Frequency-Dependent Cable Modeling for Power-Loss and Voltage-Drop Assessment in Wind Farm Collection Networks: A Tehuantepec Case Study

Abstract

Accurate representation of frequency-dependent cable parameters is essential for evaluating power losses and series-voltage effects in medium-voltage wind-farm collection networks. This paper develops a MATLAB-based electromagnetic framework that derives frequency-dependent series-impedance (Z) and shunt-admittance (Y) matrices for underground cables, including conductor skin and proximity effects and earth-return impedance. Four earth-return formulations—Saad–Gaba–Giroux, Wedepohl series, Wedepohl, and infinite-earth—are implemented and benchmarked against RSCAD from 10 Hz to 1 MHz. The AC series parameters evaluated at 60 Hz are applied to a 7.5 MW wind farm in the Isthmus of Tehuantepec, Oaxaca, Mexico, comprising five 1.5 MW turbines connected at 13.8 kV through two radial underground circuits. The Saad–Gaba–Giroux and Wedepohl-series formulations provide the closest agreement with the RSCAD reference. At a power factor of 0.9, the simplified DC core-resistance baseline underestimates active-power losses by 34.35% in Circuit 1 and 42.83% in Circuit 2 relative to the 60 Hz AC series-resistance model. At rated turbine output and the same power factor, the accumulated AC series-voltage indicators at the farthest turbine are 0.17% and 0.38%, compared with 0.11% and 0.20% using core-only DC resistance. These indicators do not represent terminal-voltage magnitudes, which require an AC network power-flow calculation. A component-level analysis for Circuit 1 identifies the core conductor as the dominant contributor to active-power dissipation, followed by the earth-return path and metallic sheath. An annual economic evaluation yields similar project-level financial indicators for the AC and DC representations, while a parametric resistance sensitivity analysis shows decreasing profitability and longer investment recovery periods as AC cable resistance increases. The frequency sweep validates the cable-parameter formulations; their application to electromagnetic-transient simulations remains future work.