# Equal area criterion

May 26 • General • 5721 Views • No Comments on Equal area criterion

POWER SYSTEM

EQUAL AREA CRITERION

The stability of a single machine with respect to infinite bu

s can be studied by the use of equal area criterion.

On Considering that the  synchronous machine is operating in steady state delivering a power Pe  equal to Pm, where Pe is ELECTRICLA POWER ,Pm is MECHANICAL POWER when there is a fault occurs in the system.

The circuit breaker is opened to clear the faults of a power system, it basically takes  about 5 to 6 cycles to open and the consequent  post-fault transient stay for another few cycles. The input power, is supplied by a prime mover which is driven by a steam turbine. The time constant in a  turbine system is of a value of very few seconds, while the electrical system time constant is of the order of  milliseconds. Therefore the mechanical power remains constant during this period when the electrical transients occur. The transient stability study thus concentrates on the ability of the power system to  remove the fault and deliver the constant power Pm  with a new load angle δ .

Given below fig of power angle curve for equal area criterion

We can assume a case when the line is reclosed at δc  where the area of acceleration will be greater  than the area of deceleration, so, A1 > A2 .  Thus the generator load angle crosses the point δm , beyond which the electrical power will be less than the mechanical power and the  accelerating power will be positive. The generator will thus  start accelerating before it slows down completely and will then be unstable. But if , A1 < A2 , i.e., the decelerating area is greater  than the accelerating area, the machine will decelerate totally before accelerating again. The rotor inertia will force the acceleration and deceleration areas will be  smaller than the first ones due to which the machine will eventually attain a steady state. If both the areas are  i.e., A1 = A2 , then the accelerating area is equal to decelerating area which defines  the boundary  of the stability limit. Therefore  ths concept s called the equal area criteron