# TCSC (Phasor Model)

This example shows the Thyristor Controlled Series Capacitor (TCSC) phasor test system.

Dragan Jovcic (University of Aberdeen, Scotland, UK)

### Phasor TCSC Model

This phasor tests system is similar to the TCSC thyristor-based tests system in the library. The phasor model however uses the equivalent impedances at the fundamental frequency, neglecting all transients, and therefore it is not as accurate as the thyristor model. Nevertheless, the phasor model is much simpler and the speed of simulation is increased. By comparing the responses with the detailed model we can observe very good matching of all variables in steady-state. Some small discrepancies are caused by the thyristor resistance and other TCSC losses which are not included in the phasor model.

### Description

A TCSC is placed on a 500kV, long transmission line, to improve power transfer. Without the TCSC the power transfer is around 110MW, as seen during the first 0.5s of the simulation when the TCSC is bypassed. The TCSC is modeled as a voltage source using equivalent impedance at fundamental frequency in each phase. The nominal compensation is 75%, i.e. assuming only the capacitors (firing angle of 90deg). The natural oscillatory frequency of the TCSC is 163Hz, which is 2.7 times the fundamental frequency. The test system is described in [1].

The TCSC can operate in capacitive or inductive mode, although the latter is rarely used in practice. Since the resonance for this TCSC is around 58deg firing angle, the operation is prohibited in firing angle range 49deg - 69deg. Note that the resonance for the overall system (when the line impedance is included) is around 67deg. The capacitive mode is achieved with firing angles 69-90deg. The impedance is lowest at 90deg, and therefore power transfer increases as the firing angle is reduced. In capacitive mode the range for impedance values is approximately 120-136 Ohm. This range corresponds to approximately 490-830MW power transfer range (100%-110% compensation). Comparing with the power transfer of 110 MW with an uncompensated line, TCSC enables significant improvement in power transfer level.

To change the operating mode (inductive/capacitive/manual) use the toggle switch in the control block dialog. The inductive mode corresponds to the firing angles 0-49deg, and the lowest impedance is at 0deg. In the inductive operating mode, the range of impedances is 19-60 Ohm, which corresponds to 100-85 MW range of power transfer level. The inductive mode reduces power transfer over the line. A constant firing angle can also be applied and the same limits will apply as above.

### TCSC Control

When TCSC operates in the constant impedance mode it uses voltage and current feedback for calculating the TCSC impedance. The reference impedance indirectly determines the power level, although an automatic power control mode could also be introduced.

A separate PI controller is used in each operating mode. The capacitive mode also employs a phase lead compensator. Each controller further includes an adaptive control loop to improve performance over a wide operating range. The controller gain scheduling compensates for the gain changes in the system, caused by the variations in the impedance.

The TCSC is simulated as a controllable voltage source in each phase. The voltage magnitude is the product of equivalent complex impedance and the line current. The expression for the TCSC impedance is given in [1].

### Simulation

Run the simulation and observe waveforms on the main variables scope block. The TCSC is in the capacitive impedance control mode and the reference impedance is set to 128 Ohm. For the first 0.5s, the TCSC is bypassed (assuming a circuit breaker), and the power transfer is 110 MW. At 0.5s TCSC begins to regulate the impedance to 128 Ohm and this increases power transfer to 610MW. Note that the TCSC starts with alpha at 90deg to enable lowest switching disturbance on the line.

### Dynamic Response

At 2.5s a 5% change in the reference impedance is applied. The response indicates that TCSC enables tracking of the reference impedance and the settling time is around 500ms. At 3.3s a 4% reduction in the source voltage is applied, followed by the return to 1p.u. at 3.8s. It is seen that the TCSC controller compensates for these disturbances and the TCSC impedance stays constant. The TCSC response time is 200ms-300ms. Note that the shape of transient response is inaccurate with phasor models and the thyristor based model should be used for studying transients.

### Reference

[1] D.Jovcic, G.N.Pillai "Analytical Modelling of TCSC Dynamics" IEEE® Transactions on Power Delivery, vol 20, Issue 2, April 2005, pp. 1097-1104