This paper addresses unit commitment under uncertainty of load and power infeed from renewables in alternating current (AC) power systems. Beside traditional unit-commitment constraints, the physics of power flow are included. To gain globally optimal solutions a recent semidefinite programming approach is used, which leads us to risk averse two-stage stochastic mixed integer semidefinite programs for which a decomposition algorithm is presented.
Accepté le :
DOI : 10.1051/ro/2016031
Mots clés : Stochastic programming, semidefinite programming, AC power flow
@article{RO_2017__51_2_391_0,
author = {Schultz, R\"udiger and Wollenberg, Tobias},
title = {Unit commitment under uncertainty in {AC} transmission systems via risk averse semidefinite stochastic {Programs}},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {391--416},
publisher = {EDP-Sciences},
volume = {51},
number = {2},
year = {2017},
doi = {10.1051/ro/2016031},
mrnumber = {3657431},
zbl = {1365.90180},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2016031/}
}
TY - JOUR AU - Schultz, Rüdiger AU - Wollenberg, Tobias TI - Unit commitment under uncertainty in AC transmission systems via risk averse semidefinite stochastic Programs JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 391 EP - 416 VL - 51 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2016031/ DO - 10.1051/ro/2016031 LA - en ID - RO_2017__51_2_391_0 ER -
%0 Journal Article %A Schultz, Rüdiger %A Wollenberg, Tobias %T Unit commitment under uncertainty in AC transmission systems via risk averse semidefinite stochastic Programs %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 391-416 %V 51 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2016031/ %R 10.1051/ro/2016031 %G en %F RO_2017__51_2_391_0
Schultz, Rüdiger; Wollenberg, Tobias. Unit commitment under uncertainty in AC transmission systems via risk averse semidefinite stochastic Programs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 2, pp. 391-416. doi : 10.1051/ro/2016031. http://www.numdam.org/articles/10.1051/ro/2016031/
and , Hydrothermal unit commitment with ac constraints by a new solution method based on benders decomposition. Energy Convers. Manage. 65 (2013) 57–65. | DOI
M.F. Anjos and J.B. Lasserre, Handbook on Semidefinite, Conic Polynomial Optimization. Vol. 166 of Internat. Ser. Oper. Res. Management Sci. Springer (2012). | MR | Zbl
and , Stochastic semidefinite programming: A new paradigm for stochastic optimization. 4OR: A Quart. J. Oper. Res. 4 (2004) 239–253. | DOI | MR | Zbl
, , and , Semidefinite programming for optimal power flow problems. Int. J. Electric Power Energy Syst. 30 (2008) 383–392. | DOI
and , Using mixed-integer programming to solve power grid blackout problems. Discrete Optim. 4 (2007) 115–141. | DOI | MR | Zbl
J.R. Birge and F. Louveaux, Introduction to Stochastic Programming. Internat. Series in Operations Research and Financial Engineering, 2nd edition. Springer (2011). | MR | Zbl
S. Bose, D.F Gayme, S. Low and K.M.i Chandy, Optimal power flow over tree networks. In Communication, Control and Computing (Allerton), 2011 49th Annual Allerton Conference on. IEEE (2011) 1342–1348.
, , and , Local solutions of optimal power flow. IEEE Trans. Power Syst. 28 (2013) 4780–4788. | DOI
C.C. Carøe and R. Schultz, A two-stage stochastic program for unit commitment under uncertainty in a hydro-thermal power system. Konrad-Zuse-Zentrum, Berlin (1998), ZIB-Preprint SC 98-11.
and , Dual decomposition in stochastic integer programming. Oper. Res. Lett. 24 (1999) 37–45. | DOI | MR | Zbl
, Contribution to the economic dispatch problem. Bull. Soc. Franc. Elect. 3 (1962) 431–447.
C. Coffrin, H.L. Hijazi and P. Van Hentenryck, The qc relaxation: Theoretical and computational results on optimal power flow. Preprint (2015). | arXiv
M. Farivar, C.R. Clarke, S.H. Low and K.M. Chandy, Inverter var control for distribution systems with renewables. In Smart Grid Communications (SmartGridComm), 2011 IEEE International Conference on. IEEE (2011) 457–462.
S. Frank and S. Rebennack, A primer on optimal power flow: Theory, formulation, and practical examples. Working Paper, Colorado School of Mines (2012).
, and , A primer on optimal power flow: A bibliographic survey (i) – formulations and deterministic methods. Energy Systems 3 (2012) 221–258. | DOI
, and , A primer on optimal power flow: A bibliographic survey (ii) – non-deterministic and hybrid methods. Energy Systems 3 (2012) 259–289. | DOI
, , and , Unit commitment in power generation - a basic model and some extensions. Ann. Oper. Res. 96 (2000) 167–189. | DOI | Zbl
T. Haukaas, Probablistic models, methods, and decisions in earthquake engineering. In Safety, Reliability, Risk and Life-Cycle Performance of Structures & Infrastructures, edited by G. Deodatis, B.R. Ellingwood and D.M. Frangopol. CRC Press (2014) 47–66.
and , Scenario tree modeling for multistage stochastic programs. Math. Program. 118 (2009) 371–406. | DOI | MR | Zbl
C. Helmberg, Semidefinite programming for combinatorial optimization. Konrad-Zuse-Zentrum, Berlin (2000), ZIB-Report ZR 00-34.
H. Hijazi, C. Coffrin and P. Van Hentenryck, Convex quadratic relaxations of mixed-integer nonlinear programs in power systems, Tech. rep. NICTA, Canberra, ACT Australia (2013).
et al., Radial distribution load flow using conic programming. IEEE Trans. Power Syst. 21 (2006) 1458–1459. | DOI
S. Kuhn, Betriebsoptimierung von elektrischen Energieerzeugungsanlagen und Übertragungssystemen bei unvollständiger Information. Ph.D. thesis, University of Duisburg-Essen (2011).
and , Zero duality gap in optimal power flow problem. IEEE Trans. Power Syst. 27 (2011) 92–107. | DOI
C. Lemaréchal, Lagrangian relaxation. In Computational Combinatorial Optimization, edited by M. Jünger and D. Naddef. Vol. 2241 of Lect. Notes Comput. Sci. Springer (2001) 112–156. | MR | Zbl
B.C. Lesieutre, D.K. Molzahn, A.R. Borden and C.L. DeMarco, Examining the limits of the application of semidefinite programming to power flow problems. In 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2011) 1492–1499.
, and , Decomposition algorithms for two-stage chance-constrained programs. Math. Program. 157 (2016) 219–243. | DOI | MR | Zbl
, , and , On parallelizing dual decomposition in stochastic integer programming. Oper. Res. Lett. 41 (2013) 252–258. | DOI | MR | Zbl
R. Madani, M. Asharphijuo and J. Lavaei, SDP Solver of Optimal Power Flow User’s Manual (2014). Available at http://www.columbia.edu/˜rm3122/OPF˙Solver˙Guide.pdf.
and , Decomposition-based interior point methods for two-stage stochastic semidefinite programming. SIAM J. Optim. 18 (2007) 206–222. | DOI | MR | Zbl
and , On the implementation of interior point decomposition algorithms for two-stage stochastic conic programs. SIAM J. Optim. 19 (2009) 1846–1880. | DOI | MR | Zbl
D. Mehta, D.K Molzahn and K. Turitsyn, Recent advances in computational methods for the power flow equations. Preprint (2015). | arXiv
D.K Molzahn, Application of Semidefinite Optimization Techniques to Problems in Electric Power Systems. Ph. D. thesis, University of Wisconsin–Madison (2013).
, , and , Implementation of a large-scale optimal power flow solver based on semidefinite programming. IEEE Trans. Power Syst. 28 (2013) 3987–3998. | DOI
, and , A sufficient condition for global optimality of solutions to the optimal power flow problem. IEEE Trans. Power Syst. 29 (2014) 978–979. | DOI
, and , A review of selected optimal power flow literature to 1993 Part i: Nonlinear and quadratic programming approaches. IEEE Trans. Power Syst. 14 (1999) 96–104. | DOI
, and , A review of selected optimal power flow literature to 1993 Part ii: Nonlinear and quadratic programming approaches. IEEE Trans. Power Syst. 14 (1999) 105–111. | DOI
A. Müller and D. Stoyan, Comparison Methods for Stochastic Models and Risks. John Wiley & Sons, INC (2002). | MR | Zbl
G.C. Pflug and W. Römisch, Modeling, Measuring and Managing Risk. World Scientific Publishing (2007). | MR | Zbl
, A regularized decomposition method for minimizing a sum of polyhedral functions. Math. Program. 35 (1986) 309–333. | DOI | MR | Zbl
A. Ruszczyński and A. Shapiro, Stochastic Programming. Vol. 10 of Handbooks Oper. Res. Manage. Sci. Elsevier (2003). | MR | Zbl
P. Sánchez-Martin and A. Ramos, Modeling transmission ohmic losses in a stochastic bulk production cost model. Instituto de Investigación Tecnológica, Universidad Pontificia Comillas, Madrid (1997).
, and , Probablistic midterm transmission planning in a liberalized market. IEEE Trans. Power Syst. 20 (2005) 2135–2142. | DOI
and , Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse. SIAM J. Optim. 14 (2003) 115–138. | DOI | MR | Zbl
A. Shapiro, D. Dentcheva and A. Ruszczyński, Lectures on Stochastic Programming, Modeling and Theory. Society for Industrial and Applied Mathematics (2009). | MR | Zbl
S. Sojoudi and J. Lavaei, Physics of power networks makes hard optimization problems easy to solve. In Power and Energy Society General Meeting, 2012 IEEE. IEEE (2012) 1–8.
UWEE University of Washington Electrical Engineering, Power Systems Test Case Archive (2014). Available at http://www.ee.washington.edu/research/pstca/.
H. Wolkowitz, R. Saigal and L. Vandenberghe, eds. Handbook of Semidefinite Progamming: Theory, Algorithms and Applications. Vol. 27 of Int. Ser. Oper. Res. Manage. Sci. Kluwer Academic Publishers (2000). | MR | Zbl
B. Zhang and D. Tse, Geometry of feasible injection region of power networks. In Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on. IEEE (201) 1508–15151.
, A log-barrier method with benders decomposition for solving two-stage stochastic linear programs. Math. Program. 90 (2001) 507–536. | DOI | MR | Zbl
J. Zhu, Optimization of Power System Operation. IEEE Press Series on Power Engineering. John Wiley & Sons, INC. (2009).
Cité par Sources :
