(a) A full-controlled full-wave bridge AC/DC converter is fed from a single-phase, 230 V, 50 Hz supply, and is in turn feeding to an R-L load (R = 10 Ω and L = 100 mH). The firing angle α = 60°. Investigate whether load current remains continuous or

Question

(a) A full-controlled full-wave bridge AC/DC converter is fed from a single-phase, 230 V, 50 Hz supply, and is in turn feeding to an R-L load (R = 10 Ω and L = 100 mH). The firing angle α = 60°. Investigate whether load current remains continuous or not. Compute r.m.s. load current considering only the dominant harmonic, and determine the power absorbed by the load. Also compute voltage ripple factor. 20 marks

(b) For the electromechanical system shown below, the air-gap flux density under steady-state operating condition is given by

B(t) = Bₘ sin ωt

Find the instantaneous coil voltage and current along with force of magnetic field origin : 20 marks

(c) (i) In case of a circuit breaker, define the terms 'restriking voltage' and 'RRRV', and express their maximum values in terms of system voltage.

(ii) Which circuit breaker is preferred for voltages 132 kV and above?

(iii) In a 132 kV system, the reactance per phase up to the location of circuit breaker is 5 Ω and capacitance to earth is 0·03 µF. Calculate the maximum value of restriking voltage, the maximum value of RRRV and frequency of transient oscillation. 20 marks

UPSC Answer Check · Accepted Answer

Solve this multi-part numerical problem by allocating approximately 35% time to part (a) due to its computational complexity involving harmonic analysis, 30% to part (b) for deriving instantaneous electromagnetic quantities, and 35% to part (c) covering circuit breaker theory and transient calculations. Begin with clear problem statements for each part, show complete derivations with intermediate steps, and conclude with physically meaningful interpretations of results.
- Part (a): Calculate extinction angle β using transcendental equation for R-L load, verify continuity condition (β > π+α), compute dominant harmonic (2nd harmonic) RMS current using Fourier analysis, determine power absorbed, and derive voltage ripple factor
- Part (a): Apply correct formula for ripple factor considering only dominant harmonic component in the output voltage
- Part (b): Derive instantaneous coil voltage using Faraday's law (e = N dΦ/dt), determine current considering coil resistance/inductance, and compute magnetic force using Maxwell stress tensor or energy method (F = ½ i² dL/dx or B²A/2μ₀)
- Part (c)(i): Define restriking voltage as transient voltage across breaker contacts post-current zero, RRRV as rate of rise of restriking voltage (kV/μs), and express V_restrike(max) = 2V_m and RRRV_max = ω₀V_m where ω₀ = 1/√(LC)
- Part (c)(ii): Identify SF6 circuit breaker as preferred for 132 kV and above due to superior dielectric strength and arc quenching capability
- Part (c)(iii): Calculate L = 5/314 = 15.92 mH, C = 0.03 μF, natural frequency f₀ = 1/(2π√(LC)), V_restrike(max) = 2√2 × 132/√3 kV, and RRRV_max = V_restrike(max) × ω₀

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	12	Correctly identifies continuous conduction condition using β > π+α criterion for part (a); applies proper electromagnetic laws (Faraday, Lorentz) for part (b); accurately defines restriking voltage phenomena and recognizes SF6 breaker superiority for EHV in part (c)	Identifies basic conduction mode but makes errors in extinction angle calculation; states relevant laws but applies them partially; defines terms correctly but confuses breaker types or makes conceptual errors in transient phenomena	Misidentifies conduction mode or uses incorrect criterion; applies wrong electromagnetic principles; provides incorrect definitions or confuses restriking voltage with recovery voltage; names wrong breaker type
Numerical accuracy	20%	12	Computes β ≈ 220-230° confirming continuous conduction, dominant harmonic current ≈ 2-3 A, power ≈ 400-500 W, ripple factor ≈ 0.4-0.5; part (c)(iii) yields f₀ ≈ 7-8 kHz, V_restrike(max) ≈ 215 kV, RRRV_max ≈ 5-6 kV/μs with all unit conversions correct	Correct method but arithmetic errors in β calculation or harmonic component; order-of-magnitude correct for circuit breaker parameters but errors in √3 factor or peak vs RMS conversion; partial credit for correct formulas	Major calculation errors (wrong orders of magnitude), incorrect formula application, omits √2 or √3 factors, confuses line and phase quantities, or leaves numerical answers incomplete
Diagram quality	15%	9	Draws full-wave bridge converter with thyristors labeled and firing angle marked; sketches electromechanical system with coil, air-gap, and movable member; illustrates restriking voltage transient waveform showing oscillatory nature and peak value; all diagrams properly labeled with variables	Basic circuit diagrams without proper labeling or missing key elements (e.g., no freewheeling diode consideration); electromechanical system sketch incomplete; restriking voltage waveform drawn but missing annotations	Missing essential diagrams, poorly drawn schematics that hinder understanding, or diagrams that contradict the textual solution; no waveform sketches where required
Step-by-step derivation	25%	15	Shows complete derivation: load current differential equation solution for (a), integration for average and Fourier coefficients; flux linkage differentiation for induced voltage in (b); LC circuit differential equation for restriking voltage in (c); all steps logically sequenced with clear justification	Shows major steps but skips intermediate algebra; states final formulas without derivation; some logical gaps in derivation flow; correct approach but incomplete working for harmonic analysis or transient solution	Jumps to final answers without derivation, incorrect mathematical approach, or omits essential steps like boundary condition application; no attempt at solving differential equations
Practical interpretation	20%	12	Interprets continuous conduction significance for motor control applications; explains force pulsation implications in electromagnetic actuators; relates RRRV to breaker contact speed requirements and Indian grid standards (CBIP/CBI&P specifications); discusses SF6 environmental considerations	Brief mention of practical relevance without elaboration; generic statements about circuit breaker importance; no specific connection to Indian power system context or engineering standards	No physical interpretation provided, purely mathematical treatment, or incorrect practical conclusions (e.g., suggesting air-blast breakers for 132 kV in modern context)

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