Power System Blockset | ![]() ![]() |
System Start-Up and Steady-State
Notice that the system is discretized, using sample time Ts
(you should already have Ts=50e-6
defined in your workspace).
The system is programmed to start and reach a steady state. Then, a step is applied on the reference current to observe the dynamic response of the regulators.
Start the simulation and observe the signals on the rectifier and inverter scopes. The waveforms are reproduced on Figure 2-33.
Figure 2-33: Start Up of the DC System and Step Applied on the Reference Current
The reference current follows a ramp from zero to 1 p.u. (2kA) in 0.4 s. Observe that the DC current starts to build up at t=20 ms, time at which the controller and the pulse generators are deblocked.The DC current and voltages start from zero and reach steady-state in approximately 0.5 s.The rectifier controls the current and the inverter controls the voltage. Trace 1 of both rectifier and inverter scopes shows the DC line voltage (1pu=500 kV). Trace 2 shows the reference current and the measured Id current (1pu=2 kA). Once steady-state is attained, the a firing angles are 18 degrees and 142 degrees respectively on the rectifier and inverter side.
Then, at t=0.6 s a step is applied on the reference current to observe the dynamic response of the regulators.
The main equations governing the steady-state operation of the DC system are given here so that you can check the theoretical values against the simulation results.
The following expression relates the mean direct voltage Vd of a 12-pulse bridge to the direct current Id and firing angle
where Vdo is the ideal no-load direct voltage for a 6-pulse bridge
Vc is the line to line rms commutating voltage that is dependent on the AC system voltage and the transformer ratio.
Rc is the equivalent commutating resistance
Xc is the commutating reactance or transformer reactance referred to the valve side.
The following rectifier parameters were used in the simulation.
The Vc voltage must take into account the effective value of the voltage on the 500kV bus and the transformer ratio. If you look at the waveforms displayed on the V_I_Rect scope, you will find 0.96 p.u. If you open the rectifier transformer dialog box, you will find a multiplication factor of 0.91 applied on the primary nominal voltage. The voltage applied to the inverter is therefore boosted by a factor 1/0.91.
Vc =0.96* 200 kV/0.90= 213.3 kV;
Id = 2 kA
= 18º;
Xc = 0.24 p.u. based on 1200 MVA and 222.2 kV = 9.874
This theoretical voltage corresponds well with the expected rectifier voltage calculated from the inverter voltage and the voltage drop in the DC line:
The µ commutation or overlap angle can be also calculated. Its theoretical value depends on , the DC current Id and the commutation reactance Xc.
Now verify the commutation angle by plotting the currents in two valves, showing for example current extinction in valve 1 and current build up in valve 3 of one six-pulse bridge of the rectifier.
Open the rectifier subsystem. Then, open the upper bridge dialog box and the select All voltages and currents for the Measurement parameter. Now, copy the Multimeter block from the Measurements library into your case5
circuit. Double-click on the Multimeter block. A window showing all the bridge voltages and currents appears. Select the following signals
uSw1: Rectifier/Universal Bridge
iSw1 : Rectifier/Universal Bridge
iSw3 : Rectifier/Universal Bridge
The number of signals (3) is displayed in the multimeter icon. Using a Demux block, send the three multimeter output signals to a two-trace scope. (Trace 1: uSw1
Trace 2: iSw1
and iSw3
). Restart the simulation. The waveforms illustrating two cycles are shown on Figure 2-34. The measured commutation angle is 14 steps of 50µs or 15.1º of a 60 Hz period. Knowing that the resolution with a 50 µs time step is 1.1º, this angle compares reasonably well with the theoretical value.
Figure 2-34: Valve Voltage and Currents (Commutation from Valve 1 to Valve 3)
![]() | Description of the Control System | Response to a Step of Reference Current | ![]() |