Optimal Placement of Phasor Measurement Units Using Gravitational Search Method

Authors: Satyendra Pratap Singh, S. P. Singh

Abstract:

This paper presents a methodology using Gravitational Search Algorithm for optimal placement of Phasor Measurement Units (PMUs) in order to achieve complete observability of the power system. The objective of proposed algorithm is to minimize the total number of PMUs at the power system buses, which in turn minimize installation cost of the PMUs. In this algorithm, the searcher agents are collection of masses which interact with each other using Newton’s laws of gravity and motion. This new Gravitational Search Algorithm based method has been applied to the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems. Case studies reveal optimal number of PMUs with better observability by proposed method.

Keywords: Gravitational Search Algorithm (GSA), Law of Motion, Law of Gravity, Observability, Phasor Measurement Unit.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1099694

References:

[1] V. Terzija, G. Valverde, D. Cai, P. Regulski, V. Madani, J. Fitch, S. Skok, M. M. Begovic, and A. Phadke, “Wide-Area Monitoring, Protection, and Control of Future Electric Power Networks” Proc. of the IEEE, Vol. 99, No. 1, Jan. 2011.
[2] A. G. Phadke, J. S. Thorp, and K. J. Karimi, “State Estimation with Phasor Measurements”, IEEE Transactions on Power Systems, Vol. 1, No. 1, pp. 233- 241, February 1986.
[3] EPRI Final Rep., 1997 “Assessment of Applications and Benefits of Phasor Measurement Technology in Power Systems,” GE Power Syst. Eng.,
[4] A. G. Phadke, “Synchronized phasor measurements in power systems”, IEEE Computer Applications in Power, Vol. 6, Issue 2, pp. 10-15, April 1993.
[5] L. Mili, T. Baldwin and R. Adapa, “Phasor Measurement Placement for Voltage Stability Analysis of Power Systems.” Proceedings of the 29th Conference on Decision and Control, Honolulu, Hawaii, Dec. 1990.
[6] T. L. Baldwin, L. Mili, M. B. Boisen, and R. Adapa, “Power System Observability With Minimal Phasor Measurement Placement”, IEEE Transactions on Power Systems, Vol. 8, No. 2, pp. 707-715, May 1993.
[7] J. Chen and A. Abur, “Placement of PMUs to Enable Bad Data Detection in State Estimation.” IEEE Trans. on Power Systems, Vol. 21, No. 4, pp. 1608-1615, Nov. 2006.
[8] B. Xu, A. Abur, “Observability analysis and measurement placement for systems with PMUs.” Proceedings of 2004 IEEE PES Conference and Exposition, vol.2, pp: 943-946, 10-13 Oct. 2004.
[9] B. Gou, “Optimal placement of PMUs by integer linear programming,” IEEE Trans. Power Syst., vol. 23, no. 3, pp. 1525–1526, Aug. 2008.
[10] B. Gou, “Generalized integer linear programming formulation for optimal PMU placement” IEEE Trans. Power Syst., 23: 1099-1104, Aug. 2008.
[11] S. P. Singh, S. P. Singh, “Optimal PMU Placement in Power System Considering the Measurement Redundancy”, Int. J. of Advances in Electronic and Electric Engineering, vol. 4, no. 6, pp. 593-598, Jan. 2014.
[12] Sadegh Azizi, Ahmad Salehi Dobakhshari, S. ArashNezam Sarmadi, and Ali Mohammad Ranjbar, “Optimal PMU placement by an equivalent linear formulation for exhaustive search”,IEEE Trans. On Smart Grid, Vol. 3, No. 1, pp. 174-182, March 2012.
[13] S. Mehdi Mahaei, M. Tarafdar Hagh, “Minimizing the number of PMUs and their optimal placement in power systems”, Elect. Power Syst. Research, Vol. 83, pp. 66-72, 2012.
[14] B. Milosevic and M. Begovic, “Nondominated Sorting Genetic Algorithm for Optimal Phasor Measurement Placement.” IEEE Trans. On Power Systems, vol. 18, No. 1, pp. 69-75, Feb. 2003.
[15] F. J. Marın, F. Garcıa-Lagos, G. Joya, and F. Sandoval, “Genetic algorithms for optimal placement of phasor measurement units in electric networks,” Electron. Lett., vol. 39, no. 19, pp. 1403–1405, Sep. 2003.
[16] F. Aminifar, C. Lucas, A. Khodaei, and M. Fotuhi, “Optimal placement of phasor measurement units using immunity genetic algorithm,” IEEE Trans. Power Del., vol. 24, no. 3, pp. 1014–1020, Jul. 2009.
[17] J. Peng, Y. Sun, and H. F. Wang, “Optimal PMU placement for full network observability using Tabu search algorithm,” Elect. Power Syst.Res., vol. 28, pp. 223–231, 2006.
[18] N. C. Koutsoukis, N. M. Manousakis, P. S. Georgilakis, G. N. Korres, “Numerical observability method for optimal phasor measurement units placement using recursive Tabu search method”, IET Gener. Transm. Distrib., Vol. 7, Iss. 4, pp. 347–356, 2013.
[19] S. Chakrabarti, and E. Kyriakides, “Optimal Placement of Phasor Measurement Units for Power System Observability” IEEE Trans. Power Syst., vol. 23, no. 3, pp. 1433-1440, Aug. 2008.
[20] R. J. Albuquerque and V. L. Paucar, “Evaluation of the PMUs Measurement ChannelsAvailability for Observability Analysis”, IEEE Trans. On Power Syst., Vol. 28, No. 3, Aug. 2013.
[21] A. Ahmadi, Y. A. Beromi, M. Moradi, “Optimal PMU placement for power system observability using binary particle swarm optimization and considering measurement redundancy”, Expert Systems with Applications,Vol. 38, pp. 7263–7269, 2011.
[22] M. Hajiana, A. M. Ranjbar, T. Amraee, B. Mozafari, “Optimal placement of PMUs to maintain network observability using a modified BPSO algorithm”, Elec. Power & Energy Sys.Vol. 33,pp. 28–34, 2011.
[23] M. Hurtgen and J.-C. Maun, “Optimal PMU placement using iterated local search”, Elec. Power & Energy Sys.Vol. 32,pp. 857–860, 2010.
[24] C. Peng, H. Sun and J. Guo, “Multi-objective optimal PMU placement using a non-dominated sortingdifferential evolution algorithm”, Elec. Power & Energy Sys.Vol. 32, pp. 886–892, 2010.
[25] N. M. Manousakis and G. N. Korres, “A Weighted Least Squares Algorithm for Optimal PMU Placement”, IEEE Trans. On Power Syst., Vol. 28, No. 3, Aug. 2013.
[26] F. Aminifar, M. Fotuhi-Firuzabad, and A. Safdarian, “Optimal PMU Placement Based on Probabilistic Cost/Benefit Analysis” IEEE Trans. Power Syst., vol. 28, no. 1, pp. 566-567, Feb. 2013.
[27] E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, "A gravitational search algorithm", Information Sciences, vol. 179, pp. 2232-2248, 2009.
[28] S. Duman, U. Guvenc, N. Yorukeren, “Gravitational search algorithm for economic dispatch with valve-point effects” IREE. Vol. 5, N. 6, pp. 2890-2995, Dec. 2010.
[29] H. R. Hassanzadeh, M. Rouhani, “A multi-objective gravitational search algorithm” Second ICCI, communication systems and networks conference, pp. 7–12, 2010.
[30] C. Li, J. Zhou, “Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm” Energy Convers Manage, vol. 52, Issue 1, pp. 374–381, Jan. 2011.