Download Voltage Instabiliy Prediction Using the Least Square and Kalman

Thevenin Equivalent
Estimation for Voltage
Instability Prediction
BY MARK NAKMALI
MENTOR DENIS OSIPOV
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Purpose
◦The purpose of this research project is to be able to find a
reliable method of estimating the Thevenin equivalent of
a large scale system, which will aid in the prediction of
voltage instability.
◦Two methods are going to be explored:
◦The Least Square Approach
◦The Kalman Filter Approach
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Why is this important?
oProvides a model that represents the parameters of the
system
oProvides information that can warn about impending
voltage collapse
oBasically, it is helpful to know the state of the system,
especially when the system is near collapse so that
corrective action can be taken.
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The PV Curve
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Effects of adding Shunt Capacitor Banks
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Maximum Power Transfer
oAt maximum power transfer, the
system is near voltage collapse
oWhen at maximum power
transfer, Apparent Load
Impedance and Equivalent
Thevenin Impedance are equal.
oThis is another way to see how
close the system is to voltage
collapse.
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The Least Square Approach
oTakes the difference between the scattered data and the proposed line and
minimizes the square of that difference.
oUtilized a “sliding time window” to have a number of measurements while
shifting it down as more data comes in.
oWith more measurements taken, the output of the line becomes smoother
oLimited because it can change dramatically based on the topology of the
system.
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The Least Square Approach
Current
Thevenin
Load
Equivalent Voltage
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Least Square - Changing the Number of Measurements
Taken - Thevenin Impedance and Load Impedance
3 Measurements
30 Measurements
300 Measurements
This small margin
is desirable.
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Least Square - Changing the Number of Measurements
Taken - Maximum Power and Power Transferred
3 Measurements
30 Measurements
300 Measurements
This small margin
is desirable.
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Least Square – Step Changes in the
System
Data Set 1
Data Set 2
Does not
react well to
instantaneous
change and
no change
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The Kalman Filter Approach
Useful because:
oProvides a good fit line
oIs good for “filtering” out noise or outliers
oIs not affected by sudden changes in the system
oRecursive - Takes previous data and provides a correction to the
current measurement.
oLimited because the initial data and amount of error can influence
the graph.
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The Kalman Filter Approach
Load Voltage
Current
Thevenin
Equivalent
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Kalman Filter Graphs
Data Set 1
Data Set 2
Undesired
Large
Margin
Reacts well
to step
changes
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Kalman Filter Graphs (Changing Error)
Changed
Error
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Hybrid Description
oThe difference between this hybrid filter and the Kalman filter is that the sliding time window
that was used in the Least Squares was put into the code.
oThis allowed for more data to be included in the calculation, causing:
o a graph that was still able to function with the sudden changes in load
o a closer margin near the end of the graph.
oAfter testing this graph, it was found that:
o at a low number of measurements, the graph behaved more like a Kalman filter
o at a high number of measurements, the graph behaved more like a least square.
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Hybrid - Changing the Number of Measurements Taken
- Thevenin Impedance and Load Impedance
3 Measurements
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Hybrid - Changing the Number of Measurements Taken
- Thevenin Impedance and Load Impedance
30 Measurements
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Hybrid - Changing the Number of Measurements Taken
- Thevenin Impedance and Load Impedance
100 Measurements
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Hybrid - Changing the Number of Measurements Taken
- Thevenin Impedance and Load Impedance
300 Measurements
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Hybrid - Changing the Number of Measurements Taken
- Maximum Power and Power Transferred
3 Measurements
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Hybrid - Changing the Number of Measurements Taken
- Maximum Power and Power Transferred
30 Measurements
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Hybrid - Changing the Number of Measurements Taken
- Maximum Power and Power Transferred
100 Measurements
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Hybrid - Changing the Number of Measurements Taken
- Maximum Power and Power Transferred
300 Measurements
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How are these models important?
By using these models, it becomes trivial to use the outcomes for incorporation into other
models such as the power transfer stability index.
Data Set 1
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How are these models important?
By using these models, it becomes trivial to use the outcomes for incorporation into other
models such as the power transfer stability index.
Data Set 2
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Thank you for your time
oAre there any questions?
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