UPDA Electrical cheat sheet

Per-unit value = actual value ÷ base value; base impedance Z_base = V_base² / S_base (line-to-line kV and three-phase MVA).

For a three-phase balanced load: S = √3·V_LL·I_L, P = √3·V_LL·I_L·cos φ, Q = √3·V_LL·I_L·sin φ.

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

Complex power S = P + jQ = V·I*; total load power factor is set by the phasor sum of all P and Q, not by averaging individual power factors.

Fault level (short-circuit MVA) = √3·V_LL·I_fault; a higher fault level means lower source impedance.

Symmetrical components: positive (1), negative (2), zero (0) sequence; a single line-to-ground fault involves all three sequences in series.

Power factor correction capacitor kVAR = P·(tan φ₁ − tan φ₂), where φ₁ and φ₂ are the initial and target power-factor angles.

In per-unit, transformer turns ratio is 1:1 when bases are chosen on each side of the transformer, which removes ratio errors from calculations.

Thermal plant efficiency = (net work output) / (heat input); overall plant efficiency = electrical output / fuel energy input.

Rankine cycle efficiency is raised by higher steam pressure/temperature and by lowering condenser pressure (reducing heat rejection temperature).

Transmission line surge impedance Z_c = √(L/C); surge impedance loading SIL = V_LL² / Z_c.

Short line (<80 km): series impedance only. Medium line (80–250 km): nominal π or T model. Long line (>250 km): distributed ABCD (hyperbolic) parameters.

Skin effect increases AC resistance above DC resistance; it is significant at high frequency and in large conductors.

Ferranti effect: on a lightly loaded or open-circuit long line, receiving-end voltage rises above sending-end voltage.

Distribution feeders are typically radial; voltage drop ≈ I·(R cos φ + X sin φ) per phase for a short feeder.

Power transfer over a line P ≈ (V_S·V_R / X)·sin δ, so angle δ (not resistance) governs steady-state transfer for high-X lines.

Transformer EMF equation: E = 4.44·f·N·Φ_max (RMS); induced EMF is proportional to frequency, turns, and peak flux.

Ideal transformer: V₁/V₂ = N₁/N₂ = I₂/I₁; VA rating is the same on both sides (neglecting losses).

Synchronous speed N_s = 120·f / P (rpm), where P is the number of poles.

Induction motor slip s = (N_s − N_r)/N_s; rotor frequency f_r = s·f.

Torque of an induction motor T ∝ (rotor input power)/slip; maximum torque occurs at slip where rotor resistance equals rotor reactance.

DC machine EMF: E = (P·Φ·N·Z)/(60·A) for a generator; for a motor E is back-EMF and armature current I_a = (V − E)/R_a.

Transformer losses: copper loss ∝ I² (varies with load), core loss is approximately constant; maximum efficiency occurs when copper loss equals core loss.

Open-circuit and short-circuit tests on a transformer give core (shunt) parameters and series (copper) parameters respectively.

Single-phase full-wave rectifier (uncontrolled): average DC output V_dc = 2·V_m/π; RMS output = V_m/√2.

Controlled rectifier average output V_dc = (2·V_m/π)·cos α for a full converter with firing angle α.

Thyristor conducts only when anode is positive relative to cathode AND a gate pulse is applied; it turns off when current falls below holding current.

DC chopper output: buck V_o = D·V_in; boost V_o = V_in/(1 − D), where D is duty cycle.

Inverter output frequency and voltage are set by switching pattern; V/f control keeps air-gap flux constant in induction motor drives.

PWM inverters reduce low-order harmonics; increasing switching frequency moves harmonics higher and eases filtering.

Freewheeling (flyback) diode protects switches from inductive kickback and provides a current path during switch-off.

Variable frequency drive (VFD) energy saving follows affinity laws: flow ∝ speed, power ∝ speed³ for centrifugal pumps and fans.

Design current I_b ≤ protective device rating I_n ≤ cable current-carrying capacity I_z.

Voltage drop limit for a final circuit is commonly 3% of nominal voltage (5% for the whole installation from origin).

Cable current-carrying capacity is corrected by factors for ambient temperature, grouping, and thermal insulation.

Earth fault loop impedance must satisfy Z_s ≤ (nominal voltage) / (protective device operating current) to ensure disconnection in time.

Diversity factor = maximum demand of an installation / sum of individual maximum demands; applied to size service and feeder.

Socket outlets and lighting are typically split across separate final circuits to limit inconvenience and load per circuit.

Bathroom and wet-location zones restrict socket placement and require supplementary equipotential bonding.

RCD (residual current device) rated 30 mA is used for additional protection against electric shock in many final circuits.

Protective relay must be selective, fast, sensitive, and reliable; grading margin between upstream and downstream devices ensures selectivity.

Overcurrent relay characteristic: inverse, very inverse, and extremely inverse curves define time-versus-current response.

IDMT relay operating time t = TMS · k / (I/Is)^α − 1, where TMS is the time multiplier setting.

Differential protection compares currents entering and leaving a protected zone; it is used for transformers, generators, and busbars.

Earth resistance is measured by the fall-of-potential (three-point) method; lower earth resistance improves fault current return.

Lightning protection system consists of air termination, down conductor, and earth termination; rolling sphere and protection angle methods define the zone of protection.

Surge protective devices (SPDs) divert transient overvoltages to earth and are coordinated in Type 1, 2, and 3 stages.

Touch voltage is the potential difference a person may bridge; step voltage is the potential difference between feet on the ground.

Codes and standards are mandatory when adopted by regulation; standards become enforceable through reference in law or contract.

Standard voltage tolerances: supply voltage typically maintained within ±6% to ±10% of nominal, depending on the national code.

Conductor sizing considers ampacity, voltage drop, short-circuit withstand, and mechanical strength - all must be satisfied.

Earthing conductor cross-section is governed by the phase conductor size and the required fault-current withstand.

Classification of hazardous areas (zones 0, 1, 2 for gas; 20, 21, 22 for dust) determines the equipment protection level required.

Inspection and testing of an installation includes continuity, insulation resistance, polarity, earth loop impedance, and RCD trip tests.

Degree of protection (IP) code: first digit = solids, second digit = liquids; higher digits indicate greater protection.

Lockout/tagout (LOTO) isolates energy sources and prevents unexpected energization during maintenance.

Live working requires a permit, insulated tools, and appropriate PPE; de-energization is the default safe practice.

Arc flash hazard is characterized by incident energy (cal/cm²) and arc flash boundary; PPE category is selected from incident energy.

Approach boundaries (limited, restricted) define how close an unqualified or qualified person may come to exposed live parts.

Electric shock severity depends on current magnitude and duration; ventricular fibrillation risk rises sharply above about 30 mA for prolonged exposure.

Safety signs follow a colour code: red = prohibition/fire, yellow = warning, blue = mandatory, green = safe condition/first aid.

Environmental controls address SF6 handling (high global warming potential), oil spill containment, and disposal of lamps containing mercury.

Critical path is the longest-duration path through the network; it determines the minimum project duration and has zero float.

Earned value: CV = EV − AC; SV = EV − PV; CPI = EV/AC; SPI = EV/PV.

Float (slack) = late start − early start = late finish − early finish; activities on the critical path have zero total float.

Common contract types: lump-sum (fixed price), unit-price (re-measured), and cost-plus (cost reimbursable); risk allocation differs by type.

A variation order changes scope, time, or price and must be authorized in writing before work proceeds.

Professional ethics require competence within one's field, disclosure of conflicts of interest, and protection of public safety, health, and welfare.

A bill of quantities supports unit-price contracts; a lump-sum contract prices the whole defined scope.

Solar PV power P = G·A·η, where G is irradiance (W/m²), A is array area, and η is module efficiency.

PV module temperature coefficient: output falls as cell temperature rises; typical power coefficient is about −0.3% to −0.5% per °C.

Wind turbine power P = ½·ρ·A·v³·Cp, where ρ is air density, A is swept area, v is wind speed, and Cp is the power coefficient (Betz limit 0.593).

Energy payback and capacity factor: capacity factor = actual energy output / (rated power × hours in period).

LED lighting efficiency is expressed in lumens per watt (lm/W); higher efficacy means more light per unit electrical power.

Power factor correction and harmonic filtering reduce losses and improve efficiency in industrial installations.

Load shifting and demand-side management reduce peak demand charges without reducing total energy consumption.

Betz limit states no wind turbine can extract more than 59.3% of the kinetic energy in the wind stream.

Per-unit value = actual value ÷ base value; base impedance Z_base = V_base² / S_base (line-to-line kV and three-phase MVA).

For a three-phase balanced load: S = √3·V_LL·I_L, P = √3·V_LL·I_L·cos φ, Q = √3·V_LL·I_L·sin φ.

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

Complex power S = P + jQ = V·I*; total load power factor is set by the phasor sum of all P and Q, not by averaging individual power factors.

Fault level (short-circuit MVA) = √3·V_LL·I_fault; a higher fault level means lower source impedance.

Symmetrical components: positive (1), negative (2), zero (0) sequence; a single line-to-ground fault involves all three sequences in series.

Power factor correction capacitor kVAR = P·(tan φ₁ − tan φ₂), where φ₁ and φ₂ are the initial and target power-factor angles.

In per-unit, transformer turns ratio is 1:1 when bases are chosen on each side of the transformer, which removes ratio errors from calculations.

Thermal plant efficiency = (net work output) / (heat input); overall plant efficiency = electrical output / fuel energy input.

Rankine cycle efficiency is raised by higher steam pressure/temperature and by lowering condenser pressure (reducing heat rejection temperature).

Transmission line surge impedance Z_c = √(L/C); surge impedance loading SIL = V_LL² / Z_c.

Short line (<80 km): series impedance only. Medium line (80–250 km): nominal π or T model. Long line (>250 km): distributed ABCD (hyperbolic) parameters.

Skin effect increases AC resistance above DC resistance; it is significant at high frequency and in large conductors.

Ferranti effect: on a lightly loaded or open-circuit long line, receiving-end voltage rises above sending-end voltage.

Distribution feeders are typically radial; voltage drop ≈ I·(R cos φ + X sin φ) per phase for a short feeder.

Power transfer over a line P ≈ (V_S·V_R / X)·sin δ, so angle δ (not resistance) governs steady-state transfer for high-X lines.

Transformer EMF equation: E = 4.44·f·N·Φ_max (RMS); induced EMF is proportional to frequency, turns, and peak flux.

Ideal transformer: V₁/V₂ = N₁/N₂ = I₂/I₁; VA rating is the same on both sides (neglecting losses).

Synchronous speed N_s = 120·f / P (rpm), where P is the number of poles.

Induction motor slip s = (N_s − N_r)/N_s; rotor frequency f_r = s·f.

Torque of an induction motor T ∝ (rotor input power)/slip; maximum torque occurs at slip where rotor resistance equals rotor reactance.

DC machine EMF: E = (P·Φ·N·Z)/(60·A) for a generator; for a motor E is back-EMF and armature current I_a = (V − E)/R_a.

Transformer losses: copper loss ∝ I² (varies with load), core loss is approximately constant; maximum efficiency occurs when copper loss equals core loss.

Open-circuit and short-circuit tests on a transformer give core (shunt) parameters and series (copper) parameters respectively.

Single-phase full-wave rectifier (uncontrolled): average DC output V_dc = 2·V_m/π; RMS output = V_m/√2.

Controlled rectifier average output V_dc = (2·V_m/π)·cos α for a full converter with firing angle α.

Thyristor conducts only when anode is positive relative to cathode AND a gate pulse is applied; it turns off when current falls below holding current.

DC chopper output: buck V_o = D·V_in; boost V_o = V_in/(1 − D), where D is duty cycle.

Inverter output frequency and voltage are set by switching pattern; V/f control keeps air-gap flux constant in induction motor drives.

PWM inverters reduce low-order harmonics; increasing switching frequency moves harmonics higher and eases filtering.

Freewheeling (flyback) diode protects switches from inductive kickback and provides a current path during switch-off.

Variable frequency drive (VFD) energy saving follows affinity laws: flow ∝ speed, power ∝ speed³ for centrifugal pumps and fans.

Design current I_b ≤ protective device rating I_n ≤ cable current-carrying capacity I_z.

Voltage drop limit for a final circuit is commonly 3% of nominal voltage (5% for the whole installation from origin).

Cable current-carrying capacity is corrected by factors for ambient temperature, grouping, and thermal insulation.

Earth fault loop impedance must satisfy Z_s ≤ (nominal voltage) / (protective device operating current) to ensure disconnection in time.

Diversity factor = maximum demand of an installation / sum of individual maximum demands; applied to size service and feeder.

Socket outlets and lighting are typically split across separate final circuits to limit inconvenience and load per circuit.

Bathroom and wet-location zones restrict socket placement and require supplementary equipotential bonding.

RCD (residual current device) rated 30 mA is used for additional protection against electric shock in many final circuits.

Protective relay must be selective, fast, sensitive, and reliable; grading margin between upstream and downstream devices ensures selectivity.

Overcurrent relay characteristic: inverse, very inverse, and extremely inverse curves define time-versus-current response.

IDMT relay operating time t = TMS · k / (I/Is)^α − 1, where TMS is the time multiplier setting.

Differential protection compares currents entering and leaving a protected zone; it is used for transformers, generators, and busbars.

Earth resistance is measured by the fall-of-potential (three-point) method; lower earth resistance improves fault current return.

Lightning protection system consists of air termination, down conductor, and earth termination; rolling sphere and protection angle methods define the zone of protection.

Surge protective devices (SPDs) divert transient overvoltages to earth and are coordinated in Type 1, 2, and 3 stages.

Touch voltage is the potential difference a person may bridge; step voltage is the potential difference between feet on the ground.

Codes and standards are mandatory when adopted by regulation; standards become enforceable through reference in law or contract.

Standard voltage tolerances: supply voltage typically maintained within ±6% to ±10% of nominal, depending on the national code.

Conductor sizing considers ampacity, voltage drop, short-circuit withstand, and mechanical strength - all must be satisfied.

Earthing conductor cross-section is governed by the phase conductor size and the required fault-current withstand.

Classification of hazardous areas (zones 0, 1, 2 for gas; 20, 21, 22 for dust) determines the equipment protection level required.

Inspection and testing of an installation includes continuity, insulation resistance, polarity, earth loop impedance, and RCD trip tests.

Degree of protection (IP) code: first digit = solids, second digit = liquids; higher digits indicate greater protection.

Lockout/tagout (LOTO) isolates energy sources and prevents unexpected energization during maintenance.

Live working requires a permit, insulated tools, and appropriate PPE; de-energization is the default safe practice.

Arc flash hazard is characterized by incident energy (cal/cm²) and arc flash boundary; PPE category is selected from incident energy.

Approach boundaries (limited, restricted) define how close an unqualified or qualified person may come to exposed live parts.

Electric shock severity depends on current magnitude and duration; ventricular fibrillation risk rises sharply above about 30 mA for prolonged exposure.

Safety signs follow a colour code: red = prohibition/fire, yellow = warning, blue = mandatory, green = safe condition/first aid.

Environmental controls address SF6 handling (high global warming potential), oil spill containment, and disposal of lamps containing mercury.

Critical path is the longest-duration path through the network; it determines the minimum project duration and has zero float.

Earned value: CV = EV − AC; SV = EV − PV; CPI = EV/AC; SPI = EV/PV.

Float (slack) = late start − early start = late finish − early finish; activities on the critical path have zero total float.

Common contract types: lump-sum (fixed price), unit-price (re-measured), and cost-plus (cost reimbursable); risk allocation differs by type.

A variation order changes scope, time, or price and must be authorized in writing before work proceeds.

Professional ethics require competence within one's field, disclosure of conflicts of interest, and protection of public safety, health, and welfare.

A bill of quantities supports unit-price contracts; a lump-sum contract prices the whole defined scope.

Solar PV power P = G·A·η, where G is irradiance (W/m²), A is array area, and η is module efficiency.

PV module temperature coefficient: output falls as cell temperature rises; typical power coefficient is about −0.3% to −0.5% per °C.

Wind turbine power P = ½·ρ·A·v³·Cp, where ρ is air density, A is swept area, v is wind speed, and Cp is the power coefficient (Betz limit 0.593).

Energy payback and capacity factor: capacity factor = actual energy output / (rated power × hours in period).

LED lighting efficiency is expressed in lumens per watt (lm/W); higher efficacy means more light per unit electrical power.

Power factor correction and harmonic filtering reduce losses and improve efficiency in industrial installations.

Load shifting and demand-side management reduce peak demand charges without reducing total energy consumption.

Betz limit states no wind turbine can extract more than 59.3% of the kinetic energy in the wind stream.