Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline

Load Embeddings for Scalable AC-OPF Learning

AC Optimal Power Flow (AC-OPF) is a fundamental building block in power system optimization. It is often solved repeatedly, especially in regions with large penetration of renewable generation, to avoid violating operational limits. Recent work has shown that deep learning can be effective in providing highly accurate approximations of AC-OPF. However, deep learning approaches may suffer from scalability issues, especially when applied to large realistic grids. This paper addresses these scalability limitations and proposes a load embedding scheme using a 3-step approach. The first step formulates the load embedding problem as a bilevel optimization model that can be solved using a penalty method. The second step learns the encoding optimization to quickly produce load embeddings for new OPF instances. The third step is a deep learning model that uses load embeddings to produce accurate AC-OPF approximations. The approach is evaluated experimentally on large-scale test cases from the NESTA library. The results demonstrate that the proposed approach produces an order of magnitude improvements in training convergence and prediction accuracy

Compact Optimization Learning for AC Optimal Power Flow

This paper reconsiders end-to-end learning approaches to the Optimal Power Flow (OPF). Existing methods, which learn the input/output mapping of the OPF, suffer from scalability issues due to the high dimensionality of the output space. This paper first shows that the space of optimal solutions can be significantly compressed using principal component analysis (PCA). It then proposes Compact Learning, a new method that learns in a subspace of the principal components before translating the vectors into the original output space. This compression reduces the number of trainable parameters substantially, improving scalability and effectiveness. Compact Learning is evaluated on a variety of test cases from the PGLib with up to 30,000 buses. The paper also shows that the output of Compact Learning can be used to warm-start an exact AC solver to restore feasibility, while bringing significant speed-ups.Comment: Submitted to IEEE Transactions on Power System

Learning Regionally Decentralized AC Optimal Power Flows with ADMM

One potential future for the next generation of smart grids is the use of decentralized optimization algorithms and secured communications for coordinating renewable generation (e.g., wind/solar), dispatchable devices (e.g., coal/gas/nuclear generations), demand response, battery & storage facilities, and topology optimization. The Alternating Direction Method of Multipliers (ADMM) has been widely used in the community to address such decentralized optimization problems and, in particular, the AC Optimal Power Flow (AC-OPF). This paper studies how machine learning may help in speeding up the convergence of ADMM for solving AC-OPF. It proposes a novel decentralized machine-learning approach, namely ML-ADMM, where each agent uses deep learning to learn the consensus parameters on the coupling branches. The paper also explores the idea of learning only from ADMM runs that exhibit high-quality convergence properties, and proposes filtering mechanisms to select these runs. Experimental results on test cases based on the French system demonstrate the potential of the approach in speeding up the convergence of ADMM significantly.Comment: 11 page

Maintaining Soft Arc Consistency in BnB-ADOPT+ During Search

Gutierrez and Meseguer show how to enforce consistency in BnB-ADOPT + for distributed constraint optimization, but they consider unconditional deletions only. However, during search, more values can be pruned conditionally according to variable instantiations that define subproblems. Enforcing consistency in these subproblems can cause further search space reduction. We introduce efficient methods to maintain soft arc consistencies in every subproblem during search, a non trivial task due to asynchronicity and induced overheads. Experimental results show substantial benefits on three different benchmarks. © 2013 Springer-Verlag.The work of Gutierrez and Meseguer was partially supported by the Spanish project TIN2009-13591-C02-02 and Generalitat de Catalunya 2009-SGR-1434.Peer Reviewe

Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often needed to be solved repeatedly under various conditions, either in real-time or in large-scale studies. This need is further exacerbated by the increasing stochasticity of power systems due to renewable energy sources in front and behind the meter. To address these challenges, this paper presents a deep learning approach to the OPF. The learning model exploits the information available in the prior states of the system (which is commonly available in practical applications), as well as a dual Lagrangian method to satisfy the physical and engineering constraints present in the OPF. The proposed model is evaluated on a large collection of realistic power systems. The experimental results show that its predictions are highly accurate with average errors as low as 0.2%. Additionally, the proposed approach is shown to improve the accuracy of widely adopted OPF linear DC approximation by at least two orders of magnitude.Comment: A version of this paper appears in AAAI 202