(a) A single-phase full bridge inverter is used to produce a 50 Hz voltage across a series R-L load (R = 10 Ω and L = 20 mH) using bipolar PWM. The DC input to the bridge is 380 V, the amplitude modulation ratio mₐ = 0·8 and frequency modulation rati

Question

(a) A single-phase full bridge inverter is used to produce a 50 Hz voltage across a series R-L load (R = 10 Ω and L = 20 mH) using bipolar PWM. The DC input to the bridge is 380 V, the amplitude modulation ratio mₐ = 0·8 and frequency modulation ratio mƒ = 21. Consider dominant harmonics to be frequency dominant and its nearby side frequencies (both sides). Assume normalized Fourier coefficient for mₐ = 0·8 to be 82% for dominant harmonic frequency and 22% for the nearby side frequencies. Determine—
(i) amplitude of 50 Hz component of output voltage and current;
(ii) power absorbed by the load resistor;
(iii) THD of the load current.
Also compare the amplitude of 50 Hz component of output voltage with square wave and quasi-square wave output. 20 marks

(b) A 3-phase, 6-pole, 460 V, 50 Hz induction generator operates at 480 V. The generator has its rated output power of 20 kW. It is driven by a turbine at a speed of 1015 r.p.m. The generator has the following electrical parameters: R₁ = 0·2 Ω, R₂ = 0·15 Ω, Rₛₕ = 320 Ω, X₁ = 1·2 Ω, X₂ = 1·29 Ω, Xₘ = 42 Ω. Find the active power delivered by the generator and reactive power it requires from the system to operate. 20 marks

(c) (i) Under what condition a single line-to-ground fault at the terminals of a generator can be more severe than a 3-phase symmetrical fault at the same location?
(ii) A 3-phase power system is represented by one-line diagram as shown in the figure below: The ratings of the equipments are the following: Generator G: 15 MVA, 6·6 kV, X₁ = 15%, X₂ = 10%; Transformers: 15 MVA, 6·6 kV delta/33 kV star, X₁ = X₂ = X₀ = 6%; Line reactance: X₁ = X₂ = 2 Ω and X₀ = 6 Ω. Find the fault current for a ground fault on one of the bus bars at B. 20 marks

UPSC Answer Check · Accepted Answer

Calculate all numerical quantities demanded across the three parts, allocating approximately 35% time to part (a) given its multi-step PWM analysis and comparison requirement, 30% to part (b) for induction generator power flow calculations, and 35% to part (c) for sequence network construction and fault analysis. Begin each part with the appropriate formula statement, show systematic substitution, and conclude with physical interpretation of results.
- Part (a): Correct application of bipolar PWM fundamental voltage formula V₁ = mₐ × Vdc and harmonic voltage calculation using normalized Fourier coefficients; impedance calculation at dominant harmonic frequency (mf × f₁ = 1050 Hz) and side frequencies
- Part (a): THD calculation using Iₕ/I₁ ratio summation for identified harmonics, and explicit comparison table showing V₁(50Hz) for PWM (304V), square wave (4Vdc/π = 484V), and quasi-square wave with pulse width δ
- Part (b): Correct determination of slip s = (Ns - N)/Ns = -0.01 for generator operation; accurate calculation of Thevenin equivalent or direct impedance method for rotor circuit; separation of air-gap power into active and reactive components
- Part (b): Proper accounting for core loss resistance Rsh and magnetizing branch in power calculations; correct sign convention for generator operation (P delivered positive, Q absorbed positive)
- Part (c)(i): Clear statement that single line-to-ground fault exceeds 3-phase fault severity when X₀ < X₁ (typically with solidly grounded neutral or low X₀/X₁ ratio), making I(LG) = 3E/(2X₁+X₀) > I(3φ) = E/X₁
- Part (c)(ii): Correct sequence network interconnection for single line-to-ground fault (series connection of positive, negative, zero sequence); proper base conversion (15 MVA, 6.6 kV base) and per-unit calculations for transformer, line impedances; final fault current in amperes at 33 kV bus B

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	12	Demonstrates flawless understanding of PWM harmonic spectrum, induction generator equivalent circuit with negative slip, and symmetrical components for LG faults; correctly identifies that LG fault severity condition (X₀ < X₁) relates to grounding practices in Indian power systems like 400 kV with low resistance grounding	Shows basic grasp of PWM principles and induction machine operation but confuses generator/motor sign conventions or makes minor errors in sequence network connections; may miss the X₀ < X₁ condition for LG severity	Fundamental misconceptions such as treating PWM as square wave, using motor equivalent circuit for generator without slip sign change, or parallel connection of sequence networks for LG fault
Numerical accuracy	20%	12	All calculations accurate to 3 significant figures: V₁ = 304 V, I₁ = 21.5 A (approx), THD ≈ 8-12% depending on harmonic summation; induction generator P ≈ 19.5 kW, Q ≈ 12-15 kVAR; fault current ≈ 2.8-3.2 kA at bus B with correct per-unit conversion	Correct method but arithmetic errors in impedance angles, slip calculation, or base conversion; final answers within 10-15% of correct values; may forget to convert per-unit to actual amperes	Major calculation errors exceeding 25% deviation; wrong formulas leading to nonsensical results like negative power or kiloampere currents in 15 MVA system; unit confusion between kV and V
Diagram quality	15%	9	Clear sketches: PWM switching pattern with carrier and reference waveforms for part (a); per-phase equivalent circuit with power flow arrows for part (b); sequence network diagram showing series connection and impedance values for part (c)	Basic diagrams present but lacking labels or with incorrect connections; may show PWM without carrier comparison or sequence networks without proper grounding representation	Missing essential diagrams or completely incorrect representations; no attempt to illustrate PWM principle, induction machine equivalent circuit, or fault network topology
Step-by-step derivation	25%	15	Systematic progression: for (a) states V₁ = mₐVdc, calculates Z at each harmonic, uses superposition; for (b) derives Thevenin or uses equivalent circuit method with clear power balance; for (c) shows base conversion, sequence impedance calculation, network reduction, and fault current formula Iₐ = 3E₁/(Z₁+Z₂+Z₀)	Some steps shown but skips critical intermediate results like harmonic impedance calculation or assumes Thevenin values without derivation; sequence network reduction partially shown	Jumps directly to answers without derivation; no evidence of systematic problem-solving; missing essential steps like per-unit conversion or harmonic frequency determination
Practical interpretation	20%	12	Interprets PWM THD implications for filter design in drives; discusses induction generator reactive power requirement and need for capacitor banks or SVC in wind farms like those in Tamil Nadu; relates LG fault severity to neutral grounding practices and equipment rating in Indian utilities	Brief mention of practical relevance without elaboration; generic statements about PWM advantages or fault current magnitude without system context	No physical interpretation; purely mathematical treatment without connecting results to engineering practice or power system operation

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