Transient Stability Angle Reference

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All angle values have a meaning only when stated with respect to a reference. Two such quantities are the angle of the bus terminal voltage and the angle of the generator's (machine's) rotor.

 

For all buses, the terminal voltage angle (that has a physical significance) can be specified in two forms. Both forms have the units of degrees, but with different references.

"V Angle No Shift": It is with respect to a fictitious synchronous reference that is rotating at 50 or 60 Hz (the system nominal frequency), and It is also the actual voltage angle algebraic state of each bus terminal during a simulation.

"V Angle": It is defined with respect to the chosen Angle Reference in Transient Stability > Options > Results Options > Angle Reference Options, i.e., "V Angle No Shift" — "Angle Reference".

 

Additionally, for all synchronous generators, the angle of the machine's rotor can be specified in three forms. All forms also have the units of degrees and refer to the same physical dynamic state of a machine, but have different references.

"Rotor Angle No Shift": It is with respect to a fictitious synchronous reference that is rotating at 50 or 60 Hz (the system nominal frequency), and it is also the actual rotor angle dynamic state that is present in each simulated machine model.

"Rotor Angle": It is defined with respect to the chosen Angle Reference in Transient Stability > Options > Results Options > Angle Reference Options, i.e., "Rotor Angle No Shift" — "Angle Reference".

"Power Angle": It is defined with respect to the Terminal "V Angle No Shift" or "V Angle", i.e., "Rotor Angle No Shift" — "V Angle No Shift", which is equivalent to "Rotor Angle" — "V Angle"

 

"V Angle No Shift" and "Rotor Angle No Shift" generally do not return to a constant value after a "new steady state" has been reached during a dynamic simulation. Instead, these quantities will have a constant positive/negative slope in a time-series plot, where the slope will be equal to "new steady state" frequency minus the "initial steady state" frequency in Hz, assuming of course that a "new steady state" was in fact reached.

 

"V Angle" and "Rotor Angle" generally do return to a constant value after a "new steady state" has been reached during a dynamic simulation. Depending on the chosen "Angle Reference", it is sometimes possible that it might skew the angle at all buses/generators. Consequently, be advised to not solely rely on "V Angle" and "Rotor Angle" to assess the stability of a simulation, but also check other signals like voltage magnitude and frequency to verify the overall system condition.

 

"Power Angle" tends to be a better indicator of a generator's stability, and it does return to a constant value after a "new steady state" has been reached during a dynamic simulation, except a few rare situations (such as during faults). In most undergraduate or graduate courses, a single-machine model is first discussed where the rotor angle dynamic state is defined with respect to the terminal voltage. It is in fact the same as "Power Angle", and is neither "Rotor Angle" nor "Rotor Angle No Shift" in PowerWorld's terminology. In large-scale power system simulations, it becomes essential to distinguish between the "Power Angle" and "Rotor Angle, and this write-up has explained the differences.