1. Computing Power System Steady-state Stability Using Synchrophasor Data Karl Reinhard ECE Power and Energy Group Colloquium 29 Oct 12 work with Peter Sauer and Alejandro Domínguez-García

2. Conjecture Collect synchrophasor measurements at 2 buses directly connected by transmission Line Compute model parameters for a pair of Thevenin sources Connect Thevenin sources by the transmission line 2

3. Conjecture Collect synchrophasor measurements at 2 buses directly connected by transmission Line Compute model parameters for a pair of Thevenin sources Connect Thevenin sources by the transmission line Resulting Thevenin source angle difference (AnglxSys) indicates system stability stress Largest AnglxSys of all directly connected buses is proposed as an indicator of the risk of losing system stability 3

4. Purpose To report progress investigating this conjecture to date 4 Take Aways Synchrophasor data is not suitable for some Thevenin equivalent formulations  equations poorly conditioned with field measurements A reduced Thevenin equivalent system meeting expected power system physical constraints can be calculated Importance of verifying that computed values are consistent with power system physics and model at each iteration

5. Stability Limits to Power System Operation 5 easy to assess from measurements. Thermal – short term and long term – typically measured in Amps or Power (MW or MVA) – easy to assess from measurements. easy to assess from measurements Voltage – plus or minus 5% of nominal – easy to assess from measurements. difficult to assess. Stability – voltage collapse, steady-state stability, transient stability, bifurcations  margins to each critical point – difficult to assess. Thermal Voltage Stability

6. Stability Limits to Power System Operation 6 69 KV  12 MW 138 KV  50 MW 230 KV  140 MW 345 KV  400 MW 500 KV  1000 MW 765 KV  2000 MW Thermal Voltage Stability  1.0 SIL = power delivered by a “lossless” line to a load resistance equal to the surge (characteristic) impedance  Voltage and current are in phase along entire line  VARS into line from shunt charging are exactly equal to the total line VAR series losses  Flat voltage profile along entire line

7. Estimating Thevenin Equivalents w/ SPD (SynchroPhasor Data) 7

8. Estimating Thevenin Equivalents w/ SPD 8

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10. Condition No. Analysis – Exact Soln 10 Condition Number

11. Condition No. Analysis 11 Condition Number

12. Condition No. Analysis 12 Condition Number

13. Condition No. Analysis – Least Squares Estimate (m x n matrix) 13

14. Estimating Reduced Thevenin Equivalent w/ SPD 14

15. Estimating Reduced Thevenin Equivalent w/ SPD Real Power Eqn 15

16. Estimating Reduced Thevenin Equivalent w/ SPD 16

17. Estimating Reduced Thevenin Equivalent w/ SPD 17

18. Estimating Reduced Thevenin Equivalent w/ SPD 18

19. RECAP Purpose: To report progress investigating the conjecture that a Thevenin Equivalent from Synchrophasor data indicates system stress 19 Take Aways Synchrophasor data is not suitable for some Thevenin equivalent formulations  equations poorly conditioned with field measurements A reduced Thevenin equivalent system meeting expected power system physical constraints can be calculated Importance of verifying that computed values are consistent with power system physics and model at each iteration Next – Does AnglxSys indicate system stress?? Simulation using MATLAB and Power World

20. QUESTIONS? Karl Reinhard reinhrd2@illinois.edu 20

21. Phasor Measurement Unit – System Model 21

22. GPS Timing Data 22 2 Satellite Signals Intersection – Circle 3 Satellite Signals Intersection – 2 Points 4th Satellite – Timing Signal Correction Satellite 4 Receiver Due to Clock errors, Unlikely 4th satellite’s sphere will intersect either of 2 intersection points… Distance from the valid GPS receiver position estimate to the 4 th satellite sphere surface enables timing error determination / correction: Satellite 3 da

23. GPS Timing Data 23