Electrical Engineering 2021 Paper II 50 marks Calculate

Q3

3.(a) A solidly earthed 400 KV, 3 phase busbar system is connected with two incoming and four outgoing lines (feeders). A differential protection is provided with switchgear of 4000 MVA capacity having the following parameters: CT secondary resistance = 0.8 Ω Lead wire resistance = 1.2 Ω Relay load = 1.0 Ω CT magnetization current = 0.3 mA/V Max. full load current in one feeder = 100 A Voltage setting of over current relay = 100 V If the O.C. relay in the spill path is set at 1.0 A, find the following: (a) The maximum 'through fault' current up to which the protection scheme remains stable. (20 marks) (b) Whether the switchgear is capable to handle maximum through fault current. (20 marks) (c) The value of minimum internal fault current that can be detected by protection scheme. (20 marks) (d) The pick-up setting for detecting minimum internal fault current of 90 Amp. (20 marks) 3.(b) Consider a signal detector with an input r = ±A + n where +A and −A occur with equal probability and the noise variable n is characterized by the Laplacian pdf shown. p(n) = (1/√2σ) e^(-|n|√2/σ) (i) Determine the probability of error as a function of the parameters A and σ. (20 marks) (ii) Determine the SNR required to achieve an error probability of 10^(-6). (20 marks) 3.(c) A coil of 300 V moving iron voltmeter has a resistance of 500 ohms and an inductance of 0.8 H. The instrument reads correctly at 50 Hz AC supply and takes 100 mA at full scale deflection. What is the percentage error in the instrument reading, when it is connected to 200 V DC supply. (10 marks)

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3.(a) दो आने वाले प्रदायकों व चार जाने वाले प्रदायकों को एक दृढ़ता से भू संपर्कित, त्रिकला, 400 KV बसबार तंत्र से जोड़ा गया है । एक 4000 MVA क्षमता वाले सिचंगियर द्वारा अंतरण संरक्षण (डिफरेंशियल प्रोटेक्शन) प्रदान कराया गया है । प्रणाली के प्राचल निम्न प्रकार हैं : CT का द्वितीयक प्रतिरोध = 0.8 Ω चालक तार का प्रतिरोध = 1.2 Ω रिले भार का प्रतिरोध = 1.0 Ω CT की चुंबकत्व धारा = 0.3 mA/V प्रत्येक प्रदायक की अधिकतम पूर्ण भार धारा = 100 A अधिधारा रिले की बोल्टता का निर्धारण = 100 V यदि अधिधारा रिले, जो परिपथ में लगाई गई है, को 1.0 पर निर्धारित किया गया है, तो निम्नलिखित तथ्यों का निर्धारण करें । (a) अधिकतम शु-फाल्ट धारा का मान, ताकि संरक्षण प्रणाली संतुलित रहे । (20 marks) (b) क्या संरक्षण प्रणाली अधिकतम शु-फाल्ट धारा को सहन करने में सक्षम है ? (20 marks) (c) संरक्षण प्रणाली द्वारा संसूचित न्यूनतम अंतरण दोष धारा का मान ज्ञात करें । (20 marks) (d) न्यूनतम अंतरण दोष धारा 90 A के लिए पिकअप सेटिंग का मान ज्ञात करें । (20 marks) 3.(b) एक संकेत संसूचक का निवेश निम्नप्रकार है r = ±A + n +A व −A समप्रायिकता के साथ घटित होता है तथा रवर (नॉयज वेरिएबल) n की विशेषता को लाप्लासियन pdf द्वारा दर्शाया गया है । p(n) = (1/√2σ) e^(-|n|√2/σ) (i) प्राचल A व σ के फलन के रूप में त्रुटि की प्रायिकता का निर्धारण करें । (20 marks) (ii) 10^(-6) त्रुटि प्रायिकता के लिए आवश्यक SNR ज्ञात करें । (20 marks) 3.(c) एक 300 V चल लोहे वोल्टमापी की कुण्डली का प्रतिरोध 500 ohm व प्रेरकत्व 0.8 H है । मापक यंत्र 50 Hz AC आपूर्ति पर दोषरहित मापन करता है तथा पूर्ण स्केल विचेषण के समय 100 mA धारा ग्रहण करता है । जब यह मापन यंत्र 200 V DC आपूर्ति के साथ जोड़ा जाता है तो प्रतिशत त्रुटि का मान ज्ञात करें । (10 marks)

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Approach

Calculate the required parameters systematically across all six sub-parts, allocating approximately 35% time to 3(a) parts (differential protection stability, switchgear capability, minimum internal fault, and pickup setting), 35% to 3(b) parts (Laplacian noise error probability and SNR calculation), and 30% to 3(c) (moving iron voltmeter DC error). Begin with clear circuit diagrams for differential protection, show all formulae with proper substitutions, and conclude with practical significance of each result for power system and communication engineering applications.

Key points expected

  • For 3(a): Calculation of CT knee-point voltage, stability limit using magnetization characteristic, and verification against switchgear fault MVA rating (4000 MVA at 400 kV)
  • For 3(a): Determination of minimum internal fault current considering relay burden and CT saturation, with correct application of 1.0 A spill path setting
  • For 3(a): Pick-up setting calculation for 90 A internal fault with proper CT ratio derivation from 100 A feeder current
  • For 3(b): Derivation of error probability P(e) = 0.5*exp(-A√2/σ) for Laplacian noise using ML detection criterion and integration of conditional densities
  • For 3(b): SNR calculation (A²/2σ²) for Pe = 10^-6, solving transcendental equation or using numerical approximation
  • For 3(c): Percentage error calculation comparing AC impedance (R + jωL) at 50 Hz with pure DC resistance, showing frequency-dependent moving iron instrument behavior

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies differential protection stability criterion (Vk ≥ If(Rct + Rlead + Rrelay)), applies ML detection for Laplacian noise, and recognizes moving iron instrument impedance variation with frequency; cites relevant standards (IEC 61869 for CTs, IS 1248 for instruments)Basic understanding of protection stability and signal detection but confuses Gaussian with Laplacian noise properties or misses frequency dependence in voltmeterFundamental conceptual errors such as treating CT magnetization as linear, applying Gaussian formulas to Laplacian noise, or ignoring inductive reactance in AC impedance calculation
Numerical accuracy25%12.5All calculations accurate to 3 significant figures: stability current ~31.25 kA, fault MVA check against 4000 MVA, minimum internal fault ~125 A, pickup setting ~0.72 A, P(e) formula correct with exact SNR ≈ 18.2 dB for Pe=10^-6, DC error ~-4.8%Correct methodology with minor arithmetic errors or unit conversion mistakes (kA/A, MVA/VA confusion)Major calculation errors, wrong order of magnitude results, or incorrect formula substitutions leading to nonsensical values
Diagram quality15%7.5Clear differential protection single-line diagram showing CT connections, spill path, and relay locations; Laplacian PDF sketch with decision regions ±A; moving iron instrument coil equivalent circuit; all diagrams properly labeled with given parametersBasic diagrams without proper labeling or missing one critical diagram (e.g., no PDF plot for 3(b))Missing diagrams or incorrect connections (e.g., CT polarity reversal not shown, wrong decision boundary sketch)
Step-by-step derivation25%12.5Complete derivation: for 3(a) shows Vk = Im×(Rct+2Rlead+Rrelay) with Im from magnetization curve; for 3(b) integrates p(n) from A to ∞ with proper conditional probability; for 3(c) derives Z_ac = √(R²+(ωL)²) and compares with I_dc = V/RSkips key steps or uses final formulas without showing integration/algebraic manipulationNo derivation shown, only final answers stated, or incorrect mathematical steps (wrong integration limits, algebra errors)
Practical interpretation15%7.5Interprets stability margin for Indian 400 kV grid protection, compares Laplacian vs Gaussian noise robustness in PLC/power line communication, explains why moving iron instruments need recalibration for DC; suggests CT class selection (e.g., PS class) for high stabilityBrief comment on results without connecting to real-world protection settings or instrument standardsNo practical interpretation or irrelevant discussion not tied to calculated values

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