N-1 Reliable Unit Commitment via Progressive Hedging
Publication: Journal of Energy Engineering
Volume 141, Issue 1
Abstract
Progressive hedging is a scenario-based decomposition method that can be applied to solve the stochastic unit commitment problem. Progressive hedging is not guaranteed to converge to the global optimal solution since unit commitment involves integer variables. Slow convergence rates and cyclic behaviors have been previously observed in practice. Hedging is conventionally performed on the unit commitment status variables. In this paper, several hedging methods are proposed to improve progressive hedging for the N-1 (single contingency) stochastic unit commitment problem. In particular, hedging on the start-up and shutdown variables is proposed and tested in this paper. The performance of the progressive hedging is rather sensitive to the choice in the penalty factors. Thus, several strategies for choosing the penalty factors are evaluated for the cases when using the unit commitment status variables versus using the start-up and shutdown binary variables as the hedging mechanisms. Finally, a hybrid approach using both progressive hedging and an extensive form stochastic programming formulation is implemented in order to obtain a set of feasible unit commitment solutions and compare different hedging methods.
Get full access to this article
View all available purchase options and get full access to this article.
References
California Independent System Operator (CAISO). (2006). “Spinning and non-spinning reserve.” 〈http://www.caiso.com/docs/2003/09/08/2003090815135425649.pdf〉 (Jan. 15, 2014).
Carøe, C. C., and Schultz, R. (1999). “Dual decomposition in stochastic integer programming.” Oper. Res. Lett., 24(1), 37–45.
Goez, J., Luedtke, J., Rajan, D., and Kalagnanam, J. (2008). “Stochastic unit commitment problem.” IBM Research Rep., 〈http://domino.watson.ibm.com/library/CyberDig.nsf/papers/A83A70DC9573F7F48525753D00526CC8/$File/rc24713.pdf〉 (Jan. 15, 2014).
Hedman, K. W., Ferris, M. C., O’Neill, R. P., Fisher, E. B., and Oren, S. S. (2010). “Co-optimization of generation unit commitment and transmission switching with N-1 reliability.” IEEE Trans. Power Syst., 25(2), 1052–1063.
Ozturk, U. A., Mazumdar, M., and Norman, B. A. (2004). “A solution to the stochastic unit commitment problem using chance constrained programming.” IEEE Trans. Power Syst., 19(3), 1589–1598.
Papavasiliou, A., and Oren, S. S. (2013). “Multi-area stochastic unit commitment for high wind penetration in a transmission constrained network.” Oper. Res., 61(3), 578–592.
Rajan, D., and Takriti, S. (2005). “Minimum up/down polytopes of the unit commitment problem with start-up costs.” IBM Research Rep., 〈http://domino.research.ibm.com/library/cyberdig.nsf/papers/CDCB02A7C809D89E8525702300502AC0/$File/rc23628.pdf〉 (Jan. 15, 2014).
Rockafellar, R. T., and Wets, R. J. B. (1991). “Scenarios and policy aggregation in optimization under uncertainty.” Math. Oper. Res., 16(1), 119–147.
Ryan, S. M., Silva-Monroy, C., Watson, J. P., Wets, R. J. B., and Woodruff, D. L. (2013). “Toward scalable, parallel progressive hedging for stochastic unit commitment,” Proc., 2013 IEEE Power and Energy Society Meeting, Vancouver, BC, Canada, 1–5.
Shiina, T., and Birge, J. R. (2004). “Stochastic unit commitment problem.” Int. Trans. Oper. Res., 11(1), 19–32.
Takriti, S., Birge, J. R., and Long, E. (1996). “A stochastic model for the unit commitment problem.” IEEE Trans. Power Syst., 11(3), 1497–1508.
University of Washington (2014). “Power systems test case archive.” 〈http://www.ee.washington.edu/research/pstca/rts/pg_tcarts.htm〉 (Jan. 15, 2014).
Wang, Q., Guan, Y., and Wang, J. (2012). “A chance-constrained two-stage stochastic program for unit commitment with uncertain wind power output.” IEEE Trans. Power Syst., 27(1), 206–215.
Watson, J. P., and Woodruff, D. L. (2011). “Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems.” Comput. Manage. Sci. 8(4), 355–370.
Information & Authors
Information
Published In
Journal of Energy Engineering
Volume 141 • Issue 1 • March 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 11, 2013
Accepted: Jan 16, 2014
Published online: Mar 10, 2014
Discussion open until: Aug 10, 2014
Published in print: Mar 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.