We introduce a quadratically-constrained approximation (QCAC) of the AC optimal power flow (AC-OPF) problem. Unlike existing approximations like the DC-OPF, our model does not rely on typical assumptions such as high reactance-to-resistance ratio, near-nominal voltage magnitudes, or small angle differences, and preserves the structural sparsity of the original AC power flow equations, making it suitable for decentralized power systems optimization problems. To achieve this, we reformulate the AC-OPF problem as a quadratically constrained quadratic program. The nonconvex terms are expressed as differences of convex functions, which are then convexified around a base point derived from a warm start of the nodal voltages. If this linearization results in a non-empty constraint set, the convexified constraints form an inner convex approximation. Our experimental results, based on Power Grid Library instances of up to 30,000 buses, demonstrate the effectiveness of the QCAC approximation with respect to other well-documented conic relaxations and a Taylor-series linear approximation. We further showcase its potential advantages over the well-documented second-order conic relaxation of the power flow equations in the optimal reactive power dispatch and photovoltaic hosting capacity problem.

With the adoption of electric planes to achieve aviation Net-Zero goals, the implementation of proper Energy Management Systems that can satisfy both the electric and thermal needs of airport buildings is paramount. However, the design of Energy Management Systems for thermo-electrical microgrids is challenging, particularly for model-based approaches, due to the complexities associated with detailed component modeling, uncertainties in renewable generation, and environmental conditions. Thus, this paper proposes a model-free Reinforcement Learning framework for the optimal operation of multi-zone airport hangar microgrids ensuring constraint satisfaction by incorporating physics-based dynamic constraints, and an implicit method to properly represent heat exchanges between zones. Simulation results, based on the operation of an actual Canadian airport microgrid with e-plane charging are benchmarked against a classical optimization-based approach, demonstrating that the proposed method achieves near optimal results. Furthermore, compared to conventional reward based approaches, the proposed framework is shown to have significantly faster convergence and more stable training behavior.

Optimization models have been applied to solve a wide variety of decision-making problems. These models are usually developed by optimization experts but are used by practitioners without optimization expertise in various application domains. As a result, practitioners often struggle to interact with and draw useful conclusions from optimization models independently. To fill this gap, we introduce OptiChat, a natural language dialogue system designed to help practitioners interpret model formulation, diagnose infeasibility, analyze sensitivity, retrieve information, evaluate modifications, and provide counterfactual explanations. By augmenting large language models (LLMs) with functional calls and code generation tailored for optimization models, we enable seamless interaction and minimize the risk of hallucinations in OptiChat. We develop a new data set to evaluate OptiChat’s performance in explaining optimization models. Experiments demonstrate that OptiChat effectively delivers autonomous, accurate, and instant responses. These findings highlight the potential of LLMs to bridge the gap between optimization models and practitioners in the real-world decision-making process.

This paper presents a parametric quadratic approximation of the AC optimal power flow (AC-OPF) problem for time-sensitive and market-based applications. The parametric approximation preserves the physics-based but simple representation provided by the DC-OPF model and leverages market and physics information encoded in the data-driven demand-dependent parameters. To enable the deployment of the proposed model for real-time applications, we propose a supervised learning approach to predict near-optimal parameters, given a certain metric concerning the dispatch quantities and locational marginal prices (LMPs). The training dataset is generated based on the solution of the accurate AC-OPF problem and a bilevel optimization problem, which calibrates parameters satisfying two market properties: cost recovery and revenue adequacy. We show the proposed approach’s performance in various test systems in terms of cost and dispatch approximation errors, LMPs, market properties satisfaction, dispatch feasibility, and generalizability with respect to N-1 network topologies.

Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in mechanisms to enforce such constraints, and existing approaches based on regularization or projection are often limited to simple constraints, computationally expensive, or lack feasibility guarantees. This paper proposes a model-agnostic framework for enforcing input-dependent linear equality and inequality constraints on neural network outputs. The architecture combines a task network trained for prediction accuracy with a safe network trained using decision rules from the stochastic and robust optimization literature to ensure feasibility across the entire input space. The final prediction is a convex combination of the two subnetworks, guaranteeing constraint satisfaction during both training and inference without iterative procedures or runtime optimization. We prove that the architecture is a universal approximator of constrained functions and derive computationally tractable formulations based on linear decision rules. Empirical results on benchmark regression tasks show that our method consistently satisfies constraints while maintaining competitive accuracy and low inference latency.

Decision-making problems can be represented as mathematical optimization models, finding wide applications in fields such as economics, engineering, transportation, and healthcare. One of the primary barriers to deploying these models in practice is the challenge of helping practitioners understand and interpret such models, particularly when they are infeasible, meaning no decision satisfies all the constraints. Existing methods for diagnosing infeasible optimization models often rely on expert systems, necessitating significant background knowledge in optimization. In this paper, we introduce OptiChat, a first-of-its-kind natural language-based system equipped with a chatbot GUI for engaging in interactive conversations about infeasible optimization models. OptiChat can provide natural language descriptions of the optimization model itself, identify potential sources of infeasibility, and offer suggestions to make the model feasible. The implementation of OptiChat is built on GPT-4, which interfaces with an optimization solver to identify the minimal subset of constraints that render the entire optimization problem infeasible, known as the Irreducible Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought, key-retrieve, and sentiment prompts to enhance OptiChat’s reliability. Our experiments demonstrate that OptiChat assists both expert and non-expert users in improving their understanding of the optimization models, enabling them to quickly identify the sources of infeasibility.