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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

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