Practical Guideline to Selecting Curve Fitting Options

It is recommended to always use the default parameters of the Frequency Dependent (Phase) Model for setting curve fitting options.  

 

However, there may be occasions where it is required to change the default parameters for certain overhead line/underground cable configurations. These should be changed very carefully. A poor parameter selection may cause inaccuracies in the simulations, or sometimes instabilities due to passivity violations. The following table gives a practical guideline to selecting the proper curve fitting parameters.

 

Parameter

Typical Values

Possible consequences as a results of significant deviation from the typical values

An increase

A decrease

Curve fitting starting frequency

1 Hz

0.5 Hz

0.1 Hz

0.01 Hz

(e.g. 10 Hz)

  • Fitting may be only accurate  between 10 Hz to the upper limit

  • Possibility of unstable simulation (due to under-fitting)

(e.g. 0.01 or 0.001 Hz)

  • May improve stability of the simulation

(A very low value, e.g.  1e-4 Hz)

  • May result in unstable simulation

  • Simulation may be slow (require a higher order function for accurate fitting at low frequency)

Curve fitting end frequency

1 MHz

(e.g. 10MHz)

  • Transmission line models are only accurate and tested up to 1 MHz

  • Possibility of unstable simulation

(e.g. 10kHz)

  • Inaccurate simulation at high frequencies

  • Possibility of unstable simulation (due to inaccuracy outside the fitting range)

Total number of frequency increments

100

 (e.g. 500)

  • Increase accuracy

 

Maximum order per delay group for propagation function

20-40

When plotted as a function of frequency, the angle of the propagation function shows an oscillatory behaviour (due to the transportation delay of the transmission line). Hence a higher order approximated function may be required to obtain an accurate fitting (compared with Yc).

Maximum order of fitting for Yc

20-30

Compared with propagation function, curve-fitting of Yc is relatively easy and hence accurate fitting may be achieved less than 20 poles for many transmission line configurations.

These values may be increased based on fitting results.

Maximum fitting error for Prop. function or Yc

1%-0.1%

(e.g.  10%)

  • Decrease the accuracy of the model

  • Possibility of unstable simulations due to under-fitting

(e.g.  0.01%, 0.001%)

  • Possibility of unstable simulations due to over-fitting

 

A common issue using any phase domain model is that the possibility of unstable simulations due to passivity violations. This is mainly caused by the error introduced by the curve fitting of the transfer function. In such cases, the below suggestions may help to obtain the stable simulation.

  1. Reduce the curve fitting starting frequency  –  (e.g. 0.1, 0.01,0.001 Hz)
  2. For underground cables, select the Saad formula or Numerical Integration as earth return formula in the Ground Plane component
  3. Verify the curve fitting parameter options (see table above)
  4. Verify curve-fitting results (Log File)
  5. Enable DC correction (specially for HVDC lines) with proper shunt conductance