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CRYSTAL
Lehr- und Lernmittel,
Informationen, Beratung
Educational Aids
Literature, Consulting
Moyens didactiques,
Informations,
Service-conseil
Material did�ctico,
Informaciones, Asesor�a
Feedback IBE e.V.
GTZ - Deutsche Gesellschaft f�r
Technische
Zusammenarbeit (GTZ) GmbH
Textbook for Vocational Training
Institut f�r berufliche Entwicklung e.V.
Berlin
Original title:
“Schaltungen, Formeln, Tabellen -
Elektrotechnik”
Author: Klaus Janoske
First Edition © IBE
Institut f�r berufliche Entwicklung e.V.
Parkstra�e
23
13187 Berlin
Order No.: 91-34-0101/2
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Preface
This Textbook is intended for all trainees in the field of electrotechnology. It contains the more important circuit diagrams and formulas and a limited number of selected tables of direct-current and alternating-current engineering.
With the help of this Textbook, the trainee will be in a position to read and interpret electrical wiring and circuit diagrams in order to perform his job according to the rules of good workmanship. At the same time, the trainee is encouraged to prepare and draw circuit diagrams without assistance and to use graphical symbols correctly.
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Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
1. Selected Graphical Symbols of Electrotechnology
1.1. Graphical Symbols for General Circuit Elements
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
Polarity |
| |
|
positive |
+ | |
|
negative |
- | |
|
centre point, neutral |
N | |
|
Directions of transmission and motion | |
|
|
energy direction |
| |
|
direction of motion |
| |
|
sense of rotation (rotating) |
| |
|
direction of turning |
| |
|
Possibilities of adjusting, setting | |
|
|
adjusting |
| |
|
setting |
| |
|
Variabilities |
| |
|
general, linear |
| |
|
non-linear |
| |
|
Pulse shapes |
| |
|
rectangular pulse, positive |
| |
|
rectangular pulse, negative |
| |
|
Shieldings |
| |
|
general |
- - - - |
|
|
electrostatic |
| |
|
electromagnetic |
| |
|
shielding of a component |
| |
1.2. Graphical Symbols for Types of Current, Voltage and Connections
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
Type of voltage and current | | |
|
direct voltage |
| |
|
direct current |
| |
|
alternating voltage, alternating current |
| |
|
alternating voltage within the range of audio frequency |
| |
|
alternating voltage within the range of high frequency |
| |
|
direct or alternating voltage |
| |
|
Alternating current connections | |
|
|
star connection |
| |
|
delta connection |
| |
|
star-delta connection |
| |
|
zig-zag connection |
| |
1.3. Graphical Symbols for Lines and Line Connections
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
Lines |
| |
|
line, general |
| |
|
2 lines |
|
|
|
3 lines |
|
|
|
4 lines |
|
|
|
n - lines |
| |
|
crossing of two lines without connection |
|
|
|
crossing of two lines with connection |
|
|
|
shielded line |
|
|
|
coaxial line |
| |
|
Line and cable connections | | |
|
earth connection |
| |
|
ground connection (chassis or the like) |
| |
|
disconnectable and non-disconnectable electrical connection, general |
| |
|
disconnectable electrical connection, e.g. terminal |
| |
|
cable termination |
| |
|
coupling sleeve |
| |
|
joint box for a branching |
| |
|
joint box for two branchings |
| |
1.4. Graphical Symbols for Resistors
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
resistor, general |
| |
|
resistor, variable, with possible circuit interruption |
| |
|
resistor, variable, without circuit interruption |
| |
|
resistor as voltage divider |
| |
|
resistor, adjustable |
|
|
|
resistor, infinitely variable resistor, voltage-dependent non-linear |
|
|
|
fusible cut-out, general |
| |
|
potential fuse, general |
| |
|
two-electrode arrester |
| |
|
ion arrester (dot = gas filing) |
| |
1.5. Graphical Symbols for Capacitors
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
capacitor, general |
| |
|
electrolyte capacitors | | |
|
polarised |
| |
|
non-polarised |
| |
|
lead-in capacitor, polarised |
| |
|
lead-in capacitor, non-polarised |
| |
|
variable capacitor |
| |
|
variable capacitor with indication of rotor |
| |
|
anti-interference capacitor |
| |
1.6. Graphical Symbols for Coils and Transformers
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
Coils |
| |
|
general |
| |
| |
or | |
|
air-cored coil |
| |
| |
or | |
|
air-cored coil with two tappings |
or | |
|
iron core |
| |
|
iron core and air gap |
| |
|
iron dust core |
| |
|
iron-core choke |
or |
|
|
Transformers |
| |
|
single-phase transformer with iron core (if errors cannot be made, the core need not be drawn) |
| |
|
single-phase transformer with iron-core and 3 windings (core not represented) |
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|
three-phase transformer in star-star connection (core not represented) |
|
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|
three-phase transformer, star-delta connection |
|
|
|
three-phase autotransformer in star connection |
|
|
1.7. Graphical Symbols for Current and Voltage Transformers
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
Current transformers | | |
|
primary winding |
| |
|
secondary winding |
| |
|
current transformer, general |
|
|
|
Voltage transformers | | |
|
general |
or |
|
|
capacitive |
or | |
or
or 
1.8. Graphical Symbols for Electrochemical and Electrothermal Sources
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
battery cell, general |
| |
|
battery, 5 cells with one tapping |
| |
|
thermoelectric element |
| |
1.9. Graphical Symbols for Tubes
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
diode, indirectly heated |
| |
|
duodiode, indirectly heated |
or | |
|
triode, indirectly heated |
or | |
|
duotriode with separated cathodes, indirectly heated, heating filament with central tapping, internal screening of the system |
| |
|
tetrode |
| |
|
pentode, suppressor grid connected with cathode |
| |
|
triode - pentode |
| |
|
triode - heptode (according to the circuit, the systems may be drawn left-and-right reversed) |
| |
1.10. Graphical Symbols for Semiconductors
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
Transistors |
| |
|
point contact transistor or junction transistor, type p-n-p |
| |
|
n-p-n transistor |
| |
|
Semiconductor diodes | | |
|
diode with rectifying function |
or | |
|
capacity diode |
| |
|
tunnel diode |
| |
|
avalanche rectifier diode |
| |
|
avalanche rectifier diode with avalanche effect in both directions |
| |
|
backward diode |
| |
|
Thyristors |
| |
|
general |
| |
|
backward blocking |
| |
|
backward conducting |
| |
|
n-type gate, controlled at anode side |
| |
|
p-type gate, controlled at cathode side |
| |
|
Semiconductor elements which can be influenced by light | | |
|
photoresistance cell |
| |
|
photodiode |
| |
|
photocell with depletion layer |
| |
|
phototriode p-n-p |
| |
|
switching diode p-n-p-n |
| |
|
Semiconductor circuits | | |
|
switching diode p-n-p-n |
| |
|
semiconductor valves in bridge connection |
|
|
1.11. Graphical Symbols for Switching Devices
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
Switching members | | |
|
make contacts, general |
|
|
|
break contacts, general |
|
|
|
change-over switch, general |
| |
|
change-over switch with central rest position |
| |
|
Relay switching members | | |
|
make contacts |
|
|
|
break contacts |
|
|
|
change-over switch with interruption in switching |
|
|
|
Switches |
| |
|
hand-actuated lever switch |
| |
|
make contacts with automatic resetting |
|
|
|
break contacts with automatic resetting |
| |
|
disconnecting switch, three-pole |
| |
|
power circuit-breaker, three-pole |
|
|
|
power breaker, three-pole |
| |
|
power switch, three-pole |
|
|
|
switch, three-pole, with one make contact and two break contacts |
|
|
|
Drive members |
| |
|
drive, general |
| |
|
drive, thermal |
| |
|
drive by centrifugal force |
| |
|
drive by piston |
| |
|
drive by electrical motor |
| |
|
drive by cams |
| |
|
drive by float |
| |
|
manual drive |
| |
|
manual drive with automatic resetting |
| |
|
foot drive |
| |
|
actuation by means of a key |
| |
|
drive by relay or contactor |
| |
|
Electrical drive systems | | |
|
relay winding only for alternating current |
| |
|
winding of a relay insensitive to alternating current |
| |
|
winding of an electro-thermal relay |
| |
|
winding of a remanence relay |
| |
|
winding of a polarised relay |
| |
|
winding for relay tripping by over-current |
|
|
|
winding for relay tripping by undercurrent |
|
|
|
winding for relay tripping by reverse current |
|
|
|
winding for relay tripping by overvoltage |
|
|
|
winding for relay tripping by undervoltage |
|
|
|
winding for relay tripping by error voltage |
|
|
|
winding for thermal tripping of relay |
|
|
|
relay winding with delay of attraction |
| |
|
relay winding with delay of dropping |
| |
|
relay winding with delay of attraction and dropping |
| |
|
relay winding with electrothermal delay |
| |
|
relay winding with electronic delay |
| |
|
winding for relay tripping by open-circuit working | |
|
|
winding for relay tripping by closed-circuit working | |
|
|
winding for relay tripping by overcurrent with time lag |
|
|
|
Plugged connections | | |
|
receptacle |
| |
|
plug |
| |
|
connector, single-pole |
| |
|
connector, four-pole |
| |
|
h.f. coaxial receptacle |
| |
|
h.f. coaxial connector |
| |
|
h.f. coaxial connector, two - core |
| |
1.12. Graphical Symbols for Machines
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
rotor with winding, commutator and brushes |
| |
|
asynchronous machine, stator in delta connection, rotor in star connection |
| |
|
direct-current generator |
|
|
|
direct-current motor |
|
|
|
three-phase generator |
|
|
|
three-phase motor (cage rotor) |
|
|
|
three-phase motor (slip-ring rotor) |
|
|
1.13. Graphical Symbols for Meter Movements and Measuring Instruments
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
voltage path of a movement |
or | |
|
current path of a movement |
or | |
|
movement of a wattmeter |
| |
|
voltage paths for summation or differentiation |
| |
|
current paths for summation or differentiation |
| |
|
movement of a two-phase wattmeter with 2 elements |
| |
|
movement of an ohmmeter |
| |
|
movement of a frequency meter |
| |
|
Measuring instruments | | |
|
voltmeter |
|
|
|
ammeter |
|
|
|
wattmeter with 2 elements |
|
|
|
electrometer |
| |
1.14. Graphical Symbols of Electroacoustics
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
Devices |
| |
|
telephone receiver |
|
or |
|
microphone | |
or |
|
throat microphone | |
|
|
hand set | |
|
|
loudspeaker |
|
or |
|
monohead, general |
|
|
|
stereohead, general |
|
|
|
record head, mechanical | |
|
|
replay head, mechanical | |
|
|
magnetic head, general | |
|
|
recording head |
|
|
|
playback head |
|
|
|
magnetic head for recording and playback | |
|
|
erasing head |
|
|
|
bell, general |
|
|
|
alternating current bell | |
|
|
direct current bell |
|
|
|
single-stroke bell |
|
|
|
buzzer | |
|
|
horn | |
|
|
siren | |
|
|
howler | |
|
|
Signs |
| |
|
electromagnetic |
|
|
|
electrodynamic by coil | |
|
|
electrodynamic by band | |
|
|
piezoelectric |
|
|
|
magnetostrictive |
|
|
|
capacitive | |
|
|
carbon | |
|
|
Examples |
| |
|
electromagnetic telephone receiver | |
|
|
carbon microphone |
|
|
|
capacitor microphone |
|
|
|
magnetostrictive loudspeaker | |
|
1.15. Graphical Symbols for Wiring Plans
|
Term |
Graphical Symbol | |
| |
in full |
simplified |
|
distribution box |
|
|
|
cut-out, single-pole |
|
|
|
cut-out, two-pole |
|
|
|
cut-out, three-pole |
|
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group switch, single-pole | |
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|
multi-circuit switch, single-pole |
|
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|
single-pole double-throw switch |
|
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|
four-way switch, single-pole |
|
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|
plug socket, single |
|
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plug socket, double |
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plug socket with protective contact, single |
|
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|
plug socket with protective contact, double | |
|
|
luminous key switch |
|
|
|
glow lamp |
| |
|
fluorescent lamp |
|
|
|
glow igniter |
| |
|
door opener |
| |
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Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
2. Bell Circuits
The reference letters and numbers in the illustrations of bell circuits have the following meanings:
|
a |
switch |
E |
voltage source |
|
b |
control switch |
f |
transducer |
|
c |
contactor |
g |
measuring instrument |
|
d |
auxiliary contactor, relay |
h |
visual and audio alarm |
|
e |
protective device |
Tr |
transformer |
2.1. Direct-current Bell
Direct-current bell to be actuated
from one place
Direct-current bell to be actuated
from two places
Bell installation for reciprocal
calls
Sell installation for reciprocal
calls with key change-over switch
Bell installation for reciprocal
calls with switch-on push-button, line-saving
Bell installation for reciprocal
calls,
line-saving
2.2. Alternating-current Bell
Alternating-current bell with bell
transformer, simple circuit
Bell installation with change-over
switch
2.3. House Bell Installation
Circuit of a house bell installation
Circuit of a house bell installation
with electric door
operator
2.4. Alarm Systems
Circuit of an alarm system with
normally open contacts b1 test key, 1 glass panel
Circuit of an alarm system with
normally closed contacts b2 test key, 1 glass
panel
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Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
3. Basic Circuits of Illumination Engineering
3.1. Circuit-breaking Arrangements
cut-out, schematic diagram
(all-pole)
cut-out, schematic diagram
(single-pole)
plug socket with protective contact
(all-pole)
plug socket with protective contact
(single-pole)
plug socket with protective contact
and separate protective conductor (all-pole)
plug socket with protective contact
and separate protective conductor (single-pole)
Cut-cuts with plug socket (all-pole)
Cut-cuts with plug socket
(single-pole)
two-pole cut-out (all-pole)
two-pole cut-out (single-pole)
three-pole cut-out (all-pole)
three-pole cut-out
(single-pole)
3.2. Series Circuits
multi-circuit switch -also know as
series switch-, schematic diagram (all-pole)
multi-circuit switch -also know as
series switch-, schematic diagram (single-pole)
series switch with plug socket
(all-pole)
series switch with plug socket
(single-pole)
3.3. Two-way Switching Circuits
two-way switch, schematic diagram
(all-pole)
two-way switch, schematic diagram
(single-pole)
two-way switch with plug socket
(all-pole)
two-way switch with plug socket
(single-pole)
two-way switch, economy circuit,
schematic diagram (all-pole)
two-way switch, economy circuit,
schematic diagram (single-pole)
two-way switch with four-way switch,
schematic diagram (all-pole)
two-way switch with four-way switch,
schematic diagram (single-pole)
two-way switch with four-way switch
(all-pole)
two-way switch with four-way switch
(single-pole)
3.4. Staircase Lighting Circuits
staircase lighting circuit with
four-way switch (all-pole)
staircase lighting circuit with
four-way switch (single-pole)
staircase lighting circuit with
four-way switch (switch positions)
staircase circuit with automatic
unit (all-pole)
staircase circuit with automatic
unit (single-pole)
t = automatic staircase lighting switch unit
3.5. Fluorescent Lamp Circuits
fluorescent lamp at single-phase
mains (single-pole)
fluorescent lamp at single-phase
mains (all-pole)
fluorescent lamp in lead-lag
connection (single-pole)
fluorescent lamp in lead-lag
connection (all-pole)
fluorescent lamp at three-phase
mains (all-pole)
fluorescent lamp at three-phase
mains
(single-pole)
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Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
4. Electrical Machines
Designation of electrical conductors
|
Alternating current |
| |
|
|
any external conductor |
L |
| |
1st external conductor |
L1 |
| |
2nd external conductor |
L2 |
| |
3rd external conductor |
L3 |
| |
neutral conductor without the function of a protective conductor |
N |
|
Direct current |
| |
|
|
any external conductor |
L |
| |
positive external conductor |
L+ |
| |
negative external conductor |
L- |
| |
central conductor without the function of a protective conductor |
M |
4.1. Direct-current Machines
4.1.1. Direct-current Generators
d.c. shunt-wound generator without
commutating poles (clockwise sense of rotation)
terminal boards (clockwise sense of
rotation)
terminal boards (anti-clockwise
sense of rotation)
d.c. shunt-wound generator with
commutating poles (clockwise sense of rotation)
The commutating poles are clamped
inside the generator terminal boards with commutating poles (clockwise sense
of rotation)
The commutating poles are clamped
inside the generator terminal boards with commutating poles (anti-clockwise
sense of rotation)
d.c. compound-wound generator with
commutating poles (clockwise sense of rotation)
terminal boards (clockwise sense of
rotation)
terminal boards (anti-clockwise
sense of
rotation)
4.1.2. Direct-current Motors
d.c. shout-wound motor with
commutating poles and starter (clockwise sense of rotation)
d.c. shout-wound motor with
commutating poles and starter (anti-clockwise sense of rotation)
The commutating poles are clamped inside the motor
terminal boards (A)
terminal boards (B)
d.c. series motor with commutating
poles (clockwise sense of rotation)
d.c. series motor with commutating
poles (anti-clockwise sense of rotation)
terminal boards (A)
terminal boards (B)
d.c. compound - wound motor with
commutating poles (clockwise sense of rotation)
d.c. compound - wound motor with
commutating poles (anti-clockwise sense of rotation)
terminal boards (A)
terminal boards (B)
d.c. shunt-wound motor with
cylindrical starter (clockwise sense of rotation)
d.c. series motor with cylindrical
starter (clockwise sense of rotation)
d.c. series motor with reversing
starter
Schematic circuit diagram for
reversing starter with d.c. series motor (clockwise sense of rotation)
Schematic circuit diagram for
reversing starter with d.c. series motor (anti-clockwise sense of rotation)
d.c. shunt-wound motor with
controller drum for clockwise and anti-clockwise sense of rotation
d.c. shunt-wound motor with
controller drum for clockwise and anti-clockwise rotation and braking
Schematic circuit diagram for
controller drum with reversing and braking circuit for d.c. shunt-wound motor
(clockwise sense of rotation)
Schematic circuit diagram for
controller drum with reversing and braking circuit for d.c. shunt-wound motor
(anti-clockwise sense of rotation)
Schematic circuit diagram for
controller drum with reversing and braking circuit for d.c. shunt-wound motor
(braking right-hand side)
Schematic circuit diagram for
controller drum with reversing and braking circuit for d.c. shunt-wound motor
(braking left-hand
side)
4.2. Three-phase Machines
4.2.1. Three-phase Generators
Three-phase generator with exciter
(A)
Three-phase generator with exciter
(B)
4.2.2. Three-phase Motors
|
Mains voltage designations |
3 N 220V/380V 50 Hz |
| |
1 N 220V 50 Hz |
Three-phase motor with star-delta
connection (star connection)
Three-phase motor with star-delta
connection (delta connection)
terminal boards (clockwise sense of
rotation)
terminal boards (anti-clockwise
sense of rotation)
terminal boards (clockwise sense of
rotation)
terminal boards (anti-clockwise
sense of rotation)
Three-phase motor with drum switch
for clockwise and anti-clockwise rotation
Three-phase motor with lever
commutator for star-delta starting
Three-phase motor with dram switch
for star-delta starting
Three-phase motor (slip ring rotor)
with rotor starter in star connection
Three-phase motor (slip ring rotor)
with rotor starter in delta connection and controller drum for clockwise and
anti-clockwise rotation
Three-phase motor with protective
motor switch for undervoltage tripping, thermal tripping and magnetic tripping
Three-phase motor (slip ring rotor)
with rotor starter and protective motor switch for manual and magnetic tripping
Three-phase motor with control
acknowledging switch and protective motor switch
Three - phase motor in Dahlander
pole-changing connection
Three-phase motor in “with
Dahlander pole-changing connection”
Three-phase motor in “reverse
Dahlander pole-changing connection”
Rotor-fed three-phase shunt-wound
commutator motor
Three-phase motor at the
single-phase mains (A)
Three-phase motor at the
single-phase mains (B)
explanations to the wiring diagram
c1 operating capacitor, c2 starting capacitor
Frequently it is necessary to connect three-phase not ors to single-phase mains. In this connection, the following disadvantages must be taken into account. The rated output (see rating plate) will be reduced to 80 % to 65 %.
The rated torque will be reduced to 30 %.
The output or power can be calculated according to the following equation:
C = capacity of the capacitor in mF
P = power in kW
U = voltage in V
f = frequency
The following approximate values can be assumed when connecting to single-phase alternating current of 220 V:
|
Power (kW) |
Capacity of the Capacitor |
|
0.10 |
7 |
|
1.00 |
50 |
|
2.00 |
100 |
Three-phase series commutator motor
1 OFF position
2 starting, operation
3 braking
Single-phase capacitor motor with
auxiliary phase
Repulsion motor
Ward-Leonard Control low-loss speed
adjustment at the direct-current motor (General wiring
diagram)
4.3. Transformers
4.3.1. Single-phase Transformers
normal circuit
economy
circuit
4.3.2. Three-phase Transformers
Three-phase transformers in parallel connection
Transformer station with two
transformers connected in parallel
Usual groups of connection for transformers
|
Designation |
|
Indicator Diagram |
Circuit Diagram | | ||
|
Identification number |
Group of connection |
High Voltage |
Lower Voltage |
High Voltage |
Lower Voltage |
Transformation |
|
Three-phase power transformers | ||||||
| |
Dd 0 |
|
|
|
|
|
|
0 |
Yy 0 |
|
|
|
|
|
| |
Dz 0 |
|
|
|
|
|
| |
Dy 5 |
|
|
|
|
|
|
5 |
Yd 5 |
|
|
|
|
|
| |
Yz 5 |
|
|
|
|
|
| |
Dd 6 |
|
|
|
|
|
|
6 |
Yy 6 |
|
|
|
|
|
| |
Dz 6 |
|
|
|
|
|
| |
Dy 11 |
|
|
|
|
|
|
11 |
Yd 11 |
|
|
|
|
|
| |
Yz 11 |
|
|
|
|
|
|
Single-phase power transformers | ||||||
| | |
|
|
|
|
|
Explanations for the table
The table shows the commonly used circuits according to the relevant Standard of the International Electrotechnical Commission (I E C). When multiplying the identification number by 30°, the phase shift of the high voltage side with respect to the lower voltage side is obtained.
Dd 6 means:
D = high voltage side delta connection
d = lower voltage side delta connection
The lower voltage is shifted with respect to the high voltage by 6 x 30° = 180°.
Due to these different circuits, different operational behaviour is attained.
The ratio of transformation is calculated as follows:
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
5. Contactor Circuits
5.1. Types of Excitation of the Control
Self-excitation
Advantage: no-voltage characteristic
Figure
Separate excitation
Figure
The contactor circuits are provided with permanent contact making
Control current locking
Advantage: By means of the control current locking contactor, no-voltage characteristic is attained in separately excited contactor circuits.
5.2. Possibilities of Representing Contactor Circuits
pulse contact making functional
diagram
mixed representation - main circuit
(single-pole); control circuit (all-pole)
control circuit - shown in the form
of a circuit diagram
sequential circuit - functional
diagram
Circuit diagram for the control of
the sequential circuit
Sequential circuit with rotation
monitors and unlocking switches
Circuit diagram for the sequential
circuit with rotating monitors and unlocking
switches
5.3. Reversing Contactor Circuits
control current - pulse locking
Circuit diagrams for reversing
contactor circuits (pulse locking)
To be used for single drives only, circuit is not safe!
Circuit diagrams for reversing
contactor circuits (pulse and holding current locking)
reversing contactor circuit - push -
button locking
Circuit diagrams for reversing
contactor circuits (Push-button locking)
Circuit diagrams for reversing
contactor circuits (Push-button locking arranged as rapid change-over circuit;
suitable for smaller motors only)
Reversing contactor circuit with
star-delta starting main circuit
Circuit diagram for the control of
the reversing contactor circuit with star-delta
starting
5.4. Arc Extinguishing Circuits
reversing contactor - rapid
changing-over
Arc extinguishing circuit for
separate excitation
Circuit diagram for the control of
the separately escited arc extinguishing
circuit
5.5. Three-contactor Star-delta Connection
main circuit
Circuit diagram for the control of
the three-contactor star-delta
connection
5.6. Squirrel-cage Induction Motor
with effective resistance for
starting in the stator and self-monitoring (unsymmetric circuit)
Circuit diagram for the control of
the starting action with effective
resistance
5.7. Sliping Rotor
with rotor contactor starter
Circuit diagram for the control of
the slip-ring rotor with rotor
starter
5.8. Interference Suppression
Interference suppression of a
universal motor
Interference suppression of a
direct-current shunt motor
Interference suppression of switch
gears
Interference suppression of electric
bells (A)
Interference suppression of electric
bells
(B)
5.9. Light-current Controlled Power Plant with Impulse Relay
Figure
Figure
Figure
|
| ||||||||||||||||||||||||
Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
6. Rectifier Circuits
6.1. Rectifier Circuits of Alternating Current
half-wave rectification
full wave rectification
opposite-contact connection
full-wave rectification - bridge
connection
full-wave rectification - thermionic
rectifier in double-way
connection
6.2. Rectifier Circuits of Three-phase Current
half-wave rectification
full-wave rectification - bridge
connection
full-wave rectification - transformer
with central
tapping
|
| ||||||||||||||||||||||||||||||
Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
7. Measurement Circuits
7.1. Measurement Circuits in Direct-current Installations
Voltage measurement (A)
Voltage measurement (B)
By connecting in series of a resistor (Rv), an extension of the measuring range of the voltmeter is obtained
Current measurement (A)
Current measurement (B)
By connecting in parallel a shunt resistor (Rp), an extension of the measuring range of the ammeter is obtained.
Voltage and current measurement for
the determination of the resistance
The current-exact connection is used when the resistance (Rx) to be determined, is very high.
Current and voltage measurement for
the determination of the resistance
The voltage-exact connection is used when the resistance (Rx) to be determined is very small if the resistance Rx is calculated according to the following equation:
7.2. Measurement Circuits in Alternating-current Installations
Voltage measurement (low voltage)
Voltage measurement (high-voltage -
voltmeter with voltage transformer)
Current measurement
Current measurement (amperemeter
with current transformer)
Power measurement (low voltage)
Power measurement (high voltage)
electric meter connections
electric meter
connections
7.3. Measurement Circuits in Three-phase Installations
Voltage measurement
2 voltage transformers in
V-connection
Current measurement
Current measurement
Power measurement
Single wattmeter method
use:
equal phase loading, accessible PEN-conductor
result:
total power = 3 × measuring result
Power measurement
Two-wattmeter method
use:
unequal phase loading, non-accessible PEN-conductor;
measuring instruments of the same type have to be used
result:
total power = P1 + P2,
when P1 > P2, the total power = P1 - P2
Power measurement
Two-wattmeter method
2 movements combined into one instrument
Power measurement
Three-wattmeter method
use: unequal phase loading, accessible PEN-conductor
result: total power = P1 + P2 + P3
Power measurement
Three - wattmeter method
3 movements combined into one instrument
Meter circuit (three-wire meter)
Meter circuit (four-wire meter)
Measurement of the power factor (cos
j)
Measurement of the frequency (single
frequency meter)
Measurement of the frequency (double
frequency meter)
Measurements in a High-voltage Power
Plant
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
8. Protective Circuits
Protective wire in a three-phase
current system
Earthing (Three-phase a-c three wire
system)
Earthing (Three-phase a-c four wire
system)
Protective Earthing
Reflux of the leakage current via
water pipe system (1)
Reflux of the leakage current via
earth
IF leakage current, In rated current of the fusible cut-out
Circuit for Generating Protective Low
Voltage
Fault-voltage Protective Circuit
in a three-phase three-wire system
1 fault-voltage circuit breaker
Fault-current Protective Circuit
in a three-phase four-wire system
1 fault-current circuit breaker
|
| ||||||||||||||||||||||||||||||||||||||||||
Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
9. Circuits in Motor Vehicles
Block diagram
The block diagram represents the simplified circuit. Only the essential parts are taken into consideration. The devices are copied by means of rectangles or squares and properly marked.
Figure
Terminal diagram
The terminal diagram represents the electrical connection between the devices. Thus it allows the exchange of products, devices and parts of devices. The components are represented with the corresponding lines, junctions and terminal designations.
Figure
Circuit diagram
The circuit diagram is the detailed representation of a circuit. It represent the operating method of an electrical system or of single devices. The devices are drawn in their basic setting and in dead condition.
Figure
9.1. Battery Charge
General wiring-diagram
Battery charger 6/12 V switchable
Battery charger 6/12 switchable with
built-in charge indicator lamp and measuring
instrument
9.2. Ignition Systems
Battery-ignition systems
General wiring diagram
Transistorized ignition systems
General wiring diagram
Variants of transistorized ignition
systems (A)
Variants of transistorized ignition
systems (B)
Transistorized ignition
(Bosch)
9.3. Starting Aid for Diesel Engines
Terminal diagram of a preheating
system
1 glow-plug and starter switch, 2 glow-plug indicator, 3 ballast resistor, 4 glow plugs
Preheating with automatic
re-annealing after starting
1 headlamp-ignition switch, 2 glow-plug and starter switch, 3 contactor, 4 charge indicator lamp (as glow-plug indicator), 5 resistor, 6 time-delay switch, 7 starter
9.4. Turn-signal Flasher
Turn-signal flasher with two
turn-signal lamps and indicator lamp
Turn-signal flasher with three
turn-signal lamps and turn-signal lamp
Turn-signal flasher with three
turn-signal lamps and two turn-signal
lamps
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
10. Tables
Table 1 Natural values of the trigonometric functions sine and cosine
|
sin 0°...sin 15° | ||||||||||||
|
minute |
0 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
|
|
degree |
,0 |
,1 |
,2 |
,3 |
,4 |
,5 |
,6 |
,7 |
,8 |
,9 |
(1,0) |
|
|
0 |
0,00000 |
00175 |
00349 |
00524 |
00698 |
00873 |
01047 |
01222 |
01396 |
01571 |
01745 |
89 |
|
1 |
01745 |
01920 |
02094 |
02269 |
02443 |
02618 |
02792 |
02967 |
03141 |
03316 |
03490 |
88 |
|
2 |
03490 |
03664 |
03839 |
04013 |
04188 |
04362 |
04536 |
04711 |
04885 |
05059 |
05234 |
87 |
|
3 |
05234 |
05408 |
05582 |
05756 |
05931 |
06105 |
06279 |
06453 |
06627 |
06802 |
06976 |
86 |
|
4 |
06976 |
07150 |
07324 |
07498 |
07672 |
07846 |
08020 |
08194 |
08368 |
08542 |
08716 |
85 |
|
5 |
08716 |
08889 |
09063 |
09237 |
09411 |
09585 |
09758 |
09932 |
10106 |
10279 |
10453 |
84 |
|
6 |
10453 |
10626 |
10800 |
10973 |
11147 |
11320 |
11494 |
11667 |
11840 |
12014 |
12187 |
83 |
|
7 |
12187 |
12360 |
12533 |
12706 |
12880 |
13053 |
13226 |
13399 |
13572 |
13744 |
13917 |
82 |
|
8 |
13917 |
14090 |
14263 |
14436 |
14608 |
14781 |
14954 |
15126 |
15299 |
15471 |
15643 |
81 |
|
9 |
15643 |
15816 |
15988 |
16160 |
16333 |
16505 |
16677 |
16849 |
17021 |
17193 |
17365 |
80 |
|
10 |
0,17365 |
17537 |
17708 |
17880 |
18052 |
18224 |
18395 |
18567 |
18738 |
18910 |
19081 |
79 |
|
11 |
19081 |
19252 |
19423 |
19595 |
19766 |
19937 |
20108 |
20279 |
20450 |
20620 |
20791 |
78 |
|
12 |
20791 |
20962 |
21132 |
21303 |
21474 |
21644 |
21814 |
21985 |
22155 |
22325 |
22495 |
77 |
|
13 |
22495 |
22665 |
22835 |
23005 |
23175 |
23345 |
23514 |
23684 |
23853 |
24023 |
24192 |
76 |
|
14 |
24192 |
24362 |
24531 |
24700 |
24869 |
25038 |
25207 |
25376 |
25545 |
25713 |
25882 |
75 |
| |
(1,0) |
,9 |
,8 |
,7 |
,6 |
,5 |
,4 |
,3 |
,2 |
,1 |
,0 |
degree |
| |
60 |
54 |
48 |
42 |
36 |
30 |
24 |
18 |
12 |
6 |
0 |
minute |
|
cos 75°...cos 90° | ||||||||||||
Natural values of the trigonometric functions sine and cosine
|
sin 15°...30° | ||||||||||||
|
minute |
0 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
|
|
degree |
,0 |
,1 |
,2 |
,3 |
,4 |
,5 |
,6 |
,7 |
,8 |
,9 |
(1,0) |
|
|
15 |
25882 |
26050 |
26219 |
26387 |
26556 |
26724 |
26892 |
27060 |
27228 |
27396 |
27564 |
74 |
|
16 |
27564 |
27731 |
27899 |
28067 |
28234 |
28402 |
28569 |
28736 |
28903 |
29070 |
29237 |
73 |
|
17 |
29237 |
29404 |
29571 |
29737 |
29904 |
30071 |
30237 |
30403 |
30570 |
30736 |
30902 |
72 |
|
18 |
30902 |
31068 |
31233 |
31399 |
31565 |
31730 |
31896 |
32061 |
32227 |
32392 |
32557 |
71 |
|
19 |
32557 |
32722 |
32887 |
33051 |
33216 |
33381 |
33545 |
33710 |
33874 |
34038 |
34202 |
70 |
|
20 |
0,34202 |
34366 |
34530 |
34694 |
34857 |
35021 |
35184 |
35347 |
35511 |
35674 |
35837 |
69 |
|
21 |
35837 |
36000 |
36162 |
36325 |
36488 |
36650 |
36812 |
36975 |
37137 |
37299 |
37461 |
68 |
|
22 |
37461 |
37622 |
37784 |
37946 |
38107 |
38268 |
38430 |
38591 |
38752 |
38912 |
39073 |
67 |
|
23 |
39073 |
39234 |
39394 |
39555 |
39715 |
39875 |
40035 |
40195 |
40355 |
40514 |
40674 |
66 |
|
24 |
40674 |
40833 |
40992 |
41151 |
41310 |
41469 |
41628 |
41787 |
41945 |
42104 |
42262 |
65 |
|
25 |
42262 |
42420 |
42578 |
42736 |
42894 |
43051 |
43209 |
43366 |
43523 |
43680 |
43837 |
64 |
|
26 |
43837 |
43994 |
44151 |
44307 |
44464 |
44620 |
44776 |
44932 |
45088 |
45243 |
45399 |
63 |
|
27 |
45399 |
45554 |
45710 |
45865 |
46020 |
46175 |
46330 |
46484 |
46639 |
46793 |
46947 |
62 |
|
28 |
46947 |
47101 |
47255 |
47409 |
47562 |
47716 |
47860 |
48022 |
48175 |
48328 |
48481 |
61 |
|
29 |
48481 |
48634 |
48786 |
48938 |
49090 |
49242 |
49394 |
49546 |
49697 |
49849 |
50000 |
60 |
| |
(1,0) |
,9 |
,8 |
,7 |
,6 |
,5 |
,4 |
,3 |
,2 |
,1 |
,0 |
degree |
| |
60 |
54 |
48 |
42 |
36 |
30 |
24 |
18 |
12 |
6 |
0 |
minute |
|
cos 75°...60° | ||||||||||||
Natural values of the trigonometric functions sine and cosine
|
sin 30°...45° | ||||||||||||
|
minute |
0 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
|
|
degree |
,0 |
,1 |
,2 |
,3 |
,4 |
,5 |
,6 |
,7 |
,8 |
,9 |
(1,0) |
|
|
30 |
0,50000 |
50151 |
50303 |
50453 |
50603 |
50754 |
50904 |
51054 |
51204 |
51354 |
51504 |
59 |
|
31 |
51504 |
51653 |
51803 |
51952 |
52101 |
52250 |
52399 |
52547 |
52696 |
52844 |
52992 |
58 |
|
32 |
52992 |
53140 |
53288 |
53435 |
53583 |
53730 |
53877 |
54024 |
54171 |
54317 |
54464 |
57 |
|
33 |
54464 |
54610 |
54756 |
54902 |
55048 |
55194 |
55339 |
55484 |
55630 |
55775 |
55919 |
56 |
|
34 |
55919 |
56064 |
56208 |
56353 |
56497 |
56641 |
56784 |
56928 |
57071 |
57215 |
57358 |
55 |
|
35 |
57358 |
57501 |
57643 |
57786 |
57928 |
58070 |
58212 |
58354 |
58496 |
58637 |
58779 |
54 |
|
36 |
58779 |
58920 |
59061 |
59201 |
59342 |
59482 |
59622 |
59763 |
59902 |
60042 |
60182 |
53 |
|
37 |
60182 |
60321 |
60460 |
60599 |
60738 |
60876 |
61015 |
61153 |
61291 |
61429 |
61566 |
52 |
|
38 |
61566 |
61704 |
61841 |
61978 |
62115 |
62251 |
62388 |
62524 |
62660 |
62796 |
62932 |
51 |
|
39 |
62932 |
63068 |
63203 |
63338 |
63473 |
63608 |
63742 |
63877 |
64011 |
64145 |
64279 |
50 |
|
40 |
0,64279 |
64412 |
64546 |
64679 |
64812 |
64945 |
65077 |
65210 |
65342 |
65474 |
65606 |
49 |
|
41 |
65606 |
65738 |
65869 |
66000 |
66131 |
66262 |
66393 |
66523 |
66653 |
66783 |
66913 |
48 |
|
42 |
66913 |
67043 |
67172 |
67301 |
67430 |
67559 |
67688 |
67816 |
67944 |
68072 |
68200 |
47 |
|
43 |
68200 |
68327 |
68455 |
68582 |
68709 |
68835 |
68962 |
69088 |
69214 |
69340 |
69466 |
46 |
|
44 |
69466 |
69591 |
69717 |
69842 |
69966 |
70091 |
70215 |
70339 |
70463 |
70587 |
70711 |
45 |
| |
(1,0) |
,9 |
,8 |
,7 |
,6 |
,5 |
,4 |
,3 |
,2 |
,1 |
,0 |
degree |
| |
60 |
54 |
48 |
42 |
36 |
30 |
24 |
18 |
12 |
6 |
0 |
minute |
|
cos 60°...45° | ||||||||||||
Natural values of the trigonometric functions sine and cosine
|
sin 45°...60° | ||||||||||||
|
minute |
0 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
|
|
degree |
,0 |
,1 |
,2 |
,3 |
,4 |
,5 |
,6 |
,7 |
,8 |
,9 |
(1,0) |
|
|
45 |
0,70711 |
70834 |
70957 |
71080 |
71203 |
71325 |
71447 |
71569 |
71691 |
71813 |
71934 |
44 |
|
46 |
71934 |
72055 |
72176 |
72297 |
72417 |
72537 |
72657 |
72777 |
72897 |
73016 |
73135 |
43 |
|
47 |
73135 |
73254 |
73373 |
73491 |
73610 |
73728 |
73846 |
73963 |
74080 |
74198 |
74314 |
42 |
|
48 |
74314 |
74431 |
74548 |
74664 |
74780 |
74896 |
75011 |
75126 |
75241 |
75356 |
75471 |
41 |
|
49 |
75471 |
75585 |
75700 |
75813 |
75927 |
76041 |
76154 |
76267 |
76380 |
76492 |
76604 |
40 |
|
50 |
0,76604 |
76717 |
76828 |
76940 |
77051 |
77162 |
77273 |
77384 |
77494 |
77605 |
77715 |
39 |
|
51 |
77715 |
77824 |
77934 |
78043 |
78152 |
78261 |
78369 |
78478 |
78586 |
78694 |
78801 |
38 |
|
52 |
78801 |
78908 |
79016 |
79122 |
79229 |
79335 |
79441 |
79547 |
79653 |
79758 |
79864 |
37 |
|
53 |
79864 |
79968 |
80073 |
80178 |
80282 |
80386 |
80489 |
80593 |
80696 |
80799 |
80902 |
36 |
|
54 |
80902 |
81004 |
81106 |
81208 |
81310 |
81412 |
81513 |
81614 |
81714 |
81815 |
81915 |
35 |
|
55 |
81915 |
82015 |
82115 |
82214 |
82314 |
82413 |
82511 |
82610 |
82708 |
82806 |
82904 |
34 |
|
56 |
82904 |
83001 |
83098 |
83195 |
83292 |
83389 |
83485 |
83581 |
83676 |
83772 |
83867 |
33 |
|
57 |
83867 |
83962 |
84057 |
84151 |
84245 |
84339 |
84433 |
84526 |
84619 |
84712 |
84805 |
32 |
|
58 |
84805 |
84897 |
84989 |
85081 |
85173 |
85264 |
85355 |
85446 |
85536 |
85627 |
85717 |
31 |
|
59 |
85717 |
85806 |
85896 |
85985 |
86074 |
86163 |
86251 |
86340 |
86427 |
86515 |
86603 |
30 |
| |
(1,0) |
,9 |
,8 |
,7 |
,6 |
,5 |
,4 |
,3 |
,2 |
,1 |
,0 |
degree |
| |
60 |
54 |
48 |
42 |
36 |
30 |
24 |
18 |
12 |
6 |
0 |
minute |
|
cos 30°...45° | ||||||||||||
Natural values of the trigonometric functions sine and cosine sin
|
sin 60°...75° | ||||||||||||
|
minute |
0 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
|
|
degree |
,0 |
,1 |
,2 |
,3 |
,4 |
,5 |
,6 |
,7 |
,8 |
,9 |
(1,0) |
|
|
60 |
0,86603 |
86690 |
86777 |
86863 |
86949 |
87036 |
87121 |
87207 |
87292 |
87377 |
87462 |
29 |
|
61 |
87462 |
87546 |
87631 |
87715 |
87798 |
87882 |
87965 |
88048 |
88130 |
88213 |
88295 |
28 |
|
62 |
88295 |
88377 |
88458 |
88539 |
88620 |
88701 |
88782 |
88862 |
88942 |
89021 |
89101 |
27 |
|
63 |
89101 |
89180 |
89259 |
89337 |
89415 |
89493 |
89571 |
89649 |
89726 |
89803 |
89879 |
26 |
|
64 |
89879 |
89956 |
90032 |
90108 |
90183 |
90250 |
90334 |
90408 |
90483 |
90557 |
90631 |
25 |
|
65 |
90631 |
90704 |
90778 |
90851 |
90924 |
90996 |
91068 |
91140 |
91212 |
91283 |
91355 |
24 |
|
66 |
91355 |
91425 |
91496 |
91566 |
91636 |
91706 |
91775 |
91845 |
91914 |
91982 |
92050 |
23 |
|
67 |
92050 |
92119 |
92186 |
92254 |
92321 |
92388 |
92455 |
92521 |
92587 |
92653 |
92718 |
22 |
|
68 |
92718 |
92784 |
92849 |
92913 |
92978 |
93042 |
93106 |
93169 |
93232 |
93295 |
93358 |
21 |
|
69 |
93358 |
93420 |
93483 |
93544 |
93606 |
93667 |
93728 |
93789 |
93849 |
93909 |
93969 |
20 |
|
70 |
0,93969 |
94029 |
94088 |
94147 |
94206 |
94264 |
94322 |
94380 |
94438 |
94495 |
94552 |
19 |
|
71 |
94552 |
94609 |
94665 |
94721 |
94777 |
94832 |
94888 |
94943 |
94997 |
95052 |
95106 |
18 |
|
72 |
95106 |
95159 |
95213 |
95266 |
95319 |
95372 |
95424 |
95476 |
95528 |
95579 |
95630 |
17 |
|
73 |
95630 |
95681 |
95732 |
95782 |
95832 |
95882 |
95931 |
95981 |
96029 |
96078 |
96126 |
16 |
|
74 |
96126 |
96174 |
96222 |
96269 |
96316 |
96363 |
96410 |
96456 |
96502 |
96547 |
96593 |
15 |
| |
(1,0) |
,9 |
,8 |
,7 |
,6 |
,5 |
,4 |
,3 |
,2 |
,1 |
,0 |
degree |
| |
60 |
54 |
48 |
42 |
36 |
30 |
24 |
18 |
12 |
6 |
0 |
minute |
|
cos 15°...30° | ||||||||||||
Natural values of the trigonometric functions sine and cosine
|
sin 75°...90° | ||||||||||||
|
minute |
0 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 | |
|
degree |
,0 |
,1 |
,2 |
,3 |
,4 |
,5 |
,6 |
,7 |
,8 |
,9 |
(1,0) |
|
|
75 |
96593 |
96638 |
96682 |
96727 |
96771 |
96815 |
96858 |
96902 |
96945 |
96987 |
97030 |
14 |
|
76 |
97030 |
97072 |
97113 |
97155 |
97196 |
97237 |
97278 |
97318 |
97358 |
97398 |
97437 |
13 |
|
77 |
97437 |
97476 |
97515 |
97553 |
97592 |
97630 |
97667 |
97705 |
97742 |
97778 |
97815 |
12 |
|
78 |
97815 |
97851 |
97887 |
97922 |
97958 |
97992 |
98027 |
98061 |
98096 |
98129 |
98163 |
11 |
|
79 |
98163 |
98196 |
98229 |
98261 |
98294 |
98325 |
98357 |
98389 |
98420 |
98450 |
98481 |
10 |
|
80 |
0,98481 |
98511 |
98541 |
98570 |
98600 |
98629 |
98657 |
98686 |
98714 |
98741 |
98769 |
9 |
|
81 |
98769 |
98796 |
98823 |
98849 |
98876 |
98902 |
98927 |
98953 |
98978 |
99002 |
99027 |
8 |
|
82 |
99027 |
99051 |
99075 |
99098 |
99122 |
99144 |
99167 |
99189 |
99211 |
99233 |
99255 |
7 |
|
83 |
99255 |
99276 |
99297 |
99317 |
99337 |
99357 |
99377 |
99396 |
99415 |
99434 |
99452 |
6 |
|
84 |
99452 |
99470 |
99488 |
99506 |
99523 |
99540 |
99556 |
99572 |
99588 |
99604 |
99619 |
5 |
|
85 |
99619 |
99635 |
99649 |
99664 |
99678 |
99692 |
99705 |
99731 |
99731 |
99744 |
99756 |
4 |
|
86 |
99756 |
99768 |
99780 |
99792 |
99803 |
99813 |
99824 |
99834 |
99844 |
99854 |
99863 |
3 |
|
87 |
99863 |
99872 |
99881 |
99889 |
99897 |
99905 |
99912 |
99919 |
99926 |
99933 |
99939 |
2 |
|
88 |
99939 |
99945 |
99951 |
99956 |
99961 |
99966 |
99979 |
99974 |
99978 |
99982 |
99985 |
1 |
|
89 |
99985 |
99988 |
99990 |
99993 |
99995 |
99996 |
99998 |
99999 |
99999 |
1.00000 |
1.00000 |
0 |
| |
(1,0) |
,9 |
,8 |
,7 |
,6 |
,5 |
,4 |
,3 |
,2 |
,1 |
,0 |
degree |
| |
60 |
54 |
48 |
42 |
36 |
30 |
24 |
18 |
12 |
6 |
0 |
minute |
|
cos 15°...0° | ||||||||||||
Table 2 Resistances and weights of copper wires
|
Diameter |
Cross section |
Resistance per km with 15°(288 k) |
Length of a wire of 1 W |
Weight per km |
Length of a wire of 1 kg |
|
mm |
mm2 |
W |
m |
kg |
m |
|
0,1 |
0,0079 |
2215 |
0,4514 |
0,070 |
14306 |
|
0,2 |
0,0314 |
553,9 |
1,856 |
0,280 |
3577 |
|
0,3 |
0,0707 |
246,2 |
4,062 |
0,629 |
1590 |
|
0,4 |
0,1257 |
138,5 |
7,222 |
1,118 |
894,1 |
|
0,5 |
0,1964 |
88,62 |
11,28 |
1,748 |
572,2 |
|
0,6 |
0,2827 |
61,54 |
16,25 |
2,516 |
397,4 |
|
0,7 |
0,3848 |
45,21 |
22,12 |
3,425 |
292,0 |
|
0,8 |
0,5026 |
34,62 |
28,89 |
4,474 |
223,5 |
|
0,9 |
0,6362 |
27,35 |
36,56 |
5,662 |
176,6 |
|
1,0 |
0,7854 |
22,15 |
45,14 |
6,990 |
143,1 |
|
1,1 |
0,9503 |
18,31 |
54,62 |
8,458 |
118,2 |
|
1,2 |
1,1310 |
15,38 |
65,00 |
10,07 |
99,35 |
|
1,3 |
1,3273 |
13,11 |
76,28 |
11,81 |
84,65 |
|
1,4 |
1,5394 |
11,30 |
88,47 |
13,70 |
72,99 |
|
1,5 |
1,7671 |
9,846 |
101,6 |
15,73 |
63,58 |
|
1,6 |
2,0106 |
8,654 |
115,6 |
17,89 |
55,88 |
|
1,7 |
2,2698 |
7,666 |
130,5 |
20,20 |
49,50 |
|
1,8 |
2,5447 |
6,838 |
146,2 |
22,65 |
44,15 |
|
1,9 |
2,8353 |
6,137 |
162,9 |
25,23 |
39,63 |
|
2,0 |
3,1416 |
5,539 |
180,6 |
27,96 |
35,77 |
|
2,1 |
3,4636 |
5,024 |
199,1 |
30,83 |
32,44 |
|
2,2 |
3,8013 |
4,577 |
218,5 |
33,83 |
29,56 |
|
2,3 |
4,1548 |
4,188 |
238,8 |
36,98 |
27,04 |
|
2,4 |
4,5239 |
3,846 |
260,0 |
40,26 |
24,84 |
|
2,5 |
4,9087 |
3,545 |
282,1 |
43,69 |
22,89 |
|
2,6 |
5,3093 |
3,277 |
305,1 |
47,25 |
21,16 |
|
2,7 |
5,7256 |
3,039 |
329,1 |
50,96 |
19,62 |
|
2,8 |
6,1575 |
2,826 |
353,9 |
54,80 |
18,25 |
|
2,9 |
6,6052 |
2,634 |
379,6 |
58,79 |
17,01 |
|
3,0 |
7,0686 |
2,462 |
406,2 |
62,91 |
15,90 |
|
3,1 |
7,5477 |
2,305 |
433,8 |
67,17 |
14,89 |
|
3,2 |
8,0425 |
2,164 |
462,2 |
71,58 |
13 79 |
|
3,3 |
8,5530 |
2,034 |
491,6 |
76,12 |
13,14 |
|
3,4 |
9,0792 |
1,916 |
521,8 |
80,80 |
12,38 |
|
3,5 |
9,6211 |
1,809 |
552,9 |
85,63 |
11,68 |
|
3,6 |
10,1790 |
1,709 |
585,0 |
90,59 |
11,04 |
|
3,7 |
10,752 |
1,618 |
617,9 |
95,69 |
10,45 |
|
3,8 |
11,341 |
1,534 |
651,8 |
100,9 |
9,907 |
|
3,9 |
11,946 |
1,457 |
686,5 |
106,3 |
9,406 |
|
4,0 |
12,566 |
1,385 |
722,2 |
111,8 |
8,941 |
|
4,1 |
13,203 |
1,318 |
758,8 |
117,5 |
8,510 |
|
4,2 |
13,854 |
1,256 |
796,2 |
123,3 |
8,110 |
|
4,3 |
14,522 |
1,198 |
834,6 |
129,2 |
7,737 |
|
4,4 |
15,205 |
1,144 |
873,9 |
135,3 |
7,389 |
|
4,5 |
15,904 |
1,094 |
914,0 |
141,5 |
7,065 |
|
4,6 |
16,619 |
1,047 |
955,1 |
147,9 |
6,761 |
|
4,7 |
17,349 |
1,003 |
997,1 |
154,4 |
6,476 |
|
4,8 |
18,096 |
0,9616 |
1040 |
161,1 |
6,209 |
|
4,9 |
18,857 |
0,9227 |
1084 |
167,8 |
5,958 |
|
5,0 |
19,635 |
0,8862 |
1128 |
174,7 |
5,722 |
|
5,1 |
20,428 |
0,8518 |
1174 |
181,8 |
5,500 |
|
5,2 |
21,237 |
0,8193 |
1221 |
189,0 |
5,291 |
|
5,3 |
22,062 |
0,7887 |
1268 |
196,4 |
5,093 |
|
5,4 |
22,902 |
0,7598 |
1316 |
203,8 |
4,906 |
|
5,5 |
23,758 |
0,7324 |
1365 |
211,5 |
4,729 |
|
5,6 |
24,630 |
0,7065 |
1416 |
219,2 |
4,562 |
|
5,7 |
25,518 |
0,6819 |
1467 |
227,1 |
4,403 |
|
5,8 |
26,421 |
0,6586 |
1518 |
235,1 |
4,253 |
|
5,9 |
27,340 |
0,6463 |
1571 |
243,3 |
4,110 |
|
6,0 |
28,274 |
0,6154 |
1625 |
251,6 |
3,974 |
|
6,1 |
29,225 |
0,5974 |
1680 |
260,1 |
3,845 |
|
6,2 |
30,191 |
0,5763 |
1735 |
268,7 |
3,722 |
|
6,3 |
31,172 |
0,5582 |
1792 |
277,4 |
3,604 |
|
6,4 |
32,170 |
0,5409 |
1849 |
286,3 |
3,493 |
|
6,5 |
33,183 |
0,5244 |
1907 |
295,3 |
3,386 |
|
6,6 |
34,212 |
0,5086 |
1966 |
304,5 |
3,284 |
|
6,7 |
35,257 |
0,4935 |
2026 |
313,8 |
3,187 |
|
6,8 |
36,317 |
0,4791 |
2087 |
323,2 |
3,094 |
|
6,9 |
37,393 |
0,4653 |
2149 |
332,8 |
3,005 |
Table 3 Specific resistance and conductivity of essential materials at 20° C (193 K)
|
Material |
Spec. Resistance |
Conductivity |
| |
|
|
|
Aluminium, soft |
0,028 |
36 |
|
Lead |
0,2 |
5 |
|
Gold |
0,022 |
45 |
|
Copper E-Cu, soft |
0,01754 |
57 |
|
Brass Ms 58 |
0,059 |
17 |
|
Brass Ms 63 |
0,071 |
14 |
|
Nickel silver NiMs |
0,5...0,15 |
2,0...6,7 |
|
Platinum |
0,098 |
10,2 |
|
Mercury |
0,960 |
1,042 |
|
Silver |
0,01629 |
61,4 |
|
Steel, ingot iron |
0,12 |
8 |
|
Grey iron |
1 |
1 |
|
Tungsten |
0,059 |
17 |
|
Zinc |
0,062 |
16 |
| |
Resistance alloy: |
|
|
Chrome nickel |
1...1,2 |
1...0,83 |
|
Constantan (WM 50) |
0,5 |
2 |
|
Manganin |
0,4 |
2,5 |
|
Niccolite |
0,5 |
2 |
|
Al-Cr-Steel |
1,4 |
0,7 |
|
Arc lamp carbon |
13...100 |
0,08...0,01 |
Table 4 Temperature coefficient
|
Material |
Temperature coefficient of an electrical resistance between 0° and 100° C (173 and 273 K) |
|
Aluminium |
+0,0037 |
|
Aluminium bronze |
+0,001 |
|
Lead |
+0,00417 |
|
Iron |
+0,0045 |
|
Electron | |
|
Constantan |
0,00005 |
|
Copper |
+0,0043 |
|
Manganin |
+0,00001 |
|
Brass |
+0,0015 |
|
Molybdenum |
+0,0043 |
|
Nickel silver |
+0,00007 |
|
Nickel |
+0,0041 |
|
Niccolite |
+0,00022 |
|
Platinum |
+0,0039 |
|
Platinum-Rhodium (10 % Rh.) |
+0,0017 |
|
Mercury |
+0,00090 |
|
Silver |
+0,0036 |
|
Steel |
+0,0045... 0,005 |
|
Tantalum |
+0,0034 |
|
Bismuth |
+0,0037 |
|
Tungsten |
+0,004-1 |
|
Zinc |
+0,0039 |
|
Tin |
+0,0042 |
Table 5 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for lines with copper conductor and plastic, silicone-rubber or glass-silk insulation
|
Conductor cross-sectional area |
Current-carrying capacity |
Rated current of overcurrent protection device |
||||||
| |
A |
A | ||||||
|
mm2 |
1 |
2 |
3 |
4 |
1 |
2 |
3 |
4 |
|
0,5 |
12 |
10 |
9 |
8 |
10 |
10 |
6 |
6 |
|
0,75 |
16 |
13 |
12 |
11 |
16 |
10 |
10 |
10 |
|
1,0 |
20 |
17 |
15 |
14 |
20 |
16 |
10 |
10 |
|
1,5 |
26 |
22 |
20 |
18 |
25 |
20 |
20 |
16 |
|
2,5 |
36 |
31 |
27 |
24 |
36 |
25 |
25 |
20 |
|
4 |
50 |
43 |
38 |
34 |
50 |
36 |
36 |
25 |
|
6 |
63 |
54 |
50 |
46 |
63 |
50 |
50 |
36 |
|
10 |
86 |
74 |
64 |
59 |
80 |
63 |
63 |
50 |
|
16 |
117 |
101 |
87 |
80 |
100 |
100 |
80 |
80 |
|
25 |
155 |
133 |
116 |
105 |
125 |
125 |
100 |
100 |
|
35 |
192 |
165 |
144 |
130 |
160 |
160 |
125 |
125 |
|
50 |
240 |
206 |
180 |
163 |
224 |
200 |
160 |
160 |
|
70 |
300 |
259 |
225 |
204 |
300 |
250 |
224 |
200 |
|
95 |
365 |
314 |
274 |
248 |
355 |
300 |
250 |
224 |
|
120 |
425 |
366 |
319 |
289 |
425 |
355 |
300 |
250 |
|
150 |
480 |
413 |
360 |
326 |
425 |
355 |
355 |
300 |
|
185 |
542 |
466 |
406 |
368 |
500 |
425 |
355 |
355 |
|
240 |
640 |
551 |
480 |
435 |
600 |
500 |
425 |
425 |
|
300 |
735 |
633 |
551 |
500 |
600 |
600 |
500 |
500 |
These values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems).Pay attention to the current-carrying capacity factors according to the Tables 9 to 12.
Table 6 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for lines with aluminium conductor and plastic, silicone-rubber and glass-silk insulation
|
Conductor cross- sectional area |
Current-carrying capacity |
Rated current of overcurrent protection device |
||||||
| |
A |
A | ||||||
| |
for number of cores carrying current in operation |
|||||||
|
mm2 |
1 |
2 |
3 |
4 |
1 |
2 |
3 |
4 |
|
2,5 |
27 |
23 |
30 |
18 |
25 |
20 |
20 |
16 |
|
4 |
37 |
32 |
28 |
24 |
36 |
25 |
25 |
20 |
|
6 |
50 |
43 |
37 |
34 |
50 |
36 |
36 |
25 |
|
10 |
67 |
57 |
50 |
46 |
63 |
50 |
50 |
36 |
|
16 |
90 |
77 |
67 |
61 |
80 |
63 |
63 |
50 |
|
25 |
120 |
103 |
90 |
81 |
100 |
100 |
80 |
80 |
|
35 |
148 |
127 |
111 |
100 |
125 |
125 |
100 |
100 |
|
50 |
187 |
161 |
140 |
127 |
160 |
160 |
125 |
125 |
|
70 |
231 |
200 |
173 |
154 |
200 |
200 |
160 |
125 |
|
95 |
282 |
243 |
212 |
191 |
250 |
224 |
200 |
160 |
|
120 |
328 |
283 |
246 |
223 | | |
224 |
200 |
|
150 |
376 |
325 |
283 |
249 |
355 |
300 |
250 |
224 |
|
185 |
480 |
370 |
322 |
292 |
425 |
355 |
300 |
250 |
|
240 |
502 |
492 |
376 |
342 |
500 |
425 |
355 |
300 |
|
300 |
578 |
497 |
433 |
395 |
500 |
425 |
425 |
355 |
Use:
With more than one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device are reduced as stated above.The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems).
Pay attention to the current-carrying capacity factors according to the tables 9 to 12.
Table 7 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for rubber-insulated lines with copper conductor
|
Conductor cross-sectional area |
Current-carrying capacity |
Rated current of overcurrent protection device |
||||||
| |
A |
A | ||||||
| |
for number of cores carrying current in operation |
|||||||
|
mm2 |
1 |
2 |
3 |
4 |
1 |
2 |
3 |
4 |
|
0,5 |
11 |
9 |
9 |
8 |
10 |
6 |
6 |
6 |
|
0,75 |
15 |
12 |
11 |
10 |
10 |
10 |
10 |
10 |
|
1 |
19 |
16 |
14 |
13 |
16 |
16 |
10 |
10 |
|
1,5 |
24 |
21 |
19 |
17 |
20 |
20 |
16 |
16 |
|
2,5 |
34 |
29 |
25 |
23 |
25 |
25 |
25 |
20 |
|
4 |
47 |
41 |
36 |
32 |
36 |
36 |
36 |
25 |
|
6 |
60 |
51 |
47 |
43 |
50 |
50 |
36 |
36 |
|
10 |
82 |
70 |
61 |
56 |
80 |
63 |
50 |
50 |
|
16 |
111 |
96 |
83 |
76 |
100 |
80 |
80 |
63 |
|
25 |
147 |
126 |
110 |
100 |
125 |
125 |
100 |
100 |
|
35 |
182 |
157 |
137 |
124 |
160 |
125 |
125 |
100 |
|
50 |
229 |
196 |
171 |
155 |
224 |
160 |
160 |
125 |
|
70 |
285 |
246 |
214 |
194 |
250 |
224 |
200 |
160 |
|
95 |
347 |
300 |
260 |
236 |
300 |
300 |
250 |
224 |
|
120 |
404 |
348 |
303 |
274 |
355 |
300 |
300 |
250 |
|
150 |
456 |
393 |
342 |
310 |
425 |
355 |
300 |
300 |
|
185 |
515 |
442 |
385 |
350 |
500 |
425 |
355 |
300 |
|
240 |
608 |
523 |
456 |
413 |
600 |
500 |
425 |
355 |
|
300 |
700 |
602 |
523 |
475 |
600 |
600 |
500 |
425 |
Use:
With more then one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device are reduced as stated above.The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems).
Pay attention to the current-carrying capacity factors according to the Tables 9 to 12.
Table 8
Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for rubber-insulated lines with aluminium conductor
|
Conductor cross-sectional area |
Current-carrying capacity |
Rated current of overcurrent protection device |
||||||
| |
A |
A | ||||||
| |
for number of cores carrying current in operation |
|||||||
|
mm2 |
1 |
2 |
3 |
4 |
1 |
2 |
3 |
4 |
|
2,5 |
26 |
22 |
19 |
17 |
25 |
20 |
16 |
16 |
|
4 |
35 |
30 |
27 |
23 |
25 |
25 |
25 |
20 |
|
6 |
47 |
41 |
35 |
32 |
36 |
36 |
25 |
25 |
|
10 |
63 |
54 |
47 |
44 |
63 |
50 |
36 |
36 |
|
16 |
85 |
73 |
64 |
58 |
80 |
63 |
63 |
50 |
|
25 |
144 |
98 |
85 |
77 |
100 |
80 |
80 |
63 |
|
35 |
141 |
121 |
105 |
95 |
125 |
100 |
100 |
80 |
|
50 |
178 |
153 |
133 |
121 |
160 |
125 |
125 |
100 |
|
70 |
220 |
190 |
164 |
146 |
200 |
160 |
160 |
125 |
|
95 |
268 |
231 |
202 |
182 |
250 |
224 |
200 |
160 |
|
120 |
312 |
269 |
234 |
212 |
300 |
250 |
224 |
200 |
|
150 |
358 |
309 |
269 |
236 |
355 |
300 |
250 |
224 |
|
185 |
408 |
351 |
306 |
278 |
355 |
300 |
300 |
250 |
|
240 |
477 |
410 |
358 |
325 |
425 |
355 |
355 |
300 |
|
300 |
550 |
472 |
412 |
374 |
500 |
425 |
355 |
355 |
Use:
With more than one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device is reduced as sated above.The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems).
Pay attention to the current-carrying capacity factors according to the Tables 9 to 12.
Current-carrying capacity factors
These are factors by which the values of current-carrying capacity given in the Tables 6 to 8 have to be multiplied when special conditions are given.
These conditions may be:
- bundled lines installed freely in air
- bundled lines installed in pipes or conduit subways
- multicore lines with more than 4 conductors (cores)
- multicore lines installed in a piled-up arrangement which are loaded at the same time
- ambient temperatures which deviate from 25° C (298 K) and are higher
If multicore lines are fastened individually by means of spacing clips side by side, the current-carrying capacity factor of 0,9 is applicable irrespective of the number of lines placed side by side.
In the case of ambient temperatures higher than 25° C (298 K), the limiting temperature for the conductor of the line used must be taken into consideration.
There are limiting temperatures of conductors
· of 60°C (333 K),
· of 70°C (343 K) and
· of 180°C (453 K).
If several current-carrying capacity factors are applicable, then the values of current-carrying capacity given in the Tables 6 to 8 must be multiplied by all of the applicable factors.
The rated current of the overcurrent protection device must be specified according to the newly calculated current-carrying capacity when factors of the current-carrying capacity are used.
In this event, the rated current of the overcurrent protection device must be below the value of the newly calculated current-carrying capacity of the line.
Table 9 Current-carrying capacity factors for single-core lines bunched and laid out as open-wire line, in pipe trench or service duct or for multi-core lines with more than 4 cores
|
Number of lines or cores |
Current-carrying capacity factor |
|
2 |
0,85 |
|
3 |
0,75 |
|
4 |
0,68 |
|
5 |
0,62 |
|
6 |
0,58 |
|
7 |
0,55 |
|
8 |
0,53 |
|
9 |
0,50 |
|
10 |
0,48 |
|
15 |
0,42 |
|
20 |
0,38 |
|
25 |
0,35 |
|
30 |
0,33 |
|
35 |
0,31 |
|
40 |
0,30 |
|
45 |
0,29 |
|
50 |
0,28 |
Table 10 Current-carrying capacity factors for bunched multi-core lines
|
Number of multi-core lines |
Current-carrying capacity factors in case of |
||
| |
open-air bunching |
direct side-by side arrangement on walls or ceilings |
bunching in pipe trench or service duct |
|
2 |
0,89 |
0,83 |
0,81 |
|
3 |
0,80 |
0,76 |
0,75 |
|
4 |
0,73 |
0,73 |
0,69 |
|
5 |
0,69 |
0,71 |
0,65 |
|
6 |
0,66 |
0,70 |
0,62 |
|
7 |
0,63 |
0,69 |
0,60 |
|
8 |
0,61 |
0,69 |
0,58 |
|
9 |
0,59 |
0,68 |
0,56 |
|
10 |
0,57 |
0,68 |
0,55 |
|
15 |
0,50 |
0,66 |
0,49 |
|
20 |
0,47 |
0,64 |
0,46 |
|
25 |
0,44 |
0,62 |
0,43 |
|
30 |
0,42 |
0,60 |
0,41 |
|
35 |
0,40 |
0,59 |
0,40 |
|
40 |
0,39 |
0,58 |
0,39 |
Table 11 Factors of current-carrying capacity in dependence of constant ambient temperatures for lines with a conductor limiting temperature in continuous operation of 60° C (333 K) and 70° C (343 K)
|
Ambient temperature |
Current-carrying with a conductor capacity factors for lines limiting temperature of | |||
|
°C |
(K) |
60°C (333 K) | |
70°C (343 K) |
|
5 |
(278) | |
1,25 | |
|
10 |
(283) | |
1,19 | |
|
15 |
(288) | |
1,13 | |
|
20 |
(293) | |
1,07 | |
|
25 |
(298) | |
1,00 | |
|
30 |
(303) |
0,92 | |
0,94 |
|
35 |
(308) |
0,83 | |
0,87 |
|
40 |
(313) |
0,74 | |
0,80 |
|
45 |
(318) |
0,63 | |
0,72 |
|
50 |
(323) |
0,51 | |
0,64 |
|
55 |
(328) |
0,36 | |
0,55 |
|
60 |
(333) |
- | |
0,46 |
|
65 |
(338) |
- | |
0,37 |
Table 12 Factors of current-carrying capacity in dependence of constant ambient temperatures for lines with a conductor limiting temperature of 180°C
|
Ambient temperature |
Current-carrying capacity factor |
Ambient temperature |
Current-carrying capacity factor | ||
|
°C |
(K) |
|
°C |
(K) |
|
|
55 |
(328) |
1,00 |
120 |
(393) |
0,69 |
|
60 |
(333) |
0,98 |
130 |
(403) |
0,63 |
|
70 |
(343) |
0,94 |
140 |
(413) |
0,56 |
|
80 |
(353) |
0,90 |
150 |
(423) |
0,49 |
|
90 |
(363) |
0,85 |
160 |
(433) |
0,40 |
|
100 |
(373) |
0,80 |
170 |
(443) |
0,28 |
|
110 |
(383) |
0,75 |
175 |
(448) |
0,20 |
Example:
A seven-core plastic-insulated line with copper conductor o and a conductor rated cross-sectional area of 1,5 mm is to be installed at a constant ambient temperature of 35°C (308 K). What is the current-carrying capacity of the line with a conductor limiting temperature of 70°C (343 K)?
Solution:
According to Table 5, the current-carrying capacity of one core is 26 A.For 7 cores, the factor of current-carrying capacity is 0,55; at a constant ambient temperature of 35°G (308 K) the factor of current-carrying capacity is 0,87 (conductor limiting temperature 70°C or 343 K) according to Table 10.
Actual current-carrying capacity
26 A · 0,55 · 0,87 = 12 A.
Rated current for the overcurrent protection device is 10 A.
Table 13 Limiting temperature for conductors
|
Type of cable |
Conductor limiting temperature | |||
| |
°C |
(K) |
| |
| |
continuously |
at short-circuit | ||
|
1-kV plastic cable |
70 |
(343) |
180 |
(453) |
|
10-,20-,30-kV plastic cable |
70 |
(343) |
200 |
(473) |
|
1-kV solid-type cable |
80 |
(353) |
200 |
(473) |
|
10-kV solid-type cable |
55 |
(328) |
165 |
(438) |
|
20-kV solid-type cable |
55 |
(328) |
145 |
(418) |
|
30-kV solid-type cable |
45 |
(318) |
130 |
(408) |
When selecting cables with respect to their current-carrying capacity, the following factors must be taken into consideration:
- The thermal resistance of the soil; it is dependent on the type of soil and the moisture content of the soil.- Loaded cables, heating lines and the like installed in close vicinity.
- Heat retention due to air cushions, protective covers, in ducts, pipes or nests of tubes.
Table 14 Current-carrying capacity of 1-kV solid-type cables for individual installation, with reduced solid sheath and fully saturated impregnation
|
Rated cross-sectional area of conductor |
Single -core cables |
Two-core cables |
Three-core and four-core cables | |||
|
mm2 |
Cu |
Al |
Cu |
Al |
Cu |
Al |
|
1,5 |
- |
- |
30 |
- |
25 |
- |
|
2,5 |
- |
- |
35 |
30 |
30 |
25 |
|
4 |
- |
- |
45 |
35 |
40 |
30 |
|
6 |
- |
- |
60 |
45 |
55 |
40 |
|
10 |
- |
- |
85 |
65 |
75 |
60 |
|
25 |
- |
- |
145 |
115 |
125 |
100 |
|
50 |
285 |
230 |
215 |
175 |
185 |
150 |
|
70 |
350 |
280 |
260 |
210 |
225 |
180 |
|
120 |
495 |
395 |
350 |
280 |
315 |
250 |
|
185 |
630 |
510 |
450 |
360 |
410 |
330 |
|
240 |
740 |
590 |
525 |
420 |
475 |
380 |
|
300 |
840 |
675 |
590 |
470 |
545 |
435 |
|
400 |
1000 |
800 |
700 |
565 |
645 |
515 |
|
500 |
1140 |
910 |
- |
- |
- |
- |
|
1000 |
1740 |
1390 |
- |
- |
- |
- |
Table 15 Current-carrying capacity of three unarmoured single-core solid-type cables with lead sheath, fully impregnated, in three-phase systems, separately lying side by side
|
Nominal cross-section of the conductor |
1 kV | |
| |
Current - carrying capacity in A | |
|
mm2 |
Cu |
Al |
|
50 |
250 |
200 |
|
70 |
300 |
240 |
|
120 |
410 |
330 |
|
185 |
510 |
405 |
|
240 |
575 |
460 |
|
300 |
640 |
510 |
|
400 |
725 |
580 |
|
500 |
790 |
630 |
|
1000 |
950 |
805 |
The values of Table 15 are applicable to cables lying side by side in a clearance of about 7 cm, in consideration of the metallic sheath losses in case of cable sheaths short-circuited at both cable ends.
The current-carrying capacity of three unarmoured single-core cables with A1-sheath separately lying side by side amounts to 90 % of the values according to Table 15.
Table 16 Current-carrying capacity of three unarmoured single-core solid-type cables with lead sheath, non-draining, in three-phase systems, separately lying side by side
|
Nominal cross-section of the conductor |
1 kV | |
|
mm2 |
Current-carrying capacity in A | |
| |
Cu |
Al |
|
50 |
250 |
200 |
|
70 |
300 |
240 |
|
120 |
410 |
330 |
|
185 |
510 |
405 |
|
240 |
575 |
460 |
|
300 |
640 |
510 |
|
400 |
725 |
580 |
|
500 |
790 |
630 |
|
1000 |
950 |
805 |
The values of Table 16 are applicable to cables lying side by side in a clearance of about 7 cm, in consideration of the metallic sheath losses in case of cable sheaths short-circuited at both cable ends.
The current-carrying capacity of three unarmoured single-core non-draining cables with Al-sheath separately lying side by side amounts to 90 % of the values according to Table 16.
The current-carrying capacity of three touching single-core non-draining cables with Al-sheath arranged in a triangle amounts to 105 % of the values according to Table 16.
Table 17 Current-carrying capacity of 1-kV-plastic cables
|
Nominal cross-section of the conductor |
Single-core cables |
Two-core cables |
Three- and four-core cables | |||
| |
Current-carrying capacity |
in A |
| |||
|
mm2 |
Cu |
Al |
Cu |
Al |
Cu |
Al |
|
1,5 |
- |
- |
25 |
- |
20 |
- |
|
2,5 |
- |
- |
30 |
25 |
25 |
20 |
|
4 |
- |
- |
40 |
50 |
35 |
25 |
|
6 |
- |
- |
55 |
40 |
45 |
35 |
|
10 |
- |
- |
75 |
55 |
65 |
50 |
|
25 |
- |
- |
120 |
95 |
110 |
90 |
|
50 |
260 |
210 |
- |
- |
165 |
125 |
|
70 |
315 |
250 |
- |
- |
200 |
155 |
|
120 |
445 |
360 |
- |
- |
285 |
220 |
|
185 |
570 |
455 |
- |
- |
370 |
285 |
|
240 |
665 |
530 |
- |
- |
430 |
335 |
|
300 |
755 |
605 |
- |
- |
- |
- |
|
400 |
880 |
720 |
- |
- |
- |
- |
|
500 |
990 |
800 |
- |
- |
- |
- |
The carrying capacity specified in the Tables 14...17 is to be reduced to the following specified percentages in case of deviations from the mentioned conditions of installation.
Table 18 Reduction in case of bunched multi-core cables in three-phase systems and cables in direct current systems
|
Number of cables in the trench | |
2 |
3 |
4 |
5 |
6 |
8 |
10 |
|
Carrying capacity in |
% |
90 |
80 |
75 |
70 |
65 |
62 |
60 |
The carrying capacity of cables under protective hoods diminishes to 90 % of the values found out in application of other reductions (see Tables 18...25).
The reductions are applicable to cables lying side by side in a clearance of about 7 cm.
Table 19 Reduction in case of bunched single-core cables in three-phase systems
|
Number of systems in the trench |
2 |
3 |
4 |
|
Carrying capacity in % |
80 |
75 |
70 |
The reductions are applicable to single-core cables lying side by side in a clearance of about 7 cm.
The values of the Tables 20 and 21 are applicable to cables in unarmoured cement pipes in the earth with a clear interior diameter of about 150 mm and 20 mm wall thickness in an horizontal arrangement with reciprocal touch and an outer diameter of 50 mm.
Table 20 Reduction in case of multi-core cables and single-wire cables in single pipes bunched in a triangle
|
Number of pipes |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Carrying capacity of the cables in % |
80 |
72 |
68 |
65 |
63 |
61 |
60 |
59 |
58 |
57 |
Table 21 Reduction, in case of single-core cables in single pipes in three-phase systems
|
Number of pipes |
3 |
6 |
9 |
|
Number of systems |
1 |
2 |
3 |
|
Carrying capacity of the cables in % |
85 |
76 |
72 |
Table 22 Reduction in case of bunched cables in the open air
|
Cable distance |
Carrying capacity in % | |
| |
3 cables or 3 cable systems |
6 cables or 6 cables systems |
|
Space between the cables is equal to the cable diameter |
93 |
87 |
|
No space between the cables (reciprocal touch) |
81 |
74 |
Table 23 Reduction in case of an ambient temperature for plastic cables deviating from 20°C
|
Rated voltage |
Carrying capacity in % in case of an ambient temperature of °C | |||||||
|
kV |
5 |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
|
1 |
115 |
110 |
105 |
100 |
95 |
89 |
84 |
77 |
Example of calculation:
For the transmission of 1,25 MVA with an operating voltage of 6 kV three-phase current a cable is required. This cable is to be hung by means of an auxiliary cable side by side with two cables hanging already in a shaft. The space between the cables is equal to the cable diameter. The ambient temperature is 30°C.
Solution:
A three-core cable with screened cores and with non-draining, intensified insulation is to be chosen.
Table 24 Reduction in case of an ambient temperature for solid-type cables deviating; from 20 %
|
Rated voltage kV |
Carrying capacity in % in case of an ambient temperature of °C | |||||||
|
|
5 |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
|
1 |
112 |
108 |
104 |
100 |
96 |
91 |
87 |
82 |
|
10,20 |
120 |
113 |
107 |
100 |
93 |
85 |
76 |
65 |
|
30 |
126 |
118 |
110 |
100 |
90 |
78 |
63 |
45 |
Occuring factors of reduction:
- 93 % for laying three cables side by side (space between the cables = cable diameter, see Table 22).- 85 % for raised ambient temperature of 30 % (see Table 23).
Total reduction factor = 0,93 · 0,85 » 0,79
Table 25 Continuous carrying capacity of the most important overhead-line materials for an over temperature of 40°C
|
Cable cross section |
Copper |
Pure aluminium |
Aldrey |
Steel-aluminium | |
| | | | |
1:6 |
1:4 |
|
mm2 |
A |
A |
A |
A |
A |
|
16 |
115 |
92 |
88 |
- |
- |
|
25 |
151 |
121 |
115 |
- |
- |
|
35 |
174 |
149 |
142 |
145 |
225 |
|
501) |
234 |
187 |
178 |
170 |
300 |
|
502) |
231 |
185 |
176 |
- |
- |
|
70 |
282 |
226 |
215 |
235 |
355 |
|
95 |
357 |
283 |
269 |
290 |
440 |
|
120 |
411 |
329 |
313 |
345 |
505 |
|
150 |
477 |
382 |
363 |
400 |
560 |
|
185 |
544 |
435 |
414 |
455 |
650 |
|
2403) |
630 |
502 |
479 |
- |
- |
|
2404) |
641 |
513 |
488 |
530 |
770 |
|
300 |
747 |
598 |
568 |
615 |
- |
1) 7-wire (1 layer)
2) 19-wire (2 layers)
3) 37-wire (3 layers)
4) 61-wire (4 layers)
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||
Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)
11. Basic symbols and formulas of electrical engineering
The following is valid:
|
I |
= current intensity in A | ||
|
E |
= empressed voltage in V | ||
|
U |
= voltage, terminal voltage in V | ||
|
R |
= resistance in w | ||
|
L |
= inductivity in H |
| |
|
w |
= gyro-frequency in | ||
|
f |
= frequency in |
||
|
C |
= capacity in F |
| |
|
r |
= resistivity in | ||
|
c |
= unit conductance in |
||
|
A |
= conductor cross-section in mm2 | ||
|
d |
= diameter in mm | ||
|
P |
= power in W (active power) | ||
|
Q |
= reactive power in Var | ||
|
S |
= apparent power in VA | ||
|
W |
= work in Wh or Ws | ||
|
cos j |
= power factor | ||
|
h |
= efficiency | ||
|
|
= flux in A | ||
|
B |
= magnetic induction in T or | ||
|
H |
= magnetic field strength in | ||
|
E |
= electric field strength in | ||
|
f |
= magnetic flux in Wb or Vs | ||
|
F |
= force in N |
| |
|
v |
= velocity in | ||
|
w |
= number of turns | ||
|
t |
= time in s or h | ||
|
J K |
= initial temperature | ||
|
J W |
= final temperature | ||
|
RK |
= resistance at initial temperature | ||
|
RW |
= resistance at final temperature | ||
|
µ |
= temperature coefficient in | ||
|
p |
= 3,14 | ||
or Hz
or
influence of the temperature on the resistance of the conductor
11.1. General direct current engineering
|
Ohm’s Law |
| |
|
power |
P = U2 · I |
[W] |
| |
P = I2 · R |
[W] |
| |
|
[W] |
|
work |
W = U · I · t |
[V · A · s = Ws] |
| |
W = P · t |
[W · s = Ws] |
|
diameter of a conductor |
|
[mm2] |
|
resistance of a conductor |
|
[W] |
| |
|
[W] |
|
influence of temperature on the resistance of the conductor |
RW = RK |
[1 + µ(J2 - J1)] |
Connection of resistances and power sources
· series connection
Figure
Figure
RG = R1 + R2 + R3 (total resistance)
U = U1 + U2 + U3.....
EG = E1 + E2 + E3
|
|
condition: Ri1 = Ri2 = Ri3 |
U = I · Ra
2. Kirchhoff’s Law
The sum of all voltages around a closed path in an electrical system is zero.
The sum of the impressed voltage is equal to the sum of the voltage drops.
· parallel connection
Figure
Figure
|
RE = equivalent resistance | |
|
IG = total current intensity | |
|
|
Condition: |
| |
Equal power sources are connected in parallel. |
| |
E = E1 = E2 = E3 |
|
for 2 resistances connected |
|
|
for n equal resistances |
|
| |
IG = I1 + I2 + I3 |
1. Kirchhoff’s Law
At each junction the sum of the currents flowing toward the junction is equal to the sum of the currents flowing away from the junction.
IG - I1 - I2 - I3 = 0
Figure
11.2. Magnetic field
|
flux: |
|
|
magnetic flux: |
|
|
magnetic resistance: |
|
|
1 = magnetically effective length in m | |
|
A = flux passage area in m2 | |
|
| |
|
comparative figure ur for air = 1, 000 000 4 |
|
|
magnetic permeability |
|
|
relative permeability |
mr - comparative figure |
|
induction constant |
|
|
magnetic field strength |
|
|
magnetic induction |
B = m · H = mo · mr · H |
| |
|
11.3. Law of induction
|
induced voltage |
|
[V] | |
|
self-induction |
| | |
| |
- self-inductance |
|
[H] |
| | |
|
[H] |
| |
- voltage of the self-induction |
|
[V] |
11.4. Electric field
|
electric field strength |
|
| |
| |
= voltage in V |
| |
| |
= thickness of the dielectric in m | |
|
|
charge |
Q = I · t |
[As] | |
|
capacity |
|
[F] | |
| |
Q = quantity of electricity in AS | |
|
|
|
C in F (1F = 1 AS/V) | | |
|
equation of dimensioning |
| | |
|
dielectric constant |
| | |
|
relative dielectric constant |
er: matter constant, relative to the vacuum | |
|
|
absolute dielectric constant |
| | |
|
dielectric flux density |
D = e · E | | |
11.5. Alternating current engineering
|
frequency |
| |
| |
T = cycle duration in s | |
|
gyro-frequency |
| |
|
phase angle |
| |
|
instantaneous value of a sinusoidal a.c. voltage |
| |
|
instantaneous value of a sinusoidal a.c. current |
| |
|
maximum value |
| |
|
|
- of a sine-wave voltage |
|
| |
U = virtual value |
|
|
|
- of a sine current |
|
| |
I = virtual value |
|
|
|
inductive resistance |
|
|
(inductive reactance) |
L in H | |
|
capacitive resistance |
| |
|
(capacitive reactance) |
C = capacity in F | |
Series connection
|
impedance |
|
[W] |
|
ohmic drop in voltage |
UR = I · R |
[V] |
|
inductive voltage drop |
UL = I · XL = I · w L |
[V] |
|
capacitive voltage drop |
|
[V] |
|
Ohm’s law for alternating current |
|
[A] |
Powers in case of single-phase alternating current
|
apparent power |
S = U · I |
[VA] |
|
active power |
P = U · I · cos z |
[W] |
|
reactive power |
Q = U · I · sin z |
[Var] |
|
power factor |
| |
Powers in case of three-phase alternating current
|
apparent power |
|
[VA] | |
|
active power |
|
[W] | |
|
reactive power |
|
[Var] | |
|
power factor |
| | |
|
efficiency for motors and generators |
| | |
| |
Pe = effective power | | |
| |
Pi = indicated power | | |
|
speed calculation of three-phase motors rotating field speed |
|
| |
| |
p = number of pole pairs | | |
|
slip |
|
[%] | |
| |
n = rotor speed |
| |
11.6. Calculation of power
calculation of power losses
PV = power loss in per cent
direct current
|
|
[%] |
single-phase alternating current
|
|
[%] |
three-phase alternating current
|
|
[%] | | |
|
|
[V]; |
|
[V] |
|
|
[V]; |
|
[V] |
|
|
[V]; |
|
[V] |
Determination of a conductor cross-section
- Calculation of the rated current from current, voltage and power factor.- Division by all suitable current-carrying capacity factors of the Tables 9 to 12.
- Determination of the conductor cross-section according to the given current-carrying capacity factors after the calculated fictive current.
- Calculation of the conductor cross-sections according to the given power and voltage loss.
- Comparison of the cross-sections found out under the third and fourth point. The greatest is chosen as the cross-section to be installed.
Conversion of the measuring units of work and power
Work
|
J |
erg |
kpm |
kWh |
PSh |
kcal |
|
1 1 |
107 |
0.102 |
0.278 · 10-6 |
0.378 · 10-6 |
0.239 · 10-3 |
|
107 |
1 |
0.102 · 10-7 |
0.278 · 10-13 |
0.378 · 10-13 |
0.239 · 10-10 |
|
9.81 |
9.81 · 107 |
1 |
2.72 · 10-6 |
3.70 · 10-6 |
2.34 · 10-3 |
|
3.60 · 106 |
3.60 · 1013 |
3.67 · 105 |
1 |
1.36 |
860 |
|
2.65 · 106 |
2.65 · 1013 |
2.70 · 105 |
0.7355 |
1 |
632 |
|
4187 |
4.19 · 1010 |
427 |
1.16 · 10-3 |
1.58 · 10-3 |
1 |
Power
|
W |
kW |
kpm s-1 |
PS |
kcal s-1 |
kcal h-1 |
|
1 |
10-3 |
0.102 |
1.36 · 10-3 |
2.39 · 10-4 |
0.86 |
|
103 |
1 |
102 |
1.36 |
0.239 |
860 |
|
9.81 |
9.81 · 10-3 |
1 |
0.0133 |
2.34 · 10-3 |
8.43 |
|
735.5 |
0.7355 |
75 |
1 |
0.1757 |
632 |
|
4187 |
4.19 |
427 |
5.69 |
1 |
3600 |
|
1.16 |
1.16 · 10-3 |
0.119 |
1.58 · 10-3 |
2.78 · 10-4 |
1 |