Control and Design of Microgrid Components - Power Systems ...

2.3 Synchronization Conditions
The grid voltage E rotates at 60 Hz in the counter clockwise direction, while the microgrid
voltage V rotates at a frequency lower than 60 Hz in the same direction. This means that if the
vectors are strobed 60 times a second, the vector E stays motionless, while vector V recedes in
the clockwise direction.
V(4)
E
V(3)
V(1)
V(2)
Figure 2.5 Receding Trajectory of Voltage Vector V.
Figure 2.5 shows the vector V rotating slower than E, so at each strobing it loses some angle
from E. As time increases, V goes from position 1 to 4. The magnitude of the current resulting
when the switch is closed is proportional to the voltage across the switch as the contacts are
closed. The voltage across the switch is given by the vectorial difference between E and V. Near
position 2 there is the maximum voltage across the switch and it would be a big mistake to close
there because large transients in the current will ensue. Position 3 is better, but position 4 is
where it is safe to close the switch.
Figure 2.6 shows the behavior in time domain: the difference in frequency has been artificially
increased to make the point. In the upper plot, the solid line is the voltage of the grid, E, while
the slower voltage, V, with longer period, is dotted. In the lower plot there is the voltage across
the static switch. The best time to close the static switch is when the voltage across the switch is
very small and contemporarily, the voltage of the grid is leading the voltage of the microsource.
Therefore, anytime between time scale values of 30 to 35 is a good time to synchronize to the
grid and close the switch.
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