Download - Understanding Electrical Laws
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UNDERSTANDING ELECTRICAL
NETWORKS
UNDERSTANDINGUNDERSTANDING
ELECTRICALELECTRICAL
NETWORKSNETWORKS
UNDERSTANDINGUNDERSTANDING
ELECTRICALELECTRICAL
NETWORKSNETWORKS
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CONTENTS
LAWS OFLAWS OF
ELECTROMAGNETISMELECTROMAGNETISM
BASIC VOCABULARYBASIC VOCABULARY
LAWS OFLAWS OF
ELECTROMAGNETISMELECTROMAGNETISM
BASIC VOCABULARYBASIC VOCABULARY
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PART 1: LAWS OF ELECTROMAGNETISM
LAWS OFLAWS OF
ELECTROMAGNETISMELECTROMAGNETISM
LAWS OFLAWS OF
ELECTROMAGNETISMELECTROMAGNETISM
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Section 1: Variables and units
Variables and units
Physicallaws
Theelectricarc
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- multiples and submultiples of units
Multiples
103 106 109 1012
k M G Tkilo mega giga tera
Submultiples
10-3 10-6 10-9 10-12
m Q n p
milli micro nano pico
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- units ofmeasure 1/2
Basic units
Dimensional equation: examplesSpeed: LT-1 Acceleration: LT-2 Force: MLT-2
Electric charge: IT Voltage: ML2T-3 I-1 ...
L length metre m
M mass kilogramme kg
T time second s
I electriccurrent ampere A
These variables form the basis of all other units
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Electrical Distribution Training - dc.-10 7
- units ofmeasure 2/2
Weight:
1 gramme = 15.4 grains
1 kilogramme = 2.2046 pounds1 ton = 0.9842 ton
Length:
1 centimetre = 0.3937 inch
1 metre = 1.094 yards
1 kilometre = 0.6214 mile
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- main variables and related units
force N Newtonenergy J Joule
power W Watt
acceleration m / s2
pressure Pa Pascal
moment of inertia
kg.m2
MECHANICAL
electric charge C Coulomb
voltage V Voltelectric field V / m
impedance ; ohm
resistance ;
reactance ;
inductance H Henry
capacitance F Farad
magnetic induction T Tesla
magnetic field A / m
magnetic flux Wb Weber
permeability Q H / m
permittivity I F / m
conductance S Siemens
resistivity ; . mfrequency Hz Hertz (s-1)
pulsation rd / s
...
ELECTRICAL
Vs
l
U = R I
R =
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- sun-earth power emission
10TW
human activity
180 .103 TW
1400W / m2
received 200TW
photosynthesis
35TW
internal
180 . 103 TWre-emitted
loss of
mass:
4.109 kg /s
390 .1012 TW
radiation
1000nucleargroups = 1 TW
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Electrical Distribution Training - dc.-10 10
Section 2: Physical laws
Physical laws
Theelectricarc
Variablesandunits
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Electrical Distribution Training - dc.-10 11
- how is electrical energy produced?
A rotating magnet near a circuit containing turns generates alternatingvoltage (Lenz'slaw)
e
= magnetic flux
e =
dt
dJ
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Electrical Distribution Training - dc.-10 12
- an alternating variable can be
represented by:
A rotating vector
A sine wave
3T/2
U 0
2T
T/2
T0 T/2 T 3T/2 2T
y = a sin U
y y
r
U
r
UU
rr
U
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- alternating current
0 U[ T[ 2T[
I
t
IdcIrms
i = Idc . sin [t
... Sameapplies forvoltage
Root mean square (rms) value: the value of direct current which
would give off the same energy by Joule effect in a resistor
I rms = Idc / V2
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- Ohm's law applied to direct current
Wire resistance: R = V l / sV = 1.8.10-8 ;.m copper
V = 2.9.10-8 ;.m aluminium
V= 100.10-8 ;.m nickel-chromium
(alloy for resistors)
I in A
U in V
R in ;
U
I R
U = R I
P in W
in . m
I in m
S in m
V ;
P = U I = R I2 = U2/ R
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- Ohm's law applied to alternating current (a.c.)
z = impedance of the a.c. circuit witha frequency f
[ = 2T f current pulsation
RL
Ci
u
u = z . i in complex numbers
z
iu
equivalentcircuit
XZ
R
z is a complex number the real partof which is the resistance R and
imaginary part the reactance X
z = R + j.X z in ;
where X = L[ - 1/ C[ X in ;
L: inductance in Henry f in HzC: capacitance in Farad
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- Ohm's law applied to alternating current (a.c.)
z
iu
z = R + j X
z = (Z , J ) in polar form
where Z2 = R2 + X2
and tgJ= X / R
z = Z e j J
i = I e j [ t
u = z . i = Z.I e j J . e j [ t
= Z.I e j([ t + J) = U e j([ t + J)
z
i
u
JJU = ZI
X
R
u = z . i in complex numbers
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- active power and reactive power
P(t) = U(t) . I(t) = U . I sin([t) sin([t N)
P(t) = U . I cos N (1 cos2 [t) + U . I sin N sin (2[t)
The integral cycle shows:
S = U.I apparent power in VAQ = U.I.sinN reactive power in VAR
P = U.I.cosN active power in W
P Q
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- do not confuse:
"Line loss" and "Voltage drops "
Source Load
line
z = R + j X
V1 V2
I
Joule effect only depends on R
P I Rline= .2
(in Watts)
Depends on R and X
( V = V1 -V2(in Volts)
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- law of impedance combination
z1
z2
Series:
z = z1 + z2
The impedances are added
z1 z2
(Admittance = inverse of impedance)
Parallel:
1 / z = 1 / z1 + 1 / z2
z = z1. z2 / (z1+ z2)
The admittances are added
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- the three-phase diagram
N
Ph3
Ph2
Ph1
2V
V3
V1U23
U12
3
2T
3
2T
3
2T
U31
V1, V2, V3 : single-phase voltages
U12, U23, U31 : phase-to-phase voltages
U12 = V2 - V1 in vectors
in balanced three-phase operating
conditions,
U = V . 3V2 lagging of behind V13
2T
3 windings with phase displacement
of120 (2T/ 3)
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Electrical Distribution Training - dc.-10 21
- why three-phase current?
The most economical means of remotely transmitting movement:
minimal number of windings to create a rotating magnetic field
A.c. generator motor
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Electrical Distribution Training - dc.-10 22
- three-phase power diagram
Active power
Pa = U.I. cos J in W (= 3 VI cosN)
Reactive power
Pr = U.I. sin J in VAR
Apparent power
S = U.I. in VA (= 3 VI)
3
3
3
J
Pa
Pr
J
RII
jXI
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*Coulomb'slaw
Two charges of the same sign repel each other
Two charges of the opposite sign attract each other
Concreteapplications:static electricity, capacitors...
q M Er4TI r2
q E =
q q' FdF
Electric field on point M created by a punctual load q
Interaction face between two punctual electric loads
q . q' F =
4TI r2
q in C
E in V
r in m
d in m
I in F/mI0 = dielectric constant of vacuum
Ir= relative permittivity of ambient material
Dielectric constant I!I0 . IrI = 10
-7/ 4 T c0 = 8.85 . 10-12 F / m
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*Kirchhof'slaw
Concreteapplications:loop networks protection
protection by open delta earth currentmeasurement
7(u = 0
Around a loop
7 i = 0
On a node
N
A
B
C D
E
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*Ampere'slaw
I
B
r
Concreteapplications: disturbance by proximity of a conductor
Magnetic permeability Q = Q0.Qr
Q0 = 4 T 10-7 = 12.6 . 10-7 0 in H/m
Qr= 1 for vacuum, air, aluminium
Qr= 600- 800 for iron
I . Q0 . c02 = 1
Q0IB =
div B = 0
An infinite rectilinear conductor, through which a current
(I) flows, creates a magnetic induction B in the
surrounding space
B in T
I in Ar in m
2
Tr
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Electrical Distribution Training - dc.-10 26
*Laplace'slawof force
Concreteapplications:electromechanical forces motors
F = i . dl 0 B
F = i . dl . B . sin E
I
B
E
F
An induction B exerts a force F on a
conductor through which a current (I)
flows
Right hand
Thumb
Middle finger
Index finger
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*Lenz'slaw
Co
ncrete
applicatio
ns: generator...
A conductive circuit forms a ring around a
surface through which the induction varies;
this circuit is subjected to an electromotive
force E along the circuit
E = - dJ/ dt
B variable(increasing)
E
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*Amperesand Laplaceslaws
Concreteapplications: electrodynamic forces busbar
withstand withdrawable circuit breaker arm
I I
Force of repulsion
---> loop effect
Proportional to the
product of the currents
I I
Force of attraction
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*Lenzsand Laplaceslaws
C
on
crete
application
s: energym
eters electric brakesover-heating of cubicle side panels by Eddy currents
Circular currents induced in the metal frames by a variation in magnetic
flux:
Aluminium
disk
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*Voltage dropcalculation
Concreteapplications: a very useful professional rule
Voltage drop in vectors V1- V2 = z . I = (R + j.X).IAs an absolute value this is very close to AB = AH + HB
Whence (V = R I cos J + X I sin JREMARK:the voltage dropmaybe negative....
Source Load
line
z = R + jX
V2
Z , N
V1
I
( V
N V2
V1
R.I
X.I
I
A H B
$ (V
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Section 3: The electric arc
The electric arc
Variablesandunits
Physicallaws
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- the electric arc
The arc is created when the voltage between two conductors is higher asthe maximum dielectric withstand value of the medium separating them
Irreversible deterioration in solid insulating materials
Ionisation of the medium separating the contacts
air SF6 gas
oil
vacuum: vapourization of the metal of the contacts
The ionised insulating medium becomes temporarily conductive
Presence of an arc voltage depending on the ionised mediumand on the nature of electrodes
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- breaking techniques: the puffer technique
Moving
contact
Fixed
contact
I
Flow ofcurrent
Separationof contacts
& arcing
Lengthening ofthe arc &
blow-out
Extinction ofthe arc as the
current reaches
zero
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- breaking techniques: the vacuum technique
Moving
contact
Fixed
contact
I
Flow of
current
Initial
RMF AMF
Diffuse
U net
Constricted
Arc control Interruption
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PART 2: BASIC VOCABULARY
BASIC VOCABULARYBASIC VOCABULARY BASIC VOCABULARYBASIC VOCABULARY
Backtothebeginningofthepart"Lawsof Electromagnetism"
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Section 1: Electrical definitions
Electrical definitions
Apparatus functions
Typesof networks
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- voltages
Three voltage values define the equipment operating characteristics
rated voltage is the maximum value of the voltage which the
equipment can withstand in normal operation
rated insulation level determines the dielectric withstand to
overvoltage and impulse voltage
- it depends on the rated voltage
service voltage is the voltage applied to the terminals of the equipment
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- voltages
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- currents
Two current values define the equipment operating characteristics:
rated normal current is the value of the current that the equipment can
withstand permanently without exceeding the temperature allowed by the
standard
rated short-time withstand current is the value of the short-circuit
current to be withstood for one second (or sometimes three seconds)
the peak value of t
he rated s
hort-time
withstand current is equal to2.5 times its rms value
Two current values define the network operating characteristics:
service current is the circuit load value calculated from the consumption
of the connected apparatus
short-circuit current is the overcurrent due to a fault or faulty operationon the circuit: Isc
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- frequency
There are two frequencies normally used in the world:
50 Hz in Europe
60 Hz in NorthAmerica.
Some countries use both frequencies:
Saudi Arabia...
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Section 2: Apparatus functions
Apparatus functions
Typesof networks
Electricaldefinitions
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- safety functions: isolating, earthing
DESIGNATION FUNCTION Switching on-off Closing and breaking
AND SYMBOL the service currents the faulted currents
Disconnector
insulate NO NO
Earthing switch
insulate NO NO(to be able toclose on c/c)
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- control functions
NO
NO
NO
DESIGNATION FUNCTION Switching on-off Closing and breaking
AND SYMBOL the service currents the faulted currents
YES
Switch on-off
not insulate
Switch
NO
NO
NO
YESSwitch on-off
insulate
Disconnector switch
NO
NO
NOYESSwitch on-offnot insulate
Contactor
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-protection functions
DESIGNATION FUNCTION Switc ing on-off Closing and breaking
AND SYMBOL theservicec rrents the fa lted c rrents
Protect
not ins late
YES YESFixed circ it-breaker
DESIGNATION FUNCTION Switching on-off Closing and breaking
AND SYMBOL theservicec rrents the fa lted c rrents
Switch on-off
Protect - ins latein withdrawn
position
YESYESWithdrawablecirc it-breaker
DESIGNATION FUNCTION Switching on-off Closing and breaking
AND SYMBOL theservicec rrents the fa lted c rrents
Protect
not ins late YES(once)
NO
Fuse
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Section 3: Types of networks
Types of networks
Electricaldefinitions
Apparatus functions
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- two types of configuration
MV distribution networks may be either:
overhead or underground
radial or loop configuration
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- radial configuration
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- open loop configuration
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- networks
The networkiseverywherein thelandscape...
andin everybuildingaswell
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-public energy network
LVconsumer
MVconsumer(tertiary,
small industry)
HVconsumer
(heavy industry)
EHVnational
MVlocal
LVlocal
HVregional
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END OF TRAINING
Thanks for the time you have spent on this training course
We hope it will be useful for your job
For any further information, you can contact us by e-mail:
And, of course, the whole Electrical Distribution Training team
remains at your disposal