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Power-Angle Dynamics for Engineers

The document discusses power-angle relationships in power systems. It describes how the power-angle curve changes when one transmission circuit goes out of service, requiring a higher rotor angle to transmit the same power. It then examines the impact of faults and different fault clearing times on power system stability, using the equal area criterion. Stable and unstable cases are shown, with the unstable case exhibiting increasing oscillations after the fault is cleared.

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164 views6 pages

Power-Angle Dynamics for Engineers

The document discusses power-angle relationships in power systems. It describes how the power-angle curve changes when one transmission circuit goes out of service, requiring a higher rotor angle to transmit the same power. It then examines the impact of faults and different fault clearing times on power system stability, using the equal area criterion. Stable and unstable cases are shown, with the unstable case exhibiting increasing oscillations after the fault is cleared.

Uploaded by

adau
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Power-Angle Relationship

Fig. 13.3 Power-angle relationship


Both transmission circuits in-service: Curve 1

operate at point "a" (Pe = Pm)


One circuit out-of-service: Curve 2

lower Pmax operate at point "b" higher reactance higher to transmit same power

Effects of Disturbance
The oscillation of is superimposed on the synchronous speed 0 ( = d dt ) << Speed deviation
r 0

the generator speed is practically equal to 0, and the per unit (pu) air-gap torque may be considered to be equal to the pu air-gap power torque and power are used interchangeably when referring to the swing equation.

Equation of Motion or Swing Equation


2 H

where: Pm Pmax H t = = = = =

d 2 dt 2

= P

max

sin

mechanical power input (pu) maximum electrical power output (pm) inertia constant (MW-sec/MVA) rotor angle (elec. radians) time (secs)

Response to a Short Circuit Fault


Illustrate the equal area criterion using the following system:

Examine the impact on stability of different fault clearing times

Stable Case

Response to a fault cleared in tcl seconds - stable case

Stable Case
Pre-disturbance:
both circuits I/S : Pe = Pm, = 0 operating point a

cont'd

Fault On:
operating point moves from a to b inertia prevents from changing instantaneously Pm > Pe

rotor accelerates to operating point c

Post Fault:
faulted circuit is tripped, operating point shifts to d

rotor decelerates rotor speed > increases


Pe > Pm
0

operating point moves from d to e such that A1 = A2 at e, speed = 0, and = m Pe > Pm

rotor decelerates; speed below

decreases and operating point retraces e to d with no damping, rotor continues to oscillate

Unstable Case

Response to a fault cleared in tc2 seconds - unstable case

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