Electrical Engineering 2025 Paper II 50 marks Solve

Q6

(a) Determine the sending-end voltage, current, power factor of a single-phase, 50 Hz, 76·2 kV transmission line delivering a load of 12 MW at 0·8 p.f. lagging. The line constants are R = 25 Ω, inductance 200 mH and capacitance between lines is 2·5 μF. Also determine the regulation and efficiency of the transmission. Use nominal-π method. Draw the phasor diagram. 20 marks (b) 24 voice signals are sampled uniformly and then time-division multiplexed. Flat-top sampling is used with one microsecond duration. Multiplexing operation provides for synchronization by adding an extra pulse of sufficient amplitude and also one microsecond duration. The highest frequency component of each voice signal is 3·4 kHz. (i) Assuming a sampling rate of 8 kHz, find the spacing between successive pulses of the multiplexed signal. (ii) Repeat your calculations by assuming the use of Nyquist rate sampling. 20 marks (c) A 3-phase, 33 kV, star-connected alternator is to be protected using circulating current protection. The pilot wires are connected to the secondary windings of 100/5 ratio current transformer. The protective relay is adjusted to operate with an out of balance current of 1 A in the pilot wires. Determine (i) the earthing resistance which will protect 90% of the winding and (ii) the percent of the winding which would be protected, if the earthing resistance is 15 Ω. 10 marks

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(a) एक एकल-कला, 50 Hz, 76·2 kV संचरण लाइन के प्रेषण-छोर पर वोल्टता, धारा तथा शक्ति गुणक का निर्धारण कीजिये, जबकि संचरण लाइन 12 MW का भार, 0·8 पश्चगामी शक्ति गुणक पर प्रदान करती है। संचरण लाइन के नियतांक R = 25 Ω, प्रेरकत्व 200 mH तथा लाइनों के मध्य धारिता 2·5 μF है। संचरण की विनियमता (रियुलेशन) एवं दक्षता का भी निर्धारण कीजिये। सांकेतिक-π विधि का प्रयोग कीजिये। कला आरेख (फेजर डायग्राम) को आरेखित कीजिये। 20 अंक (b) 24 ध्वनि संकेतों को एकसमान रूप से पहले प्रतिचयनित (सैम्पल्ड) किया जाता है, उसके उपरान्त उन्हें काल-विभाजन (टाइम-डिविजन) से बहुल (मल्टीप्लेक्स्ड) किया जाता है। एक माइक्रोसेकंड अवधि के समतल-शीर्ष (फ्लैट-टॉप) प्रतिचयन का उपयोग किया जाता है। बहुल संचालन, पर्याप्त आयाम एवं एक माइक्रोसेकंड अवधि की एक अतिरिक्त पल्स संयोजित कर तुल्यकालन (सिंक्रोनाइजेशन) प्रदान करता है। प्रत्येक ध्वनि संकेत का उच्चतम आवृत्ति घटक 3·4 kHz है। (i) प्रतिचयन दर को 8 kHz मानते हुए बहुल संकेत के उत्तरोत्तर पल्स के मध्य अन्तराल प्राप्त कीजिये। (ii) नाइक्विस्ट प्रतिचयन दर का उपयोग मानते हुए अपनी गणना को दोहराइये। 20 अंक (c) एक 3-कला, 33 kV, तारा (स्टार)-संयोजित प्रत्यावर्ती धारा जनित्र को परिसंचारी धारा संरक्षण का उपयोग कर संरक्षित किया जाता है। सूचक तारों (पाइलट वायर) को 100/5 अनुपात के धारा परिणामित्र (करेंट ट्रांसफॉर्मर) की द्वितीयक कुंडली से संयोजित किया गया है। संरक्षी रिले का संचालन, सूचक तारों में 1 A की असंतुलित धारा के लिये समायोजित किया गया है। निर्धारण कीजिये (i) भूसंपर्कन प्रतिरोध (अर्थिंग रेजिस्टेंस) का मान, जो कि 90% कुंडली को संरक्षित करेगा और (ii) संरक्षित कुंडली का प्रतिशत, यदि भूसंपर्कन प्रतिरोध 15 Ω है। 10 अंक

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Approach

Solve this multi-part numerical problem by allocating approximately 40% time to part (a) given its 20 marks and complexity, 40% to part (b) for its dual sampling calculations, and 20% to part (c) for protection settings. Begin each part with stated assumptions and formulas, proceed through systematic calculations, and conclude with clearly boxed final answers. For part (a), explicitly draw the phasor diagram showing sending-end and receiving-end quantities.

Key points expected

Part (a): Correct application of nominal-π method with proper ABCD parameters calculation; accurate sending-end voltage (magnitude and angle), current, power factor, regulation and efficiency
Part (a): Phasor diagram showing VR, VS, IS, IR, and capacitor currents with proper phase relationships
Part (b)(i): Correct calculation of frame duration (125 μs), total slots (25), and pulse spacing (4 μs) for 8 kHz sampling
Part (b)(ii): Recalculation with Nyquist rate (6.8 kHz) showing modified frame duration and pulse spacing
Part (c)(i): Determination of earthing resistance for 90% winding protection using sequence networks and fault current distribution
Part (c)(ii): Calculation of protected percentage when earthing resistance is fixed at 15 Ω

Evaluation rubric

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies nominal-π model for (a), flat-top sampling and TDM principles for (b), and circulating current protection with percentage winding protection concept for (c); no conceptual confusion between methods	Minor errors in model selection (e.g., using nominal-T instead of nominal-π) or confusion between flat-top and natural sampling; protection scheme understood but sequence network application shaky	Fundamental misunderstanding of transmission line modeling, sampling theorem application, or protection philosophy; treats all parts with incorrect foundational concepts
Numerical accuracy	25%	12.5	All calculations precise to 2-3 decimal places; correct handling of complex arithmetic in (a), proper unit conversions (μF to F, mH to H), accurate frame duration and slot calculations in (b), correct fault current ratios in (c)	Minor arithmetic slips (e.g., power factor angle error, frame duration miscalculation by one slot) but methodologically sound; final answers within 5-10% of correct value	Significant calculation errors, wrong formula substitutions, or unit conversion failures; answers orders of magnitude incorrect or physically impossible
Diagram quality	15%	7.5	Clear, labeled phasor diagram for (a) showing reference VR, lagging load current, capacitor currents leading voltage, and resultant sending-end voltage with angle; proper scale and vector addition evident	Phasor diagram present but poorly labeled, missing key vectors (IC1, IC2), or incorrect phase relationships; diagram drawn but not referenced in solution	No diagram, or completely wrong phasor relationships; diagram shows series circuit instead of π-network configuration
Step-by-step derivation	25%	12.5	Explicit derivation of ABCD parameters for nominal-π, clear progression from receiving-end to sending-end quantities; systematic slot allocation calculation in (b) with synchronization pulse inclusion; detailed sequence network analysis for (c)	Steps present but condensed or skips key intermediate results; some 'therefore' statements without showing work; protection calculation jumps to formula without derivation	No intermediate steps shown, only final answers stated; or completely wrong derivation sequence leading to invalid results
Practical interpretation	15%	7.5	Comments on practical significance: regulation within acceptable limits for 76.2 kV line, efficiency typical for medium line; discusses why 8 kHz exceeds Nyquist rate for voice signals (guard band); explains why 100% winding protection is impossible with resistance grounding	Brief mention of practical relevance without elaboration; states values are 'reasonable' without justification; misses guard band discussion in (b)	No interpretation of results; or makes incorrect practical claims (e.g., 'efficiency should be 100%', 'Nyquist rate is sufficient without guard band')

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