Optimal Placement of Phasor Measurement Units Using Gravitational Search Method
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:69262", author = "Satyendra Pratap Singh and S. P. Singh", title = "Optimal Placement of Phasor Measurement Units Using Gravitational Search Method", 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.", volume = "9", number = "3", pages = "307-5", }
