Contingency-Constrained PMUPlacement 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 1bus 2

bus 3bus 4

bus 5 bus 8bus 7

bus 9bus 11bus 6

bus 14bus 13bus 12

bus 10

ILP Notation

Traditional ILP Formulation

bus 1bus 2

bus 3bus 4

bus 5bus 8bus 7

bus 9bus 11bus 6

bus 14

bus 13bus 12

bus 10

a12 =1

New Constraints in This Work

• Effect of Zero-Injection Buses• Loss of Measurement Contingency• Line Outage Contingency• Measurement Limitations

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

Zero-Injection Buses

Zero-Injection Buses (Cont.)

bus 1bus 2

bus 3bus 4

bus 5bus 8bus 7

bus 9bus 11bus 6

bus 14

bus 13bus 12

bus 10

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 ResultsTest System Base case

systemNo PMU at Zero-Injection

Line Outage Loss of Measurement

Line Outage or Loss of Measurement

IEEE 14-Bus 3 3 7 7 8

IEEE 30-Bus 7 7 13 15 17

IEEE 39-Bus 8 8 15 18 22

IEEE 57-Bus 11 11 19 26 26

IEEE 118-Bus 28 28 53 63 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.

Thanks

• Questions?