Electrical Engineering 2024 Paper II 50 marks Calculate

Q7

(a) Calculate the real and reactive power at sending end of a transmission line while delivering 10 MVA load at 0·85 lagging power factor at receiving end of line. The line parameters are A = 1, B = 12·12 ∠64·64° Ω, D = 1 and receiving end voltage of line is 33 kV. (20 marks) (b) (i) A binary transmission system with a transmitted power of 300 mW uses a channel with zero-mean AWGN of two-sided PSD equal to 10⁻¹⁵ W/Hz and a total transmission loss of 80 dB. If the probability of error, Pₑ is not to exceed 10⁻⁴, calculate the maximum allowable bit rate using non-coherent ASK. (10 marks) (ii) A 2Vₚₚ audio frequency signal band-limited to 8 kHz is to be transmitted using a PCM system. If the quantization error of any sample is to be at the most ±1% of the dynamic range of the message signal, determine the minimum value of n, the minimum sampling rate and corresponding bit rate of transmission. (10 marks) (c) (i) Mention the techniques of increasing the voltage and current rating of converter station of HVDC transmission system. (5 marks) (ii) Write the requirements of valves used in HVDC transmission system. (5 marks)

हिंदी में प्रश्न पढ़ें

(a) एक संचरण लाइन के प्रेषण छोर पर वास्तविक एवं प्रतिघाती शक्तियों की गणना कीजिए जबकि संचरण लाइन अपने ग्रहण छोर पर 10 MVA, 0·85 पश्चगामी शक्ति गुणांक का भार प्रदान करती है । लाइन के प्राचल A = 1, B = 12·12 ∠64·64° Ω, D = 1 और ग्रहण छोर पर लाइन की वोल्टता 33 kV है । (20 अंक) (b) (i) 300 mW संचरित शक्ति के साथ एक द्विआधारी संचरण तंत्र 10⁻¹⁵ W/Hz के बराबर द्विशोर PSD के शून्य माध्य AWGN तथा 80 dB कुल संचरण ह्रास वाले चैनल का उपयोग करता है । यदि त्रुटि की संभावना Pₑ, 10⁻⁴ से अधिक नहीं होनी है, तो असुसंगत ASK का प्रयोग करते हुए अधिकतम स्वीकार्य बिट दर की गणना कीजिए । (10 अंक) (ii) एक 2Vₚₚ ध्वनि आवृत्ति संकेत जो कि 8 kHz तक बैंड-लिमिटेड है, को एक PCM तंत्र के माध्यम से प्रेषित किया जाना है । यदि किसी नमूने की अधिकतम क्वांटाइजेशन त्रुटि सूचना संकेत की गतिक सीमा की ±1% होनी है, तो n का न्यूनतम मान, न्यूनतम प्रतिचयन (सैंपलिंग) दर तथा तत्संगत प्रेषण की बिट दर का निर्धारण कीजिए । (10 अंक) (c) (i) HVDC संचरण प्रणाली के कनवर्टर स्टेशन की वोल्टता तथा धारा की दर निर्धारण (रेटिंग) को बढ़ाने वाली तकनीकों का उल्लेख कीजिए । (5 अंक) (ii) HVDC संचरण प्रणाली में प्रयुक्त वाल्वों की अपेक्षाओं का उल्लेख कीजिए । (5 अंक)

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Directive word: Calculate

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Approach

Calculate requires precise numerical solutions with clear methodology. Spend ~40% time on part (a) as it carries 20 marks—draw the transmission line equivalent, apply ABCD parameters correctly, and solve for sending end power using complex power equations. Allocate ~30% to part (b) covering both ASK bit rate and PCM parameters—apply non-coherent ASK error probability formula and quantization step calculations. Reserve ~30% for part (c) on HVDC techniques and valve requirements—use bullet points for these descriptive sub-parts. Conclude with brief practical significance of each calculation.

Key points expected

  • Part (a): Correct application of transmission line ABCD parameters with A=1, B=12.12∠64.64°, D=1 to find sending end voltage, then calculate complex power using Ss = Vs·Is* with proper angle handling for 0.85 lagging pf load
  • Part (b)(i): Application of non-coherent ASK error probability Pe = 0.5·exp(-γ/4) ≤ 10⁻⁴, solving for required SNR, then using link budget with 80 dB loss and noise PSD to find maximum bit rate
  • Part (b)(ii): Determination of quantization levels L = 100 (from ±1% error), n = 7 bits, minimum sampling rate = 16 kHz (Nyquist), bit rate = 112 kbps
  • Part (c)(i): Techniques for HVDC converter rating enhancement—series/parallel connection of valves, use of 12-pulse converters, multi-level converters, and synchronous operation of multiple bridges
  • Part (c)(ii): Valve requirements—high voltage/current capability, fast switching, low forward voltage drop, high dv/dt and di/dt capability, series/parallel grading circuits, and proper cooling arrangements

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies ABCD parameter model for (a), recognizes non-coherent ASK error formula for (b)(i), applies uniform quantization theory for (b)(ii), and accurately describes HVDC valve technologies for (c); no conceptual confusion between coherent and non-coherent detectionMostly correct concepts but minor errors like using coherent ASK formula, confusing sampling theorem application, or incomplete valve requirement listingFundamental errors such as wrong ABCD parameter usage, incorrect error probability formula, or confused HVDC terminology
Numerical accuracy25%12.5Precise calculations: (a) correct sending end power magnitude and angle, (b)(i) accurate bit rate within 5% tolerance, (b)(ii) exact n=7, fs=16 kHz, Rb=112 kbps; proper unit handling throughoutCorrect methodology but arithmetic errors leading to 10-20% deviation in final answers, or unit conversion mistakes (kW/MW, dB calculations)Major calculation errors, wrong order of magnitude, or missing critical steps like dB to linear conversion
Diagram quality10%5Clear two-port network representation for (a) with voltage-current phasor diagram, ASK receiver block diagram for (b)(i), and PCM system block diagram for (b)(ii); properly labeled with all relevant parametersBasic diagrams present but missing labels or incomplete block diagrams for communication systemsMissing essential diagrams or poorly drawn figures that hinder understanding of the solution approach
Step-by-step derivation25%12.5Systematic derivation: (a) shows Vs = A·Vr + B·Ir with complex arithmetic, (b)(i) derives SNR from Pe formula then applies link budget, (b)(ii) shows step size Δ = 2Vp-p/2ⁿ and error constraint; each step justifiedCorrect final formulas but skips intermediate derivation steps or assumes results without showing complex number operationsJumps directly to answers without derivation, or incorrect formula substitution without explanation
Practical interpretation20%10Interprets (a) results for line loading and stability, discusses (b) bit rate limitations for practical communication systems, and relates (c) to Indian HVDC projects like Rihand-Delhi or Talcher-Kolar; mentions real-world constraintsBrief mention of practical significance without specific examples or generic statements about transmission efficiencyPurely mathematical treatment with no physical interpretation of results or engineering relevance

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