Contingency-Constrained PMU Placement in Power Networks

1. Contingency-Constrained PMUPlacement in Power Networks FarrokhAminifar, AminKhodaei, Mahmud Fotuhi-Firuzabad, and Mohammad Shahidehpour

2. Outline • Introduction • Problem Formulation • Integer Linear Programming • Experimental Results • Conclusion

3. Definition • PMU is a device for synchronizing ac voltage and current measurements with a common time reference. http://criepi.denken.or.jp/en/system/common/img/unit/unit1_ind_pic2.gif http://www.phasor-rtdms.com/phaserconcepts/images/pmu.jpg

4. Problem Formulation • The objective of PMU placement problem is to find the minimum # of PMUs as well as their placement to make the power network topologically observable. bus 12 bus 13 bus 14 bus 10 bus 9 bus 6 bus 11 bus 7 bus 8 bus 5 bus 4 bus 3 bus 1 bus 2

5. ILP Notation

6. Traditional ILP Formulation bus 12 bus 13 bus 14 bus 10 bus 9 bus 6 bus 11 bus 7 bus 8 bus 5 bus 4 bus 3 bus 1 bus 2 a12 =1

7. New Constraints in This Work • Effect of Zero-Injection Buses • Loss of Measurement Contingency • Line Outage Contingency • Measurement Limitations

8. Zero-Injection Buses Parameter “z” is a binary parameter that is equal to 1 if bus is a zero-injection bus and 0 otherwise

9. Zero-Injection Buses (Cont.) bus 12 bus 13 bus 14 bus 10 bus 9 bus 6 bus 11 bus 7 bus 8 bus 5 bus 4 bus 3 bus 1 bus 2

10. Loss of Measurement Contingency

11. Loss of Measurement Contingency (Cont.)

12. Line Outage Contingency

13. Line Outage Contingency (Cont.)

14. Measurement Limitations

15. Experimental Setup • The standard IEEE 14, IEEE 30, IEEE 39, IEEE 57 and IEEE 118 are investigated. • CPLEX solver is used to solve the ILP.

16. Experimental Results

17. Comparing to other works (Cont.)

18. Conclusions • A fast and practical model based on integer linear programming is proposed for solving the optimal PMU placement problem. • Different contingency conditions associated with power systems, i.e., line outages and loss of measurements were considered. • Communication constraints of power networks were considered as measurement limitations and included in the model.

19. Thanks • Questions?