Session: Optimization in Power Systems and Energy
Chair: Paprapee Buason
Cluster: nan
Talk 1: Beyond Traditional Linearizations: Enhancing Power Flow Approximations with Second-Order Sensitivities
Speaker: Paprapee Buason
Abstract: The power flow equations are fundamental to power system planning, analysis, and control, but their nonlinear and nonconvex nature presents significant challenges for optimization and decision-making. While linear approximations offer computational efficiency, they often rely on broad assumptions that may not hold across diverse operating conditions, leading to inaccuracies. In particular, these methods often fail to consistently over- or under-estimate critical quantities, such as voltage magnitudes, which can result in constraint violations when applied to optimization problems. Furthermore, they do not account for the varying curvature of the power flow equations, limiting their ability to provide reliable approximations In this talk, we introduce advanced techniques to enhance the accuracy and reliability of power flow linearizations. Specifically, we focus on conservative linear approximations (CLAs), which systematically over- or under-estimate key quantities to ensure constraint satisfaction and deliver safer, more reliable solutions. Our approach leverages a sample-based framework combined with constrained linear regression while maintaining tractability and parallelizability. Additionally, we employ second-order sensitivity analysis to assess curvature and guide the selection of high-accuracy approximations. Building on these insights, we develop conservative piecewise linear approximations (CPLAs), which selectively apply piecewise linear functions in directions exhibiting significant nonlinearities, further improving accuracy beyond what standard linear approximations can achieve. Through extensive evaluations, we demonstrate that these methods enhance both accuracy and reliability, broadening their applicability to power system optimization. References: P. Buason, S. Misra, J.P. Watson, and D.K. Molzahn, "Adaptive Power Flow Approximations with Second-Order Sensitivity Insights," to appear in IEEE Transactions on Power Systems. P. Buason, S. Misra, and D.K. Molzahn, "Sample-Based Piecewise Linear Power Flow Approximations Using Second-Order Sensitivities," submitted.
Talk 2: Learning to Optimize: An Accelerated Deep Learning Framework for AC Optimal Power Flow Problem
Speaker: Yu Zhang
Abstract: The Alternating Current Optimal Power Flow (AC-OPF) problem plays a critical role in ensuring efficient and reliable power grid operations, especially with the increasing penetration of renewable energy. However, traditional solvers struggle to meet the real-time requirements due to their computational complexity. This work presents a novel semi-supervised learning framework that leverages physics-informed gradient estimation techniques to accelerate deep learning-based AC-OPF solutions. By integrating data augmentation and developing batch-mean gradient estimators with a reduced branch set, we achieve significant improvements in both feasibility and optimality. Numerical simulations on benchmark systems demonstrate that the proposed method consistently delivers near-optimal solutions with minimal constraint violations while achieving substantial speed-ups compared to conventional nonlinear programming solvers. These results highlight the potential of deep learning to transform real-time energy market operations and support the growing demand for renewable integration. Reference: K. Chen, S. Bose, Y. Zhang, "Physics-Informed Gradient Estimation for Accelerating Deep Learning based AC-OPF," IEEE Transactions on Industrial Informatics, Feb. 2025 (accepted)
Talk 3: Stationary battery energy management problem: a comparative study of several optimization models
Speaker: Daniel Mimouni
Abstract: Energy Management Systems (EMS) are crucial in optimizing energy production and minimizing costs in modern power networks. The inherent complexity of EMS problems arises from their multiperiod nature, where decisions at each stage are interplayed with outcomes of a random vector representing fluctuations in both production and consumption over time. In this paper, we focus on the EMS of a stationary battery, using ground truth measurements of electricity consumption and production from a predominantly commercial building in France. We compare several optimization models tailored to the problem for this particular EMS. Classical approaches such as MPC and risk-free multi-stage stochastic programming with recourse rely on specific assumptions (e.g. knowing the probability distribution). Therefore, they often lack robustness to distributional shifts. To enhance robustness, we explore other models. By introducing a policy variance penalty into the multi-stage stochastic model, inspired by regularization techniques in machine learning, we mitigate sensitivity to distributional shifts. Furthermore, we consider a distributionally robust optimization that offers a middle ground between robust and risk-neutral models, improving robustness by optimizing over an ambiguity set. Reinforcement learning, in contrast, offers a data-driven approach that bypasses explicit scenario generation but introduces challenges related to stability and convergence. Through numerical experiments, we evaluate these models in terms of cost efficiency, computational scalability, and out-of-sample robustness, offering a comprehensive comparison and insights into their practical interest for real-world EMS problems.
