# Delta-Hexagonal Phase Shifting Transformer

This example shows the operation of two models of delta-hexagonal Phase Shifting Transformer (PST) using On Load Tap Changers (OLTC).

Gilbert Sybille (Hydro-Quebec)

### Description

Two 120 kV 1000 MVA networks are interconnected through a phase shifting transformer (PST). The phase shift can be varied on load by means of On Load Tap Changers (OLTC).

### Simulation

**Open loop control of power transfer**

In order to observe impact of phase shift on power transfer, the phase shift is increased from zero to 32.2 degrees lagging (tap +5), then phase shift is reduced to zero and increased again up to 32.2 degrees leading. This is performed by sending 5 pulses to the "Up" input, and then, 10 pulses to the "Down" input ". As the tap selection is a relatively slow mechanical process (3 sec per tap as specified in the "Tap selection time" parameter of the block menus), the simulation Stop time is set to 50 s.

Start simulation and observe PST operation on the Scope. Results obtained with the two models are superimposed on five traces.

Trace 1 shows the tap position.

Trace 2 shows a superposition of positive-sequence voltages measured at bus B1 (yellow) and bus B3 (magenta).

Trace 3 shows the phase shifts of positive-sequence voltages measured at output terminals (abc) with respect to input terminals (ABC).

Trace 4 compares the active power measured at bus B1 (yellow) and bus B3 (magenta).

Trace 5 compares the phase currents at bus B1 (yellow) and bus B3 (magenta).

When simulation starts the OLTCs are at position 0 (zero phase shift). As the two networks are symmetrical with both internal angles set at 0 degree, there is no current flowing. Then, phase shift is increased and bus B2 (or B4) is lagging bus B1 (or B3). As B2 is lagging the internal voltage of the source located on right side, power flows from right to left. Power measured from left to right is therefore negative for positive tap positions. The maximum power is obtained at tap +5, or -5 when the phase shift is respectively -32.2 degrees and +32.2 degrees. The active power can be computed from P= V1.V2*sin(psi)/ (X1 +X2 + Xpst) , where: V1=V2=internal voltages= 1.0 pu ; X1= X2 = network reactances = 1pu /1000 MVA Xpst= PST leakage reactance at tap 5. The PST leakage reactance varies with tap position (from zero at tap zero to 0.15 pu at maximum tap (10)). The positive-sequence impedance of the phasor model is available as a signal at its measurement output "m". The reactance obtained at tap 5 is Xpst=0.1067 pu/ 300 MVA. The total reactance expressed in pu/100 MVA is X= 0.1 +0.1 + 0.1067/3 =0.2356 pu/100 MVA. The expected active power at tap 5 is P= 1*sin(32.2deg)/0.2356 = 2.26 pu/100 MVA or 226 MW, which corresponds well with the measured value on trace 4 (224 MW). Because of the voltage developed across the PST leakage reactance, the phase shift measured between PST input and output voltages (trace 3) is lower than the expected value. For example, 27.2 degrees is obtained at tap 5, instead of the 32.2 degrees theoretical value computed at no load. The phase shift variation depends on load current.

**Initializing the phasor model**

For the phasor model to start initialized at t=0, the current sources used in the model must be initialized with current values corresponding to steady state. Suppose that you want to start with the initial tap position 5. First, in the two block menus, "set Initial tap" parameter to 5. Then disconnect the signals connected to the "Up" and "Down" inputs of the two models, so that the taps stay at position 5. If you start simulation you will notice a transient in the phasor model signals at t=0 because the model is not initialized. Use the "Steady-State Voltages and Currents" option of the powergui to obtain the initial current flowing in the detailed model at bus B4. The phase A output current identified "B2/Ia" is 1129.4 A rms, 169 degrees. This current converted to per unit based on PST rating is 1129/1443 = 0.7824 pu/ 300MVA. Specify [ 0.7824 169] in the "Initial pos. seq. output current" parameter. If you now restart simulation, you should observe no transient at t=0.

**Operation under unbalanced conditions**

The phasor model is valid for unbalanced conditions. If you check "Phase A Fault" in the two fault breakers, a single phase fault will be applied at t=5s. The currents measured at buses B1 and B3 should be identical. (For example at tap position +5: Ia=3.48 pu, Ib=2.25 pu Ic=2.10 pu ).

**Simulation with phasor model only**

In order to appreciate the gain in simulation speed provided by the phasor model, delete the detailed PST model and replace it with a duplicate of the phasor model. Reconnect control signals to the "Up" and "Down" inputs. Restart simulation. The model runs approximately 5 times faster, mainly because the OLTC switches of the detailed model are not simulated.