This example shows time domain and frequency domain performance of distributed parameter line model and PI section line model.
G. Sybille (Hydro-Quebec)
A 200 km line is connected on a 1 kV, 60 Hz infinite source. The line is deenergized and then reenergized after 2 cycles. The simulation is performed simultaneously with two different line models:
- Distributed parameter line
- PI section line consisting of two 100 km sections.
Currents at the sending end and voltages at the receiving end are compared for the two line models. Impedance Measurement blocks are connected at the open end of both lines in order to compare their frequency responses.
Open the Powergui block and select Steady-State Voltages and Currents to display the voltage and current phasors. Observe that the values obtained with the two models are the same.
2. Time domain comparison
Open the two scopes and start the simulation. Observe the difference in current and voltage waveforms at breaker opening and reclosing. Note the sharp edges of the distributed parameter model. These voltage and current steps which are due to travelling wave reflections at line ends are filtered by the PI model.
3. Frequency domain comparison
Open the Powergui block and select Impedance vs Frequency Measurement. A new window appears, listing the two Impedance Measurement blocks Z_Dist and Z_PI connected to your circuit. Note also that parameters are set to compute impedance in the 0:2000 Hz frequency range by steps of 2 Hz. Using the Ctrl key, select both Z_Dist and Z_PI in the upper right window. Then, click on the Display button. The two impedances are computed and displayed on the same graph.
Note that the distributed parameter line shows a succession of poles and zeros equally spaced, every 486 Hz. The first pole occurs a 243 Hz, corresponding to frequency f = 1 / (4*T), where :
T = travelling time = length*sqrt(L*C) = 200*sqrt(2.137e-3*12.37e-9) = 1.028 ms
The PI section line only shows two poles because it consists of two PI sections. Impedance comparison shows that a two-PI line gives a good approximation of the distributed line for the 0-350 Hz frequency range.