Transmission and Distribution
Transmission and distribution
Transmission questions usually reduce to line parameters, voltage drop, and thermal or voltage limits. Compute per-phase resistance and reactance from per-mile or per-km data, then use the sending-end voltage V_s = V_r + I(R + jX) for a short line. For a quick drop estimate, ΔV_phase ≈ I(R cosθ + X sinθ); the line-to-line drop is √3 times that. Remember that R is temperature-dependent and X depends on spacing and bundling; transposition balances mutual coupling. Longer lines need the nominal-π or long-line hyperbolic model, and Ferranti rise can make the receiving-end voltage higher than sending-end under light load. Insulation coordination, surge impedance, corona, sag, and grounding are common conceptual topics; sag increases with temperature and ice, and surge impedance Z_c = √(L/C) governs traveling-wave behavior.
Traps: using total three-phase impedance instead of per-phase, ignoring power factor, confusing line-to-line and line-to-neutral voltage, and treating a short line as lossless. For cables, capacitance is much larger than overhead, so charging current matters.
Worked example: a 5 km three-phase line has R = 0.2 Ω/km and X = 0.4 Ω/km per phase. It delivers 2 MVA at 12.47 kV and 0.9 lagging. I = 2,000,000/(√3 × 12,470) = 92.6 A; R = 1 Ω, X = 2 Ω. ΔV_phase ≈ 92.6(1 × 0.9 + 2 × 0.436) = 164 V, so ΔV_LL ≈ 284 V, or about 2.3%. Rule of thumb: keep steady-state drop within roughly 5%.