(a) A 20 kW, 500 V DC shunt motor (having 90% full-load efficiency) has 40% armature copper losses of its full-load losses. Calculate the resistance values of a 4-section starter suitable for limiting starting current between 120% to 200% of full-loa

Question

(a) A 20 kW, 500 V DC shunt motor (having 90% full-load efficiency) has 40% armature copper losses of its full-load losses. Calculate the resistance values of a 4-section starter suitable for limiting starting current between 120% to 200% of full-load current. Assume field resistance of 250 Ω. 20 marks

(b) (i) Differentiate between characteristic impedance and surge impedance of a line. What do you mean by surge impedance loading (SIL) of a transmission line?

(ii) A three-phase, 50 Hz transmission line is 400 km long. The voltage at the sending end is 220 kV. The line parameters are r = 0·125 ohm/km, x = 0·4 ohm/km and y = 2·8×10⁻⁶ mho/km. Find the sending-end current and receiving-end voltage when there is no load on the line. Make a comment on the value of receiving-end voltage. 20 marks

(c) A boost converter is required to have an output voltage of 48 V and supply a load current of 5 A. The input varies from 12 V–24 V. A control circuit adjusts the duty ratio to keep the output voltage constant. Select the switching frequency to be 200 kHz. Determine a value of inductor such that the variation in inductor current is no more than 40% of average inductor current for all operation. Prescribe a suitable value of capacitor such that output ripple is no more than 2%. 20 marks

UPSC Answer Check · Accepted Answer

This is a calculation-heavy question demanding precise numerical work across three distinct domains. Begin with part (a) by first computing full-load current and losses, then establishing the current limits for starter design, and systematically deriving the four resistance sections. For part (b), first differentiate the impedance concepts conceptually, then apply the long-line ABCD parameters (or nominal π approximation) for the 400 km line to find sending-end current and receiving-end voltage under no-load, commenting on the Ferranti effect. For part (c), design the boost converter by calculating duty ratios for both input extremes, determining inductor value for worst-case ripple condition, and sizing capacitor for output voltage ripple. Allocate approximately 35% time to (a), 35% to (b), and 30% to (c), ensuring all derivations are shown stepwise with proper units.
- Part (a): Calculation of full-load current (40 A), total losses (2222.22 W), armature copper loss (888.89 W), armature resistance (0.556 Ω), and starter resistances R1-R4 (2.083 Ω, 1.25 Ω, 0.75 Ω, 0.45 Ω approximately) with current limits 48-80 A
- Part (b)(i): Clear distinction that characteristic impedance Zc = √(z/y) is frequency-dependent complex quantity while surge impedance Zs = √(L/C) is real and lossless; SIL = V²/Zs where natural power flow occurs at unity power factor
- Part (b)(ii): Application of long transmission line equations or nominal π method with ABCD parameters for 400 km line; calculation of sending-end current (approximately 180-200 A) and receiving-end voltage (approximately 245-260 kV, higher than sending end due to Ferranti effect)
- Part (c): Duty ratio calculation for Vin=12V (D=0.75) and Vin=24V (D=0.5); inductor selection based on worst-case ripple at D=0.5 or D=0.75 with ΔIL ≤ 40% of IL; L ≈ 45-60 μH; capacitor for 2% ripple (≈960V peak-to-peak at 48V means 0.96V ripple) yielding C ≈ 10-15 μF
- Practical interpretation: Comment on starter step transition currents, Ferranti effect significance for 400 km Indian transmission corridors (e.g., HVDC back-to-back stations), and converter continuous conduction mode verification

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	12	Correctly identifies that starter design requires current limiting between 120-200% of full-load current; accurately distinguishes surge impedance as lossless √(L/C) versus characteristic impedance √(z/y) including resistance effects; properly applies long-line or nominal π model for 400 km line recognizing distributed parameter nature; correctly states boost converter voltage transfer function Vo/Vin = 1/(1-D) and recognizes worst-case inductor ripple occurs at specific duty ratio	Minor conceptual errors such as using short-line approximation for 400 km, confusing surge and characteristic impedance definitions, or incorrect duty ratio formula application; understands starter principle but miscalculates current limits	Fundamental misconceptions like treating 400 km as short line, using simple series resistance model for starter without current limit consideration, or applying buck converter equations to boost topology
Numerical accuracy	20%	12	Precise calculations: full-load current 40 A, armature resistance ~0.556 Ω, starter sections summing to ~4.53 Ω with geometric progression; sending-end current ~186∠-87° A, receiving-end voltage ~258 kV; inductor ~50 μH, capacitor ~12 μF with all intermediate steps shown and unit consistency maintained	Correct method but arithmetic errors in final values; correct order of magnitude but 10-20% deviation in final answers; minor unit conversion errors (kV/V, km/m)	Order-of-magnitude errors; incorrect base formulas leading to nonsensical results (negative resistances, duty ratio >1); missing critical values or leaving answers in symbolic form
Diagram quality	15%	9	Clear 4-section starter circuit diagram with proper labeling of R1-R4, interlocks, and field circuit; transmission line equivalent π or T diagram with sending/receiving end marked; boost converter schematic showing inductor, switch, diode, capacitor with current directions and switching states	Basic circuit sketches without proper labeling; missing one diagram (e.g., no converter schematic); hand-drawn appearance acceptable but key components unlabeled	No diagrams despite requirement; incorrect topologies (e.g., buck instead of boost); messy or misleading sketches that contradict written solution
Step-by-step derivation	25%	15	Explicit derivation of starter resistance values using current limit equations I1 = V/(Ra+R1) and ratio relationships; complete ABCD parameter derivation or hyperbolic line equations for transmission line with propagation constant and characteristic impedance calculation; thorough inductor volt-second balance and capacitor charge balance for both input voltage extremes with ripple derivations	Jumps between steps with some intermediate results assumed; uses standard formulas without derivation where derivation is expected; correct final formulas but unclear origin	Final answers stated without derivation; incorrect or missing formulas; logical gaps that prevent following the solution path
Practical interpretation	20%	12	Insightful comment on Ferranti effect causing ~17% voltage rise at 400 km necessitating shunt reactors in Indian EHV systems (400 kV lines); recognizes starter resistance progression follows geometric series for smooth acceleration; notes boost converter operates in CCM throughout range with inductor sizing ensuring ripple limit; mentions practical component selection (standard values, ESR considerations)	Generic statements about voltage rise or current limiting without specific context; basic acknowledgment of practical implications without system-level insight	No interpretation provided; irrelevant or incorrect practical comments; misses significance of results entirely

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