10h30 - 10h55
Short-Term Unit Commitment and Loading Problem for a Hydroelectric Production System
Presentation of a method for solving the short-term 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 two-phase optimization process. The first phase consists of solving the relaxation of a nonlinear mixed-integer 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. Start-up 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 Multi-Reservoir System
For most real-size problems, the SDP algorithm applied to multi-reservoir 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 non-uniform 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 short-term reservoir management problem with stochastic inflows. Existing models include stochastic dynamic programming and 2-stage 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 large-scale multistage stochastic programs defined on a scenario tree. Instead of using the conventional scenario decomposition scheme, we apply a multi-scenario decomposition scheme and partition the scenario set in order to minimize the number of non-anticipativity 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.