• In the given system, working at a lagging power factor means that the load is consuming reactive power.
• The synchronous motor working at an over-excited condition means that it is generating reactive power and acting as a source of reactive power. .
• The direct grid connection does not consume or generate any reactive power.
• The induction generator is connected to the grid, which means that its output must match the grid frequency and voltage.
• If the induction generator is generating excess reactive power, it cannot be fed back into the grid. Instead, it must be absorbed by some other device in the system.
• Since the load is consuming reactive power and the synchronous motor is generating reactive power, we can conclude that the synchronous motor is a source of reactive power, while the load is a sink of reactive power.
• The induction generator must therefore be absorbing the excess reactive power generated by the synchronous motor, making it a sink of reactive power.

Therefore, the correct statement is:

The synchronous motor is a source of reactive power, and the synchronous generator and the induction generator are sinks of reactive power.