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The complexities of information processing across Dynamic Data Driven Applications Systems drive the development and adoption of Artificial Intelligence-based optimization solutions. Traditional solvers often suffer from slow response times and an inability to adapt swiftly to real-time input variations. To address these deficiencies, we will expand on our previous research in neural-based optimizers by introducing a machine learning-enabled neural approximation model called LOOP-PE (Learning to Optimize the Optimization Process -- Permutation Equivariance version). This model not only enhances decision-making efficiency but also dynamically adapts to variations of data collections from sensor networks. In this work, we focus on mitigating the heterogeneity issues of data collection from sensor networks, including sensor dropout and failures, communication delays, and the complexities involved in integrating new sensors during system scaling. The proposed LOOP-PE model specifically overcomes these issues with a unique structure that is permutation equivariant, allowing it to accommodate inputs from a varying number of sensors and directly linking these inputs to their optimal operational outputs. This design significantly boosts the system's flexibility and adaptability, especially in scenarios characterized by unordered, distributed, and asynchronous data collections. Moreover, our approach increases the robustness of decision-making by integrating physical constraints through the generalized gauge map method, which theoretically ensures the decisions' practical feasibility and operational viability under dynamic conditions. We use a DDDAS case study to demonstrate that LOOP-PE model reliably delivers near-optimal and adaptable solutions, significantly outperforming traditional methods in managing the complexities of multi-sensor environments for real-time deployments.

The evolution towards a more distributed and interconnected grid necessitates large-scale decision-making within strict temporal constraints. Machine learning (ML) paradigms have demonstrated significant potential in improving the efficacy of optimization processes. However, the feasibility of solutions derived from ML models continues to pose challenges. It's imperative that ML models produce solutions that are attainable and realistic within the given system constraints of power systems. To address the feasibility issue and expedite the solution search process, we proposed LOOP-LC 2.0(Learning to Optimize the Optimization Process with Linear Constraints version 2.0) as a learning-based approach for solving the power dispatch problem. A notable advantage of the LOOP-LC 2.0 framework is its ability to ensure near-optimality and strict feasibility of solutions without depending on computationally intensive post-processing procedures, thus eliminating the need for iterative processes. At the heart of the LOOP-LC 2.0 model lies the newly proposed generalized gauge map method, capable of mapping any infeasible solution to a feasible point within the linearly-constrained domain. The proposed generalized gauge map method improves the traditional gauge map by exhibiting reduced sensitivity to input variances while increasing search speeds significantly. Utilizing the IEEE-200 test case as a benchmark, we demonstrate the effectiveness of the LOOP-LC 2.0 methodology, confirming its superior performance in terms of training speed, computational time, optimality, and solution feasibility compared to existing methodologies.

Amid the increasing interest in the deployment of Distributed Energy Resources (DERs), the Virtual Power Plant (VPP) has emerged as a pivotal tool for aggregating diverse DERs and facilitating their participation in wholesale energy markets. These VPP deployments have been fueled by the Federal Energy Regulatory Commission's Order 2222, which makes DERs and VPPs competitive across market segments. However, the diversity and decentralized nature of DERs present significant challenges to the scalable coordination of VPP assets. To address efficiency and speed bottlenecks, this paper presents a novel machine learning-assisted distributed optimization to coordinate VPP assets. Our method, named LOOP-MAC(Learning to Optimize the Optimization Process for Multi-agent Coordination), adopts a multi-agent coordination perspective where each VPP agent manages multiple DERs and utilizes neural network approximators to expedite the solution search. The LOOP-MAC method employs a gauge map to guarantee strict compliance with local constraints, effectively reducing the need for additional post-processing steps. Our results highlight the advantages of LOOP-MAC, showcasing accelerated solution times per iteration and significantly reduced convergence times. The LOOP-MAC method outperforms conventional centralized and distributed optimization methods in optimization tasks that require repetitive and sequential execution.

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms that explore the feasible domain in the search for the best solution. These iterative methods are often the computational bottleneck in decision-making and adversely impact time-sensitive applications. Recently, neural approximators have shown promise as a replacement for the iterative solvers that can output the optimal solution in a single feed-forward providing rapid solutions to optimization problems. However, enforcing constraints through neural networks remains an open challenge. This paper develops a neural approximator that maps the inputs to an optimization problem with hard linear constraints to a feasible solution that is nearly optimal. Our proposed approach consists of four main steps: 1) reducing the original problem to optimization on a set of independent variables, 2) finding a gauge function that maps the infty-norm unit ball to the feasible set of the reduced problem, 3)learning a neural approximator that maps the optimization's inputs to an optimal point in the infty-norm unit ball, and 4) find the values of the dependent variables from the independent variable and recover the solution to the original problem. We can guarantee hard feasibility through this sequence of steps. Unlike the current learning-assisted solutions, our method is free of parameter-tuning and removes iterations altogether. We demonstrate the performance of our proposed method in quadratic programming in the context of the optimal power dispatch (critical to the resiliency of our electric grid) and a constrained non-convex optimization in the context of image registration problems.

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.

Agent-based solutions lend themselves well to address privacy concerns and the computational scalability needs of future distributed electric grids and end-use energy exchanges. Decentralized decision-making methods are the key to enabling peer-to-peer energy trading between electricity prosumers. However, the performance of existing decentralized decision-making algorithms highly depends on the algorithmic design and hyperparameter tunings, limiting applicability. This paper aims to address this gap by proposing a decentralized inexact projection method that does not rely on parameter tuning or central coordination to achieve the optimal solution for Peer-to-Peer (P2P) energy trading problems. The proposed algorithm does not require parameter readjustments, and once tuned, it converges for a wide range of P2P setups. Moreover, each prosumer only needs to share limited information (i.e., updated coupled variable) with neighboring prosumers. The IEEE 13 bus test system is used to showcase our proposed method's robustness and privacy advantages.

Leveraging machine learning to facilitate the optimization process is an emerging field that holds the promise to bypass the fundamental computational bottleneck caused by classic iterative solvers in critical applications requiring near-real-time optimization. The majority of existing approaches focus on learning data-driven optimizers that lead to fewer iterations in solving an optimization. In this paper, we take a different approach and propose to replace the iterative solvers altogether with a trainable parametric set function, that outputs the optimal arguments/parameters of an optimization problem in a single feed forward. We denote our method as Learning to Optimize the Optimization Process (LOOP). We show the feasibility of learning such parametric (set) functions to solve various classic optimization problems including linear/nonlinear regression, principal component analysis, transport-based coreset, and quadratic programming in supply management applications. In addition, we propose two alternative approaches for learning such parametric functions, with and without a solver in the LOOP. Finally, through various numerical experiments, we show that the trained solvers could be orders of magnitude faster than the classic iterative solvers while providing near optimal solutions.

With the increasing impact of low inertia due to the high penetration of distributed generation, virtual synchronous generator (VSG) technology has been proposed to improve the stability of the inverter-interfaced distributed generator by providing "virtual inertia". This paper presents a recent review of virtual inertia control covering significance, features, design principles, and state-of-art inertia strategies from both physical and mathematical perspectives to facilitate the wide application of the VSG. The definition and source of virtual inertia are given to help researchers to establish the concept of "virtual inertia". Then, this paper covers influencing mechanism studies of virtual inertia to reveal its functions. Also, a design framework of the virtual inertia is established by considering both the characteristics of the control system and the limitation of energy storage systems and renewable energy resources. Finally, several novel adaptive inertia control strategies are reviewed, and some aspects of potential future research are recommended.