research highlights
A Synchrophasor Measurement Based Method for Assessing Damping Torque
Contributions from Power System Stabilizers
Damping torques for power system swing modes are typically provided by power system stabilizers (PSSs)
acting through voltage regulation of generators. In particular, inter-area mode damping contributions
normally come from many generators. It is not trivial to check whether a PSS is providing positive damping
contribution in a power system simulation program, let alone using field tests or measured data from
generator testing.
At CURENT we are developing a damping torque assessment method based on synchronized measurements
of the generator rotor angle and its terminal bus voltage phasor, as an extension of the deMello-Concordia
synchronizing and damping torque decomposition. The method involves extracting the modal components
from the measurements and comparing the phases of these components.
The linearized block diagram for the local mode of a single-machine infinite-bus (SMIB) system is shown
below. It is important to note that the ∆ quantities in the diagram are the local mode components of the
measured quantities.
Figure 1 - SMIB block diagram
Figure 2 - SMIB local mode phasor relationship diagram
The quantity of interest is the electrical torque (∆Te2) from the generator internals. ∆Te2 can be decomposed
into ∆Te2=∆Ts2+j∆Td2 where ∆Ts2 is the synchronizing torque in the direction of ∆δ and ∆Td2 is the damping
torque in the direction of ∆ω. From Figure 1, we see that ∆Te2 is in the direction of ∆E ’q but it is difficult to
measure Te2 or E ’q directly. Instead, we note that the terminal bus angle θ is mainly dependent on the rotor
angle δ and E ’q and therefore we can develop the relationships as shown in the phasor diagram in Figure
2. As can be seen, we only need to examine the phase difference between ∆θ and ∆δ. A generator with a
working PSS providing positive ∆Td2 is indicated by ∆θ having a noticeable phase lead over ∆δ. If the ∆θ-∆δ
phase difference is small or negative, then the generator and its PSS settings should be examined.
The new assessment method can be extended to inter-area modes within multi-machine systems. The
method has been tested on both the SMIB system and a multi-machine system using both linear analysis and
non-linear simulations, and the results have been consistent with the theoretical predictions.
This method can be applied if unstable or lightly damped oscillations are observed on a power system after
major disturbances, without the need to do specific generator testing. Only synchronized measurements of
δ and θ are needed. The method can also be applied to time responses from simulation programs. Thus for
inter-area modes, this method is useful in determining which PSSs are providing damping torque and which
PSSs are not.
newsletter Spring 2014
4