB) to solve power flow problem. BX Fast
                                                                                   34


Decoupled is the faster way for MATLAB to compute power flow analysis for every
bus test system compared to other methods. In comparison with the Newton-Raphson
method, the total CPU times obtained are closely similar, but the decoupled version
requires less memory. Also BX Fast Decoupled takes a little time for per iteration of
numerical analysis compared to Newton-Raphson. The bigger interconnected power
systems in terms number of bus, all numerical methods need more time (CPU times)
and more iterations to complete solve power flow problem.



       The smaller value of power flow tolerances will make all numerical methods
needs extra number iteration to completely converge. Increasing power demand from
loads also make number of iterations for all methods will increase also and
MATLAB need more time to complete power flow results (CPU times). For this case
of study, only BX Fast Decoupled method had power mismatch via iteration in term
of real and reactive power.



       Finally, this project will conclude that all objectives of this project already
done and clear. All performance of all methods for power flow analysis already
determined regarding certain specifications for this project. MATLAB via PSAT
software was the tool to determine all that mention before.       All three methods
suitable for all bus test system for interconnected power system. Newton-Raphson is
the best method in term of fast convergence. BX Fast Decoupled is the best method
for MATLAB to compute power flow analysis for interconnected power system
because it takes only short duration (CPU times).
                                                                                     35


6.2       Recommendation


          In future, this project can be upgraded using even more advanced approach. A
couple of recommendations that can consider are as follows:



      •   In the test performance, the BX Fast Decoupled method approach has present
          a very good performance and it must be investigate in different conditions for
          future works.
      •   Test power flow analysis with test system that had renewable energy like
          wind turbine and PV solar to see more detail on performance for each
          numerical methods including other methods that did not present in this
          project.
      •   The scope can be widen by include faulted transmission status.



          There are the several recommendations that can be done for future studies.
Also, three phase load flow studies have a bright future in load forecasting and power
system maintenance prospect, so future studies are recommended.
                                                                          36


                             REFERENCES




1. Ganesan A/L Kalianan (2007). Power Flow Analysis for Unbalanced Power
   System Using MATLAB. Bachelor of Electrical Engineering. Universiti
   Teknologi Malaysia, Skudai.

2. M. A. PAI (1980). Computer Technique in Power System Analysis (1st ed.).
   New Delhi, McGraw-Hill.

3. J. Grainger and W. Stevenson, Power System Analysis, McGraw-Hill, New
   York, 1994.

4. Hadi Saadat (2004). Power System Analysis. (2nd ed.). Singapore, McGraw-
   Hill.

5. W. Hubbi. (1991). Effects of Neglecting Resistances in XB and BX Load-Flow
   Methods. IEEE Proceedings-C, Vol.138, N0.5, September 1991.
                                                                                  37


                                  APPENDIX A




Description of Related Component


       In this project, there are several component has been used for completing the
power system such Slack bus, PV generator, constant PQ load, Transmission line,
Transformer, Tap Ratio Transformer, Shunt Admittance, Static Compensator,
Synchronous Generator, and Automatic Voltage Regulator.




Symbol of Slack Bus


       Known as swing bus and taken as a reference where the magnitude and phase
angle of the voltage are specified. In the PSAT, symbol for slack bus is shown in the
Figure A.1.




                                 Figure A.1     Slack Bus




Symbol of PV Generator


       Known as generator buses and real power and magnitude voltage is specified.
In the PSAT symbol for PV generator is shown in the Figure A.2.




                            Figure A.2     PV Generator
                                                                                     38


Symbol of Load Buses


       In this component, the active and reactive powers are specified. It is also
known as a P-Q bus. In the PSAT, symbol for load buses is shown in the Figure A.3.




                              Figure A.3     Load Buses




Symbol of Transmission Line


       In the transmission lines, it used to connect between two buses where the real
and reactive power is transmit via transmission line. Data for the transmission lines is
taken from the IEEE. The symbol for transmission line in the PSAT is showed in
Figure A.4.




                          Figure A.4     Transmission Lines
                                                                                   39


Symbol of Transformer


       In the transformer, it work as a step-up and step down voltage depends on it
applications. In this project, 2 types of transformer is used which is transformer and
Tap ratio transformer. Data for parameter in the transformer is taken from the IEEE
data. The symbols in PSAT are showed in Figure A.5.




             Figure A.5     (a) Transformer, (b) Tap Ratio Transformer




Symbol of Shunt Admittance


       Shunt reactors or capacitors, which may be used for voltage control purpose,
are represented a shunt admittances that will strengthen or weaken the diagonal
elements of the admittance matrix for the busbars to which they are connected. The
symbols in PSAT are showed in Figure A.6.




                          Figure A.6     Shunt Admittance
                                                                                 40


Symbol of Static Compensator


       Static Compensator is an electrical device for providing fast-acting reactive
power compensation on high voltage electricity transmission networks. The symbols
in PSAT are showed in Figure A.7.




                        Figure A.7.    Static Compensator




Symbol of Synchronous Generator


       The synchronous generator is the dominating generator type in power
systems. It can generate active and reactive power independently and has an
important role in voltage control. The symbols of Synchronous Generator in PSAT
are showed in Figure A.7.




                      Figure A.8.     Synchronous Generator
                                                                                    41


Symbol of Automatic Voltage Regulator


       Automatic voltage regulator controls the output voltage of the generator by
controlling its excitation current. The symbols in PSAT are showed in Figure A.9.




                    Figure A.9.    Automatic Voltage Regulator
                                                                                   42


                                        APPENDIX B




Result of Power Flow Analysis


          All the power flow analysis results for 9, 14, 30 and 57 bus test system are
showed in this section. All analysis was based on 100MVA. The method that used
was Newton-Raphson method and power flow tolerance was set = 0.00001 p.u. It
was in normal kW loads (1*P). Frequency that used was 60 Hz.




9 Bus Test Systems


NETWORK STATISTICS

Buses:                            9
Lines:                            6
Transformers:                     3
Generators:                       3
Loads:                            3

SOLUTION STATISTICS
Number of Iterations:             4
Maximum P mismatch [p.u.]         0
Maximum Q mismatch [p.u.]         0
Power rate [MVA]                  100
POWER FLOW RESULTS


Bus           V           phase          P gen      Q gen     P load     Q load
              [p.u.]      [rad]          [p.u.]     [p.u.]    [p.u.]     [p.u.]

Bus   1       1.04        0              0.71641    0.27046   0          0
Bus   2       1.025       0.16197        1.63       0.06654   0          0
Bus   3       1.025       0.08142        0.85      -0.1086    0          0
Bus   4       1.0258     -0.03869        0          0         0          0
Bus   5       0.99563    -0.06962        0          0         1.25       0.5
Bus   6       1.0127     -0.06436        0          0         0.9        0.3
Bus   7       1.0258      0.06492        0          0         0          0
Bus   8       1.0159      0.0127         0          0         1          0.35
Bus   9       1.0324      0.03433        0          0         0          0

LINE FLOWS
From Bus      To Bus      Line           P Flow     Q Flow    P Loss     Q Loss
                                         [p.u.]     [p.u.]    [p.u.]     [p.u.]
Bus   8       Bus   9     1             -0.24095   -0.24296   0.00088   -0.21176
Bus   7       Bus   8     2              0.7638    -0.00797   0.00475   -0.11502
Bus   9       Bus   6     3              0.60817   -0.18075   0.01354   -0.31531
Bus   7       Bus   5     4              0.8662    -0.08381   0.023     -0.19694
Bus   5       Bus   4     5             -0.4068    -0.38687   0.00258   -0.15794
Bus   4       Bus   6     6              0.30704    0.0103    0.00166   -0.15513
Bus   2       Bus   7     7              1.63       0.06654   0          0.15832
Bus   3       Bus   9     8              0.85      -0.1086    0          0.04096
Bus   1       Bus   4     9              0.71641    0.27046   0          0.03123
                                                                                   43

LINE FLOWS
From Bus     To Bus      Line             P Flow    Q Flow    P Loss     Q Loss
                                          [p.u.]    [p.u.]    [p.u.]     [p.u.]
Bus   9      Bus   8     1               0.24183    0.0312    0.00088   -0.21176
Bus   8      Bus   7     2              -0.75905   -0.10704   0.00475   -0.11502
Bus   6      Bus   9     3              -0.59463   -0.13457   0.01354   -0.31531
Bus   5      Bus   7     4              -0.8432    -0.11313   0.023     -0.19694
Bus   4      Bus   5     5               0.40937    0.22893   0.00258   -0.15794
Bus   6      Bus   4     6              -0.30537   -0.16543   0.00166   -0.15513
Bus   7      Bus   2     7              -1.63       0.09178   0          0.15832
Bus   9      Bus   3     8              -0.85       0.14955   0          0.04096
Bus   4      Bus   1     9              -0.71641   -0.23923   0          0.03123


TOTAL GENERATION
REAL POWER [p.u.]                3.1964
REACTIVE POWER [p.u.]            0.2284
TOTAL LOAD

REAL POWER [p.u.]                3.15
REACTIVE POWER [p.u.]            1.15

TOTAL LOSSES
REAL POWER [p.u.]                0.04641
REACTIVE POWER [p.u.]           -0.9216




IEEE 14 Bus Test Systems


NETWORK STATISTICS

Buses:                           14
Lines:                           17
Transformers:                    3
Generators:                      5
Loads:                           11

SOLUTION STATISTICS
Number of Iterations:            4
Maximum P mismatch [p.u.]        0
Maximum Q mismatch [p.u.]        0
Power rate [MVA]                 100
POWER FLOW RESULTS

Bus          V           phase            P gen     Q gen     P load     Q load
             [p.u.]      [rad]            [p.u.]    [p.u.]    [p.u.]     [p.u.]

Bus01        1.06        0                2.3241   -0.1623    0          0
Bus02        1.045      -0.08705          0.4       0.45126   0.217      0.127
Bus03        1.01       -0.22251          0         0.25236   0.942      0.19
Bus04        1.0155     -0.1798           0         0         0.478      0.039
Bus05        1.0188     -0.15278          0         0         0.076      0.016
Bus06        1.07       -0.25879          0         0.1518    0.112      0.075
Bus07        1.0611     -0.23804          0         0         0          0
Bus08        1.09       -0.23804          0         0.17881   0          0
Bus09        1.0558     -0.26684          0         0         0.295     -0.0458
Bus10        1.0509     -0.27039          0         0         0.09       0.058
Bus11        1.0569     -0.26685          0         0         0.035      0.018
Bus12        1.0551     -0.2734           0         0         0.061      0.016
Bus13        1.0504     -0.27448          0         0         0.135      0.058
Bus14        1.0355     -0.28762          0         0         0.149      0.05
                                                                                 44

LINE FLOWS
From Bus     To Bus     Line            P Flow    Q Flow    P Loss     Q Loss
                                        [p.u.]    [p.u.]    [p.u.]     [p.u.]
Bus01        Bus02      1           1.5703       -0.20439   0.04306    0.07297
Bus10        Bus11      2          -0.02916      -0.02034   9e-005     0.00022
Bus09        Bus07      3          -0.29331      -0.04656   0          0.0087
Bus07        Bus08      4           0            -0.17407   0          0.00474
Bus10        Bus09      5          -0.06084      -0.03766   0.00015    0.00039
Bus11        Bus06      6          -0.06426      -0.03856   0.00048    0.001
Bus12        Bus06      7          -0.07612      -0.02425   0.0007     0.00147
Bus13        Bus06      8          -0.17096      -0.07007   0.00205    0.00403
Bus13        Bus14      9           0.05102       0.02027   0.00047    0.00095
Bus14        Bus09      10         -0.09845      -0.03069   0.00126    0.00268
Bus13        Bus12      11         -0.01506      -0.00819   6e-005     5e-005
Bus05        Bus02      12         -0.40474      -0.02552   0.00899   -0.00875
Bus03        Bus02      13         -0.71075       0.01664   0.02334    0.05208
Bus05        Bus04      14          0.62836      -0.11862   0.00524    0.00329
Bus03        Bus04      15         -0.23125       0.04571   0.00378   -0.02585
Bus04        Bus02      16         -0.5456        0.01672   0.01685    0.01141
Bus05        Bus01      17         -0.72618       0.01847   0.02755    0.06057
Bus04        Bus07      18          0.29331      -0.09936   0          0.01945
Bus04        Bus09      19          0.16239      -0.0067    0          0.01425
Bus05        Bus06      20          0.42656       0.10968   0          0.0471
LINE FLOWS
From Bus     To Bus     Line            P Flow    Q Flow    P Loss     Q Loss
                                        [p.u.]    [p.u.]    [p.u.]     [p.u.]
Bus02        Bus01      1          -1.5273        0.27737   0.04306    0.07297
Bus11        Bus10      2           0.02926       0.02056   9e-005     0.00022
Bus07        Bus09      3           0.29331       0.05527   0          0.0087
Bus08        Bus07      4           0             0.17881   0          0.00474
Bus09        Bus10      5           0.06099       0.03805   0.00015    0.00039
Bus06        Bus11      6           0.06473       0.03956   0.00048    0.001
Bus06        Bus12      7           0.07683       0.02571   0.0007     0.00147
Bus06        Bus13      8           0.173         0.0741    0.00205    0.00403
Bus14        Bus13      9          -0.05055      -0.01931   0.00047    0.00095
Bus09        Bus14      10          0.09971       0.03337   0.00126    0.00268
Bus12        Bus13      11          0.01512       0.00825   6e-005     5e-005
Bus02        Bus05      12          0.41373       0.01677   0.00899   -0.00875
Bus02        Bus03      13          0.73409       0.03543   0.02334    0.05208
Bus04        Bus05      14         -0.62312       0.12191   0.00524    0.00329
Bus04        Bus03      15          0.23502      -0.07157   0.00378   -0.02585
Bus02        Bus04      16          0.56245      -0.00531   0.01685    0.01141
Bus01        Bus05      17          0.75373       0.0421    0.02755    0.06057
Bus07        Bus04      18         -0.29331       0.11881   0          0.01945
Bus09        Bus04      19         -0.16239       0.02094   0          0.01425
Bus06        Bus05      20         -0.42656      -0.06258   0          0.0471

TOTAL GENERATION
REAL POWER [p.u.]              2.7241
REACTIVE POWER [p.u.]          0.87194
TOTAL LOAD

REAL POWER [p.u.]              2.59
REACTIVE POWER [p.u.]          0.6012

TOTAL LOSSES
REAL POWER [p.u.]              0.13406
REACTIVE POWER [p.u.]          0.27074
                                                                                 45


IEEE 30 Bus Test Systems


NETWORK STATISTICS
Buses:                          30
Lines:                          38
Transformers:                   4
Generators:                     6
Loads:                          21
SOLUTION STATISTICS
Number of Iterations:           4
Maximum P mismatch [p.u.]       0
Maximum Q mismatch [p.u.]       0
Power rate [MVA]                100

POWER FLOW RESULTS
Bus          V          phase          P gen      Q gen     P load     Q load
             [p.u.]     [rad]          [p.u.]     [p.u.]    [p.u.]     [p.u.]
Bus01        1.05       0              1.3862    -0.02846   0          0
Bus02        1.0338    -0.04775        0.5756     0.02419   0.217      0.127
Bus03        1.0313    -0.08187        0          0         0.024      0.012
Bus04        1.0263    -0.09806        0          0         0.076      0.016
Bus05        1.0058    -0.15697        0.2456     0.22547   0.942      0.19
Bus06        1.0209    -0.11268        0          0         0          0
Bus07        1.007     -0.14007        0          0         0.228      0.109
Bus08        1.023     -0.11297        0.35       0.348     0.3        0.3
Bus09        1.0327    -0.14039        0          0         0          0
Bus10        1.0177    -0.1741         0          0         0.058      0.02
Bus11        1.0913    -0.10729        0.1793     0.3106    0          0
Bus12        1.0397    -0.16398        0          0         0.112      0.075
Bus13        1.0883    -0.14305        0.1691     0.37938   0          0
Bus14        1.0235    -0.17997        0          0         0.062      0.016
Bus15        1.0177    -0.18107        0          0         0.082      0.025
Bus16        1.0231    -0.1731         0          0         0.035      0.018
Bus17        1.0139    -0.17757        0          0         0.09       0.058
Bus18        1.0053    -0.19129        0          0         0.032      0.009
Bus19        1.0011    -0.19389        0          0         0.095      0.034
Bus20        1.0045    -0.18997        0          0         0.022      0.007
Bus21        1.0057    -0.18252        0          0         0.175      0.112
Bus22        1.0064    -0.18236        0          0         0          0
Bus23        1.0053    -0.18787        0          0         0.032      0.016
Bus24        0.99732   -0.19069        0          0         0.087      0.067
Bus25        1.0102    -0.19327        0          0         0          0
Bus26        1.0082    -0.19946        0          0         0.035      0.023
Bus27        1.0189    -0.1913         0          0         0          0
Bus28        1.0154    -0.11969        0          0         0          0
Bus29        0.99894   -0.21295        0          0         0.024      0.009
Bus30        0.98741   -0.2285         0          0         0.106      0.019

LINE FLOWS
From Bus     To Bus     Line           P Flow     Q Flow    P Loss     Q Loss
                                       [p.u.]     [p.u.]    [p.u.]     [p.u.]
Bus28        Bus27      1              0.17911    0.10703   0          0.01672
Bus04        Bus12      2              0.27809   -0.0983    0          0.02114
Bus06        Bus10      3              0.11044    0.07855   0          0.0098
Bus06        Bus09      4              0.14263   -0.13448   0          0.00767
Bus10        Bus20      5              0.08889    0.02514   0.00077    0.00172
Bus10        Bus17      6              0.05236    0.02603   0.00011    0.00028
Bus08        Bus06      7              0.00708    0.04516   3e-005    -0.0093
Bus11        Bus09      8              0.1793     0.3106    0          0.02246
Bus21        Bus22      9             -0.01878   -0.02361   1e-005     2e-005
Bus22        Bus24      10             0.05647    0.0152    0.00039    0.0006
Bus23        Bus24      11             0.0202     0.01991   0.00011    0.00021
Bus06        Bus02      12            -0.36887    0.03981   0.00778   -0.01586
Bus07        Bus05      13             0.13137   -0.05119   0.00086   -0.0185
Bus04        Bus03      14            -0.44424    0.01895   0.00248   -0.00177
Bus05        Bus02      15            -0.56589    0.00278   0.01497    0.0194
Bus12        Bus16      16             0.07366    0.05221   0.00071    0.0015
Bus22        Bus10      17            -0.07527   -0.03883   0.00051    0.00106
Bus13        Bus12      18             0.1691     0.37938   0          0.02039
Bus02        Bus01      19            -0.89172   -0.0002    0.0143    -0.0145
Bus25        Bus24      20             0.01105    0.0331    0.00022    0.00039
Bus27        Bus26      21             0.02116    0.02756   0          0.00046
Bus27        Bus25      22             0.0251     0.02938   0.00016    0.0003
Bus27        Bus30      23             0.07094    0.01666   0.00164    0.00308
Bus14        Bus15      24             0.01719    0.01035   8e-005     8e-005
Bus16        Bus17      25             0.03794    0.03271   0.0002     0.00046
Bus01        Bus03      26             0.48017   -0.01417   0.00946   -0.00545
                                                                                   46

Bus30        Bus29      27              -0.0367    -0.00543   0.00034    0.00064
Bus21        Bus10      28              -0.15622   -0.08839   0.00111    0.00239
Bus27        Bus29      29               0.06191    0.01671   0.00087    0.00165
Bus08        Bus28      30               0.04292    0.00285   0.00015   -0.04399
Bus06        Bus28      31               0.13669    0.04797   0.00035   -0.01223
Bus04        Bus02      32              -0.28813    0.03876   0.00468   -0.0248
Bus19        Bus20      33              -0.06597   -0.0161    0.00016    0.00031
Bus18        Bus19      34               0.02911    0.01805   7e-005     0.00015
Bus15        Bus23      35               0.05259    0.03671   0.0004     0.0008
Bus18        Bus15      36              -0.06111   -0.02705   0.00047    0.00097
Bus25        Bus26      37               0.01389   -0.00402   5e-005     8e-005
Bus14        Bus12      38              -0.07919   -0.02635   0.00082    0.0017
Bus06        Bus04      39              -0.37666   -0.02836   0.00163   -0.00377
Bus09        Bus10      40               0.32193    0.14598   0          0.01289
Bus12        Bus15      41               0.18152    0.08428   0.00245    0.00483
Bus07        Bus06      42              -0.35937   -0.05781   0.00346   -0.00684
LINE FLOWS
From Bus     To Bus     Line             P Flow     Q Flow    P Loss     Q Loss
                                         [p.u.]     [p.u.]    [p.u.]     [p.u.]
Bus27        Bus28      1               -0.17911   -0.09031   0          0.01672
Bus12        Bus04      2               -0.27809    0.11944   0          0.02114
Bus10        Bus06      3               -0.11044   -0.06875   0          0.0098
Bus09        Bus06      4               -0.14263    0.14215   0          0.00767
Bus20        Bus10      5               -0.08812   -0.02341   0.00077    0.00172
Bus17        Bus10      6               -0.05225   -0.02576   0.00011    0.00028
Bus06        Bus08      7               -0.00705   -0.05445   3e-005    -0.0093
Bus09        Bus11      8               -0.1793    -0.28813   0          0.02246
Bus22        Bus21      9                0.01879    0.02363   1e-005     2e-005
Bus24        Bus22      10              -0.05609   -0.0146    0.00039    0.0006
Bus24        Bus23      11              -0.02009   -0.0197    0.00011    0.00021
Bus02        Bus06      12               0.37665   -0.05568   0.00778   -0.01586
Bus05        Bus07      13              -0.13051    0.03269   0.00086   -0.0185
Bus03        Bus04      14               0.44672   -0.02072   0.00248   -0.00177
Bus02        Bus05      15               0.58086    0.01662   0.01497    0.0194
Bus16        Bus12      16              -0.07294   -0.05071   0.00071    0.0015
Bus10        Bus22      17               0.07578    0.03989   0.00051    0.00106
Bus12        Bus13      18              -0.1691    -0.35899   0          0.02039
Bus01        Bus02      19               0.90602   -0.01429   0.0143    -0.0145
Bus24        Bus25      20              -0.01082   -0.03271   0.00022    0.00039
Bus26        Bus27      21              -0.02116   -0.0271    0          0.00046
Bus25        Bus27      22              -0.02494   -0.02908   0.00016    0.0003
Bus30        Bus27      23              -0.0693    -0.01357   0.00164    0.00308
Bus15        Bus14      24              -0.01711   -0.01028   8e-005     8e-005
Bus17        Bus16      25              -0.03775   -0.03224   0.0002     0.00046
Bus03        Bus01      26              -0.47072    0.00872   0.00946   -0.00545
Bus29        Bus30      27               0.03704    0.00607   0.00034    0.00064
Bus10        Bus21      28               0.15733    0.09078   0.00111    0.00239
Bus29        Bus27      29              -0.06104   -0.01507   0.00087    0.00165
Bus28        Bus08      30              -0.04277   -0.04683   0.00015   -0.04399
Bus28        Bus06      31              -0.13634   -0.0602    0.00035   -0.01223
Bus02        Bus04      32               0.29281   -0.06356   0.00468   -0.0248
Bus20        Bus19      33               0.06612    0.01641   0.00016    0.00031
Bus19        Bus18      34              -0.02903   -0.0179    7e-005     0.00015
Bus23        Bus15      35              -0.0522    -0.03591   0.0004     0.0008
Bus15        Bus18      36               0.06158    0.02801   0.00047    0.00097
Bus26        Bus25      37              -0.01384    0.0041    5e-005     8e-005
Bus12        Bus14      38               0.08001    0.02805   0.00082    0.0017
Bus04        Bus06      39               0.37829    0.02459   0.00163   -0.00377
Bus10        Bus09      40              -0.32193   -0.13309   0          0.01289
Bus15        Bus12      41              -0.17906   -0.07945   0.00245    0.00483
Bus06        Bus07      42               0.36283    0.05097   0.00346   -0.00684

TOTAL GENERATION
REAL POWER [p.u.]               2.9058
REACTIVE POWER [p.u.]           1.2592
TOTAL LOAD
REAL POWER [p.u.]               2.834
REACTIVE POWER [p.u.]           1.262
TOTAL LOSSES

REAL POWER [p.u.]               0.07179
REACTIVE POWER [p.u.]          -0.00282
                                                                           47


IEEE 57 Bus Test Systems


NETWORK STATISTICS
Buses:                         57
Lines:                         62
Transformers:                  18
Generators:                    7
Loads:                         42
SOLUTION STATISTICS
Number of Iterations:          4
Maximum P mismatch [p.u.]      0
Maximum Q mismatch [p.u.]      0
Power rate [MVA]               100

POWER FLOW RESULTS
Bus        V           phase         P gen     Q gen     P load   Q load
           [p.u.]      [rad]         [p.u.]    [p.u.]    [p.u.]   [p.u.]
Bus01      1.04        0             4.791     1.292     0.55     0.17
Bus02      1.01       -0.02076       0        -0.00749   0.03     0.88
Bus03      0.985      -0.10463       0.4       0.01016   0.41     0.21
Bus04      0.98032    -0.12762       0         0         0        0
Bus05      0.97635    -0.14853       0         0         0.13     0.04
Bus06      0.98       -0.15066       0         0.01377   0.75     0.02
Bus07      0.98416    -0.13169       0         0         0        0
Bus08      1.005      -0.07695       4.5       0.62144   1.5      0.22
Bus09      0.98       -0.16578       0         0.01699   1.21     0.26
Bus10      0.98573    -0.19879       0         0         0.05     0.02
Bus11      0.97476    -0.17507       0         0         0        0
Bus12      1.015      -0.18214       3.1       1.28      3.77     0.24
Bus13      0.97943    -0.17075       0         0         0.18     0.023
Bus14      0.96873    -0.16635       0         0         0.105    0.053
Bus15      0.98766    -0.12617       0         0         0.22     0.05
Bus16      1.0134     -0.15418       0         0         0.43     0.03
Bus17      1.0175     -0.09395       0         0         0.42     0.08
Bus18      0.99504    -0.20742       0         0         0.272    0.098
Bus19      0.98952    -0.24443       0         0         0.033    0.006
Bus20      0.97742    -0.24074       0         0         0.023    0.01
Bus21      1.0097     -0.22842       0         0         0        0
Bus22      1.0095     -0.22564       0         0         0        0
Bus23      1.008      -0.22679       0         0         0.063    0.021
Bus24      0.9979     -0.23304       0         0         0        0
Bus25      0.97886    -0.31995       0         0         0.063    0.032
Bus26      0.95755    -0.22803       0         0         0        0
Bus27      0.98072    -0.20259       0         0         0.093    0.005
Bus28      0.99602    -0.18464       0         0         0.046    0.023
Bus29      1.0097     -0.17229       0         0         0.17     0.026
Bus30      0.96389    -0.33356       0         0         0.036    0.018
Bus31      0.93517    -0.3455        0         0         0.058    0.029
Bus32      0.94609    -0.33073       0         0         0.016    0.008
Bus33      0.94379    -0.33143       0         0         0.038    0.019
Bus34      0.9549     -0.25232       0         0         0        0
Bus35      0.96163    -0.24809       0         0         0.06     0.03
Bus36      0.97105    -0.24332       0         0         0        0
Bus37      0.98085    -0.23918       0         0         0        0
Bus38      1.0123     -0.22272       0         0         0.14     0.07
Bus39      0.97815    -0.24069       0         0         0        0
Bus40      0.9671     -0.24481       0         0         0        0
Bus41      0.97115    -0.30261       0         0         0.063    0.03
Bus42      0.94801    -0.32234       0         0         0.071    0.04
Bus43      1.0153     -0.17959       0         0         0.02     0.01
Bus44      1.0162     -0.2082        0         0         0.12     0.018
Bus45      1.0353     -0.1647        0         0         0        0
Bus46      1.0526     -0.21482       0         0         0        0
Bus47      1.0377     -0.21305       0         0         0.297    0.116
Bus48      1.0291     -0.21708       0         0         0        0
Bus49      1.0319     -0.22683       0         0         0.18     0.085
Bus50      1.0197     -0.23557       0         0         0.21     0.105
Bus51      1.0499     -0.22076       0         0         0.18     0.053
Bus52      0.98021    -0.20297       0         0         0.049    0.022
Bus53      0.96794    -0.21405       0         0         0.2      0.1
Bus54      0.99384    -0.20515       0         0         0.041    0.014
Bus55      1.0288     -0.18978       0         0         0.068    0.034
Bus56      0.95548    -0.32404       0         0         0.076    0.022
Bus57      0.95565    -0.32759       0         0         0.067    0.02
                                                                        48

LINE FLOWS
From Bus     To Bus   Line    P Flow     Q Flow    P Loss     Q Loss
                              [p.u.]     [p.u.]    [p.u.]     [p.u.]
Bus02        Bus01    1      -1.0087    -0.84086   0.01317   -0.09115
Bus03        Bus02    2      -0.95068    0.04504   0.02798   -0.0016
Bus12        Bus09    3      -0.02729    0.0871    0.00106   -0.07202
Bus12        Bus10    4       0.17542    0.18114   0.00188   -0.02426
Bus13        Bus09    5      -0.02856   -0.01422   4e-005    -0.03883
Bus13        Bus14    6      -0.02072    0.24286   0.00085   -0.00763
Bus14        Bus15    7      -0.73153   -0.09941   0.00991    0.01753
Bus13        Bus15    8      -0.47578    0.05461   0.00647   -0.00135
Bus01        Bus15    9       1.4976     0.34155   0.03948    0.10021
Bus01        Bus16    10      0.79028   -0.00868   0.02623    0.06147
Bus01        Bus17    11      0.93123    0.03937   0.01915    0.05662
Bus12        Bus16    12     -0.33195    0.08739   0.00209   -0.01276
Bus03        Bus04    13      0.5917    -0.0667    0.00407   -0.0234
Bus17        Bus12    14      0.49208   -0.09725   0.00949   -0.00638
Bus13        Bus12    15      0.01033   -0.63165   0.00674   -0.03812
Bus03        Bus15    16      0.34898   -0.17818   0.00242   -0.04501
Bus07        Bus08    17     -0.7824    -0.12391   0.00897    0.02677
Bus13        Bus11    18      0.06928    0.03159   0.00016   -0.01746
Bus19        Bus18    19     -0.03985   -0.02913   0.00093   -0.09708
Bus19        Bus20    20      0.00685    0.02313   0.00017    0.00026
Bus04        Bus05    21      0.13589   -0.04564   0.00127   -0.02201
Bus21        Bus22    22     -0.01632    0.01255   3e-005     5e-005
Bus22        Bus23    23      0.09854    0.03367   0.00011    0.00016
Bus23        Bus24    24      0.03544    0.01251   0.00025   -0.00806
Bus26        Bus27    25     -0.10548   -0.01761   0.00206    0.00317
Bus27        Bus28    26     -0.20054   -0.02578   0.00263    0.00405
Bus28        Bus29    27     -0.24916   -0.05283   0.00273    0.00384
Bus04        Bus06    28      0.13897   -0.05322   0.00092   -0.03025
Bus25        Bus30    29      0.07766   -0.00719   0.00091   -0.05431
Bus30        Bus31    30      0.04075    0.02911   0.00088    0.00134
Bus32        Bus31    31      0.01832    0.00151   0.00019    0.00029
Bus33        Bus32    32     -0.038     -0.019     8e-005     7e-005
Bus35        Bus34    33      0.07277    0.03298   0.00036   -0.00239
Bus36        Bus35    34      0.13377    0.06273   0.001     -0.00025
Bus37        Bus36    35      0.19406    0.10909   0.00149    0.00189
Bus38        Bus37    36      0.25852    0.14867   0.00567    0.0068
Bus39        Bus37    37     -0.05868   -0.03259   0.00011    0.00018
Bus06        Bus07    38     -0.17991   -0.01624   0.00067   -0.02318
Bus40        Bus36    39     -0.05863   -0.04421   0.00017    0.00027
Bus38        Bus22    40      0.11515    0.02156   0.00026    0.0004
Bus42        Bus41    41     -0.06537   -0.02338   0.00111    0.00189
Bus44        Bus38    42      0.23341   -0.04564   0.00158    0.00114
Bus46        Bus47    43      0.60496    0.26134   0.00903   -0.00082
Bus47        Bus48    44      0.29892    0.14616   0.00187    0.0024
Bus06        Bus08    45     -0.42754   -0.06495   0.00652   -0.01306
Bus49        Bus48    46     -0.04618    0.05015   0.00038   -0.0045
Bus50        Bus49    47     -0.09541   -0.03757   0.00081    0.00129
Bus51        Bus50    48      0.11694    0.07117   0.00236    0.00374
Bus42        Bus56    49     -0.00563   -0.01662   7e-005     0.00012
Bus49        Bus38    50      0.03541    0.08858   0.00104   -0.00466
Bus41        Bus56    51      0.03204   -0.00415   0.00061    0.00061
Bus09        Bus08    52     -1.7432    -0.09283   0.03137    0.10603
Bus57        Bus56    53     -0.00832    0.00621   2e-005     3e-005
Bus44        Bus45    54     -0.35341    0.02764   0.0076     0.01092
Bus38        Bus48    55     -0.24747   -0.19378   0.00301    0.00465
Bus54        Bus55    56     -0.11763   -0.06309   0.00312    0.00409
Bus53        Bus54    57     -0.07505   -0.04715   0.00157    0.00195
Bus52        Bus53    58      0.12626   -0.00523   0.00131   -0.05808
Bus29        Bus52    59      0.17991    0.0228    0.00465    0.00603
Bus05        Bus06    60      0.00462   -0.06363   0.00011   -0.01164
Bus10        Bus09    61     -0.1734     0.05349   0.00135   -0.03634
Bus11        Bus09    62     -0.11239   -0.03593   0.00036   -0.01964
Bus04        Bus18    63      0.17687    0.02341   0          0.01424
Bus11        Bus41    64      0.15352    0.07137   0          0.02259
Bus24        Bus26    65     -0.10548   -0.01707   0          0.00054
Bus07        Bus29    66      0.60181    0.13085   0          0.02538
Bus34        Bus32    67      0.0724     0.03537   0          0.00679
Bus09        Bus55    68      0.18875    0.10709   0          0.00591
Bus11        Bus43    69      0.02799    0.01361   0          0.00016
Bus24        Bus25    70      0.06893    0.01845   0          0.00629
Bus24        Bus25    71      0.07173    0.01919   0          0.00654
Bus41        Bus43    72     -0.00799   -0.00234   0          0.00111
Bus04        Bus18    73      0.13591    0.03215   0          0.01126
Bus21        Bus20    74      0.01632   -0.01255   0          0.00032
Bus15        Bus45    75      0.36101   -0.0028    0          0.01392
Bus14        Bus46    76      0.60496    0.29691   0          0.03557
Bus13        Bus49    77      0.26545    0.29381   0          0.03122
Bus10        Bus51    78      0.29694    0.13191   0          0.00774
Bus39        Bus57    79      0.05868    0.03259   0          0.00638
Bus40        Bus56    80      0.05863    0.04421   0          0.00689
                                                                        49

LINE FLOWS
From Bus     To Bus   Line    P Flow     Q Flow    P Loss     Q Loss
                              [p.u.]     [p.u.]    [p.u.]     [p.u.]
Bus01        Bus02    1       1.0218     0.74971   0.01317   -0.09115
Bus02        Bus03    2       0.97866   -0.04664   0.02798   -0.0016
Bus09        Bus12    3       0.02835   -0.15912   0.00106   -0.07202
Bus10        Bus12    4      -0.17354   -0.20539   0.00188   -0.02426
Bus09        Bus13    5       0.02861   -0.02461   4e-005    -0.03883
Bus14        Bus13    6       0.02158   -0.2505    0.00085   -0.00763
Bus15        Bus14    7       0.74144    0.11694   0.00991    0.01753
Bus15        Bus13    8       0.48225   -0.05596   0.00647   -0.00135
Bus15        Bus01    9      -1.4581    -0.24135   0.03948    0.10021
Bus16        Bus01    10     -0.76404    0.07014   0.02623    0.06147
Bus17        Bus01    11     -0.91208    0.01725   0.01915    0.05662
Bus16        Bus12    12      0.33404   -0.10014   0.00209   -0.01276
Bus04        Bus03    13     -0.58764    0.0433    0.00407   -0.0234
Bus12        Bus17    14     -0.48259    0.09087   0.00949   -0.00638
Bus12        Bus13    15     -0.00359    0.59354   0.00674   -0.03812
Bus15        Bus03    16     -0.34656    0.13317   0.00242   -0.04501
Bus08        Bus07    17      0.79137    0.15068   0.00897    0.02677
Bus11        Bus13    18     -0.06913   -0.04905   0.00016   -0.01746
Bus18        Bus19    19      0.04078   -0.06794   0.00093   -0.09708
Bus20        Bus19    20     -0.00668   -0.02288   0.00017    0.00026
Bus05        Bus04    21     -0.13462    0.02363   0.00127   -0.02201
Bus22        Bus21    22      0.01635   -0.01251   3e-005     5e-005
Bus23        Bus22    23     -0.09844   -0.03351   0.00011    0.00016
Bus24        Bus23    24     -0.03518   -0.02057   0.00025   -0.00806
Bus27        Bus26    25      0.10754    0.02078   0.00206    0.00317
Bus28        Bus27    26      0.20316    0.02983   0.00263    0.00405
Bus29        Bus28    27      0.2519     0.05667   0.00273    0.00384
Bus06        Bus04    28     -0.13804    0.02297   0.00092   -0.03025
Bus30        Bus25    29     -0.07675   -0.04711   0.00091   -0.05431
Bus31        Bus30    30     -0.03987   -0.02777   0.00088    0.00134
Bus31        Bus32    31     -0.01813   -0.00123   0.00019    0.00029
Bus32        Bus33    32      0.03808    0.01907   8e-005     7e-005
Bus34        Bus35    33     -0.0724    -0.03537   0.00036   -0.00239
Bus35        Bus36    34     -0.13277   -0.06298   0.001     -0.00025
Bus36        Bus37    35     -0.19256   -0.10721   0.00149    0.00189
Bus37        Bus38    36     -0.25285   -0.14187   0.00567    0.0068
Bus37        Bus39    37      0.05879    0.03277   0.00011    0.00018
Bus07        Bus06    38      0.18059   -0.00694   0.00067   -0.02318
Bus36        Bus40    39      0.0588     0.04447   0.00017    0.00027
Bus22        Bus38    40     -0.11489   -0.02117   0.00026    0.0004
Bus41        Bus42    41      0.06648    0.02527   0.00111    0.00189
Bus38        Bus44    42     -0.23183    0.04679   0.00158    0.00114
Bus47        Bus46    43     -0.59592   -0.26216   0.00903   -0.00082
Bus48        Bus47    44     -0.29705   -0.14377   0.00187    0.0024
Bus08        Bus06    45      0.43405    0.0519    0.00652   -0.01306
Bus48        Bus49    46      0.04657   -0.05466   0.00038   -0.0045
Bus49        Bus50    47      0.09622    0.03886   0.00081    0.00129
Bus50        Bus51    48     -0.11459   -0.06743   0.00236    0.00374
Bus56        Bus42    49      0.00571    0.01674   7e-005     0.00012
Bus38        Bus49    50     -0.03437   -0.09324   0.00104   -0.00466
Bus56        Bus41    51     -0.03142    0.00476   0.00061    0.00061
Bus08        Bus09    52      1.7746     0.19886   0.03137    0.10603
Bus56        Bus57    53      0.00834   -0.00618   2e-005     3e-005
Bus45        Bus44    54      0.36101   -0.01673   0.0076     0.01092
Bus48        Bus38    55      0.25048    0.19842   0.00301    0.00465
Bus55        Bus54    56      0.12075    0.06718   0.00312    0.00409
Bus54        Bus53    57      0.07663    0.04909   0.00157    0.00195
Bus53        Bus52    58     -0.12495   -0.05285   0.00131   -0.05808
Bus52        Bus29    59     -0.17526   -0.01677   0.00465    0.00603
Bus06        Bus05    60     -0.00451    0.052     0.00011   -0.01164
Bus09        Bus10    61      0.17476   -0.08983   0.00135   -0.03634
Bus09        Bus11    62      0.11275    0.01629   0.00036   -0.01964
Bus18        Bus04    63     -0.17687   -0.00917   0          0.01424
Bus41        Bus11    64     -0.15352   -0.04878   0          0.02259
Bus26        Bus24    65      0.10548    0.01761   0          0.00054
Bus29        Bus07    66     -0.60181   -0.10547   0          0.02538
Bus32        Bus34    67     -0.0724    -0.02859   0          0.00679
Bus55        Bus09    68     -0.18875   -0.10118   0          0.00591
Bus43        Bus11    69     -0.02799   -0.01345   0          0.00016
Bus25        Bus24    70     -0.06893   -0.01216   0          0.00629
Bus25        Bus24    71     -0.07173   -0.01265   0          0.00654
Bus43        Bus41    72      0.00799    0.00345   0          0.00111
Bus18        Bus04    73     -0.13591   -0.02089   0          0.01126
Bus20        Bus21    74     -0.01632    0.01288   0          0.00032
Bus45        Bus15    75     -0.36101    0.01673   0          0.01392
Bus46        Bus14    76     -0.60496   -0.26134   0          0.03557
Bus49        Bus13    77     -0.26545   -0.26259   0          0.03122
Bus51        Bus10    78     -0.29694   -0.12417   0          0.00774
Bus57        Bus39    79     -0.05868   -0.02621   0          0.00638
Bus56        Bus40    80     -0.05863   -0.03732   0          0.00689
                                   50

TOTAL GENERATION
REAL POWER [p.u.]        12.791
REACTIVE POWER [p.u.]    3.2269
TOTAL LOAD
REAL POWER [p.u.]        12.508
REACTIVE POWER [p.u.]    3.36
TOTAL LOSSES

REAL POWER [p.u.]        0.28295
REACTIVE POWER [p.u.]   -0.13314

				
DOCUMENT INFO
Shared By:
Stats:
views:7896
posted:7/22/2010
language:Albanian
pages:67
Description: Thesis