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Thevenin Equivalent Estimation for Voltage Instability PredictionBY 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 systemoProvides information that can warn about impending voltage collapseoBasically, 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 TransferoAt maximum power transfer, the system is near voltage collapseoWhen 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 ApproachoTakes 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 ApproachCurrent Load

VoltageThevenin

Equivalent

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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 MeasurementsThis 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 lineoIs good for “filtering” out noise or outliersoIs not affected by sudden changes in the systemoRecursive - 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 GraphsData Set 1 Data Set 2

Reacts well to step changes

Undesired Large Margin

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Kalman Filter Graphs (Changing Error)

Changed Error

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Hybrid DescriptionoThe 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 loado 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 filtero 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 timeoAre there any questions?