.PowerGrids.Electrical.Test.TwoBusesInductiveTransmissionLine

Information

This model demonstrates the dissipation of reactive power of a purely inductive transmission line, connected to two infinite buses, one with a phase-to-phase voltage U = 10 kV, one with a phase-to-phase voltage U = 9 kV, both with a 30 deg phase. The reactance of each conductor is 1 Ohm.

As a consequence, the current flowing in each conductor is

I = (VA - VB)/X = ((UA-UB)/sqrt3)/X = 577.35 A.

The active power flow in the line is zero. The reactive power entering the line from portA is

3*VA*I' = UA*(UA - UB)*X = 10 MW

while the reactive power dissipated by the transmission line is

portA.P + portB.P = 3*(VA - VB)*I = (UA - UB)^2/R = 1 MW

By choosing a base power of 10 MW and a base voltage of 10 kV, the current flowing through the line is 1 p.u., the active power entering portA of the line is 1 p.u. and the active power leaving portB of the line is 0.9 p.u. All currents and voltages have 30 deg phase.


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