Session: Optimisation and machine learning in energy
Chair: Hongyu Zhang
Cluster: Optimization Applications (Communication, Energy, Health, ML, ...)
Talk 1: A Computationally Efficient Cutting Plane Modelling to Generate Alternatives Algorithm
Speaker: Michael Lau
Abstract: Contemporary macro-energy systems modelling is characterized by the need to represent energy systems strategic and operational decisions with high temporal and spatial resolution, which provides more accurate results than more abstracted models. This drive towards greater fidelity, however, conflicts with a push towards greater model representation of inherent complexity in decision-making, including methods like Modelling to Generate Alternatives. Modelling to Generate Alternatives aims to map the feasible space of a model within a cost slack by varying investment parameters without changing the operational constraints, a process which frequently requires hundreds of solutions. For large, highly representative energy system models this is impossible with traditional methods, leading researchers to reduce complexity with either more zonal or temporal aggregation. This research presents a new solution method for Modelling to Generate Alternatives-type problems. Using Cutting Plane methods based on a reformulation of Bender’s Decomposition, we break down the problem structure into a strategic master problem and operational subproblems and pass information between master problems to accelerate convergence with each new objective. We find that our new solution method is several times faster and requires less memory than existing parallelized monolithic Modelling to Generate Alternatives solution methods, enabling rapid computation of a greater number of solutions to highly resolved models.
Talk 2: Multi-timescale stochastic programming with application in power systems
Speaker: Yihang Zhang
Abstract: We introduce a multi-timescale stochastic programming framework for decision-making under multi-timescale uncertainty. Aggregated state variables are used to coordinate decisions across timescales, similar to the role of state variables in a multistage problem. Based on this setup, we describe instantiation strategies that use either multi-horizon scenario trees (to model multi-lag dependence on a timescale) or a specialized value function to fully exploit independence of the randomness within the timescale. We develop decomposition algorithms (price-directive or resource-directive) to incrementally approximate and solve the resulting problem. In addition to techniques used in multistage problems, we describe solution-reusing heuristics to accelerate the solution process by leveraging similarities between subproblems.
Talk 3: A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization
Speaker: Aron Brenner
Abstract: Two-stage adaptive robust optimization (ARO) is a powerful approach for planning under uncertainty, balancing first-stage decisions with recourse decisions made after uncertainty is realized. To account for uncertainty, modelers typically define a simple uncertainty set over which potential outcomes are considered. However, classical methods for defining these sets unintentionally capture a wide range of unrealistic outcomes, resulting in overly-conservative and costly planning in anticipation of unlikely contingencies. In this work, we introduce AGRO, a solution algorithm that performs adversarial generation for two-stage adaptive robust optimization using a variational autoencoder. AGRO generates high-dimensional contingencies that are simultaneously adversarial and realistic, improving the robustness of first-stage decisions at a lower planning cost than standard methods. To ensure generated contingencies lie in high-density regions of the uncertainty distribution, AGRO defines a tight uncertainty set as the image of “latent" uncertainty sets under the VAE decoding transformation. Projected gradient ascent is then used to maximize recourse costs over the latent uncertainty sets by leveraging differentiable optimization methods. We demonstrate the cost-efficiency of AGRO by applying it to both a synthetic production-distribution problem and a real-world power system expansion setting. We show that AGRO outperforms the standard column-and-constraint algorithm by up to 1.8% in production-distribution planning and up to 11.6% in power system expansion.
