Branch Flow Research Articles

Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories

Higher-form symmetries have proved useful in constraining the dynamics of a number of quantum field theories. In the context of the Argyres-Douglas (AD) theories of the (G, G′) type, we find that the 1-form symmetries are invariant under the Higgs branch flow, and that they are captured by the non-Higgsable sector at a generic point on the Higgs branch of the AD theory in question. As a consequence, dimensional reduction of an AD theory with a non-trivial 1-form symmetry to 3d leads to a free sector. We utilize these observations, along with other results, to propose systematically the mirror theories for the AD theories of the (An, Em) type. As a by-product of these findings, we discover many important results: the Flip-Flip duality for all T[G] theories with simply-laced group G, including the exceptional ones; the class mathcal{S} descriptions of exceptional affine Dynkin diagram such that all gauge groups are special unitary; the universality of the mirror theories for {D}_{h_G^{vee }} (G) with {h}_G^{vee } the dual Coxeter number of G; and the triviality of the 2-group structure in the (An, Em) theories.

Rapid Identification of Interwell Fracture-Cavity Combination Structure in Fracture-Cavity Reservoir Based on Tracer-Curve Morphological Characteristics

Rapid and effective identification of interwell fracture-cavity composite structures is a necessary prerequisite for a detailed and in-depth understanding of interwell connectivity in fracture-cavity reservoirs. Current identification methods and technologies have the problems of being large-scale and low-resolution; in view of these problems, a method is proposed for rapidly identifying interwell fracture-cavity combination structures using tracer-curve morphological characteristics (peak number and characteristics of two wings). Based on concentration models of tracer curves for an interwell single fracture/pipe/cavity, the morphological characteristics of tracer curves were researched in five different series-parallel combination modes consisting of fractures, pipes, and cavities. The tracer curves of fracture-cavity reservoirs are categorized into three types: single sharp peak, single slow peak, and multipeak. Furthermore, a matching relationship between different fracture-cavity combination structures and the morphological characteristics of tracer curves is clarified. The single-sharp-peak curve with basically symmetrical wings reflects that of an interwell single fracture/pipe; the single-slow-peak curve with a steep ascending branch and a slow descending branch (obvious trailing phenomenon) reflects that of an interwell single cavity or fracture/pipe series cavity; the multipeak curve reflects that of an interwell multifracture/pipe/cavity in parallel; according to the flow difference of each branch flow channel, they can be divided into independent multipeak and continuous multipeak forms. Taking tracer monitoring results from a well group in the Tahe oilfield as an example, field application analysis and verification were carried out. The results show that this method is simple and reliable and can provide a fast and effective means for identifying interwell fracture-cavity combination structures. Meanwhile, the research results can lay a foundation for quantitative interpretation modeling of interwell tracers in fracture-cavity reservoirs considering fracture-cavity configuration.

Optimal cooling of an internally heated disc.

Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an internally heated disc. Heat enters via a distributed source, is passively advected and diffused, and exits through the boundary at a fixed temperature. We seek an advecting flow to optimize this exchange. Previous work on energy-constrained cooling with a constant source has conjectured that global optimizers should resemble convection rolls; we prove one-sided bounds on energy-constrained cooling corresponding to, but not resolving, this conjecture. In the case of an enstrophy constraint, our results are more complete: we construct a family of self-similar, tree-like 'branching flows' whose cooling we prove is within a logarithm of globally optimal. These results hold for general space- and time-dependent source-sink distributions that add more heat than they remove. Our main technical tool is a non-local Dirichlet-like variational principle for bounding solutions of the inhomogeneous advection-diffusion equation with a divergence-free velocity. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Research Advances in Plant Physiology and Ecology of Desert Riparian Forests under Drought Stress

Under drought stress, desert riparian forest plants are highly self-regulating and have their own unique water use and regulation strategies, which can respond positively in several aspects such as physiology, ecology, and individual phenotypes when coping and adapting to the stresses brought by external environmental changes. In addition, as an important component of arid zone ecosystems, desert riparian forest plants maintain the cycling process of energy and material in desert areas. Therefore, it is of great ecological value to study the role played by desert riparian forest plants in desertification control and biodiversity conservation in arid zones. The purpose of this study is to provide basic data and scientific basis for the conservation, and restoration of desert riparian forests in the inland river basin of arid zone. In this paper, the physiological and ecological responses of desert riparian plants under drought stress were analyzed by reviewing the literature and focusing on the key scientific issues such as drought avoidance mechanisms, water use, and water redistribution, and the relationship between interspecific water competition and resource sharing of desert riparian plants. The results showed that: (1) In the inland river basin of arid zone, desert riparian plants show a mutual coordination of increasing soluble sugars, proline, malondialdehyde (MDA), and decreasing peroxidase (POD), to form a unique drought avoidance mechanism, and improve their drought tolerance by changing leaf stomatal conductance resulted from regulating abscisic acid (ABA) and cytokinin (CTK) content. (2) Desert riparian forest plants have their own unique water use and regulation strategies. When the degree of drought stress increased, Populus euphratica enhanced the water flow of dominant branches by actively sacrificing the inferior branches to ensure and improve the overall survival chances of the plant, while Tamarix ramosissima weaken hydraulic conductance, and increase subsurface material inputs by reducing plant height to cope with drought stress. (3) The root systems of desert riparian plants have hydraulic uplift and water redistribution functions, and, in the hydraulic uplift process of P. euphratica and T. ramosissima root systems, there is a possibility of assisting with other species in water utilization and the existence of a resource sharing mechanism.

Surface Current Variations and Hydrological Characteristics of the Penghu Channel in the Southeastern Taiwan Strait

Coastal ocean dynamics application radar (CODAR) SeaSonde high-frequency (HF) radars deployed along the coast of Taiwan were used to reveal ocean surface current variations both hourly and through climatological seasons in the Penghu Channel (PHC), southeastern Taiwan Strait (TS), from December 2014 to December 2020. The ocean current in the PHC has a semidiurnal tidal cycle, and the seasonal main flow, wind direction, and wind strength significantly affect the direction and speed of the flow passing through the PHC. The speed of the tidal current in the PHC area can reach more than 1 m/s, and the monthly average flow speed in the PHC is between 0.12 (winter) and 0.24 m/s (summer). Several buoys indicated that the southward flow along the western coast of Taiwan drifted through the PHC in fall and winter. The HF radar observations confirmed the same, implying that this occurred during the strong northeastern monsoon. For a weak northerly wind or even southerly wind, the flow in the PHC can be northward. Different wind directions can affect the speed of the flow passing through the PHC and the branch flow in the northern PHC. The HF radar results are highly consistent with the spatial characteristics of satellite data regarding the sea surface temperature, sea surface salinity, and chlorophyll concentrations; however, there are significant differences from the satellite-derived ocean current.

Research on the Probabilistic Load Flow Method of Power System Considering Wind Power Integration

Abstract Due to the uncertainty of renewable energy and load, probabilistic power flow as an effective method to analyse the probabilistic properties of power systems. In this paper, a linearized ac probabilistic power flow model is established, and Monte Carlo simulation method is used to analyze the probabilistic power flow of the power grid containing wind farms. By connecting wind farm to node 13 of IEEE14-bus system, the voltage accumulative distribution curves of node 4, node 5 and node 13 are obtained. The results show that the random output of wind farm increases the fluctuation of node voltage, and the fluctuation phenomenon of node voltage becomes serious as the distance of the access point of the wind farm approaches. By connecting wind farms at node 4 and node 14, the voltage accumulative distribution curves of access nodes were obtained. Through comparison, it is concluded that the access of wind farm has a small effect on the voltage of PQ nodes close to PV nodes, but has great influence on the voltage of PQ nodes away from PV nodes. By adding wind farms at node 13, the active power cumulative distribution curves of branch 2-5, branch 3-4, branch 5-6 and branch 6-13 were obtained. By comparison, the active power flow of different branches of the system is affected differently after access to the wind farm. The fluctuation of the active power flow of the branch becomes serious with the shortening of the distance from the access point of the wind farm. The simulation analysis can provide more comprehensive and useful information for the planning and operation personnel of power system including wind farm.

Two-dimensional numerical pore-scale investigation of oxygen evolution in proton exchange membrane electrolysis cells

Oxygen blocking the porous transport layer (PTL) increases the mass transport loss, and then limits the high current density condition of proton exchange membrane electrolysis cells (PEMEC). In this paper, a two-dimensional transient mathematical model of anode two-phase flow in PEMEC is established by the fluid volume method (VOF) method. The transport mechanism of oxygen in porous layer is analyzed in details. The effects of liquid water flow velocity, porosity, fiber diameter and contact angle on oxygen pressure and saturation are studied. The results show that the oxygen bubble transport in the porous layer is mainly affected by capillary pressure and follows the transport mechanism of ‘pressurization breakthrough depressurization’. The oxygen bubble goes through three stages of growth, migration and separation in the channel, and then be carried out of the electrolysis cell by liquid water. When oxygen breaks through the porous layer and enters the flow channel, there is a phenomenon that the branch flow is merged into the main stream, and the last limiting throat affects the maximum pressure and oxygen saturation during stable condition. In addition, increasing the liquid water velocity is helpful to bubble separation; changing the porosity and fiber diameter directly affects the width of pore throat and the correlative capillary pressure; increasing porosity, reducing fiber diameter and contact angle can promote oxygen breakthrough and reduce the stable saturation of oxygen.

A Large Subsurface Anticyclonic Eddy in the Eastern Equatorial Indian Ocean

AbstractSubsurface eddies are pervasive in the ocean, but those in the eastern equatorial Indian Ocean are not well understood due to the lack of in‐situ observations. Using multiple‐platform observations and reanalysis product, we investigate the characteristics, evolutionary process, origin, and underlying generation mechanism of a subsurface anticyclonic eddy (SAE) in the eastern equatorial Indian Ocean during January‒February 2020. Results show that the horizontal radius of the SAE was slightly greater than 250 km, and the SAE core was located at ∼100‐m depth near the 24.7σ0 isopycnal. This warm, saline and oxygen‐rich SAE was weakly stratified and characterized by tilted lens structures. Further water‐mass tracing analysis indicates that the SAE shifted westward along 4°N with a mean propagation speed of 0.18 m/s from the northwest coast of Sumatra Island. The hydrographic characteristics of the SAE are similar to those of the strong Equatorial Undercurrent, it is speculated that the SAE was probably generated by the north branch flow as the eastward undercurrent reached Sumatra Island. Both lateral shear of undercurrent and conservation of potential vorticity were attributed to the formation of the observed SAE.

Fast Coscheduling of Discrete and Continuous Resources in Active Distribution Systems

This article proposes a novel fast method for flexibility scheduling and steady-state voltage control in smart distribution systems enabled with both conventional discrete controllable devices (DCDs), e.g., capacitor banks and <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> -load tap changers, and continuous and faster control devices, e.g., distributed energy resources, renewable resources, and static voltage regulators. By approximating the active and reactive losses, a linear branch flow model is presented for the optimal power flow (OPF) problem in distribution systems. Accurate models are also proposed for DCDs which suit the proposed OPF formulation and require fewer binary variables compared to those available in the literature. Conservation voltage reduction (CVR) scheme is modeled in the proposed OPF methodology. The CVR effects on energy saving, peak-load reduction, line losses, and transformer losses are analyzed in the case studies. As shown in various case studies, the proposed method is fast enough for quasi-real-time applications and is efficacious in minimizing the system operation cost, holding an acceptable level of power quality based on the available standards and evading the conflict between control actions.

An iterative linear DistFLow for dynamic optimization in distributed generation planning studies

This paper implements an iterative linear DistFlow for the modelling of radial distribution grids. The method is intended for dynamic optimizations under gird constraints, and in the presence of distributed generation including storage units with time coupled constraints. It is demonstrated that traditional piecewise linearization for the losses estimation in conventional linear DistFlow can lead to significant errors. This is due in particular to the setting of static upper bounds for the active and reactive branch flows in the linearization process, which may differ greatly from the actual power. The proposed iterative approach addresses this shortcoming with successive runs of linear DistFlow and updates for the flows upper bounds, dynamically along the simulated horizon. The method is compared to conventional linear DistFlow as well as other relaxed formulations such as Second Order Conic Programming and Quadratic Programming. All the methods are discriminated with regard to a reference AC power flow, in terms of error for the voltages and losses profiles on different test systems. The proposed iterative procedure displays the lowest error for the line losses with five to forty times more accuracy than conventional linearized formulations. It also outperforms the Second Order Conic relaxation in terms of scalability with one month dynamic simulation (at 1 h time step) run in 7 min with 30 distributed units on a 69-bus system. The approach is further validated with typical uses cases for the operation, the sizing, and the siting of distributed assets consisting of solar generators and storage units. Especially, the procedure is coupled with a genetic algorithm in order to test different system configurations on a 90-bus system. The solutions are discriminated in terms of number of assets, installed capacities, connection bus(es), installation costs, system losses and system self-sufficiency.

Distribution Grid Optimal Power Flow (D-OPF): Modeling, Analysis, and Benchmarking

In the power distribution systems, optimal power flow (D-OPF) is formulated as a non-convex and non-linear programming (NLP) problem. Convex relaxation and linear approximation models have been increasingly adopted to achieve computational efficiency for D-OPF. Despite the benefits of scalability and global optimality, each method is based on certain assumptions, performs differently, and may lead to solutions that are physically not meaningful. In this context, this work numerically evaluates the relative performance of second-order cone programming (SOCP), semi-definite programming (SDP), and linear programming (LP) formulations of D-OPF in terms of their feasibility, optimality, and scalability with respect to NLP-based formulations. We also compare the bus injection (in bus voltage and current variables) and branch flow (in active and reactive power flow variables) based on NLP formulations. The performance is evaluated using small (123-node), medium (730-node), and large (2522-node) sized distribution feeders. Case studies, which are backed up by visualization of the analytical models for the solution space to the extent possible, show that (1) the feasibility and exactness of relaxed D-OPF formulations depend upon the problem type, (2) some NLP formulations are computationally more tractable than others, (3) different NLP formulations can converge to different local solutions, and (4) the approximate linear model may underestimate or overestimate the cost function (depending upon the problem type) and may lead to AC-infeasible solutions.

ADMM-based Distributed Active and Reactive Power Control for Regional AC Power Grid with Wind Farms

A distributed active and reactive power control (DARPC) strategy based on the alternating direction method of multipliers (ADMM) is proposed for regional AC transmission system (TS) with wind farms (WFs). The proposed DARPC strategy optimizes the power distribution among the WFs to minimize the power losses of the AC TS while tracking the active power reference from the transmission system operator (TSO), and minimizes the voltage deviation of the buses inside the WF from the rated voltage as well as the power losses of the WF collection system. The optimal power flow (OPF) of the TS is relaxed by using the semidefinite programming (SDP) relaxation while the branch flow model is used to model the WF collection system. In the DARPC strategy, the large-scale strongly-coupled optimization problem is decomposed by using the ADMM, which is solved in the regional TS controller and WF controllers in parallel without loss of the global optimality. The boundary information is exchanged between the regional TS controller and WF controllers. Compared with the conventional OPF method of the TS with WFs, the optimality and accuracy of the system operation can be improved. Moreover, the proposed strategy efficiently reduces the computation burden of the TS controller and eliminates the need of a central controller. The protection of the information privacy can be enhanced. A modified IEEE 9-bus system with two WFs consisting of 64 wind turbines (WTs) is used to validate the proposed DARPC strategy.

Formulations and Approximations of Branch Flow Model for General Power Networks

The formulations and approximations of the branch flow model for general (radial and mesh) power networks (General-BranchFlow) are given in this paper. Using different sets of the power flow equations, six formats of the exact General-BranchFlow model are listed. The six formats are mathematically equivalent with each other. Linear approximation and second-order cone programming (SOCP) are then used to derive the six formats of the convex General-BranchFlow model. The branch ampacity constraints considering the shunt conductance and capacitance of the transmission line <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Pi$</tex> -model are derived. The key foundation of deriving the ampacity constraints is the correct interpretation of the physical meaning of the transmission line II-model. An exact linear expression of the ampacity constraints of the power loss variable is derived. The applications of the General-BranchFlow model in deriving twelve formats of the exact optimal power flow (OPF) model and twelve formats of the approximate OPF model are formulated and analyzed. Using the Julia programming language, the extensive numerical investigations of all formats of the OPF models show the accuracy and computational efficiency of the General-BranchFlow model. A penalty function based approximation gap reduction method is finally proposed and numerically validated to improve the AC-feasibility of the approximate General-BranchFlow model.

On the optimal reconfiguration of radial AC distribution networks using an MINLP formulation: A GAMS-based approach

This paper deals with the problem of the optimal reconfiguration of medium voltage distribution networks by proposing a mixed-integer nonlinear programming (MINLP) model. This optimization model has as objective function the minimization of the total power losses in all the branches of the network constrained by active and reactive power balance equations, voltage regulation bounds and device capabilities, among others. The proposed MINLP formulation works with branch-to-node incidence that allows representing the active and reactive power flow in branches as a function of the real and imaginary parts of the voltages and currents. The solution of the MINLP model is reached through the general algebraic modeling system widely know as GAMS package by presenting it in a tutorial form. This software allows implementing in compact form the proposed model and solve it via branch and bound methods. Two test feeders composed by 5 and 14 nodes permits demonstrating the fidelity of the proposed MINLP model regarding power losses minimization when compared with literature reports.

Using the Helical Free Flap Based on the Retrograde Flow From Frontal Branch of Superficial Temporal Vessels in Lower Third Nasal Reconstruction.

Although the helical free flap is 1 of the most effective option for the lower third nasal reconstruction, the main limitation is still related to having a short pedicle length. In this report, the authors presented our experience in using the long pedicle helical free flap based on the frontal branch of the superficial temporal vessels in nasal reconstruction. Five patients, 3 alar full-thickness defects, 1 columellar defect, and 1 multiple subunit defect, underwent reconstruction using this technique. The pedicle length ranged from 4 to 6 cm. All the flaps were survived completely. However, vein congestion was seen post-operation in 1 case. This flap was saved by using medical leech. No vascular graft was needed. The helical free flap based on the retrograde flow of the frontal branch of the superficial temporal artery offers an option to overcome the limitation of short pedicle length. This composite flap is valuable for nasal alar and columellar reconstruction or even the larger defects, which involve multiple subunits.

Seasonal Variations and Driving Factors of the Eastern Maine Coastal Current

AbstractTo investigate the coastal current in the Gulf of Maine (GoME) and its relation to forcing from outside of the gulf, a high‐resolution circulation model was developed and validated. Our model shows that the Eastern Maine Coastal Current (EMCC) possesses two cores, an offshore and a nearshore core that peak in summer and spring, respectively. The two cores can be traced back to outflows from the Bay of Fundy from opposite sides of Grand Manan Island, and both cores are deeper and slightly more onshore in summer and fall in response to tidal mixing, surface thermal stratification and wind. The two cores merge south of Pleasant Bay, then split into two branches again east of Mount Desert Rock, where the nearshore branch flows along the coast, while the offshore branch turns southward to recirculate in the eastern GoME. Subject to variations of Scotian Shelf Water and Slope Water (SW) inflows, the offshore veering occurs further upstream (northeastward) in late winter and summer, but gradually shifts downstream (southwestward) from summer to winter. Diagnosis of momentum balance demonstrates that the EMCC is primarily driven by the pressure gradient force (PG), of which the barotropic PG is dominant and offshore, while the baroclinic PG is onshore and increases with depth. The large baroclinic PG at depths, modulated by SW, that is, blended by tidal mixing, offsets the barotropic PG. Near the surface, the barotropic PG is nearly balanced by the Coriolis force, forming the geostrophic EMCC.

Numerical simulation of the branching blood flow in a model of the femoral artery-graft junction

AnnotationThe results of numerical simulation of pulsating blood flow in a three-dimensional model of the femoral artery-graft junction are presented. The study is focused on the influence of the flow rates ratio in two branches of the branching flow on the location and size of the recirculation flow areas in the shunt and in the common femoral artery, with an emphasis on the analysis of the anastomotic zone. Areas with small values of the cycle-averaged shear stresses and increased values of the shear stress oscillation index, potentially dangerous from the point of view of the neointima growth in the shunt, are identified.

A generalized computationally efficient copula-polynomial chaos framework for probabilistic power flow considering nonlinear correlations of PV injections

This paper develops a general computationally efficient copula-polynomial chaos expansion (copula-PCE) framework for power system probabilistic power flow that can handle both linear and nonlinear correlations of uncertain power injections, such as wind and PVs. A data-driven copula statistical model is used to capture both nonlinear and linear correlations of uncertain power injections. This allows us to resort to the Rosenblatt transformation to transform correlated variables into independent ones while preserving the dependence structure. It paves the way for leveraging PCE for surrogate modeling and uncertainty quantification of power flow results. To further improve the computational efficiency of the proposed method without sacrificing accuracy, two strategies are developed and unified together. Specifically, the branch flow sensitivity analysis (BFSA) is used to select an appropriate number of outputs that need PCE surrogate modeling while the analysis of variance (ANOVA) scheme enables us to reduce the number of basis functions and coefficients evaluations for each PCE surrogate. Simulations carried out on the IEEE 57-bus and 118-bus and PEGASE 1354-bus systems show that the proposed framework can obtain better accuracy and computational efficiency than the existing PCE-based methods with linear correlation assumption and other Monte Carlo-based methods. The sensitivities to different copula types and parameters are also investigated.

A New Second-Order Cone Programming Model for Voltage Control of Power Distribution System With Inverter-Based Distributed Generation

In this article, a novel second-order cone programming based branch flow model is proposed for optimal power flow (OPF) in radial distribution networks. The main advantage of the proposed architecture is that it can recover the bus voltage angle difference and, thus, control the reactive power flow (PF), leading to a better voltage regulation in the network. Based on the line PF and the line impedance, a convex equation is derived and included with the model to retrieve the bus voltage angle difference. Finally, using the retrieved bus voltage angle difference within the global optimal solution space, an algorithm is developed to control the reactive flow for voltage regulation. The proposed model has been tested on modified IEEE 32 bus (IEEE 33 bus network) and IEEE 123 bus power network systems for different test cases. The simulation results are verified with the OpenDSS PF and the MatPower nonlinear programming (NLP) based OPF solutions. The computational efficiency of the proposed model is superior to the NLP models. Also, the proposed reactive flow control algorithm improves the voltage regulation of a network and promises a globally optimal solution.

Laboratory-Scale Investigation of the Pressurization of T-Junctions in Hydraulic Systems

The increasing frequency of intense rain events will worsen the operational conditions of stormwater systems, including the frequency in which these systems experience pressurization. Unfortunately, there has been limited research on the issue, particularly the pressurization of junctions in stormwater systems that are subject to rapid filling. Past research provided valuable insights on flows in junctions operating either on pressurized or open-channel flow conditions, but did not focus on the transition between these two flow regimes. This work summarizes the results of an experimental investigation that focused on describing the pressurization processes in a junction undergoing rapid filling. The experimental program considered a total of 67 unique combinations, with variables including different slopes of the upstream and lateral pipes, as well as different inflow rates in each one of these conduits. Fast blockage of the flow led to the pressurization process, that was characterized through video-recording and pressure monitoring at selected points along in the apparatus. This innovative research identified for the first time five unique pressurization modes based on the video recordings of the pressurization. The pressurization modes were dependent on the experimental setup, including lateral and main branch flows as well as their slopes. An independent clustering-based analysis of the experimental data was used and confirmed this classification. These results are the first ones of its kind and clearly indicates potential limitations of numerical models in representing flows in the junctions when air pocket entrapment occurs due to rapid filling conditions. Future research should address the limitations of the present experimental work in terms of scale effects, including a wider range of tested flow conditions and slopes, besides different junction geometries with storage.