Q7
The following test data are obtained for a three-phase, 195 MVA, 15 kV, 50 Hz star connected synchronous machine. Open circuit test : | I_f (A) | 150 | 300 | 450 | 600 | 750 | 900 | 1200 | |---------|-----|-----|-----|-----|-----|-----|------| | V_LL (kV) | 3·75 | 7·5 | 11·2 | 13·6 | 15 | 15·8 | 16·5 | Short circuit test : I_f = 750 A, I_a = 7000 A The armature resistance is small. (i) Draw the open circuit characteristic, the short circuit characteristic, the airgap line and the modified airgap line. (ii) Determine the unsaturated and saturated values of the synchronous reactance in pu. (iii) Find the field current required, if the synchronous machine is to deliver 100 MVA at rated voltage, at 0·8 leading power factor. (20 marks) (b) A three-phase, full-wave thyristor bridge converter is operated from a three-phase, Y-connected 220 V, 50 Hz supply and the load resistance is 20 Ω. It is required to obtain an average output voltage of 50% of the maximum possible output voltage. Determine the following : (i) The delay angle α (ii) The rms and average output currents (iii) The rms and average thyristor currents (iv) The rectification efficiency (v) The input PF (20 marks) (c) A lossless transmission line has characteristic impedance Z₀ = 50 Ω. Its length is 30 m and operates at 5 MHz. The line is terminated with a load Zₗ = 60 + j50 Ω. If the phase velocity u = 0.6c on the line, find the following : (i) The reflection coefficient 'Γ' (ii) The standing wave ratio 'S' (iii) The input impedance 'Zᵢₙ' (10 marks)
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एक त्रि-कला, 195 MVA, 15 kV, 50 Hz तारा (स्टार) संयोजित तुल्यकालिक यंत्र के लिए निम्नलिखित परीक्षण आँकड़े प्राप्त हुए हैं : खुला परिपथ परीक्षण : | I_f (A) | 150 | 300 | 450 | 600 | 750 | 900 | 1200 | |---------|-----|-----|-----|-----|-----|-----|------| | V_LL (kV) | 3·75 | 7·5 | 11·2 | 13·6 | 15 | 15·8 | 16·5 | लघु परिपथ परीक्षण : I_f = 750 A, I_a = 7000 A आर्मेचर का प्रतिरोध थोड़ा है । (i) खुला परिपथ लक्षण वक्र, लघु परिपथ लक्षण वक्र, वायु अंतराल रेखा तथा परिवर्तित वायु अंतराल रेखा आरेखण कीजिए । (ii) तुल्यकालिक प्रतिघात का असंतृप्त तथा संतृप्त मान pu में ज्ञात कीजिए । (iii) यदि तुल्यकालिक यंत्र को निर्धारित वोल्टता तथा 0·8 अग्रगामी शक्ति गुणक पर 100 MVA प्रदान करना हो, तो वांछित क्षेत्र धारा का मान ज्ञात कीजिए । (20 अंक) (b) एक त्रि-कला, पूर्ण-तरंग थाइरिस्टर सेतु परिवर्तक, एक त्रि-कला, Y-संयोजित, 220 V, 50 Hz प्रदाय से चालित है तथा भार प्रतिरोध 20 Ω है। यदि औसत निर्गत वोल्टता, अधिकतम संभव निर्गत वोल्टता की 50% चाहिए, तो निम्नलिखित का मान ज्ञात कीजिए : (i) विलम्बन कोण α (ii) निर्गत धारा का rms तथा औसत मान (iii) थाइरिस्टर धारा का rms तथा औसत मान (iv) दिष्टकरण की दक्षता (v) निवेश PF (20 अंक) (c) एक हानिरहित संप्रेषण लाइन की लाक्षणिक प्रतिबाधा Z₀ = 50 Ω है। इसकी लम्बाई 30 m है तथा यह 5 MHz पर कार्य करती है। लाइन को एक Zₗ = 60 + j50 Ω भार के साथ अन्तस्थ किया गया है। यदि लाइन पर कला वेग u = 0.6c हो, तो निम्नलिखित का मान ज्ञात कीजिए : (i) परावर्तन गुणांक 'Γ' (ii) अप्रगामी तरंग अनुपात 'S' (iii) निवेश प्रतिबाधा 'Zᵢₙ' (10 अंक)
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How this answer will be evaluated
Approach
Solve this multi-part numerical problem by allocating approximately 40% time to part (a) synchronous machine analysis (20 marks), 40% to part (b) thyristor converter calculations (20 marks), and 20% to part (c) transmission line parameters (10 marks). Begin with clear identification of given data, proceed with systematic derivations for each sub-part, and conclude with verification of results against physical constraints.
Key points expected
- Part (a)(i): Correct plotting of OCC, SCC, airgap line and modified airgap line with proper scaling and identification of knee point
- Part (a)(ii): Calculation of unsaturated and saturated synchronous reactance in per-unit using V_OC/I_SC at appropriate field currents
- Part (a)(iii): Determination of field current for 100 MVA, 0.8 leading PF using Potier triangle or ASA method with correct phasor diagram
- Part (b)(i)-(v): Complete converter analysis including delay angle α=60°, rms/average output currents, thyristor currents, rectification efficiency, and input power factor
- Part (c)(i)-(iii): Transmission line calculations with correct electrical length (βl), reflection coefficient Γ=0.326∠56.3°, SWR S=1.97, and input impedance Z_in using Smith chart or analytical formulas
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Concept correctness | 20% | 10 | Correctly identifies synchronous machine saturation characteristics, three-phase full-wave converter operation with delay angle control, and transmission line standing wave phenomena; applies appropriate methods (Potier/ASA for (a), standard converter equations for (b), Smith chart or hyperbolic functions for (c)) | Identifies basic concepts but confuses unsaturated vs saturated reactance calculation or makes minor errors in converter mode identification; uses approximate methods for transmission line | Fundamental conceptual errors such as treating leading PF as lagging, using single-phase converter formulas for three-phase, or incorrect reflection coefficient formula |
| Numerical accuracy | 20% | 10 | All calculations accurate: X_s(unsat)≈1.63 pu, X_s(sat)≈1.0 pu, I_f≈1050-1100 A for (a); α=60°, I_orms≈8.6A, I_oavg≈7.43A, efficiency≈96.5%, PF≈0.955 lagging for (b); βl=180°, Γ=0.326∠56.3°, S=1.97, Z_in≈30-j35 Ω for (c) | Minor arithmetic errors in 1-2 parts, correct order of magnitude but incorrect final values, or unit conversion errors between kV/V or pu/ohms | Major calculation errors, wrong orders of magnitude, or consistent failure to use base values for pu calculations |
| Diagram quality | 20% | 10 | Clear, labeled OCC/SCC plot with distinct airgap and modified airgap lines, knee point marked; neat converter voltage/current waveforms showing 60° delay; transmission line phasor or Smith chart construction with proper scaling | Diagrams present but poorly scaled, missing labels, or incorrect curve shapes; waveforms lack proper commutation intervals | Missing essential diagrams, unrecognizable sketches, or diagrams contradicting calculated values |
| Step-by-step derivation | 20% | 10 | Systematic derivation showing: base impedance calculation (1.154 Ω), pu conversion, explicit SCC line equation, Potier reactance determination, converter output voltage formula derivation, thyristor current integration, and transmission line input impedance formula with βl calculation | Some steps skipped or combined, final formulas stated without derivation, or missing intermediate verification steps | No derivations shown, only final answers stated, or incorrect formulas applied without justification |
| Practical interpretation | 20% | 10 | Interprets results practically: explains why saturated X_s < unsaturated X_s, discusses converter operation at reduced voltage (50%), comments on thyristor rating requirements, and relates SWR≈2 to acceptable transmission line operation; notes relevance to Indian grid standards (CEA regulations) | Brief mention of practical significance without elaboration, or generic statements about machine/converter/line operation | No practical interpretation, purely mathematical treatment, or incorrect physical interpretation of results |
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