Distributed optimal power flow.

Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet

Due to the increase of intermittent renewable energy sources, it is becoming more important to consider renewable generation forecast error when solving the optimal power flow (OPF) problem. The stochastic OPF, which uses multiple forecast scenarios, generally leads to a lower cost compared to the standard deterministic OPF, which uses a single forecast. However, the stochastic OPF is computationally more demanding than the deterministic OPF. Both cost savings and computation times further increase when storage units or ramp-constrained generators are included, as they require solving a multi-period OPF problem. Our contribution is a hybrid method approaching the cost performance of the stochastic OPF while maintaining a computational burden close to the deterministic OPF. The method combines elements from both the stochastic and the deterministic OPF, and relies on Benders Cuts to interface them. Using a receding horizon approach over one year, we find that, based on eleven test cases, one version of our hybrid method leads to at least 70% of the cost improvement of the stochastic OPF, while the computation time increase is at most 40% of the stochastic OPF time increase. Furthermore, the computational advantage of our method increases with the system size. Two different versions of the method allow favoring of either the computational improvement or the cost improvement. We also identify directions for further improvement. Finally, our method can be used for more general problems in which one wishes to combine two models with different levels of complexity.

In modern power engineering, the optimal operation aims to achieve the basic requirements of the electrical power grid, meet various technical and economic aspects, and preserve the environmental limits within their accepted bounds. In this line, the current paper finds the optimal operational scheduling of the power generation units that cover the load requirements, considering different frameworks of the optimal power flow (OPF) problem involving single- and multi-objective functions. Technical, economic, and emissions objective functions are considered. Artificial rabbits' optimization (ARO) is developed to find the optimal OPF framework solution. The effectiveness of the proposed algorithm is evaluated through a comprehensive comparison study with the existing works in the literature. With six IEEE standard power systems, 22 different cases are implemented to test the ARO performance as an alternative to solve the OPF problem. Two of these systems are considered small-size systems, 30-, and 57-test systems, while the other four are large-scale power systems (IEEE 300, 1354, 3012, and 9241 test systems) to expand the validation scope of this paper. This comparison validates the scalability and efficiency of the ARO algorithm. The impact of varied population size and maximum iteration number is tested for two test systems, the most benchmarking test systems. It was proven that the routine of ARO has robust and superior competitive performance compared with others at fine convergence rates. Significant improvements are acquired in the range of 47% in the technical and economic issues by accepting the environmental concerns.

Since conventional optimal power flow (OPF) algorithms are limited and too slow for operational planning, power system operation and planning engineers have been seeking efficient OPF algorithms for three decades. The interior point method is one of the most efficient algorithms. In this paper, an improved quadratic interior point (IQIP) method is used to solve comprehensive OPF problems with a variety of objective functions, including economic dispatch, VAr planning and loss minimization. The IQIP method features a general starting point (rather than selected good point as in the general interior point method) and fast convergence. Consequently, the OPF package described in this paper offers huge improvements in speed, accuracy and convergence in solving multi-objective and multi-constraint optimization problems. It will be a very useful tool for the power industry.

Purpose Due to the increase of the traffic, issues are appearing on DC electrified railway feeding systems. One candidate solution to solve these issues and to improve their performances is to add storage systems in the railway DC electrical network. The paper presents a method based on an Optimal Power Flow (OPF) for the analysis and design of DC railway feeding systems with storage. Design/methodology/approach The paper describes a new methodology based on optimization to study DC electrified railways, including storage systems. A load flow model of a DC 1500V railway electrification system is presented, including the mobility of the train sets. Then, an Optimal Power Flow model of the DC network, including energy storage systems and feeding substation rectifiers has been developed. Finally, the OPF model has been tested on a real application case showing its benefits while searching solutions in order to improve the network performances. Findings An OPF model suitable for analysis of DC networks with storage is presented. It shows its ability to solve large scale problems. Research limitations/implications The paper focuses on the physical model of the network. The optimization model will have to be extended with application constraints. Originality/value The hypothesis presented in this paper allows to remove the discontinuities of the system in order to use a continuous optimization approach.

For operating electrical power networks, the Optimal Power Flow (OPF) problem plays a central role. The problem is nonconvex and NP hard. Therefore, designing efficient solution algorithms is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems for which zero duality holds, whereas for non-convex problems there is a lack of solution methods of provable performance. In this paper, an efficient novel method to address the general nonconvex OPF problem is investigated. The proposed method is based on alternating direction method of multipliers combined with sequential convex approximations. The global OPF problem is decomposed into smaller problems associated to each bus of the network, the solutions of which are coordinated via a light communication protocol. Therefore, the proposed method is highly scalable. The convergence properties of the proposed algorithm are mathematically and numerically substantiated.

Objective: This work involves a convex-based mathematical reformulation for the optimal power flow problem in DC networks. The objective of the proposed optimization model corresponds to the minimization of the power losses through all the network branches considering a convex conic model that warranties finding the global optimal. Methodology: This is split into three stages: The first stage presents the mathematical model of optimal power flow for DC networks and all its geometric features that make it non-convex; the second stage presents the convex reformulation from a second order conic relaxation; the third stage shows the main characteristics of the DC system under study; and the fourth stage presents the optimal solution of the power flow problem and its comparisons with some methods reported in the specialized literature. Results: The numerical validations demonstrate that the model of proposed convex optimal power flow obtains the same solution as the exact model of the problem with an efficiency of 100%, which is in contrast with the variability of the results that are presented by the metaheuristic techniques reported as comparison methodologies. Conclusions: The proposed second-order conic relaxation warrantied the convexity of the solution space and therefore, the finding of the optimal solution at each execution; besides of this, demonstrated that for optimal power flow problems in DC networks, the numerical performance is better than most of the comparative metaheuristic methods; and the provided solution by the proposed relaxation is equivalent to that provided by the exact model. Keywords: Direct current networks, second-order conic relaxation, non-linear programming model, convex optimization.

Optimal power flow (OPF) is at the heart of many power system operation tools and market clearing processes. Several mathematical and heuristic approaches have been presented in literature to solve OPF. The recent flourish of machine learning (ML) algorithms and advancement of computational resources, with unforeseen data availability, has motivated the power system community to embrace ML. Although many papers are published on the applications of ML for solving various power system problems, in case of OPF, the same research orientation is still in its early days. This paper presents a survey of recent studies that have applied ML to solve OPF-related problems and provides readers with visions on potential research directions in this field. The surveyed literature is categorized according to the type of studied OPF problems.

This paper presents an efficient genetic algorithm for solving non-convex optimal power flow (OPF) problems with bus voltage constraints for practical application. In this method, the individual is the binary-coded representation that contains a mixture of continuous and discrete control variables, and crossover and mutation schemes are proposed to deal with continuous/discrete control variables, respectively. The objective of OPF is defined that not only to minimize total generation cost but also to improve the bus voltage profile.. The proposed method is demonstrated for a IEEE 30-bus four generator ystem, and it is compared with conventional method.The experimental results show that the GA OPF method is superior to the conventional.

Electricity market design and implementation in the presence of asymmetrically informed strategic producers and consumers: A surrogate optimization-based mechanism

Power systems are transitioning toward renewable sources and electrification, introducing significant uncertainties in generation and demand that optimal power flow (OPF) methods must manage. Traditional deterministic methods struggle with these variabilities. Additionally, addressing uncertainty in OPF calculations incurs computational burdens due to the need for multiple evaluations across various scenarios. This necessitates the use of advanced surrogate models. However, these models require significant data for training, and surrogate-based optimization can yield unreliable results due to inaccuracies in constraint handling. To overcome these issues, this paper proposes a novel surrogate-based hybrid chance-constrained optimal power flow (HCC-OPF) methodology employing enhanced multi-fidelity graph neural networks (EMF-GNN) as power flow solver surrogates. This model integrates low-fidelity and high-fidelity simulations to significantly reduce training cost while maintaining high accuracy. We further enhance the robustness and accuracy of OPF solutions through a hybrid methodology that selectively uses exact power flow solver to correct surrogate inaccuracies near critical thresholds. Extensive testing on multiple IEEE systems under high-dimensional correlated uncertainty of load and generation shows the EMF-GNN model outperforms existing single-fidelity and multi-fidelity models. Furthermore, the proposed HCC-OPF methodology accurately solves OPF problems across various system sizes and conditions, exhibiting scalability and efficiency. Additionally, it effectively manages N-1 security constraints to further exhibit its robustness under operational challenges.

SummaryFull-physics models in history matching (HM) and optimization can be computationally expensive because these problems usually require hundreds of simulations or more. In a previous study, a physics-based data-driven network model was implemented with a commercial simulator that served as a surrogate without the need to build a 3D geological model. In this paper, the network model is reconstructed to account for complex reservoir conditions of mature fields and successfully apply it to a diatomite reservoir in the San Joaquin Valley, California, for rapid HM and optimization.The reservoir is simplified into a network of 1D connections between well perforations. These connections are discretized into gridblocks, and the grid properties are calibrated to historical production data. Elevation change, saturation distribution, capillary pressure, and relative permeability are accounted for to best represent the mature field conditions. To simulate this physics-based network model through a commercial simulator, an equivalent Cartesian model is designed where rows correspond to the previously mentioned connections. Thereafter, the HM can be performed with the ensemble smoother with multiple data assimilation (ESMDA) algorithm under a sequential iterative process. A representative model after HM is then used for well control optimization.The network model methodology has been successfully applied to the waterflood optimization for a 56-well sector model of a diatomite reservoir in the San Joaquin Valley. HM results show that the network model matches with field level production history and gives reasonable matches for most of the wells, including pressure and volumetric data. The calibrated posterior ensemble of HM yields a satisfactory production prediction that is verified by the remaining historical data. For well control optimization, the P50 model is selected to maximize the net present value (NPV) in 5 years under provided well/field constraints. This confirms that the calibrated network model is accurate enough for production forecasts and optimization. The use of a commercial simulator in the network model provided flexibility to account for complex physics, such as elevation difference between wells, saturation nonequilibrium, and strong capillary pressure. Unlike the traditional big-loop workflow that relies on a detailed characterization of geological models, the proposed network model only requires production data and can be built and updated rapidly. The model also runs much faster (tens of seconds) than a full-physics model because of the use of much fewer gridblocks.To our knowledge, this is the first time this physics-based data-driven network model is applied with a commercial simulator on a field waterflood case. Unlike approaches developed with analytic solutions, the use of a commercial simulator makes it feasible to be further extended for complex processes (e.g., thermal or compositional flow). It serves as a useful surrogate model for both fast and reliable decision-making in reservoir management.

Full-physics models in history matching and optimization can be computationally expensive since these problems usually require hundreds of simulations or more. We have previously implemented a physics-based data-driven network model with a commercial simulator that serves as a surrogate without the need to build the 3-D geological model. In this paper, we reconstruct the network model to account for complex reservoir conditions of mature fields and successfully apply it to a diatomite reservoir in the San Joaquin Valley (SJV) for rapid history matching and optimization. The reservoir is simplified into a network of 1-D connections between well perforations. These connections are discretized into grid blocks and the grid properties are calibrated to historical production data. Elevation change, saturation distribution, capillary pressure, and relative permeability are accounted for to best represent the mature field conditions. To simulate this physics-based network model through a commercial simulator, an equivalent 2-D Cartesian model is designed where rows correspond to the above-mentioned connections. Thereafter, the history matching can be performed with the Ensemble Smoother with Multiple Data Assimilation (ESMDA) algorithm under a sequential iterative process. A representative model after history matching is then employed for well control optimization. The network model methodology has been successfully applied to the waterflood optimization for a 56-well sector model of a diatomite reservoir in the SJV. History matching result shows that the network model honors field-level production history and gives reasonable matches for most of the wells, including pressure and flow rate. The calibrated ensemble from the last iteration of history matching yields a satisfactory production prediction, which is verified by the remaining historical data. For well control optimization, we select the P50 model to maximize the Net Present Value (NPV) in 5 years under provided well/field constraints. This confirms that the calibrated network model is accurate enough for production forecasts and optimization. The use of a commercial simulator in the network model provided flexibility to account for complex physics, such as elevation difference between wells, saturation non-equilibrium, and strong capillary pressure. Unlike traditional big-loop workflow that relies on a detailed characterization of geological models, the proposed network model only requires production data and can be built and updated rapidly. The model also runs much faster (tens of seconds) than a full-physics model due to the employment of much fewer grid blocks. To our knowledge, this is the first time this physics-based data-driven network model is applied with a commercial simulator on a field waterflood case. Unlike approaches developed with analytic solutions, the use of commercial simulator makes it feasible to be further extended for complex processes, e.g., thermal or compositional flow. It serves as an useful surrogate model for both fast and reliable decision-making in reservoir management.

We describe a powerful framework for designing efficient batch algorithms for certain large-scale dynamic problems that must be solved using external memory. The class of problems we consider, which we call colorable eztemaldecomposable problems, include rectangle intersection, orthogonal line segment intersection, range searching, and point location. We are particularly interested in these problems in two and higher dimensions. They have numerous applications in geographic information systems (GIS), spatial databases, and VLSI and CAD design. We present simplied algorithms for problems previously solved by more complicated approaches (such as rectangle intersection), and we present efficient algorithms for problems not previously solved in an efficient way (such as point location and higherdimensional versions of range searching and rectangle intersection). communication is the bottleneck in many large-scale applications such as those arising in VLSI and CAD design, spatial databases, and geographic information systems (GIS). In this paper we consider I/O-efficient algorithms for batched searching problems. We consider both batched static and batched dynamic problems, and use the correspondence which often exists between a ddimensional static problem and a (dl)-dimensional dynamic problem to obtain a number of new d-dimensional algorithms. We give experimental results concerning the running time for our approach applied to the red-blue rectangle intersection problem, which is a key component of the extremely important database operation spatial join. Our algorithm scales well with the problem size, and for large problems sizes it greatly outperforms the well-known sweepline approach. One prominent example of the problems we consider is the rectangle intersection problem, which is a key component in VLSI design rule checking [31] and in the extremely important database operation spatial join [34]. We illustrate the practical significance of our algorithms by comparing the empirical performance of our algorithm for this problem with the well-known sweepline algorithm developed for internal memory. 1.1 Problem definition and memory model

A detailed network model for distribution systems with high penetration of renewable generation sources