(a) The figure below shows the single-line diagram of a generator connected through parallel transmission lines to an infinite bus. The machine is delivering 1 pu power, and both the terminal voltage and the infinite bus voltage are 1 pu. The numbers

Question

(a) The figure below shows the single-line diagram of a generator connected through parallel transmission lines to an infinite bus. The machine is delivering 1 pu power, and both the terminal voltage and the infinite bus voltage are 1 pu. The numbers on the diagram indicate the values of the reactances on a common system base. The transient reactance of the generator is 0·20 pu as indicated. Determine the power-angle equation for the system applicable to the operating conditions. Also develop the swing equation of the machine :
Given H = 4 MJ/MVA. (20 marks)

(b) Draw the diagram of a 1/3 rate convolution encoder. Write the corresponding code tree for the 1/3 rate convolution encoder. (20 marks)

(c) The capacitances of a 3-core cable of belted type are measured and found to be as follows :
(i) Between 3 cores bunched together and the sheath, 8 µF
(ii) Between one conductor and the other two connected together to the sheath, 5 µF
Calculate the capacitance to the neutral and the total charging kVA, when the cable is connected to an 11 kV, 50 Hz, 3-phase supply. (10 marks)

UPSC Answer Check · Accepted Answer

Solve this multi-part numerical problem by allocating approximately 40% time to part (a) given its 20 marks and computational complexity, 40% to part (b) for the encoder diagram and code tree construction, and 20% to part (c) for cable capacitance calculations. Begin with a brief system description, then present each part sequentially with clear headings, ensuring all derivations show intermediate steps and final answers are boxed with proper units.
- Part (a): Calculate equivalent reactance of parallel transmission lines (0.4||0.4 = 0.2 pu), total reactance between generator internal bus and infinite bus (0.2+0.2+0.2+0.2 = 0.8 pu), power-angle equation P = (1×1/0.8)sinδ = 1.25sinδ, and swing equation (H/πf)(d²δ/dt²) = Pm - Pe with H=4 MJ/MVA
- Part (b): Draw 1/3 rate convolutional encoder with constraint length K and generator polynomials (typically g0, g1, g2), showing shift registers and modulo-2 adders; construct complete code tree showing all possible state transitions and output sequences for input bits 0 and 1
- Part (c): Use given measurements to find core-to-core capacitance Cc and core-to-sheath capacitance Cs from equations: 3Cs = 8 µF and 2Cc + Cs = 5 µF, yielding Cs = 8/3 µF and Cc = 7/6 µF; calculate capacitance to neutral Cn = 3Cc + Cs = 8.5 µF and charging kVA = √3×VLL×IC = √3×11×10³×2π×50×8.5×10⁻⁶×11×10³/√3
- Correct application of per-unit system and conversion to actual values where required
- Proper labeling of all diagrams with component values and clear state representation in code tree

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies power-angle relationship for synchronous machine connected to infinite bus, understands convolutional encoding principles with code tree construction, and applies correct belted cable capacitance model with proper interpretation of bunched conductor measurements	Identifies basic power transfer equation but makes minor errors in equivalent circuit reduction; understands encoder structure but code tree has missing branches; applies cable capacitance formulas with some confusion between Cc and Cs definitions	Confuses steady-state with transient stability analysis, omits swing equation entirely; draws block diagram instead of convolutional encoder; applies single-core cable formulas to 3-core belted cable problem
Numerical accuracy	20%	10	All calculations accurate: parallel reactance 0.2 pu, total reactance 0.8 pu, power-angle coefficient 1.25, swing equation constant 0.0255; code tree outputs match generator polynomials; cable capacitances Cs=2.667 µF, Cc=1.167 µF, Cn=8.5 µF, charging current and kVA correct	Minor arithmetic errors in one part (e.g., incorrect parallel combination or sign error in swing equation); code tree has correct structure but some output bit errors; cable capacitance values slightly off due to algebraic manipulation errors	Major calculation errors in multiple parts, wrong base values, incorrect formula application (e.g., using series instead of parallel for lines), or missing numerical answers entirely
Diagram quality	20%	10	Clear single-line diagram for part (a) with all reactances labeled; neat convolutional encoder diagram showing shift registers, connections to modulo-2 adders, and output lines; code tree properly branched with states and outputs at each level	Diagrams present but poorly labeled or missing some components; encoder diagram lacks clarity in showing constraint length or generator connections; code tree drawn but missing some state transitions or labels	Diagrams absent or unrecognizable; no attempt at code tree; part (c) has no diagram when cable cross-section would aid explanation
Step-by-step derivation	20%	10	Shows complete derivation: equivalent circuit reduction with intermediate values, power-angle equation development from P=(EV/X)sinδ, swing equation from M(d²δ/dt²)=Pm-Pe with M=GH/πf; encoder state equations; simultaneous equations for Cc, Cs with substitution steps; final charging kVA calculation with intermediate current computation	Shows some steps but skips key derivations (e.g., jumps to final power-angle equation); encoder description without state transition logic; cable capacitance equations stated but solution steps condensed	Only final answers stated without derivation; no intermediate working shown; appears to copy formulae without application to given data
Practical interpretation	20%	10	Interprets swing equation for stability analysis (e.g., for Indian grid frequency 50 Hz), notes significance of H=4 for hydro vs thermal machines; explains 1/3 rate coding for error correction in power line communication; relates cable charging kVA to reactive power compensation needs in 11 kV distribution systems	Brief mention of practical relevance without elaboration; generic statement about stability importance; minimal connection to real-world applications	No practical interpretation; treats problem as purely mathematical exercise; no units or physical significance discussed

Q8

Directive word: Solve

How this answer will be evaluated

Approach

Key points expected

Evaluation rubric

Practice this exact question

More from Electrical Engineering 2025 Paper II