# Three-Phase Harmonic Filters

This example shows three-phase harmonic filters in HVDC installations.

### Description

In HVDC installations, AC harmonic shunt filters are used to:

1) reduce harmonic voltages and currents in the power system,

2) supply the reactive power consumed by the converter. To illustrate these concepts, a 1000-MW (500 kV, 2kA) HVDC rectifier is simulated.

The HVDC rectifier is built up from two 6-pulse thyristor bridges connected in series. The converter is connected to the system with a 1200-MVA Three-Phase transformer (three windings). A 1000-MW resistive load is connected to the DC side through a 0.5 H smoothing reactor. The filters set is made of the following four components of the powerlib/Elements library:

- one capacitor banks (C1) of 150 Mvar modeled by a "Three-Phase Series RLC Load",

- three filters modeled using the "Three-Phase Harmonic Filter"

(1) one C-type high-pass filter tuned to the 3rd (F1) of 150 Mvar

(2) one double-tuned filter 11/13 th (F2) of 150 Mvar

(3) one high-pass filter tuned to the 24th (F3) of 150 Mvar

The total Mvar rating of the filters set is then 600 Mvar. A three-phase circuit breaker (Brk1) is used to connect the filters set on the AC bus.

### Simulation

Time-domain simulation

Run a first simulation with an alpha firing angle of 19 degrees. You should get a DC voltage level of 500 kV. Now, look inside Scope1. Compare the currents flowing into Bus B1 (Iabc_B1, axis 2) with those flowing into Bus B2 (Iabc_B2, axis 3). You can see that the harmonic filters almost eliminate the harmonics generated by the converter. If you use the FFT tool of the powergui, you will find that the harmonic filters reduce the THD of the current injected in the system from 9% to 0.7%. You can also perform other simulations with various values of alpha. Notice the impact on the DC level and on the generated harmonics.

Frequency response

You will now plot the impedance vs frequency of the harmonic filters:

1) Disconnect the filters from the AC bus. To do so, double-click on the breaker Brk1, select 'open' for initial status of breakers and click on the OK button.

2) Open the powergui and select "Impedance vs Frequency Measurement".

3) Click on the Display/Save button. Specialized Power Systems will compute and display the filters frequency response.

4) Double-click on the block "Show filters impedance vs frequency". A second figure, showing the pre-computed filters frequency response will be displayed. The impedance data of the two figures should be identical.

5) If you zoom the figure (using the "Tool" menu), you should find an impedance of 417 ohms capacitive (-90deg.) at 60 Hz. This value confirms that the total reactive power of the filters at 60 Hz is: Qc =V^2/Xc = 500e3^2/417 = 600 Mvar.