SimPowerSystems    

Frequency Analysis

One particular characteristic of series-compensated systems is the existence of subsynchronous modes (poles and zeros of the system impedance below the fundamental frequency). Dangerous resonances can occur if the mechanical torsion modes of turbine/generator shafts are in the vicinity of the zeros of the system impedance. Also, high subsynchronous voltages due to impedance poles at subsynchronous frequencies will drive transformers into saturation. The transformer saturation due to subsynchronous voltages is illustrated at the end of this case study. The torque amplification on a thermal machine is illustrated in another demonstration (see the psbthermal model).

Now measure the positive-sequence impedance versus frequency seen from bus B2.

Session 2 of the Tutorial chapter already explained how the Impedance Measurement block allows you to compute the impedance of a linear system from its state-space model. However, your case1 model contains several nonlinear blocks (machine and saturation of transformers). If you connect the Impedance Measurement block to your system, all nonlinear blocks are ignored. This is correct for the transformer, but you get the impedance of the system with the machine disconnected. Before measuring the impedance, you must therefore replace the machine block with an equivalent linear block having the same impedance.

Delete the Simplified Synchronous Machine block from your case1 model and replace it with the 3-Phase Source block from the Electrical Sources library. Open the block dialog box and set the parameters as follows in order to get the same impedance value (L = 0.22 p.u./ (6 * 350 MVA) Quality factor = 15).

Save your modified model as case1Zf.

Open the Measurements library of powerlib and copy the Impedance Measurement block into your model. This block is used to perform the impedance measurement. Connect the two inputs of this block between phase A and phase B of the B2 bus. Measuring the impedance between two phases gives two times the positive-sequence impedance. Therefore you must apply a factor of 1/2 to the impedance in order to obtain the correct impedance value. Open the dialog box and set the multiplication factor to 0.5.

In the powergui select Impedance vs Frequency Measurement. A new window opens, showing your Impedance Measurement block name. Fill in the frequency range by entering 0:500. Select the linear scales to display Z magnitude vs. frequency plot. Check the Save data to workspace button and enter Zcase1 as the variable name to contain the impedance vs. frequency. Click the Display button.

When the calculation is finished, the magnitude and phase as a function of frequency are displayed in the two graphs on the window. If you look in your workspace, you should have a variable named Zcase1. It is a two-column matrix containing frequency in column 1 and complex impedance in column 2.

The impedance as a function of frequency (magnitude and phase) is shown here:

Figure 2-7: Impedance vs. Frequency Seen from Bus B2

You can observe three main modes: 9 Hz, 175 Hz, and 370 Hz. The 9 Hz mode is mainly due to a parallel resonance of the series capacitor with the shunt inductors. The 175 Hz and 370 Hz modes are due to the 600 km distributed parameter line. These three modes are likely to be excited at fault clearing.

If you zoom in on the impedance in the 60 Hz region, you can find the system's short-circuit level at bus B2. You should find a value of 58 at 60 Hz, corresponding to a three-phase short-circuit power of (735 kV)2 / 58 = 9314 MVA.


  Transient Performance for a Line Fault Transient Performance for a Fault at Bus B2