In my article I introduce, why the use of power flow controllers are needed on the transmission network, what kind of devices are they and how they are working.
In Europe the most common is the use of phase shifting transformers (PST).
I give details about how do the PSTs work, and how they can be modeled.
On the high voltage grid, which is very looped, the control of transformers influences primarily the flows not the voltages of the grid.
The control can be modeled as a voltage source, which is in series with the line.
This voltage source makes a loop flow on the impedance of the loop, which is superponated on the line flows.
In case of inductive lines (R/X<0.1) the control of the amplitude of the voltage influences the reactive power flows, the phase shifting influences the active power flow.
I started my work with modelling a simple case, where there is one generator, one load and two parallel lines between them. If the line impedances are different, the active power flow will be different on them without control. But by a PST we can achieve, that the line flow will be equal. By the PST we can influence the transmission capacity between the generator and the load, and the power loss.