Electrical Engineering 2021 Paper II 50 marks Solve

Q4

4.(a)(i) The configuration of a 400 KV 3 phase line is shown in figure. The radius of each sub-conductor is 2 cm. Calculate the charging mega volt-amperes if line is operating at 50 Hz and has a length of 300 km. (10 marks) 4.(a)(ii) Calculate the most economical overall diameter of insulation of a cable to be operated at 400 KV, 3 phase power system if maximum stress is limited to 100 KV/cm. (10 marks) 4.(b) Derive the conditions of balance of an Anderson's bridge and also draw the phasor diagram of the bridge under balanced condition. Determine the unknown quantities in terms of known parameters and comment on easy convergence of balance of the bridge. (20 marks) 4.(c) The approximate magnitude plot, obtained experimentally, of a nonminimum phase system is shown in figure. Calculate the phase in degrees at w = 3 rad/sec. (10 marks)

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4.(a)(i) एक 400 KV, त्रिकला लाइन का विन्यास चित्र में दर्शाया गया है । प्रत्येक सहिषित चालक की त्रिज्या 2 cm है । यदि लाइन की लम्बाई 300 km हो और 50 Hz पर संचालित हो तो लाइन का आवेशक (चार्जिंग) मेगा वोल्ट-एम्पीयर ज्ञात करें । (10 marks) 4.(a)(ii) 400 KV, त्रिकला शक्ति तंत्र में प्रयोग होने वाले केबल का अति मितव्ययी विद्युत रोधन सहित संपूर्ण व्यास का निर्धारण करें । केबल का सीमान्त अधिकतम रोधक प्रतिबल 100 KV/cm है । (10 marks) 4.(b) ऐण्डरसन सेतु के संतुलन की शर्त को व्युत्पन्न कीजिए व संतुलित अवस्था में कला आरेख (फेजर डायग्राम) बनाइए । ज्ञात प्राचलों के रूप में अज्ञात राशियों का मान ज्ञात करें । सेतु के संतुलन के सुगम अभिसरण पर टिप्पणी कीजिए । (20 marks) 4.(c) एक अनिम्नतम कला तंत्र का अनुमानित परिमाण आलेख प्रयोगात्मक विधि द्वारा प्राप्त किया गया है व जैसे चित्र में दर्शाया गया है । w = 3 rad/sec के लिए कला के मान की अंश में गणना करें । (10 marks)

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Approach

Solve this multi-part numerical and derivation problem by systematically addressing each sub-question: first calculate charging MVA for the 400 kV transmission line using geometric mean distance and capacitance formulas, then determine optimal cable insulation diameter using maximum stress criterion, followed by complete derivation of Anderson's bridge balance conditions with phasor diagram, and finally compute phase angle from the given Bode plot. Structure as: direct calculations for parts (a)(i)-(ii), rigorous derivation with diagram for part (b), and frequency response analysis for part (c).

Key points expected

  • Part (a)(i): Calculate geometric mean distance (GMD) from conductor configuration, then capacitance per phase C = 2πε₀/ln(GMD/r), and charging MVA = 3 × Vph² × ωC × length (in appropriate units)
  • Part (a)(ii): Apply most economical cable design condition where d = 2r = V/(gmax×e) for single-core cable, giving D = d×e, with overall diameter derived from maximum stress limitation
  • Part (b): Derive balance condition using star-delta transformation or mesh analysis: R1/R2 = R3/R4 + C3/C4 (approximately), with exact relation involving frequency-independent balance for inductance measurement
  • Part (b): Phasor diagram showing voltage drops across arms with proper phase relationships, indicating quadrature components due to capacitive branch
  • Part (c): Identify transfer function from asymptotic Bode plot slopes (±20 dB/decade changes), locate corner frequencies, reconstruct poles/zeros including right-half plane zero for non-minimum phase, evaluate phase at ω=3 rad/s

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies GMD calculation for bundled conductors, applies Laplace's equation for cable stress optimization, understands Anderson's bridge as modified Maxwell's bridge for precise inductance measurement with frequency-independent balance, and recognizes non-minimum phase characteristics from magnitude plot slope changesUses correct basic formulas but makes errors in GMD calculation for asymmetric configurations, confuses cable optimization with simple ratio, states bridge balance without transformation derivation, misses RHP zero identification in part (c)Confuses charging MVA with charging current alone, applies solid conductor formulas to hollow cables, treats Anderson's bridge as simple Wheatstone bridge, cannot interpret Bode plot slopes for system identification
Numerical accuracy20%10Precise calculations: charging MVA ≈ 85-95 MVA with correct unit conversions (cm to m, km to m), cable diameter ≈ 5.5-6.5 cm using ln(D/d) optimization, accurate phase angle computation within ±5° including proper sign convention for non-minimum phase contributionCorrect methodology but arithmetic errors in logarithmic calculations, unit conversion mistakes (cm vs m), approximate bridge balance expressions without numerical verification, phase calculation missing 180° contribution from RHP zeroOrder of magnitude errors in MVA (kVA instead), incorrect stress formula application (using rms instead of peak voltage), no numerical substitution in derivation, completely wrong phase angle due to missing frequency terms
Diagram quality20%10Clear conductor configuration diagram with dimensions labeled for GMD calculation, cable cross-section with D and d marked, neat Anderson's bridge circuit with all five arms (R1-R4, C3, C4, L), properly scaled phasor diagram showing I1, I2, I3, I4 with 90° phase relationships, and reproduced Bode plot with identified slopesBasic circuit diagrams without component labels, phasor diagram missing current directions or phase angles, hand-drawn sketches without proper scaling, Bode plot sketch missing corner frequency annotationsMissing diagrams for any part, incorrect bridge configuration (omitting capacitive arms), phasor diagram showing DC conditions, no attempt to sketch given magnitude plot
Step-by-step derivation20%10Complete derivation showing: capacitance from potential coefficients or direct integration, cable optimization using dF/dD=0, Anderson's bridge via mesh equations or star-delta transformation with explicit intermediate steps, transfer function reconstruction from slope changes (+20/-20 dB/decade) with clear pole-zero mappingJumps between steps without showing intermediate algebra, states optimization condition without proof, gives final balance equations without derivation, identifies transfer function form but skips magnitude-to-phase conversion stepsOnly final formulas quoted without derivation, incorrect optimization approach (minimizing D instead of d), no attempt at bridge derivation, cannot relate magnitude plot to transfer function poles and zeros
Practical interpretation20%10Comments on charging MVA significance for 400 kV Indian grid (EHV lines require shunt compensation), notes cable design trade-offs for XLPE insulation in urban Indian installations, explains why Anderson's bridge converges faster than Maxwell's (separate resistive and reactive balance adjustments), discusses non-minimum phase implications for stability analysis in power system controllersGeneric statements about transmission efficiency without specific context, mentions shunt reactors without explaining sizing, states bridge is 'accurate' without convergence reasoning, notes phase lag without stability implicationsNo practical relevance discussed, confuses charging MVA with line losses, suggests bridge is obsolete without justification, ignores non-minimum phase characteristics entirely or misinterprets as measurement error

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