Mathematical Analysis of Power Loss in High-Voltage Transmission Lines Across the North West Grid

This study applies mathematical models of electrical power transmission to analyse resistive and reactive power losses in high-voltage transmission lines forming part of the North West regional grid of Nigeria, encompassing transmission corridors in Sokoto, Kebbi, Zamfara, Kano, Katsina, and Jigawa states. The Nigerian electricity transmission network suffers from significant technical losses estimated at between 7 and 12 percent of total energy transmitted, representing a substantial economic and infrastructural inefficiency in a country facing severe electricity supply deficits. The study obtains technical parameters including conductor resistance, reactance, voltage levels, and current loading data from the Transmission Company of Nigeria's North West Region and publicly available network data from the Nigerian Electricity Regulatory Commission. The long transmission line equivalent circuit model, which accounts for distributed resistance, inductance, and shunt capacitance, is applied to compute sending-end voltage, power factor, and efficiency for representative 132 kV and 330 kV transmission corridors. Phasor diagram analysis and complex power calculations are performed for peak and off-peak loading scenarios. Results identify three corridor segments with resistive losses exceeding regulatory efficiency benchmarks, attributable to ageing conductors and suboptimal conductor sizing relative to current loading levels. Reconductoring with high-temperature low-sag conductors is evaluated as a cost-effective technical intervention. Keywords: power transmission, resistive losses, high-voltage lines, electrical mathematics, North West grid