Data-driven alternating current optimal power flow: A Lagrange multiplier based approach

Alternating current optimal power flow (ACOPF) problems are nonconvex and nonlinear optimization problems. Utilities and independent service operators (ISO) require ACOPF to be solved in almost real time. Interior point methods (IPMs) are one of the powerful methods for solving large-scale nonlinear optimization problems and are a suitable approach for solving ACOPF with large-scale real-world transmission networks. Moreover, the choice of the formulation is as important as choosing the algorithm for solving an ACOPF problem. In this paper, different ACOPF formulations with various linear solvers and the impact of employing box constraints are evaluated for computational viability and best performance when using IPMs. Different optimization structures are used in these formulations to model the ACOPF problem representing a range of sparsity. The numerical experiments suggest that the least sparse ACOPF formulations with polar voltages yield the best computational results. Additionally, nodal injected models and current-based branch flow models are improved by enforcing box constraints. A wide range of test cases, ranging from 500-bus systems to 9591-bus systems, are used to verify the test results.

This paper presents a three-phase iterative direct current optimal power flow (DCOPF) algorithm with fictitious nodal demand. Power losses and realistic distribution system operating constraints such as line flow limits and phase imbalance limits are carefully modeled in the DCOPF formulation. The definition of locational marginal prices (LMPs) is extended to three-phase distribution systems. The three-phase LMP decomposition is derived based on the Lagrangian function. The proposed algorithm is implemented in an IEEE test case and compared with three-phase alternating current optimal power flow (ACOPF) algorithm. The simulation results show that the proposed DCOPF algorithm is effective in coordinating the operations of distributed energy resources (DERs) and managing phase imbalance and thermal overloading. The proposed iterative three-phase DCOPF algorithm provides not only a computationally efficient solution but also a good approximation to the ACOPF solution.

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Fast-falling renewable energy costs and recent policy focus on rapid decarbonization of electricity grids have brought the distribution level planning under microscope. In this paper, we carry out the siting and sizing of distributed generation based on distribution locational marginal prices (DLMPs). The DLMP at each bus is computed using convex relaxation of alternating current optimal power flow (ACOPF). The optimality of the solution is compared with the existing results which use power loss as a metric for performance evaluation. The proposed approach is tested on an IEEE 69-bus distribution network, first on peak load demand and then on a time-varying load using actual solar and wind generation data. The time-varying load curve is predicted using a recurrent neural network. Furthermore, computation and accuracy for two different convex relaxations of ACOPF are compared to highlight the significance of the proposed method.

Toward a scalable robust security-constrained optimal power flow using a proximal projection bundle method

Successive linear programming (SLP) is a practical approach for solving large-scale nonlinear optimization problems. Alternating current optimal power flow (ACOPF) is no exception, particularly the large size of real-world networks. However, in order to achieve tractability, it is essential to tune the SLP algorithm presented in the literature. This paper presents a modified SLP algorithm to solve the ACOPF problem, specified by the U.S. Department of Energy’s (DOE) Grid Optimization (GO) Competition Challenge 1, within strict time limits. The algorithm first finds a near-optimal solution for the relaxed problem (i.e., Stage 1). Then, it finds a feasible solution in the proximity of the near-optimal solution (i.e., Stage 2 and Stage 3). The numerical experiments on test cases ranging from 500-bus to 30,000-bus systems show that the algorithm is tractable. The results show that our proposed algorithm is tractable and can solve more than 80% of test cases faster than the well-known Interior Point Method while significantly reduce the number of iterations required to solve ACOPF. The number of iterations is considered an important factor in the examination of tractability which can drastically reduce the computational time required within each iteration.

The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. This paper proposes a scalable decomposition approach in which the power network is decomposed into a master network and a number of subnetworks, where each network has its own AC-OPF subproblem. This formulates a two-stage optimization problem and requires only a small amount of communication between the master and subnetworks. The key contribution is a smoothing technique that renders the response of a subnetwork differentiable with respect to the input from the master problem, utilizing properties of the barrier problem formulation that naturally arises when subproblems are solved by a primal-dual interior-point algorithm. Consequently, existing efficient nonlinear programming solvers can be used for both the master problem and the subproblems. The advantage of this framework is that speedup can be obtained by processing the subnetworks in parallel, and it has convergence guarantees under reasonable assumptions. The formulation is readily extended to instances with stochastic subnetwork loads. Numerical results show favorable performance and illustrate the scalability of the algorithm which is able to solve instances with more than 11 million buses.

Using deep neural networks to predict the solutions of AC optimal power flow (ACOPF) problems has been an active direction of research. However, because the ACOPF is nonconvex, it is difficult to construct a good data set that contains mostly globally optimal solutions. To overcome the challenge that the training data may contain suboptimal solutions, we propose a Lagrangian-based approach. First, we use a neural network to learn the dual variables of the ACOPF problem. Then we use a second neural network to predict solutions of the partial Lagrangian from the predicted dual variables. Since the partial Lagrangian has a much better optimization landscape, we use the predicted solutions from the neural network as a warm start for the ACOPF problem. Using standard and modified IEEE 22-bus, 39-bus, and 118-bus networks, we show that our approach is able to obtain the globally optimal cost even when the training data is mostly comprised of suboptimal solutions.

One of the most used artificial intelligence techniques for maximum power point tracking is artificial neural networks. In order to achieve successful results in maximum power point tracking, the training process of artificial neural networks is important. Metaheuristic algorithms are used extensively in the literature for neural network training. An important group of metaheuristic algorithms is swarm-intelligent-based optimization algorithms. In this study, feed-forward neural network training is carried out for maximum power point tracking by using 13 swarm-intelligent-based optimization algorithms. These algorithms are artificial bee colony, butterfly optimization, cuckoo search, chicken swarm optimization, dragonfly algorithm, firefly algorithm, grasshopper optimization algorithm, krill herd algorithm, particle swarm optimization, salp swarm algorithm, selfish herd optimizer, tunicate swarm algorithm, and tuna swarm optimization. Mean squared error is used as the error metric, and the performances of the algorithms in different network structures are evaluated. Considering the results, a success ranking score is obtained for each algorithm. The three most successful algorithms in both training and testing processes are the firefly algorithm, selfish herd optimizer, and grasshopper optimization algorithm, respectively. The training error values obtained with these algorithms are 4.5 × 10−4, 1.6 × 10−3, and 2.3 × 10−3, respectively. The test error values are 4.6 × 10−4, 1.6 × 10−3, and 2.4 × 10−3, respectively. With these algorithms, effective results have been achieved in a low number of evaluations. In addition to these three algorithms, other algorithms have also achieved mostly acceptable results. This shows that the related algorithms are generally successful ANFIS training algorithms for maximum power point tracking.

Neural networks have emerged as a cornerstone in the field of machine learning, driving significant advancements across various domains such as computer vision, natural language processing, and autonomous systems. This paper explores the fundamental principles of neural networks, including their structural design, activation functions, and training algorithms. Key architectures such as feedforward neural networks, convolutional neural networks, recurrent neural networks, and generative adversarial networks are discussed in detail, highlighting their unique capabilities and applications. The training process of neural networks, involving techniques like backpropagation and gradient descent, is examined alongside methods to enhance performance and prevent overfitting, such as regularization and optimization strategies. This paper also reviews major applications of neural networks, showcasing their impact on image and speech recognition, language translation, and autonomous vehicles. Recent advancements in the field, including the rise of deep learning, improved model explainability, and the development of specialized hardware accelerators, are analyzed to provide insights into current trends and future prospects. The ongoing research in areas like unsupervised learning, few-shot learning, and the integration of neural networks with other AI paradigms is highlighted as a promising avenue for further innovation. By providing a comprehensive overview of neural networks and their applications, this paper underscores their transformative role in advancing machine learning technologies and anticipates future developments that will continue to shape the landscape of artificial intelligence.

Survey on Deep Neural Networks in Speech and Vision Systems

Deep Learning (DL) has become a prominent machine learning technique due to the availability of efficient computational resources in the form of Graphics Processing Units (GPUs), large-scale datasets and a variety of models. The newer generation of GPUs are being designed with special emphasis on optimizing performance for DL applications. Also, the availability of easy-to-use DL frameworks—like PyTorch and TensorFlow— has enhanced productivity of domain experts to work on their custom DL applications from diverse domains. However, existing Deep Neural Network (DNN) training approaches may not fully utilize the newly emerging powerful GPUs like the NVIDIA A100—this is the primary issue that we address in this paper. Our motivating analyses show that the GPU utilization on NVIDIA A100 can be as low as 43% using traditional DNN training approaches for small-to-medium DL models and input data size. This paper proposes AccDP—a data-parallel distributed DNN training approach—to accelerate GPU-based DL applications. AccDP exploits the Message Passing Interface (MPI) communication library coupled with the NVIDIA’s Multi-Process Service (MPS) to increase the amount of work assigned to parallel GPUs resulting in higher utilization of compute resources. We evaluate our proposed design on different small-to-medium DL models and input sizes on the state-of-the-art HPC clusters. By injecting more parallelism into DNN training using our approach, the evaluation shows up to 58% improvement in training performance on a single GPU and up to 62% on 16 GPUs compared to regular DNN training. Furthermore, we conduct an in-depth characterization to determine the impact of several DNN training factors and best practices—including the batch size and the number of data loading workers— to optimally utilize GPU devices. To the best of our knowledge, this is the first work that explores the use of MPS and MPI to maximize the utilization of GPUs in distributed DNN training.

With the development of intermittent renewable energy sources, modern power systems are facing significant uncertainties as well as voltage deviations. In order to respond quickly to power fluctuations and contingencies such as transmission line tripping due to faults, real-time optimal grid control is required. A real-time alternating current (AC) optimal power flow (OPF) method through deep reinforcement learning (DRL) combined with imitation learning (IL) in continuous action space is proposed in this paper. A Markov decision process (MDP) is constructed to describe the real-time AC OPF problem. This proposed method is tested on the IEEE 30-bus system and the results show the significant potential for the optimal online control for power systems compared with the state-of-the-art techniques.

Contact-map of a protein sequence dictates the global topology of structural fold. Accurate prediction of the contact-map is thus essential to protein 3D structure prediction, which is particularly useful for the protein sequences that do not have close homology templates in the Protein Data Bank. We developed a new method, ResPRE, to predict residue-level protein contacts using inverse covariance matrix (or precision matrix) of multiple sequence alignments (MSAs) through deep residual convolutional neural network training. The approach was tested on a set of 158 non-homologous proteins collected from the CASP experiments and achieved an average accuracy of 50.6% in the top-L long-range contact prediction with L being the sequence length, which is 11.7% higher than the best of other state-of-the-art approaches ranging from coevolution coupling analysis to deep neural network training. Detailed data analyses show that the major advantage of ResPRE lies at the utilization of precision matrix that helps rule out transitional noises of contact-maps compared with the previously used covariance matrix. Meanwhile, the residual network with parallel shortcut layer connections increases the learning ability of deep neural network training. It was also found that appropriate collection of MSAs can further improve the accuracy of final contact-map predictions. The standalone package and online server of ResPRE are made freely available, which should bring important impact on protein structure and function modeling studies in particular for the distant- and non-homology protein targets. https://zhanglab.ccmb.med.umich.edu/ResPRE and https://github.com/leeyang/ResPRE. Supplementary data are available at Bioinformatics online.

In the training process of convolutional neural networks (CNN), a batch normalization (BN) layer is often inserted after a convolution layer to accelerate the convergence of CNN training. In this work, we propose a BN processor that supports both the training and inference processes. To speed up the training of CNN, the proposed work develops an efficient dataflow integrating a novel BN processor design and the processing elements for convolution acceleration. We exploited the similarities in the calculations required for the BN forward and backward passes by sharing hardware elements between both passes, therefore reducing the area overhead. In addition to functional verification of the BN processor, we also completed Automatic Placement & Routing (APR) and conducted post-APR simulation on neural network training. Finally, the proposed solution not only significantly speeds up the CNN training process, but also achieves hardware saving.