The Open University of Sri Lanka Diploma in Technology ECX 3232-Electrical Power Final Examination-2004 Duration Three Hours Date: May 22nd 2005 Time: 0930-1130 hrs. This paper contains Eight (8) questions. Answer any five (5). All questions carry equal marks. Graph papers will be available on your request. 1. Show that the voltage drop V=(VS-VR) of a distribution line as shown below can be estimated as: VS VR R+jX (Impedance) P + jQ (Load) (VS-VR) = V PR+QX VR An industrial customer is located 6 km. far from the main source substation and a 11 kV, 1 overhead line connects it. The maximum load consumed by the customer is 1200 kW and 1000 kvar respectively. Resistance and reactance per kilometer of the overhead line are 0.6 /km. and 0.4 /km. What would be the voltage drop at full load of the customer? Find out the reactive power of the capacitor bank (11 kV name plate rating), which is needed to reduce the voltage drop to 5% of the nominal voltage. 2. A 10 kVA single phase transformer, for 2000V/400V at no load, has resistances and leakage reactances as follows: Primary winding: Resistance, 5.5; Reactance, 12. Secondary winding: Resistance, 0.2; Reactance, 0.45. Determine: The approximate value of the secondary voltage at full load and 0.8 power factor The percentage voltage regulation Efficiency of the transformer at full load 3. Show that the most economical phase angle to which a given load should be improved is given by Sin-1(B/A), where A is the annual cost per kVA of demand and B is the annual cost per kvar of loss-free, power factor correction device. If B is 1/3 of A, find the required capacitor kvar to correct a load of 400 kW at power factor 0.8 for annual minimum operating cost. 4. Why are single-phase motors not self started? What are the methods of starting single-phase induction motor? Explain with diagram in details any one of them? As measured at 50 Hz., the two windings of a single-phase motor show the following impedances. Page [1] of [3] Starter Wdg. Capacitor Main Wdg. Supply Voltage Rotor Zm = 3.1 + j 2.9 Zs = 7.0 + j 3.1 Main winding Starter Winding Find the capacitor size that will produce the phase angel shift =900. 5. What non-linear equipments installed in power system, generate harmonic frequencies? Define the term Total harmonic Distortion (THD)? A circuit consists of a resistance (R=10), an inductance (L=1.0 H) and a Capacitance (C=500F). They are connected in series and connected to a system voltage of having 1st, 3rd and 5th Harmonics. The voltage waveform is given as: V(t)=90 sin t + 30 sin (3t-1000) + 20 sin (5t+450) Volts. The frequency of the fundamental Harmonic is 50 Hz. (i) (ii) (iii) Calculate the current in each harmonic Determine the Total harmonic distortion factor of current and Voltage Sketch the time variation of the current 6. Variation of daily load pattern (including week-ends & holidays) of an industrial customer “ABC” metered at 400V/230V (working on 3 shifts) is as given under. The industry operates at 0.7 power factor. Industry “ABC” Load Shift-1 6.00 a.m.------7.00 a.m. 7.00 a.m.------1.00 p.m. 1.00 p.m.------2.00 p.m. 10 kW 45 kW 10 kW Shift-2 2.00 p.m.------3.00 p.m. 3.00 p.m.------9.00 p.m. 9.00 p.m.-----10.00 p.m. 10 kW 45 kW 10 kW Shift-3 10.00 p.m.----11.00 p.m. 11.00 p.m.----- 5.00 a.m. 5.00 a.m.----- 6.00 a.m. 10 kW 45 kW 10 kW Page [2] of [3] a) Draw the daily load pattern of customer “ABC”? b) What would be the industry “ABC” annual energy consumption? c) Calculate the annual cost and the average price per unit for “ABC”? (You may use the following tariff chargeable for industrial customers) d) What would be the annual energy savings, if customer improves his power factor to 0.9? Tariff table for Q6, chargeable for industrial customers Customer Category Maximum demand charge (Rs./kVA) per month Conditions Industrial Time-of-day option Metered at 400V/230V, contract demand less than 42 kVA Metered at 400V/230V, contract demand more than 42 kVA Metered above at 11kV or Energy Charge (Rs./kwh) Fixed Charge (Rs./Month) None 15.00 bet 7-10 p.m. 6.90 at other times 30.00 up to 10 kVA 230.00 above 10 kVA 380.00 14.70 bet 7-10 p.m. 6.50 at other times 800.00 360.00 14.00 bet 7-10 p.m. 6.10 at other times 800.00 7. (a) What are the different types of D. C. motors? Explain with diagrams. (b) A 6-pole DC generator has 400 armature conductors and useful flux is 0.06 Wb. If this generator is lap wound and running at 1000 r.p.m., what e.m.f. it will induce.? If this generator is wave wound, at what speed it should run so that it may induce the same voltage? (c) Find the speed of a 4-pole 440 V wave wound D.C. shunt motor having flux per pole of 3 mega lines. The armature is having 39 slots with 12 conductors per slot. Armature resistance is 0.25 Ohms. Current taken by the motor is 42 Amps. (Assume 1 Wb=108 flux lines) 8. The power input to the rotor (i.e. air gap power) of a 440 V, 50 Hz, 6 pole 3 phase induction motor is 80 kW. The rotor electromotive force (rotor E.M.F) is observed to make 120 complete alternates per minute. Calculate: a) b) c) d) e) The motor slip (s) The rotor speed (Nr) The Mechanical power (Pm) developed (assume stator core loss is negligible) The rotor copper loss per phase The rotor resistance per phase, if the rotor current is 65 A Page [3] of [3]