What is equal area criterion in power system stability analysis?

Short Answer:

The equal area criterion is a simple graphical method used in power system stability analysis to determine whether a synchronous machine will remain stable after a disturbance. It compares the areas under the accelerating and decelerating parts of the power-angle curve.

If the area of acceleration (machine gaining speed) is equal to the area of deceleration (machine slowing down), the system remains stable. If the decelerating area is smaller, the machine loses synchronism, and the system becomes unstable. This method is mainly applied to single-machine-infinite-bus systems.

Detailed Explanation:

Equal area criterion in power system stability analysis

The equal area criterion is an analytical method used in transient stability analysis of power systems. It provides a simple way to determine whether a synchronous generator will remain in synchronism with the power system (often modeled as an infinite bus) after experiencing a large disturbance, such as a fault or a sudden change in load.

This method is based on the swing equation, which describes the motion of the generator rotor due to an imbalance between mechanical input power and electrical output power. The swing equation is a second-order differential equation, but the equal area criterion simplifies this problem using energy principles and a graphical approach.

Concept of equal area criterion

When a fault occurs, the balance between mechanical and electrical power is disturbed:

  • If mechanical power > electrical power, the generator accelerates (gains kinetic energy).
  • If mechanical power < electrical power, the generator decelerates (loses kinetic energy).

The equal area criterion uses a graph of electrical power output (Pe) vs. rotor angle (δ), known as the power-angle curve. It assumes that:

  • The mechanical power remains constant during the disturbance.
  • Electrical power depends on the sine of the rotor angle, Pe = Pmax·sin(δ).

On the power-angle curve:

  • The area A1 (accelerating area) is the energy gained during the fault or acceleration period.
  • The area A2 (decelerating area) is the energy lost after fault clearance.

For the system to be stable:

Area A1=Area A2\text{Area A1} = \text{Area A2}Area A1=Area A2

If A1 is greater than A2, the rotor keeps accelerating, and synchronism is lost.

Application of equal area criterion

  • Mainly used in single-machine-infinite-bus (SMIB) systems.
  • Helpful in estimating the critical clearing angle (δcr) and critical clearing time (tcr)—the maximum allowed time to clear the fault before losing stability.
  • Can be used in manual calculations without solving the swing equation numerically.
  • Provides a quick understanding of system behavior for various types of disturbances.

Advantages

  • Simple and intuitive graphical method.
  • Requires less computation.
  • Gives a good visual idea of stability margins.
  • Helps in understanding the impact of fault clearing time on system stability.

Limitations

  • Limited to single-machine-infinite-bus or equivalent two-machine systems.
  • Cannot be directly used for large interconnected systems.
  • Assumes constant mechanical power and ignores damping.
  • Requires knowledge of the power-angle curve, which must be plotted beforehand.
Conclusion:

The equal area criterion is a graphical technique used to determine transient stability of a power system. It compares the energy gained and lost by the generator rotor during a disturbance. If these areas are equal, the system remains stable. Though simple, it is a powerful tool in basic stability analysis, especially for single-machine-infinite-bus systems.