, 2 Contour plot of Q k (x) for a 2-dimensional Bellman function, p.95

, Upper bounded approximate value function

, Contour ofV t+1

.. .. Topology,

, Upper bound values of MIDAS

, Upper bound values of SDDP

, Expected Profit from a policy computed by MIDAS under simulation, p.148

, Expected Profit from a policy computed by SDDP under simulation, p.148

. .. , Mean daily price at OTA2201 node in the NZEM, p.152

. .. , Example of a value function V t (x t , p t ), p.155

. .. Autoregressive-price-scenarios, , p.156

. .. , Value function approximation for price, p.157

. .. , Computing approximation in backwardpass, p.159

. .. , Interpolating value function by two cutting planes, p.163

, Single reservoir MIDAS upper bound comparison by ? x, p.170

. .. , Single reservoir MIDAS lower bound comparison by ? x, p.170

.. .. , 171 7.10 2 reservoir MIDAS lower bound comparison by ? x

, Single reservoir MIDAS state trajectories

, Single reservoir SDDP state trajectories

. .. Midas, Single reservoir simulated offers, p.175

. .. Sddp, Single reservoir simulated offers, p.175

, Simulated price and offers of 5 reservoir hydro scheme, p.176

. .. , Simulated policies for 5 reservoir hydro scheme, p.178

W. .. Headwater, , p.180

. .. , Example power function by headwater levels, p.181

, Piecewise linear approximation of nominal power function, p.184

, Approximated power generation function

, Error measurement of the approximate power function, p.192

S. .. Convergence, , p.193

. .. , State trajectories with headwater effects in MIDAS

E. K. Aasgård, G. Andersen, S. E. Fleten, and D. Haugstvedt, Evaluating a stochastic-programming-based bidding model for a multireservoir system, IEEE Transactions on, vol.29, issue.4, pp.1748-1757, 2014.

H. Abgottspon, K. Njalsson, M. A. Bucher, and G. Andersson, Risk-averse medium-term hydro optimization considering provision of spinning reserves, 2014 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), pp.1-6, 2014.

, Energy policies of IEA countries: France 2009 review, IEA, 2009.

, International Energy Agency. Technology roadmap hydropower, 2012.

, Energy policies of IEA countries: European Union 2014 review, 2015.

W. T. Alley, Hydroelectric plant capability curves, IEEE Transactions on Power Apparatus and Systems, vol.96, issue.3, pp.999-1003, 1977.

G. Angulo, S. Ahmed, and S. S. Dey, Improving the integer l-shaped method, INFORMS Journal on Computing, vol.28, issue.3, pp.483-499, 2016.

G. Angulo, S. Ahmed, S. S. Dey, and V. Kaibel, Forbidden vertices. Mathematics of Operations Research, vol.40, issue.2, pp.350-360, 2014.

M. F. Anjos, Recent progress in modeling unit commitment problems, Modeling and Optimization: Theory and Applications, pp.1-29, 2013.

L. Bacaud, C. Lemaréchal, A. Renaud, and C. Sagastizábal, Bundle methods in stochastic optimal power management: A disaggregated approach using preconditioners, Computational Optimization and Applications, vol.20, issue.3, pp.227-244, 2001.

E. Balas, Disjunctive programming, Annals of Discrete Mathematics, vol.5, pp.3-51, 1979.

E. Beale and J. J. Forrest, Global optimization using special ordered sets, Mathematical Programming, vol.10, issue.1, pp.52-69, 1976.

A. Belloni, A. D. Lima, P. Maceira, and C. Sagastizábal, Bundle relaxation and primal recovery in unit commitment problems. the brazilian case, Annals of Operations Research, vol.120, issue.1-4, pp.21-44, 2003.

D. P. Bertsekas and S. E. Shreve, Stochastic optimal control: The discrete time case, vol.23, 1978.

A. Borghetti, C. Ambrosio, A. Lodi, and S. Martello, An milp approach for short-term hydro scheduling and unit commitment with head-dependent reservoir, IEEE Transactions on Power Systems, vol.23, issue.3, pp.1115-1124, 2008.

S. Brignol and A. Renaud, A new model for stochastic optimization of weekly generation schedules, Advances in Power System Control, Operation and Management, 1997. APSCOM-97. Fourth International Conference on, vol.2, pp.656-661, 1997.

J. P. Catalão, S. J. Mariano, V. M. Mendes, and L. A. Ferreira, Scheduling of head-sensitive cascaded hydro systems: a nonlinear approach, IEEE Transactions on Power Systems, vol.24, issue.1, pp.337-346, 2009.

S. Cerisola, J. M. Latorre, and A. Ramos, Stochastic dual dynamic programming applied to nonconvex hydrothermal models, European Journal of Operational Research, vol.218, issue.3, pp.687-697, 2012.

G. W. Chang, M. Aganagic, J. G. Waight, J. Medina, T. Burton et al., Experiences with mixed integer linear programming based approaches on short-term hydro scheduling, IEEE Transactions on power systems, vol.16, issue.4, pp.743-749, 2001.

H. C. Chang and P. H. Chen, Hydrothermal generation scheduling package: a genetic based approach, IEE Proceedings-Generation, Transmission and Distribution, vol.145, issue.4, pp.451-457, 1998.

Z. Chen and W. B. Powell, Convergent cutting-plane and partial-sampling algorithm for multistage stochastic linear programs with recourse, Journal of Optimization Theory and Applications, vol.102, issue.3, pp.497-524, 1999.

A. I. Cohen and V. R. Sherkat, Optimization-based methods for operations scheduling, Proceedings of the IEEE, vol.75, issue.12, pp.1574-1591, 1987.

I. Cplex and . Ilog, 12.6 user manual, 2010.

A. K. David and F. Wen, Strategic bidding in competitive electricity markets: a literature survey, Power Engineering Society Summer Meeting, vol.4, pp.2168-2173, 2000.

D. De-ladurantaye, M. Gendreau, and J. Potvin, Strategic bidding for price-taker hydroelectricity producers. Power Systems, IEEE Transactions on, vol.22, issue.4, pp.2187-2203, 2007.

V. L. De-matos, A. B. Philpott, and E. C. Finardi, Improving the performance of stochastic dual dynamic programming, Journal of Computational and Applied Mathematics, vol.290, pp.196-208, 2015.

A. L. Diniz and M. E. Maceira, A four-dimensional model of hydro generation for the short-term hydrothermal dispatch problem considering head and spillage effects, IEEE transactions on power systems, vol.23, issue.3, pp.1298-1308, 2008.

C. J. Donohue and J. R. Birge, The abridged nested decomposition method for multistage stochastic linear programs with relatively complete recourse, Algorithmic Operations Research, vol.1, issue.1, 2006.

L. Dubost, R. Gonzalez, and C. Lemaréchal, A Primal-Proximal Heuristic Applied to the Unit-Commitment Problem, INRIA, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00071600

, IEA Renewable Energy Essentials. Hydropower, 2010.

E. C. Finardi, E. L. Da, and . Silva, Unit commitment of single hydroelectric plant. Electric Power Systems Research, vol.75, pp.116-123, 2005.

S. E. Fleten, D. Haugstvedt, M. M. Belsnes, J. A. Steinsbø, and F. Fleischmann, Bidding hydropower generation: Integrating short-and long-term scheduling, 17th Power Systems Computations Conference PSCC, pp.352-358, 2011.

S. E. Fleten and T. K. Kristoffersen, Stochastic programming for optimizing bidding strategies of a nordic hydropower producer, European Journal of Operational Research, vol.181, issue.2, pp.916-928, 2007.

J. Garcia-gonzalez and G. A. Castro, Short-term hydro scheduling with cascaded and head-dependent reservoirs based on mixed-integer linear programming, Power Tech Proceedings, vol.3, 2001.

L. Gaudard and F. Romerio, The future of hydropower in europe: Interconnecting climate, markets and policies, Environmental Science & Policy, vol.37, pp.172-181, 2014.

P. Girardeau, V. Leclere, and A. B. Philpott, On the convergence of decomposition methods for multistage stochastic convex programs, Mathematics of Operations Research, vol.40, issue.1, pp.130-145, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01208295

A. Gjelsvik, M. M. Belsnes, and A. Haugstad, An algorithm for stochastic mediumterm hydrothermal scheduling under spot price uncertainty, Proceedings of 13th

, Power Systems Computation Conference, 1999.

A. Gjelsvik, B. Mo, and A. Haugstad, Long-and medium-term operations planning and stochastic modelling in hydro-dominated power systems based on stochastic dual dynamic programming, Handbook of Power Systems I, pp.33-55, 2010.

M. Hindsberger and A. B. Philpott, Resa: A method for solving multistage stochastic linear programs, Journal of Applied Operational Research, vol.6, issue.1, pp.2-15, 2014.

N. A. Iliadis, A. Tilmant, R. Chabar, S. Granville, and M. Pereira, Optimal operation of hydro-dominated multireservoir systems in deregulated electricity markets, Proceedings of the International Conference for Reservoir Operation and River Management, 2005.

K. Imran and I. Kockar, A technical comparison of wholesale electricity markets in north america and europe. Electric Power Systems Research, vol.108, pp.59-67, 2014.

D. R. Jiang and W. B. Powell, An approximate dynamic programming algorithm for monotone value functions, 2014.

D. R. Jiang and W. B. Powell, Optimal hour ahead bidding in the real time electricity market with battery storage using approximate dynamic programming, 2014.

T. K. Kristoffersen and S. E. Fleten, Stochastic programming models for shortterm power generation scheduling and bidding, Energy, Natural Resources and Environmental Economics, pp.187-200, 2010.

G. Laporte and F. V. Louveaux, The integer L-shaped method for stochastic integer programs with complete recourse, Operations research letters, vol.13, issue.3, pp.133-142, 1993.

P. Lino, L. A. Barroso, M. V. Pereira, R. Kelman, and M. H. Fampa, Bid-based dispatch of hydrothermal systems in competitive markets, Annals of Operations Research, vol.120, issue.1-4, pp.81-97, 2003.

N. Löhndorf, D. Wozabal, and S. Minner, Optimizing trading decisions for hydro storage systems using approximate dual dynamic programming, Operations Research, vol.61, issue.4, pp.810-823, 2013.

L. Meeus, R. Belmans, and J. Glachant, Regional electricity market integration france-belgium-netherlands, vol.122, p.17, 2006.

, Ministry of Business, Innovation and Employment, 2015.

G. Morales-españa, J. M. Latorre, and A. Ramos, Tight and compact milp formulation of start-up and shut-down ramping in unit commitment, IEEE Transactions on Power Systems, vol.28, issue.2, pp.1288-1296, 2013.

P. J. Neame, A. B. Philpott, and G. Pritchard, Offer stack optimization in electricity pool markets, Operations Research, vol.51, issue.3, pp.397-408, 2003.

N. Newham, Power system investment planning using stochastic dual dynamic programming. phdthesis, 2008.

N. Newham and A. Wood, Transmission investment planning using sddp, Power Engineering Conference, 2007. AUPEC 2007. Australasian Universities, pp.1-5, 2007.

J. Ostrowski, M. F. Anjos, and A. Vannelli, Tight mixed integer linear programming formulations for the unit commitment problem, IEEE Transactions on Power Systems, vol.1, issue.27, pp.39-46, 2012.

M. V. Pereira and L. Pinto, Multi-stage stochastic optimization applied to energy planning. Mathematical programming, vol.52, pp.359-375, 1991.

A. B. Philpott, M. Craddock, and H. Waterer, Hydro-electric unit commitment subject to uncertain demand, European Journal of Operational Research, vol.125, issue.2, pp.410-424, 2000.

A. B. Philpott, A. Dallagi, and E. Gallet, On cutting plane algorithms and dynamic programming for hydroelectricity generation, Handbook of Risk Management in Energy Production and Trading, pp.105-127, 2013.

A. B. Philpott and Z. Guan, On the convergence of stochastic dual dynamic programming and related methods, Operations Research Letters, vol.36, issue.4, pp.450-455, 2008.

A. B. Philpott, Z. Guan, J. Khazaei, and G. Zakeri, Production inefficiency of electricity markets with hydro generation, Utilities Policy, vol.18, issue.4, pp.174-185, 2010.

N. Porter, A. B. Philpott, A. Downward, and G. Zakeri, River Valley Optimization for Hydro-Electricity Generation, 2012.

W. B. Powell, Approximate Dynamic Programming: Solving the curses of dimensionality, vol.703, 2007.

W. B. Powell, Clearing the jungle of stochastic optimization, Informs TutORials, 2014.

. Mighty-river and . Power, , 2009.

G. Pritchard, Stochastic inflow modeling for hydropower scheduling problems, European Journal of Operational Research, vol.246, issue.2, pp.496-504, 2015.

G. Pritchard and G. Zakeri, Market offering strategies for hydroelectric generators, Operations Research, vol.51, issue.4, pp.602-612, 2003.

. Rte, Generation adequecy report, RTE, 2014.

S. Ruzic and R. Rajakovic, Optimal distance method for Lagrangian multipliers updating in short-term hydro-thermal coordination, IEEE transactions on power systems, vol.13, pp.1439-1444, 1998.

N. V. Sahinidis, Optimization under uncertainty: state-of-the-art and opportunities, Computers & Chemical Engineering, vol.28, issue.6, pp.971-983, 2004.

M. S. Salam, K. M. Nor, and A. R. Hamdam, Hydrothermal scheduling based lagrangian relaxation approach to hydrothermal coordination, IEEE Transactions on Power Systems, vol.13, issue.1, pp.226-235, 1998.

S. Sen, Algorithms for stochastic mixed-integer programming models, vol.12, pp.515-558, 2005.

A. Shapiro, On complexity of multistage stochastic programs. Operations Research Letters, vol.34, 2006.

A. Shapiro, Analysis of stochastic dual dynamic programming method, European Journal of Operational Research, vol.209, issue.1, pp.63-72, 2011.

A. Shapiro and D. Dentcheva, Lectures on stochastic programming: modeling and theory, vol.16, 2014.

Z. K. Shawwash, T. K. Siu, and S. D. Russell, The BC Hydro short term hydro scheduling optimization model, IEEE Transactions on Power Systems, vol.15, issue.3, pp.1125-1131, 2000.

G. Steeger, L. A. Barroso, and S. Rebennack, Optimal bidding strategies for hydroelectric producers: A literature survey. Power Systems, IEEE Transactions on, vol.29, issue.4, pp.1758-1766, 2014.

G. Steeger and S. Rebennack, Strategic bidding for multiple price-maker hydroelectric producers, IIE Transactions, vol.47, issue.9, pp.1013-1031, 2015.

G. Steeger and S. Rebennack, Dynamic convexification within nested Benders decomposition using Lagrangian relaxation: An application to the strategic bidding problem, European Journal of Operational Research, vol.257, issue.2, pp.669-686, 2017.

F. Thome, M. V. Pereira, S. Granville, and M. Fampa, Non-convexities representation on hydrothermal operation planning using SDDP

K. Verhaegen, L. Meeus, and R. Belmans, Development of balancing in the internal electricity market in europe, Proceedings 2006 European Wind Energy Conference, 2006.

J. P. Vielma, S. Ahmed, and G. Nemhauser, Mixed-integer models for nonseparable piecewise-linear optimization: unifying framework and extensions, Operations research, vol.58, issue.2, pp.303-315, 2010.

J. P. Vielma and G. L. Nemhauser, Modeling disjunctive constraints with a logarithmic number of binary variables and constraints, Mathematical Programming, vol.128, issue.1-2, pp.49-72, 2011.

S. W. Wallace and S. E. Fleten, Stochastic programming models in energy. Handbooks in operations research and management science, vol.10, pp.637-677, 2003.

J. Zou, S. Ahmed, and X. Sun, Nested decomposition of multistage stochastic integer programs with binary state variables. Available on Optimization Online, 2016.

. Titre, Optimisation de la rivière : enchères à court terme de l'hydroélectricité sous incertitude Mots clés : Optimisation stochastique, Hydro-ordonnancement, Optimisation non convexe Résumé

. Le-problème-de-l'hydro-offre-consiste-À-calculer-des-d'offre-optimales-afin-de-maximiser-le, un producteur hydroélectrique participant à un marché de l'électricité. Ces problèmes peuvent être difficiles à résoudre lorsque la fonction de valeur n'est pas concave. Dans cette thèse, nous étudions quelques-unes des limites du problème hydro-bidding et proposons une nouvelle méthode d'optimisation stochastique appelée le Mixed-Integer Dynamic Approximation Scheme (MIDAS). MIDAS résout des programmes stochastiques non convexe avec des fonctions de valeurs monotones. Il fonctionne de manière similaire à la Stochastic Dual Dynamic Programming (SDDP), mais au lieu utiliser des hyperplans, il utilise des fonctions d'étape pour créer une approximation externe de la fonction de valeur

, Nous utilisons MIDAS pour re?soudre trois types de proble?mes hydro-bidding non convexes. Le premier mode?le d'hydro-bidding que nous re?solvons a des variables d'e?tat entier car les productions sont discre?tes

. Dans-ce-mode?le, . Meilleur-que, and . Sddp, Le mode?le suivant d'hydro-bidding utilise des processus de prix autore?gressifs au lieu d'une chaîne de Markov. Le dernier mode?le d'hydrobidding inte?gre les effets de hauteur d'eau, ou? la fonction de production d'e?nergie de?pend du niveau de stockage du re?servoir et du de?bit d'eau de la turbine, tous ces mode?les, nous démontrons que la convergence de MIDAS en un nombre fini d'itération. Title: River Optimization: short-term hydro-bidding under uncertainty Keywords: Stochastic optimization