Contingency-Constrained PMU
Placement in Power Networks
Farrokh Aminifar, Amin Khodaei, Mahmud Fotuhi-Firuzabad,
and Mohammad Shahidehpour

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

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

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 6 bus 5 bus 11 bus 10 bus 4 bus 1 bus 2 bus 9 bus 7 bus 3 bus 8

ILP Notation

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

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

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

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

Loss of Measurement Contingency

Loss of Measurement Contingency (Cont.)

Line Outage Contingency

Line Outage Contingency (Cont.)

Measurement Limitations

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.

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

Comparing to other works (Cont.)

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.

• Questions?
Thanks