2022 Optimization Days

HEC Montréal, Québec, Canada, 16 — 18 May 2022

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MB2 - Energy, environment and renewable resources

May 16, 2022 03:30 PM – 05:10 PM

Location: Trudeau Corporation (green)

Chaired by Imene Benkalai

4 Presentations

  • 03:30 PM - 03:55 PM

    Pathways to decarbonizing electricity in northeastern North America

    • Florian Mitjana, presenter, HEC Montréal
    • Michel Denault, HEC Montréal
    • Dominique Orban, GERAD - Polytechnique Montréal
    • Pierre-Olivier Pineau, HEC Montréal

    To analyze pathways to GHG targets in 2050, we develop a stochastic multi-stage investment & operation model that covers generation, transmission, and storage capacities. Long-term uncertainties are handled, such as demand growth and investment costs. The best strategies show that early decisions, as well as transmission investments, play a crucial role in decarbonizing at reasonable cost.

  • 03:55 PM - 04:20 PM

    Optimal planning of preventive maintenance tasks on power transmission systems

    • Mariana Rocha, presenter, Polytechnique Montréal
    • Miguel F. Anjos, University of Edinburgh
    • Michel Gendreau, Department of Mathematical and Industrial Engineering, University of Polytechnique Montreal

    The components of a transmission power system are susceptible to failure. The selection of the optimal period to remove a transmission line from operations to perform preventive maintenance is described by the transmission maintenance scheduling problem. We present a mixed-integer linear formulation of this problem for a long-term period of one year. This formulation ensures that the network remains connected and considers unexpected failures. A new decomposition algorithm is proposed to solve the problem. It divides the large formulation into two smaller problems, one is solved using Benders decomposition with CPLEX, and then the second validates the solution. We present results that demonstrate that our algorithm solves the scheduling with appropriate accuracy and more efficiently than solving the large-scale problem without decomposition.

  • 04:20 PM - 04:45 PM

    Modernization of a nonlinear least-squares algorithm operated for short-term electricity demand forecast in Québec

    • Pierre Borie, presenter, Université de Montréal / DIRO

    An accurate forecast of electricity consumption is at the heart of the operations of Hydro-Québec, the main supplier of electricity in Québec. Short-term demand is estimated with a parametric model whose parameters are calibrated by nonlinear least-squares, using a Fortran 77 library. While this model has been successfully applied for more than 30 years, its maintenance is increasingly more complicated, posing the need to modernize it. We present a reimplementation of the least-squares optimization method in Julia, which offers more reliability and readability compared to the original library. We discuss the underlying mathematical aspects of the algorithm and compare the results and performance of our implementation to two versions of the original Fortran 77 algorithm. We present several numerical experiments on standard nonlinear least-squares test problems. The preliminary results show very good agreement with respect to the intermediate results and the final outputs. Finally, we discuss different areas for improvement.

  • 04:45 PM - 05:10 PM

    Combining Decomposition with Discretised Optimisation Techniques and Application to a Hydrothermal Energy Production Problem

    • Luc Marchand, presenter, Université de Sherbrooke
    • Jean-Pierre Dussault, Université de Sherbrooke
    • Philippe Mahey, Institut Supérieur d'Informatique, Modélisation et de leurs Applications

    In this talk, we will look at medium-term hydrothermal production optimisation problem. This convex optimisation problem could be solved by combining two different algorithms, namely ADMM (alternating direction method of multipliers) and a discretised method, such as variants of Dynamic Programming. ADDM is an algorithm which received a lot of attention in recent years. Combining such algorithms requires to analyse in more detail the precision that needs to be achieved in the discretised algorithm in order to ensure convergence.

    First, we will review some convergence results of ADMM and provide precision bounds required for convergence through weaker hypotheses than in the litterature.

    In the second part, we will look more closely at the model previously presented. This model aggregates multiple hydro and thermal power sources in zones and looks for solutions minimizing the production cost while satisfying almost surely stochastic demand on energy. Some of the problem features, such as the problem not being strongly convex and having no structure restrictions for the transfers between zones, make a direct application of ADMM harder. We will look into the application of the aforementionned combination of ADMM and a specific dynamic programming scheme on this problem and show some preliminary numerical results.