Q8
(a) Two sources M₁ and M₂ emit messages x₁, x₂, x₃ and y₁, y₂, y₃ with the joint probability P(X,Y) as shown below in the matrix form. P(X, Y) → Determine H(X), H(Y), H(X/Y) and H(Y/X). (20 marks) (b) Calculate the current setting of a relay for fault that draws up to 400% of the rated current. The relay is used for differential protection of a delta-star, 50 MVA, 66/11 kV transformer. The CT ratio on secondary side is 3000 : 5 and primary side is 600 : 5. (20 marks) (c) Calculate the peak voltage which appears across the terminals of a circuit breaker when it suddenly interrupts 20 A current at 20% of its peak value in a circuit. The inductance and stray capacitance of circuit are 15 H and 3000 pF respectively. (10 marks)
हिंदी में प्रश्न पढ़ें
(a) दो स्रोत M₁ एवं M₂ दो सूचनाओं x₁, x₂, x₃ तथा y₁, y₂, y₃ को संयुक्त संभावना P(X, Y) के साथ उत्सर्जित करते हैं, जैसा कि नीचे आवृत्त में दर्शाया गया है । P(X, Y) → H(X), H(Y), H(X/Y) एवं H(Y/X) का निर्धारण कीजिए । (20 अंक) (b) एक रिले की धारा सेटिंग की गणना कीजिए जो दोष (फॉल्ट) के समय निर्धारित (रेटेड) धारा की 400% दोष-धारा ग्रहण करती है । एक डेल्टा-स्टार, 50 MVA, 66/11 kV परिणामित्र के अवकलीय संरक्षण के लिए रिले का प्रयोग किया गया है । द्वितीयक तरफ CT का अनुपात 3000 : 5 तथा प्राथमिक तरफ 600 : 5 है । (20 अंक) (c) एक परिपथ विचोजक के टर्मिनलों के आर-पार उत्पन्न शिखर वोल्टता की गणना कीजिए जो परिपथ में 20 A धारा को तब अचानक बाधित करता है जब परिपथ में धारा शिखर मान की 20% होती है । परिपथ का प्रेरकत्व एवं अवांछित (स्ट्रे) धारिता क्रमशः: 15 H तथा 3000 pF है । (10 अंक)
Directive word: Calculate
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How this answer will be evaluated
Approach
Calculate the required quantities systematically across all three sub-parts. For (a), spend ~40% time computing entropy measures H(X), H(Y), H(X/Y), H(Y/X) using marginal and conditional probability formulas. For (b), allocate ~35% time on relay current setting calculation involving CT ratio matching and percentage differential protection settings for delta-star transformers. For (c), use ~25% time applying transient recovery voltage (TRV) theory for circuit breaker interruption analysis. Present each part with clear problem identification, formula application, step-wise computation, and final boxed answers.
Key points expected
- Part (a): Correct computation of marginal probabilities P(X) and P(Y) from joint probability matrix; application of entropy formula H = -Σpᵢlog₂pᵢ; calculation of conditional entropies using H(X/Y) = H(X,Y) - H(Y) relationship
- Part (b): Determination of rated currents on primary (437.4 A) and secondary (2624.3 A) sides; selection of appropriate CT ratios considering delta-star phase shift compensation; calculation of relay setting current considering 400% fault current and percentage bias characteristic
- Part (c): Application of LC circuit transient analysis for current chopping; use of energy conservation ½Li² = ½CV² to find peak recovery voltage; consideration of 20% current interruption point
- Correct handling of log base 2 for entropy in bits, natural log conversion where needed, and proper unit management (kV, A, pF, H) throughout
- Recognition that delta-star transformer requires phase compensation in differential protection—either through CT connection or relay design
- Physical interpretation: for (a) mutual information significance; for (b) relay coordination with transformer inrush; for (c) circuit breaker TRV rating implications
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Concept correctness | 20% | 10 | Correctly identifies and applies: Shannon entropy definitions for (a); percentage differential protection principle with CT ratio matching for delta-star transformers for (b); current chopping phenomenon and LC oscillation theory for TRV calculation for (c) | Identifies most concepts correctly but confuses conditional entropy calculation order or misapplies CT ratio selection criteria; partial understanding of TRV phenomenon | Fundamental errors such as using wrong entropy formula, confusing differential protection with overcurrent protection, or applying DC circuit analysis to AC interruption problem |
| Numerical accuracy | 25% | 12.5 | All calculations precise to 2-3 significant figures: entropy values in correct bits/symbol; relay setting current properly calculated with correct CT secondary current matching; peak voltage accurately computed considering 20% current interruption point | Correct method but arithmetic errors in probability summation, CT ratio conversion, or LC circuit energy calculation; correct order of magnitude but imprecise final values | Major calculation errors: wrong probability normalization, CT ratio inversion, or missing square root in voltage calculation; answers without units or with incorrect units |
| Diagram quality | 10% | 5 | Clear probability tree or Venn diagram for entropy relationships in (a); neat differential protection schematic showing CT connections, relay coils, and percentage bias characteristic for (b); LC equivalent circuit with current waveform showing chopping point for (c) | Basic sketches present but missing key labels or showing incorrect connections; diagrams support answer but lack clarity in showing relationships | No diagrams where essential (especially for protection scheme), or completely incorrect circuit representations; messy unlabelled sketches |
| Step-by-step derivation | 25% | 12.5 | Systematic derivation: marginal probabilities → joint entropy → conditional entropies for (a); rated current → CT secondary current → mismatch calculation → percentage setting for (b); stored energy → equivalent capacitance voltage → peak TRV for (c); each step explicitly stated | Correct final answers but skipped intermediate steps; jumps from given data to final answer without showing probability summations or algebraic manipulations | No derivation shown—only final answers; or incorrect sequence of steps leading to wrong conclusions; missing essential formulas |
| Practical interpretation | 20% | 10 | Interprets H(X)-H(X/Y) as mutual information/channel capacity significance; explains why 400% setting prevents maloperation during magnetizing inrush while ensuring fault sensitivity; discusses circuit breaker RRRV rating and need for surge arresters based on calculated peak voltage | Brief mention of practical relevance without elaboration; generic statements about protection importance or breaker duty without specific numerical context | Purely mathematical treatment with no physical interpretation; or incorrect practical conclusions (e.g., suggesting relay will operate for through faults) |
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