POWER SYSTEM STABILITY Equal Area Criterion Equal Area

POWER SYSTEM STABILITY Equal Area Criterion

Equal Area Criterion ■ Quickly predicts the stability after a major disturbance – graphical interpretation of the energy stored in the rotating masses – method only applicable to a few special cases: o one machine connected to an infinite bus o two machines connected together ■ Method provides physical insight to the dynamic behaviour of machines ■ relates the power angle with the acceleration power

Equal Area Criterion Objective Determine Rotor Stability after Disturbance BY i. Clearing Angle and Critical Clearing Angle ii. Clearing Time and Critical Clearing Time THROUGH Power – Angle Curve Analysis

Rotor Angle Time

Fault occurs Rotor angle continues to increase Lost Synchronism / Unstable Power output is reduced Rotor continues to gain speed Fault occurs long time For stable condition, rotor angular velocity must equal zero:

Equal Area Criterion ■

Equal Area Criterion ■

Equal Area Criterion ■

Equal Area Criterion ■

Equal Area Criterion ■

Equal Area Criterion ■

Equal Area Criterion ■

Equal Area Criterion ■

Equal Area Criterion ■

Equal Area Criterion – Sudden Change in Mechanical Input ■ E. A. C is used to determine the maximum additional power, P which can be applied for stability to be maintained. m ■ With sudden increase in the power input, stability is maintained ONLY IF A 2 at least equal to A 1 can be located above Pm. ■ If area A 2 less than area A 1; the accelerating momentum can NEVER be overcome.

Equal Area Criterion – Sudden Change in Mechanical Input ■ Equal-area criterion maximum power limit

Equal Area Criterion – 3 Phase Fault (fault at the sending end)

Equal Area Criterion – 3 Phase Fault (fault at the sending end) ■

Equal Area Criterion – 3 Phase Fault (fault at the sending end) ■

Equal Area Criterion – 3 Phase Fault (fault at the sending end) ■

Equal Area Criterion – 3 Phase Fault (fault away from the sending end)

Equal Area Criterion – 3 Phase Fault (fault away from the sending end)

Equal Area Criterion – 3 Phase Fault (fault away from the sending end)

Equal Area Criterion – 3 Phase Fault (fault away from the sending end) ■

Example 1 A 60 Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X’d = 0. 3 p. u. is connected to an infinite bus through a purely reactive circuit as shown below. Reactance's are marked on the diagram on a common system base. The generator is delivering real power Pe = 0. 8 p. u. and Q = 0. 074 p. u. to an infinite bus at a voltage of V = 1. 0 p. u. a) Determine the transient internal voltage, E’. b) A three phase fault occurs at the middle of one of transmission lines. The fault is cleared, and the faulted line is isolated. Determine the critical clearing angle. c) Repeat (a) and (b) with fault occurs at sending end.

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End of Lecture

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