EKT103 ELECTRICAL ENGINEERING
|
|
- Candace Armstrong
- 6 years ago
- Views:
Transcription
1 EKT13 EECTRCA ENGNEERNG Chater 1 Three-Phase System 1
2 COURSE OUTCOME (CO) CO1: Ability to define and exlain the concet of single-hase and threehase system. 2
3 Revision A sinusoid is a signal that has the form of the sine or cosine function. A general exression for the sinusoid, v( t) sin( ω t + φ) m where m the amlitude of the sinusoid ω the angular frequency in radians/s Ф the hase 3
4 Revision A eriodic function is one that satisfies v(t) v(t + nt), for all t and for all integers n. T 2π ω f 1 Hz f T ω 2π Only two sinusoidal values with the same frequency can be comared by their amlitude and hase difference. f hase difference is zero, they are in hase; if hase difference is not zero, they are out of hase. 4
5 Revision Examle 1 o Given a sinusoid, 5 sin( 4πt 6 ), calculate its amlitude, hase, angular frequency, eriod, and frequency. 5
6 Revision Examle 1 o Given a sinusoid, 5 sin( 4πt 6 ), calculate its amlitude, hase, angular frequency, eriod, and frequency. Solution: Amlitude 5, hase 6 o, angular frequency 4π rad/s, Period.5 s, frequency 2 Hz. 6
7 Revision Examle 2 Find the hase angle between i 1 4sin(377t + and o i 5cos(377t 4 ), does i 1 lead or lag i 2? 2 25 o ) 7
8 Revision Examle 2 Find the hase angle between i 1 4sin(377t + and o i 5cos(377t 4 ), does i 1 lead or lag i 2? 2 25 o ) Solution: Since sin(ωt+9 o ) cosωt o o i 5sin(377t ) 5sin(377t o o o i 4sin(377t + 25 ) 4sin(377t ) 4sin(377t + 1 therefore, i 1 leads i o. o ) 25 o 8 )
9 Revision medance transformation Z 3Z Y Z Y 1 Z 3 9
10 Single-Phase Circuit A single hase circuit consists of a generator connected through a air of wires to a load Two wire system Three wired system same magnitude same hase
11 Two-Phase Circuit a A Three wired system Second source with 9 out of hase Three wired system same magnitude different hase
12 What is a Three-Phase Circuit? t is a system roduced by a generator consisting of three sources having the same amlitude and frequency but out of hase with each other by 12. Three sources with 12 out of hase Four wired system 12
13 Balance Three-Phase oltages A three-hase generator consists of a rotating magnet (rotor) surrounded by a stationary winding (stator). A three-hase generator The generated voltages 13
14 Balance Three-Phase oltages Two ossible configurations: Three-hase voltage sources: (a) Y-connected ; (b) -connected 14
15 Balance Three-Phase oltages Phase sequences a) abc or ositive sequence b) acb or negative sequence 15
16 Balance Three-Phase oltages f the voltage source have the same amlitude and frequency ω and are out of hase with each other by 12 o, the voltage are said to be balanced. an + bn + cn an bn cn Balanced hase voltages are equal in magnitude and out of hase with each other by 12 o 16
17 Balance Three-Phase oltages abc sequence or ositive sequence: an bn cn acb sequence or negative sequence: an cn bn is the effective or rms value 17
18 Balance Three-Phase oltages Examle 1 Determine the hase sequence of the set of voltages. v v v an bn cn 2 cos( ωt + 1 ) 2 cos( ωt 23 ) 2 cos( ωt 11 ) 18
19 Solution: Balance Three-Phase oltages The voltages can be exressed in hasor form as an bn cn We notice that an leads cn by 12 and cn in turn leads bn by 12. Hence, we have an acb sequence. 19
20 Balance Three-Phase oltages Two ossible three-hase load configurations: a) a wye-connected load b) a delta-connected load 2
21 Balance Three-Phase oltages A balanced load is one in which the hase imedances are equal in magnitude and in hase. For a balanced wye connected load: Z 1 Z2 Z3 ZY For a balanced delta connected load: Z a Z Z Z b c Z 3Z Y Z Y 1 Z 3 21
22 Balance Three-Phase Connection Four ossible connections 1. Y-Y connection (Y-connected source with a Y-connected load) 2. Y- connection (Y-connected source with a -connected load) 3. - connection 4. -Y connection 22
23 Balance Y-Y Y Y Connection A balanced Y-Y system is a three-hase system with a balanced y-connected source and a balanced y-connected load.
24 Balance Y-Y Y Y Connection Z Z Z Z s l Y Source imedance ine imedance oad imedance Total imedance er hase Since all imedance are in series, Thus Z Y Z s + Zl + Z Z Y Z 24
25 Balance Y-Y Y Y Connection a Z an Y
26 Balance Y-Y Y Y Connection Alying K to each hase: a Z an Y 12 bn an b a 12 ZY ZY 24 cn an c a 24 ZY ZY nn Znn a + b + c n 26
27 Balance Y-Y Y Y Connection ine to line voltages or line voltages: ab bc ca Magnitude of line voltages: 3 an ab bn bc cn ca
28 Balance Y-Y Y Y Connection Examle 2 Calculate the line currents in the three-wire Y-Y system shown below: 28
29 Balance Y-Y Y Y Connection Examle 2 Calculate the line currents in the three-wire Y-Y system shown below: Ans a b c A A A 29
30 Balance Y- Connection A balanced Y- system is a three-hase system with a balanced y-connected source and a balanced -connected load. 3
31 Balance Y- Connection A single hase equivalent circuit a Z an Y Z an / 3 Z Y Z 3
32 Balance Y- Connection A single hase equivalent circuit ine voltages: ab bc ca AB BC CA
33 Balance Y- Connection A single-hase equivalent circuit of a balanced Y- circuit ine currents: a b c AB BC CA CA AB BC Phase currents: AB AB AB AB BC CA Z Z Z AB BC CA
34 Balance Y- Connection A single-hase equivalent circuit of a balanced Y- circuit CA a AB AB 24 CA AB ( ) a AB 3 3 Magnitude line currents: 3 a AB b BC c CA
35 Examle 3 A balanced abc-sequence Y-connected source with ( an 1 1 ) is connected to a -connected load (8+j4)Ω er hase. Calculate the hase and line currents. Solution Balance Y- Connection Using single-hase analysis, 1 1 an Z / a A Other line currents are obtained using the abc hase sequence 35
36 Balance - Connection A balanced - system is a three-hase system with a balanced -connected source and a balanced -connected load. 36
37 ine voltages: Balance - Connection ine currents: Phase currents: ab bc ca AB BC CA Magnitude line currents: 3 a b c AB BC CA CA AB BC Total imedance: Z Y AB AB AB Z AB BC CA Z Z Z AB BC CA 37
38 Examle 4 A balanced -connected load having an imedance 2-j15 Ω isconnected to a -connected ositive-sequence generator having ( ab 33 ). Calculate the hase currents of the load and the line currents. Ans: The hase currents A; A; A AB BC AB The line currents A; A; A a Balance - Connection b c 38
39 Balance -Y Connection A balanced -Y system is a three-hase system with a balanced y-connected source and a balanced y-connected load. 39
40 Balance -Y Connection Alying K to loo aanbba: From: a b Z b a 12 a b a 3 3 Y ine currents: a 3 Z Y 3 4
41 Balance -Y Connection Relace connected source to equivalent Y connected source. Phase voltages: an bn cn
42 Balance -Y Connection A single hase equivalent circuit a Z an Y 3 Z Y 3 42
43 Balance -Y Connection Examle 5 A balanced Y-connected load with a hase imedance 4+j25 Ω is sulied by a balanced, ositive-sequence -connected source with a line voltage of 21. Calculate the hase currents. Use ab as reference. Answer The hase currents AN BN CN A; A; A; 43
44 Power in a Balanced System Comaring the ower loss in (a) a single-hase system, and (b) a three-hase system 2 P P ' loss 2R 2, single - hase 2 ( ) R 2R, single- hase P loss P P P loss ( ' ) R' 3R' R', three - hase ' 2 P 2 f same ower loss is tolerated in both system, three-hase system use only 75% of materials of a single-hase system 44
45 Power in a Balanced System For Y connected load, the hase voltage: v AN 2 cos ωt v BN 2 cos( ωt 12 ) v CN 2 cos( ωt + 12 ) 45
46 Power in a Balanced System Phase current lag hase voltage by θ. f Z Y Z θ The hase current: i a 2 cos( ω t θ ) i b 2 cos( ωt θ 12 ) i c 2 cos( ωt θ + 12 ) 46
47 Power in a Balanced System Total instantaneous ower: + + v i + v i + a b c AN 3 cos a θ BN b v CN i c Average ower er hase: P cos θ Reactive ower er hase: Q sin θ Aarent ower er hase: Comlex ower er hase: S S P + jq * 47
48 Power in a Balanced System Total average ower: P 3P 3 cos θ 3 cos θ Total reactive ower: Q 3Q 3 sin θ 3 sin θ Total comlex ower: S 3S 3 3 Z * 2 3 Z 2 * S P + jq 3 θ 48
49 Power in a Balanced System Power loss in two wires: P 2 R loss 2 2R P 2 2 Power loss in three wires: P P loss P R 3R R 2 2 P 3 : ower absorbed by the load : magnitude of line current : line voltage R : line resistance 49
50 Examle 6 A three-hase motor can be regarded as a balanced Y-load. A three-hase motor draws 5.6 kw when the line voltage is 22 and the line current is 18.2 A. Determine the ower factor of the motor. 5
51 Examle 6 A three-hase motor can be regarded as a balanced Y-load. A three-hase motor draws 5.6 kw when the line voltage is 22 and the line current is 18.2 A. Determine the ower factor of the motor. The aarent ower is S 3 3(22)(18.2) A The real ower is P S cos θ 56W The ower factor is f P cos θ.875 S 51
52 Exercise 6 Calculate the line current required for a 3-kW three-hase motor having a ower factor of.85 lagging if it is connected to a balanced source with a line voltage of
53 Exercise 6 Calculate the line current required for a 3-kW three-hase motor having a ower factor of.85 lagging if it is connected to a balanced source with a line voltage of 44. Answer :
Chapter 12: Three-Phase Circuits
Chater 1: Three-Phase Circuits 1.1 ntroduction 1. Balanced Three-Phase oltages 1.3 Balanced Wye-Wye connection 1.4 Balanced Wye-Delta Connection 1.7 Power in a Balanced System 1.1 NTRODUCTON A single-hase
More informationThree Phase Circuits
Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/ OUTLINE Previously on ELCN102 Three Phase Circuits Balanced
More informationECE 421/521 Electric Energy Systems Power Systems Analysis I 2 Basic Principles. Instructor: Kai Sun Fall 2014
ECE 41/51 Electric Energy Systems Power Systems Analysis I Basic Princiles Instructor: Kai Sun Fall 014 1 Outline Power in a 1-hase AC circuit Comlex ower Balanced 3-hase circuit Single Phase AC System
More informationUnit-3. Question Bank
Unit- Question Bank Q.1 A delta connected load draw a current of 15A at lagging P.F. of.85 from 400, -hase, 50Hz suly. Find & of each hase. Given P = = 400 0 I = 15A Ans. 4.98, 5.7mH So I P = 15 =8.66A
More informationECE 420. Review of Three Phase Circuits. Copyright by Chanan Singh, Panida Jirutitijaroen, and Hangtian Lei, For educational use only-not for sale.
ECE 40 Review of Three Phase Circuits Outline Phasor Complex power Power factor Balanced 3Ф circuit Read Appendix A Phasors and in steady state are sinusoidal functions with constant frequency 5 0 15 10
More informationChapter 10: Sinusoidal Steady-State Analysis
Chapter 10: Sinusoidal Steady-State Analysis 1 Objectives : sinusoidal functions Impedance use phasors to determine the forced response of a circuit subjected to sinusoidal excitation Apply techniques
More informationTHREE PHASE SYSTEMS Part 1
ERT105: ELECTRCAL TECHNOLOGY CHAPTER 3 THREE PHASE SYSTEMS Part 1 1 Objectives Become familiar with the operation of a three phase generator and the magnitude and phase relationship. Be able to calculate
More information2. Electromagnetic fundamentals
2. Electromagnetic fundamentals Prof. A. Binder 2/1 AMPERE s law: Excitation of magnetic field by electric current Examle: Two different currents I 1, I 2 with two different numbers of turns 1 and N and
More informationGeneration, transmission and distribution, as well as power supplied to industrial and commercial customers uses a 3 phase system.
Three-phase Circuits Generation, transmission and distribution, as well as power supplied to industrial and commercial customers uses a 3 phase system. Where 3 voltages are supplied of equal magnitude,
More informationE p,rms = 240 V E rms = 120 V N p N s C. f = 60 Hz R = 3.8 L
Discussion Question 1A P1, Week 1 Power in AC Circuits An electronic device, consisting of a simle C circuit, is designed to be connected to an American-standard ower outlet delivering an EMF of 1 V at
More informationTHREE-PHASE CIRCUITS. Historical Profiles
C H A P T E R THREE-PHASE CIRCUITS 1 2 Society is never prepared to receive any invention. Every new thing is resisted, and it takes years for the inventor to get people to listen to him and years more
More informationUniversity of North Carolina-Charlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009
University of North Carolina-Charlotte Deartment of Electrical and Comuter Engineering ECG 4143/5195 Electrical Machinery Fall 9 Problem Set 5 Part Due: Friday October 3 Problem 3: Modeling the exerimental
More informationChapter 2-3 Transformers
Principles of Electric Machines and Power Electronics Chapter 2-3 Transformers Third Edition P. C. Sen Auto transformer Per unit system S b = S rate V b1 = V rate1 V b2 = V rate2 S b I b1 = = S rate =
More informationElectric Circuits II Power Measurement. Dr. Firas Obeidat
Electric Circuits II Power Measurement Dr. Firas Obeidat 1 Table of contents 1 Single-Phase Power Measurement 2 Three-Phase Power Measurement 2 Single-Phase Power Measurement The wattmeter is the instrument
More informationLO 1: Three Phase Circuits
Course: EEL 2043 Principles of Electric Machines Class Instructor: Dr. Haris M. Khalid Email: hkhalid@hct.ac.ae Webpage: www.harismkhalid.com LO 1: Three Phase Circuits Three Phase AC System Three phase
More informationLecture 3: Three-phase power circuits
1/24/28 Lecture : Three-phase power circuits 1 nstructor: Dr. Gleb. Tcheslavski Contact: gleb@ee.lamar.edu Office Hours: TBD; Room 2 Class web site: MyLamar ntroduction 2 Almost all electric power generation
More informationChapter 10: Sinusoids and Phasors
Chapter 10: Sinusoids and Phasors 1. Motivation 2. Sinusoid Features 3. Phasors 4. Phasor Relationships for Circuit Elements 5. Impedance and Admittance 6. Kirchhoff s Laws in the Frequency Domain 7. Impedance
More informationFourier Series Tutorial
Fourier Series Tutorial INTRODUCTION This document is designed to overview the theory behind the Fourier series and its alications. It introduces the Fourier series and then demonstrates its use with a
More informationSinusoidal Steady State Analysis (AC Analysis) Part II
Sinusoidal Steady State Analysis (AC Analysis) Part II Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/
More informationRevision of Basic A.C. Theory
Revision of Basic A.C. Theory 1 Revision of Basic AC Theory (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) Electricity is generated in power stations
More informationMATHEMATICS FOR ENGINEERING TRIGONOMETRY TUTORIAL 3 PERIODIC FUNCTIONS
MATHEMATICS FOR ENGINEERING TRIGONOMETRY TUTORIAL 3 PERIODIC FUNCTIONS This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.
More informationTHREE-PHASE CIRCUITS
THR-HAS CIRCUITS 4.1 Introduction Generation, Transmission and distribution of electricity via the National Grid system is accomplished by three-phase alternating currents. The voltage induced by a single
More informationLecture (5) Power Factor,threephase circuits, and Per Unit Calculations
Lecture (5) Power Factor,threephase circuits, and Per Unit Calculations 5-1 Repeating the Example on Power Factor Correction (Given last Class) P? Q? S? Light Motor From source 1000 volts @ 60 Htz 10kW
More informationEDEXCEL NATIONAL CERTIFICATE UNIT 28 FURTHER MATHEMATICS FOR TECHNICIANS OUTCOME 3 TUTORIAL 1 - TRIGONOMETRICAL GRAPHS
EDEXCEL NATIONAL CERTIFICATE UNIT 28 FURTHER MATHEMATICS FOR TECHNICIANS OUTCOME 3 TUTORIAL 1 - TRIGONOMETRICAL GRAPHS CONTENTS 3 Be able to understand how to manipulate trigonometric expressions and apply
More informationBasics of Electric Circuits
António Dente Célia de Jesus February 2014 1 Alternating Current Circuits 1.1 Using Phasors There are practical and economic reasons justifying that electrical generators produce emf with alternating and
More informationLectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits. Nov. 7 & 9, 2011
Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits Nov. 7 & 9, 2011 Material from Textbook by Alexander & Sadiku and Electrical Engineering: Principles & Applications,
More informationLecture 11 - AC Power
- AC Power 11/17/2015 Reading: Chapter 11 1 Outline Instantaneous power Complex power Average (real) power Reactive power Apparent power Maximum power transfer Power factor correction 2 Power in AC Circuits
More informationCircuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18
Circuit Analysis-III Sinusoids Example #1 ü Find the amplitude, phase, period and frequency of the sinusoid: v (t ) =12cos(50t +10 ) Signal Conversion ü From sine to cosine and vice versa. ü sin (A ± B)
More informationIntroduction to Three-phase Circuits. Balanced 3-phase systems Unbalanced 3-phase systems
Intrductin t Three-hase Circuits Balanced 3-hase systems Unbalanced 3-hase systems 1 Intrductin t 3-hase systems Single-hase tw-wire system: Single surce cnnected t a lad using tw-wire system Single-hase
More informationConsider Figure What is the horizontal axis grid increment?
Chapter Outline CHAPER 14 hree-phase Circuits and Power 14.1 What Is hree-phase? Why Is hree-phase Used? 14.2 hree-phase Circuits: Configurations, Conversions, Analysis 14.2.1 Delta Configuration Analysis
More informationCHAPTER 33. Answer to Checkpoint Questions
CHAPTE 33 ELECTOMAGNETIC OSCILLATIONS 887 CHAPTE 33 Answer to Checkoint Questions. (a) T; (b) T ; (c) T; (d) T4. (a) 5 V; (b) 50 J 3. (a) ; (b) 4. (a) C, B, A; (b) A, B, 3 S, 4 C; (c) A 5. (a) increases;
More informationExercise Dr.-Ing. Abdalkarim Awad. Informatik 7 Rechnernetze und Kommunikationssysteme
Exercise1 1.10.015 Informatik 7 Rechnernetze und Kommunikationssysteme Review of Phasors Goal of phasor analysis is to simplify the analysis of constant frequency ac systems v(t) = max cos(wt + q v ) i(t)
More informationREACTANCE. By: Enzo Paterno Date: 03/2013
REACTANCE REACTANCE By: Enzo Paterno Date: 03/2013 5/2007 Enzo Paterno 1 RESISTANCE - R i R (t R A resistor for all practical purposes is unaffected by the frequency of the applied sinusoidal voltage or
More informationFigure 5.2 Instantaneous Power, Voltage & Current in a Resistor
ower in the Sinusoidal Steady-State ower is the rate at which work is done by an electrical component. It tells us how much heat will be produced by an electric furnace, or how much light will be generated
More informationChapter 5 Steady-State Sinusoidal Analysis
Chapter 5 Steady-State Sinusoidal Analysis Chapter 5 Steady-State Sinusoidal Analysis 1. Identify the frequency, angular frequency, peak value, rms value, and phase of a sinusoidal signal. 2. Solve steady-state
More informationSinusoids and Phasors
CHAPTER 9 Sinusoids and Phasors We now begins the analysis of circuits in which the voltage or current sources are time-varying. In this chapter, we are particularly interested in sinusoidally time-varying
More informationElectric Circuit Theory
Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 11 Sinusoidal Steady-State Analysis Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 11.1
More informationLesson 17: Synchronous Machines
Lesson 17: Synchronous Machines ET 332b Ac Motors, Generators and Power Systems Lesson 17_et332b.pptx 1 Learning Objectives After this presentation you will be able to: Explain how synchronous machines
More informationPart 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is
1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field
More informationAC Electric Machines. Objectives. Introduction. 1. To understand what the meant by the term ac circuit. 2. To understand how to analyze ac circuits.
AC Electric Machines Objectives 1. To understand what the meant by the term ac circuit.. To understand how to analyze ac circuits. 3. To understand the basic construction and operation of an ac machine.
More informationLecture 9: Space-Vector Models
1 / 30 Lecture 9: Space-Vector Models ELEC-E8405 Electric Drives (5 ECTS) Marko Hinkkanen Autumn 2017 2 / 30 Learning Outcomes After this lecture and exercises you will be able to: Include the number of
More informationRefresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas
Refresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas A specifically designed programme for Da Afghanistan Breshna Sherkat (DABS) Afghanistan 1 Areas Covered Under this Module
More informationCh 8. Three-phase systems
Ch 8. Three-ase systems Lecture outcomes (what you are supposed to learn): Generation of three-ase voltages Connection of three-ase circuits Wye-Delta transformation Power of three-ase connected loads
More informationLecture 05 Power in AC circuit
CA2627 Building Science Lecture 05 Power in AC circuit Instructor: Jiayu Chen Ph.D. Announcement 1. Makeup Midterm 2. Midterm grade Grade 25 20 15 10 5 0 10 15 20 25 30 35 40 Grade Jiayu Chen, Ph.D. 2
More informationLecture 1: Induction Motor
1 / 22 Lecture 1: Induction Motor ELEC-E8402 Control of Electric Drives and Power Converters (5 ECTS) Marko Hinkkanen Aalto University School of Electrical Engineering Spring 2016 2 / 22 Learning Outcomes
More information12. Introduction and Chapter Objectives
Real Analog - Circuits 1 Chapter 1: Steady-State Sinusoidal Power 1. Introduction and Chapter Objectives In this chapter we will address the issue of power transmission via sinusoidal or AC) signals. This
More informationLecture 2 Introduction
EE 333 POWER SYSTEMS ENGNEERNG Lecture 2 ntroduction Dr. Lei Wu Departent of Electrical and Coputer Engineering Clarkson University Resilient Underground Microgrid in Potsda, NY Funded by NYSERDAR + National
More informationI. Impedance of an R-L circuit.
I. Impedance of an R-L circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the R-L circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC
More informationTransformer. Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.).
. Transformers Transformer Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.). f the primary side is connected to an AC voltage source v (t), an AC flux (t) will be
More informationALTERNATING CURRENT
ATENATING UENT Important oints:. The alternating current (A) is generally expressed as ( ) I I sin ω t + φ Where i peak value of alternating current.. emf of an alternating current source is generally
More informationSinusoidal Steady State Analysis
Sinusoidal Steady State Analysis 9 Assessment Problems AP 9. [a] V = 70/ 40 V [b] 0 sin(000t +20 ) = 0 cos(000t 70 ).. I = 0/ 70 A [c] I =5/36.87 + 0/ 53.3 =4+j3+6 j8 =0 j5 =.8/ 26.57 A [d] sin(20,000πt
More informationCHAPTER 5. Solutions for Exercises
HAPTE 5 Slutins fr Exercises E5. (a We are given v ( t 50 cs(00π t 30. The angular frequency is the cefficient f t s we have ω 00π radian/s. Then f ω / π 00 Hz T / f 0 ms m / 50 / 06. Furthermre, v(t attains
More informationHomework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1. Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω.
Homework 2 SJTU233 Problem 1 Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω. Express Zab in polar form. Enter your answer using polar notation. Express argument in degrees.
More informationSinusoidal Steady-State Analysis
Chapter 4 Sinusoidal Steady-State Analysis In this unit, we consider circuits in which the sources are sinusoidal in nature. The review section of this unit covers most of section 9.1 9.9 of the text.
More informationECE 421/521 Electric Energy Systems Power Systems Analysis I 2 Basic Principles. Instructor: Kai Sun Fall 2013
ECE 41/51 Electric Energy Systems Power Systems Analysis I Basic Principles Instructor: Kai Sun Fall 013 1 Outline Power in a 1-phase AC circuit Complex power Balanced 3-phase circuit Single Phase AC System
More informationOn Line Parameter Estimation of Electric Systems using the Bacterial Foraging Algorithm
On Line Parameter Estimation of Electric Systems using the Bacterial Foraging Algorithm Gabriel Noriega, José Restreo, Víctor Guzmán, Maribel Giménez and José Aller Universidad Simón Bolívar Valle de Sartenejas,
More informationPower Systems - Basic Concepts and Applications - Part I
PDHonline Course E104 (1 PDH) Power ystems Basic Concepts and Applications Part I Instructor: hihmin Hsu PhD PE 01 PDH Online PDH Center 57 Meadow Estates Drive Fairfax A 006658 Phone & Fax: 709880088
More informationELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT
Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the
More informationUNIT- I Phase Sequence:
UNIT- I Phase Sequence: Phase sequence refers to the relation between voltages (or currents, as well) in a three-phase system. The common representation of this relation is in terms of a phasor diagram,
More informationECE 201 Fall 2009 Final Exam
ECE 01 Fall 009 Final Exam December 16, 009 Division 0101: Tan (11:30am) Division 001: Clark (7:30 am) Division 0301: Elliott (1:30 pm) Instructions 1. DO NOT START UNTIL TOLD TO DO SO.. Write your Name,
More information2.3 Oscillation. The harmonic oscillator equation is the differential equation. d 2 y dt 2 r y (r > 0). Its solutions have the form
2. Oscillation So far, we have used differential equations to describe functions that grow or decay over time. The next most common behavior for a function is to oscillate, meaning that it increases and
More informationReview of DC Electric Circuit. DC Electric Circuits Examples (source:
Review of DC Electric Circuit DC Electric Circuits Examples (source: http://hyperphysics.phyastr.gsu.edu/hbase/electric/dcex.html) 1 Review - DC Electric Circuit Multisim Circuit Simulation DC Circuit
More informationJournal of System Design and Dynamics
Vol. 5, No. 6, Effects of Stable Nonlinear Normal Modes on Self-Synchronized Phenomena* Hiroki MORI**, Takuo NAGAMINE**, Yukihiro AKAMATSU** and Yuichi SATO** ** Deartment of Mechanical Engineering, Saitama
More informationUniversity of Jordan Faculty of Engineering & Technology Electric Power Engineering Department
University of Jordan Faculty of Engineering & Technology Electric Power Engineering Department EE471: Electrical Machines-II Tutorial # 2: 3-ph Induction Motor/Generator Question #1 A 100 hp, 60-Hz, three-phase
More informationCHAPTER 4 FOURIER SERIES S A B A R I N A I S M A I L
CHAPTER 4 FOURIER SERIES 1 S A B A R I N A I S M A I L Outline Introduction of the Fourier series. The properties of the Fourier series. Symmetry consideration Application of the Fourier series to circuit
More information4.5. Applications of Trigonometry to Waves. Introduction. Prerequisites. Learning Outcomes
Applications of Trigonometry to Waves 4.5 Introduction Waves and vibrations occur in many contexts. The water waves on the sea and the vibrations of a stringed musical instrument are just two everyday
More informationChapter 33. Alternating Current Circuits
Chapter 33 Alternating Current Circuits 1 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt AC power source The AC power source provides an alternative voltage, Notation - Lower case
More informationBEF BEF Chapter 2. Outline BASIC PRINCIPLES 09/10/2013. Introduction. Phasor Representation. Complex Power Triangle.
BEF 5503 BEF 5503 Chapter BASC PRNCPLES Outline 1 3 4 5 6 7 8 9 ntroduction Phasor Representation Coplex Power Triangle Power Factor Coplex Power in AC Single Phase Circuits Coplex Power in Balanced Three-Phase
More informationModule 4. Single-phase AC Circuits. Version 2 EE IIT, Kharagpur 1
Module 4 Single-phase A ircuits ersion EE IIT, Kharagpur esson 4 Solution of urrent in -- Series ircuits ersion EE IIT, Kharagpur In the last lesson, two points were described:. How to represent a sinusoidal
More informationJRE SCHOOL OF Engineering
JRE SCHOOL OF Engineering Class Test-1 Examinations September 2014 Subject Name Electromechanical Energy Conversion-II Subject Code EEE -501 Roll No. of Student Max Marks 30 Marks Max Duration 1 hour Date
More informationCourse Updates. Reminders: 1) Assignment #10 due Today. 2) Quiz # 5 Friday (Chap 29, 30) 3) Start AC Circuits
ourse Updates http://www.phys.hawaii.edu/~varner/phys272-spr10/physics272.html eminders: 1) Assignment #10 due Today 2) Quiz # 5 Friday (hap 29, 30) 3) Start A ircuits Alternating urrents (hap 31) In this
More informationENE 104 Electric Circuit Theory
Electric Circuit Theory Lecture 11: : Dejwoot KHAWPARSUTH http://webstaff.kmutt.ac.th/~dejwoot.kha/ Objectives : Ch12 Page 2 single-phase and polyphase systems Y- and Δ- connected three-phase system per-phase
More informationBASIC NETWORK ANALYSIS
SECTION 1 BASIC NETWORK ANALYSIS A. Wayne Galli, Ph.D. Project Engineer Newport News Shipbuilding Series-Parallel dc Network Analysis......................... 1.1 Branch-Current Analysis of a dc Network......................
More informationThe individual electric and magnetic waves are in phase. The fields peak at the same position at the same time.
1 Part 3: Otics 3.1: Electromagnetic Waves An electromagnetic wave (light wave) consists of oscillating electric and magnetic fields. The directions of the electric and magnetic fields are erendicular.
More informationElectric Machines I Three Phase Induction Motor. Dr. Firas Obeidat
Electric Machines I Three Phase Induction Motor Dr. Firas Obeidat 1 Table of contents 1 General Principles 2 Construction 3 Production of Rotating Field 4 Why Does the Rotor Rotate 5 The Slip and Rotor
More informationPower Factor Improvement
Salman bin AbdulazizUniversity College of Engineering Electrical Engineering Department EE 2050Electrical Circuit Laboratory Power Factor Improvement Experiment # 4 Objectives: 1. To introduce the concept
More informationLecture 12. Time Varying Electromagnetic Fields
Lecture. Time Varying Electromagnetic Fields For static electric and magnetic fields: D = ρ () E = 0...( ) D= εe B = 0...( 3) H = J H = B µ...( 4 ) For a conducting medium J =σ E From Faraday s observations,
More information11. AC Circuit Power Analysis
. AC Circuit Power Analysis Often an integral part of circuit analysis is the determination of either power delivered or power absorbed (or both). In this chapter First, we begin by considering instantaneous
More informationFACULTY OF ENGINEERING LAB SHEET
FCLTY F ENGNEERNG LB SHEET EEL1196 nstrumentation & Measurement Techniques TRMESTER 2 2017-2018 M2: Power Measurement sing Two Wattmeter Method *Note: Students will have to tabulate the theoretical values
More informationEXP. NO. 3 Power on (resistive inductive & capacitive) load Series connection
OBJECT: To examine the power distribution on (R, L, C) series circuit. APPARATUS 1-signal function generator 2- Oscilloscope, A.V.O meter 3- Resisters & inductor &capacitor THEORY the following form for
More informationChapter 15 Power And Harmonics in Nonsinusoidal Systems
Chapter 15 Power And Harmonics in Nonsinusoidal Systems 15.1. Average power in terms of Fourier series 15.2. RMS value of a waveform 15.3. Power factor THD Distortion and Displacement factors 15.4. Power
More informationBASIC PRINCIPLES. Power In Single-Phase AC Circuit
BASIC PRINCIPLES Power In Single-Phase AC Circuit Let instantaneous voltage be v(t)=v m cos(ωt+θ v ) Let instantaneous current be i(t)=i m cos(ωt+θ i ) The instantaneous p(t) delivered to the load is p(t)=v(t)i(t)=v
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 18 121025 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review RMS Values Complex Numbers Phasors Complex Impedance Circuit Analysis
More informationy 2 Well it is a cos graph with amplitude of 3 and only half a waveform between 0 and 2π because the cos argument is x /2: y =3cos π 2
Complete Solutions Eamination Questions Complete Solutions to Eamination Questions 4. (a) How do we sketch the graph of y 3? Well it is a graph with amplitude of 3 and only half a waveform between 0 and
More information12 Chapter Driven RLC Circuits
hapter Driven ircuits. A Sources... -. A ircuits with a Source and One ircuit Element... -3.. Purely esistive oad... -3.. Purely Inductive oad... -6..3 Purely apacitive oad... -8.3 The Series ircuit...
More information22 ELECTROMAGNETIC INDUCTION
CHAPTER ELECTROMAGNETIC INDUCTION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS. 3.5 m/s. (e) The work done by the hand equals the energy dissiated in the bulb. The energy dissiated in the bulb equals the ower
More informationmywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel
esson 6 Solution of urrent in Parallel and Seriesparallel ircuits n the last lesson, the following points were described:. How to compute the total impedance/admittance in series/parallel circuits?. How
More informationEE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following time-domain circuit to the RMS Phasor Domain.
Name If you have any questions ask them. Remember to include all units on your answers (V, A, etc). Clearly indicate your answers. All angles must be in the range 0 to +180 or 0 to 180 degrees. 1) [6 pts]
More information1 Phasors and Alternating Currents
Physics 4 Chapter : Alternating Current 0/5 Phasors and Alternating Currents alternating current: current that varies sinusoidally with time ac source: any device that supplies a sinusoidally varying potential
More informationRevised October 6, EEL , Henry Zmuda. 2. Three-Phase Circuits 1
Three Phase Circuitsit Revised October 6, 008. Three-Phase Circuits 1 Preliminary Comments and a quick review of phasors. We live in the time domain. We also assume a causal (nonpredictive) world. Real-world
More informationDriven RLC Circuits Challenge Problem Solutions
Driven LC Circuits Challenge Problem Solutions Problem : Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs
More informationEE221 - Practice for the Midterm Exam
EE1 - Practice for the Midterm Exam 1. Consider this circuit and corresponding plot of the inductor current: Determine the values of L, R 1 and R : L = H, R 1 = Ω and R = Ω. Hint: Use the plot to determine
More information2.4 Models of Oscillation
2.4 Models of Oscillation In this section we give three examples of oscillating physical systems that can be modeled by the harmonic oscillator equation. Such models are ubiquitous in physics, but are
More informationSimulation of 3-Phase 2- Stator Induction Motor Using MATLAB Platform
International Journal of Alied Engineering Research ISSN 0973-456 Volume 3, Number (08). 9437-944 Simulation of 3-Phase - Stator Induction Motor Using MATLAB Platform Pallavi R.Burande Deartment of Electrical
More informationIndirect Rotor Field Orientation Vector Control for Induction Motor Drives in the Absence of Current Sensors
Indirect Rotor Field Orientation Vector Control for Induction Motor Drives in the Absence of Current Sensors Z. S. WANG *, S. L. HO ** * College of Electrical Engineering, Zhejiang University, Hangzhou
More informationToolbox: Electrical Systems Dynamics
Toolbox: Electrical Systems Dynamics Dr. John C. Wright MIT - PSFC 05 OCT 2010 Introduction Outline Outline AC and DC power transmission Basic electric circuits Electricity and the grid Image removed due
More informationModule 4. Single-phase AC Circuits
Module 4 Single-phase AC Circuits Lesson 14 Solution of Current in R-L-C Series Circuits In the last lesson, two points were described: 1. How to represent a sinusoidal (ac) quantity, i.e. voltage/current
More informationTSTE25 Power Electronics. Lecture 3 Tomas Jonsson ICS/ISY
TSTE25 Power Electronics Lecture 3 Tomas Jonsson ICS/ISY 2016-11-09 2 Outline Rectifiers Current commutation Rectifiers, cont. Three phase Inrush and short circuit current Exercises 5-5, 5-8, 3-100, 3-101,
More informationChapter 31: AC Circuits
hapter 31: A ircuits A urrents and Voltages In this chapter, we discuss the behior of circuits driven by a source of A. Recall that A means, literally, alternating current. An alternating current is a
More informationEEE3405 ELECTRICAL ENGINEERING PRINCIPLES 2 - TEST
ATTEMPT ALL QUESTIONS (EACH QUESTION 20 Marks, FULL MAKS = 60) Given v 1 = 100 sin(100πt+π/6) (i) Find the MS, period and the frequency of v 1 (ii) If v 2 =75sin(100πt-π/10) find V 1, V 2, 2V 1 -V 2 (phasor)
More information