Engineer Electric Work cheat sheet

Ohm's law: V = I·R; power P = V·I = I²R = V²/R. In AC, use RMS values and include power factor: P = V·I·cosφ.

Three-phase power: P = √3·V_LL·I_L·cosφ; reactive power Q = √3·V_LL·I_L·sinφ; apparent power S = √3·V_LL·I_L.

Impedance Z = R + jX, with |Z| = √(R²+X²) and phase angle φ = arctan(X/R); inductive reactance X_L = 2πfL, capacitive X_C = 1/(2πfC).

Series circuits share current; parallel circuits share voltage. Series resistances add; parallel conductances add (1/R_T = Σ1/R_i).

Kirchhoff's laws: sum of currents at a node = 0; sum of voltages around any closed loop = 0. Use mesh or nodal analysis for multi-source networks.

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

Transformer and per-unit basics: turns ratio a = N1/N2 = V1/V2; per-unit impedance Z_pu = Z_actual/Z_base, with Z_base = V_base²/S_base.

Power factor correction: capacitor kvar needed = P·(tanφ1 − tanφ2), where φ1 and φ2 are the pre- and post-correction angles.

Thermal plant efficiency: overall efficiency = (net electrical output)/(fuel heat input). Heat rate (kJ/kWh) = 3600/η; lower heat rate means better efficiency.

Transmission line models: short lines (<80 km) use series impedance only; medium lines (80–250 km) use nominal π or T; long lines use distributed (ABCD) parameters.

Voltage drop on a feeder ≈ I·(R·cosφ + X·sinφ) per phase for a short line; keeping drop within limits drives conductor sizing and tap settings.

Surge impedance loading (SIL) = V_LL²/Z_c; a line loaded near SIL has near-flat voltage profile and minimal reactive flow.

Distribution system types: radial (single path, cheapest, least reliable), ring/loop, and interconnected networks; protection coordination depends on configuration.

Fault level at a bus ≈ S_base/Z_pu or V²/Z_thévenin; switchgear interrupting rating must exceed the calculated maximum fault current.

Renewable integration: inverter-based sources reduce system inertia, so frequency nadir and rate of change of frequency (RoCoF) become limiting constraints.

Per-unit conversion across transformers: base voltage changes by the turns ratio, so per-unit impedances remain continuous through ideal transformers.

DC machine EMF: E = (p·Φ·N·Z)/(60·a); torque T = (p·Φ·I·Z)/(2π·a). Shunt, series, and compound fields give different speed-load characteristics.

Induction motor slip s = (n_s − n_r)/n_s, with synchronous speed n_s = 120f/p; rotor frequency = s·f. Slip rises with load up to breakdown torque.

Starting methods for induction motors: direct-on-line, star-delta (reduces starting current and torque to one-third), autotransformer, soft starter, and VFD.

Synchronous machine: EMF per phase E = 4.44·f·Φ·T·k_w; the machine can supply or absorb reactive power by adjusting field excitation.

Transformer losses: core (iron) loss is constant with load and frequency; copper loss varies with I². Maximum efficiency occurs when copper loss equals core loss.

Transformer voltage regulation depends on per-unit impedance and load power factor; leading power factor can produce negative regulation (voltage rise).

Motor protection: overload relays protect against sustained overcurrent; short-circuit protection is provided by fuses or circuit breakers; thermal protection uses embedded sensors.

Generator grounding: solid, low-resistance, and high-resistance grounding trade off fault current magnitude against transient overvoltage risk.

Protection zones must overlap so no equipment is unprotected; backup protection covers failure of primary relays or breakers with a time delay.

Overcurrent coordination: time-current curves are graded so downstream devices trip first; the coordination time interval (CTI) is typically 0.2–0.4 s.

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

Distance relays use impedance measurement (Z = V/I) with mho, quadrilateral, or offset characteristics; zones are set as percentages of line impedance.

Symmetrical components: positive, negative, and zero sequence networks model unbalanced faults; zero-sequence current requires a ground path.

Instrument transformers: CTs step current down (e.g., 1000/5 A), VTs step voltage down; burden and accuracy class determine measurement and protection performance.

Stability: the equal-area criterion and swing equation describe transient stability; critical clearing time is the maximum fault duration before loss of synchronism.

SCADA and control: RTUs report to a master station; automatic generation control (AGC) adjusts setpoints to hold frequency and interchange schedules.

Design current I_b ≤ protective device rating I_n ≤ cable current-carrying capacity I_z; the device must also protect the cable against overload and fault current.

Voltage drop limits: commonly 3% for lighting and 5% for other loads from the origin of the installation; verify with mV/A/m tables or impedance calculations.

Cable sizing factors: ambient temperature, grouping, thermal insulation, and installation method all derate tabulated current capacity.

Earthing and bonding: protective conductors must withstand prospective fault current for the disconnection time; verify with the adiabatic equation S = √(I²t)/k.

Protection against electric shock: automatic disconnection of supply requires Z_s ≤ U_0/I_a, where I_a is the current causing disconnection within the required time.

RCDs: 30 mA for additional protection in socket circuits; selectivity requires upstream RCD time delay or a higher rated residual current.

Cable tray, conduit fill, and bending radius: conduit fill typically limited to 40% for three or more conductors; minimum bending radius depends on cable type.

Load balancing across phases reduces neutral current and voltage unbalance; keep phase imbalance within limits (commonly 2–3% voltage unbalance).

IEC 60364 covers low-voltage electrical installations; IEC 61439 covers low-voltage switchgear and controlgear assemblies; IEC 60909 covers short-circuit current calculation.

IEEE C2 (NESC) governs supply conductors and communication lines; NFPA 70 (NEC) governs premises wiring in the United States; IEC and NEC differ in terminology and rules.

Equipment certification: CE marking indicates conformity with EU directives; UL listing and IECEE CB certificates are common evidence of compliance in other markets.

Arc flash standards: NFPA 70E and IEEE 1584 cover arc flash risk assessment, incident energy calculation, and PPE selection.

Hazardous area classification: IEC 60079 zones (0, 1, 2 for gas; 20, 21, 22 for dust) determine equipment protection level (Ex ia, Ex d, Ex e).

Earthing system types per IEC 60364: TN-S, TN-C, TN-C-S, TT, and IT; each determines protective device requirements and RCD use.

Commissioning and documentation: as-built drawings, test certificates, protection settings, and operation and maintenance manuals are required deliverables.

Lockout/tagout (LOTO): isolate, lock, tag, verify absence of voltage with a tested instrument, and apply temporary protective grounds before work on de-energized equipment.

Arc flash: incident energy depends on fault current, clearing time, working distance, and electrode configuration; PPE category is selected from calculated incident energy.

Approach boundaries: limited, restricted, and arc flash boundaries define unqualified and qualified person access; shock hazard depends on voltage and distance.

Electrical safety program elements: risk assessment, job briefing, energized work permit, PPE, insulated tools, and qualified-person training records.

Energy management: ISO 50001 provides a framework for energy performance; energy baseline and energy performance indicators (EnPIs) track improvement.

Energy efficiency measures: power factor correction, high-efficiency motors (IE3/IE4), VFDs on variable-torque loads, LED lighting, and transformer loss evaluation.

Environmental compliance: SF6 is a potent greenhouse gas (GWP ~23,500); handling, recovery, and leak reporting are regulated under the Kyoto Protocol and EU F-gas rules.

Environmental impact assessment (EIA) and permits are typically required before constructing generation or transmission projects; monitoring and reporting continue during operation.

Project management: scope, schedule, cost, quality, risk, and stakeholder management are integrated through a project management plan and change control.

Earned value: EV = % complete × BAC; CV = EV − AC; SV = EV − PV; CPI = EV/AC; SPI = EV/PV. CPI < 1 or SPI < 1 indicates overrun or delay.

Critical path method: the critical path is the longest path through the network and has zero total float; float = LS − ES = LF − EF.

Risk management: identify, analyze (probability × impact), plan responses (avoid, mitigate, transfer, accept), and monitor throughout the project lifecycle.

Engineering ethics: hold paramount public safety, health, and welfare; practice only within competence; disclose conflicts of interest; maintain confidentiality; report unethical conduct.

Professional responsibility: sign and seal only work you prepared or directly supervised; maintain records; avoid misrepresentation of qualifications and results.

Contract types: lump-sum (fixed price), unit-price, cost-plus, and time-and-materials; each allocates risk differently between owner and contractor.

Quality management: inspection and test plans (ITPs), hold points, non-conformance reports (NCRs), and corrective actions close the loop on quality.

Ohm's law: V = I·R; power P = V·I = I²R = V²/R. In AC, use RMS values and include power factor: P = V·I·cosφ.

Three-phase power: P = √3·V_LL·I_L·cosφ; reactive power Q = √3·V_LL·I_L·sinφ; apparent power S = √3·V_LL·I_L.

Impedance Z = R + jX, with |Z| = √(R²+X²) and phase angle φ = arctan(X/R); inductive reactance X_L = 2πfL, capacitive X_C = 1/(2πfC).

Series circuits share current; parallel circuits share voltage. Series resistances add; parallel conductances add (1/R_T = Σ1/R_i).

Kirchhoff's laws: sum of currents at a node = 0; sum of voltages around any closed loop = 0. Use mesh or nodal analysis for multi-source networks.

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

Transformer and per-unit basics: turns ratio a = N1/N2 = V1/V2; per-unit impedance Z_pu = Z_actual/Z_base, with Z_base = V_base²/S_base.

Power factor correction: capacitor kvar needed = P·(tanφ1 − tanφ2), where φ1 and φ2 are the pre- and post-correction angles.

Thermal plant efficiency: overall efficiency = (net electrical output)/(fuel heat input). Heat rate (kJ/kWh) = 3600/η; lower heat rate means better efficiency.

Transmission line models: short lines (<80 km) use series impedance only; medium lines (80–250 km) use nominal π or T; long lines use distributed (ABCD) parameters.

Voltage drop on a feeder ≈ I·(R·cosφ + X·sinφ) per phase for a short line; keeping drop within limits drives conductor sizing and tap settings.

Surge impedance loading (SIL) = V_LL²/Z_c; a line loaded near SIL has near-flat voltage profile and minimal reactive flow.

Distribution system types: radial (single path, cheapest, least reliable), ring/loop, and interconnected networks; protection coordination depends on configuration.

Fault level at a bus ≈ S_base/Z_pu or V²/Z_thévenin; switchgear interrupting rating must exceed the calculated maximum fault current.

Renewable integration: inverter-based sources reduce system inertia, so frequency nadir and rate of change of frequency (RoCoF) become limiting constraints.

Per-unit conversion across transformers: base voltage changes by the turns ratio, so per-unit impedances remain continuous through ideal transformers.

DC machine EMF: E = (p·Φ·N·Z)/(60·a); torque T = (p·Φ·I·Z)/(2π·a). Shunt, series, and compound fields give different speed-load characteristics.

Induction motor slip s = (n_s − n_r)/n_s, with synchronous speed n_s = 120f/p; rotor frequency = s·f. Slip rises with load up to breakdown torque.

Starting methods for induction motors: direct-on-line, star-delta (reduces starting current and torque to one-third), autotransformer, soft starter, and VFD.

Synchronous machine: EMF per phase E = 4.44·f·Φ·T·k_w; the machine can supply or absorb reactive power by adjusting field excitation.

Transformer losses: core (iron) loss is constant with load and frequency; copper loss varies with I². Maximum efficiency occurs when copper loss equals core loss.

Transformer voltage regulation depends on per-unit impedance and load power factor; leading power factor can produce negative regulation (voltage rise).

Motor protection: overload relays protect against sustained overcurrent; short-circuit protection is provided by fuses or circuit breakers; thermal protection uses embedded sensors.

Generator grounding: solid, low-resistance, and high-resistance grounding trade off fault current magnitude against transient overvoltage risk.

Protection zones must overlap so no equipment is unprotected; backup protection covers failure of primary relays or breakers with a time delay.

Overcurrent coordination: time-current curves are graded so downstream devices trip first; the coordination time interval (CTI) is typically 0.2–0.4 s.

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

Distance relays use impedance measurement (Z = V/I) with mho, quadrilateral, or offset characteristics; zones are set as percentages of line impedance.

Symmetrical components: positive, negative, and zero sequence networks model unbalanced faults; zero-sequence current requires a ground path.

Instrument transformers: CTs step current down (e.g., 1000/5 A), VTs step voltage down; burden and accuracy class determine measurement and protection performance.

Stability: the equal-area criterion and swing equation describe transient stability; critical clearing time is the maximum fault duration before loss of synchronism.

SCADA and control: RTUs report to a master station; automatic generation control (AGC) adjusts setpoints to hold frequency and interchange schedules.

Design current I_b ≤ protective device rating I_n ≤ cable current-carrying capacity I_z; the device must also protect the cable against overload and fault current.

Voltage drop limits: commonly 3% for lighting and 5% for other loads from the origin of the installation; verify with mV/A/m tables or impedance calculations.

Cable sizing factors: ambient temperature, grouping, thermal insulation, and installation method all derate tabulated current capacity.

Earthing and bonding: protective conductors must withstand prospective fault current for the disconnection time; verify with the adiabatic equation S = √(I²t)/k.

Protection against electric shock: automatic disconnection of supply requires Z_s ≤ U_0/I_a, where I_a is the current causing disconnection within the required time.

RCDs: 30 mA for additional protection in socket circuits; selectivity requires upstream RCD time delay or a higher rated residual current.

Cable tray, conduit fill, and bending radius: conduit fill typically limited to 40% for three or more conductors; minimum bending radius depends on cable type.

Load balancing across phases reduces neutral current and voltage unbalance; keep phase imbalance within limits (commonly 2–3% voltage unbalance).

IEC 60364 covers low-voltage electrical installations; IEC 61439 covers low-voltage switchgear and controlgear assemblies; IEC 60909 covers short-circuit current calculation.

IEEE C2 (NESC) governs supply conductors and communication lines; NFPA 70 (NEC) governs premises wiring in the United States; IEC and NEC differ in terminology and rules.

Equipment certification: CE marking indicates conformity with EU directives; UL listing and IECEE CB certificates are common evidence of compliance in other markets.

Arc flash standards: NFPA 70E and IEEE 1584 cover arc flash risk assessment, incident energy calculation, and PPE selection.

Hazardous area classification: IEC 60079 zones (0, 1, 2 for gas; 20, 21, 22 for dust) determine equipment protection level (Ex ia, Ex d, Ex e).

Earthing system types per IEC 60364: TN-S, TN-C, TN-C-S, TT, and IT; each determines protective device requirements and RCD use.

Commissioning and documentation: as-built drawings, test certificates, protection settings, and operation and maintenance manuals are required deliverables.

Lockout/tagout (LOTO): isolate, lock, tag, verify absence of voltage with a tested instrument, and apply temporary protective grounds before work on de-energized equipment.

Arc flash: incident energy depends on fault current, clearing time, working distance, and electrode configuration; PPE category is selected from calculated incident energy.

Approach boundaries: limited, restricted, and arc flash boundaries define unqualified and qualified person access; shock hazard depends on voltage and distance.

Electrical safety program elements: risk assessment, job briefing, energized work permit, PPE, insulated tools, and qualified-person training records.

Energy management: ISO 50001 provides a framework for energy performance; energy baseline and energy performance indicators (EnPIs) track improvement.

Energy efficiency measures: power factor correction, high-efficiency motors (IE3/IE4), VFDs on variable-torque loads, LED lighting, and transformer loss evaluation.

Environmental compliance: SF6 is a potent greenhouse gas (GWP ~23,500); handling, recovery, and leak reporting are regulated under the Kyoto Protocol and EU F-gas rules.

Environmental impact assessment (EIA) and permits are typically required before constructing generation or transmission projects; monitoring and reporting continue during operation.

Project management: scope, schedule, cost, quality, risk, and stakeholder management are integrated through a project management plan and change control.

Earned value: EV = % complete × BAC; CV = EV − AC; SV = EV − PV; CPI = EV/AC; SPI = EV/PV. CPI < 1 or SPI < 1 indicates overrun or delay.

Critical path method: the critical path is the longest path through the network and has zero total float; float = LS − ES = LF − EF.

Risk management: identify, analyze (probability × impact), plan responses (avoid, mitigate, transfer, accept), and monitor throughout the project lifecycle.

Engineering ethics: hold paramount public safety, health, and welfare; practice only within competence; disclose conflicts of interest; maintain confidentiality; report unethical conduct.

Professional responsibility: sign and seal only work you prepared or directly supervised; maintain records; avoid misrepresentation of qualifications and results.

Contract types: lump-sum (fixed price), unit-price, cost-plus, and time-and-materials; each allocates risk differently between owner and contractor.

Quality management: inspection and test plans (ITPs), hold points, non-conformance reports (NCRs), and corrective actions close the loop on quality.