* Introduction to Electric Power and Energy Systems

Power Engineering = The Power to Transform and RestorePaulo F. Ribeiro, MBA, Ph.D., PEInterim 2008Calvin CollegeEngineering DepartmentFrom a GardenTo a City

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Despite its limitations and dangers, technology can alleviate in part the bind in which humankind naturally finds itself. Appropriate technology can increase lifes possibilities, decrease physical burdens and difficulties at work, and free people from routine activities while opening the door to all kinds of mental creative labor. Natural disasters can be averted, illness overcome, and, in a certain sense, with the aid of electronics and microprocessors, the deaf can hear, the blind can see, and the lame walk again. Technology development can provide a degree of social security, and increase available information so as to extend and deepen communications. Adapted from Perspectives on Technology and Culture, by Egbert Schuurman

A Reflection on Technology

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Calvin College - January 2008 A C.S. Lewis Quote Calendar - Meditations for Interim 2008 (Complied by P. F. Ribeiro)

I believe in Christianity as I believe that the sun has risen, not only because I see it but because by it I see everything else. Is Theology Poetry?

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Prayer is either a sheer illusion or a personal contact between embryonic, incomplete persons (ourselves) and the utterly concrete Person. Prayer in the sense of petition, asking for things, is a small part of it; confession and penitence are its threshold, adoration its sanctuary, the presence and vision and enjoyment of God its wine. The Worlds Last Night

1 "'There are no accidents. Our guide is Aslan.'"

The Silver Chair

2 All that is not eternal is eternally out of date.

The Four Loves

3 Die before you die. There is no chance after.

Till We Have Faces

4 Where, except in the present can the eternal be met.

Christian Reflections

5 "For in self-giving, if anywhere, we touch a rhythm not only of all creation but of all being."

The Problem of Pain

6 Do not waste your time bothering whether you love you neighbor; act as if you did.

Mere Christianity

7 "Badness is only spoiled goodness."

Mere Christianity

8 Joy is the serious Business of heaven.

Letters to Malcolm

9 "No good work is done anywhere without aid from the Father of Lights."

Reflections on the Psalms

10 "Christ died for men precisely because men are not worth dying for; to make them worth it."

The World's Last Night

11 "Every sin is the distortion of an energy breathed into us..."

Letters to Malcolm

12 "Until you have given up your self to Him you will not have a real self..."

Mere Christianity

13 "The surest way of spoiling a pleasure [is] to start examining your satisfaction."

Surprised by Joy

14 "Human intellect is incurably abstract."

Myth Became Fact

15 "Poetry too is a little incarnation, giving body to what had been before invisible and inaudible."

Reflections on the Psalms

16 "The most valuable thing the Psalms do for me is to express the same delight in God which made David dance."

Reflections on the Psalms

17 "Though we cannot experience our life as an endless present, we are eternal in God's eyes; that is, in our deepest reality."

Letters to Malcolm

18 'Nothing, not even what is lowest and most bestial, will not be raised again if it submits to death.'"

The Great Divorce

19 "History is a story written by the finger of God."

Christian Reflections

20 "Every story of conversion is the story of a blessed defeat."

Foreword to Joy Davidman's Smoke on the Mountain

21 "Without the aid of trained emotions the intellect is powerless against the animal organism."

The Abolition of Man

22 "No doubt those who really founded modern science were usually those whose love of truth exceeded their love of power."

The Abolition of Man

23 "The very nature of Joy makes nonsense of our common distinction between having and wanting."

Surprised by Joy

24 "You would not have called to me unless I had been calling to you,'" said the Lion."

The Silver Chair

25 "Perfect humility dispenses with modesty."

The Weight of Glory

26 Mere change is not growth. Growth is the synthesis of change and continuity, and where there is no continuity there is no growth.

Selected Literary Essays

27 "Where, except in uncreated light, can the darkness be drowned?"

Letters to Malcolm

28 "Mercy, detached from Justice, grows unmerciful."

The Humanitarian Theory of Punishment

29 "The road to the promised land runs past Sinai."

The Problem of Pain

30 Authority exercised with humility, and obedience accepted with delight are the very lines along which our spirits live."

Transposition and Other ...

31 I'm going to live as like a Narnian as I can even if there isn't any Narnia.

The Silver Chair

"Aslan," said Lucy, "you're bigger."

"That is because you are older, little one," answered he.

"Not because you are?"

"I am not. But every year you grow, you will find me bigger."

Prince Caspian

Continue seeking Him with seriousness. Unless He wanted you, you would not be wanting Him. Letters of C.S. Lewis

PMS/UNIFEI/GQEEExample 1 Example 2Example 3

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* Syllabus - Schedule - 2:00PM 5:00PM - - - Room SB 128

Professor:Paulo F. Ribeiro SB134 x 6407pfribeiro@ieee.org Skype: aslan52

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Tuesday

Wednesday

Thursday

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Introduction

Structure of Power Systems

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Introduction Structure of Power Systems

Visit to Consumers Energy (Prof. Visit 9AM)

Visit to Newberry Place

3:30PM

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Generators

Transformers

Trans. Lines

Lines, etc.

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Grid Operation

Load Flow

Problem

Visit to Plainwell, Hydro Plant

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Grid Operation

SimPower

PowerWorld

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Grid Operations

PowerWorld

Examples

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Grid Operations

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Projects

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Projects

(E-Learning

Skype - E-Mail)

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Presentations

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Presentations

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ENGR W84 A Intro. to Power/Energy Systems08/INNH05402:00PM - 05:00PMMTWTHF

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* TextClass Notes; Internet / Web ResourcesReferences: The Electric Power Engineering Handbook. CRC / IEEE Press, 2000.Power System Analysis, Hadi Saadat, 2nd Edition, McGraw-Hill, 2002.Power System Analysis, 2nd Edition, Arthur R. Bergen and Vijay Vittal, Prentice-Hall, 1999. Power Systems Analysis John J. Grainger and William D. Stevenson McGraw-Hill, 1994. Elements of Power Systems Analysis, 4th Edition, William D. Stevenson, McGraw-Hill, 1982. Electrical Energy Systems Theory, Olle Elgerd, McGraw-Hill, 1971; Power Systems Analysis, Charles Gross, John Wiley & Sons, 1979Power System Analysis & Design, J.D. Glover and M. Sarma, 2nd Edition, PWS Publishers, 1994

Web Resources (?????????????????????????????????????????????)

Some Suggested Topics For Final Paper

Distributed Generation, Energy Efficiency, Renewable Energy Sources Exploring Grid Operations With PowerWorld Exploring Power Systems and Power Electronics Transients With PSCAD/EMTDC Designing A Distribution System With EasyPower Harmonic Propagation Analysis (Using PSpice and/or MathCAD) Power Quality Survey/Diagnostic at Calvin College (Using Fluke 43) Perspectives on Deregulation of the Power Utility Industry Environmental Impact of Power Systems Using the Internet for Power Systems MonitoringGrades (based on homework assignments, class participation, final paper/presentation, class log/notes)Pass(S)Pass Honor(H) For Outstanding WorkFail(U)(*)

(*) incomplete/insufficient assignments and/or missed two class periodsCourse InstructionsPaper 8-10 Pages (IEEE Paper Format)Presentation 20 minutesTeams of two students

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* My objective is to provide you with a learning environment in which you will learn the fundamentals of power systems.

My approach is to encourage the student to learn how to learn. To take ownership of the learning process: Initiative, involvement, interactive participation are the keys to an effective learning experience.

Please keep me informed if you do not feel that I have been successful in this goal. Do not wait until evaluation time to express your frustrations. I want to listen to your concerns or difficulties with the material, and am always available to help you outside the classroom.

Course Instructions

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* To introduce a broad range of theory and methods related to AC power system analysis and design. To develop familiarity with power system engineering components, equipment and analytical tools To understand and study of the largest machine ever built-the integrated power grid. To understand the use of transmission grids as a means of transport/delivery of energy. To use tools for the analysis of power systems (PowerWorld, EasyPower, PSCAD/EMTP). To investigate flow of power on a power grid. To understand voltage regulation, real and reactive power, three phase power, power quality, efficiency, practical stability limits, etc., etc. To become familiar with management and environmental issues associated with transmission grids / power systems.

Objectives/Introductory Words:

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* Introduction to Power Systems: Syllabus

Concepts and Applications:Introduction (Structure of Power Systems)Basic Principles (AC Power)GenerationTransmission LinesTransformersPower FlowStabilityTransient and Harmonic Studies

Computer ProgramsMathCAD, PSpice, MATLAB / Simulink (PowerSym), PowerWord, EasyPower, EMTDC/PSCAD

Advanced Topics:Distributed Generation, Renewable Power, Efficiency

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Projects* 1 Small Hydro Power Plant City of Plainwell, MichiganFeasibility Study for Recovery of Plant

2 Belknap Lookout Community Feasibility Study of Developing Wind Power Generation Project

3 Consumers Energy Control Center in Ada Work on possible projects at the Control Center.

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* ProjectsErik Wilson, ManagerCity of Plainwell

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* ProjectsSteve FaberNewberry Place

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* ProjectsMark Luehmann, Consumers Energy

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* Power System Analysis, Computing and Economics Computing applications Distribution system analysis Economics, market organization, cost structures, pricing, and risk management Intelligent system applications Reliability, uncertainty, and probability and stochastic system applications Power System Dynamic Performance Power system dynamic modeling: components and systems Power system stability: phenomena, analysis, and techniques Power system stability controls: design and applications Power system dynamic measurements Power system interaction with turbine generators Dynamic security assessment: techniques and applications, risk-based methods Power System Operations Power system dynamic modeling: components and systems Power system stability: phenomena, analysis, and techniques Energy control centers Distribution operation System control Operating economics and pricing An Overview of Power and Energy Systems

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* Power System Planning & Implementation Generation system resource planning Transmission system planning Distribution system planning Integrated resource planning and distributed resource planning Load forecasting Customer products and services planning and implementation Industry restructuring planning and policy issues Insulated Conductors Construction and design of cables (materials and manufacturing) Construction, design and testing of cable accessories (cable terminations and joints) Construction, operation, and testing of cable system Assembly, operation, and testing of station, control (including fiberoptic), and utilization cables (non-transmission and distribution cables) Power Engineering Education New instruction methods (software/ internet / laboratory / combined with research) Virtual classrooms/laboratory Distance education Life-long learningAn Overview of Power and Energy Systems

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* Electric Machinery DC Machines Permanent magnet machinery systems Switched and variable reluctance machines Integral horsepower induction machinery Wound rotor induction machinery Single phase induction motors Electronic drives for electric machinery Induction generators for grid and isolated applications Synchronous generators Motor/generator sets for pumped storage Synchronous motors materials to electric machinery Electrical machinery theory Numerical analysis of electric machinery Power processing equipment Insulation for electric machinery Application of magnetic materials to electric machinery Application of superconductingPower System Communications Communication systems Communication media Communication protocols Communication standardization Home automation and communicationAn Overview of Power and Energy Systems

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* Power System Instrumentation and Measurements Digital technology for measurements Electricity metering High voltage testing Measurement techniques for impedance elements Power System Relaying Digital protection systems Adaptive protections Power system protection Protection of electrical equipment Relaying communications Relaying for consumer interface Substations Substation automation Intelligent electronic devices (IEDs) Programmable logic controllers (PLCs) Substation design High voltage power electronics stations Gas insulated substations (GIS)An Overview of Power and Energy Systems

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* Surge Proctective Devices Design/testing of high voltage surge protective devices (>1000V) Application of high voltage surge protective devices (>1000V) Design/testing of low voltage surge protective devices (

* Transmission and Distribution AC transmission and distribution facilities Lightning phenomena and insulator performance Overhead line conductors: thermal and mechanical aspects Corona, electric, and magnetic fields Towers, poles, and hardware Capacitors, shunt and series capacitor banks, and harmonic filter banks HVDC transmission and distribution, FACTS and power electronic applications to ac transmission Harmonics and power quality Transients, switching surges, and electromagnetic noise Maintenance and operation of overhead lines Work procedures, safety, tools, and equipment Superconductivity analysis and devices Distributed resourcesEnergy Development and Power Generation Excitation systems Power system stabilizers Advanced energy technologies, Renewable energy technologies Station design, operations, and control Modeling, simulation and control of power plants Monitoring and instrumentation of power plants Control of distributed generation Hydroelectric power plants, Power plant scheduling, Engineering economic issues International practices in energy development An Overview of Power and Energy Systems

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* Make sure you have your students run LOTS of load flows...PowerWorld has an excellent demo package for schools. You can be sure to tell them that in the "real world" though, we are running 30,000+ bus load flows!However, they will NOT have to know anything about wavelets! :-)

We have a lot of positions open and will have more in the near future.

Regards,

W.G, Ph.D., P.E.Supervisor, Operations EngineeringSouthwest Power PoolAn Overview of Power and Energy Systems

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* The Big PictureObjectives/Introductory Words:

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* A 18 kV to 525 kV transformer for 825 MVA To increase the voltage of the generators, transformers with a capacity of 825 MVA and 768 MV, for 50 and 60 Hz respectively, were specified Electricity (AC) leaving ITAPU to Sao Paulo - 6,300 MW of electrical power generated by the 60 Hz units is transported by an 891 km AC transmission system, formed by three lines of 750 kV.Inside the ITAIPU Powerhouse Dimensions: length: 986 m, maximum height: 112 m and width: 99m. The red line on the floor indicates the border of Brazil and Paraguay Source: http://www.solar.coppe.ufrj.br/itaipu_conv.html Itaipu - A Great StoryObjectives/Introductory Words:The control center of the 18 generators - Left half of it (in Brazil) controls the 60 Hz units, right half (in Paraguay) controls the 50 Hz units

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* Power System Components

Electrical Components

Light bulbSocketWire to switchSwitchWire to circuit boxCircuit breakerWatthourmeterConnection to distribution systemDistribution transformerDistribution systemSubstationCapacitorsCircuit breakersDisconnectsBusesTransformersSubtransmission systemCapacitor banksTap changersCurrent transformersPotential transformersProtective relayingReactorsMetal-oxide varistorsTransmission systemSuspension insulatorsLightning arrestorsGenerator step-up transformersGenerators

Objectives/Introductory Words:

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* Non-Electrical Components

Glass for bulbsManufacture of bulbsSocketsSwitchesCircuit boxSteel for circuit boxCopper for wireAluminum for wirePoles for overhead linesTransmission towersMaintenancePlastics for capacitor insulationControls for protec. relaying schem.Communications for data and protectionFiber optics for communicationsFoundations for substation equipmentExcavation equipment and crewsCeramics and polymers for suspension insulatorsOil for transformers and circuit breakersGas for insulated substationsSprings for circuit breakersProcess control for component manufacturingComputers for process controlComputers for generation control and dispatchTurbines for turning generatorCoal for making steam to turn turbineTrains for hauling coalCarsBridgesPeopleObjectives/Introductory Words:

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* Basics Facts, Issues and Questions

Electricity discovery and development The value of electricity as a commodity Voltage and current, AC vs DC, single phase vs three phase What is the difference between power and energy? Reactive power, power factor and power factor correction How is electricity generated? Costs and characteristics of different types of generation traditional and emerging (fossil, nuclear, hydro, wind, solar, fuel cell, microturbine, etc.) System impacts of distributed generation How can electricity be stored? Generation Transmission Distribution Why are different voltage levels use? Why do we have overhead lines instead of all underground? Why do we interconnect?Objectives/Introductory Words:

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* Power system operation and control

Typical load demand cycles: daily, seasonal; Load forecasting How is power transmitted from one place to another and what are the costs? Differences between short, medium and long lines Why is it important to maintain frequency, voltages, synchronism, etc.? Active and reactive power losses, voltage drop, reactive power transfer How is frequency maintained?

Technical issues

Power system limits, stability Power system reliability, security, contingencies, reserve margins Lightning and Over-voltage Protection Harmonics and distortion and their effects Voltage sags and short-term interruptions: causes and effects Power system transients (switching, fault initiation and clearing, transient recovery voltage)Objectives/Introductory Words:

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* Regulatory and policy issues

History of regulation in the US and abroad Federal and National organizations Conservation: what works and are there new ideas? The role of regulators in the US Electricity restructuring The role of the US Federal vs. State governments What happened in California?Objectives/Introductory Words:

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* Historical Context

Static electricity discovered about 600 BC by Thales. Electromagnetism studied systematically by William Gilbert, 1600 First battery, Allessandro Volta, 1800 Relationship between current and magnetism, Andre Ampere, 1825 Ohms law, George Ohm, 1827 Faradays law, Michael Faraday, 1831 Maxwells Equations, James Clerk Maxwell, 1864 First practical generator and motor, Zenobe Thoephile Gramme, 1873 Incandescent Lamp, Thomas Edison, 1879 First power station Pearl Street, Manhattan, Thomas Edison, 1882 First Hydroelectric plant, Appleton Wisconsin, 1882 DC motor produced, Frank J. Sprague, 1884 Transformer demonstrated, William Stanley, 1886 Polyphase AC system, induction and synchronous motors, Nicola Tesla, 1888 First single-phase Transmission line in US, Oregon, 1889 - By 1900, over 3000 Stations Objectives/Introductory Words:

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* Recent Developments

High-speed relay systems High-speed, EHV circuit breakers Surge Arresters (MOVs)Communications applications in power systems Energy control centers with SCADA and AGC Development of power electronics devices Adjustable speed drives / motors Electric and Hybrid Electric Vehicles Flexible AC Transmission System (FACTS) Unified Power Flow Controller (UPFC) Objectives/Introductory Words:

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* Current Issues

Two extensive outages in 1996 July 2, 1996 Combined issues of Power system stability Protective Relaying System Planning Two million customers affected in 14 states, Canada and Mexico Initiating event related to power line touching a tree August 10, 1996 4 million customers affected in 9 states Initiating event: over heated transmission lines sag to trees

Utility Deregulation The intention is that removing state regulation from utility operation will reduce prices. A number of states already have legislation in place requiring deregulation, California is already phasing it in. Objectives/Introductory Words:

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PMS/UNIFEI/GQEE12 - 34,5 kV ItaipPer Generator750 MVA, 18 kV => 24.000 A

PMS/UNIFEI/GQEETransformer to 500 kV890 ATransformation

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PMS/UNIFEI/GQEE... Transmission

PMS/UNIFEI/GQEESubstations

PMS/UNIFEI/GQEELT Itumbiara Nova Ponte 500 kVLT Emborcao Nova Ponte 500 kVLT Nova Ponte - Estreito 500 kVLT Nova Ponte So Gotardo - Bom Despacho 500 kVLT Arauai 2 Irap230 kV

PMS/UNIFEI/GQEENorte-Nordeste500 kVNorte-Sul III 500 kV Acre/Rondnia-SE/CO 230 kV

Tucuru-Manaus 500 kV

Reforos nas Regies SE/CO 500 kV Sul-Sudeste 525 kV

Jurupari-Macap 230kV

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Mechanical Energy Rotational Energy Electrical Energy Power Electrical Power

Analytical BackgroundObjectives/Introductory Words:Plus

Circuit Analysis

Electronics

Signal Processing

Communications

Controls

Economics

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* Why do we use Alternating Current (AC) for Electric Power?Construction of Generators:Key component is the 3 phase generatorSimple in raising and lowering voltages:Generators limited to about 25kVTransmission at 345,500 and 765kV (low losses)Subtransmission at 115, 69, 22kVDistribution at 12, 8, 4kVKey component: power transformer

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* * Power GenerationItaipu - One 715 MW electrical generator The diameter of the rotor is almost 16 m, the rotating mass is 2 650 t

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* Voltage from generator to CustomerTypical voltages for different parts of the American power system: System TypeFromToResidential110 V220 V (split single Phase)Commercial480 V(three Phase)Industrial480 V4160 V.Distribution2300 V32000 VSubtransmission25 kV130 kVTransmission115 kV765 kVGeneration13.2 kV36 kV

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* Power Transformers

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* Substations: where transmission lines interconnect

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* Where does AC come from?AC voltages and currents are usually produced by rotating generators in a power system and are represented by sine wavesAC voltages and currents can also be produced by an electronic oscillator.

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* A one phase AC generator

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* Phase AngleFor AC circuits we must be concerned with the phase angle between voltage and current.Current may be in phase with voltage in which case the phase angle is zeroCurrent may lead or lag voltage

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* A phasor is a representation of a sinusoidal voltage or current as a vector rotating about the origin of the complex plane. Example of Voltage and current calculations without phasors:

For a simple RL circuit with the above excitation voltage, find the current:

This becomes a very difficult problem to solve, with the solution:

AC Power and Phasors

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* Eulers Equation Representation of voltages and currents as complex numbers:

We then shorten the notation, assuming that all phasors that will be used in a system are at the same frequency, the (ejwt) term is implicit in all references to the value. Another assumption that is made is that the magnitude of any voltage or current as a function of time is the real part of its complex representation. Hence, may be represented in any of the following ways:

being called the exponential, polar, and rectangular forms respectively, where is the root mean square (rms) of the voltage wave form.

Definition of RMS

AC Power and Phasorsvoltages using rotating vectors (called phasors)

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* Phasor representation of Resistance, Inductance, Capacitance Advantages of Phasors Less Cumbersome (short hand notation) Simpler Calculations (complex arithmetic, calculators can do), generally less need for integration and differentiation Additional insights may be obtained about relations between currents, voltages, and power Limitations Applies only to sinusoidal steady-state systems Power Calculated using phasors is only the time average AC Power and Phasors

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* Voltage and Current are the same(phase angle is zero)

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* Current leads voltage by a phase angle of 45 deg

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* Current lags voltage by a phase angle of 45 deg

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* Instantaneous Power in an AC CircuitMultiply Voltage at time t by the current at time t.Note that power may flow in both directions.HW 1 - Verify behavior of AC instantaneous power (using MathCAD, Mathematica, PSpice). Assume sinusoidal (different phase-shifts) and non-sinusoidal voltages / currents. Use a half-wave rectification load to generate a non-sinusoidal load. Interpret the results.

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* Phase angle zeroCurrent leading Voltage by 45 degreesInstantaneous Power in an AC Circuit

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* Current leading Voltage by 90 degCurrent lagging Voltage by 90 degInstantaneous Power in an AC Circuit

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* Average Real Power

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* Complex Power Real and Reactive

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* Real and Reactive PowerInstantaneous power may flow in both directionsInstantaneous power may be broken up into two components:Real Power only flows in one direction, its average value is zero or positiveReactive Power always oscillates in one direction and then reverses an equal amount. Its average value is always zero.

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* Phase Angle zeroCurrent leading Voltage by 45 degreesReal and Reactive Power in an AC Circuit

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* Current leading Voltage by 90 degCurrent lagging Voltage by 90 degReal and Reactive Power in an AC Circuit

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* What is RMS voltage and current?If we use DC voltage and current then the power delivered to a load is: If we are given an AC voltage and current that are in phase then:Where

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* Why must we use RMS voltages and currents?Use RMS so that the product of voltage and current gives the correct power value, or the effective value of energy delivered per second to the load.If the current is not in phase with the voltage then:The reactive power is

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* What is MVA, MW and MVARSMW for Mega Watts (millions of watts)The product of RMS voltage and RMS current is the MVA (mega volt amperes) being delivered by a circuit.

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* What is a 3 Phase AC system?Three phase is generated by a generator with three sets of independent windings which are physically spaced 120 degrees around the stator.Voltages are labeled phase a, phase b, and phase c and are the same magnitude but differ in phase angle by 120 degrees.

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* 3 Phase Generator

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* 3 Phase Voltages

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* Representing Three Phase voltages using Phasors

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* Why use 3 phases?Smooth torque on generator shaftDelivery of constant power to a 3 phase load3 Wires and not 6What about unbalanced conditions?

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* Single Phase CircuitVoltage=V 0 degCurrent = IRequires 2 wires to deliver power

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* 3 phase circuitIf the three phase load is balanced the neutral carries no current and can be eliminated.Voltage a=V 0 degPhase aVoltage c=V +120 degVoltage b=V -120 degPhase bPhase cNeutral3 PhaseLoad

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* 3 phase circuit without a neutral wire3 PhaseLoadVoltage a=V 0 degPhase aVoltage c=V +120 degVoltage b=V -120 degPhase bPhase c

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* 3 Phase QuantitiesVaVbVcVabIaIabIaVa

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* Voltage Drop and Reactive Power CompensationV2 / 2ZLine = 1 +j7V1 = 13.2*10^3 + j0 IP&QZLoad = 10 +j30C = ?HW 2 - Calculate the voltage at the receiving end of the line. If the voltage is too low, compute the size of the capacitor which will recover the voltage to the same value of the sending end. Use MathCAD/Mathematica to calculate the value of C and then PSpice to verify behavior.

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* RXLV 0 degV 0 degRXLAC Power - Class ExerciseCalculate the real and reactive power absorbed by the two configurations below (as a function of V, R and L).

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* AC Transmission - Power Flow - HW 3Bus 1Bus 2IS12 = P12 + jQ12Z = R +jXV1 d1 degV2 d2 degd = d1 - d2Demonstrate that What happens when R

* Network Equations

KCL and KVL in phasor domainFormulation of mesh equations Formulation of nodal equations Conversion of system of equations to matrices

Matrix operations Inverse Transpose Conjugate

Solution of matrix equations

Example Discussion (Admittance and Impedance Matrix)

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* AC Power Transmission lines usually consist of multiples of three wiresShort, Medium, Long LinesWhat is the difference?

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* ShortMediumLongTransmission lines

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* Double Circuit Lines

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* Transmission Line Design Considerations Conductors Conductor types ACSR AAC AAAC ACAR Configurations bundles Insulators Porcelain Polymer Support Structures Wood Lattice Tubular Steel Concrete Fiberglass Shield Wires Ground Wires Lightning Protection Electrical factors Resistance and thermal loading Dielectric integrity and clearance Inductance Capacitance Mechanical Factors Structural Integrity Vibration Thermal Environmental Factors Visual Impact EM exposure Right of Way Danger to Wildlife

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Transmission Line Differential Equations

Derived from differential equations

Two Port Network Representation

Transmission Line Equations All Aluminium Conductors (AAC) Aluminium Conductors Steel Re-inforce (ACSR) All Aluminium Alloy Conductors (AAAC)

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GeneratorsPower TransformersThe Per Unit System

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* http://hydropower.inel.gov/state/stateres.htmGeneration /Generators

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* Generation /GeneratorsHW 4 - Analyze the actual composition of US power sources (compare with other countries) and propose a more sustainable / realistic composition. Use the internet for your research - substantiate your considerations.

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* Why use very high voltages?In this example the load is connected through a transmission line with resistance R. The motor is designed to operate at the same voltage as the generator terminal voltage. Losses are large and motor voltage is low.Discuss DC vs. AC and importance of Reactive Power on AC systems for voltage regulation.

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* Why use very high voltages?Transformer increases voltage to 10 times the generator terminal voltage. Current in transmission line is 1/10 I, losses are 1/100, and motor voltage is V-IR/100

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* High Voltage TransmissionReduces lossesTransmission conductor can have a smaller cross sectionProvides better voltage regulation at the load bus

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* Power Transformers

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* Transformer Basics

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* Power IN = Power OUTThis neglects the internal losses in the transformer

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* Real TransformersTest to Determine Parameters Open Circuit Test: Energize Low voltage winding at rated voltage, leaving other winding open Measure Current (Ioc) and Power (Poc) into energized winding. Calculate Re+h and Xm Short Circuit Test: Energize Low current (high voltage) winding at rated current with a solid short circuit applied across the other winding Measure Voltage and Power at terminals of energized winding Calculate other parameters

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* Transformer Types Power Transformers Current Transformers Voltage Transformers Series Transformers Transformer Purchasing Issues Efficiency Audible Noise Installation Costs Manufacturing Facilities Performance Record

Questions? Discussions... Real Transformers

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* Tap Changing TransformersChanging taps changes the turns ratio

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* Auto Transformer used for Tap Changing Under Load or TCUL Transformer

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* TCUL TransformerAssume primary side voltage begins to go down with heavy loadTCUL transformer changes taps to keep secondary voltage within limitsRaise secondary voltage during heavy loadReduce secondary voltage during light load

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* Transformer Connections Each leg is a single phase transformer Y-Y connections (no phase shift) D-D connections (no phase shift) Y-D connections (-30 degrees phase shift) D-Y connections (+30 degrees phase shift) Three-Phase Transformers

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* The Per Unit SystemAllows engineers to analyze a single phase network where:All P and Q quantities are three phaseVoltage magnitudes are represented as a fractional part of their standard or base valueAll phase angles are represented in the same units as normally used

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* Advantages

1. Per-unit representation results in a more meaningful and correlated data. It gives relative magnitude information. 2. There will be less chance of missing up between single - and three-phase powers or between line and phase voltages. 3. The p.u. system is very useful in simulating machine systems on analog, digital, and hybrid computers for steady-state and dynamic analysis. 4. Manufacturers usually specify the impedance of a piece of apparatus in p.u. (or per cent) on the base of the name plate rating of power ( ) and voltage ( ). Hence, it can be used directly if the bases chosen are the same as the name plate rating. 5. The p.u. value of the various apparatus lie in a narrow range, though the actual values vary widely. 6. The p.u. equivalent impedance (Zsc) of any transformer is the same referred to either primary or secondary side. For complicated systems involving many transformers or different turns ratio, this advantage is a significant one in that a possible cause of serious mistakes is removed. 7. Though the type of transformer in 3-phase system, determine the ratio of voltage bases, the p.u. impedance is the same irrespective of the type of 3-phase transformer. (Y D , D Y, D D , or Y Y) 8. Per-unit method allows the same basic arithmetic operation resulting in per-phase end values, without having to worry about the factor '100' which occurs in per cent system.

*

* Conversion Procedure -Specify the MVA base. Typically this will be related to the rating of a generator, transformer, or transmission line. Just choose the one that will result in the least amount of computation. This base will remain constant throughout the system. -At any location in the circuit, specify a voltage base. This will typically be the nominal voltage for that particular location. -Determine the voltage base for all other areas in the circuit by adjusting by the turns ratio every time a transformer is encountered. -Having specified the voltage and MVA base throughout the system, current and impedance bases may be determined as:

-For each value, the per unit quantity is the actual value divided by the base value.

-For 3phase circuits, the following relationships must also be included:

*

* Set Up the Per Unit SystemEach region of the power system is uniquely defined by a standard voltage determined by the transformer windings, this sets base voltageThe entire system is given a base power to which everything in the power flow is referred

*

* Per Unit Conversions

*

* Sample Power System

*

* Power System Divided into base voltage regions

*

* Numerical ExampleLet. V = 118 00 voltsZ = 5 300 ohmsThen I = 23.6 -300 amperes& S = V I* = (118 00)(23.6 +300) va= 2,784.8 300 vaFor this example, it is appropriate to choose:SlB = 3,000 vaVlB = 120-voltsThen IlB = = 25 amperes& ZlB = = 4.8 ohms

*

*

*

Three-Phase Systems

Three-phase systems may be normalized by picking appropriate three-phase bases.

Wye (Y)

Delta ( )

Choose (1) S3B = 3SlB

(1) S3B = 3SlB

(2) VB (ll) =

(2) VB(ll)

IB (l) =

IB (l) =

Since S3B = VB(ll)IB(l)

IB(ph) =

ZB(Y) =

ZB( ) =

ZB(Y) =

ZB( ) =

* A three phase system consists of a generator, two transformers, two transmission lines, and two loads, as follows:

G1 is a 300 MVA generator rated at 25 kV, with an impedance of .05 p.u. (Assume that generator is operating at rated terminal voltage) T1 is a bank of three single phase 25 kV/199.2 kV transformers, each rated at 100 MVA, connected D-Y with a leakage reactance of 2.5% T2 is a three phase 200 MVA transformer rated 345 kV/13.8 kV, with X=j.08. T3 is a three phase 1 MVA transformer rated 345 kV/4160, with X=j.02. L1 is a transmission line having an impedance of j75 W L2 is a distribution line having an impedance of j5 W Z1 is an industrial facility with an effective impedance of 1 ohm at .85 power factor lagging Z2 is a substation load with an effective impedance of 17.5 ohm at .7 power factor leading Using the MVA and voltage bases of the generator, Draw the per unit equivalent circuit, neglecting shunt elements in transformers Calculate the total current and power delivered by the generator (give answers in per unit and actual values). Calculate the magnitude of the terminal voltage of load Z1 (per unit and actual).

*

* Typical Per Unit QuantitiesVoltages: 0.95 to 1.05 pu voltsSystem Base 100MVAReal Power: 100 MW = 1.0 pu, 1000MW=10puTransmission Line: All quantities in per unit

*

* Transmission Line Model

*

* The Power FlowUsed to design the power systemUsed to upgrade the power systemUsed to study the power system in real time for secure operationBy far the most useful calculation used by power system engineers

*

* The Power Flow Problem Compute voltage magnitude and phase angle at each bus Calculate real and reactive power flow through all equipment Input Data Transmission line data Transformer Data Bus Data

Bus TypeKnown ParametersUnknown ParametersSwing BusV=1

* Power Flow Equations

*

* Power Flow Bus OperationLoad Bus: uses both P and Q equationSolves for V and Generation Bus: Uses only the P equation and assumes V to be fixed (regulated voltage)Reference or swing bus, assumes V and are fixed (no P or Q equation possible.

*

* Power FlowFigure from Power World Simulator

*

* Power Flow Standard PrintoutBUS 1 Bus 1 345.0 MW MVAR MVA % 1.0000 0.00 2 2 GENERATOR 1 141.16 -14.21R 141.9 LOAD 1 100.00 0.00 100.0 TO 2 Bus 2 1 -36.75 8.09 37.6 25 TO 3 Bus 3 1 77.91 -22.30 81.0 27BUS 2 Bus 2 345.0 MW MVAR MVA % 1.0000 3.51 1 Home GENERATOR 1 363.00 100.22R 376.6 LOAD 1 200.00 100.00 223.6 TO 1 Bus 1 1 37.18 -5.83 37.6 25 TO 4 Bus 4 1 125.86 6.05 126.0 50BUS 3 Bus 3 345.0 MW MVAR MVA % 1.0083 -3.73 1 Home LOAD 1 100.00 15.00 101.1 SWITCHED SHUNT 0.00 81.33 81.3 TO 1 Bus 1 1 -76.92 27.55 81.7 27 TO 4 Bus 4 1 -23.15 38.71 45.1 23BUS 4 Bus 4 138.0 MW MVAR MVA % 0.9813 -2.33 1 Home TO 2 Bus 2 1 -123.48 6.66 123.7 49 TO 3 Bus 3 1 23.45 -37.11 43.9 22 TO 5 Bus 5 1 100.04 30.44 104.6 10 0.9625TA 0.0BUS 5 Bus 5 34.5 MW MVAR MVA % 0.9946 -7.99 1 Home LOAD 1 100.00 20.00 102.0 TO 4 Bus 4 1 -100.04 -19.92 102.0 10 0.9625NT 0.0

*

* Linear Power Flow AnalysisIgnore bus Voltage Magnitude (only be concerned with bus phase angle)Ignore reactive power flows and loads (only be concerned with MW flow)Ignore transmission line resistance and charging capacitanceAccuracy suffers!

*

* Linear Power Flow Equation

*

* How does power flow?Flow from production point to purchase point uses every transmission path availableFlow on each intermediate transmission facility is determined by its impedance

*

* Power Transfer Distribution Factors (PTDFs)

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* Line Outage Distribution Factors (LODFs)PTDFs and LODFs can be combined to calculate the resulting post contingency flow with a large transaction.

*

* Load Flow ProblemLoad flow calculations are used to determine the voltage, current, and real and reactive power at various points in a power system under normal steady-state conditions.

For power systems with a large number of buses, the load flow problem becomes computationally intensive. Therefore, for large power systems, the load flow is solved using specific programs based on iterative techniques, such as the Newton-Raphson method.

Power systems of smaller size, however, require considerably less computational effort, and load flow algorithms can be developed which function easily on personal computers.

*

* The approach used here for solving the load flow is based on the Newton-Raphson iterative method. The required input to the problem is the generated and load power at each bus and the voltage magnitude on generating buses.

This information is acquired from load data and the normal system operating conditions. The solution provides the voltage magnitude and phase angle at all buses and the power flows and losses of the transmission lines. Load Flow Problem

*

* For load flow calculations, the system buses are classified into three types:The slack bus: There is only one such bus in the system. Due to losses in the network, the real and reactive power cannot be known at all buses. Therefore, the slack bus will provide the necessary power to maintain the power balance in the system. The slack bus is usually a bus where generation is available. For this bus, the voltage magnitude and phase angle are specified (normally the voltage phase angle is set to zero degrees). The voltage phase angle of all other buses is expressed with the slack bus voltage phasor as reference.

The generating or PV-bus: This bus type represents the generating stations of the system. The information known for PV-buses is the net real power generation and bus-voltage magnitude. The net real power generation is the generated real power minus the real power of any local load.The load or PQ-bus: For these buses, the net real and reactive power is known. PQ-buses normally do not have generators. However, if the reactive power of a generator reaches its limit, the corresponding bus is treated as a PQ-bus. This is equivalent to adjusting the bus voltage until the generator reactive power falls within the prescribed limits.

Distribution substations and feeders may be treated as generating buses in distribution networks.Load Flow Problem

*

* The load flow equations are written in terms of the net power injection to each bus. With reference to figure below, the net power injection into the kth bus is the combination of generated and load power. The power flowing out of this bus must equal the net injected power. Therefore, the power balance equation at the kth bus is written as follows in terms of the system voltagewhereN is the number of network buses,Pk is the net real power injected into the kth bus,Qk is the net reactive power injected into the kth bus,Yk,i is the total admittance between bus k and i: this total can be found from the bus admittance matrix, Ybus, of the system, Vi is the voltage of the ith bus.Load Flow Problem

*

* where qk,n is the angle of the admittance, Yk,n, and dj is the voltage phase angle at bus, j.A real power equation is written for every PV- and PQ-bus and a reactive power equation is written for every PQ-bus. Thus, for a power system with N buses of which L are PQ-buses there are (N-1) real power equations (excluding the slack bus) and L reactive power equations (a total of N-1+L equations). The unknowns are the magnitude and phase angle of the L PQ-bus voltages and the phase angle of the (N-1-L) PV-bus voltages (a total of N-1+L unknowns).

The left-hand side of these equations are known and an iterative process is used for finding the unknown voltages and phase angles such the above equations are balanced. Load Flow Problem

*

* The Newton-Raphson method provides a reliable approach for solving non-linear equations such as the previous equations. The main advantages of this method are its convergence characteristics and its speed. The procedure for applying the Newton-Raphson method is as follows:From the network configuration and parameters the bus-admittance matrix is constructed. The elements of this matrix are used to calculate the power flows according to the equations.Each network bus is assigned a type and, accordingly, information about the bus real and reactive power and bus voltage is collected.From the above steps, the load flow equations can be assembled into the following form, with reference to previous equations:whereP is the vector of the known net real power injections at PV- and PQ-buses,Q is the vector of the known reactive power injections at PQ-buses,V is the vector of the unknown bus voltage magnitudes,d is the vector of the unknown bus voltage phase angles, andfp, fq are functions defined according to Equations (3.1.2).Load Flow Problem

*

* Solution of the load flow problem requires finding the values of V and d such that the right-hand side of the equation equals the known power injections at the network buses. For any estimation of V and d, the difference between the known power injections, P and Q and the power injections calculated by the equation is called the power mismatch.where DS is the net real and reactive power mismatch:The power mismatch is a measure of how close to the solution the estimations of V and d are. A correction to these estimations is obtained using the Newton-Raphson method, resulting in an iterative calculation process.where the superscript, j, denotes variables calculated at the jth iteration step. J is the Jacobian matrix of the equations:Load Flow Problem

*

* The iteration process continues until the power mismatch at the jth step is smaller than a preset number e.To start the above iterative solution, an estimation of the unknown voltages and their phase angles is required. This first solution approximation is called initial guess. Typically, the initial guess for the voltage magnitudes is 1 pu and for their phase angles is 0 degrees (or radians).

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* http://www.deregulation.com/electric.html

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