relation b/w active power and frequency

Sounds like a tuned system. Are you familiar with resonance?

No.Im not familiar with resonance..

Im related Electrical power system..

what Im expecting is,

If the active power generation is less than the actve power requirement for a load in a grid connected power system, what happened to the grid frequency..?Is it drops or increases and If so, why?wolud you give the relation between active power and frequency?

My mistake. I misunderstood your question the first time.

Total power = Active power plus the Re-active power. That is to say that the total power is the vector sum of the power in phase with the generator and the portion which is 90° out of phase due to reactive (inductive or capacitive) loading. In order to meet the requirements of the load, the generator must produce enough power to supply both components. Only the power that is in phase with the generator is useful for doing work. The other (reactive) component sets up the power factor for the system. Ideally you would like the maximum power factor of 1.0 but it can be tricky to keep the inductive and capacitive loading balanced to achieve this.

When the system is balanced, however, it is tuned so that all of the generated power goes to the (resistive) load. In this respect, the system is in resonance at your primary (generator) frequency and your power factor is 1.

Much like driving an automobile up a hill that is very steep; when the power required to maintain a constant speed is greater than the power of the engine, it will slow down. So when the active power required is more than the source of power, it will reduce the RPM or frequency accordingly.

The other option is to let the voltage output drop, but this creates a larger draw of current to satisfy the load. The ultimate answer is to add more power generation equipment to satisfy the demand or load.