(a) Two generators are connected in parallel to the low-voltage side of a 3-phase, Δ-Y transformer as shown below :
Generator 1 is rated 60 MVA, 13·8 kV
Generator 2 is rated 30 MVA, 13·8 kV

Each generator has a subtransient reactance of 20%. The tra

Question

(a) Two generators are connected in parallel to the low-voltage side of a 3-phase, Δ-Y transformer as shown below :
Generator 1 is rated 60 MVA, 13·8 kV
Generator 2 is rated 30 MVA, 13·8 kV

Each generator has a subtransient reactance of 20%. The transformer is rated 90 MVA, 13·8 Δ/69 Y kV with a reactance of 10%. Before the fault occurs, the voltage on the high-tension side of the transformer is 66 kV. The transformer is unloaded, and there is no circulating current between the generators. Find the subtransient current in each generator, when a 3-phase short circuit occurs on the high-tension side of the transformer : (20 marks)

(b) (i) What is line coding? For the data sequence 10101110, draw the waveforms for the following line coding schemes :
1. Polar NRZ scheme
2. Bipolar NRZ scheme
3. Differential Manchester scheme
4. RZ polar scheme (10 marks)

(ii) A PCM system uses 4096 quantization levels to handle telephone signals with a volume range of 40 dB.
1. What is the SNR for maximum sinusoidal signal level?
2. What is the SNR level for the smallest sinusoidal signal level?
3. With a 10 dB compression provided, what will be the new SNR? (10 marks)

(c) With the help of schematic and circuit diagrams, describe the operation of a static differential protection relay, using the rectifier bridge amplitude comparator. (10 marks)

UPSC Answer Check · Accepted Answer

Calculate the subtransient fault currents in part (a) by first converting all reactances to a common base and constructing the equivalent circuit, then apply per-unit analysis. For part (b), define line coding with clear waveform drawings for all four schemes, then calculate SNR values using the PCM quantization formula with proper dB conversions. For part (c), describe the static differential relay operation with complete schematic and circuit diagrams showing the rectifier bridge comparator. Allocate approximately 40% time to (a) given its 20 marks, 30% to (b) covering both sub-parts, and 30% to (c) for diagrams and description.
- Part (a): Convert generator and transformer reactances to common 90 MVA base; calculate subtransient reactances as Xg1=0.3 pu, Xg2=0.6 pu, Xt=0.1 pu; determine pre-fault voltage as 0.957 pu on HV side; compute fault current distribution using current division between parallel generators
- Part (a): Calculate subtransient current in Generator 1 as approximately 4.78 kA and Generator 2 as approximately 2.39 kA (or equivalent in per-unit with proper base current calculations)
- Part (b)(i): Define line coding as the process of converting binary data into digital signals for transmission; draw correct waveforms for Polar NRZ (high=1, low=0), Bipolar NRZ (alternate polarity for 1s), Differential Manchester (transition at start of bit, mid-bit for 0), and RZ polar (return to zero mid-bit)
- Part (b)(ii): Calculate SNRmax = 6.02×12 + 1.76 = 74 dB for 4096 levels (n=12 bits); SNRmin = 74 - 40 = 34 dB; with 10 dB compression, new SNR = 44 dB using proper dynamic range and companding formulas
- Part (c): Describe static differential protection using rectifier bridge amplitude comparator with schematic showing CT connections, restraint and operating coils, and full-wave rectifier bridge; explain operation for internal faults (operate) vs external faults (restrain) with proper polarized relay characteristics

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding of per-unit system for fault analysis, PCM quantization theory with companding, and static relay operating principles; correctly identifies Δ-Y transformer phase shift implications for fault current calculation	Shows basic understanding of per-unit conversions and quantization but makes minor errors in base selection or SNR formula application; relay description lacks clarity on restraint vs operating quantities	Confuses per-unit bases, applies wrong SNR formulas, or fundamentally misunderstands differential protection principle; cannot distinguish between static and electromechanical relays
Numerical accuracy	20%	10	All calculations in (a) and (b)(ii) are precise with correct significant figures; fault currents properly converted to actual values; SNR calculations include proper dB arithmetic and companding effects	Correct methodology but arithmetic errors in final values; per-unit fault currents correct but conversion to amperes may have base current errors; SNR values approximately correct but rounding errors present	Major calculation errors in reactance conversion, current division, or quantization levels; incorrect application of formulas leading to order-of-magnitude errors; missing units or incorrect unit conversions
Diagram quality	20%	10	Clear, labeled single-line diagram for (a) showing generators, transformer, and fault point; four distinct, properly timed waveforms for (b)(i) with bit boundaries marked; detailed schematic and circuit diagrams for (c) showing CT polarities, bridge rectifier, and relay coils	Diagrams present but lacking clarity in labels or scaling; waveforms recognizable but timing marks unclear; relay schematic misses some component labels or connection details	Missing or unrecognizable diagrams; waveforms confused between schemes; no circuit diagram for relay or completely incorrect representation of rectifier bridge comparator
Step-by-step derivation	20%	10	Systematic progression from base conversion → equivalent circuit → fault calculation in (a); clear derivation of SNR formulas with n=12 bits from 4096 levels; logical explanation of relay operation sequence from CT secondary to trip output	Steps present but some logical jumps; missing intermediate calculations like base current derivation; relay description sequential but lacks clear cause-effect explanation	Disorganized or missing steps; no derivation shown—only final answers; relay description as disconnected facts without operational logic
Practical interpretation	20%	10	Interprets unequal generator current sharing due to different MVA ratings; explains why line coding matters for clock recovery and DC balance; relates differential protection to Indian power grid protection standards (CBIP/IEC); discusses companding relevance for Indian telephone networks	Brief mention of practical implications without elaboration; generic statements about protection importance; no specific Indian context or real-world application	Purely theoretical treatment with no practical insight; fails to recognize why 40 dB dynamic range matters or why percentage differential is used in practice

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