1 Introduction to Electric Power and Energy Systems Power Engineering = The Power to Transform and Restore Paulo F. Ribeiro, MBA, Ph.D., PE Interim 2008.

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Introduction to Electric Power and Energy Systems

Power Engineering = The Power to Transform and Restore

Paulo F. Ribeiro, MBA, Ph.D., PEInterim 2008

Calvin CollegeEngineering Department

From a Garden To 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 life’s 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 World’s 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2 “All that is not eternal is eternally out of date.”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

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Sunday Monday Tuesday Wednesday Thursday Friday Saturday 30

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3 Introduction Structure of Power Systems

4 Introduction Structure of Power Systems Visit to Consumers Energy (Prof. Visit – 9AM) Visit to Newberry Place 3:30PM

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7 Generators Transformers Trans. Lines Lines, etc.

8 Grid Operation Load Flow Problem Visit to Plainwell, Hydro Plant

9 Grid Operation SimPower PowerWorld

10 Grid Operations PowerWorld Examples

11 Grid Operations

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14 Projects

15 Projects (E-Learning Skype - E-Mail)




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21 Wrap-Up

22 Paper Presentations

23 Paper Presentations

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

Professor: Paulo F. Ribeiro SB134 x [email protected] Skype: aslan52

ENGR W808/INNH05402:00PM MTWTHF

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ENGR W84 A Intro. to Power/Energy Systems

08/IN NH 05402:00PM - 05:00PM

MTWTHF

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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 Monitoring

Grades (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 periods

Course Instructions

Paper 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: SyllabusConcepts 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

Projects

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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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Projects

Erik Wilson, ManagerCity of Plainwell

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Projects

Steve FaberNewberry Place

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Projects

Mark Luehmann, Consumers Energy

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Power System Analysis, Computing and Economics

Computing applicationsDistribution system analysisEconomics, market organization, cost structures, pricing, and risk managementIntelligent system applicationsReliability, uncertainty, and probability and stochastic system applications

Power System Dynamic Performance

Power system dynamic modeling: components and systemsPower system stability: phenomena, analysis, and techniquesPower system stability controls: design and applicationsPower system dynamic measurementsPower system interaction with turbine generatorsDynamic security assessment: techniques and applications, risk-based methods

Power System Operations

Power system dynamic modeling: components and systemsPower system stability: phenomena, analysis, and techniquesEnergy control centersDistribution operationSystem controlOperating economics and pricing

An Overview of Power and Energy Systems

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Power System Planning & Implementation

Generation system resource planningTransmission system planningDistribution system planningIntegrated resource planning and distributed resource planningLoad forecastingCustomer products and services planning and implementationIndustry 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 systemAssembly, 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/laboratoryDistance educationLife-long learning


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Electric Machinery

DC MachinesPermanent magnet machinery systemsSwitched and variable reluctance machinesIntegral horsepower induction machineryWound rotor induction machinerySingle phase induction motorsElectronic drives for electric machineryInduction generators for grid and isolated applicationsSynchronous generatorsMotor/generator sets for pumped storageSynchronous motors materials to electric machineryElectrical machinery theoryNumerical analysis of electric machineryPower processing equipmentInsulation for electric machineryApplication of magnetic materials to electric machineryApplication of superconducting

Power System Communications

Communication systemsCommunication mediaCommunication protocolsCommunication standardizationHome automation and communication


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Power System Instrumentation and Measurements

Digital technology for measurementsElectricity meteringHigh voltage testingMeasurement techniques for impedance elements

Power System Relaying

Digital protection systemsAdaptive protectionsPower system protectionProtection of electrical equipmentRelaying communicationsRelaying for consumer interface

Substations

Substation automationIntelligent electronic devices (IEDs)Programmable logic controllers (PLCs)Substation designHigh voltage power electronics stationsGas insulated substations (GIS)


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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 (<1000V)Application of low voltage surge protective devices (<1000V)

Nuclear Power Engineering

Nuclear power plant controlsModeling, simulations and controlmonitoring and instrumentation

Transformer

Power and instrument transformersInsulating fluidsDielectric testingAudible noise and vibrationTransformer modeling techniques


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Transmission and Distribution

AC transmission and distribution facilitiesLightning phenomena and insulator performanceOverhead line conductors: thermal and mechanical aspectsCorona, electric, and magnetic fieldsTowers, poles, and hardwareCapacitors, shunt and series capacitor banks, and harmonic filter banksHVDC transmission and distribution, FACTS and power electronic applications to ac transmissionHarmonics and power qualityTransients, switching surges, and electromagnetic noiseMaintenance and operation of overhead linesWork procedures, safety, tools, and equipmentSuperconductivity analysis and devicesDistributed resources

Energy Development and Power Generation

Excitation systemsPower system stabilizersAdvanced energy technologies, Renewable energy technologiesStation design, operations, and controlModeling, simulation and control of power plantsMonitoring and instrumentation of power plantsControl of distributed generationHydroelectric power plants, Power plant scheduling, Engineering economic issuesInternational practices in energy development


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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 Pool


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The Big Picture


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A 18 kV to 525 kV transformer for 825 MVATo 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 PowerhouseDimensions: 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 bulb Socket Wire to switch

Switch Wire to circuit box Circuit breaker

Watthourmeter Connection to distribution system Distribution transformer

Distribution system Substation Capacitors

Circuit breakers Disconnects Buses

Transformers Subtransmission system Capacitor banks

Tap changers Current transformers Potential transformers

Protective relaying Reactors Metal-oxide varistors

Transmission system Suspension insulators Lightning arrestors

Generator step-up transformers Generators


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Non-Electrical Components

Glass for bulbs Manufacture of bulbs Sockets

Switches Circuit box Steel for circuit box

Copper for wire Aluminum for wire Poles for overhead lines

Transmission towers Maintenance Plastics for capacitor insulation

Controls for protec. relaying schem. Communications for data and protection Fiber optics for communications

Foundations for substation equipment Excavation equipment and crews Ceramics and polymers for suspension insulators

Oil for transformers and circuit breakers Gas for insulated substations Springs for circuit breakers

Process control for component manufacturing Computers for process control Computers for generation control and dispatch

Turbines for turning generator Coal for making steam to turn turbine Trains for hauling coal

Cars Bridges People


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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?


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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)


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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?


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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

Ohm’s law, George Ohm, 1827

Faraday’s law, Michael Faraday, 1831

Maxwell’s 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


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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)


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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.


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12 - 34,5 kV ItaipúPer Generator750 MVA, 18 kV => 24.000 A

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Transformer to 500 kV890 A

TransformationTransformation

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7,2 kV

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7,2 kV

... Transmission ... Transmission

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SubstationsSubstations

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LT Itumbiara – Nova Ponte 500 kV

LT Emborcação – Nova Ponte 500 kV

LT Nova Ponte - Estreito 500 kV

LT Nova Ponte – São Gotardo - Bom Despacho 500 kV

LT Araçuai 2 – Irapé230 kV

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Norte-Nordeste500 kV

Norte-Sul III 500 kV

Acre/Rondônia-SE/CO 230 kV

Tucuruí-Manaus 500 kV

Reforços nas Regiões SE/CO

500 kV

Sul-Sudeste 525 kV

Jurupari-Macapá 230kV

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Transformers Transformers

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•Mechanical Energy •Rotational Energy •Electrical Energy •Power

•Electrical Power

Analytical Background


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 generator• Simple in raising and lowering voltages:

– Generators limited to about 25kV– Transmission at 345,500 and 765kV (low losses)– Subtransmission at 115, 69, 22kV– Distribution at 12, 8, 4kV– Key component: power transformer

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Power Generation

Itaipu - 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 Customer

Typical voltages for different parts

of the American power system:

System Type From To

Residential 110 V 220 V (split single Phase)

Commercial 480 V (three Phase)

Industrial 480 V 4160 V.

Distribution 2300 V 32000 V

Subtransmission 25 kV 130 kV

Transmission 115 kV 765 kV

Generation 13.2 kV 36 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 waves”

• AC 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 Angle

• For 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 zero

• Current 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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Euler’s 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


voltages 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


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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 Circuit

• Multiply 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 degrees


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Current leading Voltage by

90 deg

Current lagging Voltage by

90 deg


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Average – Real Power

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Complex Power – Real and Reactive

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Real and Reactive Power

• Instantaneous power may flow in both directions• Instantaneous power may be broken up into two

components:– Real Power only flows in one direction, its

average value is zero or positive– Reactive 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 degrees

“Real and Reactive” Power in an AC Circuit

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Current leading Voltage by

90 deg

Current lagging Voltage by

90 deg

“Real 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 MVARS

• MW 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 shaft

• Delivery of constant power to a 3 phase load

• 3 Wires and not 6

What about unbalanced conditions?

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Single Phase Circuit

Voltage=

V 0 deg

Current = I

Requires 2 wires to deliver power

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3 phase circuit

If the three phase load is “balanced” the neutral carries no current and can be eliminated.

Voltage a=V 0 deg

Phase a

Voltage c=V +120 deg Voltage b=

V -120 degPhase b

Phase c

Neutral3 Phase

Load

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3 phase circuit without a neutral wire

3 PhaseLoad

Voltage a=V 0 deg

Phase a

Voltage c=V +120 deg Voltage b=

V -120 degPhase b

Phase c

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3 Phase Quantities

Va

VbVc

Vab

Ia

Iab

Ia

Va

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Voltage Drop and Reactive Power Compensation

V2 / 2

ZLine = 1 +j7

V1 = 13.2*10^3 + j0

IP&Q

ZLoad = 10 +j30 C = ?

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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R

XL

V 0 deg

V 0 deg R XL

AC Power - Class Exercise

Calculate 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 3

Bus 1 Bus 2

I

S12 = P12 + jQ12

Z = R +jX

V1 deg V2 deg

Demonstrate that

What happens when R<<X ?

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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 wires

Short, Medium, Long Lines…

What is the difference?

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Short

Medium

Long

Transmission 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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– Generators– Power Transformers– The “Per Unit” System

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http://hydropower.inel.gov/state/stateres.htm

Generation /Generators

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Generation /Generators

HW 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 Transmission

• Reduces losses• Transmission conductor can have a smaller cross

section• Provides 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 OUT

This neglects the internal losses in the transformer

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Real Transformers

Test 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

125

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

126

Tap Changing Transformers

Changing taps changes the turns ratio

127

Auto Transformer used for “Tap Changing Under Load” or

TCUL Transformer

128

TCUL Transformer

• Assume primary side voltage begins to go down with heavy load

• TCUL transformer changes taps to keep secondary voltage within limits– Raise secondary voltage during heavy load– Reduce secondary voltage during light load

129

Transformer Connections

Each leg is a single phase transformer

Y-Y connections (no phase shift)

connections (no phase shift)

Y- connections (-30 degrees phase shift)

Y connections (+30 degrees phase shift)

Three-Phase Transformers

130

The Per Unit System

• Allows engineers to analyze a single phase network where:– All P and Q quantities are three phase– Voltage magnitudes are represented as a

fractional part of their standard or “base” value– All phase angles are represented in the same

units as normally used

131

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. (Yç D , D ç Y, D ç D , or Yç 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.

132

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:

133

Set Up the Per Unit System

• Each region of the power system is uniquely defined by a standard voltage determined by the transformer windings, this sets base voltage

• The entire system is given a base power to which everything in the power flow is referred

134

Per Unit Conversions

135

Sample Power System

136

Power System Divided into base voltage regions

137

Numerical Example

Let. V = 118 00 volts

Z = 5 300 ohms

Then I = 23.6 -300 amperes

& S = V I* = (118 00)(23.6 +300) va

= 2,784.8 300 va

For this example, it is appropriate to choose:

SlB = 3,000 va

VlB = 120-volts

Then IlB = = 25 amperes

& ZlB = = 4.8 ohms

138

139

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).

140

Typical Per Unit Quantities

• Voltages: 0.95 to 1.05 pu volts• System Base 100MVA

– Real Power: 100 MW = 1.0 pu, 1000MW=10pu• Transmission Line: All quantities in per unit

141

Transmission Line Model

142

The Power Flow

• Used to design the power system• Used to upgrade the power system• Used to study the power system in real time for

secure operation• By far the most useful calculation used by power

system engineers

143

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 Type Known Parameters Unknown Parameters

Swing Bus V=1<0o P, Q

Load Bus P+jQ V, delta

Gen Bus (Voltage Control) V, P Q, delta

The Power Flow

144

Power Flow Equations

145

Power Flow Bus Operation

• Load Bus: uses both P and Q equation– Solves 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.

146

Power Flow

Figure from Power World Simulator

147

Power Flow Standard Printout

BUS 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 27

BUS 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 50

BUS 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 23

BUS 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 0.0

BUS 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

148

Linear Power Flow Analysis

• Ignore 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 capacitance

• Accuracy suffers!

149

Linear Power Flow Equation

150

How does power flow?

• Flow from production point to purchase point uses every transmission path available

• Flow on each intermediate transmission facility is determined by its impedance

151

Power Transfer Distribution Factors (PTDF’s)

152

Line Outage Distribution Factors (LODF’s)

PTDF’s and LODF’s can be combined to calculate the resulting post contingency flow with a large transaction.

153

Load Flow Problem

Load 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.

154

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

155

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

156

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 voltage

where

N 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

157

where k,n is the angle of the admittance, Yk,n, and j 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

158

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:

where

P 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,

is the vector of the unknown bus voltage phase angles, and

fp, fq are functions defined according to Equations (3.1.2).

Load Flow Problem

159

Solution of the load flow problem requires finding the values of V and such that the right-hand side of the equation equals the known power injections at the network buses. For any estimation of V and , the difference between the known power injections, P and Q and the power injections calculated by the equation is called the power mismatch.

where S 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 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

160

The iteration process continues until the power mismatch at the jth step is smaller than a preset number .

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).

161

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

1 Introduction to Electric Power and Energy Systems Power Engineering = The Power to Transform and Restore Paulo F. Ribeiro, MBA, Ph.D., PE Interim 2008.

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