Line Types

Abstract base type for all lines

    PiModelLine(from, to, y, y_shunt_km, y_shunt_mk)

A line modelled according to the PI-Model.

See also the Chapter 2 in Göran Andersson, Power System Analysis, Lecture 227-0526-00, ITET ETH Zurich, 2012

Arguments

• from : node k
• to : node m
• y: admittance of line between k and m
• y_shunt_km: shunt admittance at the end connected to node k
• y_shunt_mk: shunt admittance at the end connected to node m
• t_km: transformer ratio at the end connected to node k
• t_mk: transformer ratio at the end connected to node m

Assumptions:

• the line admittance is symmetric

RLLine(; from, to, R, L, ω0)

dynamic line with series resistance R and series inductance L.

When setting initial conditions for this line type be aware that every line carries four variables. The first two for the current from source to destination and the second from destination to source. Since isrcdst = - idstsrc, the inital condtions need to be chosen as negatives of each other as well, i.e. ic[1:2] == -ic[3:4].

Keyword Arguments

• from: start node of the line
• to: end node of the line
• R: series resistance R
• L: series inductance L
• ω0: rated frequency in [rad/s] of the power grid, often $2π50$Hz

Mathematical Representation

Using RLLine for the line from–to applies Eqn. (2) from Brouillon, J. S., Colombino, M., Groß, D., & Dörfler, F. (2018). The effect of transmission-line dynamics on a globally synchronizing controller for power inverters. In 2018 European Control Conference (ECC) (pp. 2242-2247). IEEE.

    StaticLine(from, to, Y)

A static model that represents a line with an admittance Y.

Arguments

• from : start node
• to : end node
• Y: scalar admittance of line between from and to

    Transformer(from, to, y, t_ratio)

assuming an ideal transformer in series with an admittance. The representation uses the Π model.

Mathematical Representation

The voltage transforms as:

\[ u_{to} = t_{ratio} u_{from}\]

Arguments

• from : start node
• to : end node
• y: transformer admittance
• t_ratio: transformation ration

Assumptions

The admittance is here taken to be on the high-voltage side.