it is a simple calculation procedure to find the maximum length of the cable that can be
allowed, as
demonstrated in 9.4.3.6.
13.3.5 Earthing Rods and Grids
An essential aspect in the design of earthing systems for land-based plants in particular is
the m

11
13
17
19
+50.43
+42.67
32.63
29.20
From the Worked Example 15.4.3.1 the combined impedance of the rotor and magnetising
branches is Zm2 = 0.00348 + j 0.5362 ohms. Adding the stator impedance gives,
Z1m2 = 0.00878 + j 0.7711 ohms
All the harmonics of th

against the ingress of water and solid particles.
14.1.2 Power Supply
Most power systems in the oil industry do not have variable speed drives and so the AC
supply is
a highly dependable and simple source of sinusoidal voltage and current. Little or no
ha

and VHF and UHF radiation will penetrate to the cores of the cable. If it is anticipated that
the
electronic equipment in a plant may be influenced by VHF or UHF radiation, for example
from a
local transmitting station, then the screens should be made of

nearby. The tabs may be on either the outer or the inner surface, depending on the type of
equipment
and its environment. Care must be taken to ensure that water and other liquids cannot pass
along the
entry hole.
Casings and heavy-duty terminal boxes are

+2
3
_=4
3
The fundamental coefficients from the 180, 120 and 60 waveforms are found to be in the
ratio 2:
3:1 respectively. The fundamental coefficient of the supply current is double the magnitude
of the 120 waveform coefficient, which is the desired re

The design of filters to reduce or eliminate harmonics from the system connected upstream
of
the source of harmonics is a specialised subject and the results will depend on many factors
such as,
a) Proximity of the harmonic source to the source of main po

and
b1 = sin(2 + 2u) sin 2 2u
2[cos cos(u + )]
(15.5)
where and u are in radians.
From which,
c1 = _a1
2 + b1
2 (15.6)
and
cos1 = a1
c1
and
u = cos1 _R 3Xc
R + 3Xc
_ radians (15.7)
The fundamental components of the rms current I in the phases of the secon

2
_cos
n
6
cos
5n
6
cos
7n
6
+ cos
11n
6
_ (15.18)
anu = 0
For which,
ia(t) = imax
n
_
j=1
bju sin jt
It is found from the integration that all even harmonics and those multiples of three are not
present in the waveform. Hence n has the following value

8. Enclosure over-temperatures X
9. Control system faults X X
10. Harmonic filter faults X X
11. Single-phase operation of the
motor
XX
12. Overcurrent of the motor X X X
13. Winding temperature of the
motor
XXX
14. Winding temperature of power
transforme

_3
2
0.798 = +236.8 amps
Ii = 761.1
_3
2
1.834 = 544.2 amps
and
I = 761.1
_3
2
(0.76802 + 1.8342)1/2
= 593.46 amps per phase
From (15.13), (15.14) and (15.15) the volt-amperes at the bridge AC terminals are,
Ssec = Psec + jQsec
Where
Psec = 3 346.0 761.1

tape is also frequently used. Paired, tripled and quadrupled conductors are often screened
with similar tapes. However, all these various layers of screening are not very effective
against low
frequency interference from sources such as adjacent power cab

Therefore the magnitude of all the harmonics decrease as u increases, which is a reasonable
expectation since the waveform more closely resembles a sine wave.
The magnitude of the sum of the four cosine terms in (15.18) is 2
3 for all values of k in
(15.1

29 1.85 89.88 1.78 89.88 0.07 89.96 5.74 0.05
31 1.62 89.89 1.56 89.88 0.06 89.96 5.37 0.04
If the above calculations are made for all the active harmonics then their results can be
added
and the waveforms synthesised. Table 15.4 summarises the results.
F

Feeder cable.
Controller.
The pump unit must be designed to operate at very onerous levels of pressure, temperature
and in the presence of contaminates such as sand, acids etc. Moreover, the unit must be
suitable for
lowering into a well-bore which can

stray signals by interference from nearby sources. These stray signals will be called noise
hereinafter,
and they occur due to several different forms of coupling: Common circuit conduction.
Electrostatic or capacitive coupling.
Electromagnetic or mutua

Let bn be denoted as bn120 for use in sub-section 15.3.4.
The lowest harmonic present is the fifth.
414 HANDBOOK OF ELECTRICAL ENGINEERING
The value of the fundamental coefficient b1 is,
b1 = 1
_4
3
2
_=2
3
15.3.2 Simplified Commutation Delay
In practice

REFERENCES
1. Albert Kloss, A basic guide to power elements. John Wiley & Sons (1984). ISBN 0 471-90432-5
2. W. Shepherd and L. N. Hully, Power electronics and motor control. Cambridge University Press
(1987).
ISBN 0 521-31283-3
3. I. K. Dortort, Extended

15.2.4.2 Active and reactive power
The rectifying elements of the bridge are assumed to be free of ohmic power losses.
Therefore the
power input to the DC motor must be equal to the AC power input to the bridge. Hence the
sum of
the active power in each p

d
_ 1_ ohms (13.5)
Where c is the back fill resistivity in ohm-metres
d is the diameter of the back fill or casing in metres.
This equation can also applied to reinforced concrete in which a steel rod is encased. A
single
rectangular strip of width () bur

of a controlled firing system for the thyristor gates, and in some cases the application of
forced
commutation circuits, see Figure 15.1.
15.2.2.1 Commutation
The commutation processes for Mode 1 operation of delay and current transfer are
essentially the

overhead line compared with that of the earth resistance path back to the source. The
calculations
required for determining the fault current and its diverted amounts are shown in Appendix H
by way
of an example, and Figure 13.12.
Figure 13.12 Earthing ci

jM3c Ro I3
Rin + Rc + Ro + Re + jLc
volts (13.8)
Let the core loop resistance be called Rcc :Rcc = Rin + Rc + Ro + Re ohms (13.9)
Note that the components R3 and L3 of the source are not included in this result because the
interference is a current source

Assume the stator resistance to be constant.
Table 15.3. Peak values of harmonic
voltage components
Harmonic
number
Peak value and sign of
the component voltage
1 338.85
3 11.06
5 67.77
7 48.41
9 3.69
11 30.80
13 26.06
15 2.21
17 19.93
19 17.83
426 HANDBO

Modern fast-acting micro-computers are capable of storing and manipulating a reasonably
detailed mathematical model of the motor. It is therefore possible to compute the model in
parallel
with the actual motor and compare the computed variables with those

come under the general heading of pole-changing motors. The method just outlined is
applied to
squirrel-cage motors but not to wound rotor motors.
In a multi-pole motor for eight-pole operation, the adjacent poles change in polarity from
North to South ar

added resistance was one of the most common and simplest methods of speed control and
is used for
motors up to 10 MW. The main disadvantage is that the resistance bank is wasteful of
energy, and
the removal of the heat produced can prove difficult. The st

Let M = M3s M3c
And Msc _ M3s or M3c because of the relative dimensions and separation distances.
The denominator of (13.12) and (13.13) becomes:a12a21 a11a22 = RssRcc + j(RccLs + RssLc) + 2(Ls(Ls Lc)
In which the extreme right-hand term is very small in

110 V or 10 A 300
240 V or 50 A 450
415 V or 500 A 600
3300 V to 33,000 V 1000
Currents above 200 A 1000
EARTHING AND SCREENING 375
Figure 13.13 Mutual coupling between spaced out cables.
In these examples the situation of interest is a combination of a s

of the variable speed drive, see also sub-section 15.1.
The most frequently used reference document based on European practice that makes
recommendations
on the levels of harmonics that can be tolerated in LV and HV systems is Reference 14,
430 HANDBOOK O

cos 3XcId
= IdR + Em (15.1)
Where R is the DC circuit resistance.
Em is the emf in the motor armature.
Xc = 2Xl is the commutating reactance.
408 HANDBOOK OF ELECTRICAL ENGINEERING
An alternative expression for Vd in terms of the commutation angle u, is,

cos
4n
6
cos
8n
6
+ cos
10n
6
_
=4
n
+2
n
(1.155) for n = 1, 5, 7, 11, 13, etc.
= 6.31
n
= 2.0085
n
And = 4
n
+2
n
(2.309) for n = 3, 9, 15, 21 etc.
=
0.618
n
=
0.1967
n
The rms value of the fundamental phase-to-neutral voltage is 415/
3 = 239.6 volts.

squirrel-cage induction motors.
Examples in this sub-group are: Star-delta stator winding.
Pole-changing motors, e.g. PAM and NS motors.
Special motors that have connections made to their rotor windings.
References 4 and 5 give descriptions of the PAM a

line current. See Reference 12, Chapter 3 which emphasises this aspect. The controlled firing
of the
delta-star bridge Tu cancels the 30 degree phase shift of the transformer. From the Fourier
analysis
point of view this can be achieved by adding a + 30 p