EQUAL AREA CRITERION
The stability of a single machine with respect to infinite bus can be studied by the use of equal area criterion.
On Considering thatthe 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. Thetime 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 removethe 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 wherethe 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 The clearing angle δc for this mode is called Critical Clearing Angle and is denoted by δcr. On substituting δc = δcr in fig above we get
We canthus calculate the critical clearing angle from the equation given above. Since the critical clearing angle depends on the equality of the areas, and this is called the equal area criterion.