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8/8/2019 15418296 Electrical Distribution Systems Questions Answers Part I
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8/8/2019 15418296 Electrical Distribution Systems Questions Answers Part I
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ELECTRICAL DISTRIBUTION SYSTEMS I.
Introduction to the course: this course is provided in a question & answer format and is divided into 5
chapters, it will become extremely useful to you:
If you want to know the parameters of the induction motors, their effect on the starting andnormal performance of the machine.
If you want to analyze an existing a.c. machine or evaluate a new one for its steady state or
transient state including starting and short circuit.
If you want to know the major components in the power distribution systems and how each
component is defined.
If you want to calculate the line and cable constants from the information found in standard
tables.
If you want to know the different types of breakers, starters and switchgear assemblies. Also, if
you want to know how they are defined.
If you want to do the necessary calculations to size the load breaking/interrupting/disconnecting
devices for normal and fault conditions.
If you want to know the types and sources of power line disturbances. Also, if you want to know
the effects of such disturbances on the major components of the power systems and the methods
of reducing these damaging effects.
If you want to know the effects of using local capacitors in increasing the circuit capacity and
how to size capacitors to improve the p.f. in motor circuits.
If you want to quantify the effect of direct and indirect lightning strokes on overhead distribution
systems.
If you want to know what are the data that have to be available in order to perform any of the
following studies: TRV, stability, load flow, fault/co-ordination, motor starting, reliability and
switching transients.
If you to know the procedure to calculate the following: basic values including base and p.u.
values, load flow, fault current/voltage sensitivity, motor starting, reliability studies for simple
radial systems.
If you want to know how steel properties, switchboard instruments, meters, relays are defined
and what are the major modules of PLC plus the building blocks of an office automation
system.
If you want to know the calculations to be performed if a major power transformer is to beprotected against short circuits or overloads.
If you want to know what are the essential programs and data for the power systems analyst (or
any other individual involved in electric power distribution and studies - for that matter).
Contents:
1. A.C. Electric machines parameters & performance.
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2. Overhead and undeground distribution systems components.
3. Switchgear, circuit breakers, MCC and starters.
4. Power line disturbances and power quality.
5. Power systems studies.
Lesson 1: AC electric machines parameters & performance.
1) What are the parameters of the induction motors and what are the tests to be performed on such
machines to be able to obtain the values of these parameters?
2) How can the performance of an induction motor be analyzed?
3) What are the important characteristics that are used in defining synchronous machines (in
general) and synchronous generators (in particular)? Sketch the equivalent circuit under the
different conditions of operation.
4) What are the data required from testing to calculate the parameters of synchronous motors?
5) Sketch the equivalent circuit of single phase transformer and list the required tests (to be
performed on transformers) to obtain the values of the parameters of the equivalent circuit?
6) A solved problem regarding the running & starting performance of an induction motor.
7) A solved problem regarding the characteristics of synchronous machines.
8) A solved problem regarding the parameters of single phase transformers.
9) A solved problem regarding the characteristics of 3-winding transformers.
10) Summarize the methods used in calculating the parameters of synchronous and induction
machines.
Lesson summary
References
1) What are the parameters of the induction motors and what are the tests to be
performed on such machines to be able to obtain the values of these parameters?
The parameters of the induction motors are: the stator resistance per phase, stator leakage
reactance/phase, rotor resistance/phase, rotor leakage reactance/phase, main flux susceptance
and conductance/phase. For motors under starting conditions the parameters are the same as
above except the values of the rotor resistance and reactance (referred to the stator) are higher
(due to skin effect) and lower (due to the skin effect & saturation), respectively. The tests to be
performed on such machines to be able to calculate the parameters of the machine are the no
load (open circuit) and locked rotor (short circuit) under full and reduced voltage. The reduced
voltage test is run to get the unsaturated reactance values (for rotor & stator). The data to be
collected from the no load test are: Primary voltage, the no load current and power at 75C (or 25
and corrected to 75); from the locked rotor: the voltage, current and power at 75C; from the
locked rotor (reduced voltage): the voltage and current. For the first 2 tests, the nominal motor
voltage is applied, if possible. Fig. 1 shows the equivalent circuit of a S.C.I.M.
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R1: stator resistance per phase, X1: stator leakage reactance/phase, R2': rotor resistance/phase
referred to stator, s: slip, X2': rotor leakage reactance referred to stator, Bm: main flux
susceptance, Gm: main flux conductance.
2) How can the performance of an induction motor be analyzed?
The performance of induction motors can be analyzed by studying the following points: heating
of winding/iron, efficiency of motor, power factor of machine, pull-out (maximum) torque,
starting torque, starting currents and the effect of the parameters on such points. a) Heating of
winding and iron: to reduce winding heating rotor and stator resistances have to be small.
Though for a high starting torque, the rotor resistance has to be high. To reduce iron losses, the
main flux has to be low. Note that the main flux and rotor current affect the torque.
b) Efficiency: to have a high efficiency motor, the windings (copper) and iron losses have to be
kept to the minimum possible.
c) Power factor: to achieve a high power factor machine, the leakage reactances (stator and
rotor) have to be low i.e. low reactive current. To have a high pullout torque, the flux has to be
high.
d) Maximum (pull-out) torque: to have a high pull-out torque in induction motors, primary
(stator) and secondary (rotor) reactances should be kept to a minimum, the rotor resistance will
only determine the slip of the maximum torque.
e) Inrush Current: reactances (and for small motors, the resistances) of the rotor and stator
windings have to be high to have a low inrush current.f) Starting torque: the rotor winding resistance has to be high to get a high starting torque, this
contravenes the efficiency requirement.
As can be seen from the above, the parameters of induction machines (i.e. their design) are a
compromise to achieve the optimum starting, pull-out and running performances required by the
different applications. When a motor is existing and the following data are available: motor HP,
terminal voltage, frequency, number of poles, stator resistance, windage losses, stray load losses
and the other motor parameters (or the results of the tests), the following are calculated: the
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rotor current referred to stator (I2'), starting torque (Tst) and the power transferred by the
rotating field to the rotor (Prot.f) for starting performance analysis. For the running
performance: the slip(s), stator and rotor currents, the developed torque and power, the
efficiency and the power transferred by rotating field at rated motor HP and at pull out
conditions or states are calculated.
3) What are the important characteristics that are used in defining synchronous machines(in general) and synchronous generators (in particular)? Sketch the equivalent circuit
under the different conditions of operation.
The characteristics of synchronous machines that define such machines are the no load, short
circuit, air gap and potier triangle.
To define a generator, the following characteristics to be investigated: no load and air gap, short
circuit and Potier triangle, load characteristics, external characteristics, regulation curve, short
circuit ratio and the determination of the direct axis reactance.
a) No load and air gap (unsaturated) ch/cs: it is expressed on a graph with the Y-axis
representing the armature (stator) e.m.f. (electromotive force) or the pole flux, with the X-axisrepresenting the field current (If) or the field m.m.f. (magnetomotive force in Ampereturn). The
air gap ch/cs is a straight line passing through the origin and the second point is the E (rated
stator voltage) value at a low field current (unsaturated conditions). The no load characteristics
under unsaturated condition coincides with the air gap characteristics - up to a point. At the
point where E is the rated induced in the armature by the flux produced from the resultant mmf
(Mr) the characteristics line is non-linear (bend inward) - saturated condition. The resultant mmf
will constitute of two portions: that part to drive the flux through the air gap and the other part
to drive the flux through the iron parts of the magnetic path. Fig.2 below shows the air gap, no
load & short circuit lines vs. If.
b) Short circuit characteristics (Potier triangle): the S.C. ch/cs represents the armature current
(Ia) as a function of the field current (If) or of the field mmf (MMF) with the armature
terminals short circuited. It is taken at synchronous speed of the generator. The S.C. ch/cs is a
straight line passing through the origin and the second point will have the X-axis equal to the
field MMF and the Y- axis equal the armature current. Potier triangle will have the following
important quantities: armature reaction mmf and the leakage reactance (impedance) of the
armature. The cos f =0 load characteristics is constructed from the no load ch/cs and Potier
triangle.
c) Load characteristics: it is the terminal voltage V as function of field current (If) or field mmf
(Mf) for constant load current (Ia) and power factor (p.f.). At a fixed load current, the field
current is required to sustain the no load voltage and it increases with the decrease of cos f, this
mainly to counteract the armature reaction. Potier triangle can be determined from the no load
ch/cs and two points on the cos f = 0 load ch/cs.
d) External characteristics: it is expressed as the terminal voltage (V) as function of the load
current (Ia) at constant If and p.f. For lagging current, the voltage drop increases as the power
factor decreases and vice versa for leading current.
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e) Regulation Curve: it describes the field current as function of either the load current with
constant p.f. or the p.f. at constant current (Ia) - provided that the terminal voltage is kept
constant. The field current increases with the increase in load current (p.f. is constant lets say at
1 or .8), the field mmf has to increase to compensate for the armature reaction increase.
f) Short circuit ratio: it is the ratio of the field current required to produce rated voltage on open
circuit to the field current required to produce rated current on short circuit. The saturated S.C.ratio is obtained from the no load curve and the rated armature current (field mmf to produce
rated V divided by the mmf producing the rated current). To get the unsaturated S.C. ratio,
divide the MMF value that produces the rated V from the air gap straight line (it is the extension
of the linear air gap line that is taken from the no load curve) by the MMF producing the rated
current under short circuit condition. A large SCR indicates a small armature reaction which
means that the machine is less sensitive to load variations. A small SCR means that the machine
is more sensitive to load variations.
g) Determination of direct axis synchronous reactance (Xd): it is obtained from the no load
linear portion (or air gap line) and S.C. characteristics. The field current induces the nominal
voltage on the air gap line. When the stator is short circuited and the field current is maintained
at the same level as with the open circuit condition, the induced emf in the stator is the same as
with the no load condition but in this case it is consumed by the drop due to the synchronous
impedance. The unsaturated short circuit ratio is used to calculate Xd, Xd = 1/SCR.
Fig.2a below shows the equivalent circuit of the synchronous machine under the different
conditions.
Xs: stator leakage reactance, Xm: main flux reactance, Xf: field leakage reactance, Xd: damper
leakage reactance.
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4) What are the data required from testing to calculate the parameters of synchronous
motors?
The tests to be performed on the synchronous machine so that the parameters can be calculated
are: the open circuit (no load) characteristics, short circuit and the air gap line. From the first
test, two values are obtained: the nominal stator volt at the field current registered; from thesecond: 2 points are obtained (4 values): the nominal stator current and its corresponding field
current and the stator current (Ia) at the field current obtained from the open circuit test; from
the final test: the voltage at the field current equal to the one producing the nominal current in
the previous test.
5) Sketch the equivalent circuit of single phase transformer and list the required tests (to
be performed on transformers) to obtain the values of the parameters of the equivalent
circuit?
Fig. 3 below shows the equivalent circuit of a single phase transformer. The tests to be
performed on transformers so that the parameters, which are the primary and secondarywindings resistances and reactances plus the main flux susceptance and conductance, can be
calculated are: the no load (open circuited primary - H.V. - winding) test from which the open
circuit volt on l.v. side and the no load current are obtained; the S.C. (l.v. - winding short
circuited) from which 3 values are registered the S.C. losses in W (or kw), the rated S.C.
currentas seen from the primary side and the voltage circulating such current. The primary
winding resistance (d.c.) should also be measured by an ohmmeter at 25 C.
R1: primary winding resistance, X1: primary winding leakage reactance, R2': secondary
winding resistance referred to the primary winding, X2': secondary winding reactance referred
to the primary, Bm: main flux susceptance, Gm: main flux conductance, r2': load resistance
referred to the primary winding, x2': load reactance referred to the primary (in primary side
terms).
6) A 3 phase induction motor, 3 HP, 440/220 V, 60 HZ, 4-pole, 1750 rpm, has the following
no-load test results: Vnl
= 440 V, Inl
=2.36 A, Pnl
=211 W; locked rotor (full voltage) results:
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Ilr
=29 A, Vlr
=440 V, Plr
=13.9 KW; locked rotor (reduced voltage): Vlr1
=76 V, Ilr1
=4.25 A -
unsaturated reactance condition. Assume windage loss=44 W, stray load loss=48 W, skin
effect factors=1.3 for rotor winding resistance (referred to stator), .97 for rotor reactance
and stator resistance/phase = 2.26 W. Determine the 6 parameters of the induction motor,
its starting and running performance data, the transient reactance and the s.c. time
constant, the s.c. current after 1 and 2 cycles from fault inception. Calculate the duration
of the inrush current assuming J=2 lb.ft2
for the rotating parts.
GIVEN: Vprim
=440 V, Ioc
=2.36 A, Poc
=211 W, Vlr
=V1
=440 V, Ilr
=29 a, Plr
=13.9 KW,
Vlrr
=76 V, Ilrr
=4.25 A, HP=3, r1
@ 25 C=2.26 OHM, windage loss=44 W, stray load
loss=48W, skin effect for r2'
, x2'
=1.3, 0.97.
SATURATED REACTANCE:
Zl=440/[(3).5(29)]=8.73W, R
l=13920/3(29)(29)=5.48 W,
X=[(8.73)2-(5.48)2].5=6.8 W, r1 @ 75 C=2.26[(234+75)/(234+25)]=2.69 W,
r2'
=R1
-r1
(@ 75 C)=5.48-2.69=2.79 W, X1
=X2
=X/2=3.4 OHM.
UNSATURATED REACTANCE:
Z=76/[(3.5)(4.25)]=10.3 W, X=[(10.3)2-(5.48)2].5=8.72 W,
X1
=X/2=4.36 OHM, Saturation factor = 4.36/3.4=1.3,
including for skin effect: r2'
=2.79/1.3=2.14 OHM,
X2'
=4.36/.97=4.5 W, Xm
=[(V1
)-(Ioc
.X1
)]/Ioc
=[(440/3.5)-(2.36)(4.36)]/2.36 = 103 OHM,
Ph+e=Poc-3(Ioc)2
(r1 @ 75C)-windage losses=211-3(2.36)2
(2.69)-44=122W.
Assuming 1/2 the iron losses are due to the main flux. Ph+e
=122/2=61W
Gm
=Ph+e
/3(E1
)2
={61}/{3[(440/3.5
)-(2.36)(4.36)]2
}=3.43/10000 MHO
Rm
=Gm
.Xm
2=[(3.43)/(10000)][103]2=3.66 W
STARTING AND RUNNING PERFORMANCE:
Base values calculations: Vb
= 440/3.5b
=3x746/3x254=2.94 A, Zb
=254/2.94=86.5 OHM.
Pb
=254x2.94=746 W, Tb
=7.04(3)(unit power)/unit speed=7.04x3x746/1800=8.8 LB.ft.
Parameters for starting performance in p.u:r
1=2.69/86.5=.0311, r
2'=2.79/86.5=.0322, x
1=x
2'=3.4/86.5=.039 (saturated conditions).
Parameters for running performance in p.u:
r1
=.0311, r2'
=2.14/86.5=.0248, x1
=4.36/86.5=.0504, x2'
=4.5/86.5=.052 (unsaturated).
Parameters common to both:
Xm
=103/86.5=1.19, Rm
=3.66/86.5=.042 p.u.
Starting performance:
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r2'
(1-s)/s=0 as at standstill s=1=(ns-n)/n
s
Z1
=(r1
2+x1
2)=[(.03)2+(0.039)2]=0.05, tan-1=x1/r
1=51.4 Z
2'=[(.032)2+(.039)2]=.0506 /_50.6
Zm
=[(1.19)2+(.042)2] =1.19, tan-11.19/.042= 87.98
V1
=I1
.Z1
+ (I1
)/[(1/Z2'
)+(Ym
)]
V1
=I1
[.05 /_51.4+ (1)/(1/.0506 /_50.6)+(1/1.19 /_87.98)]; where Ym
= 1/Zm
, V1
=I1
.Zeq
,
V1
=1/_0
I1
=V1/{.05 /_51.4+{[(.0506)(1.19) /_138.58]/[.0506 /_50.6+1.19 /_87.98]}}
I2'
=I1
[Zm/(Z
2'+Z
m)]=9.66/_-50.4
Prot field
=I2'
2(r2'/s)= (9.66)2(.0322) = 3p.u.
Tst
=3p.u.=3x8.8=26.4 LB.ft
Running Performance:
s=.03, r2'(1-s/s)=.8, Z1 =.0593 /_58.3, Z2'=.825 /_3.6, Zm=1.19 /_87.98,
I1={1/_0}/{[.0593/_58.3]+[(.825 /_3.6 . 1.19 /_87.98)/(.825 /_3.6+1.19 /_87.98)]}
Input p.f.=cos 38.2=.785
I2'
=1.42/_-38.2[1.19 /_87.98/(.825 /_3.6+1.19 /_87.98)]=1.12 /_-5.74
Prot field
= I2'
2.(r
2'/s) = (1.12)
2(.0248/.03)=1.025 p.u.
Tdeveloped
=1.025 p.u.=1.025(8.8)=9.02 LB.ft.
Mechanical loss Torque=7.04(stray load loss+windage+main flux iron loss)/ns(Torque
base)
=7.04 (48+44+61)/1800 (8.8)=.068
Tnet developed
=1.025-.068=.957 p.u. x 8.8=8.4 LB.ft.
Power input=3(1)(1.42)( cos 38.2)=3.35 p.u.
Losses (stator-copper)=3(1.42)2(.0311)=.189 p.u.
Losses (rotor-copper)=3(1.12)2 x .0248=.093 p.u.
No load iron losses=122/746=.163 p.u.
Losses (stray load)=48/746=.064 p.u.
Losses (friction & windage)=.059 p.u.
Total losses=.568 p.u.
Pdeveloped=3.35-.568=2.78 p.u. x 746=2076 W=2.78 HPeff.=2.78/3.35=83%
slip = 3(1.12)2
(.0248)/[3.35-(.189+(.163/2))]=.03
snormal
=3/2.78=.0324
spullout
(@ max Torque)=[(1 + (X1/X
m))(r
2')/[X
1+ (1 + (X
1/X
m))X
2']
=[(1.0+.0504/1.19)(.0248)/[.0504+(1.042)(.052)]=.246 p.u.
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r2'
(1-s/s)=0.0758 (@ s=.246), Z2'
=r2'
+ r2'
(1-s/s) + jX2'
= {[r2'
+ r2'
(1-s/s)]2 + X2'
2}.5
=[(.0248+.0758)2
+(.052)2
].5
=.113/_27.3 tan-1
(.052)/(.0248+.0758) = 27.3
I1
=6.12/_-41, I2'
=5.85/_-36, Protating field
=I2'
2(r2'/s
p.o.)=3.44 p.u.
Tp.o.
=3.44x8.8=30.2 LB. ft.
Tdeveloped (@ 3HP & s=.0324)=5250 x 3/1800(1-.0324)=9.02 Lb.ft
Starting Torque/Normal Torque (rated) = 3/1.025 = 2.92
Pull out Torque/rated Torque = 3.44/1.025 = 3.36
Transient Analysis:
Transient reactance = .0504+[(.052)(1.19)/(.052+1.19)] = X" =. 1p.u.
P.F. = .785, efficiency = 83%, Ib = 2.94 A
I1
= 3x746/.785(.83)(440)(1.732) = 4.5 A = 1.53 p.u.
E1'
=1-[(.03+j.1)(1.53 x cos 38.2 - j1.53 x sin 38.2)] = .874 p.u. /_-6
Initial S.C. current = .874/.1 = 8.74 x 2.94 = 25.7 AT
o'= open circuit transient time constant = (X2+Xm)/2(pi)fr
2, where pi = 3.141592654
T' = To'
[X"/(X1
+Xm
)] = S.C. time constant
IS.C.
= Initial S.C.C. (e-t/T)
To'
= .052+1.19/2(pi)60(.0248)=.133 sec.
T' = .133(.1)/.124= .011 sec.
IS.C.
(after 1 cycle i.e. .0166 sec.) = 8.74(e.01666/.011) = 2 p.u.
I
S.C.
(after 2 cycles) = 8.74(.048) = .43 p.u.
Starting Time:
An approximate solution if the load and motor speed-torque curves are not available is as
follows:
t = J(rpm1-rpm2)2(pi)/60 g Tn
J = 2 lb ft2, rpm1 = 1740, rpm2 = 0, g = 32.2 ft/sec, Tst
= 26.4, Trated
(@ rated HP)= 9.02
Tn
= accelerating torque between rpm2 to rpm1 = Tst
+Trated
/2 = (26.4+9.02)/2 = 17.7 LB. ft.
t=.7 sec.
7) A synchronous machine rated 45 KVA, 3 phase, 220 Vl.l.
, was tested under open circuit
(no load) and short circuit (locked rotor), the following were the results: OPEN CIRCUIT:
Vl.l.
= 220 V, Ifield
= 2.84 A, SHORT CIRCUIT: Iarm.1
= 118 A (first point), Ifield1
= 2.2 A,
Iarm.2
= 152 A (second point), Ifield2
= 2.84 A, the machine was tested at a power factor = 0
from short circuited armature condition to no load condition. The no load and air gap
plus the short circuit curves can thus be plotted (as shown in question 3, fig.2 above) and
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the characteristics of the machine can be obtained graphically. The air gap line is plotted
from: Ifield
= 2.2 A, Vl.l.
= 202 V at rated armature current = 118 A, assume s.c. load losses
(3-phase losses) = 1.8 KW @ 25 C, armature resistance @ 25 C = .0335 W/phase, field
resistance @ 25 C = 29.8 W/phase. Calculate the saturated and unsaturated reactance,
the effective armature resistance and the s.c. ratio. If this machine runs as a motor at V =
230 V, input power to armature = 45 KW, .8 p.f. leading current, field current = 5.5 A,
then calculate the efficiency of the motor.
Line to neutral voltage = 202/1.732 = 116.7V on the air gap line; for the same field current of
2.2a, on the S.C. line, the armature current = 118 amp.
The saturated reactance = Xs
The unsaturated reactance= Xs air gap
= 116.7/118 = .987 OHM, ratio of unsaturated reactance to
saturated reactance = .987/.836 = 1.18
Short circuit ratio = 2.84/2.2 = 1.29 (saturated), Xs(saturated)
= 1/1.29 = .775 p.u.
Air gap field current corresponding to 220v line - line armature voltage = (220/202)(2.2)=2.39
A
short circuit ratio=2.39/2.2=1.086 p.u. (unsaturated), Xs(unsaturated)
=1/1.086=.92 p.u.
The armature effective resistance:
S.C. load loss/phase = 1800/3 = 600W/ph.
ra(eff)
= 600/(118)2 = .043 W/phase
in p.u.: S.C. load loss = 1.8/45 = .04 p.u.
ra(eff)
in p.u. = .04/(1)2 = .04 p.u.
ratio of a.c./d.c. resistance =.043/0335=1.28 (skin effect and proximity)
Note: armature resistance of m/cs above few hundreds KVA is less than 0.01 p.u.
For the m/c operating as a motor with leading power factor:
Ia
= 45/(1.732)(.8) = 141 amp.
Assume stray load loss of 30% of S.C. load loss = .54 KW
Resistance for copper winding of armature at 75 C = 0.335[234+75/234+25] = .04 OHM/ph
Resistance for copper winding of field at 75 C = 29.8[(234+75)/(234+25)] = 35.5 OHM/ph
Armature Cu losses (assume ra
= .04 or .035W/ph) = 3 Ia
2 ra = 3(141)2 (.04)=2.38 KW
Field Cu losses = (5.5)2 (35.5) = 1.07 KW E = internal voltage of motor = V t - Ia ra =
(230/1.732)-(141)(.8+j.6)(.04) = 128.4-j3.4 Vphase
Vline to line
= 220 V at which core losses = 1.2 KW
Total losses = 2.38+1.07+.56+1.2+.91 = 6.12 KW
Input = 45+1.07 = 46.07 KW
Efficiency = 1-(6.12)/(46.07) = 86.7%
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8) Calculate the equivalent circuit parameters for the following single phase transformer.
The results of the open circuit test ( H.V. wdg open) are: Vo.c.
= 347 V, Io.c.
= 18 A, Po.c.
=
980 W. The results from the short circuit test (L.V. wdg shorted) are: Vs.c.
= 70 V, Is.c.
=
Irated
, Ps.c.
= 1050 W. The 2-winding transformer ratings are: 2400/347 V, 100 KVA,
primary winding resistance at 25 C= .24 W. Also, calculate the regulation and effeciency
at unity and .8 p.f. full load current.
Transformer ratio: 2400/346 V, Irated
= (100)/2.4 = 41.6 A
Transformation ratio = a = 2400/346 = 7, Zsc
= Vsc
/Isc
=70/41.6 = 1.68 OHM
Rsc
= Psc
/(Isc
)2 = 1050/(41.6)2 = .607 OHM
Xsc
= [(1.68)2-(.607)2].5 = 1.57 OHM Rsc
(at 75 C) = .607[(234+75)/(234+25)] = .723 OHM
r1
(at 75 C) =.24[234+75/234+25] = .28 OHM
r2' = Rsc-r1 = .723-.28 = .44 OHMX
1= X
2'= X
sc/2 = .785 OHM
From open circuit tests: (L.V. wdg. excited):
Ph+e
= Po.c.
-(Io.c.
/a)2r1
= 980-(18/7)2(.28) = 978 W
E1
= 2400-(Io.c.
/a)X1
= 2400-(18/7)(.785) = 2400 V
Xm
= 2400/18/7 = 934 OHM, gm
=Ph+e
/E1
2=.00017 MHO
rm
= gm
(Xm
)2 = .00017 (934)2 = 148 OHM
Zb = 2400/41.6 = 57.7 OHM, Zpu = 1.68/57.7 = .03 puX
pu= 1.57/57.7 = .027 pu, R
pu= .0125 p.u.
Regulation and efficiency:
Regulation at 1p.f.: Reg. = (.0125)+(.027)
9)A 3-winding transformer (primary, secondary, tertiary)- single phase- rated 7960 V
(1000 KVA), 2400 V (500 KVA) & 2400 V (500 KVA). The results of the s.c. tests are as
follows:
Test WDG Excited WDG Short Circuited Applied Voltage Value Current In Excited WDG
1 1 2 252 62.7
2 1 3 252 62.7
3 2 3 100 208
The 3 transformers are connected in a Y-D-D configuration on 13.8/2.4/2.4 KV. When the tertiary
windings are short circuited (3-phase), calculate the s.c. current and the voltage on the terminals of the
secondary windings of this bank.
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For primary winding: Vb
= 7960 V, Ib
= 1000/7.96 = 125.4 A
For secondary winding: Vb
= 2400 V, Ib
= 1000/2.4 = 416 A
For teritiary winding: Vb
= 2400, Ib
= 416 A
Test Z between terminals Vpu Ipu Zpu = Vpu/Ipu
1 1-2 252/7960=.0316 62.7/125=.5 .06322 1-3 252/7960=.0316 62.7/125=.5 .0632
3 2-3 100/2400=.0416 208/416=.5 .0832
Z1
= 1/2 [.0632+.0632-.0832] = .0216 pu
Z2
= 1/2 [.0832+.0632-.0632] = .0416 pu
Z3
= 1/2 [.0632+.0832-.0632] = .0416 pu
Isc
=1/(.0216+.0416)=15.8 p.u. (S.C. teritiary) = 15.8 x 125.4 = 1984 A
V2
= voltage on secondary bus while teritiary is short circuited = Is.c.
x Z3
- Isec
x Z2, Isec
is the load
current
= 15.8(.0416)-1(.0416)=62.4-4.16= .5824 p.u. To calculate the S.C. current assuming a base MVA = .5
MVA = 500 KVA:
Znew
= Zold
[KVAnew
/KVAold
] p.u.
Z3new
= .5(.0416) = .0208, Z1new
= .5 (.0216) = .0108, Isc
= 1/.5 (.0632) = 1/(.0208+.0108) = 31.6 p.u.,
Ibase
= 500/7.96 = 62.8 A, Isc
= 31.6(62.8) = 1984 A
10. Summarize the methods used in calculating the parameters of synchronous and induction
machines.
Synchronous machines:
Positive sequence (synchronous parameters): The air gap, no load and short circuit characteristics: the
machine is run at synchronous speed in the proper direction. The three phase armature terminals are
kept open and line to line voltage readings are taken at different field current (a rheostat) in the field
winding is used to vary the field current). The excitation is reduced to a minimum and the 3 phase are
shorted and the field reading plus the current flowing in one of the lines are taken (to draw the short
circuit unsaturated characteristics line passing through the origin).
Subtransient reactance: short circuit the field through an ammeter, apply a single phase voltage to any
of the three line terminals, rotate the rotor by hand. At the position indicating maximum field current in
the field ammeter, half the voltameter reading in the armature circuit divided by the armature current in
one line (using an ammeter in one of the line terminals) is equal the subtransient direct axis reactance.
At the minimum field current reading, half the armature voltage divided by the armature current will
give the subtransient reactance in the q-axis.
Negative Sequence reactance: the field is shorted on itself, two phases are connected to each other
through an ammeter and a single phase voltage is applied to this armature configuration. The field is
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rotated at rated speed and the voltage applied to the armature will correspond to approximately
circulating the rated machine current. The negative sequence impedance = V/1.7321( I). This method
can also be used with induction m/cs.
Zero sequence impedance: zero sequence impedance is much smaller than the positive and negative
and in theory is close to zero. The machine is at stand still, the field is open, the six terminals ofthe
machine are available outside the machine and the three windings are connected in series. A reducedvoltage is applied across the 3 connected windings and the zero sequence impedance will be equal to
one third the voltage read on the voltameter divided by the circulated current read on the ammeter in
the armature circuit.
Induction Machine:
Steady state reactance: from the three tests, no load (open circuit), locked rotor (short circuit) - full
voltage (for saturated reactance) and locked rotor (short circuit) - reduced voltage (for unsaturated
reactance), the parameters are obtained.
Transient reactance: is calculated from the parameters of the machine obtained from the above tests. X"
= [X2(Xm)/(X2+Xm)]+X1.
SUMMARY:
In this chapter, the parameters and performance of a.c. electric machines were presented. The tests
performed on such machines to obtain their parameters were given, the parameters and their effects on
the machines performance were covered, too. Numerical examples were given to show and clarify the
interrelations between the machine parameters and the performance. The induction machines
parameters are: stator resistance & reactance, the rotor resistance and reactance, the main flux
susceptance and conductance. These parameters affect the machine during starting (inrush current &
starting torque), at nominal load (full load current & nominal torque), and for the maximum (pull-out)
machine torque. They, also, affect the losses (heating of iron & winding), efficiency and power factor .
The characteristics of synchronous machines in general and generators in particular presented in this
chapter were: the air gap and no load (armature emf or pole flux vs. mmf or field current), short circuit
(armature current vs. field current), load ch/cs (terminal voltage vs. field current provided that the load
current and the p.f. are kept constant), external (voltage vs. load curent with constant field current &
p.f.), regulation (field current vs. load current with constant p.f. or field current vs. p.f. with constant
load current, voltage is kept constant in either case), short circuit ratio (field current producing nominal
voltage under open circuit condition vs. field current producing rated current under - armature - short
circuit condition) and direct-axis synchronous reactance determination (which is equal to 1 divided by
the SCR). For the transformers, 2 & 3 winding parameters were presented and their effect on
regulation/efficiency of 2 windings transformers and for 3 windings short circuit plus voltage
sensitivity of the unfaulted bus were given and emphasized by numerical examples.
REFERENCES:
1. Greenwood, Allan "Electrical Transients in Power Systems", Wiley.
2. Granger & Stevenson "Power System Analysis", McGraw Hill.
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3. Tuma, Jan "Engineering Mathematics Handbook", McGraw Hill.
4. Fitzgerald, Kingsley & Kusko "Electric Machinery", McGraw Hill.
5. Kheir, "Automating Power Systems Analysis", Kheir
Home page of VePi
Lesson 2: Overhead and underground distribution systems components.
1) How would EPR (ethylene propylene rubber) cables, up to 35 KV, be classified?
2) How would underground XLPE (cross linked polyethylene) cables classified?
3) What are the defining parameters of cables?
4) What are the factory and site tests to be performed on cables?
5) What are the defining parameters for low voltage secondary cables?
6) What are the different types of transformers found in distribution systems?
7) What are the different types of overhead switches, padmounted switchgear and those of
lightninig arresters?
8) What are the standards that govern distribution transformers? How are distribution
transformers defined?
9) How are wooden and concrete poles defined?10) What are the different applications of oil switches and what are their defining parameters?
11) How are overhead air switches classified?
12) How are padmounted switchgear defined?
13) What are the important parameters by which lightninig arresters are defined?
14) How would copper conductors be defined?
15) How would ACSR (aluminum conductor steel reinforced) and ASC (aluminum stranded
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conductor) be defined?
16) How would AASC (aluminum alloy stranded conductor) and self-dampening/compact
ACSR be defined?
17) What are the different types of cable splices and terminations?
18) What are the different types of connectors and elbows?
19) What are the design tests performed on the separable connectors?20) What are the different types of insulators, their material and characteristics?
21) What are the functions of DAC (distribution automation and control)? Sketch the typical
underground distribution arrangements and the overhead distribution system.
22) What are the major information obtained from a distribution system SCADA? Show a block
diagram of the major components of a SCADA (system supervisory control & data acquisition).
Sketch a diagram to show a typical automated distribution system with power and
communication lines.
23) What are the basic modules in a PLC (programmable logic controller) system? Sketch a
front plate of 2 of the basic modules. Sketch a block diagram showing the interrelation of the
major modules.
24) A solved problem regarding constants of overhead conductors?
25) A solved problem regarding constants of underground cables?
26) A solved problem regarding reflected & refracted powers at a conductor/cable junction?
27) A solved problem regarding power transformer protection?
Lesson summary
References
1) How would EPR (ethylene propylene rubber) cables, up to 35 KV, be classified?
The classification of EPR (up to 35KV) cables is as follows: the voltage class, the conductor
material/size (which is function of the normal/overload/short circuit current values and the
installation method/configuration), the insulation thickness (whether 100% or 133%), jacketed
or unjacketed, neutral size (either full or 1/3 rating), cable in conduit configuration/direct buried
or concrete encased conduits.
2) How would underground XLPE (cross linked polyethylene) cables classified?
The classification of XLPE (up to 46KV) cables is as follows: the voltage class, the conductor
material/size, insulation thickness, jacketed or unjacketed, neutral (concentric neutral and rating
full or 1/3 main conductor) or shielded (Cu tape), single or 3-conductor cables, jacket-type
(whether encapsulated or sleeved), the use of strand-fill or water blocking agent between the
insulation and jacket.
3) What are the defining parameters of cables?
The defining parameters can be classified broadly into dimensional, insulation material
properties and current carrying capacity. For dimensional parameters, conductor size/number of
strands/type of strands, diameter over conductor, diameter over insulation, diameter over
insulation screen, number and size of neutral conductors or tape details (thickness, width & lap
type) and diameter over the jacket are the defining data. Other important data are: weight/1000
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ft length, size of reels and length/reel. The insulation/jacket defining parameters are: before and
after aging tensile strength and elongation, hot creep elongation/set, dielectric constant,
capacitance (SIC) during and after the stability period, insulation resistance constant, water
absorption properties. The last set of defining parameters are the current levels at the nominal
voltage under the different operating conditions which are function of: the layout and proximity
of current carrying cables, the method of laying/pulling of cables, provision of future additionalloads with their corresponding maximum allowable voltage drop and finally the maximum
acceptable temperature rise & duration for the cable insulating material.
4) What are the factory and site tests to be performed on cables?
The different types of tests that are performed on cables at the factory are: partial discharge, DC
resistance of central conductor, AC high voltage dielectric withstandability, DC high voltage
withstandability, insulation resistance, physical dimensions of cable components, cold bend, low
temperature impact, jacket integrity, water penetration and high temperature drip test for the
strand fill (if applicable). For conductor shield the tests are: volume resistivity, elongation at
rupture, void and protrusions, irregularities verification. For the insulation are: tensile strength(aged and unaged)/elongation at rupture (aged and unaged)/dissipation factor (or power
factor)/hot creep (elongation and set)/voids and contamination/solvent extraction (if applicable).
For the insulation shield are: volume resistivity/elongation at rupture/void and protrusions
irregularities/strippability at room temperature and at -25C/water boil test. For the jacket are:
tensile strength, elongation at rupture (aged and unaged), absorption coefficient (of water), heat
shock and distortion. On the cable the following tests may be performed: structural stability and
insulation shrink back for certain insulation materials. The tests performed on site are: visual
inspection, size/ratings verification and D.C. withstandability tests at voltage level below those
used in the factory.
5) What are the defining parameters for low voltage secondary cables?
The defining parameters for l.v. secondary cables are: material of phase conductor, number of
strands, class of strand, type of conductor (ie. concentric, compact or compressed), conductor
size, insulation thickness, over all diameter per cable, overall diameter per assembly (ie. triplex
or quadruplex), the neutral conductor size (equal to the phase or reduced), if applicable,
insulation and jacket materials, jacket thickness and the weight per assembly per 1000 ft length.
6) What are the different types of transformers found in distribution systems?
The different types of transformers found in distribution systems are: Power (up to 10MVA)
liquid filled (oil), power (over 10 up to 100 MVA) oil filled with radiators/fans (one or 2 sets),
single phase distribution transformers/oil filled (with or without radiators/fans) up to 500 KVA,
three phase distribution transformers/oil filled (with or without radiators/fans) up to 1.5MVA,
dry type power transformers/3 phase 300 KVA to 2MVA or silicone filled or epoxy resin
insulated for indoor installations. All oil filled transformers are installed outdoor unless a
special layout with fire proof (resisting) material and appropriate barriers are used, then indoor
installation is possible. Distribution transformers can be of the pole mounted, vault or
padmounted type. The primary voltage of power transformers can be as high as 750 KV, though
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the most common are 345KV, 220KV, 115KV, for distribution transformers as high as 72KV
though the most common are 34.5, 25KV (27.6KV), 15KV.
7) What are the different types of overhead switches, padmounted switchgear and those of
lightninig arresters?
The different types of overhead switches are: either single or three phase, either manually
operated or electric/manual operated, either local control or remote/local control, oil insulatedor air or SF6. The different types of padmounted switchgear are: either manually or
manually/motor operated, controlled locally or locally/remotely, air or oil or SF6/vacuum
insulated, protective devices are either fuses or electronic devices. The configuration will,
generally, have four compartments with any combination of fuse or interrupter, switch, solid or
empty compartment. The different types of lightning arresters are: station, intermediate,
distribution (heavy duty, normal or light duty) and may be riserpole type.
8) What are the standards that govern distribution transformers? How are distribution
transformers defined?
The standards that govern distribution transformers are: CSA "Single phase & three phasedistribution transformers" Std. C2, CSA "Dry type transformers" C9, CSA "Guide for loading
Dry-type distribution and power transformers" C9.1 and CSA "Insulating oil" C50. The
distribution transformers are defined as follows: the voltage ratings (insulation class level of
primary -h.v.- winding, the primary and secondary windings rated voltage), short circuit
capability for a fault on the bushings of the transformer (current value and its corresponding
duration), dielectric test values (applied voltage for 1 minute, full wave and chopped BIL and
time to flash over for the chopped), outdoor transformer bushings ratings (defined by their
insulation class, 60HZ 1 minute/dry, 10 second/wet dielectric withstandability, the full wave and
chopped BIL), audible sound levels and induced voltage tests.9) How are wooden and concrete poles defined?
The wooden poles are defined as follows: the class (1 to 7-4500LB to 1200 minimum horizontal
breaking load when applied 2 ft. from pole top), the minimum circumference at pole top level
(27" to 15"), length of pole (25 to 110 ft, generally), minimum circumference at the ground level
(distance from butt), the wood species (Western Red Cedar, Southern Yellow Pine, Douglas Fir,
Western Larch), the treatment against attack from fungi and insects (eg. creosote oil, ammonical
copper fatty acid, pentachlorphenol or chromated copper arsenates) and the weight per pole.
The concrete poles are defined accordingly: ultimate load (class A to J, 600 LB to 4500 LB,
respectively), the length, the manufacturing process (regular or prestressed class), the steel
reinforcing rods (cage) tensile strength, the diameter, the raceway diameter, spacing and
diameter of holes in the pole, grounding bars (galvanized or coated) surface treatment.
10) What are the different applications of oil switches and what are their defining
parameters?
The different applications of overhead oil switches in utility distribution systems are: general
purpose for inductive and resistive loads & capacitor (capacitive current switching). The
defining parameters are: the rated maximum voltage, the basic impulse level, the dielectric
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withstand, continuous current, inductive load switching, capacitive switching current, making
current, momentary current, short time current rating; for the control circuit: nominal and range
of operating voltage, trip coil current. The weight, dimensions, oil volume and speed of
operation for the switch are also important defining data. The other two devices that may use oil
as the switching medium are the sectionalizes and reclosers.
11) How are overhead air switches classified?The following is the classification of the air insulated switches according to their breaking type:
side break switches, vertical break and double break. The different types of mountings for such
switches are: upright, vertical, triangular, tiered outboard mounting and pedestal. The insulators
of the switch may be epoxy or porcelain, the base is insulated or steel.
12) How are padmounted switchgear defined?
Padmounted switchgear can be defined (specified) accordingly: the insulating material used i.e.
air insulated, oil or gas, the nominal voltage class, maximum operating voltage, the basic
impulse level, the current ratings for the different sides i.e. continuous current, load interruption
(resistive, inductive including no load transformer magnetizing and capacitive including cablecharging), momentary, fault close, the dimensions of the gear, the opening for the cable entry,
properties of steel work (like thickness -gauge, surface treatment and finish), the weight and the
assembly voltage withstandability tests (A.C. and D.C.). The speed of operation (current time
curves) for the fuses or protective devices had to be specified.
13) What are the important parameters by which lightning arresters are defined?
The important parameters by which L.A. are defined are: duty cycle voltage, impulse test crest
voltage, power frequency voltage (dry and wet - for outdoor installations), impulse current
rating, maximum continuous operating voltage, switching surges capability, high current/short
time and low current/long duration rating, material of housing, design of internals ie. gapped or
gapless elements (non-linear resistance material).
14) How would copper conductors be defined?
The construction of copper conductors is defined as follows: cross section area, class of
conductor (indication of degree of flexibility), number of wires, diameter of wire, tensile
strength, elongation, diameter of conductor, type (concentric lays, compact or compressed) and
weight per 1000 ft.
15) How would ACSR (aluminum conductor steel reinforced) and ASC (aluminum
stranded conductor) be defined?
The defining parameters for aluminium conductor steel reinforced designs are: the Al area, the
total conductor area, steel/Al area ratio, number of Al wires, diameter of Al wire, area of steel
wire, diameter of steel wire, diameter of core (steel), diameter of conductor, tensile strength,
AWG size, total conductor weight per 1000 ft. and the ratio of Al weight to the total weight. The
defining parameters for aluminium stranded conductors are: the aluminum conductor area, the
quantity (number) of Al wires, diameter of each wire, the diameter of the conductor, the tensile
strength, the elongation and the total weight of conductor per 1000 ft.
16) How would AASC (aluminum alloy stranded conductor) and self-dampening/compact
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ACSR be defined?
The defining parameters for Aluminium alloy stranded conductors are: Al alloy area and the
equivalent Al area, number of Al alloy wire, diameter per wire, overall diameter of conductor,
AWG/KCMIL, weight/1000 ft, tensile strength and elongation. The defining parameters for self-
dampening conductors and compact ACSR are: aluminium area, total conductor area, steel to Al
area (ratio), number of Al wires, number of steel wires, core (steel) diameter, overall conductordiameter, conductor weight/1000 ft length, ratio of Al weight to total weight, tensile strength
and elongation.
17) What are the different types of cable splices and terminations?
The different types of cable splices are: tapped, heat shrinkable and cold shrinkable. The major
components of a splice are: cable adapters, splice housing, conductor contact, conductive insert,
retaining rings/tube, interference fit and grounding eye. The different types of cable
terminations are: the fully taped, moulded stress cone and tape, one piece moulded cable
termination, porcelain terminators, heat shrinkables and potheads.
18) What are the different types of connectors and elbows?The different types of connectors are: the mechanical (for Al and/or Cu conductors), the
compression, the wedge (to connect main conductors to taps), hot line clamps (the main
overhead to equipment connection) and the stirrups (wedged or bolted). The two types of
separable connectors (elbows) are the dead break and load break. The major components of
elbows are: the connector, the moulded insulating body, cable adapter, the test point, the semi-
conducing shield, semi-conducting insert, grounding tabs the pulling eye, the probe (for load
break, it is field replaceable with abelative material arc follower).
19) What are the design tests performed on the separable connectors?
The design tests performed on the elbows are: partial discharge inception and extinction levels(corona), withstand power frequency voltage capability (a.c. and d.c.), impulse voltage
withstand level, short time current rating, switching test, fault closure rating, current cycling for
insulated and uninsulated connectors, cable pullout from elbow (connector), operating force,
pulling eye operation, test point cap pulling test, shielding test, interchangeability, accelerated
thermal and sealing life, test point capacitance (voltage presence indication) test.
20) What are the different types of insulators, their material and characteristics?
The different types of insulators are: the pin, the suspension and the post (vertical and
horizontal). The different insulators materials are: porcelain, glass, fibreglass, polymer and
silicone. The properties of insulators can be broadly classified into: mechanical, electrical,
environmental and maintenance. The mechanical can further be classified into: different loads
the insulators is subjected to due to weights of supported components, short circuit, ice, etc.
(normal, design, cyclic, torsional, overloads - exceptional), safety factors, single or multiple
insulator assemblies and aging effect on strength of insulator. The electrical parameters defining
the insulators are: BIL, power frequency withstandability (dry, wet and flashover level), leakage
distance, power arcs effect, performance under steep front voltage wave, clearances and
performance under contamination. The environmental characteristics can be further broke down
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into: insulator ageing under ultra-violet rays and dry arcing, type of contamination, radio
interference voltage, washing requirements, corrosive environments and temperature range.
21) What are the functions of DAC (distribution automation and control)? Sketch the
typical underground distribution arrangements and the overhead distribution system.
Distribution automation and control functions can be classified into: load management, real
time operational management and remote metering. The first function may be subclassified into:discretionary load switching, peak load pricing, load shedding and cold load pick-up. The
second function is subclassified into: load reconfiguration, voltage regulation, transformer load
management, feeder load management, capacitor control, fault indication/location/isolation,
system analysis/studies, state/condition monitoring and remote connect/disconnect of services.
Fig. 4 shows the underground arrangements and fig. 5 shows the typical overhead system.
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22) What are the major information obtained from a distribution system SCADA? Show a
block diagram of the major components of a SCADA (system supervisory control & data
acquisition). Sketch a diagram to show a typical automated distribution system with power
and communication lines.
The major information obtained from a SCADA in a power distribution system are: indications
(eg. state change like opening or closing of circuit breakers, load break switches, reclosures,
disconnects, operation of a relay or fault indicators) of events or alarms, levels (eg. oil level, tap
changer position, reading from pressure gauges), pulses (eg. energy meter counters),
measurands (eg. current, voltage, power reading, temperature of oil or windings, leakage
current). Fig. 6 shows a typical SCADA and fig. 7 shows a single line for an automated system.
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23) What are the basic modules in a PLC (programmable logic controller) system? Sketch
a front plate of 2 of the basic modules. Sketch a block diagram showing the interrelation of
the major modules.
The basic modules of a PLC system are: the processor, the input/output (they can further be
classified into digital and analog), process control (proportional/integral/derivative), stepper
motor, interface modules (they can be further classified into: local and remote, local and remote
transfer, network, network transfer, multimedia network interface, peripheral devices (they
include loader/monitor, process control stations, CRT programmers, hand held programmers,
tape loader). Fig. 8 shows the front plates of the local and remote interface units, fig. 9 shows a
typical block diagram including the racks, interface/ input/ output/ network interface modules.
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24)For an overhead conductor with size = 556.5 MCM, aluminum core with 19 strands
and operating voltage of 25 KV, calculate the reactance at 60 c/s and 50HZ per 1000 ft, the
resistance (AL1350) per 1000 ft, the capacitance, charging current/1000ft and surge
impedance.
Given: Conductor details: 556.5 MCM/19 strands/Al 1359.
Nominal voltage: 25 KV, frequency: 60 & 50 c/s, length 1000 ft, conductor diameter: .855"
(from tables), area: .437 inch2 (from tables or 7.854(1000)(556.5)/(10+7) = .437 in.2)
L = (2)/(10+7)[ln(d/r')] H/m = (2/10+7)ln 12(2)/.855(.7788) (at 1 ft spacing)
L= 7.17(1000)/3.28(10+6) = 2185/10000000 H/1000ft.
XL
= 2 pi 60 L = .082 OHM @ 60 c/s and XL
= .068 OHM @ 50 c/s , where pi=3.141592654
R = .0927 microOHM ft (1000)/.437/(12)(12) = .0305 - ignoring skin effect, taking into account
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approximate skin effect then R = .0305(1.15) = .035 OHM
C = 1/ (10+9
)(18)(ln d/r)F/m = 1/ (10+9
)(18)(ln 12/.855/2) = .0166/10+9
C = .0166(1000)/3.28(10+9) F/1000ft = 5.08(10-9) farad/1000ft
XC
= 1/2 pi f C = 5.22 (10+5) OHM,
charging current = 25000/1.732(5.2)(10
+5
) = .028 amp/1000ftZ = surge impedance under these conditions = (L/C).5)= 207 OHM
25) For an underground XLPE cable, size = 250 MCM, aluminum 1350 core with 37
strands and operating on 25 KV system, calculate the reactance at 60 & 50 HZ per 1000 ft,
resistance per 1000 ft, capacitance, surge impedance, charging current/1000 ft, speed of
propagation of the wave and the insulation resistance.
Given: cable data: 250 MCM, XLPE, AL1350, 37 strands, 25 KV, 1000 ft length, conductor
dia.: .575 in, area = .196 in2), dia. over insulation: 1.16 ", e = 3.5, where e is the dielectric
constant
L = (2/10+7)[ln 12(2)/(.575)(.7788) = 2427/(10+7) H/1000 ft at 1 ft spacing
XL
= .092 OHM @ 60 c/s and .076 OHM @ 50 c/s
R/1000 ft = .0927(1000)(144)/.196 = .068 OHM (1.15) = .078 OHM
C = 3.5/)10+9
)(18)(ln 1.16/.575) = .277/(10 )F/m(1000)/3.28 = 84/(10+9
) F/1000ft
L at insulation neutral or sheath = 2 ln 1.16/.575(.7788)/(10+7) = 2 (10-7) H/m
Z = surge impedance = (L/C).5
) = 27 OHM, XC
= 1/2 pi C 60 = 31578 OHM/1000ft
Charging current for 1000 ft cable length =(25000/1.732)(31578) = .46 amp.
v = speed of propagation = (1)/(LC).5
) = 1.34(10+8
) m/sec.
Volumetric insulation resistance = (ra) (ln 1.16/.575)/(2pl)(12)(2.54), where ra is the resistivity
or specific resistance of the dielectric
assume ra = 6(10+14), Rvolumetric
= 6(10+14)(.7)/191511 = 2193 MegaOHM/1000 ft.
26) If the overhead conductor and the underground cable of problems 24 & 25 are
connected in series and a voltage wave of 25 KV is travelling through the overhead portion,
calculate the reflected and refracted powers at the junction point.
Zline
= 207, Zcable
= 27, KV = 25
reflacted voltage = (27-207)25/1.732(207+27) = -11.1 KV
refracted voltage = (2)(27)(25)/1.732(207+27) = 3.33 KV
refracted power = 3 (Vph)(Vph)/Zcable = 3(3.33)(3.33)/27 = 1232 KW
reflected power = 3(-11.1)(-11.1)/207 = 1785 KW
27) Provide the differential and gas accumulation/sudden release protection to a 100 MVA
power transformer, 220/25KV with +/-16% tap changer. Assume that the available relays
have a pick-up setting between 20-50% of relay rating with an adjustable slope of 20-50%
and another with fixed slope and restrained pick-up between 20 and 50% and
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unrestrained pick-up of 8, 13, 20 x relay nominal current. The pressure gas relays have two
settings, for the trip 5.2 - 17.2 KPa and for the alarm 200-400 CC. The tap changer gas
pressure trip can be set between 35-390 KPa.
I excitation = 5% of full load primary, C.T. error = 2.5%, relay rating = 5A, C.T. primary
current = 1.5 x full load current of transformer.
I primary = 100 (1000)/(220)(1.732) = 262 AI secondary = 262 x 220/25 = 2300 A
Using a 1200/800/200:5A C.T. on the primary side (the C.Ts are delta connected), 3500 : 5A
C.T. on secondary side (the C.Ts are wye connected) of the power transformer. Turns ratio of
C.T. on primary winding = 800/5 = 160, on secondary = 3500/5 = 700. Relay current due to
primary C.T. at f.l. = (262/160) 1.732 = 2.8 amp, relay current due to secondary C.T. at f.l. =
2300/700 = 3.28 amp, relay current ratio = 3.28/2.8 = 1.17. Mismatch at midpoint changer and
full load = 17%.
At 220 + 16% = 255KV tap, maintaining secondary voltage at 25KV, primary full load current
= 100 (1000)/255 (1.732) = 226 amp, relay current = 226/160(1.732) = 2.45amp.,voltage of 25KV on the secondary while primary = 220 - 16 % = 185 KV primary full load current =
100(1000)/185(1.732) = 312 amp., relay current = 312/160 (1.732) = 3.4 A
Mismatch for + 16% = 3.28/2.45, mismatch for -16% = 3.28/3.4 which are 34 % and -4 %,
respectively. The maximum mismatch = 34 %, add 6 % as safety margin. Thus the slope
adjustment = 40 % (range is 20 to 50 %). The pick-up level under full load current =
inacccuracies + esciting current + allowance for the limited restraint at emergency load through
currents = 2.5(5/100) + (1.732)(5(262)/160)(100) + (3.28-2.45) = .125 + .14 + .83 = 1.1 amp, the
pick-up setting = 40%(5) = 2 A (range 20 to 50 %).
The unrestrained instantaneous triping current = 13 x 5 = 65 amp. secondary relay current.
VERIFICATIONS:
Assuming a 100 MVAbase and 220/25 KVbase, Ibase (@ primary side) = 100/1.732)(220) =
262 amp., Ibase (@ secondary side) = 2300 amp.
Assuming an infinite source, 11% impedance transformer, a 3-phase fault on the secondary of
the transformer beyond the differential protection zone will produce 9 p.u. fault current (1/.11),
Iprimary = 2358 amp., Isec. = 20700 amp. The current from the primary side into the relay =
(1.732)2358/160 25.5 amp., from the secondary side = 20700//700 = 29.6 amp. A mismatch of
29.6/25.5 = 16 %.
Assuming the tap changer to be at 220KV + 16% = 255 KV and the impedance = 14%, the short
circuit fault current of a 3-phase fault = 1/.14 = 7.16 p.u., full load primary current = 232 amp.,
SCC on the primary side = 1661 A, SCC on the secondary side = 16468 A, relay current from
primary side = 1661(1.732)/160 = 18 A, relay current from the secondary side = 16468/700 =
23.5, the mismatch = 30%.
Assuming the tap changer at 220 KV - 16% = 185 KV and the impedance = 8%, a 3-phase fault
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current = 1/.08 = 12.5 p.u., primary current = 312 A, SCC on primary side = 3900 A, SCC on
secondary side = 28750 A, relay current from prim. side = 42.2 A, relay current from sec. side =
41.1 A, mismatch = 3%
GAS RELAYS:
Main tank alarm = 200 cc, main tank trip = 17 KPa above static head at relay level, tap changer trip =
100 KPa.
SUMMARY:
In this chapter, the defining parameters, classifications, tests and typical configurations of distribution
systems components were presented. The general properties of medium voltage EPR & XLPE cables
were given plus factory & site tests. For low voltage secondary cables, the defining parameters were
listed. For transformers, a broad classification was given. The defining parameters and the CSA
standards that govern the ratings, design, manufacturing and testing of distribution transformers were
presented. Other components found in overhead and underground distribution systems were covered
from their types and defining parameters point of view. These components are: lightning arresters,conductors, terminations, splices, connectors, elbows and insulators. Distribution systems automation
and SCADA were presented by covering the functions and data collected from such systems. Typical
systems were given to clarify this topic. The major modules found in a typical PLC (programmable
logic controllers) installation were presented. The numerical examples at the end of this chapter showed
how the line and cable constants (inductance, capacitance, resistance, inductive/capacitive reactances,
surge impedance, charging current and propagation speed) and the effect of the surge impedance on
travelling waves are calculated. They also demonstrated a method to select/adjust/verify the settings of
relays (differential & gas) used in the protection of power transformers.
REFERENCES:
1. Wildi, T "Electrotechnique", Les Presses de l'Universit Laval.
2. CSA, "Canadian Electricity Code", Part 1, std C22.1.
3. CSA, "Single phase & three phase distribution transformers", std C2.
4. Gonen "Electric power distribution systems engineering", McGraw Hill.
5. Kurtz, "The lineman's & cableman's Handbook", McGraw Hill.
6. Perry, "Chemical Engineers handbook", McGraw Hill.
7. ICEA S-66-524, "Cross linked thermosetting polyethylene insulated wire & cable for the
transmission & distribution of electrical energy".8. ASTM 2.03, "Non-ferrous metal products - electrical conductors.
9. Brady, "Materials handbook", Mcgraw Hill.
10.Kheir, "Computer Programming for Power System Analysts", Kheir.
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Lesson 3: Switchgear, circuit breakers, MCCS and contactors.
1) What are the defining parameters for low voltage circuit breakers?
2) What are the defining parameters for medium voltage circuit breakers?
3) What are the different types of interrupting media used in m.v.c.b.? What are the commonproperties for such quenching media?
4) What are the different types of switchgear assemblies and what are the subclassification of
each type? What are the standards governing switchgear assemblies & circuit breakers? What
are the types of batteries found in such equipment? Give a brief description of each type.
5) What are the defining parameters for low voltage alternating current magnetic
contactors/starters?
6) What are the defining parameters of l.v. combination starters?
7) What are the defining parameters for full voltage 2-speed starters?
8) What are the defining parameters of low voltage, reduced voltage starter units?9) What would a table defining the motor protection circuit breakers have as headings?
10) What would a table defining motor protection fuses have as headings?
11) What are the headings of a table defining m.v. controllers?
12) What are the general properties of constructional and stainless steels?
13)What are the different types of switchboard instruments and the different mechanisms? What
are the defining parameters for such devices?
14) What are the defining parameters for KWH, KVAR and solid state meters?
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15) What are the different constructions of protective relays? Give the defining parameters for
the different types of the following relays: overcurrent, over/undervoltage, differential and
distance.
16) A solved problem regarding the sizing of the breaking devices of a switchgear assembly.
Lesson summary
References1) What are the defining parameters for low voltage circuit breakers?
The defining parameters of low voltage circuit breakers are: the rated voltage, the circuit breaker
current rating, symmetrical interrupting capacity (with instantaneous and delayed integral
protective relays), close and latch rating for a second, the sensors current ratio, the functions
of protection on the integral overcurrent protective device, electrically/manually operated or
manually only, the weight and dimensions of circuit breakers, the indicators of the integral
protective device (if available). For electrically operated breakers, the range of operating
voltages and currents plus the nominal values for the solenoids/motors/trip coils are important
parameters, too.2) What are the defining parameters for medium voltage circuit breakers?
The defining parameters of medium voltage circuit breakers are: the voltage ratings (nominal,
maximum and minimum), the 3-phase MVA breaker rating, the rated current, the K factor
(Max./Min. ratio), symmetrical interrupting ratings (at maximum, nominal and minimum
voltage) in KA, the asymmetrical factor, the short time rating, the close and latch, the insulation
level (power frequency, impulse level), the weight, the dimensions, the interrupting medium, the
TRV capability, any arcing medium monitoring devices, circuit breaker closing time, tripping
time, interrupting time, spring charging time, the control voltages (nominal and range), the
spring charging current, close coil current requirement, the trip coil current rating and surges
switching capabilities.
3) What are the different types of interrupting media used in m.v.c.b.? What are the
common properties for such quenching media?
The interrupting media used in medium voltage circuit breakers are: air, oil SF6 and vacuum.
The general properties of fluids used in arc extinguishing chambers in m.v. c.b. are: high
dielectric strength of the gas or liquid, thermally and chemically stable, non-inflammable, high
thermal conductivity, low dissociation temperature, short thermal time constant, should not
produce conducting material during arcing. Gases used so far in m.v. c.b. can be classified into
simple (air) or electronegative (SF6).
4) What are the different types of switchgear assemblies and what are the subclassification
of each type? What are the standards governing switchgear assemblies & circuit breakers?
What are the types of batteries found in such equipment? Give a brief description of each
type.
The different types for switchgear assemblies are: indoor and outdoor. The subclassification for
the indoor is: standard, sprinkler proof, arc proof, dust proof, seismic proof, metalclad
construction vs. metal enclosed, enclosure with or without a drip hood; for the outdoor is: walk
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in, walk in with working area, walk-in double row, non-walk in with or without working area,
enclosure for cable/bus entry or transformer throat, enclosure with thermal insulation/isle
heaters and finally indoor cubicle design installed in an outdoor house.
The standards that govern circuit breakers/switchgear design testing and application are: ANSI
C37 series including .09 "Test procedure for A.C. high voltage circuit breakers rated on a
symmetrical current basis", .04 "Rating structure for A.C. high voltage circuit breakers rated ona symmetrical current basis", .06 "Preferred ratings and related required capabilities for A.C.
high voltage circuit breakers rated on a symmetrical current basis", .20 "Switchgear
assemblies", IEC 56 "High voltage A.C. circuit breakers", IEC 60 series "High voltage test
techniques", IEC 694 "Common clauses for high voltage switchgear and controlgear",
C22.2#31" switchgear assemblies" and CAN3-C13 "Instrument transformers.".
The different types of stationary batteries used in conjunction with these equipment are: lead
acid and nickel cadmium. The first has three possibilities of positive plates which are: the
pasted, multitubular and plante type. The negative plates will be of the pasted type, the grid for
the plante and multitubular is made of lead antimony and that for the pasted is made of either
lead antimony or lead calcium. The active material in the +ve plate is lead oxide and in the -ve
plate is sponge lead. The electrolyte is a solution of diluted sulphuric acid with specific gravity
of approximately 1.2. For the nickel-cad batteries, the plates may be of the pocket or the sintered
type. The active material (nickel hydrated for the +ve plate and cadmium sponge for the -ve) is
placed in nickel plated steel holders. The electrolyte is a solution of potassium hydroxide diluted
in water with a specific gravity of 1.16 to 1.19 at 25 C.
5) What are the defining parameters for low voltage alternating current magnetic
contactors/starters?
The defining ratings for low voltage alternating current magnetic contactors/starters are: the
NEMA size, the voltage rating, the maximum HP for single phase and three phase motors (for
both nonplugging/nonjogging and plugging/jogging applications), the continuous current rating
of the contactor/starter, the service limit, transformer switching capability rating for single and
three phase applications, the capacitive switching capability (in volt and KVAR), the
dimensions, the weights, the overload protective element type and rating.
6) What are the defining parameters of l.v. combination starters?
The defining parameters of low full voltage combination starter units: the starter size, the
maximum motor HP at the different standard voltages (200v, 230, 460 and 575v), whether the
unit is reversing or non-reversing, the fuse or circuit breaker size (used as a protection against
short circuit or protection/load break device), the size of the unit in inches or space factor, the
weight of the unit, method of attachment to riser bus bars of MCC (bolt-on or plug in) and size
plus type of motor overload protection element/relay.
7) What are the defining parameters for full voltage 2-speed starters?
The defining parameters for full voltage 2-speed starter units are: the starter size, the HP
(maximum) at the different nominal voltages, the circuit breaker or fuse size for the short circuit
protection, the dimension in inches or space factor for the 1-winding and 2-winding motor
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starter unit, unit weight, method of attachment to MCC and the type plus size of o/c protection
device.
8) What are the defining parameters of low voltage, reduced voltage starter units?
The defining parameters of low voltage reduce voltage starter units (applicable to part winding
and auto-transformer units): the starter size, the maximum motor HP at the different rated
voltages, the circuit breaker or fuse rating, the dimensions or space factor for the units, theweight, the size plus type of the o/l element, the installation method in the MCC.
9) What would a table defining the motor protection circuit breakers have as headings?
The table will have the following headings: 3-phase motor HP, the motor full load current at the
different nominal voltages, the circuit breaker continuous current, the different adjustments (eg.
7x/11x/13x), the weight and dimension, the adjustable range.
10) What would a table defining motor protection fuses have as headings?
The fuses for motor protection table will have the following: the maximum motor HP rating, the
motor full load current rating, the fuse size for the different voltage classes, the fuse type (50KA
interrupting fuse, HRC-200 KA I.c., code fuse - 10KA or size L over 600a - 200KA), the fuseweight.
11) What are the headings of a table defining m.v. controllers?
The table for a medium voltage controller (contactor and fuse) will have the following headings:
the contactor maximum continuous current, the interrupting capacity (at the specified KV), the
designation, the voltage rating and range, the interrupting capacity of the fuse (in KA and MVA
@ the rated voltage), the maximum HP motor rating for the motor design/p.f./voltage/controller
current rating, the dielectric withstand voltage, the controller -type (full voltage, reversing vs
non-reversing, reduced voltage - auto transformer vs reactor). The m.v. fuses for controllers can
be defined when the following values are given: the motor locked rotor current, motor full loadcurrent x service factor, the maximum continuous current rating of the fuse inside the
compartment, the fuse size, the peak current let through characteristics.
12) What are the general properties of constructional and stainless steels?
The mechanical properties of constructional steels are: the ASTM designations, the thickness
range, yield point, elongation as a percent of the length (eg. in 8 inches), tensile strength and
weldability. Those for stainless steel are: A1SI designation, condition, .2% yield point,
elongation in 2 inches length, tensile strength and area reduction.
13)What are the different types of switchboard instruments and the different
mechanisms? What are the defining parameters for such devices?The different types of switchboard instruments: voltmeters, wattmeters (single phase and
polyphase), varmeters, power factor meters, frequency meters, ammeters. The different
mechanisms are: taut band suspension, repulsion vane, electrodynamic, D'Arsonval/zener diode.
The defining parameters: impedance, input resistance, inductance, voltampere/W/RVA/p.f. of
mechanism (burden), mechanism type (self-contained or transformer), instrument transformer
ratio, scale and units/scale division.
14) What are the defining parameters for KWH, KVAR and solid state meters?
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The defining parameters of KWH meters are: type of meter and number of elements, connection
method, weight/dimension, burden data for each type/elements number (phase, potential circuit
and current circuit), KVA attachment data (meter, volt, scale/multiplier, amp range), disk
constant-WH/disk revolution, register ratio. Those for KVAR are: burden (potential and current
circuits), weight and dimensions (for the different designs), temperature rise, ratings and
enclosures for the different types/numbers of elements. Those for solid state meters are:potential input ratings (input voltage, impedance, burden, overload capability, current input
ratings (burden, input current and impedance, overload), weight & dimensions, control power
requirements, communication capability (protocol, baud rate, standards), measured parameters
(measurands).
15) What are the different constructions of protective relays? Give the defining
parameters for the different types of the following relays: overcurrent, over/undervoltage,
differential and distance.
Relays can be classified based on their construction into electromechanical (magnetic induction,
magnetic attraction, thermal and D'Arsonval), solid state and microprocessor/digital based.The defining parameters for electromechanical based o/c relays are: weight and dimensions,
type of relay time current characteristics curves (inverse definite minimum time, short time,
very inverse, extremely inverse), current tap range, time dial range, operating time, burden and
thermal ratings (continuous current, 1 sec. rating and power factor, at tap setting, at 3 times tap,
at 10 times tap and at 20 times tap). Those for o/c solid state relays are: weight and dimensions,
current rating, frequency, d.c. supply voltage and burden, burden on C.T., setting range for the
instantaneous and time delay functions, time multiplier setting, operating times for time delay
and instantaneous functions. The parameters for the microprocessor based are: weight and
dimensions, rated current, setting range, rated current for the ground fault unit and the setting
range, operating times, burden, overload capacity, control power voltage and burden, resetting
times and contacts ratings.
The defining parameters for the over/undervoltage electromechanical relays are: the weight and
dimensions, the continuous input voltage rating, the short time (eg. 2 minute) voltage rating, the
taps' range, burden, time dial range. Those, for the solid state are: weight and dimension, input
voltage ratings, pick-up range, drop-out setting range, time delay setting (pick-up and drop- out),
control (auxiliary) supply voltage and range.
The defining parameters for a electromechanical differential relays are: the weight and
dimensions, the application i.e. transformer differential or motor or generator differential
protection, number of phases i.e. single or three phase, number of operate and restraint circuits,
minimum trip current, burden, operating time, type i.e. fixed or variable percentage (biased)
relay, current inputs.
The defining parameters for solid state percentage (biased) relays with instantaneous tripping
and harmonics restraint: weight and dimensions including interposing relays (if any), the
currents input, overload capacity, frequency, interposing C.T. ratio (if any), burden, operating
current, restraint current settings, unrestrained current setting range, operate time, reset ratio,
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order of harmonics restrained i.e. 2nd or 5th, auxiliary power voltage and power consumption,
burden of operating and restraint circuits.
The defining parameters for the electromechanical distance relays are: the weight and
dimensions, characteristics type i.e. impedance/reactance/admittance/angle impedance
(OHM)/offset MHO/modified impedance/complex/elliptical/quadrilateral, relay reach, taps,
variation in reach and maximum torque angle over the range of taps, burden on instrumenttransformers. Those for solid state relays, the parameters are: weight and dimensions, input
circuits, burden, control voltage and consumption, characteristics torque (angle), reset ratio.
16) A unit substation is connected to the utility line through a 25KV circuit breaker which
feeds a 5 MVA transformer, 5% impedance 3-phase, 25KV/600v. The low voltage winding
of the transformer is connected through a 600v main breaker to a low voltage switchgear.
The switchgear has 3 circuit breakers feeding each a 400 HP motor, .25 reactance, 1800
RPM. A fourth circuit breaker is feeding a 750 KVA, 4.5% impedance 600/208v and the
last breaker in this lineup feeds the other 600/347v loads (2 MVA). For a fault (L-L-L) on
the main bus, calculate the fault current with and without motor contribution and give the
contribution of each motor. Calculate also the motor breaker fault current for a fault on
the motor terminals. Assume on infinite source. Give the breakers' size on the low voltage
side of transformer, give a typical unit substation layout.
MVAbase
= 5, KVbase
(primary side of power transformer) = 25, KVbase (secondary side) = .6,
Ibase = 5 (1000)/1.732(.6) = 4811 amp= full load current. Full load current on primary side =
4811(600)/25000 = 115 amp. Fault current for 3-phase fault on main bus = 1/.05 = 20 p.u. =
20(4811) =96 KA (from suply side).
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Xmotor
= .25 (5000/350) = 3.5 p.u. (assuming motor p.f. = .85)
3 motors cotribution for a 3-phase fault on main bus = 1/1.16 = .85 p.u. = .85(4811 = 4089 amp.
Total fault current = 96 + 4 = 100 KA
Contribution per motor = .283 (4811) = 1370 amp.
For L-L-L fault on motor terminals, the fault current through the motor breaker = 2(1.37) + 96 =
98.7 KA.Motor full load current = 400(746)/1.732(.85)(.9)(600) = 375 amp. (assuming a motor efficiency
of .9)
F.L. current to 750 KVA transformer = 750 (1000)/1.732(600) = 722 amp.
F.L. current to the 2 MVA load = 2000/1.732(.6) = 1924 amp.
For the main low voltage circuit breaker:
Continuous curent (frame size) = 5000 amp., I.C. = 120 KA
For the motors circuit breakers (fused or current limiting):
Continuous current = 800 Amp, I.C. = 100 KA , Sensors ratio + 400/5 amp.
For the 750 KVA transformer (fused or current limiting):Continuous current = 1600 amp., I.C. = 100 KA, Sensor = 800/5 amp.
For the 2 MVA load (fused or current limiting):
Continuous current = 2000 amp., I.C. = 100 KA, Sensor = 2000/5 amp.
Fig. 11 shows the typical layout.
SUMMARY:
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In this chapter, circuit breakers, switchgear assemblies, starters and controllers were presented
from the definition, standards and brief description points of view. For low voltage circuit
breakers, the coverage included the ratings of the power and electric control circuits. For
medium voltage circuit breakers and switchgear assemblies, the coverage included the breakers
interrupting media, breakers ratings, governing standards, different types of switchgear
assemblies and types of stationary batteries found in such assemblies. For l.v. starters, thecoverage included the defining parameters for the following devices: contactors, combination
starters (full voltage/single speed, full voltage/two speed, autotransformer/part winding reduced
voltage), motor protection fuses and magnetic element only circuit breakers). For medium
voltage starters, the coverage included the contactors and fuse defining parameters. Certain
related miscellaneous topics were also covered briefly like the gene