1. Contingency-Constrained PMU Placement in Power Networks
Farrokh Aminifar, Amin Khodaei, 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.
The most common time reference is
the GPS signal which has an accuracy of less than 1 [2].
In this way, the ac quantities are measured, converted to phasors
(i.e., complex numbers represented by magnitude and phase
angle), and time stamped [3]. Phasors at different nodes, which
refer to the same time space coordinates, can improve the performance
of monitored control systems in various fields of modern
power systems.

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
auxiliary binary variables
added to zero-injection buses

9. Zero-Injection Buses (Cont.)

10. Loss of Measurement Contingency
indicates that all buses will remain observable
when a singlePMUis lost. Here, when bus is
not observable by considering zero-injection buses. Accordingly,
which indicates that bus would need a minimum of
two observability sources

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 Test System Base case system No PMU at
Zero-Injection
Line Outage
Loss of
Measurement
Line Outage or Loss
of Measurement
IEEE 14-Bus 3 7 8
IEEE 30-Bus 13 15 17
IEEE 39-Bus 18 22
IEEE 57-Bus 11 19 26
IEEE 118-Bus 28 53 63 65

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?