This example shows the use of three-level converters and zig-zag phase-shifting transformers in a 48-pulse square-wave GTO converter.
P. Giroux and G. Sybille (Hydro-Quebec)
In this example, ideal switches and zig-zag phase shifting transformers are used to build a GTO-type 100 MVA, 138 kV voltage source inverter. This type of converter is used in high-power (up to 200 MVA) Flexible AC Transmission Systems (FACTS) which are used to control power flow on transmission grids. It can be used, for example, to build a model of shunt or series static compensator (STATCOM or SSSC) or, using two such converters, a combination of shunt and series devices known as Unified Power Flow Controller (UPFC).
The inverter described in this example is a harmonic neutralized, 48-pulse GTO converter described in reference. It consists of four 3-phase, 3-level inverters and four phase-shifting transformers. Open the "48-pulse inverter" subsystem. Notice that the DC bus (Vdc = +/-9650 V) is connected to the four 3-phase inverters.The four voltages generated by the inverters are applied to secondary windings of four zig-zag phase-shifting transformers connected in Wye (Y) or Delta (D). The four transformer primary windings are connected in series and the converter pulse patterns are phase shifted so that the four voltage fundamental components sum in phase on the primary side.
Each 3-level inverter generates three square-wave voltages which can be +Vdc, 0, -Vdc. The duration of the +Vdc or -Vdc level (Sigma) can be adjusted between 0 and 180 degrees from the Sigma input of the Firing Pulse Generator block. Each inverter uses a Three-Level Bridge block where the specified power electronic devices are Ideal Switches. In this model, each leg of the inverter uses 3 ideal switches to obtain the 3 voltage levels (+Vdc, 0, - Vdc). This simple model simulates the behavior of a physical inverter where each leg consists of 4 GTOs, 4 antiparallel diodes and 2 neutral clamping diodes. Despite this simplified switch arrangement, the model still requires 4 pulses per arm as in the physical model. The pulse pattern sent to each leg of a 3-phase inverter is described inside the Firing Pulse Generator.
You can also select GTO/Diodes pairs instead of Ideal Switches as power electronic devices. It would allow you to specify forward voltage drops for GTOs and diodes and to observe currents flowing in GTOs and diodes by means of the Multimeter block.
The phase shifts produced by the secondary delta connections (-30 degrees) and by the primary zig-zag connections (+7.5 degrees for transformers 1Y and 1D, and -7.5 degrees for transformers 2Y and 2D) allows to neutralize harmonics up to 45th harmonic, as explained below:
The 30-degree phase-shift between the Y and D secondaries cancels harmonics 5+12n (5, 17, 29, 41, ...) and 7+12n (7, 19, 31, 43, ...). In addition, the 15-degree phase shift between the two groups of transformers (1Y and 1D leading by 7.5 degrees, 2Y and 2D lagging by +7.5 degrees) allows cancellation of harmonics 11+24n (11, 35, ...) and 13+24n (13, 37, ...). Considering that all the 3n harmonics are not transmitted by the Y and D secondaries, the first harmonics which are not cancelled by the transformers are 23rd, 25th, 47th and 49th. By choosing an appropriate conduction angle for the 3-level inverters (sigma = 180 - 7.5 = 172.5 degrees), the 23rd and 25th can be minimized. The first significant harmonics are therefore the 47th and 49th. This type of inverter generates an almost sinusoidal waveform consisting of 48-steps.
The inverter is operated in open loop at constant DC voltage, therefore, the voltage angle (alpha) which is normally kept close to zero is not used. You can look at the STATCOM (Detailed Model) example that shows the operation of a 48-pulse GTO STATCOM in closed-loop.
Initially, the inverter operates at no load. Then, at t = 0.025 s, a 100 MVA resistive load is connected at the 138-kV terminals.
Run the simulation and observe the following waveforms on the Scope block:
Voltages generated by the inverter (trace 1), load currents (trace 2), phase-neutral voltage and phase-phase voltage of one of the four inverters (1Y) superimposed on trace 3. When the inverter is operating at no load, you can observe the three 48-step voltage waveform. When the load is switched on the voltage becomes smoother because harmonics are filtered by the transformer leakage reactances.
Once the simulation is completed, open the Powergui and select "FFT Analysis" to display the 0-4000 Hz frequency spectrum of signals saved in the two "psb48pulse_str" structure. Select signal labeled 'Vabc (pu)'. The FFT will be performed on a 1-cycle window of phase A voltage starting at t = 0.025-1/60 s (inverter operating at no load). Click on Display and observe the frequency spectrum.
The fundamental component of Voltage (in pu) as well as THD are displayed above the spectrum window. Notice that the first significant harmonics are 47th and 49th (approx. 2%). Notice also that 23rd and 25th are reduced below 0.3%. In order to appreciate the efficiency of harmonic neutralization, you can also observe the frequency spectrum of phase-phase voltage generated by each individual inverter. Select input labeled "Van Vab Converter 1Y" and signal number 2 and click on Display. Observe that THD in the 0 - 4000 Hz frequency range is 25%.
You can also run another simulation by specifying different values of sigma at the input of the pulse generator. You can verify that, in order to cancel a particular harmonic n in the phase-phase voltage of each individual converter, the Sigma value (in degrees) is given by:
Verify also that choosing Sigma = 180 degrees is equivalent to using 2-level converters and that the voltage waveform is degraded to 24 pulses.
Narain G. Hingorani and Laszlo Gyuyi, "Understanding FACTS", IEEE® Press, 2000