This paper proposes a neural stochastic optimization method for efficiently solving the two-stage stochastic unit commitment (2S-SUC) problem under high-dimensional uncertainty scenarios. The proposed method approximates the second-stage recourse problem using a deep neural network trained to map commitment decisions and uncertainty features to recourse costs. The trained network is subsequently embedded into the first-stage UC problem as a mixed-integer linear program (MILP), allowing for explicit enforcement of operational constraints while preserving the key uncertainty characteristics. A scenario-embedding network is employed to enable dimensionality reduction and feature aggregation across arbitrary scenario sets, serving as a data-driven scenario reduction mechanism. Numerical experiments on IEEE 5-bus, 30-bus, and 118-bus systems demonstrate that the proposed neural two-stage stochastic optimization method achieves solutions with an optimality gap of less than 1%, while enabling orders-of-magnitude speedup compared to conventional MILP solvers and decomposition-based methods. Moreover, the model's size remains constant regardless of the number of scenarios, offering significant scalability for large-scale stochastic unit commitment problems.

The Unit Commitment (UC) problem is a classic challenge in the optimal scheduling of power systems. Years of research and practice have shown that formulating reasonable unit commitment plans can significantly improve the economic efficiency of power systems' operations. In recent years, with the introduction of technologies such as machine learning and the Lagrangian relaxation method, the solution methods for the UC problem have become increasingly diversified, but still face challenges in terms of accuracy and robustness. This paper proposes a Function Space Search (FunSearch) method based on large language models. This method combines pre-trained large language models and evaluators to creatively generate solutions through the program search and evolution process while ensuring their rationality. In simulation experiments, a case of unit commitment with \(10\) units is used mainly. Compared to the genetic algorithm, the results show that FunSearch performs better in terms of sampling time, evaluation time, and total operating cost of the system, demonstrating its great potential as an effective tool for solving the UC problem.

This article investigates the ability of graph neural networks (GNNs) to identify risky conditions in a power grid over the subsequent few hours, without explicit, high-resolution information regarding future generator on/off status (grid topology) or power dispatch decisions. The GNNs are trained using supervised learning, to predict the power grid's aggregated bus-level (either zonal or system-level) or individual branch-level state under different power supply and demand conditions. The variability of the stochastic grid variables (wind/solar generation and load demand), and their statistical correlations, are rigorously considered while generating the inputs for the training data. The outputs in the training data, obtained by solving numerous mixed-integer linear programming (MILP) optimal power flow problems, correspond to system-level, zonal and transmission line-level quantities of interest (QoIs). The QoIs predicted by the GNNs are used to conduct hours-ahead, sampling-based reliability and risk assessment w.r.t. zonal and system-level (load shedding) as well as branch-level (overloading) failure events. The proposed methodology is demonstrated for three synthetic grids with sizes ranging from 118 to 2848 buses. Our results demonstrate that GNNs are capable of providing fast and accurate prediction of QoIs and can be good proxies for computationally expensive MILP algorithms. The excellent accuracy of GNN-based reliability and risk assessment suggests that GNN models can substantially improve situational awareness by quickly providing rigorous reliability and risk estimates.

This letter proposes a few-shot physics-guided spatial temporal graph convolutional network (FPG-STGCN) to fast solve unit commitment (UC). Firstly, STGCN is tailored to parameterize UC. Then, few-shot physics-guided learning scheme is proposed. It exploits few typical UC solutions yielded via commercial optimizer to escape from local minimum, and leverages the augmented Lagrangian method for constraint satisfaction. To further enable both feasibility and continuous relaxation for integers in learning process, straight-through estimator for Tanh-Sign composition is proposed to fully differentiate the mixed integer solution space. Case study on the IEEE benchmark justifies that, our method bests mainstream learning ways on UC feasibility, and surpasses traditional solver on efficiency.

We investigate the utility of graph neural networks (GNNs) as proxies of power grid operational decision-making algorithms (optimal power flow (OPF) and security-constrained unit commitment (SCUC)) to enable rigorous quantification of the operational risk. To conduct principled risk analysis, numerous Monte Carlo (MC) samples are drawn from the (foretasted) probability distributions of spatio-temporally correlated stochastic grid variables. The corresponding OPF and SCUC solutions, which are needed to quantify the risk, are generated using traditional OPF and SCUC solvers to generate data for training GNN model(s). The GNN model performance is evaluated in terms of the accuracy of predicting quantities of interests (QoIs) derived from the decision variables in OPF and SCUC. Specifically, we focus on thermal power generation and load shedding at system and individual zone level. We also perform reliability and risk quantification based on GNN predictions and compare with that obtained from OPF/SCUC solutions. Our results demonstrate that GNNs are capable of providing fast and accurate prediction of QoIs and thus can be good surrogate models for OPF and SCUC. The excellent accuracy of GNN-based reliability and risk assessment further suggests that GNN surrogate has the potential to be applied in real-time and hours-ahead risk quantification.

Benders decomposition is widely used to solve large mixed-integer problems. This paper takes advantage of machine learning and proposes enhanced variants of Benders decomposition for solving two-stage stochastic security-constrained unit commitment (SCUC). The problem is decomposed into a master problem and subproblems corresponding to a load scenario. The goal is to reduce the computational costs and memory usage of Benders decomposition by creating tighter cuts and reducing the size of the master problem. Three approaches are proposed, namely regression Benders, classification Benders, and regression-classification Benders. A regressor reads load profile scenarios and predicts subproblem objective function proxy variables to form tighter cuts for the master problem. A criterion is defined to measure the level of usefulness of cuts with respect to their contribution to lower bound improvement. Useful cuts that contain the necessary information to form the feasible region are identified with and without a classification learner. Useful cuts are iteratively added to the master problem, and non-useful cuts are discarded to reduce the computational burden of each Benders iteration. Simulation studies on multiple test systems show the effectiveness of the proposed learning-aided Benders decomposition for solving two-stage SCUC as compared to conventional multi-cut Benders decomposition.

Security-constrained unit commitment (SCUC) is solved for power system day-ahead generation scheduling, which is a large-scale mixed-integer linear programming problem and is very computationally intensive. Model reduction of SCUC may bring significant time savings. In this work, a novel approach is proposed to effectively utilize machine learning (ML) to reduce the problem size of SCUC. An ML model using logistic regression (LR) algorithm is proposed and trained with historical nodal demand profiles and the respective commitment schedules. The ML outputs are processed and analyzed to reduce variables and constraints in SCUC. The proposed approach is validated on several standard test systems including IEEE 24-bus system, IEEE 73-bus system, IEEE 118-bus system, synthetic South Carolina 500-bus system and Polish 2383-bus system. Simulation results demonstrate that the use of the prediction from the proposed LR model in SCUC model reduction can substantially reduce the computing time while maintaining solution quality.

Security-Constrained Unit Commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via Mixed-Integer Linear Programming, sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning (ML) techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions and affine subspaces where the optimal solution is likely to lie, leading to significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that, using the proposed techniques, SCUC can be solved on average 12 times faster than conventional methods, with no negative impact on solution quality.