Thevenin Equivalent Estimation for Voltage Instability Prediction BY MARK NAKMALI MENTOR DENIS OSIPOV 1

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 2

Why is this important? o Provides a model that represents the parameters of the system o Provides information that can warn about impending voltage collapse o Basically, it is helpful to know the state of the system, especially when the system is near collapse so that corrective action can be taken. 3

The PV Curve 4

Effects of adding Shunt Capacitor Banks 5

Maximum Power Transfer o At maximum power transfer, the system is near voltage collapse o When at maximum power transfer, Apparent Load Impedance and Equivalent Thevenin Impedance are equal. o This is another way to see how close the system is to voltage collapse. 6

The Least Square Approach o Takes the difference between the scattered data and the proposed line and minimizes the square of that difference. o Utilized a “sliding time window” to have a number of measurements while shifting it down as more data comes in. o With more measurements taken, the output of the line becomes smoother o Limited because it can change dramatically based on the topology of the system. 7

The Least Square Approach Current Load Voltage Thevenin Equivalent 8

Least Square - Changing the Number of Measurements Taken - Thevenin Impedance and Load Impedance 3 Measurements 30 Measurements 300 Measurements This small margin is desirable. 9

Least Square - Changing the Number of Measurements Taken - Maximum Power and Power Transferred 3 Measurements30 Measurements 300 Measurements This small margin is desirable. 10

Least Square – Step Changes in the System Data Set 1Data Set 2 Does not react well to instantaneous change and no change 11

The Kalman Filter Approach Useful because: o Provides a good fit line o Is good for “filtering” out noise or outliers o Is not affected by sudden changes in the system o Recursive - Takes previous data and provides a correction to the current measurement. o Limited because the initial data and amount of error can influence the graph. 12

The Kalman Filter Approach Load Voltage Current Thevenin Equivalent 13

Kalman Filter Graphs Data Set 1Data Set 2 Reacts well to step changes Undesired Large Margin 14

Kalman Filter Graphs (Changing Error) Changed Error 15

Hybrid Description o The 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. o This 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. o After 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. 16

Hybrid - Changing the Number of Measurements Taken - Thevenin Impedance and Load Impedance 3 Measurements 17

Hybrid - Changing the Number of Measurements Taken - Thevenin Impedance and Load Impedance 30 Measurements 18

Hybrid - Changing the Number of Measurements Taken - Thevenin Impedance and Load Impedance 100 Measurements 19

Hybrid - Changing the Number of Measurements Taken - Thevenin Impedance and Load Impedance 300 Measurements 20

Hybrid - Changing the Number of Measurements Taken - Maximum Power and Power Transferred 3 Measurements 21

Hybrid - Changing the Number of Measurements Taken - Maximum Power and Power Transferred 30 Measurements 22

Hybrid - Changing the Number of Measurements Taken - Maximum Power and Power Transferred 100 Measurements 23

Hybrid - Changing the Number of Measurements Taken - Maximum Power and Power Transferred 300 Measurements 24

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 25

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 26

Thank you for your time o Are there any questions? 27