FAKULTEIT INGENIEURSWESE
FACULTY OF ENGINEERING
Elektriese Aandryfstelsels 324
Hooftoets I
Main Test II
29 Maart 2012
29 Maart 2012
Electrical Drive Systems 324
Tydsduur:
Duration:
2h
Eksaminator
Examiner
Interne Moderator
Internal Moderator
Dr. P.J. Randewijk
Mnr. J.C. Bekker
Instruksies
Totaal:
Total:
65
Instructions
1. Alle berekening stappe moet duidelik getoon
word.
1. All calculation steps must be shown clearly.
2. Maak deurgaans van eenvoudige sketse of ekwivalente stroombaandiagramme gebruik om u
antwoorde te illustreer.
2. Continuously make use of simple sketches or
equivalent circuit diagrams to illustrate all answers.
3. Die finale antwoorde moet in ink geskryf word.
3. The final answers must be written in ink.
4. Punte sal afgetrek word indien antwoorde se
eenhede nie getoon word nie, b.v. 123,45 V,
123,45 mA, 123,456 kW, ens.
4. Marks will be deducted if no units for answers
are shown, e.g. 123,45 V, 123,45 mA, 123,45 kW,
etc.
5. Werk met ten minste vier (4) beduidende syfers,
b.v. 123,4 V, 12,34 V, 1,234 V, ens.
5. Work with at least four (4) significant numbers,
e.g. 123,4 V, 12,34 V, 1,234 V, etc.
6. Sakrekenaars soos voorgeskryf vir die eerste
twee jaar van B.Ing. mag gebruik word.
6. Pocket calculators as prescribed for the first two
years of B.Eng. may be used.
7. As daar, na u mening, enige parameters ontbreek
of verkeerd is, maak redelike aannames, verklaar
duidelik waarom u aannames gebruik en gaan
voort.
7. If, in your opinion, there are any missing or
incorrect parameters, make reasonable assumptions, stating them clearly and continue.
8. Indien daar ’n verskil tussen die “Afrikaanse” en
“Engelse” gedeeltes is, stel duidelik watter taal
se inligting u gebruik vir u antwoord.
8. If there is a difference between the “Afrikaans”
and “English” section, state clearly which language’s information you are using for your answer.
9. Geen selfone word toegelaat nie.
9. No cellphones are allowed.
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page 1 of 5
Vraag 1:
Algemeen Vrae
[20]
Question 1:
General Questions
[20]
(a) Wat is die funksie van die kommutator [1]
by GS masjiene?
(a) What is the function of the commutator [1]
in DC machines?
(b) Wat is die funksie van kommutasiepole [1]
by GS masjiene?
(b) What is the function of commutating [1]
poles in DC machines?
(c) Vir ’n afsonderlik gemagnetiseerde GS
motor:
i. lei ’n vergelyking af vir die ont- [4]
wikkelde
draaimoment,
τind ,
as ’n funksie van spoed, ωm ,
vir ’n gegewe ankerklemspanningswaarde, VA .
(c) For a separately excited DC motor:
i.
deduce an equation for the devel- [4]
oped torque, τind , as a function of
speed, ωm , for a certain armature
terminal voltage, VA .
ii. stip nou die verwantskap tussen [2]
τind en ωm vir VA1 en VA2 met VA2 >
VA1 .
ii. now plot the relationship between [2]
τind and ωm for VA1 and VA2 with
VA2 > VA1 .
(d) Indien ons die ankerweerstand by [5]
sinchroon masjiene ignoreer, bewys
vanaf ’n fasordiagram vir die sinchroon
masjien tydens generator werking, dat
die ontwikkelde drywing van ’n
sinchroon masjien deur die volgende
vergelyking gegee kan word:
(d) If we ignore the armature resistance [5]
of a synchronous machine, prove from
a phasor diagram of the synchronous
machine for generator operation, that
the developed power of the synchronous machine can be given by the
following equation:
Pconv =
3Vφ E A
sin δ
XS
(e) Vanaf die onderstaande ekwivalente [7]
per fase stroombaandiagram vir
driefase induksiemasien,
+
R1
jX1
(e) From the per phase equivalent circuit [7]
diagram for a three-phase induction
machine shown below,
jX2
I1
Vφ
R2
I2
RC
jXm
R2 1−s
s
−
verduidelik wat elke komponent in die
ekwivalente stroombaan modelleer.
Vraag 2:
GS-Masjiene
’n 120 V, 20 A newegeskakelde GS masjien
met ’n ankerweerstand, R A = 1,0 Ω, ’n
veldweerstand, R F = 60 Ω en ’n eksterne
verstelbare veldweerstand, Radj = 60 Ω het
’n magnetiseringskenkromme soos op die
volgende bladsy getoon.
bladsy 2 van 5
explain what each component in the
equivalent circuit is modelling.
[10]
Question 2:
DC Machines
[10]
A 120 V, 20 A shunt connected DC machine
with an armature resistance, R A = 1,0 Ω, a
field resistance, R F = 60 Ω and an external
adjustable field resistance, Radj = 60 Ω has
a magnetisation curve as shown on the next
page.
page 2 of 5
Indien die GS masjien aan ’n 120 V toevoer
verbind word en ons die spanningval oor
die borsels ignoreer:
If the DC machine is connected to a 120 V
supply and we ignore the voltage drop
across the brushes:
(a) Bereken die ken ontwikkelde drywing
van die GS masjien met,
(a) Calculate the rated developed/induced
power of the DC machine when,
i.
die eksterne verstelbare veldweer- [2]
stand, Radj = 0 Ω
i.
ii. die eksterne verstelbare veldweer- [1]
stand, Radj = 60 Ω
(b) Bereken die kenspoed van die GS
masjien met,
i.
the external adjustable field resis- [2]
tance, Radj = 0 Ω
ii. the external adjustable field resis- [1]
tance, Radj = 60 Ω
(b) Calculate the rated speed of the DC machine when,
die eksterne verstelbare veldweer- [3]
stand, Radj = 0 Ω
i.
the external adjustable field resis- [3]
tance, Radj = 0 Ω
ii. die eksterne verstelbare veldweer- [2]
stand, Radj = 60 Ω
ii. the external adjustable field resis- [2]
tance, Radj = 60 Ω
(c) Wat sal met die spoed van die GS [2]
masjien gebeur indien die eksterne
veldweerstand sou uitbrand?
Verduidelik.
(c) What will happen to the speed of this [2]
DC machine if the external field resistances were to burn out? Explain.
Oopklemspanning / Open Circuit Voltage, VT [V]
160
140
Spoed / Speed = 1 500 r/min
120
100
80
60
40
20
0
0, 0
0, 5
1, 0
1, 5
2, 0
2, 5
3, 0
3, 5
4, 0
Veldstroom / Field Current, IF [A]
Vraag 3:
GS-Masjiene
[15]
Question 3:
DC Machines
[15]
Die volgende toetse word op ’n 225 kW,
830 o.p.m., 440 V, 560 A afsonderlik gemagnetiseerde GS masjien gedoen.
The following tests are conducted on a
225 kW, 830 r.p.m., 440 V, 560 A separately
excited DC machine.
Vashou-rotor toets data:
Blocked-rotor test data:
VT
IA
bladsy 3 van 5
=
=
16,9 V (insluitende borsels / including brushes)
500 A
VF
IF
=
=
440 V
7,52 A
page 3 of 5
Nullas toets data:
VT
IA
n
=
=
=
No-load test data:
440 V (insluitende borsels / including brushes)
23,1 A
863 o.p.m. / r.p.m.
VF
IF
=
=
440 V
7,52 A
N.B. Aanvaar dat die spanningsval oor die
borsels gelyk is aan 2 V in totaal en
dat ons die diverse verliese kan ignoreer.
N.B. Assume that the voltage drop across
the brushes is 2 V in total and that the
stray losses can be ignored.
(a) Bereken die ankerweerstand, R A .
[2]
(b) Bereken die roterende wrywingskoeff- [3]
isiënt, B, wat met die rotasieverliese
van die GS masjien geassosieer kan
word.
(c) Vanaf die vashou-rotor en nullas toets
data en met IF = 7,52 A,bereken,
(a) Calculate the armature resistance, R A . [2]
(b) Calculate the rotational friction coeffi- [3]
cient, B, that can be associated with the
rotational loss of the DC machine.
i.
die kenspoed van die masjien en [4]
lewer kommentaar oor hoe dit met
die naamplaat ken gegewens vergelyk.
(c) From the blocked-rotor and no-load
test data and with IF = 7,52 A, calculate,
i. the rated speed of the machine and [4]
comment on how it compares to the
name plate rated values.
ii. die ken uittreedrywing van die [3]
masjien en lewer kommentaar oor
hoe dit met die naamplaat ken
gegewens vergelyk.
ii. the rated output power of the ma- [3]
chine and comment on how it compares to the name plate rated values.
iii. die ken benuttingsgraad van die [3]
masjien.
iii. the rated efficiency of the machine.
Vraag 4:
Sinchroon Masjiene
[8]
Question 4:
Synchronous Machines
[3]
[8]
Hierdie vraag handel oor ’n 11 kV, 50 MVA,
0,9 nalopende arbeidsfaktor, 50 Hz, vierpool, ster geskakelde sinchroon generator
met ’n sinchroon reaktansie van 2,0 Ω en ’n
ankerweerstand van 0,2 Ω.
Die oop klem magnetiseringskenkromme
van hierdie sinchroon generator word op
die volgende bladsy getoon.
This question concerns a 11 kV, 50 MVA, 0,9
lagging power factor, 50 Hz, four pole, star
(Y) connected synchronous generator with
a synchronous reactance of 2,0 Ω and an armature resistance of 0,2 Ω.
The open circuit magnetisation characteristic curve for this synchronous generator is
shown on the next page.
(a) Bereken die GS veldstroom benodig [5]
wanneer die sinchroon generator by sy
kenwaardes bedryf word.
(a) Calculate the DC field current required [5]
for the synchronous generator to operate at its rated values.
(b) Teken ’n netjiese fasor diagram vir hi- [3]
erdie bedryfstoestand en toon duidelik die spanningsval oor die sinchroonreaktansie, jXS I A , en ankerweerstand,
R A I A , die geı̈nduseerde spanning, E A ,
die belastingshoek, δ, asook die toevoerlynstroom, I A .
(b) Draw a neat phasor diagram for this [3]
operating condition and clearly show
the voltage across the synchronous reactance, jXS I A , and the armature resistance, R A I A , the induced voltage, E A ,
the power angle, δ, as well as the supply line current, I A .
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page 4 of 5
Oopklemspanning / Open Circuit Voltage, VT [kV]
20
18
16
14
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
Veldstroom / Field Current, IF [A]
Vraag 5:
Sinchroon Masjiene
[12]
Question 5:
Synchronous Machines
[12]
Hierdie vraag handel oor ’n 1,0 MVA,
2,4 kV stergekoppelde driefase 50 Hz
sinchroonmotor
met
’n
sinchroonreaktansie van 0,9 per eenheid.
This question concerns a 1,0 MVA, 2,4 kV
wye connected three-phase 50 Hz synchronous motor with a synchronous reactance of 0,9 per-unit.
Die motor word gesinchroniseer aan ’n
oneindige 2,4 kV driefase 50 Hz bus.
The motor is synchronised to an infinite
2,4 kV driefase 50 Hz bus.
Sonder om die GS veldstroom te verander nadat dit gesinchroniseer is, word
die meganiese las verhoog tot by 750 kW.
Without changing the DC field current after synchronisation, the mechanical load on
the motor is increased to 750 kW.
(a) Bereken die belastingshoek, δ van die [4]
motor vir hierdie bedryfstoestand.
(a) Calculate the power angle, δ of the mo- [4]
tor for this operating condition.
(b) Met hoeveel persent moet die GS [6]
veldstroom vermeerder word sodat
die sinchroonmotor 450 kVAr reaktiewe
drywing kan lewer ten einde die arbeidsfaktor van die fabriek/aanleg te
verbeter indien E A ∝ IF .
(b) With what percentage must the DC [6]
field current be increased so that the
synchronous motor will be able to deliver 450 kVAr of reactive power in order to improve the power factor of the
factory/plant if E A ∝ IF .
(c) Met Vφ , die toevoerspanning, as ver- [2]
wysing, teken ’n netjiese fasordiagram (vir die nuwe bedryfstoestand)
en toon duidelik die spanningsval oor
die sinchroonreaktansie, jXS I A , die
geı̈nduseerde spanning, E A , die belastingshoek, δ, asook die toevoerlynstroom, I A .
(c) With Vφ , the supply voltage, as ref- [2]
erence, draw a neat phasor diagram
(for the new operating condition) and
clearly show the voltage across the synchronous reactance, jXS I A , the induced
voltage, E A , the power angle, δ, as well
as the supply line current, I A .
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page 5 of 5