EC&M’s Electrical Calculations Handbook - Chapter 2 pptx

Chapter Three-Phase Systems Figure 2-1 shows the most common electrical system voltages for 60-hertz (Hz) systems, and Fig 2-2 shows the most common electrical system voltages for 50-Hz systems In general, 60-Hz systems are designed to be in compliance with Institute of Electrical and Electronics Engineers (IEEE)/American National Standards Institute (ANSI)/National Electrical Manufacturers Association (NEMA)/National Electrical Code (NEC) requirements, whereas, generally, 50-Hz systems are designed to be in compliance with International Electrotechnical Commission (IEC) or Australian standards This book concentrates on 60Hz systems but notes 50-Hz system information where it is pertinent The immediate question arises as to how to select the most correct voltage for a system that is being designed, and the answer is equally straightforward and is shown in the flowchart in Fig 2-3 The ultimate goal of this flowchart is to provide the load with proper current and voltage but not to exceed approximately 2500 amperes (A) at any one bus because of switchgear construction physical constraints In the simplest case of a single-phase circuit, an alternating-current (ac) system consists of a generator, a load, and conductors that connect them together The generator is 55 v Copyright 2001 by The McGraw-Hill Companies, Inc Click here for Terms of Use 56 Chapter Two SYSTEM VOLTAGE Notes 115 Volt single-phase 115/230 Volt single-phase 120/208 Volt, 3-phase 4-wire wye 240 Volt, 3-phase, 3-wire delta 277/480 Volt, 3-phase 4-wire wye 460 Volt, 3-phase 3-wire delta 600/347 Volt, 3-phase, 4-wire wye 2400 Volt, 3-phase, 3-wire delta 2400 Coltm 3-phase, 4-wire wye 4160/2400 Volt, 3-phase, 4-wire wye 12470/7200 Volt, 3-phase, 4-wire wye 24940/14400 Volt, 3-phase, 4-wire wye 34500/19920 Volt, 3-phase, 4-wire wye 46000 69000 115000 138000 161000 230000 345000 500000 765000 Note Note Note Note Note Note Note Note Note Notes Also known as 120 Volt, single-phase Also known as 120/240 Volt, single-phase "Professionally" referred to as 208Y/120 instead of as 120/208 This connection is not in frequent use any longer "Professionally" referred to as 480Y/277 or 460Y/265 instead of as 277/480 Actual voltage setting in this system may be from 12470 Volts to 13800 volts "Professionally" referred to as 600 Volts instead of 575 Volts "Professionally" referred to as 24940Y/14400 Volts "Professionally" referred to as 34500Y/19920 Volts Figure 2-1 This is a listing of the most common 60-Hz ac electrical power system voltages simply a coil of conductors by which a magnetic field is passed repeatedly by rotating an electromagnet within the coil The voltage output of the generator is proportional to the number of lines of magnetic flux that “cut” the coil, and the number of lines of flux is governed by the amount of current that flows through the electromagnet Therefore, the generator output voltage is regulated simply by increasing or decreasing the “field” current through the electromagnet Three-Phase Systems SYSTEM VOLTAGE Notes 220 Volt single-phase 220/380 Volt 3-phase 4-wire wye 3300/1900 Volt, 3-phase 4-wire wye 6600/3800 Volt, 3-phase, 4-wire wye 11000/6350 Volt, 3-phase 4-wire wye 57 Note Note Notes Also known as 230 Volt, single-phase Also known as 400/230 Volt or 415/240 Volt single-phase This is a listing of the most common 50-Hz ac electrical power system voltages Figure 2-2 From the generator to the load are two wires so as to form a complete circuit, in addition to a “safety ground” conductor that is run with, or encloses, the circuit conductors Chapter and article 250 of the National Electrical Code explain when and how an ac system must be grounded Figure 2-4 shows a generator and a motor with three singlephase circuits that are entirely separate from one another Note that the voltage of each of these circuits originates in a generator coil and that the load of each circuit is a motor coil that consists of resistance and inductance All three of these coils are shown inside one generator housing within which one electromagnet is spinning, known as the field The generator contains three single-phase systems, so it is called a threephase generator The one voltage regulator provides regulated field magnetic flux for all three phases simultaneously In a three-phase generator, the three phases are identified as phases a, b, and c As the magnetic field piece rotates, it passes first by phase coil a, then by phase coil b, and then by phase coil c Because of this action, the voltage is generated in coil a first, then in coil b, and finally in coil c, as shown graphically in Fig 2-5 Note that the voltage of one phase is displaced from the voltage of the next phase by onethird of a 360-electrical-degree rotation, or by 120 electrical degrees The figure also shows graphically how these voltages can be shown as vectors, and it shows the relationship of one voltage vector to the next 58 Chapter Two Use this logic to select the proper system voltage for an electrical load Figure 2-3 Wye-Connected Systems Noting that the three vectors seem to form a semblance of the letter Y, it is apparent that all three of these voltage vectors begin at a “zero” or common point This common point is called the neutral point In actuality, generators that are connected in wye have one point of each of their windings connected together and to ground, and the other ends of each of the windings of phases a, b, and c are extended out to the circuit loads, as shown in Fig 2-6 The voltage generated in one coil of the wye-connected generator is known as the phase-to-ground voltage, or line-to- Three-Phase Systems 59 ground voltage Since any two different phase coils within the generator are not displaced from one another by 180 electrical degrees, their voltage vectors cannot be added without considering their relative phase angle Assuming that a generator coil voltage is 120 volts (V), Fig 2-7 illustrates that the phase-to-phase (or line-to-line) voltage is calculated as ෆ 120 ∠ 0° ϩ 120 ∠ 120° ϭ 120 (͙3) ϭ 120 (1.713) ϭ 208 V This relationship is true for all wye connections: Phase-tophase voltage is equal to phase-to-neutral voltage multiplied by 1.713 60 Chapter Two CALCULATE THE 2-POLE GENERATOR RPM FOR AN OUTPUT FREQUENCY OF 60 HERTZ CURRENT FLOW XL 60 Hz GENERATOR RPM = RPM = motor coil inductance 120f P (120)(60) RPM = 3600 RPM E R motor coil resistance CALCULATE THE 2-POLE MOTOR RPM FROM THIS 60 HERTZ SOURCE 120f P (120)(60) RPM = RPM = EQUIVALENT CIRCUIT FOR EACH OF THE THREE PHASES RPM = 3600 RPM RPM RPM N S S 3-PHASE GENERATOR R E TO UR MO AT M AR N 3-PHASE MOTOR A 3-phase system consists of three 1-phase circuits Figure 2-4 Solve for generator rpm or motor rpm from frequency and quantity of magnetic poles Common voltages from wye-connected systems include 120/208, 277/480, 343/595, 2400/4160, and 7200/12,470 V Where these systems are grounded, the phase-to-neutral voltage is also the phase-to-ground voltage Delta-Connected Systems An even more straightforward method of connecting the three phases together at the generator is known as the delta connection, as illustrated in Fig 2-8 In this connection, the 61 Figure 2-5 A graph of three ac voltages from a 60-Hz three-phase generator 62 N 3-PHASE MOTOR S R E N TO UR MO AT M AR RPM a 3-PHASE MOTOR Source-to-load external circuit connections 3-PHASE GENERATOR c b Connections with motor load connected "in delta." Generator and motor coil interconnections 3-PHASE GENERATOR S RPM Question: How would a "wye" generator be connected to a "delta" motor? 63 N 3-PHASE MOTOR S R E N TO UR MO AT M AR RPM a 3-PHASE MOTOR Source-to-load external circuit connections 3-PHASE GENERATOR c b Figure 2-6 A wye three-phase system consists of three one-phase circuits connected together at a common neutral point that is normally grounded, and from the generator, connections can be made to either wye or delta loads Connections with motor load connected "in wye." Note: The dotted wire is not needed because the neutral conductor in a balanced "wye" (all three phases have the same load) carries no current Generator and motor coil interconnections 3-PHASE GENERATOR S RPM Question: How would a "wye" generator be connected to a "wye" motor? 64 a 3-PHASE MOTOR Diagram the system under analysis 3-PHASE GENERATOR c n b Making a diagram of the circuit: = 180 -j 104 = +60 -j 104 = 120 + j 0.0 = 208 (180)2 + (104)2 ARCTAN (- 0.577) ARCTAN (-104/180) + 30° - 180° = 208 -150° TOTAL VOLTS = 43199 180 -j 104 = THEN CHANGE BACK TO POLAR FORM Minus Phase b voltage - (120 120° = - 120 -60°) = -(-120 COS 60 -j 120 SIN 60) = -[(-120)(5) -j (120)(.866)] = -[-60 +j 103.92] Phase a voltage: 120 0° = 120 COS + j 120 SIN = [ (120)(1) +j (120)(0)] CALCULATE THE DIFFERENCE BETWEEN THE VOLTAGE VECTORS IN RECTANGULAR FORM Calculate the voltage across each delta-connected motor coil if wye-connected generator coil voltage is 120 volts 65 phase c phase a 120 volts 0° 120 volts 120° 120° Sketch adding voltage vectors 120 volts 0° phase a phase b 120 volts 120° ° Add voltage vectors 60° Figure 2-7 Solve for motor coil voltage using vectors given wye-connected generator coil voltage Phase-to-phase voltage = (120) (1.732) = 208 Volts Phase-to-phase voltage = delta-connected motor coil voltage = Wye coil voltage times Applying this general finding in the problem stated above: Therefore the phase-to-phase voltage in a "wye" equals coil voltage times Stated in another way, the phase-to-phase voltage equals the phase-to-neutral voltage times Note that the Tangent of 180° minus 120°, or 60°, also equals the , which is 1.732 Sketch generator coil voltage vectors phase b s tor ec tv ult an Re 0v 12 R es r cto -60 olt s ve nt ult a 66 voltage Figure 2-8 Ecoil = 460V E coil = 460V 3-PHASE GENERATOR Ephase-to-phase 3-PHASE GENERATOR S N coil = 460V E RPM In a delta three-phase system, coil voltage is equal to phase-to-phase If a generator is connected in “delta” with a coil voltage of 460 volts, what is its phase-to-phase output voltage? = 460V 3-PHASE MOTOR 3-PHASE MOTOR S N OR RE OT TU M A M AR RPM Three-Phase Systems 67 end of one phase coil is connected to the end of the next phase coil, and it is connected to the other end of the first coil The magnetic field effectively rotates within these three coils, forming voltages that are 120 electrical degrees apart, but with delta connections, the coil voltage is equal to the line-to-line voltage Common voltages from delta-connected systems include 240, 460, and 2400 V Where these systems are grounded, the phase-to-ground voltages are unequal to one another, thus creating extra considerations in the load circuits  ... b voltage - ( 120 120 ° = - 120 -6 0°) = -( - 120 COS 60 -j 120 SIN 60) = -[ (-1 20 )(5) -j ( 120 )(.866)] = -[ -6 0 +j 103. 92] Phase a voltage: 120 0° = 120 COS + j 120 SIN = [ ( 120 )(1) +j ( 120 )(0)] CALCULATE... 3-phase 3-wire delta 600/347 Volt, 3-phase, 4-wire wye 24 00 Volt, 3-phase, 3-wire delta 24 00 Coltm 3-phase, 4-wire wye 4160 /24 00 Volt, 3-phase, 4-wire wye 124 70/ 720 0 Volt, 3-phase, 4-wire wye 24 940/14400... Chapter Two SYSTEM VOLTAGE Notes 115 Volt single-phase 115 /23 0 Volt single-phase 120 /20 8 Volt, 3-phase 4-wire wye 24 0 Volt, 3-phase, 3-wire delta 27 7/480 Volt, 3-phase 4-wire wye 460 Volt, 3-phase