(a) A DC motor has an armature resistance of 0·5 Ω and Kφ of 3 Vs. The motor is driven by a single-phase thyristorized full converter. The input to the converter is an AC source of 230 V, 50 Hz. The motor is used as a prime mover of a forklift. In th

Question

(a) A DC motor has an armature resistance of 0·5 Ω and Kφ of 3 Vs. The motor is driven by a single-phase thyristorized full converter. The input to the converter is an AC source of 230 V, 50 Hz. The motor is used as a prime mover of a forklift. In the upward direction, the mechanical load is 69 Nm and the triggering angle is α = 15°. In the downward direction, the load torque is 180 Nm. Calculate the triggering angle required to keep the downward speed equal in magnitude to upward speed. Assume continuous motor current for all operation. Also calculate the triggering angle to keep the motor at holding position while it was moving upward. 12 marks

(b) The primary side of an ideal transformer (having 400 turns in primary winding and 720 turns in secondary winding) is excited by a 1000 V, 50 Hz AC source. The secondary of the transformer is connected to a resistive load of 80 kW. There is one tapping in secondary winding at 480 turns and this tapping is supplying a pure inductive load of 100 kVA. Determine the primary current and its power factor. 12 marks

(c) (i) Obtain an expression for the total average power of a sinusoidal AM wave
v_c = V_c sin ω_c t
v_m = V_m sin ω_m t

(ii) An AM transmitter broadcasts a carrier power of 100 kW. Determine the radiated power at the amplitude modulation index of 0·8. 12 marks

(d) Given a unity feedback system with G(s) = K/s(s+a) as shown in the figure :

(i) Find the values of K and a, when the closed-loop system has K_v = 100 and admits 20% peak overshoot.

(ii) Find the values of K and a, when the closed-loop system has settling time (2% tolerance band) of 2 seconds and admits 10% peak overshoot. 12 marks

(e) Two relays R_1 and R_2 are connected in two sections of a feeder as shown in the following figure. CTs are of ratio 1000/5. The plug setting of relay R_1 is 100% and of R_2 is 125%. The operating time characteristics of the relay is given in the following table :

Operating time characteristics for TMS = 1
PSM | 2 | 4 | 5 | 8 | 10 | 20
Operating time (seconds) | 10 | 5 | 4 | 3 | 2·8 | 2·4

The time multiplier setting of the relay R_1 is 0·3. The time grading scheme has a discriminative margin of 0·5 s between the relays. A three-phase short circuit at F results in a fault current of 5000 A. Find the actual operating time of R_1 and R_2. What is the time multiplier setting (TMS) of R_2? 12 marks

UPSC Answer Check · Accepted Answer

Solve all five numerical sub-parts systematically, allocating approximately 20% time to each part given equal 12-mark weighting. Begin with clear identification of given data and required unknowns for each sub-part. Present derivations first where asked (AM power expression in c-i, control system parameters in d-i and d-ii), followed by numerical substitutions and final answers with proper units. For relay coordination in part (e), clearly show PSM calculations and time grading logic.
- Part (a): Apply full converter voltage equation V_a = (2V_m/π)cosα for upward motion; use torque-speed relation T = KφI_a and back EMF E_b = Kφω to find speed; for downward motion with regenerative braking, determine α for same speed magnitude; calculate holding angle when E_b = 0
- Part (b): Calculate secondary voltages using turns ratio; determine currents in each secondary section using S = VI; apply ampere-turn balance equation N_1I_1 = N_2I_2 + N_3I_3 with proper phase consideration for inductive load; compute primary current magnitude and power factor
- Part (c): Derive AM wave expression v(t) = V_c[1 + m sin(ω_m t)]sin(ω_c t); expand and identify carrier, upper and lower sideband components; integrate over period to obtain average power P_avg = P_c(1 + m²/2); substitute m = 0.8 to find radiated power
- Part (d): Use standard second-order system relations: K_v = K/a, ζ from overshoot formula %OS = exp(-ζπ/√(1-ζ²)) × 100, settling time t_s = 4/(ζω_n); solve simultaneous equations for K and a in both cases
- Part (e): Calculate PSM for both relays as I_fault/I_pickup; interpolate operating time from given table for TMS=1; apply actual TMS for R_1; ensure time grading margin of 0.5s between R_2 and R_1; back-calculate TMS for R_2

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	12	Correctly identifies all governing principles: full converter operation with continuous current for (a), ampere-turn balance with complex power for (b), AM sideband power distribution for (c), second-order system specifications for (d), and IDMT relay coordination with PSM-TMS relationship for (e)	Identifies most principles correctly but confuses converter operation modes, misapplies transformer MMF balance, or makes errors in relating damping ratio to overshoot	Fundamental conceptual errors such as treating full converter as half-wave, ignoring phase shift in transformer loads, or incorrect relay characteristic interpretation
Numerical accuracy	20%	12	All calculations precise with correct significant figures: upward speed ≈ 67.5 rad/s, downward α ≈ 112-115°, holding α = 90°, primary current ≈ 250-260 A at pf ≈ 0.8 lagging, radiated power = 132 kW, K and a values accurate to 2 decimal places, relay times within 0.1s tolerance	Minor arithmetic slips in 1-2 parts, correct method but calculation errors in final steps, or unit conversion mistakes	Major calculation errors, wrong formula substitutions, or answers without units; more than 3 parts with incorrect final values
Diagram quality	15%	9	Clear circuit diagrams for full converter-fed DC motor showing thyristor bridge, free-wheeling path; transformer connection diagram with tapping points; control system block diagram with unity feedback; feeder protection scheme with CTs and relays properly labelled	Basic sketches without proper labelling, missing some circuit elements, or diagrams that don't clearly support the solution approach	No diagrams where essential, or completely incorrect circuit representations that would mislead the solution
Step-by-step derivation	25%	15	Complete stepwise working: for (a) shows voltage equation → torque balance → speed calculation → regenerative condition; for (c-i) full AM expansion with trigonometric identities and power integration; for (d) explicit ζ calculation from overshoot, then ω_n from settling time; for (e) clear PSM → time interpolation → TMS calculation chain	Some steps skipped or combined, missing intermediate substitutions, or correct final answers without showing how standard formulae were applied	Only final answers with no working, or incorrect derivations that happen to give right answers by coincidence; missing essential steps in AM power derivation
Practical interpretation	20%	12	Interprets physical significance: explains why α > 90° needed for regenerative braking in forklift operation, discusses transformer loading effects on primary pf, comments on AM transmission efficiency and sideband power utility, validates control system design for specified performance, and explains relay coordination importance in Indian distribution systems like state electricity boards	Brief mention of practical context without elaboration, or generic statements not tied to specific numerical results	No physical interpretation, or incorrect practical conclusions such as suggesting motoring operation for braking, or ignoring coordination requirements in protection

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