Abstract
In the past decade there have been multiple high-profile cases of cascading blackouts, often resulting in the disconnection of tens of millions of consumers in large areas. It appears that in hindsight many of these disturbances could have been prevented by timely interventive action. In the actual cases, however, lack of complete knowledge about the state of the system undergoing a blackout event has prevented such action. This chapter reviews approaches to the problem of finding optimal interventions for a power system in the early stages of a cascading blackout. Conceptually the problem is one of optimization under uncertainty or robust optimization: the goal is to find a set of corrective actions that will guarantee power supply to as many customers as possible, in all, or at least most, of the possible states that the system may be in. To tackle the problem directly as a stochastic or robust optimization problem is intractable due to the complexities involved, foremost the number of possible states that would have to be considered. We argue, guided by example, that a robust response is to disconnect lines in such a manner as to create an island containing the affected part of the network. We give an overview of such approaches, notably those involving mixed-integer programming to directly design islands that admit a stable steady-state operating point.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The value of \({V }^{\text{min}}\) is somewhat arbitrary, and any other value (notably \(\hat{v} = 1\)) could be used for the auxiliary variables \(\hat{v}_{Ib}\) for disconnected lines. It is important that both ends of the disconnected line are set to the same value, so that the expressions in (9.12) cancel for θ l  = 0. Using \({V }^{\text{min}}\) allows (9.13a) to be modelled with a single set of inequalities each.
References
Agematsu S, Imai S, Tsukiu R, Watanabe H, Nakamura T, Matsushima T (2001) Islanding protection system with active and reactive power balancing control for Tokyo metropolitan power system and actual operational experience. In: Proceedings of the 7th IEE international conference developments in power systems protection 2001. IEEE Computer Society, London, pp 351–354
Ahmed SS, Sarker NC, Khairuddin AB, Ghani MRBA, Ahmed H (2003) A scheme for controlled islanding to prevent subsequent blackout. IEEE Trans Power Syst 18(18):136–143
Andersson G, Donalek P, Farmer R, Hatziargyriou N, Kamwa I, Kundur P, Martins N, Paserba J, Pourbeik P, Sanchez-Gasca J, Schulz R, Stankovic A, Taylor C, Vittal V (2005) Causes of the 2003 major grid blackouts in North America and Europe, and recommended means to improve system dynamic performance. IEEE Trans Power Syst 20(4):1922–1928
Archer BA, Davis JB (2002) System islanding considerations for improving power system restoration at Manitoba Hydro. In: Proceedings of the 2002 Canadian conference on electrical and computer engineering. IEEE Computer Society, London, pp 60–65
Avramovic B, Kokotovic PK, Winkelman JR, Chow JH (1980) Area decomposition for electromechanical models of power systems. Automatica 16:637–648
Belotti P, Lee J, Liberti L, Margot F, Wächter A (2009) Branching and bounds tightening techniques for non-convex MINLP. Optim Methods Software 24(4–5):597–634
Bialek JW (2003) Are blackouts contagious? IEE Power Eng 17(6):10
Bialek JW (2004) Recent blackouts in us and continental Europe: is liberalisation to blame? Technical report CWPE 0407, University of Cambridge, Department of Applied Economics
Bialek JW (2005) Blackouts in the US/Canada and continental Europe in 2003: is liberalisation to blame? In: IEEE powertech conference, Russia, June 2005
Bienstock D, Mattia S (2007) Using mixed-integer programming to solve power grid blackout problems. Discrete Optim 4:115–141
Bonami P, Biegler LT, Conn AR, Cornuejols G, Grossmann IE, Laird CD, Lee J, Lodi A, Margot F, Sawaya N, Wächter A (2005) An algorithmic framework for convex mixed integer nonlinear programs. Technical research report RC23771, IBM, Oct 2005
Fan N, Izraelevitz D, Pan F, Pardalos PM, Wang J (2012) A mixed integer programming approach for optimal power grid intentional islanding. Energy Syst 3:77–93
Final Report of the Investigation Committee on the 28 September 2003 Blackout in Italy (2004) Final report, Union for the Coordination of the Transmission of Electricity (UCTE), April 2004
Final Report System Disturbance on 4 November 2006 (2007) Final report, Union for the Coordination of the Transmission of Electricity (UCTE)
Fisher EB, O’Neill RP, Ferris MC (2008) Optimal transmission switching. IEEE Trans Power Syst 23(3):1346–1355
Hamada IA, Israelsa B, Rikvolda PA, Porosevab SV (2010) Spectral matrix methods for partitioning power grids: applications to the italian and floridian high-voltage networks. Phys Procedia 4:125–129
Hiskens IA, Davy RJ (2001) Exploring the power flow solution space boundary. IEEE Trans Power Syst 16:389–395
Jin M, Sidhu TS, Sun K (2007) A new system splitting scheme based on the unified stability control framework. IEEE Trans Power Syst 22(1):433–441
Larsson S, Danell A (2006) The black-out in southern Sweden and eastern Denmark, September 23, 2003. In: IEEE power systems conference and exposition, Atlanta
Li H, Rosenwald GW, Jung J, Liu C (2005) Strategic power infrastructure defence. IEEE Proc 93:918–933
Liu Y, Liu Y (2006) Aspects on power systems islanding for preventing widespread blackout. In: Proceedings of the 2006 IEEE international conference on networking, sensing and control, ICNSC’06. IEEE, Ft. Lauderdale, pp 1090–1095
Müller N, Quintana VH (1992) A sparse eigenvalue-based approach for partitioning power networks. IEEE Trans Power Syst 7:520–527
Newman DE, Carreras BA, Kirchner M, Dobson I (2011) The impact of distributed generation on power transmission grid dynamics. In: 44th Hawaii international conference on system science, Hawaii
Peiravi A, Ildarabadi R (2009) A fast algorithm for intentional islanding of power systems using the multilevel kernel k-means approach. J Appl Sci 9:2247–2255
Quintana VH, Müller N (1991) Partitioning of power networks and applications to security control. In: IEE Proc Generation, Transmission and Distribution, Part C 138:535–545
Rajamani K, Hambarde UK (1999) Islanding and load shedding schemes for captive power plants. IEEE Trans Power Delivery 14:805–809
Report on the blackout in Italy on 28 September 2003 (2003) Technical report, Swiss Federal Office of Energy (SFOE), November 2003
Sun K, Zheng D-Z, Lu Q (2003) Splitting strategies for islanding operation of large-scale power systems using OBDD-based methods. IEEE Trans Power Syst 18:912–923
Trodden PA, Bukhsh WA, Grothey A, McKinnon KIM (2013) MILP formulation for controlled islanding of power networks. Int J Electr Power Energy Syst 45:501–508
Trodden PA, Bukhsh WA, Grothey A, McKinnon KIM (2013) Optimization-based islanding of power networks using piecewise linear AC power flow. Technical report ERGO 13-011, Edinburgh Research Group in Optimization, School of Mathematics, University of Edinburgh, April 2013
US-Canada Power System Outage Task Force (2004) Final report on the August 14, 2003 blackout in the United States and Canada: causes and recommendations. Final report, April 2004
Wang X, Vittal V (2004) System islanding using minimal cutsets with minimum net flow. In: IEEE power systems conference and exposition, New York
Wang CG, Zhang BH, Li P, Shu J, Cheng LY, Hao ZG, Bo ZQ, Klimek A (2008) Power systems islanding based on multilevel reduced graph partitioning algorithm. In: Proceedings of the 43rd international universities power engineering conference, vol 25, pp 1–6
Wang CG, Zhang BH, Hao ZG, Shu J, Li P, Bo ZQ (2010) A novel real-time searching method for power system splitting boundary. IEEE Trans Power Syst 25(4):1902–1909
Xu G, Vittal, V (2010) Slow coherency based cutset determination algorithm for large power systems. IEEE Trans Power Syst 25(2):877–884
Yang B, Vittal V, Heydt GT (2006) Slow-coherency-based controlled islanding—a demonstration of the approach on the August 14, 2003 blackout scenario. IEEE Trans Power Syst 21:1840–1847
You H, Vittal V, Wang X (2004) Slow coherency-based islanding. IEEE Trans Power Syst 19(1):483–491
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Grothey, A., Bukhsh, W., McKinnon, K.I.M., Trodden, P.A. (2013). Controlled Islanding as Robust Operator Response Under Uncertainty. In: Kovacevic, R., Pflug, G., Vespucci, M. (eds) Handbook of Risk Management in Energy Production and Trading. International Series in Operations Research & Management Science, vol 199. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9035-7_9
Download citation
DOI: https://doi.org/10.1007/978-1-4614-9035-7_9
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-9034-0
Online ISBN: 978-1-4614-9035-7
eBook Packages: Business and EconomicsBusiness and Management (R0)