Introducing Power Electronics

Introduction

In this section you

• Learn how to use power electronics components

• Learn how to use transformers

• Change initial conditions of a circuit

Simscape™ Electrical™ Specialized Power Systems software is designed to simulate power electronic devices. This section uses a simple circuit based on thyristors as the main example.

Consider the circuit shown below. It represents one phase of a static var compensator (SVC) used on a 735 kV transmission network. On the secondary of the 735 kV/16 kV transformer, two variable susceptance branches are connected in parallel: one thyristor-controlled reactor (TCR) branch, in blue, and one thyristor-switched capacitor (TSC) branch, in red.

One Phase of a TCR/TSC Static Var Compensator

The TCR and TSC branches are both controlled by a valve consisting of two thyristor strings connected in antiparallel. An RC snubber circuit is connected across each valve. The TSC branch is switched on/off, thus providing discrete step variation of the SVC capacitive current. The TCR branch is phase controlled to obtain a continuous variation of the net SVC reactive current.

Simulation of the TCR Branch

1. Enter power_new at the command line to open a new model. Save it as power_TCRTSC.

2. Add a Thyristor block from the Simscape > Electrical > Specialized Power Systems > Power Electronics library to the model.

3. Open the Thyristor Block Parameters window and set the parameters as follows:

   Ron	1e-3
   Lon	0
   Vf	14*0.8
   Rs	500
   Cs	0.15e-6

   Notice that the snubber circuit is integral to the Thyristor dialog box.

4. Rename this block TCR 1 and duplicate it.

5. Connect this new thyristor TCR 2 in antiparallel with TCR 1, as shown in One Phase of a TCR/TSC Static Var Compensator.

   As the snubber circuit has already been specified with TCR 1, the snubber of TCR 2 must be eliminated.

6. Open the TCR 2 dialog box and set the snubber parameters to

   Rs	Inf
   Cs	0

   Notice that the snubber disappears on the block icon.

7. Add a Linear Transformer block from the Simscape > Electrical > Specialized Power Systems > Passives library. Set its nominal power, frequency, and winding parameters (winding 1 = primary; winding 2 = secondary) as shown in One Phase of a TCR/TSC Static Var Compensator.

   The Units parameter allows you to specify the resistance R and leakage inductance L of each winding as well as the magnetizing branch Rm/Lm, either in SI units (ohms, henries) or in per units (pu). Keep the default pu setting to specify directly R and L in per unit quantities. As there is no tertiary winding, deselect Three windings transformer. Winding 3 disappears on the TrA block.

   Finally, set the magnetizing branch parameters Rm and Xm at [500, 500]. These values correspond to 0.2% resistive and inductive currents. For more information on the per unit (pu) system, see Per-Unit System of Units.

8. Add a voltage source, Ground block, and two Series RLC Branch blocks and set the parameters as shown in the One Phase of a TCR/TSC Static Var Compensator figure.

9. Add a Current Measurement block from the Simscape > Electrical > Specialized Power Systems > Sensors and Measurements library to measure the primary current.

10. Notice that the Thyristor blocks have an output identified by the letter m. This output returns a Simulink^® vectorized signal containing the thyristor current (Iak) and voltage (Vak). These outputs are connected to terminators blocks. Select the signal line connected at the m output of the TCR 1 block and the signal connected at the i output of the i prim block. From the Simulation Data Inspector, select Log Selected Signals.

11. Copy two Pulse Generator blocks into your system, name them Pulse1 and Pulse2, and connect them to the gates of the thyristor blocks.

12. Now you have to define the timing pulses of the two thyristors. At every cycle a pulse has to be sent to each thyristor α degrees after the zero crossing of the thyristor commutation voltage. Set the Pulse1 and Pulse2 block parameters as follows:

    Amplitude	1
    Period	1/60 s
    Pulse width (% of period)	1% (3.6 degrees pulses)
    Phase Delay	1/60+T for Pulse1 1/60+1/120+T for Pulse2

13. The pulses sent to TCR 2 are delayed by 180 degrees with respect to pulses sent to TCR 1. The delay T is used to specify the firing angle α. To get a 120 degree firing angle, specify T in the workspace by entering

    T = 1/60/3;
    

14. Set the stop time to 0.1, then start the simulation. The results can be observed in the Simulation Data Inspector, as shown in the figure.

    TCR Simulation Results

    

Simulation of the TSC Branch

You can now create the TSC branch.

1. Duplicate the TCR branch (shown in blue), rename the blocks, and specify resistance and inductance value as shown in the One Phase of a TCR/TSC Static Var Compensator figure.

2. Connect a capacitor of 308e-6 Farad in series with the TSC 1 and TSC 2 valve.

3. Connect a Voltage Measurement block across the capacitor. Connect the output of the block to a terminator block. Select the signal and stream the selected signal to the Simulation Data Inspector.

4. Contrary to the TCR branch, which was fired by a synchronous pulse generator, a continuous firing signal is now applied to the two thyristors. Delete the two pulse generators. Add a Step block and connect its output at both gates of TSC 1 and TSC 2. Set its step time at 1/60/4 (energizing at the first positive peak of the source voltage).

5. Start the simulation.

   As the capacitor is energized from zero, you can observe in the Simulation Data Inspector a low damping transient at 200 Hz, superimposed with the 60 Hz component in the capacitor voltage and primary current. During normal TSC operation, the capacitor has an initial voltage left since the last valve opening. To minimize the closing transient with a charged capacitor, the thyristors of the TSC branch must be fired when the source voltage is at maximum value and with the correct polarity. The initial capacitor voltage corresponds to the steady-state voltage obtained when the thyristor switch is closed. The capacitor voltage is 17.67 kVrms when the valve is conducting. At the closing time, the capacitor must be charged at the peak voltage.

   $$U_c=17670\times \sqrt{2}=24989V$$

6. Double-click the powergui block, and in the Tools tab, click Initial State. A list of all the state variables with their default initial values appears. The value of the initial voltage across the capacitor C (variable Uc_C) should be -0.3141 V. This voltage is not exactly zero because the snubber allows circulation of a small current when both thyristors are blocked. Now select the Uc_C state variable and enter 24989 in the upper right field. Then click the Apply button to make this change effective.

7. Start the simulation. As expected the transient component of capacitor voltage and current has disappeared. The voltages obtained with and without initial voltage are compared in the Simulation Data Inspector as shown in the figure.

   Transient Capacitor Voltage With and Without Initial Charge