Introduction:
The equal area criterion is a method used to assess the transient stability of a power system. It involves the analysis of the area under the power versus time curve during a disturbance. If the area is equal on both sides of the curve, then the system is considered to be transiently stable. The damping parameter plays a crucial role in determining the transient stability of the system.

Explanation:
The damping parameter represents the damping present in the system, which controls the rate at which oscillations dampen out after a disturbance. It is directly related to the system's ability to recover and stabilize after a disturbance.

Independent of system damping:
The equal area criterion does not depend on the value of the damping parameter. It only considers the area under the power versus time curve. Therefore, the transient stability is assured by the equal area criterion regardless of the value of the damping parameter.

Only when the damping is exactly zero:
When the damping parameter is exactly zero, there is no damping present in the system. This means that the oscillations caused by a disturbance will not dampen out naturally. In such a case, the equal area criterion becomes particularly important in assessing the system's transient stability. The equal area criterion provides a measure of the damping required to stabilize the system and prevent sustained oscillations.

Not for all values of damping parameters:
While the equal area criterion is valid for all values of the damping parameter, it does not guarantee transient stability for all values. The damping parameter affects the rate at which oscillations dampen out, and if it is too low or too high, the system may not be able to recover and stabilize properly. Therefore, although the equal area criterion can be applied to any value of the damping parameter, it does not guarantee transient stability for all values.

Only when the damping is positive and finite:
For the equal area criterion to assure transient stability, the damping parameter must be positive and finite. This means that there must be some level of damping present in the system to dampen out the oscillations caused by a disturbance. If the damping parameter is negative or infinite, the system may exhibit sustained oscillations that prevent it from achieving transient stability.

Conclusion:
The transient stability assured by the equal area criterion is independent of the system damping. However, the equal area criterion becomes particularly important when the damping parameter is exactly zero, as it provides a measure of the damping required to stabilize the system. The equal area criterion is valid for all values of the damping parameter but does not guarantee transient stability for all values. It only assures transient stability when the damping parameter is positive and finite, ensuring that there is sufficient damping to dampen out oscillations and stabilize the system.