Abstract
We present a brief, informal overview of the physical reality of electric power systems, its mathematical models, and some of the associated optimization problems. Many references are provided.
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References
U. Aldasoro, L.F. Escudero, M. Merino, J.F. Monge, G. Perez, On parallelization of a stochastic dynamic programming algorithm for solving large-scale mixed 0-1 problems under uncertainty. TOP 23, 703–742 (2015)
U. Aldasoro, L.F. Escudero, M. Merino, G. Perez, An algorithmic framework for solving large-scale multistage stochastic mixed 0-1 problems with nonsymmetric scenario trees. part ii: parallelization. Comput. Oper. Res. 40, 2950–2960 (2013)
U. Aldasoro, L.F. Escudero, M. Merino, J.F. Monge, G. Perez, A parallel branch-and-fix coordination based matheuristic algorithm for solving large-scale multistage stochastic mixed 0-1 problems. Eur. J. Oper. Res. 258, 590–606 (2017)
T. Al-Khamis, R. M’Hallah, A two-stage stochastic programming model for the parallel machine scheduling problem with machine capacity. Comput. Oper. Res. 38(12), 1747–1759 (2011)
A. Alonso-Ayuso, L.F. Escudero, M.T. Ortuño, BFC, a branch-and-fix coordination algorithmic framework for solving stochastic 0-1 programs. Eur. J. Oper. Res. 151, 503–519 (2003)
L. Aranburu, L.F. Escudero, M.A. Garin, G. Perez, A so-called cluster benders decomposition approach for solving two-stage stochastic linear programs. TOP 20, 279–295 (2012)
T. Asamov, W.B. Powell, Regularized decomposition of highdimensional multistage stochastic programs with markov uncertainty (2015). arXiv:1505.02227
L. Baringo, A.J. Conejo, Transmission and wind power investment. IEEE Trans. Power Syst. 27(2), 885–893 (2012)
M. Beaudin, H. Zareipour, A. Schellenberglabe, W. Rosehart, Energy storage for mitigating the variability of renewable electricity sources: an updated review. Energy Sustain. Dev. 14(4), 302–314 (2010)
C. Beltran-Royo, L.F. Escudero, J.F. Monge, R.E. Rodriguez-Ravines, An effective heuristic for multistage stochastic linear optimization. Comput. Oper. Res. 51, 237–250 (2014)
Y. Ben-Haim, Info-Gap Decision Theory (Academic Press, Cambridge, 2006)
P. Beraldi, L. Grandinetti, R. Musmanno, C. Triki, Parallel algorithms to solve two-stage stochastic linear programs with robustness constraints. Parallel Comput. 26, 1889–1908 (2000)
A. Bernstein, L. Reyes-Chamorro, J.-Y. Le Boudec, M. Paolone, A composable method for real-time control of active distribution networks with explicit power setpoints. part I: Framework. Electr. Power Syst. Res. 125, 254–264 (2015)
A. Bernstein, E. Dall’Anese, A. Simonetto, Online primal-dual methods with measurement feedback for time-varying convex optimization. IEEE Trans. Signal Process. 67(8), 1978–1991 (2019)
F. Capitanescu, L. Wehenkel, An AC OPF-based heuristic algorithm for optimal transmission switching, in Power Systems Computation Conference (PSCC), 2014 (IEEE, Piscataway, 2014), pp. 1–6
C.C. Carøe, R. Schultz, Dual decomposition in stochastic integer programming. Oper. Res. Lett. 24, 37–45 (1999)
J. Carpentier, Contribution a l’etude du dispatching economique. Bull. Soc. Fr. Elect. 3(1), 431–447 (1962)
J. Carpentier, Optimal power flows. Int. J. Electr. Power Energy Syst. 1(1), 3–15 (1979)
K. Chen, W. Wu, B. Zhang, H. Sun, Robust restoration decision-making model for distribution networks based on information gap decision theory. IEEE Trans. Smart Grid 6(2), 587–597 (2015)
W.Y. Chiu, H. Sun, H.V. Poor, A multiobjective approach to multimicrogrid system design. IEEE Trans. Smart Grid 6(5), 2263–2272 (2015)
S. Ci, N. Lin, D. Wu, Reconfigurable battery techniques and systems: a survey. IEEE Access 4, 1175–1189 (2016)
C. Coffrin, H.L. Hijazi, K Lehmann, P. Van Hentenryck, Primal and dual bounds for optimal transmission switching, in Power Systems Computation Conference (PSCC), 2014 (IEEE, Piscataway, 2014), pp. 1–8
Common solution on phase shift transformers on ceps-50hertz interconnector, in Czech-German High-Level Meeting on Unplanned Flows Prague (2013)
M.P. Cristobal, L.F. Escudero, J.F. Monge, On stochastic dynamic programming for solving large-scale planning problems under uncertainty. Comput. Oper. Res. 36(8), 2418–2428 (2009)
E. Dall’Anese, S. Guggilam, A. Simonetto, Y.C. Chen, S.V. Dhople, Optimal regulation of virtual power plants. IEEE Trans. Power Syst. 33(2), 1868–1881 (2018)
E. Dall’Anese, A. Simonetto, Optimal power flow pursuit. IEEE Trans. Smart Grid 9(2), 942–952 (2018)
G. Emiel, C. Sagastizabal, Incremental like bundle methods with applications to energy planning. Comput. Optim. Appl. 46, 305–332 (2009)
L.F. Escudero, M.A. Garin, M. Merino, G. Perez, A general algorithm for solving two-stage stochastic mixed 0-1 first-stage problems. Comput. Oper. Res. 36, 2590–2600 (2009)
L.F. Escudero, M. Araceli, M.A. Garin, G. Perez, A. Unzueta, Scenario cluster decomposition of the lagrangian dual in two-stage stochastic mixed 0-1 optimization. Comput. Oper. Res. 40(1), 362–377 (2013)
L.F. Escudero, M.A. Garin, C. Pizarro, A. Unzueta, On the strongest lagrangean bounds for stochastic location-assignment problems, in 59 XXII EURO Working Group on Locational Analysis (2015)
L.F. Escudero, J.F. Monge, D.R. Morales, An SDP approach for multiperiod mixed 0-1 linear programming models with stochastic dominance constraints for risk management. Comput. Oper. Res. 58(Supplement C), 32–40 (2015)
L.F. Escudero, M.A. Araceli Garin, M. Merino, G. Perez, On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs. Eur. J. Oper. Res. 249(1), 164–176 (2016)
L.F. Escudero, J.F. Monge, D.R. Morales, On the time-consistent stochastic dominance risk averse measure for tactical supply chain planning under uncertainty. Comput. Oper. Res. (2017)
L.F. Escudero, M.A. Garin, C. Pizarro, A. Unzueta, On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems. Comput. Optim. Appl. 70(3), 865–888 (2018)
P. Ferraro, E. Crisostomi, M. Raugi, F. Milano, Analysis of the impact of microgrid penetration on power system dynamics. IEEE Trans. Power Syst. 32(5), 4101–4109 (2017)
P. Ferraro, E. Crisostomi, M. Raugi, F. Milano, On the impact of microgrid energy management systems on power system dynamics, in IEEE PES General Meeting (2017)
E.B. Fisher, R.P. OŃeill, M.C. Ferris, Optimal transmission switching. IEEE Trans. Power Syst. 23(3), 1346–1355 (2008)
B. Ghaddar, J. Marecek, M. Mevissen, Optimal power flow as a polynomial optimization problem. IEEE Trans. Power Syst. 31(1), 539–546 (2016)
H. Glavitsch, Switching as means of control in the power system. Int. J. Elect. Power Energy Syst. 7(2), 92–100 (1985)
R. Gollmer, F. Neise, R. Schultz, Stochastic programs with first-order dominance constraints induced by mixed-integer linear recourse. SIAM J. Optim. 19(2), 552–571 (2008)
R. Gollmer, U. Gotzes, R. Schultz, A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse. Math. Program. 126(1), 179–190 (2011)
Grid energy storage. Technical report, Department of Energy (2013)
V. Guigues, SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning. Comput. Optim. Appl. 57(1), 167–203 (2014)
A. Hauswirth, A. Zanardi, S. Bolognani, Florian Dörfler, G. Hug, Online optimization in closed loop on the power flow manifold, in Proceedings of the IEEE PowerTech conference, Manchester (2017)
K.W. Hedman, R.P. O’Neill, E.B. Fisher, S.S. Oren, Optimal transmission switching with contingency analysis. IEEE Trans. Power Syst. 24(3), 1577–1586 (2009)
K.W. Hedman, M.C. Ferris, R.P O’Neill, E.B Fisher, S.S. Oren, Co-optimization of generation unit commitment and transmission switching with N-1 reliability. IEEE Trans. Power Syst. 25(2), 1052–1063 (2010)
K.W. Hedman, S.S. Oren, R.P. O’Neill, Optimal transmission switching: economic efficiency and market implications. J. Regul. Eco. 40(2), 111–140 (2011)
R. Hemmati, R. Hooshmand, A. Khodabakhshian, Comprehensive review of gen-eration and transmission expansion planning. IET Gen. Trans. Distrib. 7, 955–964 (2013)
H. Ibrahim, A. Ilinca, J. Perron, Energy storage systems-characteristics and comparisons. Renew. Sustain. Energy Rev. 12(5), 1221–1250 (2008)
R.A. Jabr, Optimization of AC transmission system planning. IEEE Trans. Power Syst. 28(3), 2779–2787 (2013)
S.R. Khuntia, B.W. Tuinema, J.L. Rueda, M.A.M.M. van der Meijden, Time-horizons in the planning and operation of transmission networks: an overview. IET Gener. Transm. Distrib. 10(4), 841–848 (2016)
B. Kocuk, S.S. Dey, X. Sun, New formulation and strong MISOCP relaxations for AC optimal transmission switching problem. IEEE Trans. Power Syst. 32(6), 4161–4170 (2017)
V. Kozmík, D.P. Morton, Evaluating policies in risk-averse multi-stage stochastic programming. Math. Program. 152(1), 275–300 (2015)
X. Kuang, L.F. Zuluaga, B. Ghaddar, J. Naoum-Sawaya, Approximating the ACOPF problem with a hierarchy of socp problems, in 2015 IEEE Power & Energy Society General Meeting (IEEE, Piscataway, 2015), pp. 1–5
G. Latorre, R.D. Cruz, J.M. Areiza, A. Villegas, Classification of publications and models on transmission expansion planning. IEEE Trans. Power Syst. 18, 938–946 (2003)
J. Lavaei, S.H. Low, Zero duality gap in optimal power flow problem. IEEE Trans. Power Syst. 27(1), 92–107 (2012)
Z. Li, M.G. Ierapetritou, Capacity expansion planning through augmented lagrangian optimization and scenario decomposition. AIChE J. 58(3), 871–883 (2012)
J. Linderoth, A. Shapiro, S. Wright, The empirical behavior of sampling methods for stochastic programming. Annal. Oper. Res. 142(1), 215–241 (2006)
J.A. López, K. Ponnambalam, V.H. Quintana, Generation and transmission expansion under risk using stochastic programming. IEEE Trans. Power Syst. 22(3), 1369–1378 (2007)
S. Lumbreras, A. Ramos, Optimal design of the electrical layout of an offshore wind farm applying decomposition strategies. IEEE Trans. Power Syst. 28(2), 1434–1441 (2013)
S. Lumbreras, A. Ramos, The new challenges to transmission expansion planning. Survey of recent practice and literature review. Elect. Power Syst. Res. 134, 19–29 (2016)
W.-J. Ma, J. Marecek, M. Mevissen, A fine-grained variant of the hierarchy of lasserre, in 57th Annual Allerton Conference on Communication, Control, and Computing. Preprint. arXiv:1906.09586 (2019)
R. Madani, A. Kalbat, J. Lavaei, Admm for sparse semidefinite programming with applications to optimal power flow problem, in 2015 IEEE 54th Annual Conference on Decision and Control (CDC) (IEEE, Piscataway, 2015), pp. 5932–5939
D. Mahlke, A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs: With Application in Energy Production (Springer, Berlin, 2011)
J. Marecek, M. Mevissen, J.C. Villumsen, Minlp in transmission expansion planning, in 2016 Power Systems Computation Conference (PSCC) (2016)
A.A. Mazi, B.F. Wollenberg, M.H. Hesse, Corrective control of power system flows by line and bus-bar switching. IEEE Trans. Power Syst. 1(3), 258–264 (1986)
D.K. Molzahn, I.A. Hiskens, A survey of relaxations and approximations of the power flow equations. Found. Trends Elect. Energy Syst. 4(1–2), 1–221 (2019)
J.M. Mulvey, A. Ruszczyński, A new scenario decomposition method for large-scale stochastic optimization. Oper. Res. 43(3), 477–490 (1995)
M.P. Nowak, W. Römisch, Stochastic lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Annal. Oper. Res. 100(1), 251–272 (2000)
W. Oliveira, C. Sagastizábal, S. Scheimberg, Inexact bundle methods for two-stage stochastic programming. SIAM J. Optim. 21(2), 517–544 (2011)
F. Oliveira, V. Gupta, S. Hamacher, I.E. Grossmann, A lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations. Comput. Chem. Eng. 50(Supplement C), 184–195 (2013)
R.P. OŃeill, R. Baldick, U. Helman, M.H. Rothkopf, W. Stewart, Dispatchable transmission in RTO markets. IEEE Trans. Power Syst. 20(1), 171–179 (2005)
R.P. O’Neill, A. Castillo, M.B. Cain, The computational testing of ac optimal power flow using the current voltage formulations. Fed. Energy Regul. Comm. (2012)
A. Ortega, F. Milano, Generalized model of VSC-based energy storage systems for transient stability analysis. IEEE Trans. Power Syst. 31(5), 3369–3380 (2016)
A. Ortega, F. Milano, Modeling, simulation, and comparison of control techniques for energy storage systems. IEEE Trans. Power Syst. 32(3), 2445–2454 (2017)
A. Pagè-Bernaus, G. Pérez-Valdés, A. Tomasgard, A parallelised distributed implementation of a branch and fix coordination algorithm. Eur. J. Oper. Res. 244(1), 77–85 (2015)
M. Pereira, L. Pinto, S. Cunha, G. Oliveira, A decomposition approach to automated generation/transmission expansion planning. IEEE Trans. Power Apparatus Syst. 104(11), 3074–3083 (1985)
M.V.F. Pereira, L.M.V.G. Pinto, Stochastic optimization of a multireservoir hydroelectric system: a decomposition approach. Water Resour. Res. 21(6), 779–792 (1985)
M.V.F. Pereira, L.M.V.G. Pinto, Multi-stage stochastic optimization applied to energy planning. Math. Program. 52(1), 359–375 (1991)
D. Pozo, E.E. Sauma, J. Contreras, A three-level static milp model for generation and transmission expansion planning. IEEE Trans. Power Syst. 28(1), 202–210 (2013)
A. Rabiee, A. Soroudi, A. Keane, Information gap decision theory based OPF with HVDC connected wind farms. IEEE Trans. Power Syst. 30, 3396–3406 (2015)
J. Ratz, Unintended cross-border electricity flows in central eastern Europe and their regulatory implications, in 14th Baltic Electricity Market Mini-Forum (2012)
R.T. Rockafellar, R.J.-B. Wets, Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16(1), 119–147 (1991)
J.H. Roh, M. Shahidehpour, Y. Fu, Market-based coordination of transmission and generation capacity planning. IEEE Trans. Power Syst. 22(4), 1406–1419 (2007)
R. Romero, J.F. Franco, F.B. Leão, M.J. Rider, E.S. de Souza, A new mathematical model for the restoration problem in balanced radial distribution systems. IEEE Trans. Power Syst. 31(2), 1259–1268 (2016)
A. Ruszczyński, Parallel decomposition of multistage stochastic programming problems. Math. Program. 58(1), 201–228 (1993)
A. Ruszczyński, On convergence of an augmented lagrangian decomposition method for sparse convex optimization. Math. Oper. Res. 20(3), 634–656 (1995)
A. Ruszczyński, A. Świȩtanowski, Accelerating the regularized decomposition method for two stage stochastic linear problems. Eur. J. Oper. Res. 101(2), 328–342 (1997)
C. Sagastizábal, Divide to conquer: decomposition methods for energy optimization. Math. Program. 134(1), 187–222 (2012)
M. Sahraei-Ardakani, A. Korad, K.W. Hedman, P. Lipka, S. Oren, Performance of AC and DC based transmission switching heuristics on a large-scale polish system, in 2014 IEEE PES General Meeting/Conference & Exposition (IEEE, Piscataway, 2014), pp. 1–5
M. Sahraei-Ardakani, K.W. Hedman, A fast LP approach for enhanced utilization of variable impedance based facts devices. IEEE Trans. Power Syst. 31(3), 2204–2213 (2016)
B. Sandikçi, O.Y. Özaltin, A scalable bounding method for multistage stochastic programs. SIAM J. Optim. 27(3), 1772–1800 (2017)
Y. Scholz, Renewable energy based electricity supply at low costs – development of the remix model and application for Europe. Ph.D. Thesis, German Aerospace Center (DLR), Institute of Technical Thermodynamics (2012)
S. Sen, Z. Zhou, Multistage stochastic decomposition: a bridge between stochastic programming and approximate dynamic programming. SIAM J. Optim. 24(1), 127–153 (2014)
M. Shahidehpour, Investing in expansion: the many issues that cloud electricity planning. IEEE Power Energy Mag. 2, 14–18 (2004)
M. Shahidehpour, Global broadcast – transmission planning in restructured systems. IEEE Power Energy Mag. 5(5), 18–20 (2007)
A. Shapiro, W. Tekaya, J. da Costa Paulo, M. Pereira Soares, Risk neutral and risk averse stochastic dual dynamic programming method. Eur. J. Oper. Res. 224(2), 375–391 (2013)
A. Simonetto, E. Dall’Anese, Prediction-correction algorithms for time-varying constrained optimization. IEEE Trans. Signal Proces. 65(20), 5481–5494 (2017)
M. Tahanan, W. van Ackooij, A. Frangioni, F. Lacalandra, Large-scale unit commitment under uncertainty. 4OR 13(2), 115–171 (2015)
Y. Tang, K. Dvijotham, S. Low, Real-time optimal power flow. IEEE Trans. Smart Grid 8(6), 2963–2973 (2017)
J.A. Taylor, F.S Hover, Linear relaxations for transmission system planning. IEEE Trans. Power Syst. 26(4), 2533–2538 (2011)
W. Van Ackooij, J. Malick, Decomposition algorithm for large-scale two-stage unitcommitment. Annal. Oper. Res. 238, 587–613 (2016)
W. Van Ackooij, C. Sagastizabal, Constrained bundle methods for upper inexact oracles with application to join chance constrained energy problems. SIAM J. Optim. 24, 733–765 (2014)
R.M. Van Slyke, R. Wets, L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. 17(4), 638–663 (1969)
J.C. Villumsen, A.B. Philpott, Column generation for transmission switching of electricity networks with unit commitment. Lecture Notes Eng. Comput. Sci. 2189, 1440–1443 (2011)
J.C. Villumsen, G. Bronmo, A.B. Philpott, Line capacity expansion and transmission switching in power systems with large-scale wind power. IEEE Trans. Power Syst. 28(2), 731–739 (2013)
J.P. Watson, D.L. Woodruff, Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Comput. Manag. Sci. 8(4), 355–370 (2011)
G.L. Zenarosa, O.A. Prokopyev, A.J. Schaefer, Scenario-tree decomposition: Bounds for multistage stochastic mixed-integer programs. Technical report, Department of Industrial Engineering, University of Pittsburgh (2014)
X. Zhou, E. Dall’Anese, L. Chen, A. Simonetto, An incentive-based online optimization framework for distribution grids. IEEE Trans. Autom. Control 63(7) (2018)
M. Zidar, P.S. Georgilakis, N.D. Hatziargyriou, T. Capuder, D. Škrlec, Review of energy storage allocation in power distribution networks: applications, methods and future research. IET Gen. Trans. Distrib. 10(3), 645–652 (2016)
J. Zou, S. Ahmed, X.A. Sun, Stochastic dual dynamic integer programming (2016)
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Marecek, J. et al. (2021). Network and Storage. In: Hadjidimitriou, N.S., Frangioni, A., Koch, T., Lodi, A. (eds) Mathematical Optimization for Efficient and Robust Energy Networks. AIRO Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-57442-0_2
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