Electrical Cables Cheatsheet

Cheatsheet Content

1. Basic Electrical Quantities & Ohm's Law Voltage (V): Electrical potential difference, measured in Volts (V). Current (I): Flow of electric charge, measured in Amperes (A). Resistance (R): Opposition to current flow, measured in Ohms ($\Omega$). Power (P): Rate at which electrical energy is transferred, measured in Watts (W). Ohm's Law: $V = I \times R$ Power Formulas: $P = V \times I$ $P = I^2 \times R$ $P = \frac{V^2}{R}$ 2. Cable Properties & Characteristics Conductor Material: Copper (Cu): High conductivity, common. Aluminum (Al): Lighter, cheaper, but lower conductivity and higher thermal expansion. Insulation Material: Protects against short circuits, determines voltage rating. PVC (Polyvinyl Chloride) XLPE (Cross-linked Polyethylene) EPR (Ethylene Propylene Rubber) Conductor Size: Measured in AWG (American Wire Gauge) or mm$^2$. Smaller AWG number = larger conductor diameter. Number of Conductors: Single-core, multi-core. Shielding: Reduces electromagnetic interference (EMI). Armoring: Provides mechanical protection. 3. Conductor Resistance Resistance Formula: $R = \rho \frac{L}{A}$ $R$: Resistance ($\Omega$) $\rho$: Resistivity of conductor material ($\Omega \cdot m$) $L$: Length of conductor (m) $A$: Cross-sectional area of conductor (m$^2$) Typical Resistivity at $20^\circ C$: Copper: $\approx 1.68 \times 10^{-8} \Omega \cdot m$ Aluminum: $\approx 2.82 \times 10^{-8} \Omega \cdot m$ Temperature Effect on Resistance: $R_T = R_{ref} [1 + \alpha (T - T_{ref})]$ $R_T$: Resistance at temperature $T$ $R_{ref}$: Resistance at reference temperature $T_{ref}$ $\alpha$: Temperature coefficient of resistance (e.g., $0.00393 /^\circ C$ for Cu) 4. Current Carrying Capacity (Ampacity) Definition: Maximum current a conductor can carry continuously without exceeding its temperature rating. Factors Affecting Ampacity: Conductor material and size Insulation type (temperature rating) Ambient temperature Number of current-carrying conductors in a conduit/cable Installation method (e.g., in air, in conduit, buried) Grouping of cables Derating Factors: Ampacity must be derated for conditions other than standard test conditions (e.g., high ambient temperature, multiple cables in a conduit). 5. Voltage Drop Calculation Importance: Excessive voltage drop can lead to poor equipment performance, overheating, and energy loss. DC Voltage Drop: $\Delta V = I \times (2RL)$ $I$: Current (A) $R$: Resistance per unit length of conductor ($\Omega/m$) $L$: One-way length of cable (m) AC Voltage Drop (Single-Phase): $\Delta V = 2 \times I \times (R \cos\phi + X \sin\phi) \times L$ $R$: Resistance per unit length ($\Omega/m$) $X$: Reactance per unit length ($\Omega/m$) $\cos\phi$: Power factor AC Voltage Drop (Three-Phase): $\Delta V = \sqrt{3} \times I \times (R \cos\phi + X \sin\phi) \times L$ Percentage Voltage Drop: $\%VD = \frac{\Delta V}{V_{source}} \times 100\%$ Recommended Limits: Often 3% for feeders and 5% total for feeders and branch circuits (refer to local codes). 6. Short Circuit Current Calculations Purpose: Determine maximum fault current to size protective devices (circuit breakers, fuses) and cable withstand ratings. Simple Calculation (approximated): $I_{sc} = \frac{V_{source}}{Z_{total}}$ $Z_{total}$: Total impedance from source to fault, including transformer, cable, and busbar impedances. Cable Withstand Rating: Cables must be able to withstand the thermal and mechanical stresses of short circuit current for a specified duration. Adiabatic Short Circuit Temperature Rise: $\frac{I^2 t}{A^2} = K \ln \left( \frac{T_f + 234.5}{T_i + 234.5} \right)$ (for copper) $I$: Short circuit current (A) $t$: Duration of short circuit (s) $A$: Conductor cross-sectional area (mm$^2$) $K$: Material constant (e.g., 170 for copper, 111 for aluminum) $T_i$: Initial conductor temperature ($^\circ C$) $T_f$: Final conductor temperature ($^\circ C$) 7. Inductance and Capacitance of Cables Inductance (L): Loop Inductance (single-phase): $L = \frac{\mu_0}{\pi} \left( \frac{1}{4} + \ln \frac{D}{r} \right)$ H/m $D$: Spacing between conductor centers $r$: Conductor radius Significant for AC circuits, especially long runs, contributing to voltage drop. Capacitance (C): Single-core cable with shield: $C = \frac{2 \pi \epsilon}{\ln(R/r)}$ F/m $\epsilon$: Permittivity of insulation $R$: Radius of insulation shield $r$: Radius of conductor Important for high voltage cables and transient analysis. 8. Cable Sizing Considerations Current Requirement: Determine maximum continuous load current. Ampacity Selection: Choose cable size based on current and installation conditions (refer to tables/standards like NEC, IEC). Apply derating factors. Voltage Drop Check: Verify voltage drop is within acceptable limits for the chosen cable size. If not, select a larger cable. Short Circuit Withstand: Ensure the cable can withstand the calculated short circuit current for the duration of fault clearance. Mechanical Strength: Ensure cable can withstand installation stresses. Cost: Balance technical requirements with economic considerations. 9. Key Standards & Codes NEC (National Electrical Code): USA standard for safe installation of electrical wiring and equipment. IEC (International Electrotechnical Commission): International standards for all electrical technologies. BS (British Standards): UK national standards body. Always consult local electrical codes and standards for specific requirements.