arXiv subjects
Publications and source records attributed to Kyri Baker.
This article addresses recent advances in artificial intelligence, which have set off an astounding race among technology frontiers to build large data centers. It provides insights into impacts of large data centers on the planning and operation of the power grid.
Maintaining instantaneous balance between electricity supply and demand is critical for reliability and grid instability. System operators achieve this through solving the task of Unit Commitment (UC),ca high dimensional large-scale Mixed-integer Linear Programming (MILP) problem that is strictly and heavily governed by the grid physical constraints. As grid integrate variable renewable sources, and new technologies such as long duration storage in the grid, UC must be optimally solved for multi-day horizons and potentially with greater frequency. Therefore, traditional MILP solvers increasingly struggle to compute solutions within these tightening operational time limits. To bypass these computational bottlenecks, this paper proposes a novel framework utilizing a transformer-based architecture to predict generator commitment schedules over a 72-hour horizon. Also, because raw predictions in highly dimensional spaces often yield physically infeasible results, the pipeline integrates the self-attention network with deterministic post-processing heuristics that systematically enforce minimum up/down times and minimize excess capacity. Finally, these refined predictions are utilized as a warm start for a downstream MILP solver, while employing a confidence-based variable fixation strategy to drastically reduce the combinatorial search space. Validated on a single-bus test system, the complete multi-stage pipeline achieves 100\% feasibility and significantly accelerates computation times. Notably, in approximately 20\% of test instances, the proposed model reached a feasible operational schedule with a lower overall system cost than relying solely on the solver.
Data centers are growing rapidly, creating the pressing need for the development of critical infrastructure build out to support these resource-intensive large loads. Their immense consumption of electricity and, often, freshwater, continues to stress an already constrained and aging power grid and water resources. This paper presents a comprehensive modeling approach to determine the optimal locations to construct such facilities by quantifying their resource use and minimizing associated costs. The interdisciplinary modeling approach incorporates a number of factors including the power grid, telecommunications, climate, water use, and collocated generation potential. This work establishes the base model whose functionality is shown through several test cases focusing on carbon-free generation collocation on a county-level in the United States. The results suggest that while capital costs are the biggest driver, having a longer future outlook and allowing more variable generation collocation influences the model to choose sites with higher renewable potential.
Wholesale power markets often use linear approximations of power system constraints. Because it does not consider inequality constraints, using AC power flow for feasibility post-processing can violate bounds on reactive power, voltage magnitudes, or thermal limits. There remains a need for a streamlined analytical approach that can guarantee AC feasibility while adhering to variable bounds. This paper suggests an augmented implementation of AC power flow that uses an additional two bus types (PQV and P) to help resolve voltage bound violations present in the traditional approach. The proposed method sacrifices the voltage setpoint at a generator in exchange for fixing the voltage at a load bus, thereby moving a degree of freedom around the network. Results on the IEEE 14-bus, 57-bus, and 300-bus test cases demonstrate how switching bus types can reduce overall network violations and help find feasible power system setpoints.
Solving the nonlinear AC optimal power flow (AC OPF) problem remains a major computational bottleneck for real-time grid operations. In this paper, we propose a residual learning paradigm that uses fast DC optimal power flow (DC OPF) solutions as a baseline, and learns only the nonlinear corrections required to provide the full AC-OPF solution. The method utilizes a topology-aware Graph Neural Network with local attention and two-level DC feature integration, trained using a physics-informed loss that enforces AC power-flow feasibility and operational limits. Evaluations on OPFData for 57-, 118-, and 2000-bus systems show around 25% lower MSE, up to 3X reduction in feasibility error, and up to 13X runtime speedup compared to conventional AC OPF solvers. The model maintains accuracy under N-1 contingencies and scales efficiently to large networks. These results demonstrate that residual learning is a practical and scalable bridge between linear approximations and AC-feasible OPF, enabling near real-time operational decision making.
Electric power grids are essential components of modern life, delivering reliable power to end-users while adhering to a multitude of engineering constraints and requirements. In grid operations, the Optimal Power Flow problem plays a key role in determining cost-effective generator dispatch that satisfies load demands and operational limits. However, due to stressed operating conditions, volatile demand profiles, and increased generation from intermittent energy sources, this optimization problem may become infeasible, posing risks such as voltage instability and line overloads. This study proposes a learning framework that combines machine learning with counterfactual explanations to automatically diagnose and restore feasibility in the OPF problem. Our method provides transparent and actionable insights by methodically identifying infeasible conditions and suggesting minimal demand response actions. We evaluate the proposed approach on IEEE 30-bus and 300-bus systems, demonstrating its capability to recover feasibility with high success rates and generating diverse corrective options, appropriate for real-time decision-making. These preliminary findings illustrate the potential of combining classical optimization with explainable AI techniques to enhance grid reliability and resilience.
Demand response is a concept that has been around since the very first electric power systems. However, we have seen an explosion of research on demand response and demand-side technologies in the past 30 years, coinciding with the shift towards liberalized/deregulated electricity markets and efforts to decarbonize the power sector. Now we are also seeing a shift towards more distributed/decentralized electric systems; we have entered the era of "distributed energy resources," which require new grid management, operational, and control strategies. Given this paradigm shift, we argue that the concept of demand response needs to be revisited, and more carefully/consistently defined to enable us to better utilize this massive resource for economic, technical, environmental, and societal aims. In this paper, we survey existing demand response definitions, highlight their shortcomings, propose a new definition, and describe how this new definition enables us to more effectively harness the value of demand response in modern power systems. We conclude with a demand response research agenda informed by a discussion of demand response barriers and enablers.
Recent developments in applying machine learning to address Alternating Current Optimal Power Flow (AC OPF) problems have demonstrated significant potential in providing close to optimal solutions for generator dispatch in near real-time. While these learning to optimize methods have demonstrated remarkable performance on steady-state operations, practical applications often demand compliance with dynamic constraints when used for fast-timescale optimization. This paper addresses this gap and develops a real-time stability-constrained OPF model (DynOPF-Net) that simultaneously addresses both optimality and dynamical stability within learning-assisted grid operations. The model is a unique integration of learning to optimize that learns a mapping from load conditions to OPF solutions, capturing the OPF's physical and engineering constraints, with Neural Ordinary Differential Equations, capturing generator dynamics, enabling the inclusion of a subset of stability constraints. Numerical results on the WSCC 9-bus and IEEE 57-bus benchmark systems demonstrate that DynOPF-Net can produce highly accurate AC-OPF solutions while also ensuring system stability, contrasting the unstable results obtained by state-of-the-art LtO methods.
Replacing fossil-fueled appliances and vehicles with electric alternatives can reduce greenhouse gas emissions and air pollution in many settings. However, residential electrification can also raise electricity demand beyond the safe limits of electrical infrastructure. This can increase the risk of blackouts or require grid reinforcement that is often slow and expensive. Here, we estimate the physical and economic impacts on distribution grids of electrifying all housing and personal vehicles in each county of the lower 48 United States. We find that space heating is the main driver of grid impacts, with the coldest regions seeing demand peaks up to five times higher than today's peaks. Accommodating electrification of all housing and personal vehicles is estimated to require 600 GW of distribution grid reinforcement nationally, at a cost of \$350 to \$790 billion, or \$2,800 to \$6,400 per household (95% confidence intervals). However, demand-side management could eliminate three-quarters of grid reinforcement costs.
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control strategies must be determined for systems governed by ordinary or stochastic differential equations. Despite its significance, the computational challenges associated with these problems have limited their practical use. To address these limitations, this paper introduces a learning-based approach to DE-constrained optimization that combines techniques from proxy optimization and neural differential equations. The proposed approach uses a dual-network architecture, with one approximating the control strategies, focusing on steady-state constraints, and another solving the associated DEs. This combination enables the approximation of optimal strategies while accounting for dynamic constraints in near real-time. Experiments across problems in energy optimization and finance modeling show that this method provides full compliance with dynamic constraints and it produces results up to 25 times more precise than other methods which do not explicitly model the system's dynamic equations.
Electricity markets often utilize the DC approximation of the AC power flow equations to facilitate solving an otherwise complex nonconvex optimization problem. These DC power flow equations have analogies to DC circuit laws such as Kirchhoff's Laws, resulting in an intuitive understanding of power flows under this model. Variables derived from the Lagrangian dual of the DC optimal power flow problem, such as locational marginal prices (LMPs) and congestion cost, are less intuitive without an understanding of optimization theory. Even with this understanding, LMP behavior, such as the conditions in which negative prices occur or the impact of individual congested lines on network-wide LMPs, remain somewhat mysterious. In this paper, we show that prices also obey DC circuit laws, which can help facilitate an intuitive understanding of their behavior and relationships throughout a network without explicitly understanding duality. In particular, prices can be modeled as voltages, and their differences can be modeled as flows, allowing for a physical interpretation of prices. This analogy also lends itself to the use of well-understood DC circuit concepts such as superposition and Kirchhoff's Laws, which can further facilitate a clearer understanding of price behavior.
This work proposes a novel method for scaling multi-timestep security-constrained optimal power flow in large power grids. The challenge arises from dealing with millions of variables and constraints, including binary variables and nonconvex, nonlinear characteristics. To navigate these complexities, techniques such as constraint relaxation, linearization, sequential optimization, and problem reformulation are employed. By leveraging these methods, complex power grid problems are solved while achieving high-quality solutions and meeting time constraints. The innovative solution approach showcases great robustness and consistently outperforms benchmark standards.
The adoption of electric vehicles (EVs), including electric taxis and buses, as a mode of transportation, is rapidly increasing in cities. In addition to providing economic and environmental benefits, these fleets can potentially participate in the energy arbitrage market by leveraging their mobile energy storage capabilities. This presents an opportunity for EV owners to contribute to a more sustainable and efficient energy system while also reducing their operational costs. The present study introduces deterministic and single-stage stochastic optimization frameworks that aim to maximize revenue by optimizing the charging, discharging, and travel of a fleet of electric vehicles in the context of uncertainty surrounding both spatial and temporal energy prices. The simulations are performed on a fleet of electric delivery trucks, which have to make deliveries to certain locations on specific dates. The findings indicate the promising potential of bidirectional electric vehicle charging as a mobile grid asset. However, it is important to note that significant revenue is only realized in scenarios where there is substantial variation in prices between different areas, and when these price variations can be accurately forecasted with a high level of confidence.
Linear approximations of the AC power flow equations are of great significance for the computational efficiency of large-scale optimal power flow (OPF) problems. Put differently, the feasibility of the obtained solution is essential for practical use cases of OPF. However, most studies focus on approximation error and come short of comprehensively studying the AC feasibility of different linear approximations of power flow. This paper discusses the merits of widely-used linear approximations of active power in OPF problems. The advantages and disadvantages of the linearized models are discussed with respect to four criteria; accuracy of the linear approximation, optimality, feasibility, and computation time. Each method is tested on five different systems.
The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics must be considered to ensure that the optimal solutions provided by these models adhere to practical dynamical constraints, avoiding frequency fluctuations and grid instabilities. Unfortunately, dynamic system models based on ordinary or partial differential equations are frequently unsuitable for direct application in control or state estimates due to their high computational costs. To address these challenges, this paper introduces a machine learning method to approximate the behavior of power systems dynamics in near real time. The proposed framework is based on gradient-enhanced physics-informed neural networks (gPINNs) and encodes the underlying physical laws governing power systems. A key characteristic of the proposed gPINN is its ability to train without the need of generating expensive training data. The paper illustrates the potential of the proposed approach in both forward and inverse problems in a single-machine infinite bus system for predicting rotor angles and frequency, and uncertain parameters such as inertia and damping to showcase its potential for a range of power systems applications.
Using machine learning to obtain solutions to AC optimal power flow has recently been a very active area of research due to the astounding speedups that result from bypassing traditional optimization techniques. However, generally ensuring feasibility of the resulting predictions while maintaining these speedups is a challenging, unsolved problem. In this paper, we train a neural network to emulate an iterative solver in order to cheaply and approximately iterate towards the optimum. Once we are close to convergence, we then solve a power flow to obtain an overall AC-feasible solution. Results shown for networks up to 1,354 buses indicate the proposed method is capable of finding feasible, near-optimal solutions to AC OPF in milliseconds on a laptop computer. In addition, it is shown that the proposed method can find "difficult" AC OPF solutions that cause flat-start or DC-warm started algorithms to diverge.
Optimal Power Flow (OPF) is a fundamental problem in power systems. It is computationally challenging and a recent line of research has proposed the use of Deep Neural Networks (DNNs) to find OPF approximations at vastly reduced runtimes when compared to those obtained by classical optimization methods. While these works show encouraging results in terms of accuracy and runtime, little is known on why these models can predict OPF solutions accurately, as well as about their robustness. This paper provides a step forward to address this knowledge gap. The paper connects the volatility of the outputs of the generators to the ability of a learning model to approximate them, it sheds light on the characteristics affecting the DNN models to learn good predictors, and it proposes a new model that exploits the observations made by this paper to produce accurate and robust OPF predictions.
Increasing levels of renewable generation motivate a growing interest in data-driven approaches for AC optimal power flow (AC OPF) to manage uncertainty; however, a lack of disciplined dataset creation and benchmarking prohibits useful comparison among approaches in the literature. To instill confidence, models must be able to reliably predict solutions across a wide range of operating conditions. This paper develops the OPF-Learn package for Julia and Python, which uses a computationally efficient approach to create representative datasets that span a wide spectrum of the AC OPF feasible region. Load profiles are uniformly sampled from a convex set that contains the AC OPF feasible set. For each infeasible point found, the convex set is reduced using infeasibility certificates, found by using properties of a relaxed formulation. The framework is shown to generate datasets that are more representative of the entire feasible space versus traditional techniques seen in the literature, improving machine learning model performance.