Journées de l'optimisation 2014
Incluant une Journée industrielle de l'optimisation
HEC Montréal, 5  7 mai 2014
JOPT2014
HEC Montréal, 5 — 7 mai 2014
MB6 Planification de la production d'électricité 1 / Electricity Production Planning 1
5 mai 2014 10h30 – 12h10
Salle: Nancy et MichelGaucher
Présidée par Michel Gendreau
4 présentations

10h30  10h55
ShortTerm Unit Commitment and Loading Problem for a Hydroelectric Production System
Presentation of a method for solving the shortterm unit commitment and loading problem of a hydropower system. Dynamic programming is used to compute maximum power output generated by a power plant. This information is then used as an input of a twophase optimization process. The first phase consists of solving the relaxation of a nonlinear mixedinteger program in order to obtain the water discharge, reservoir volume and optimal number of units working at each period in the planning horizon. The second stage solves a linear integer problem to determine which combination of turbines to use at each period. The goal is to maximize total power produced over all periods of the planning horizon which consists of a week divided in hourly periods. Startup of turbines are penalized. Two power plants with five turbines each are used to test the approach on thirty different test cases.

10h55  11h20
Adaptive Discretization Method of the State Space for Stochastic Dynamic Programming Applied to MultiReservoir System
For most realsize problems, the SDP algorithm applied to multireservoir systems suffers from the curse of dimensionality. A priori discretization of both control and state space should be avoided to apply SDP in higher dimensions: with more reservoirs or/and hydrological variables. The proposed method starts from an initial grid of the state space and refines it by using a splitting process, until some desired approximation of the Bellman function is achieved. Discretization of the state space is done online and our strategy yields a nonuniform and adaptive discretization grid. Numerical results on real hydropower systems are presented.

11h20  11h45
A Robust Optimization Model for the Short Term Reservoir Management Problem with Stochastic Inflows
This talk presents a robust optimization model for the shortterm reservoir management problem with stochastic inflows. Existing models include stochastic dynamic programming and 2stage stochastic programs. The former presents significant computational limitations while the latter cannot take into account the full dynamic nature of the problem. Robust optimization offers a third tractable alternative that remedies most of these shortcomings. Our model specifically incorporates water delays, correlations across time and reservoirs, variable water head as well as other complex physical constraints. We evaluate the use of simplifying assumptions which allow us to formulate the affinely adjustable robust counterpart (AARC) as a conic program. We discuss various ways to represent the underlying stochastic process and their repercussions on the feasibility of the program. Preliminary results are presented.

11h45  12h10
Optimal Scenario Set Partitioning for Multistage Stochastic Programming Using the Progressive Hedging Algorithm
In this presentation, we propose a new approach to speed up the progressive hedging algorithm (PHA) for solving largescale multistage stochastic programs defined on a scenario tree. Instead of using the conventional scenario decomposition scheme, we apply a multiscenario decomposition scheme and partition the scenario set in order to minimize the number of nonanticipativity constraints (NACs) on which an augmented Lagrangian relaxation must be applied. We demonstrate the efficiency of our method on an hydroelectricity generation scheduling problem with stochastic inflows.