The circuit shows the capability of ARTEMiS-SSN solver to make the real-time simulation of an FD-line (Marti type) within Simulink and SimPowerSystems.

### Demonstration

In the demo, a 200 km line is energized with an unbalanced RL load (at the end of phase C). The RL load disconnects at 0.2 sec. The figure below shows the line configuration and the energization simulation results under the described unbalanced load.

The FD-line model has 3 modes that fitted with a total of 11 poles for the characteristic admittance Yc and 6 for the propagation function H.

Real-time simulation at a 6 microseconds time-step can be achieved for this model, with 2 cores of a 2.4 i7 Intel target (one core for each end of the line) with 11+6 poles (Yc and H).

If we increased the number of poles used in the fittings to 39 for Yc and 67 poles for H, then a time step of 7 microseconds can be achieved.

### More about the FD-line model and SSN

The FD-line model is a power line model that includes the frequency dependence of its parameters. For example, a line has more attenuation, described by its propagation function H(w), at high frequencies than at lower ones and this is taken into account in the FD-line model, as opposed to the Bergeron-type model with losses which assumes constant losses across all frequencies.

The characteristic impedance Zc(w) of the line (Yc is the inverse of Zc) typically diminishes at higher frequencies while it is considered constant in non-FD models.

Both propagation function and impedance functions are computed as a Laplace rational sum and obtained with a fitting routine like the one found in EMTP-RV.

A frequency-dependent parameter line (FD-line) is a line model similar to the Bergeron type in that it uses explicitly the propagation delay of the line inside the model.

This has the advantage of allowing the decoupling of simulation of a network located at both ends, a feature that is fundamental to achieving real-time simulation of large power grids.

**The line parameters are specified in a MATLAB structure with the following format:**

Nph | number of phases |

NpolY | number of poles for Yc (Yc=1/Zc) |

Ypol | poles of Yc |

Yres | residues of Yc |

YDmat | constant residues of Yc |

NpolH | poles of H |

Hpol | residues of H |

Hres | residues of H |

HDmat | constant residues of H |

taumin | minimum propagation delays |

Ti | current transformation matrix |

Tv | voltage transformation matrix |

The document untitled **Obtaining FD-line model parameters from EMTP-RV** explains how to get these parameters from the fitting routines of EMTP-RV.

A particularity of the FD-line model is that it has a very efficient formulation in the nodal method and a very poor one with the state-space method. This is caused by the numerous poles of the characteristic impedance of the FD-line model that would have to be included in the complete system state-space matrices (in ABCD formulation).

The SSN method allows the connection of the FD-line, coded in its native nodal method, with other SSN standard groups (computed with state-space method in the current implementation of SSN). More generally speaking, the SSN solver allows the connection of any sub-circuit that has a discrete Norton or Thevenin equivalent at all time step, found by SSN methodology or classic EMTP.

### Reference

*C. Dufour, J. Mahseredjian, J. Bélanger, J. L. Naredo, "An Advanced Real-Time Electro-Magnetic Simulator for Power Systems with a Simultaneous State-Space Nodal Solver", IEEE/PES T&D 2010 - Latin America, São Paulo, Brazil, Nov. 8-10, 2010*