Skip to main content
SpringerLink
Log in

Offline preemptive bottom left decreasing height scheduling of power loads in smart grids

  • Original Paper
  • Published:
Energy Systems Aims and scope Submit manuscript

Abstract

We are considering the scheduling of flexible preemptable electric loads in a smart grid so as to minimize peak load when all loads have the same earliest start time and deadline. We show that when this scheduling is done using the bottom left decreasing height heuristic, the ratio of the peak load of the schedule generated by this heuristic and the optimal peak load has the tight bound \(4/3-1/(3D)\), where D is the duration of the scheduling interval. This settles an outstanding conjecture regarding the worst-case performance of this heuristic. Our experiments indicate a reduction in peak load of up to 45% using the bottom left decreasing height heuristic and benchmark data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. Interestingly, Alamdari et al. [2] have demonstrated an instance of preemptive OCOSP in which the duration of all jobs is 1, D is an integer and the optimal schedule has preemptions at non integer times. This instance has a 1% lower peak load requirement than any schedule that preempts only at integer times.

  2. Recall that the definition of a slice only requires that there be no preemption within a slice.

References

  1. U.S. energy information administration (eia): International energy outlook (2014). http://www.eia.gov/forecasts/ieo/pdf/0484(2014).pdf

  2. Alamdari, S., Biedl, T., Chan, T., Grant, E., Jampani, K., Keshav, S., Lubiw, A., Pathak, V.: Strip packing with slicing. http://csclub.uwaterloo.ca/~egrant/Elyot Research Papers/Strip Packing with Slicing.pdf

  3. Alamdari, S., Biedl, T., Chan, T., Grant, E., Jampani, K., Keshav, S., Lubiw, A., Pathak, V.: Smart-grid electricity allocation via strip packing with slicing. In: F. Dehne, R. Solis-Oba, J.R. Sack (eds.) Algorithms and Data Structures, Lecture Notes in Computer Science, vol. 8037, pp. 25–36. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40104-6_3

  4. Baker, B., Coffman Jr., E., Rivest, R.: Orthogonal packings in two dimensions. SIAM J. Comput. 9(4), 846–855 (1980). https://doi.org/10.1137/0209064

    Article  MathSciNet  MATH  Google Scholar 

  5. Bandana, M., Anand, N.: Home energy management system (hems): concept, architecture, infrastructure, challenges and energy management schemes (2019). https://doi.org/10.1007/s12667-019-00364-w

  6. Becker, B., Allerding, F., Reiner, U., Kahl, M., Richter, U., Pathmaperuma, D., Schmeck, H., Leibfried, T.: Decentralized energy-management to control smart-home architectures. In: Müller-Schloer, C., Karl, W., Yehia, S. (eds.) Architecture of Computing Systems - ARCS 2010, pp. 150–161. Springer, Berlin (2010)

    Chapter  Google Scholar 

  7. Burke, E.K., Hellier, R.S.R., Kendall, G., Whitwell, G.: A new placement heuristic for the orthogonal stock-cutting problem. Oper. Res. 52(4), 655–671 (2004). http://www.extenza-eps.com/INF/doi/abs/10.1287/opre.1040.0109

  8. Coffman Jr., E., Garey, M., Johnson, D., Tarjan, R.: Performance bounds for level-oriented two-dimensional packing algorithms. SIAM J. Comput. 9(4), 808–826 (1980). https://doi.org/10.1137/0209062

    Article  MathSciNet  MATH  Google Scholar 

  9. Feng, X., Xu, Y., Zheng, F.: Online Scheduling for Electricity Cost in Smart Grid, pp. 783–793. Springer International Publishing, Cham (2015)

  10. Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17(2), 416–429 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hopper, E., Turton, B.: An empirical investigation of meta-heuristic and heuristic algorithms for a 2d packing problem. Eur. J. Oper. Res. 128(1), 34–57 (2001). https://doi.org/10.1016/S0377-2217(99)00357-4

    Article  MATH  Google Scholar 

  12. Ibars, C., Navarro, M., Giupponi, L.: Distributed demand management in smart grid with a congestion game. pp. 495 – 500 (2010). https://doi.org/10.1109/SMARTGRID.2010.5622091

  13. Koutsopoulos, I., Tassiulas, L.: Control and optimization meet the smart power grid: Scheduling of power demands for optimal energy management. In: Proceedings of the 2Nd International Conference on Energy-Efficient Computing and Networking, e-Energy ’11, pp. 41–50. ACM, New York, NY, USA (2011). https://doi.org/10.1145/2318716.2318723

  14. Krishnan, R.: Meters of tomorrow [in my view]. IEEE Power Energ. Mag. 6(2), 96–94 (2008). https://doi.org/10.1109/MPE.2007.915179

    Article  Google Scholar 

  15. Kugler, M., Reinhart, F., Schlieper, K., Masoodian, M., Rogers, B., Andre, E., Rist, T.: Architecture of a ubiquitous smart energy management system for residential homes. pp. 101–104 (2011). https://doi.org/10.1145/2000756.2000770

  16. Liu, F., Liu, H.H., Wong, P.W.H.: Optimal nonpreemptive scheduling in a smart grid model. (2016). arxiv:1602.06659

  17. Luh, P., Ho, Y., Muralidharan, R.: Load adaptive pricing: an emerging tool for electric utilities. IEEE Trans. Autom. Control 27(2), 320–329 (1982)

    Article  MATH  Google Scholar 

  18. Masters, G.: Renewable and Efficient Electric Power Systems. Wiley, Amsterdam (2013). https://books.google.com/books?id=6HPCBwAAQBAJ

  19. Michael A. C., Chitru, S. F., Paul, R. K.: The theory of peak-load pricing: a survey. In: Journal of Regulatory Economics, p. 215–248 (1995)

  20. Mohsenian-Rad, A., Wong, V.W.S., Jatskevich, J., Schober, R., Leon-Garcia, A.: Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid. IEEE Trans. Smart Grid 1(3), 320–331 (2010)

    Article  Google Scholar 

  21. Mumford-Valenzuela, C.L., Vick, J., Wang, P.Y.: Metaheuristics. chap. Heuristics for Large Strip Packing Problems with Guillotine Patterns: An Empirical Study, pp. 501–522. Kluwer Academic Publishers, Norwell (2004)

  22. Ntene, N., Van Vuuren, J.H.: A survey and comparison of guillotine heuristics for the 2d oriented offline strip packing problem. Discret. Optim. 6(2), 174–188 (2009). https://doi.org/10.1016/j.disopt.2008.11.002

    Article  MathSciNet  MATH  Google Scholar 

  23. Ranjan, A., Khargonekar, P., Sahni, S.: Offline preemptive scheduling of power demands to minimize peak power in smart grids. In: 2014 IEEE Symposium on Computers and Communications (ISCC), pp. 1–6 (2014). https://doi.org/10.1109/ISCC.2014.6912525

  24. Ranjan, A., Khargonekar, P., Sahni, S.: Offline first fit scheduling in smart grids. In: 2015 IEEE Symposium on Computers and Communication (ISCC), pp. 758–763 (2015). https://doi.org/10.1109/ISCC.2015.7405605

  25. Ranjan, A., Khargonekar, P., Sahni, S.: Smart grid power scheduling via bottom left decreasing height packing. In: 2016 IEEE Symposium on Computers and Communication (ISCC), pp. 1128–1133 (2016). https://doi.org/10.1109/ISCC.2016.7543888

  26. Samadi, P., Mohsenian-Rad, H., Schober, R., Wong, V.W.S.: Advanced demand side management for the future smart grid using mechanism design. IEEE Trans. Smart Grid 3(3), 1170–1180 (2012)

    Article  Google Scholar 

  27. Sanchez-Martin, P., Sanchez, G.: Optimal electric vehicles consumption management at parking garages. In: PowerTech, 2011 IEEE Trondheim, pp. 1–7 (2011). https://doi.org/10.1109/PTC.2011.6019396

  28. Son, Y., Pulkkinen, T., Moon, K., Kim, C.: Home energy management system based on power line communication. IEEE Trans. Consum. Electron. 56(3), 1380–1386 (2010)

    Article  Google Scholar 

  29. Yudong, T., Hongkun, S., Funian, H., Yun, Z.: Investigation on tou pricing principles. In: 2005 IEEE/PES Transmission Distribution Conference Exposition: Asia and Pacific, pp. 1–9 (2005)

  30. Zeng, S., Li, J., Ren, Y.: Research of time-of-use electricity pricing models in china: a survey. pp. 2191 – 2195 (2009). https://doi.org/10.1109/IEEM.2008.4738260

Download references

Acknowledgements

This research was supported, in part, by the National Science Foundation under Grants CNS0829916, CNS0905308, and CNS-1239274.

Author information

Authors and Affiliations

  1. Bloomberg LP, New York City, NY, USA

    Anshu Ranjan

  2. University of California, Irvine, CA, USA

    Pramod Khargonekar

  3. University of Florida, Gainesville, FL, USA

    Sartaj Sahni

Authors
  1. Anshu Ranjan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pramod Khargonekar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sartaj Sahni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anshu Ranjan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest. A preliminary version of this paper has been published at ISCC conference [25]. The conference paper did not contain the mathematical proof provided in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

A preliminary version of this paper has been published at ISCC conference [25]. The conference paper did not contain the mathematical proof provided in this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ranjan, A., Khargonekar, P. & Sahni, S. Offline preemptive bottom left decreasing height scheduling of power loads in smart grids. Energy Syst 14, 959–984 (2023). https://doi.org/10.1007/s12667-021-00453-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12667-021-00453-9

Keywords

Search

Navigation