PGCIL Field Engineer & DT cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R. In AC, use RMS values and include power factor: P = VI cos φ.

Thevenin equivalent: open-circuit voltage V_th across the terminals and R_th found by de-energizing independent sources (voltage sources shorted, current sources opened).

Maximum power transfer to a load occurs when R_L = R_th, giving efficiency of 50% for a purely resistive source-load pair.

Superposition applies only to linear circuits: compute each source's contribution separately, then add algebraically; it fails for power because power is nonlinear.

Series resonance: f_r = 1/(2π√(LC)); at resonance X_L = X_C, impedance is purely resistive and current is maximum in a series RLC circuit.

Three-phase relations: for star V_L = √3 V_ph, I_L = I_ph; for delta I_L = √3 I_ph, V_L = V_ph; total power P = √3 V_L I_L cos φ.

Power factor correction: Q_c = P(tan φ₁ − tan φ₂); capacitor kVAR = P × (tan φ₁ − tan φ₂).

Kirchhoff's laws: KCL sums currents at a node to zero; KVL sums voltages around a closed loop to zero.

Norton equivalent: I_N is the short-circuit current between terminals and R_N = R_th; source conversion V_th = I_N R_N.

Per-unit: Z_pu = Z_actual/Z_base with Z_base = V_base²/S_base; per-unit impedances transform across transformers by the square of the turns ratio only if bases are chosen per zone.

Load flow: slack bus fixes V and δ, PV bus fixes P and |V|, PQ bus fixes P and Q; the number of unknowns equals twice the buses minus slack and PV constraints.

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 I_f = V_ph/Z_1; single line-to-ground fault current I_f = 3V_ph/(Z_1 + Z_2 + Z_0).

Transmission line surge impedance Z_c = √(L/C); surge impedance loading SIL = V_L²/Z_c.

Stability: steady-state stability limit of a lossless line is P_max = EV/X; equal-area criterion compares accelerating and decelerating areas.

Economic dispatch: equal incremental cost dC_i/dP_i = λ for all units, subject to ΣP_i = P_load + losses.

Corona: critical disruptive voltage V_c = 21.1 m₀ δ r ln(D/r) kV (r in cm), where δ is air density factor.

Distance relay zones: Zone 1 covers about 80% of the line, Zone 2 about 120% with time delay, Zone 3 covers backup for the next line.

Mho relay characteristic is a circle through the origin, inherently directional; impedance relay is non-directional and needs a directional element.

Differential protection (Merz-Price) operates on the vector difference of currents and is the standard for transformers and busbars.

CT saturation causes relay maloperation; the CT knee-point voltage must exceed the maximum secondary voltage during through-faults.

Buchholz relay protects oil-immersed transformers against incipient faults (gas accumulation) and oil surges; it is not used on dry-type units.

Circuit breaker rating terms: rated normal current, rated short-circuit breaking current, rated short-time withstand current (1 s or 3 s), and rated making current.

SF6 breakers interrupt in an electronegative gas; vacuum breakers are preferred up to about 36 kV for distribution.

Buchholz and overcurrent protections are backup to differential; restricted earth fault (REF) protects the transformer winding to ground.

Arc interruption: recovery voltage and restriking voltage transient frequency f = 1/(2π√(LC)); current chopping causes overvoltages in vacuum and air-blast breakers.

Single-phase fully controlled bridge: V_dc = (2V_m/π) cos α; the same expression applies to a single-phase half-wave controlled rectifier with resistive load.

Three-phase fully controlled bridge: V_dc = (3√3 V_m/π) cos α = 1.35 V_LL cos α.

Buck converter: V_o = D V_in; boost: V_o = V_in/(1 − D); buck-boost: V_o = −V_in D/(1 − D).

DC motor speed: N ∝ (V − I_a R_a)/Φ; armature voltage control gives constant torque, field control gives constant power.

Induction motor speed: N_s = 120f/P; slip s = (N_s − N)/N_s; rotor frequency f_r = s f.

V/f control maintains constant flux below base speed; above base speed field weakening reduces torque capability.

Thyristor turn-on requires gate pulse plus forward anode-cathode voltage; turn-off requires anode current below holding current.

Inverter output voltage control by PWM: fundamental amplitude scales with modulation index m_a; overmodulation occurs when m_a > 1.

Chopper classification: Type A (step-down), Type B (step-up), Type C (two-quadrant), Type D (two-quadrant with reversed polarity), Type E (four-quadrant).

Transformer EMF equation: E = 4.44 f N Φ_m; voltage per turn is the same in primary and secondary.

Transformer efficiency is maximum when copper loss equals iron loss; at that load, load fraction x = √(P_i/P_cu,full-load).

Equivalent circuit referred to primary: R_01 = R_1 + a²R_2, X_01 = X_1 + a²X_2, where a = N_1/N_2.

Synchronous speed N_s = 120f/P; a 4-pole, 50 Hz machine runs at 1500 rpm.

DC generator EMF: E_g = (ΦPNZ)/(60A); for a DC motor, torque T = 0.159 Φ I_a Z P/A (SI units).

Slip at maximum torque: s_m = R_2/X_2; maximum torque is independent of rotor resistance but occurs at higher slip as R_2 increases.

No-load and blocked-rotor tests on an induction motor yield shunt branch and series branch parameters respectively.

Parallel operation of transformers requires equal voltage ratio, same polarity, and similar per-unit impedance to share load in proportion.

Armature reaction in DC machines shifts the magnetic neutral axis; compensating windings counteract it in large machines.

Short line (under 80 km): nominal T or π model with series impedance only; medium line (80–250 km): nominal π or T; long line (above 250 km): distributed parameters with hyperbolic functions.

ABCD constants for a short line: A = 1, B = Z, C = 0, D = 1; for a symmetrical network AD − BC = 1.

Voltage regulation = (|V_no-load| − |V_full-load|)/|V_full-load| × 100%.

Ferranti effect: receiving-end voltage exceeds sending-end voltage on light or no load in long lines, corrected by shunt reactors.

Skin effect raises AC resistance above DC resistance; the ratio increases with frequency and conductor diameter.

Substation bus schemes: single bus, double bus, one-and-a-half breaker, ring bus; the one-and-a-half breaker scheme gives high reliability with fewer breakers.

Earthing: station earth resistance should be low enough to limit step and touch potentials; typical grid resistance is below 1 Ω for EHV stations.

Sag formula: S = wL²/(8T) for level supports; sag increases with span squared and decreases with tension.

Insulator string efficiency improves with grading rings, longer cross-arms, and capacitance grading.

Wheatstone bridge balances when R_1/R_2 = R_3/R_4; Maxwell bridge measures inductance, Schering bridge measures capacitance and loss angle.

PMMC instruments measure DC average values; moving iron instruments measure RMS and respond to both AC and DC.

CT ratio: secondary current is 5 A or 1 A standard; burden is expressed in VA at rated secondary current.

PT (VT) ratio error and phase error affect power measurement accuracy; class 0.2 or 0.5 is used for metering.

Energy meter: 1 kWh = 1 unit; meter constant is revolutions per kWh; disc speed is proportional to load power.

Transfer function of a first-order system: G(s) = K/(1 + τs); time constant τ gives 63.2% of final value.

PID control: proportional acts on present error, integral removes steady-state offset, derivative damps overshoot and improves stability.

Strain gauge gauge factor GF = (ΔR/R)/(ΔL/L); a Wheatstone bridge converts resistance change to voltage.

Thermocouple Seebeck effect converts temperature difference to EMF; cold-junction compensation is required.

Percentage change: new value = old value × (1 ± p/100); successive changes of a% and b% give net change a + b + ab/100 percent.

Time and work: if A does work in x days and B in y days, together they finish in xy/(x + y) days.

Speed, time, distance: D = S × T; for a train crossing a platform, total distance = train length + platform length.

Simple interest SI = PRT/100; compound interest CI = P(1 + R/100)^T − P.

Number series and coding-decoding questions: identify the constant difference, ratio, or letter-position shift before applying the rule.

Syllogism: use Venn diagrams; a conclusion is valid only if it holds in every possible diagram consistent with the premises.

Blood relations: draw a family tree with gender markers; do not assume gender from names.

Direction sense: track net displacement by resolving north-south and east-west components separately.

Average and mixtures: alligation rule gives ratio of quantities as (mean − cheaper):(dearer − mean).

Subject-verb agreement: a singular subject takes a singular verb; phrases between subject and verb do not change the number.

Active to passive: object becomes subject, verb becomes be + past participle, and the agent is introduced by 'by'.

Direct to indirect speech: present tense shifts to past, 'today' becomes 'that day', 'tomorrow' becomes 'the next day'.

Articles: 'a' before consonant sounds, 'an' before vowel sounds; 'the' for specific or unique references.

Prepositions with fixed verbs: depend on, insist on, consist of, comply with, prefer to, capable of.

Common error pairs: 'affect' (verb) vs 'effect' (noun); 'principal' (main) vs 'principle' (rule); 'its' vs 'it's'.

Reading comprehension: locate the topic sentence, distinguish stated fact from inference, and answer only from the passage.

Idioms: 'to bite the bullet' means to endure a difficult situation; 'to burn the midnight oil' means to work late.

Para jumbles: find the opening sentence with a general statement, then follow pronoun and connector links.

Grid operation: NLDC (National Load Despatch Centre) coordinates national grid operation; regional load despatch centres operate under it.

Regulatory framework: CERC sets interstate transmission tariffs; state electricity regulatory commissions set intra-state tariffs.

Key legislation: Electricity Act 2003 governs generation, transmission, distribution, and trading; the Energy Conservation Act 2001 governs efficiency standards.

Renewable targets: India targets 500 GW non-fossil capacity by 2030, with solar and wind as the largest contributors.

Transmission planning: the National Electricity Plan (Transmission) is prepared by CEA and reviewed periodically.

Grid stability standards: CEA regulations specify frequency operating range around 49.90–50.05 Hz for normal operation in India.

Power sector schemes: UDAY addressed discom financial health; Saubhagya and DDUGJY targeted household and rural electrification.

Standards bodies: BIS publishes Indian Standards; IEC and IEEE publish international electrical standards.

Safety and environment: SF6 is a potent greenhouse gas; leakage monitoring and end-of-life recovery are mandatory practices.

Ohm's law: V = IR; power P = VI = I²R = V²/R. In AC, use RMS values and include power factor: P = VI cos φ.

Thevenin equivalent: open-circuit voltage V_th across the terminals and R_th found by de-energizing independent sources (voltage sources shorted, current sources opened).

Maximum power transfer to a load occurs when R_L = R_th, giving efficiency of 50% for a purely resistive source-load pair.

Superposition applies only to linear circuits: compute each source's contribution separately, then add algebraically; it fails for power because power is nonlinear.

Series resonance: f_r = 1/(2π√(LC)); at resonance X_L = X_C, impedance is purely resistive and current is maximum in a series RLC circuit.

Three-phase relations: for star V_L = √3 V_ph, I_L = I_ph; for delta I_L = √3 I_ph, V_L = V_ph; total power P = √3 V_L I_L cos φ.

Power factor correction: Q_c = P(tan φ₁ − tan φ₂); capacitor kVAR = P × (tan φ₁ − tan φ₂).

Kirchhoff's laws: KCL sums currents at a node to zero; KVL sums voltages around a closed loop to zero.

Norton equivalent: I_N is the short-circuit current between terminals and R_N = R_th; source conversion V_th = I_N R_N.

Per-unit: Z_pu = Z_actual/Z_base with Z_base = V_base²/S_base; per-unit impedances transform across transformers by the square of the turns ratio only if bases are chosen per zone.

Load flow: slack bus fixes V and δ, PV bus fixes P and |V|, PQ bus fixes P and Q; the number of unknowns equals twice the buses minus slack and PV constraints.

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 I_f = V_ph/Z_1; single line-to-ground fault current I_f = 3V_ph/(Z_1 + Z_2 + Z_0).

Transmission line surge impedance Z_c = √(L/C); surge impedance loading SIL = V_L²/Z_c.

Stability: steady-state stability limit of a lossless line is P_max = EV/X; equal-area criterion compares accelerating and decelerating areas.

Economic dispatch: equal incremental cost dC_i/dP_i = λ for all units, subject to ΣP_i = P_load + losses.

Corona: critical disruptive voltage V_c = 21.1 m₀ δ r ln(D/r) kV (r in cm), where δ is air density factor.

Distance relay zones: Zone 1 covers about 80% of the line, Zone 2 about 120% with time delay, Zone 3 covers backup for the next line.

Mho relay characteristic is a circle through the origin, inherently directional; impedance relay is non-directional and needs a directional element.

Differential protection (Merz-Price) operates on the vector difference of currents and is the standard for transformers and busbars.

CT saturation causes relay maloperation; the CT knee-point voltage must exceed the maximum secondary voltage during through-faults.

Buchholz relay protects oil-immersed transformers against incipient faults (gas accumulation) and oil surges; it is not used on dry-type units.

Circuit breaker rating terms: rated normal current, rated short-circuit breaking current, rated short-time withstand current (1 s or 3 s), and rated making current.

SF6 breakers interrupt in an electronegative gas; vacuum breakers are preferred up to about 36 kV for distribution.

Buchholz and overcurrent protections are backup to differential; restricted earth fault (REF) protects the transformer winding to ground.

Arc interruption: recovery voltage and restriking voltage transient frequency f = 1/(2π√(LC)); current chopping causes overvoltages in vacuum and air-blast breakers.

Single-phase fully controlled bridge: V_dc = (2V_m/π) cos α; the same expression applies to a single-phase half-wave controlled rectifier with resistive load.

Three-phase fully controlled bridge: V_dc = (3√3 V_m/π) cos α = 1.35 V_LL cos α.

Buck converter: V_o = D V_in; boost: V_o = V_in/(1 − D); buck-boost: V_o = −V_in D/(1 − D).

DC motor speed: N ∝ (V − I_a R_a)/Φ; armature voltage control gives constant torque, field control gives constant power.

Induction motor speed: N_s = 120f/P; slip s = (N_s − N)/N_s; rotor frequency f_r = s f.

V/f control maintains constant flux below base speed; above base speed field weakening reduces torque capability.

Thyristor turn-on requires gate pulse plus forward anode-cathode voltage; turn-off requires anode current below holding current.

Inverter output voltage control by PWM: fundamental amplitude scales with modulation index m_a; overmodulation occurs when m_a > 1.

Chopper classification: Type A (step-down), Type B (step-up), Type C (two-quadrant), Type D (two-quadrant with reversed polarity), Type E (four-quadrant).

Transformer EMF equation: E = 4.44 f N Φ_m; voltage per turn is the same in primary and secondary.

Transformer efficiency is maximum when copper loss equals iron loss; at that load, load fraction x = √(P_i/P_cu,full-load).

Equivalent circuit referred to primary: R_01 = R_1 + a²R_2, X_01 = X_1 + a²X_2, where a = N_1/N_2.

Synchronous speed N_s = 120f/P; a 4-pole, 50 Hz machine runs at 1500 rpm.

DC generator EMF: E_g = (ΦPNZ)/(60A); for a DC motor, torque T = 0.159 Φ I_a Z P/A (SI units).

Slip at maximum torque: s_m = R_2/X_2; maximum torque is independent of rotor resistance but occurs at higher slip as R_2 increases.

No-load and blocked-rotor tests on an induction motor yield shunt branch and series branch parameters respectively.

Parallel operation of transformers requires equal voltage ratio, same polarity, and similar per-unit impedance to share load in proportion.

Armature reaction in DC machines shifts the magnetic neutral axis; compensating windings counteract it in large machines.

Short line (under 80 km): nominal T or π model with series impedance only; medium line (80–250 km): nominal π or T; long line (above 250 km): distributed parameters with hyperbolic functions.

ABCD constants for a short line: A = 1, B = Z, C = 0, D = 1; for a symmetrical network AD − BC = 1.

Voltage regulation = (|V_no-load| − |V_full-load|)/|V_full-load| × 100%.

Ferranti effect: receiving-end voltage exceeds sending-end voltage on light or no load in long lines, corrected by shunt reactors.

Skin effect raises AC resistance above DC resistance; the ratio increases with frequency and conductor diameter.

Substation bus schemes: single bus, double bus, one-and-a-half breaker, ring bus; the one-and-a-half breaker scheme gives high reliability with fewer breakers.

Earthing: station earth resistance should be low enough to limit step and touch potentials; typical grid resistance is below 1 Ω for EHV stations.

Sag formula: S = wL²/(8T) for level supports; sag increases with span squared and decreases with tension.

Insulator string efficiency improves with grading rings, longer cross-arms, and capacitance grading.

Wheatstone bridge balances when R_1/R_2 = R_3/R_4; Maxwell bridge measures inductance, Schering bridge measures capacitance and loss angle.

PMMC instruments measure DC average values; moving iron instruments measure RMS and respond to both AC and DC.

CT ratio: secondary current is 5 A or 1 A standard; burden is expressed in VA at rated secondary current.

PT (VT) ratio error and phase error affect power measurement accuracy; class 0.2 or 0.5 is used for metering.

Energy meter: 1 kWh = 1 unit; meter constant is revolutions per kWh; disc speed is proportional to load power.

Transfer function of a first-order system: G(s) = K/(1 + τs); time constant τ gives 63.2% of final value.

PID control: proportional acts on present error, integral removes steady-state offset, derivative damps overshoot and improves stability.

Strain gauge gauge factor GF = (ΔR/R)/(ΔL/L); a Wheatstone bridge converts resistance change to voltage.

Thermocouple Seebeck effect converts temperature difference to EMF; cold-junction compensation is required.

Percentage change: new value = old value × (1 ± p/100); successive changes of a% and b% give net change a + b + ab/100 percent.

Time and work: if A does work in x days and B in y days, together they finish in xy/(x + y) days.

Speed, time, distance: D = S × T; for a train crossing a platform, total distance = train length + platform length.

Simple interest SI = PRT/100; compound interest CI = P(1 + R/100)^T − P.

Number series and coding-decoding questions: identify the constant difference, ratio, or letter-position shift before applying the rule.

Syllogism: use Venn diagrams; a conclusion is valid only if it holds in every possible diagram consistent with the premises.

Blood relations: draw a family tree with gender markers; do not assume gender from names.

Direction sense: track net displacement by resolving north-south and east-west components separately.

Average and mixtures: alligation rule gives ratio of quantities as (mean − cheaper):(dearer − mean).

Subject-verb agreement: a singular subject takes a singular verb; phrases between subject and verb do not change the number.

Active to passive: object becomes subject, verb becomes be + past participle, and the agent is introduced by 'by'.

Direct to indirect speech: present tense shifts to past, 'today' becomes 'that day', 'tomorrow' becomes 'the next day'.

Articles: 'a' before consonant sounds, 'an' before vowel sounds; 'the' for specific or unique references.

Prepositions with fixed verbs: depend on, insist on, consist of, comply with, prefer to, capable of.

Common error pairs: 'affect' (verb) vs 'effect' (noun); 'principal' (main) vs 'principle' (rule); 'its' vs 'it's'.

Reading comprehension: locate the topic sentence, distinguish stated fact from inference, and answer only from the passage.

Idioms: 'to bite the bullet' means to endure a difficult situation; 'to burn the midnight oil' means to work late.

Para jumbles: find the opening sentence with a general statement, then follow pronoun and connector links.

Grid operation: NLDC (National Load Despatch Centre) coordinates national grid operation; regional load despatch centres operate under it.

Regulatory framework: CERC sets interstate transmission tariffs; state electricity regulatory commissions set intra-state tariffs.

Key legislation: Electricity Act 2003 governs generation, transmission, distribution, and trading; the Energy Conservation Act 2001 governs efficiency standards.

Renewable targets: India targets 500 GW non-fossil capacity by 2030, with solar and wind as the largest contributors.

Transmission planning: the National Electricity Plan (Transmission) is prepared by CEA and reviewed periodically.

Grid stability standards: CEA regulations specify frequency operating range around 49.90–50.05 Hz for normal operation in India.

Power sector schemes: UDAY addressed discom financial health; Saubhagya and DDUGJY targeted household and rural electrification.

Standards bodies: BIS publishes Indian Standards; IEC and IEEE publish international electrical standards.

Safety and environment: SF6 is a potent greenhouse gas; leakage monitoring and end-of-life recovery are mandatory practices.