Departement Elektriese, Elektroniese en Rekenaar-Ingenieurswese Eksamenvraestel Kopiereg voorbehou Module ELX 311 27 Mei 2009 Department of Electrical, Electronic and Computer Engineering Examination Question Paper Copyright reserved Module ELX 311 27 May 2009 Student se besonderhede: Student's details: Naam Name): Tel. nr. gedurende eksamen: Tel no. during examination: Studentenommer: Student number: Tel. nr. na eksamen: Tel. no. after examination: Eksameninligting: Examination information: Maksimum punte: Maximum marks: 90 Duur van vraestel: Duration of paper: 3 ure 3 hours Totale aantal bladsye (hierdie blad ingesluit): Total numer of pages (including this page): Volpunte: Full marks: 85 Oopboek / toeboek: Open / closed book: Toe Closed BELANGRIK- IMPORTANT 1. Die eksamenregulasies van die Universiteit van Pretoria geld. The examination regulations of the University of Pretoria apply. 2. Hierdie vraestel mag slegs in Afrikaans of Engels beantwoord word. This question paper may only be answered in Afrikaans or English. 3. ALLE berekening moet getoon word. ALL calculations must be shown. Interne Eksaminator(e): Internal examiner(s): 1. Mr. W. Badenhorst 2 Eksterne Eksaminator: External Examiner: Prof. MN Gitau Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 B Total 12 6 8 4 8 6 4 10 5 11 16 90
SECTION A / AFDELING A QUESTION 1 / VRAAG 1 [12] The relative permeability of the ferromagnetic material of Fig. Q1 is 1200. Neglect magnetic leakage and assume 5% increase in the effective air gap area due to fringing. All dimensions are in centimeters and the magnetic material has a square cross-sectional area. Die relatiewe permeabiliteit van die ferromag-netiese material van Fig. Q1 is 1200. Ignoreer magnetiese lekkasie en neem aan dat die effektiewe luggapingoppervlak met 5% toeneem weens ranteffekte. Alle dimensies is in centimeter en die magnetiesemateriaal het n vierkantige deursnit oppervlakte. Fig. Q1: Magnetic circuit taken from Principles of Electric Machines and Power Electronics, 2 nd edition, p12, PC Sen. Q1.1: First draw the equivalent magnetic circuit diagram and then calculate the different reluctances for the circuit. (7) V1.1: Teken eers die ekwivalente magnetiese stroombaandiagram en bereken dan die verskeie reluktansies vir die stroombaan. (7) Diagram / Stroombaan: ELX 311 Exam 2009 2
Q1.1 cont V1.1 verv Q1.2: Calculate the flux density inside the air gap. Hint: Use source transformation or superposition to solve the circuit. (5) V1.2: Bereken die vloeddigtheid in die luggaping. Wenk: Gebruik brontransformasie of superposisie om die stroombaan op te los. (5) ELX 311 Exam 2009 3
Question 2 / Vraag 2 [6] The electromagnet lift system shown in Fig. Q2 has 2500 turns on an ideal core material. The air gap is at g = 10mm and the flux density is 1.25 T. Ignore fringing effects. Die elektromagnetiese hysstelsel in Fig. Q2 het 2500 draaie op n ideale kern material. Die luggaping is by g = 10mm en die vloeddigtheid is 1.25T. Ignoreer rant-effekte. Fig. Q2: Magnetic circuit taken from Principles of Electric Machines and Power Electronics, 2 nd edition, p117, PC Sen Q2.1: Determine the coil current. (4) V2.1: Bepaal die windingstroom. (4) ELX 311 Exam 2009 4
Q2.2: Determine the energy stored in the magnetic system. (1) V2.2: Bepaal die energie wat in die magnetise stelsel gestoor is. (1) Q2.3: For a current of 20 A, what is the maximum load mass in kg the system will be able to pick up? (1) V2.3 Vir n stroom van 20 A, wat is die maksimum las massa in kg wat die stelsel sal kan optel? (1) ELX 311 Exam 2009 5
The linear DC machine shown in Fig. Q3 has a magnetic flux density of 0.5 T directed into the page, a resistance of 0.25 Ω, a bar length of 1.0m and a battery voltage of 100V. Question 3 / Vraag 3 [8] Die lineêre GS masjine in Fig. Q3 het n magnetise vloeddigtheid van 0.5T in die bladsy in, n weerstand van 0.25 Ω, n staaf lengte van 1.0m en n batteryspanning van 100V. Fig. Q3: A linear dc machine. The magnetic field points into the page. Q3.1: What is the initial force magnitude and direction on the bar at starting? (2) V3.1: Wat is die aanvanklike krag grootte en rigting op die staaf? (2) Q3.2: What is the no-load stead-state speed of the bar? (1) V3.2: Wat is die nul-las bestendige toestand spoed van die staaf? (1) ELX 311 Exam 2009 6
Q3.3: If the bar is loaded with a force of 25N opposite to the direction of motion, what are the new steady state speed and the efficiency of the machine under these conditions? (5) V3.3: Indien die staaf belas word met n krag van 25N teenoorgesteld aan die rigting van beweging, was sat die nuwe bestendige toestand spoed en die effektiwiteit van die masjien onder hierdie omstandighede wees? (5) ELX 311 Exam 2009 7
Question 4 / Vraag 4 [4] A square magnetic core having 750 windings has a mean length of 2.25m, a cross sectional area of 200 cm 2 and the magnetizing curve of Fig. Q4. n Vierkantige magnetiesekern met 750 windings het n gemiddelde lengthe van 2.25m, n deursnit oppervlakte 200 cm 2 en die magnetiseringskurwe in Fig. Q4. Fig. Q4: Magnetizing curve for question 4. Q4.1: Calculate the flux in mwb that will result in the core from a winding current of 1.5 A. (3) V4.1: Bereken die vloed in mwb wat in die kern sal ontstaan in geval van n 1.5 A windingstroom. (3) Q4.2: What is the relative permeability of the core at this operating point? (1) V4.2: Wat is die relatiewe permeabiliteit van die kern by hierdie werkspunt? (1) ELX 311 Exam 2009 8
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Question 5 / Vraag 5 [8] A three phase Y-Y 50Hz 60 kva V 1 /V 2 = 11kV rms /400 V rms transformer has the given per phase equivalent-circuit parameters at rated load having a lagging power factor of 0.85. Use the given equivalent transformer model to answer the questions below. n Driefase 50Hz 60kVA V 1 /V 2 = 11kV rms /400 V rms transformator het die gegewe per fase ekwivalente stroombaan parameters by vollas met n nalopende drywingsfaktor van 0.85. Gebruik die gegewe ekwivalente model om die onderstaande vrae te beantwoord. R 1 = 20Ω, R 2 = 0.04 Ω, X 1 = 210 Ω, X 2 = 0.2 Ω, R c = 250 kω, X m = 40 kω + V source I 1 I 2 + V 1 + V 2 = V load Q5.1: What are the values of V 1 and I 1 (2) V5.1 Wat is die waardes van V 1 en I 1 (2) Q5.2: Calculate the source voltage required to achieve rated load voltage. (2) V5.2: Bereken die bronspanning benodig om aanslag lasspanning te verseker. (2) ELX 311 Exam 2009 10
Q5.3: Given that I 1 = 3 A and V source = 7140 kv, calculate the efficiency of the transformer. (4) V5.3: Gegee dat I 1 = 3 A en V source = 7140 kv, bereken die effektiwiteit van die transformator. (4) ELX 311 Exam 2009 11
Question 6 / Vraag 6 [6] The following information is given about the simple rotating loop in Fig. Q6. Die volgende inligting word gegee met betrekking tot die roterende lus in Fig. Q6. B = 0.8 T V B = 24V l = 0.5m R = 0.4 Ω r = 0.125m ω = 275 rad/s Q6.1: Is the machine operating as a motor or as a generator? Motivate. (2) V6.1: Funksioneer die masjien as n motor of as n generator? Motiveer. (2) Q6.2: How much energy in kwh does the machine provide or consume over a 1 hour period? (2) V6.2: Hoeveel energy in kwh verskaf of verbruik die masjien oor n 1 uur periode? (2) ELX 311 Exam 2009 12
Q6.3: A simplex 2-pole, eight coil lap wound DC machine has a flux density of 1.0 T in the air gap, a coil radius of 0.1m, a coil side length of 0.4m and is rotating at 1800 rpm. What is the magnitude of the voltage between the brushes? (2) V6.3 n Simpleks 2-pool, agt winding lap wound GS motor het n vloeddigtheid van 1.0 T in die luggaping, n winding radius van 0.1 m, n winding sy lengte van 0.4m en roteer teen 1800 rpm. Wat is die grootte van die spanning tussen die borsels? (2) ELX 311 Exam 2009 13
Question 7 / Vraag 7 [4] The following information for a 120V 25 kw DC generator is provided below: Die volgende inligting met betrekking tot n 120V 25 kw GS Generator word hier onder gegee: Pole(s) = 8 Duplex Lap Wound 64 Coils 16 turns per coil rated speed 2400rpm Q7.1: How much flux per pole is required to produce rated voltage under no-load conditions? (2) V7.1: Hoeveel vloed word per pool benodig om aanslag spanning op te wek onder nul-las toestande? (2) Q7.2: What is the current per path in the armature of this generator at rated load? (1) V7.2: Wat is die stroom per pad in die anker van die generator by aanslag las? (1) Q7.3: What is the induced torque in this machine at rated load? (1) V7.3: Wat is die geinduseerde wringkrag in die masjien by aanslag las? (1) ELX 311 Exam 2009 14
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Question 8 / Vraag 8 [10] The following information is given for a 120V series dc motor at full load conditions along with the magnetizing curve in Fig. Q8. Die volgende inligting word gegee vir n 120V GS motor onder vollas toestand tesame met die magnetiseringskurwe in Fig. Q8. Armature Resistance 0.2 Ohm Anker-weerstand Series Field Resistance 0.16 Ohm Serie Veldweerstand Input current 58 A Inset stroom Speed 1050 rpm Spoed Core losses (constant) 200 W Kernverliese (konstant) Mechanical losses, proportional to the n 3. 240 W Meganieseverliese, direk eweredig aan n 3. Stray losses - Diverse verliese Fig. Q8: Magnetizing curve for the series motor in question 8. Q8.1: What is the efficiency of the motor? (2) V8.1: Wat is die effektiwiteit van die motor? (2) ELX 311 Exam 2009 16
Q8.2: What will the speed of the motor be if operated at an armature current of 35 A? (5) V8.2: Wat sal die spoed van die motor wees indien die ankerstroom 35 A is? (5) Q8.3: Assuming the new speed to be 1330 rpm at an armature current of 35 A, what will the efficiency of the motor be? (3) V8.3: Aangeneem dat die nuwe spoed 1330 rpm is met n ankerstroom van 35A, wat sal die effektiwiteit van die motor wees? (3) ELX 311 Exam 2009 17
This question refers to the following shunt connected dc motor having the magnetizing curve in Fig. Q9 and operating under rated full load conditions. 11.9 kw Question 9 / Vraag 9 [5] Die vraag verwys na die volgende parallel gekoppelde GS motor met die magnetiseringskurwe in Fig. Q9 wat onder aanslag vollas toestand werk. test 175 Ω Fig. Q9: Magnetizing curve for Question 9 ELX 311 Exam 2009 18
Q9.1: Calculate the field current I F. (1) V9.1: Bereken die veld stroom I F. (1) Q9.2: Calculate the armature current I A. (1) V9.2: Bereken die ankerstroom stroom I A. (1) Q9.3: Calculate the internal generated voltage E A. (1) V9.3: Bereken interne gegenereerde spanning E A. (1) Q9.4: Calculate the full load speed of the machine. (2) V9.4: Bereken die vollas spoed van die masjien (2) ELX 311 Exam 2009 19
Question 10 / Vraag 10 [11] A 440-V, 50 Hz, two-pole Y-connected induction motor is rated at 75 kw operating at a slip of 0.04 resulting in a line current I A of 149.4 18. 3 A. The equivalent circuit parameters are provided below. n 440 V, 50 Hz, twee-pool Y-gekoppelde induksie motor het n aanslag drywing van 75 kw en werk by n glip van 0.04 wat n lynstroom van I A = 149.4 18. 3 A tot gevolg het. Die ekwivalente stroombaan parameters word hieronder gegee. Q10.1: Calculate the stator and rotor power factors. (2) V10.1: Bereken die rotor en stator drywingsfaktore. (2) Q10.2: Calculate the stator copper losses P SCL. (1) V10.2: Bereken die stator koperverliese P SCL. (1) Q10.3: Calculate the air gap power P AG. (2) V10.3: Bereken die luggaping drywing P AG. (2) ELX 311 Exam 2009 20
Q10.4: Given the P AG is 103 kw, calculate the power converted from electrical to mechanical form P conv and the induced torque. (1) V10.4: Gegewe dat P AG 103 kw is, bereken die drywing wat vanaf elektriese na meganiese energie omgeskakel is P conv en die geinduseerde wringkrag. (1) Q10.5: Calculate output power P out, the rotational speed n m and hence finally the output torque. (4) V10.5: Bereken die uitset drywing P out, die rotasie spoed n m en dan die uitset wringkrag. (4) Q10.6: Finally calculate the efficiency of the motor. (1) V10.6: Bereken laastens die effektiwiteit van die motor. (1) ELX 311 Exam 2009 21
SECTION B [15] / AFDELING B [15] Question B1 [3] Even if a transformer s secondary side is open circuited, there is always a current flowing consisting of two components. - The first is the core-loss current. Which losses do this current represent? - What are the second current component and its function? - What is the total combined current called? Vraag B1 [3] Selfs al is n transformator se sekondêre kant n opebaan, is daar altyd n stroom wat vloei wat bestaan uit twee komponente. - Die eerste is die kern-verlies stroom. Watter verliese word deur die stroom verteenwoordig? - Wat is die tweede component en die se funksie? - Wat word die totale gekombineerde stroom genoem? B1.1: The core loss current represents the following losses: (1) B1.1: Die kernverliese stroom verteenwoordig die volgende verliese: (1) & B1.2: The second component and its function are: (1) Die tweede component en die se funksie is: (1) B1.3: The total combined current is called: (1) The totale gekombineerde stroom word genoem: (1) ELX 311 Exam 2009 22
Question B2 [2] Refer to the machine winding shown in Fig. B2. How many parallel paths are there through the rotor and how wide should the brushes be? Motivate. [2] Vraag B2 [2] Verwys na die masjienwinding in Fig. B2. Hoeveel parallel paaie is daar deur die rotor en hoe wyd moet die borsels wees? Motiveer. [2] Question B3 [2] Name the two primary problems caused by Armature Reaction and briefly mention the end result of both these problems inside the machine Vraag B3 [2] Noem die twee primêre probleme wat deur Ankerreaksie veroorsaak word en noem kortliks die eind resultaat van beide die probleme in die masjien. ELX 311 Exam 2009 23
Question B4 [6] Fill in the missing words in the following sentences describing how torque is developed in a 400V, 50 Hz, 4 pole 3-phase squirrel cage induction machine operating at a slip of 5%. No calculations need to be shown. When a 3-phase voltage is applied to the of the induction machine it sets up a rotating at (value) rpm. This induces a at a frequency of (value) Hz that flows in the of the machine, which in turn causes a rotating on the rotor rotating at (value) rpm. The on the is attracted by the on the thus resulting in the induced torque causing the rotor to rotate at (value) rpm. Vraag B4 [6] Vul die ontbrekende woorde en waardes in die volgende sinne in wat beskryf hoe die wringkrag in n 400V. 50Hz, 4 pool 3-fase squirrel cage induksie masjien ontwikkel word wat werk by n glip van 5%. Geen berekeninge hoef getoon te word nie. Wanneer n 3-fase spanning gekoppel word aan die van die induksiemasjien skep dit n wat roteer teen (waarde) rpm. Dit induseer n teen n frekwensie van (waarde) Hz wat in die van die masjien vloei wat op sy beurt n roterende skep op die rotor wat roteer teen (waarde) rpm. Die op die word dan aangetrek deur die op die wat der halwe wringkrag teweeg bring wat veroorsaak dat die rotor roteer teen (waarde) rpm. ELX 311 Exam 2009 24
Question B5 [3] Vraag B5 [3] Draw the basic torque vs speed curve for an Skets die basiese wringkrag teen spoed kurwe vir n induction machine and indicate the following thereon: induksie masjien en toon die volgende daarop aan: Starting and pullout torque as well as the normal Begin en uittrek wringkrag asook die normale operating region. werksgebied. ELX 311 Exam 2009 25