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

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 cur-rent tha

Three-Phase Systems

Figure 2-1 shows the most common electrical system volt-ages 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

(ANSI)/National Electrical Manufacturers Association

(NEMA)/National Electrical Code (NEC) requirements,

whereas, generally, 50-Hz systems are designed to be in com-pliance with International Electrotechnical Commission (IEC) or Australian standards This book concentrates on

60-Hz systems but notes 50-60-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 alter-nating-current (ac) system consists of a generator, a load, and conductors that connect them together The generator is

Chapter

2

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SYSTEM VOLTAGE Notes

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

46000

69000

115000

138000

161000

230000

345000

500000

765000

Notes

1 Also known as 120 Volt, single-phase

2 Also known as 120/240 Volt, single-phase

3 "Professionally" referred to as 208Y/120 instead of as 120/208

4 This connection is not in frequent use any longer.

5 "Professionally" referred to as 480Y/277 or 460Y/265 instead of as 277/480

6 Actual voltage setting in this system may be from 12470 Volts to 13800 volts.

7 "Professionally" referred to as 600 Volts instead of 575 Volts.

8 "Professionally" referred to as 24940Y/14400 Volts.

9 "Professionally" referred to as 34500Y/19920 Volts

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 cur-rent that flows through the electromagnet Therefore, the generator output voltage is regulated simply by increasing

or decreasing the “field” current through the electromagnet

power system voltages.

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

7 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 single-phase 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 three-phase generator The one voltage regulator provides regulated

field magnetic flux for all three phases simultaneously

In a three-phase generator, the three phases are

identi-fied 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 gener-ated 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 one-third of a 360-electrical-degree rotation, or by 120 electrical degrees The figure also shows graphically how these volt-ages can be shown as vectors, and it shows the relationship

of one voltage vector to the next

3300/1900 Volt, 3-phase 4-wire wye

6600/3800 Volt, 3-phase, 4-wire wye

11000/6350 Volt, 3-phase 4-wire wye

Notes

1 Also known as 230 Volt, single-phase

2 Also known as 400/230 Volt or 415/240 Volt single-phase

electrical power system voltages.

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 vec-tors 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

electrical load.

ground voltage Since any two different phase coils within

the generator are not displaced from one another by 180 elec-trical degrees, their voltage vectors cannot be added without considering their relative phase angle Assuming that a gen-erator coil voltage is 120 volts (V), Fig 2-7 illustrates that

the phase-to-phase (or line-to-line) voltage is calculated as

120 ∠ 0°  120 ∠ 120°  120 (兹3苶)  120 (1.713)  208 V

This relationship is true for all wye connections: Phase-to-phase voltage is equal to Phase-to-phase-to-neutral voltage multiplied

by 1.713.

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

RPM =

EQUIVALENT CIRCUIT FOR EACH

OF THE THREE PHASES

N

S

CALCULATE THE 2-POLE GENERATOR RPM FOR

AN OUTPUT FREQUENCY

OF 60 HERTZ.

E

60 Hz

GENERATOR

R

120f P (120)(60) RPM = 2 RPM = 3600 RPM

MOTOR ARMATURE

motor coil inductance

motor coil resistance

CALCULATE THE 2-POLE MOTOR RPM FROM THIS

60 HERTZ SOURCE

S

N

RPM = RPM = RPM = 3600 RPM 2 P 120f (120)(60)

A 3-phase system consists of three 1-phase circuits.

CURRENT FLOW

quantity of magnetic poles.

Figure

S

MOTOR ARMATURE

S N

3-PHASE GENERATOR

S

N

S

MOTOR ARMATURE

N

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.

3-PHASE GENERATOR

° = - 120 -60

° )

° - 180

phase a

2 Sketch generator coil voltage vectors.

3 Sketch adding voltage vectors.

Resultant vector.

Resultant vector.

120 volts -60

° minus 120

°, or 60

°, also equals the 3 , which is 1.732

Therefore the phase-to-phase voltage in a "wye" equals coil voltage times 3 Stated in another way, the phase-to-phase voltage equals the phase-to-neutral voltage times 3 Applying this general finding in the problem stated above:

If a generator is connected in “delta” with a coil voltage of 460 volts, what is its phase-to-phase output voltage?

3-PHASE GENERATOR 3-PHASE GENERATOR

3-PHASE MOTOR 3-PHASE MOTOR

E phase-to-phase

E coil

RPM E coil

S N

S

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