Grid Interconnection & Tie-Line Synchronization (2D)

Area Generation

Grid A generation P_genA 100 MW

Grid B generation P_genB 100 MW

Tie-line reactance X 0.20 pu

Breaker

Areas islanded — watch the synchroscope

Loads are fixed at 100 MW each. Bring both areas to the same frequency and phase before closing, or expect a synchronizing transient.

Live Readings

Freq A

50.00 Hz

Freq B

50.00 Hz

Tie flow A→B

0.0 MW

Rotor angle Δδ

0.0°

How it works

Each area's generators run governor droop control: frequency settles where mismatch between generation and load is proportional to the deviation from 50 Hz —

f = f0 − R·(Pgen − Pload)

With the breaker open, the two islands can sit at different frequencies, so their voltage phasors slip past each other — the synchroscope needle spins at a rate equal to |f_A − f_B|, exactly like the instrument used to close real tie breakers.

Once the breaker closes, both areas are forced onto one common frequency, and the power actually carried by the tie-line obeys the classic AC power-angle equation:

P = (Vs·Vr / X) · sin(δs − δr)

A larger reactance X needs a wider angle Δδ to carry the same power (the tie is "softer"); a smaller X can move more power at a smaller angle (a "stiffer" interconnection). If A has more surplus generation than B, power flows A→B and the two rotors settle at a steady angle offset instead of a common phase — this is exactly how interconnected grids and neighbouring countries share reserves and even out local imbalances.

P_genA / P_genB — generation set-point in each island; loads are fixed at 100 MW each.
Tie-line reactance X — coupling stiffness between the two areas once tied.
Close/Open breaker — closing far out of sync (large Δf or Δδ) produces a visible transient "kick", just as a mistimed real synchronizing operation stresses the machines.

Grid A phasor Grid B phasor Tie-line power flow