Modified branch‐and‐bound algorithm for unravelling optimal PMU placement problem for power grid observability: : A comparative analysis
Pages 450 - 470
Abstract
Safe operation of the power grid requires a complete and robust control network to ensure full observability. However, redundancy measurements can create problems in expense, management, and control. The optimal phasor measurement unit (PMU) positioning problem (OPPP) is proposed to limit the number of PMUs deployed in the power grid and ensure the whole grid's observability in the meantime. A modified branch‐and‐bound algorithm (MBBA) to unravel the OPPP is presented. Original BBA, which uses a single search order to create a binary tree, gives only one solution to the OPPP, although more than one optimal solution exists. The proposed MBBA method consists of two different stages: the vertexes in the search tree are investigated by depth‐first search (DFS) in stage 1, and the search route continues as the breadth‐first search. In stage 1, the LP relaxing problems are solved by dual simplex, and in stage 2, the basic viable solution from stage 1 is used to configure the primary simplex until the optimum solution is found. OPPP is formulated as a binary decision variable MBBA model, minimizing linear objective function subject to linear matrix observability constraints. The MBBA model is unravelled using a linear integer‐based external approximation scheme. IEEE test systems are used to check the feasibility of the proposed approach. Matlab software performs simulation based on a number of graph theory‐based methods such as DFS, graph‐theoretical method, simulated annealing, and recursive N‐algorithms. These algorithms are compared to the algorithmic perspective of the proposed MBBA method. IEEE test network results confirm the validity of the proposed methodology.
References
[1]
Phadke, A.G., et al.: State estimation with phasor measurements. IEEE Power Eng. Rev., PER‐6(2), 48 (1986)
[2]
Arghira, N., et al.: Modern SCADA philosophy in power system. Univ. Polytech. Buchar. Sci. Bull. Ser. C: Electr. Eng. Comput. Sci., 73(2), 153–166 (2011)
[3]
Donolo, M.A.: Advantages of synchrophasor measurements over SCADA measurements for power system state estimation, Schweitzer Engineering Laboratories, Inc., Hopkins (2006)
[4]
Almutairi, A.M., Milanovic, J.V.: Comparison of different methods for optimal placement of PMUs. Proceedings of the IEEE Bucharest PowerTech, Bucharest (2009)
[5]
Heydt, G.T, et al.: Solution for the crisis in electric power supply, IEEE Comput. Appl. Power. 14(3), 22–30 (2001)
[6]
Cho, K.‐S., et al.: Optimal placement of phasor measurement units with GPS receiver. Proceedings of the IEEE Power Engineering Society Winter Meeting, Columbus (2001)
[7]
Phadke, A.G., Thorp, J.S.: Synchronized Phasor Measurements and Their Applications, . Springer, Blacksburg (2008) https://www.springer.com/gp/book/9781441945631
[8]
Othman, A.K.A., Irving, M.R.: A comparative study of two methods for uncertainty analysis in power system state estimation. IEEE Trans. Power Syst., 20(2), 1181–1182 (2005)
[9]
Othman, A.K.A., Irving, M.R.: Uncertainty modeling in power system state estimation. IET Gener. Transm. Distrib., 152(2), 233–239 (2005)
[10]
Schweitzer, E.O., Whitehead, D.E.: Real‐world synchrophasor solutions. Proceedings of the 62nd Annual Conference for Protective Relay Engineers, Austin (2009)
[11]
Maji, T.K., Acharjee, P.: Multiple solutions of optimal PMU placement using exponential binary PSO algorithm. Proceedings of the Annual IEEE India Conference (INDICON), New Delhi (2015)
[12]
Rahman, N.H.A.: Optimal allocation of phasor measurement units using practical constraints in power systems (PhD thesis). Brunel University London, Uxbridge, UK (2017) https://bura.brunel.ac.uk/handle/2438/14143
[13]
Manousakis, N.M., et al.: Taxonomy of PMU placement methodologies. IEEE Trans. Power Syst. 27(2), 1070–1077 (2012)
[14]
Nazari‐Heris, M., Mohammadi‐Ivatloo B.: Application of heuristic algorithms to optimal PMU placement in electric power systems: an updated review. Renew. Sustain. Energy Rev., 50, 214–228 (2015)
[15]
Zapata, H., et al.: A hybrid swarm algorithm for collective construction of 3D structures. Int. J. Artif. Intell. 18(1), 1–18 (2020)
[16]
Precup, R.‐E., David, R.‐C.: Nature‐Inspired Optimization Algorithms for Fuzzy Controlled Servo Systems. Butterworth‐Heinemann; Elsevier (Politehnica University of Timisoara, Romania 2020) https://www.elsevier.com/books/nature‐inspired‐optimization‐algorithms‐for‐fuzzy‐controlled‐servo‐systems/precup/978‐0‐12‐816358‐0
[17]
Precup, R.‐E., et al.: Grey wolf optimizer‐based approach to the tuning of Pi‐fuzzy controllers with a reduced process parametric sensitivity. IFAC‐PapersOnLine. 49(5), 55–60 (2016)
[18]
Gee, S.B., et al.: Solving multiobjective optimization problems in unknown dynamic environments: an inverse modeling approach. IEEE Trans. Cybern., 47(12), 4223–4234 (2017)
[19]
Abed‐alguni, B.H.: Island‐based cuckoo search with highly disruptive polynomial mutation. Int. J. Artif. Intell. 17(1) (2019)
[20]
Babu, R., Bhattacharyya, B.: Strategic placements of PMUs for power network observability considering redundancy measurement. Measurement. 134, 606–623 (2019)
[21]
Zhou, X., et al.: Optimal placement of PMUs using adaptive genetic algorithm considering measurement redundancy. Int. J. Rel. Qual. Saf. Eng. 23(3), 1640001 (2016)
[22]
Wang, Z., et al.: Differential evolution‐based optimal placement of phase. Int. J. Model. Simul. Sci. Comput. 6(1), 1550016‐1–1550016‐11 (2015)
[23]
Khiabani, V., et al.: Reliability‐based placement of phasor measurement units in power systems. Proc. IMechE. 226(1), 109–117 (2012)
[24]
Karimi, E., et al.: How optimal PMU placement can mitigate cascading. Int. Trans. Electr. Energy Syst. 29(6), 1–19 (2019)
[25]
Theodorakatos, N.P.: Fault location observability using phasor measurement units in a power network through deterministic and stochastic algorithms. Electr. Power Compon. Syst. 47(3), 1–18 (2019)
[26]
Abdelsalam, A.A., Abdelaziz, A.Y.: Minimizing the cost of wide area monitoring systems by optimal allocation of PMUs and their communication infrastructure. Arab. J. Sci. Eng. 45, 6453–6466 (2020)
[27]
Zhu, X., et al.: Optimal PMU‐communication link placement for smart grid wide‐area measurement systems. IEEE Trans. Smart Grid. 10(4), 4446–4456 (2019)
[28]
Babu, R., Bhattacharyya, B.: Weak bus‐oriented installation of phasor measurement unit for power network observability. Int. J. Emerg. Electr. Power Syst. 18(5), 1–14 (2017)
[29]
Babu, R., et al.: Weak bus‐constrained PMU placement for complete observability of a connected power network considering voltage stability indices. Prot. Control Mod. Power Syst. 5,1, 1–14 (2020)
[30]
Lakshminarayana, P., Venkatesan, M.: A multi‐constrained binary ILP method for optimal allocation of PMUs in network. SN Appl. Sci., 2, 1–10 (2020)
[31]
Theodorakatos, N.P.: Optimal phasor measurement unit placement for numerical observability using branch‐and‐bound and a binary‐coded genetic algorithm. Electr. Power Compon. Syst. 47, (4–5), 357–371 (2019)
[32]
Guo, X.‐C., et al.: Enhanced optimal PMU placements with limited observability propagations. IEEE Access. 8, 22515–22524 (2020)
[33]
Lu, C., et al.: An optimal PMU placement with reliable zero injection observation. IEEE Access. 6, 54417–54426 (2018)
[34]
Babu, R., Bhattacharyya, B.: An approach for optimal placement of phasor measurement unit for power network observability considering various contingencies. Iran. J. Sci. Technol. Trans. Electr. Eng. 42(2), 161–183 (2018)
[35]
Razavi, S.‐E., et al.: An effective approach for the probabilistic and deterministic multistage PMU placement using Cuckoo search: Iran's national power system, Iran. J. Sci. Technol. Trans. Electr. Eng. 44, 237–252 (2020)
[36]
Almunif, A., Fan, L.: Optimal PMU placement for modeling power grid observability with mathematical programming methods. Int. Trans. Electr. Energy Syst. 30(2), 1–13 (2019)
[37]
Zargar, S.F., et al.: Probabilistic multi‐objective state estimation‐based PMU placement in the presence of bad data and missing measurements. IET Gener. Transm. Distrib. 14(15), 3042–3051 (2020)
[38]
Manousakis, N.M., Korres, G.N.: Optimal allocation of phasor measurement units considering various contingencies and measurement redundancy. IEEE Trans. Instrum. Meas. 69(6), 3403– 3411 (2020)
[39]
Wang, S., et al.: Risk‐oriented PMU placement approach in electric power systems. IET Gener. Transm. Distrib. 14(2), 301–307 (2020)
[40]
Jamei, M., et al.: Phasor measurement units optimal placement and performance limits for fault localization. IEEE J. Select. Areas Commun., 38(1), 180–192 (2020)
[41]
Chen, X., et al.: PMU placement for measurement redundancy distribution considering zero injection bus and contingencies. IEEE Syst. J., 14(4), 5396–5406 (2020)
[42]
Xu, P.: https://github.com/xupei0610/OPP. Accessed 20 Oct 2020
[43]
Xu, P.: Power System Observability And Optimal Phasor Measurement Unit Placement. Department of Electrical and Computer Engineering, College of Science and Engineering, University of Minnesota – Twin Cities, Minnesota, USA (2015) https://github.com/xupei0610/OPP/blob/master/%5BEE8725%5D%5BProject%20Report%5D%20Power%20System%20Observability%20and%20Optimal%20Phasor%20Measurement%20Unit%20Placement%20‐%20Pei%20Xu%2C%205186611.pdf. Accessed 12 October 2020
[44]
Abur, A., Expósito, A.G.: Power system State Estimation: Theory And Implementation. Marcel Dekke, New York (2004) https://www.routledge.com/Power‐System‐State‐Estimation‐Theory‐and‐Implementation/Abur‐Exposito/p/book/9780824755706
[45]
Baldwin, T.L., et al.: Power system observability with minimal phasor measurement placement. IEEE Trans. Power Syst., 8, 707–715 (1993)
[46]
Babu, R., Bhattacharyya, B.: Optimal allocation of phasor measurement unit for full observability of the connected power network. Int. J. Electr. Power Energy Syst., 79, 89–97 (2016)
[47]
Mohammadi‐Ivatloo, B.: Optimal placement of PMUs for power system observability using topology based formulated algorithms. J. Appl. Sci., 9, 2463–2468 (2009)
[48]
Dua, D., et al.: Optimal multistage scheduling of PMU placement: an ILP approach. IEEE Trans. Power Deliv., 23, 1812–1820 (2008)
[49]
Mazlumi, K., et al.: Optimal multistage scheduling of PMU placement for power system observability, Int. J. Tech. Phys. Probl. Eng., 4(13), 119–124 (2012)
[50]
Chakrabarti, S., Kyriakides, E.: Optimal placement of phasor measurement units for state estimation. Proceedings of the IASTED International Conference on Power Energy Systems (EuroPES), Palma de Mallorca, Spain (2007)
[51]
Chakrabarti, S., Kyriakides, E.: Optimal placement of phasor measurement units for power system observability. IEEE Trans. Power Syst., 23(3), pp. 1433–1440 (2008)
[52]
Kozen, D.C.: Depth‐first and breadth‐first search. In: The Design and Analysis of Algorithms. Texts and Monographs in Computer Science, pp. 19–24.Springer, New York (1992)
[53]
Babu, R., Bhattacharyya, B.: Phasor measurement unit allocation with different soft computing technique inconnected power network. Proceedings of the Michael Faraday IET International Summit 2015, Kolkata (2015)
[54]
Van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated Annealing: Theory and Applications. Springer‐Science+ Business Media, B. V., Eindhoven, The Netherlands (1992) https://www.springer.com/gp/book/9789027725134
[55]
Russell, S.J., Norvig, P.: Artificial Intelligence: Modern Approach (4th ed.). Pearson, Hoboken; New Zealand (2020) http://aima.cs.berkeley.edu/
[56]
Gopakumar, P., et al.: Pragmatic multi‐stage simulated annealing for optimal placement of synchrophasor measurement units in smart power grids. Front. Energy. 9, 148–161 (2015)
[57]
Gopakumar, P., et al.: Novel multi‐stage simulated annealing for optimal placement of PMUs in conjunction with conventional measurements. Proceedings of the 12th International Conference on Environment and Electrical Engineering, Wroclaw, Poland, 5–8 May (2013)
[58]
Prasad, S., Kumar, D.M.V.: Trade‐offs in PMU and IED deployment for active distribution state estimation using multi‐objective evolutionary algorithm, IEEE Trans. Instrum. Meas., 67(6), 1298–1307 (2018)
[59]
Kerdchuen, T., Ongsakul, W.: Optimal measurement placement for power system state estimation using hybrid genetic algorithm and simulated annealing. Proceedings of the IEEE International Conference on Power System Technology, Chongqing, China, 22–26 October (2006)
[60]
Girish, V., et al.: Heuristic based optimal PMU routing in KPTCL power grid. Int. J. Electr. Eng. Technol., 7(1), 1–16 (2016)
[61]
Denegri, G.B., et al.: A security oriented approach to PMU positioning for advanced monitoring of a transmission grid. Proceedings of the international conference on power system technology, Kunming, China, 13–17 October (2002)
[62]
Babu, R., Bhattacharyya, B.: Optimal placement of PMU for complete observability of the interconnected power network considering zero‐injection bus: a numerical approach. Int. J. Appl. Power Eng. 9(2), 135–146 (2020)
[63]
TOMLAB : The TOMLAB optimization environment, TOMLAB®. https://tomopt.com/tomlab/
[64]
Wolsey, L.A., Nemhauser, G.L.: Integer and Combinatorial Optimization. John Willey and Sons, New York (1999). https://www.wiley.com/en‐in/Integer+and+Combinatorial+Optimization‐p‐9780471359432
[65]
Arora, R.K.: Optimization: Algorithms and Application. Taylor & Francis Group, New York (2015). https://www.routledge.com/Optimization‐Algorithms‐and‐Applications/Arora/p/book/9781498721127
[66]
Karlof, J.K.: Integer Programming: Theory and Practice, 1st ed. CRC Press,Boca Raton, FL (2005). https://www.routledge.com/Integer‐Programming‐Theory‐and‐Practice/Karlof/p/book/9780367392116
[67]
Chen, D.S., et al.: Applied Integer Linear Programming: Modelling and Solution. John Willey and Sons, New York (2010). https://www.wiley.com/en‐us/Applied+Integer+Programming%3A+Modeling+and+Solution‐p‐9780470373064
[68]
Floudas, C.: Nonlinear and Mixed‐Integer Optimization: Fundamentals and Applications. Oxford University Press, New York (1995). https://oxford.universitypressscholarship.com/view/10.1093/oso/9780195100563.001.0001/isbn‐9780195100563
[69]
Cormen, T.H., et al.: Introduction to Algorithms. MIT Press, Cambridge (2009). https://mitpress.mit.edu/books/introduction‐algorithms‐third‐edition
[70]
Chong, E.K., Zak, S.H.: An introduction to Optimization. John Willey and Sons, New York (2001). https://www.wiley.com/en‐in/An+Introduction+to+Optimization%2C+4th+Edition‐p‐9781118279014
[71]
Babu, R.: https://github.com/rohitbabu1986/OPPP. Accessed 01 Feb 2021
[72]
Arora, J.: Introduction to Optimum Design. 4th ed. Elsevier, University of Iowa, Iowa City, IA (2016). https://www.elsevier.com/books/introduction‐to‐optimum‐design/arora/978‐0‐12‐800806‐5
Recommendations
Solving the multistage PMU placement problem by integer programming and equivalent network design model
Recently, phasor measurement units (PMUs) are becoming widely used to measure the electrical waves on a power grid to determine the health of the system. Because of high expense for PMUs, it is important to place minimized number of PMUs on power grids ...
A New Dantzig-Wolfe Reformulation and Branch-and-Price Algorithm for the Capacitated Lot-Sizing Problem with Setup Times
Although the textbook Dantzig-Wolfe decomposition reformulation for the capacitated lot-sizing problem, as already proposed by Manne [Manne, A. S. 1958. Programming of economic lot sizes. Management Sci.4(2) 115--135], provides a strong lower bound, it ...
Branch-And-Price: Column Generation for Solving Huge Integer Programs
We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound ...
Comments
Information & Contributors
Information
Published In
© 2021 The Authors. CAAI Transactions on Intelligence Technology published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology and Chongqing University of Technology.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Publisher
John Wiley & Sons, Inc.
United States
Publication History
Published: 14 April 2021
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 04 Oct 2024
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in