A Goal Programming Approach for Optimal PMU Placement

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


This article proposes a multi-objective goal programming based approach with two objectives of maximizing the reliability and minimizing the placement cost of Phasor Measurement Units (PMUs) for full observability in power systems. The weighted sum goal programming formulation incorporates the reliability of individual PMUs and finds a placement to resolve the conflicting objectives of minimum number of PMUs cost-wise and maximum level of system-wide reliability. This multi-objective problem is formulated as a nonlinear goal programming model in which weights are associated with the objectives. The model is solved for several weight scenarios for the IEEE 14, 30, 57 and 118 bus test systems. The benefit of the proposed model has been demonstrated by comparing the results with the traditional optimal cost-wise only PMU placement and existing reliability based placement models.  The system reliability is improved by ~45% compared to optimal PMU placement models. Also, the number of PMUs is reduced by ~40% compared to reliability based placement models with the proposed goal programming approach.
Copyright © 2013 Praise Worthy Prize - All rights reserved.


Phasor Measurement Units; Power System Observability; Goal Programming; Multi-Objective Optimization; Nonlinear Programming; Reliability Modeling

Full Text:



A.G. Phadke, J.S. Thorp, Synchronized Phasor Measurements and Their Applications New York: Springer, 2008.

D. Novosel, V. Madani, B. Bhargava, K. Vu, J. Cole, Dawn of the Grid Synchronization, IEEE Power and Energy Magazine 2008; 6(1): 49-60.

D. Dua, S. Dhambhare, R.K. Gajbhiye, S.A. Soman, Optimal multistage scheduling of PMU placement: An ILP approach, IEEE Trans. Power Delivery 2008; 23(4): 1812-2388.

X. Dongjie, H. Renmu, W. Peng, X. Tao, Comparison of several PMU placement algorithms for state estimation, In Proc. Inst. Elect. Eng. Int. Conf. Develop. Power Syst. Protection 2004; 32–35.

G.B. Denegri, M. Invernizzi, F. Milano, A security oriented approach to PMU positioning for advanced monitoring of a transmission grid, in Proc. IEEE Int. Conf. Power Syst 2002; 2: 798–803.

A.G. Phadke, R.M. de Moraes, The wide world of wide-area measurement, IEEE Power Energy 2008; 6(5): 52–65.

N. M. Manousakis, G. N. Korres, P. S. Georgilakis, Taxonomy of PMU Placement Methodologies, IEEE Trans. Power Systems 2012; 27(2): 1070-1077.

T. L. Baldwin, L. Mili, M. B. Boisen, R. Adapa, Power system observability with minimal phasor measurement placement, IEEE Trans. Power Systems 1993; 8(2): 707-715.

B. Xu, A. Abur, Observability analysis and measurement placement for systems with PMUs, IEEE Power Systems Conf. Expo 2004; 2: 943-946.

B. Gou, Generalized integer linear programming formulation for optimal PMU placement, IEEE Trans. Power Systems 2008; 23(3): 1099-1104.

D. J. Brueni, L.S. Heath, The PMU placement problem, SIAM J. Discrete Math 2005; 19(3): 744-761.

S. Chakrabarti, E. Kyriakides, Optimal placement of phasor measurement units for power system observability, IEEE Trans. Power Systems 2008; 23(3): 1433-1440.

R. Kavasseri, S.K. Srinivasan, Joint optimal placement of PMU and conventional measurements in power systems, Circuits and Systems (ISCAS), Proceedings of IEEE International Symposium 2010; 3449-3452.

R.F. Nuqui, A. G. Phadke, Phasor Measurement unit placement techniques for complete and incomplete observability, IEEE Trans. PowerDel., 2005; 20(4): 2381-2388.

Alinejad-Beromi, Y., Ahmadi, A., Soleymanpour, H.R., Optimal PMU placement considering contingencies by using a hybrid discrete particle swarm optimization technique, (2011) International Review of Electrical Engineering (IREE), 6 (4), pp. 1927-1938.

V. H. Khiabani, O. P. Yadav, R. Kavasseri, Reliability-based placement of Phasor measurement Unit in Power Systems, Proc. Institution of Mechanical Engineers (IMechE), Part O: Journal of Risk and Reliability 2012; 226(1): 109-117.

Khiabani, V., Kavasseri, R., Farahmand, K., A reliability based multi-objective formulation for optimal PMU placement, (2012) International Review on Modelling and Simulations (IREMOS), 5 (4), pp. 1640-1644.

R. Kavasseri, S.K. Srinivasan, Joint placement of Phasor and Flow Measurements for Observability of Power Systems, IEEE Trans. Power Systems 2011; 8(2): 707-715.


  • There are currently no refbacks.

Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize