I have a question about transient stability analysis. When we use computer software to perform the transient stability analysis, it plots the graph with power angle at the y-axis and time on the x-axis. If, after disturbance, the angle comes back close enough to the original angle before disturbance, the system is stable. Does anybody know that what is the acceptable limit of variation in the power angle after which the system will become unstable? For example, if the angle before disturbance is 40-degree, what will be the angle after the disturbance (plus/minus) beyond which the system will become unstable? (This information is not available in the traditional power engineering texts because they don’t draw curves of power angle Vs time, they use a different approach of transfer impedance.) Thanks for help!
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Transient Stability
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In the attached sheet, the angle before disturbance is about 35 Deg. The disturbance starts at time t=0.5 Sec, after which the system again becomes stable at t=4 Sec. The angle at t = 4 Sec is about 32 degree. If the angle at t = 4 Sec be 20 Deg or 50 Deg (instead of 32 Deg), will the system still be stable?
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What you are referring to is the steady-state stability of the system, and this is more or less related to the loading of the generator(s).
Check out page 5 of This shows the simplest case of a generator connected to an infinite bus via a line modelled as a pure reactance. The result is the classic power-angle relationship P = P_max sin(delta). So to answer your question, a power angle of anything below 90 degrees is considered stable, but 90 degrees is marginally stable and you wouldn't want to operate there.
In a transient stability simulation, you usually have some disturbance (e.g. a fault) and then some network response to clear that disturbance (e.g. circuit breakers opening to clear the fault). The pre-disturbance network configuration is therefore different to the post-disturbance configuration (e.g. opening breakers may trip out a bunch of loads). So the steady-state rotor angles often settle to values that are different to the pre-disturbance values.
So in the example that you mentioned, the pre-disturbance angle at t=0 is 35 deg and the post-disturbance angle at t=4s is 32 deg. One possible explanation is that some loads were tripped and the machine is less heavily loaded post-disturbance, hence the relative rotor angle decreases.
Check out page 5 of This shows the simplest case of a generator connected to an infinite bus via a line modelled as a pure reactance. The result is the classic power-angle relationship P = P_max sin(delta). So to answer your question, a power angle of anything below 90 degrees is considered stable, but 90 degrees is marginally stable and you wouldn't want to operate there.
In a transient stability simulation, you usually have some disturbance (e.g. a fault) and then some network response to clear that disturbance (e.g. circuit breakers opening to clear the fault). The pre-disturbance network configuration is therefore different to the post-disturbance configuration (e.g. opening breakers may trip out a bunch of loads). So the steady-state rotor angles often settle to values that are different to the pre-disturbance values.
So in the example that you mentioned, the pre-disturbance angle at t=0 is 35 deg and the post-disturbance angle at t=4s is 32 deg. One possible explanation is that some loads were tripped and the machine is less heavily loaded post-disturbance, hence the relative rotor angle decreases.
timm33333
This graph is an exponential damped (rotor angle,time) of the generator that was connected to the system. Who lost stability is generator, not system.
Yes, generator is stable with the system after disturbance char becomes almost horizontal to x-axis.
Attached are graphics of Juleselec. Exponential damped are: Fig.E13.7a- yellow, magenta.--- Fig.E13.8- yellow
This graph is an exponential damped (rotor angle,time) of the generator that was connected to the system. Who lost stability is generator, not system.
Yes, generator is stable with the system after disturbance char becomes almost horizontal to x-axis.
Attached are graphics of Juleselec. Exponential damped are: Fig.E13.7a- yellow, magenta.--- Fig.E13.8- yellow
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Thanks Juleselec and Odlanor! ETAP transient stability also has other charts like "Exciter Current Vs Time", “Reactive/Real Power Vs Time", “Exciter Voltage Vs Time”, “Speed Vs Time”, And “Generator Terminal Current Vs Time”. Should we also plot these charts to determine the stability of an industrial plant, or only the chart of “Rotor Angle Vs Time” is enough?
All of these plots have their uses and you should look at them to interpret what is happening during the simulation. Examples:
- When a system loses synchronism or is poorly damped, this will often be reflected in oscillations in the real / reactive power outputs.
- The exciter current and voltage will show you the dynamics of your excitation system and if over/under-excitation limiters are being activated during the simulation.
- Speed is a proxy for frequency and will help you understand whether under/over frequency relays will operate during the simulation. This is useful if you have a load shedding system in place.
- When a system loses synchronism or is poorly damped, this will often be reflected in oscillations in the real / reactive power outputs.
- The exciter current and voltage will show you the dynamics of your excitation system and if over/under-excitation limiters are being activated during the simulation.
- Speed is a proxy for frequency and will help you understand whether under/over frequency relays will operate during the simulation. This is useful if you have a load shedding system in place.
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