.PowerSystems.AC3ph.Transformers

Information

Transformer models in different abstraction levels.

All transformers allow the choice between Y- and Delta-topology both at primary and secondary side.
For Delta an additional phase-shift may be chosen in order to adapt to a given phase-numbering scheme.
The impedance parameters are defined 'as seen from the terminals', directly relating terminal voltage and terminal current. With this definition same parameters lead to same network properties, independent of topology. The necessary scaling is performed automatically.

In Delta-topology the conductor voltage is sqrt(3) higher, the current sqrt(3) lower, compared to the terminal voltage and current. Therefore the impedance relating conductor current and voltage is a factor 3 larger, the admittance a factor 1/3 smaller than the impedance and admittance as seen from the terminal.

If impedance parameters are given for the Deta-connected WINDINGS, choose:

  input values impedance parameters = 1/3 * (impedance parameters of windings)

In the dq0-representation the following relations hold between terminal-voltage v_term and -current i_term on the one hand and conductor-voltage v_cond and -current i_cond on the other.

A) Y-topology.

  v_cond = v_term - {0, 0, sqrt(3)*v_n};
  i_term = i_cond;
  i_n = sqrt(3)*i_term[3];

where v_n denotes the voltage at the neutral point and i_n the current neutral to ground.

B) Delta-topology.

  v_cond[1:2] = sqrt(3)*R30*v_term[1:2];
  i_term[1:2] = sqrt(3)*transpose(R30)*i_cond[1:2];
  v_cond[3] = 0;
  i_term[3] = 0;

where R30 denotes a rotation by 30deg in positive sense.
(Alternative solutions corresponding to permuted phases are R-90 and R150 instead of R30).

The winding scaled voltage- and current-variables v and i are related to the corresponding conductor quantities through the relation:

  v = v_cond/w
  i = i_cond*w

Contents