Transcript REU Poster - CURENT Education

Thevenin Equivalent Estimation for
Voltage Instability Prediction
Mark Nakmali1, Denis Osipov2
University of Oklahoma1, University of Tennessee2
Introduction:
Methods:
Voltage instability occurs when the
demanded amount of power required for the
load exceeds that which the system can
transfer, ultimately leading to voltage
collapse. This makes it paramount to be
able to produce a model that reliably and
accurately displays the state of a system
based on measurements taken. Two
methods are explored, and a hybrid method
is proposed. Their outputs are visualized
and compared.
Two data sets, a constant increase in load (Ramp Change) and a step
increase in load (Step Change), were used as inputs to the methods to
calculate the Thevenin Equivalent and subsequently, the Maximum Power
Transfer.
Least Square: This works by utilizing a set amount of previous measurements
in a sliding time window and applying a line that minimizes the square of the
deviation of each point.
Kalman Filter: This works by taking a single previous measurement and
comparing it with the current measurement in order to make an estimate of the
true value.
Hybrid: This works by combining the use of a sliding time window from the
Least Square into the equation of the Kalman Filter.
Least Square:
Kalman Filter:
Hybrid Filter:
Ramp Change Step Change Ramp Change Step Change Ramp Change Step Change
Normal
Maximum Power (Blue) Power Transferred (Green)
[per unit]
3 Measurements
3 Measurements
Voltage collapse occurs at the end of
the graph where Maximum Power
and Power Transferred intersect.
30 Measurements
Least Square: It realistically shows a
smaller margin when near voltage
collapse, but i does not do well with
instantaneous changes and no
changes of the step change.
30 Measurements
Kalman Filter: It is able to handle the
step changes, but it does not have a
close margin near voltage collapse.
300 Measurements
Hybrid: It is resistant to step changes
and provides a smaller margin near
voltage collapse.
300 Measurements
Time [seconds]
Application:
Conclusion:
Their results can easily be used directly, or for other modeling methods
such as the Power Transfer Stability Index. (Power Transferred divided by
Maximum Power Transfer) (shown with a 20% safety margin)
The Least Square method provides a
more accurate graph as more
measurements are taken while the
Kalman Filter provides a more
adaptable graph toward step changes.
By combining the two into a hybrid
model, a compromise can be made
between them as more measurements
are taken into account. This allows for
the strengths of both methods to be
present in the output of the hybrid
model, leading to a smoother, more
reliable graph.
Least Square
Ramp
Change
Index
Step
Change
Kalman Filter
Hybrid
Time [seconds]
This work was supported in part by the Engineering Research Center
Program of the National Science Foundation and the Department of Energy
under NSF Award Number EEC-1041877 and the CURENT Industry Partnership Program.