Curve Fitting Starting and End Frequencies

The Frequency Dependent (Phase) Model utilizes curve fitting to approximate the impedance and admittance (calculated by the

Transmission Line and Cable Constants program) with a Nth order approximation. These calculations are performed over a frequency range (defined by the Curve Fitting Starting Frequency and Curve Fitting End Frequency parameters).

Starting Frequency

The selection of the Curve Fitting Starting Frequency will affect the Shunt Conductance (G) of the line as it will effectively limit the DC surge impedance. This occurs because the solution at the minimum frequency is used for all frequencies from DC to the minimum. Since the surge impedance at low frequencies or DC is , and this is equated to the value at the Curve Fitting Starting Frequency (say 0.5 Hz), an effective G will result (based on the surge impedance at 0.5 Hz and the DC resistance). This effective G will often be much larger than the Shunt Conductance G entered in the Overhead Line Tower. If the starting frequency is too high, then the effective G can result in an effective real resistance to ground at each conductor terminal. When used for DC transmission lines, if the starting frequency is too high, then the effective G can result in a loss of DC current between the rectifier and inverter ends of the DC link.

For modeling of AC lines under open-circuit conditions, the shunt conductance (G) will also affect how long it takes for the trapped charge on the line to discharge.

End Frequency

The Curve Fitting End Frequency can usually be left at 1 MHz. The time step used in the simulation (say 50 ms) will place an upper limit on the frequencies which can be represented in any simulation (i.e. the Nyquist Criteria), so the line/cable model will truncate any elements of the RLC curve fitted approximations, which are more then 1 decade above the Nyquist Criteria (to

make the model run faster).

For very complex line/cable geometries (often when you have more than 6 conductors), the frequency range must sometimes be reduced (usually by reducing the upper frequency limit). This is because the line constants solves the equations for impedance and admittance of the line (to generate the input waveforms for the curve fitting) at approximately 100 different

frequencies (spaced evenly on a LOG scale over the frequency range). For complex geometries, the impedance and admittance waveforms can change rapidly within this frequency range, which can result in inaccurate curve fitting (identified in the Log file). By narrowing the frequency range of the curve fitting, more impedance/admittance calculations are available to

the curve fitting in the critical non-linear region, so a better overall accuracy can be obtained.