TSGENCO AE cheat sheet

Per-unit: Z_pu = Z_actual/Z_base; Z_base = V_base²/S_base (single-phase), and for three-phase S_base(3φ) = √3·V_LL,base·I_base.

Symmetrical components: I_a0 = (I_a+I_b+I_c)/3, I_a1 = (I_a+aI_b+a²I_c)/3, I_a2 = (I_a+a²I_b+aI_c)/3 with a = 1∠120°.

Fault levels: three-phase fault current = V_ph/(Z1); LG fault = 3V_ph/(Z1+Z2+Z0); LL fault = √3V_ph/(Z1+Z2).

Y-bus formation: off-diagonal Y_ij = −y_ij (negative of series admittance); diagonal Y_ii = sum of all admittances connected to bus i, including shunt.

Surge impedance loading SIL = V_LL²/Z_c; for a lossless line Z_c = √(L/C), and SIL ≈ 132 kV→~35 MW, 220 kV→~120 MW, 400 kV→~400 MW order.

Equal-area criterion: steady-state stability requires P_max sinδ > P_mech; critical clearing angle is found by equating accelerating area to decelerating area.

Corona onset (Peek): E_c = 21.1·m·δ·(1+0.0301/√(δr)) kV/cm (rms), where δ = air density factor and r = conductor radius in cm.

Distance relay zones: Zone 1 ≈ 80% of line (instantaneous), Zone 2 ≈ 120–150% with time delay, Zone 3 covers remote backup; mho relay is directional.

Transformer EMF: E = 4.44·f·Φ_m·N; voltage regulation = (V_no-load − V_full-load)/V_full-load, and efficiency peaks when copper loss equals iron loss.

Induction motor: synchronous speed N_s = 120f/P; slip s = (N_s − N)/N_s; rotor frequency = sf; torque ∝ s·E2²/(R2² + (sX2)²).

DC machine EMF: E = (P·Φ·N·Z)/(60A) for generator; torque T = 0.159·P·Φ·Z·I_a/A; shunt motor speed falls with load, series motor torque ∝ I_a².

Parallel operation of transformers: load sharing ∝ kVA rating / per-unit impedance, provided voltage ratios and polarities match; unequal ratios cause circulating current.

Synchronous generator: E_f = V + I_a(R_a + jX_s); power P = (E_f·V/X_s)·sinδ; excitation controls reactive power, prime-mover input controls real power.

Armature reaction: in a DC generator it is cross-magnetizing (distorts field); in a motor it is also cross-magnetizing but opposite in direction; interpoles neutralize it.

Single-phase induction motor has no starting torque from the double-reversing field; split-phase, capacitor-start and shaded-pole designs create phase displacement.

Slip at maximum torque: s_m = R2/X2; maximum torque is independent of rotor resistance, so adding rotor resistance raises starting torque without changing T_max.

Single-phase full-controlled bridge: V_dc = (2V_m/π)·cosα; for a half-controlled bridge V_dc = (V_m/π)(1+cosα).

Three-phase fully controlled converter: V_dc = (3√3·V_m/π)·cosα = 1.35·V_LL·cosα; inverter mode when α > 90°.

Buck converter: V_o = D·V_s; boost: V_o = V_s/(1−D); buck-boost: V_o = −V_s·D/(1−D); D = duty cycle, continuous conduction assumed.

Ripple: buck ΔI_L = V_s·D(1−D)/(f_s·L); boost output ripple ΔV_o = I_o·D/(f_s·C).

SCR turn-on requires anode positive, gate pulse, and latching current exceeded; turn-off needs current below holding current and reverse bias for t_q.

Half-bridge inverter output fundamental (square wave) V_1(rms) = 2√2·V_dc/π ≈ 0.9·V_dc; PWM reduces low-order harmonics at the cost of switching loss.

Thyristor ratings: latching current > holding current; dv/dt triggering avoided by snubber RC across device; di/dt limited by series inductor.

Cycloconverter converts fixed AC to variable-frequency AC directly; a 3-pulse bridge gives output frequency ≤ about one-third of supply frequency.

Wheatstone bridge balance: R1/R2 = R3/R4; Maxwell bridge measures inductance using a standard capacitor; Schering bridge measures capacitance and loss angle.

PMMC instrument reads average value and has linear scale; moving iron reads RMS; electrodynamometer reads RMS and works on both AC and DC.

CT and PT burden expressed in VA; a CT must never be open-circuited on the secondary with primary energized (dangerous voltage, core saturation).

Error: %error = (measured − true)/true × 100; a wattmeter's pressure-coil circuit consumes power, causing a small positive or negative error depending on connection.

Second-order system: ω_n natural frequency, ζ damping ratio; % overshoot = 100·exp(−ζπ/√(1−ζ²)); peak time t_p = π/(ω_n√(1−ζ²)).

Routh–Hurwitz: number of sign changes in the first column equals number of right-half-plane poles; a zero row signals marginal stability.

Steady-state error: type-0 system to step = 1/(1+K_p); type-1 to ramp = 1/K_v; type-2 to parabola = 1/K_a.

Bode: gain margin = 0 − |G(jω)| at phase crossover; phase margin = 180° + ∠G(jω) at gain crossover; both positive means stable.

Rankine efficiency = (h1 − h2) − (h4 − h3))/(h1 − h4); regeneration raises mean temperature of heat addition; reheat raises dryness fraction at exhaust.

Carnot efficiency = 1 − T_L/T_H; Rankine cycle efficiency is always below Carnot for the same temperature limits.

Boiler efficiency (direct method) = (steam energy output)/(fuel energy input) × 100; indirect method uses losses (dry flue gas, moisture, radiation, unburnt carbon).

Drum pressure and water level: three-element feedwater control uses steam flow, feedwater flow, and drum level; swell and shrinkage are transient level effects.

Impulse turbine: pressure drop occurs in nozzles only; reaction turbine: pressure drop across both fixed and moving blades, degree of reaction R = enthalpy drop in rotor/total stage drop.

Nozzle flow chokes when pressure ratio p2/p1 ≤ (2/(γ+1))^(γ/(γ−1)) ≈ 0.528 for γ = 1.4; beyond this mass flow is constant.

Condenser vacuum improves cycle efficiency; 1 mm Hg back pressure change affects heat rate appreciably; cooling water temperature sets the achievable vacuum.

Air preheater and economizer recover flue-gas heat; superheater raises steam temperature at constant pressure, improving cycle efficiency without exceeding metal limits.

Bernoulli (ideal): p/ρg + v²/2g + z = constant; real flow adds head loss h_f = f·(L/D)·(v²/2g) (Darcy–Weisbach).

Reynolds number Re = ρvD/μ; laminar pipe flow Re < 2000, turbulent Re > 4000; friction factor f = 64/Re for laminar flow.

Pump affinity laws: Q ∝ N, H ∝ N², P ∝ N³; specific speed N_s = N√Q/H^(3/4) classifies impeller type (radial, mixed, axial).

Cavitation occurs when local pressure falls below vapour pressure; NPSH_available must exceed NPSH_required, NPSH_a = (p_atm − p_v)/ρg + z − h_f.

Hydraulic turbine: Pelton uses high head/low flow (impulse), Francis medium head, Kaplan low head/high flow; draft tube recovers exit kinetic energy.

Machine design: factor of safety = yield (or ultimate) strength/working stress; Soderberg, Goodman and Gerber criteria handle fluctuating stresses with stress concentration factor K_f.

Shaft design under combined bending and torsion: equivalent torque T_e = √(M² + T²); equivalent bending moment M_e = (M + √(M² + T²))/2.

Belt drive: ratio = D2/D1; centrifugal tension T_c = m·v²; maximum power transmitted when T_c = T_max/3 for flat belts.

Simply supported beam with UDL w over span L: M_max = wL²/8 at midspan; max shear = wL/2 at supports.

Cantilever with point load P at free end: M_max = PL at fixed end; deflection δ = PL³/(3EI).

Working stress design: modular ratio m = 280/(3σ_cbc); lever arm and neutral axis depth from cracked-section theory; limit state design uses partial safety factors 1.5 (dead+live) and 0.87 f_y for steel stress.

Soil: effective stress σ' = σ − u; Terzaghi bearing capacity q_u = cN_c + qN_q + 0.5γBN_γ; φ = 0 gives N_c = 5.7 for strip footing.

Compaction: standard Proctor (light) vs modified Proctor (heavy, higher energy); OMC decreases and max dry density increases with higher compactive effort.

Permeability: Darcy's law v = ki; k for sand from Hazen's formula k = C·D10² (cm/s with D10 in mm); falling-head test suits fine-grained soils.

Gravity dam: overturning, sliding (factor = μΣV/ΣH) and foundation pressure checked; uplift reduces effective weight, relief drains lower uplift.

Open channel: Manning V = (1/n)·R^(2/3)·S^(1/2); hydraulic jump sequent depth from momentum equation; most efficient trapezoidal section has half-hexagon geometry.

Percentage change: successive changes a% then b% give net change a + b + ab/100; a 20% rise then 20% fall yields a net 4% fall.

Time–speed–distance: average speed for equal distances at speeds x and y is 2xy/(x+y), not the arithmetic mean.

Simple vs compound interest: SI = PRT/100; CI = P(1+R/100)^T − P; difference for 2 years = P(R/100)².

Permutations and combinations: nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!); number of diagonals of an n-gon = n(n−3)/2.

Blood relations and direction sense: draw a diagram; for direction problems, net displacement uses Pythagoras when turns are at right angles.

Syllogism: a conclusion follows only if it is true in every possible Venn arrangement of the premises; 'some' and 'no' statements need careful conversion.

Data interpretation: percentage share = (component/total) × 100; growth rate = (new − old)/old × 100; read units and base year before computing.

Series completion: check differences, then ratios, then alternating patterns; number series often combine two interleaved sequences.

Telangana formed on 2 June 2014 as the 29th state; Hyderabad is the joint capital; the state has 33 districts after reorganisation.

TSGENCO (Telangana State Power Generation Corporation) operates major thermal stations including Kothagudem, Ramagundam (NTPC-shared), and the Singareni-linked stations; TS TRANSCO handles transmission.

Telangana's key power utilities: TSGENCO (generation), TS TRANSCO (transmission), TSSPDCL and TSNPDCL (distribution, southern and northern).

Major irrigation projects: Kaleshwaram (Medigadda, Annaram, Sundilla barrages on Godavari), Srisailam, Nagarjuna Sagar, and Sriram Sagar on the Godavari basin.

Telangana's state symbols: animal - chital (spotted deer), bird - Indian roller (pala pitta), flower - jasmine (malli), tree - prosopis (jammi chettu).

National power facts: India's installed capacity is dominated by thermal (coal) followed by renewable and hydro; southern region grids are interconnected through synchronous links.

Current affairs approach: track appointments, schemes, indices and awards for the 12 months preceding the exam date; energy-sector news (renewables, discom reforms) is high-yield for a power-generation exam.

Telangana economy: IT and pharma cluster around Hyderabad; Singareni Collieries supplies coal to state thermal plants; Ramagundam is a major coal-belt power hub.