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At least 433 records · Page 24

A modified homotopy method for solving the principal-agent bilevel programming problem

In this paper, the principal-agent bilevel programming problem with integral operator is considered, in which the upper-level object is the agent that maximizes its expected utility with respect to an agreed compensation contract. The constraints are the principal’s participation and the agent’s incentive compatibility. The latter is a lower-level optimization problem with respect to its private action. To solve an equivalent single-level nonconvex programming problem with integral operator, a modified homotopy method for solving the Karush–Kuhn–Tucker system is proposed. This method requires only an interior point and, not necessarily, a feasible initial approximation for the constraint shifting set. Global convergence is proven under some mild conditions. Numerical experiments were performed by our homotopy method as well as by fmincon in Matlab, LOQO and MINOS. The experiments showed that: designing a piecewise linear contract is much better than designing a piecewise constant contract and only needs to solve a much lower-dimensional optimization problem and hence needs much less computation time; the optimal value of the principal-agent model with designing piecewise linear contract tends to a limitation, while the discrete segments gradually increase; and finally, the proposed modified homotopy method is feasible and effective.

97 MATHEMATICS AND COMPUTING↗

J-variational inequalities and zeroes of a family of maximal monotone operators by sunny generalized nonexpansive retraction

In this paper, using generalized resolvents and retractions onto shrinking closed subsets, we present new extragradient algorithms for finding the solution of a J-variational-like inequality, the zero points of a family of maximal monotone operators, and the solution set of mixed equilibrium problems for a J-α-inverse-strongly monotone-like operator in a 2-uniformly convex and 2-uniformly smooth Banach space. By introducing the new definitions, we prove strong convergence of generated iterates in the extragradient methods. Using FMINCON optimization toolbox in MATLAB, we give some numerical examples and compare them with several existence results in the literature to illustrate the usability of our results.

97 MATHEMATICS AND COMPUTING↗

Initial conceptual demonstration of control co-design for WEC optimization

Abstract While some engineering fields have benefited from systematic design optimization studies, wave energy converters have yet to successfully incorporate such analyses into practical engineering workflows. The current iterative approach to wave energy converter design leads to sub-optimal solutions. This short paper presents an open-source MATLAB toolbox for performing design optimization studies on wave energy converters where power take-off behavior and realistic constraints can be easily included. This tool incorporates an adaptable control co-design approach, in that a constrained optimal controller is used to simulate device dynamics and populate an arbitrary objective function of the user’s choosing. A brief explanation of the tool’s structure and underlying theory is presented. To demonstrate the capabilities of the tool, verify its functionality, and begin to explore some basic wave energy converter design relationships, three conceptual case studies are presented. In particular, the importance of considering (and constraining) the magnitudes of device motion and forces in design optimization is shown.

16 TIDAL AND WAVE POWER↗

Analysis of N-dimensional Klein–Gordon equation for hydrogen molecule in the non-central potential field

We investigate a complete normalized relativistic solutions for N-dimensional Hartmann potential and relativistic effects of non-central potential field for hydrogen molecule within the framework of asymptotic iteration approach. We also discuss in detail the influence of dimensions on the angular probability distribution of hydrogen molecule. N-dimensional bound state wavefunction solutions including angular and radial solutions are expressed in terms of the Jacobi and Laguerre polynomials, respectively. N-dimensional angular wavefunctions of hydrogen molecule were visualized with Matlab software. In hyperspherical coordinates, the recurrence relations between diagonal matrix elements have been derived for N-dimensional Hartmann potential in relativistic theory. We also obtain analytical expressions of diagonal matrix elements and the recurrence formula between off-diagonal matrix elements in N-dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A unified approach to Plasmon–Polariton and Brewster mode dynamics in media with interfacial surface-admittance

In this article we develop an ab-initio formulation for the analysis of certain solutions to the macroscopic Maxwell equations in bulk homogeneous materials that are separated by a planar interface that may sustain field-dependent electric currents induced by a surface admittance tensor. Based on Clemmow’s description of complex inhomogeneous plane time-harmonic waves, a systematic procedure is given that yields particular global solutions in terms of solutions to a system of bivariate polynomial and linear eigen-value equations for a set of six complex dimensionless scalars. This algebraic system is amenable to rapid numerical analysis using Maple or Matlab on a laptop. From the resulting solutions, analytic formulae for the electromagnetic fields can be expressed in terms of values for these six scalars and the electromagnetic phenomenological properties of the bulk media and their interface. We show explicitly how general properties of Surface Plasmon–Polariton (SPP) and Brewster modes follow from this unified viewpoint without appeal to any reflections in a Fresnel formulation. In particular we emphasise that endowing the material interface with (in general) anisotropic admittance properties can lead to new global electromagnetic field characteristics offering new possibilities for the control of surface characteristics by using recent advances in the fabrication of meta-materials. We illustrate our results by showing how a mono-layer of graphene in a normal magneto-static field can be used to construct a tunable meta-surface for SPP generation and how a simple conducting Ohmic interface can be used to excite both transverse electric and transverse magnetic Brewster modes as a function of the interface admittance.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Design of an advanced energy management system for microgrid control using a state machine

A state machine is proposed as the solution for an automated microgrid energy management system (EMS) to improve transient performance during transition operations. It characterizes microgrid operation by seven states that cover all the operating modes: two for steady-state operation (grid-connected and islanded), four for transition operation (preparing for disconnection, transitioning to islanding, preparing for reconnection, and transitioning to grid-connected), and one for emergency operation (black-start operation). A unique dispatch algorithm is developed for each state to achieve the control objective, and the transition function is implemented in the state machine as control logics to transition the system from one state to the next. The feasibility and effectiveness of the developed state machine is validated by simulation in MATLAB with an example microgrid, and the test results show excellent performance of the state machine to achieve the target control objective in each state and to improve the system's transient performance during transition operation.

36 MATERIALS SCIENCE↗

Evaluating the Feasibility of Transactive Approach for Voltage Management Using Inverters of a PV Plant

This article evaluates the feasibility of a double-auction-based Transactive Energy System (TES) for engaging the reactive power (Var) capability of inverters in a utility-scale pho¬tovoltaic (PV) plant for voltage management in distribution feed¬ers. In this approach, a PV plant owner (seller) provides Var supply curves in terms of price-quantity pairs consider¬ing the inverters’ P-Q capability, efficiency, opportunity cost for real power curtail¬ment, losses, etc. At the same time, the utility (buyer) proposes Var demand curves in price-quantity pairs exhibiting the marginal price of Var. Then, market clearing points are obtained from the intersection points of supply and demand curves which are then used to create Var dispatch sig-nals from the PV plant. To conduct a fea¬sibility study of this approach, an Australian distribution network with a utility-scale PV plant (capacity 3.275 MWP) is modeled in RSCAD and simu¬lated in real-time on MATLAB, RSCAD-RTDS co-simulation platform using real historical data. Consid¬ering a use case, namely, conservation voltage reduction (CVR), the operational feasibility along with cost-benefit analysis is demonstrated in software-in-the-loop (SIL) and hardware-in-the-loop (HIL) platform. Another use case, exploring the benefit from tap-change reduction of step-voltage-regulator, is investigated. These studies explore further use cases, e.g., PV hosting capacity, network reconfiguration, etc., to be incorporated in TES for experiencing substantial economic benefits.

Alam, Mollah Rezaul↗

Simulation and power quality analysis of a Loose-Coupled bipolar DC microgrid in an office building

With distributed generation and battery storage technologies thriving in microgrids, the use of direct current (DC) microgrids in the building sector offers multiple advantages in energy efficiency and power quality compared with alternating current (AC) systems. This study developed a new concept of a loose-coupled bipolar DC building power system. In this work, the concept was used to design a real-world office building in Shenzhen, China. A power system model was developed to study the stability and control of the DC power system and to verify DC power quality. The design and modeling of the DC power control system is discussed in detail. The study developed a few common fault scenarios in DC building microgrids that were simulated in the MATLAB-Simulink environment to validate the design of a loose-coupled bipolar DC system. The results indicate that the proposed loose-coupled bipolar DC system schema, when implemented with proper control algorithms, can achieve good fault-tolerant performance with reliable power quality, even during disruptive system events.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Distributed Wind-Hybrid Microgrids with Autonomous Controls and Forecasting

Distributed wind-hybrid microgrids have the potential to provide key resilience and economic benefits to both the customers they serve and the utility grids they are connected to. Such microgrids will likely be a key part of the grid of the future, whether connected to large utility grids or linked together in multi-microgrid systems. Through the hybridization of distributed wind and solar photovoltaics, autonomous device-level and system-level controls, battery energy storage systems with smart inverters, and forecasting, these microgrids could maintain local stability and provide grid services - all with renewable power. In the literature, these elements have been considered individually. However, they have not been combined and demonstrated at a high fidelity, which is essential to prove the concept's operation before moving to hardware-in-the-loop and physical demonstrations. In this work, we develop a high-fidelity MATLAB-Simulink model of a real distributed wind-hybrid microgrid that includes all these elements. We demonstrate the microgrid maintaining stability and production in a variety of islanded, grid-connected, and transition scenarios. This includes riding through faults and grid transitions, handling resource variability, and providing grid services. The results demonstrate, at a high fidelity, how distributed wind-hybrid microgrids can operate in an economic and resilient fashion. Finally, we provide recommendations for future research to move advanced distributed wind-hybrid microgrids toward deployment.

ancillary services↗

Coupled modeling of a directly heated tubular solar receiver for supercritical carbon dioxide Brayton cycle: Optical and thermal-fluid evaluation

In single phase performance and appealing thermo-physical properties supercritical carbon dioxide (s-CO 2 ) make a good heat transfer fluid candidate for concentrating solar power (CSP) technologies. The development of a solar receiver capable of delivering s-CO 2 at outlet temperatures ~973 K is required in order to merge CSP and s-CO 2 Brayton cycle technologies. A coupled optical and thermal-fluid modeling effort for a tubular receiver is undertaken to evaluate the direct tubular s-CO 2 receiver’s thermal performance when exposed to a concentrated solar power input of ~0.3–0.5 MW. Ray tracing, using SolTrace, is performed to determine the heat flux profiles on the receiver and computational fluid dynamics (CFD) determines the thermal performance of the receiver under the specified heating conditions. Moreover, an in-house MATLAB code is developed to couple SolTrace and ANSYS Fluent. CFD modeling is performed using ANSYS Fluent to predict the thermal performance of the receiver by evaluating radiation and convection heat loss mechanisms. Understanding the effects of variation in heliostat aiming strategy and flow configurations on the thermal performance of the receiver was achieved through parametric analyses. Finally, a receiver thermal efficiency ~85% was predicted and the surface temperatures were observed to be within the allowable limit for the materials under consideration.

54 ENVIRONMENTAL SCIENCES↗

Empirical validation and comparison of methodologies to simulate micro and macro-encapsulated PCMs in the building envelope

Thermal Energy Storage (TES) has the potential to shift peak electricity demand. Passive TES is usually implemented in building envelope as micro and macro encapsulated phase change materials (PCM) to shift electric energy demand and therefore requires careful heat transfer analysis. Whole building energy modelling with simplified heat transfer analysis has become extremely important for designers, architects, engineers, and researchers to predict energy performance of buildings. It is important to validate PCM modelling algorithms used in building energy programs to quantify their error and prove their capacity to model different PCM encapsulation types. This study uses data from a microencapsulated PCM and two macroencapsulated PCMs (Bio based PCM and hydrate salts) tested in full-scale using the Advanced Multiscale Building Energy Research (AMBER) Lab located at the Colorado School of Mines and is used to validate a numerical algorithm written in MATLAB language. To approximate the heat transfer through a wall assembly with macroencapsulated PCM pouches, several modelling techniques that can reduce 3D heat transfer characteristics to 1D are explored in this research. A parallel path heat transfer modelling approach is found to give the closest agreement with the experimental data for the pouched PCMs in building envelope applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Spectral Mesh-Free Quadrature for Planar Regions Bounded by Rational Parametric Curves

This article presents spectral, mesh-free, Green’s theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region’s boundary curves corresponding to Green’s theorem. (2) We then use a high-order quadrature rule to compute the numerical antiderivative of the integrand along a coordinate axis, which is used to evaluate the Green’s theorem line integral. We present two methods to compute the intermediate quadrature rule. The first is spectrally accurate (it converges faster than any algebraic order with respect to number of quadrature points) and is relatively easy to implement, but has no guarantee of polynomial exactness. The second guarantees exactness for polynomial integrands up to a pre-specified degree with an a priori-known number of quadrature points and retains the convergence properties of the first, but is slightly more complicated. The quadrature schemes have applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order meshes, and initialization of multi-material simulations with rational geometry. We compare the quadrature schemes produced using our method to other methods in the literature and show that they are much more efficient both in terms of number of quadrature points and computational time. We provide an open-source implementation of the algorithm in MATLAB.

97 MATHEMATICS AND COMPUTING↗

High-Accuracy Mesh-Free Quadrature for Trimmed Parametric Surfaces and Volumes

This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We iteratively reduce the dimensionality of integration using the generalized Stokes theorem to line integrals over trimming curves, and (2) we employ numerical antidifferentiation in the generalized Stokes theorem using high-order quadrature rules. Additionally, the scheme achieves exponential convergence up to trimming curve approximation error and has applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order curvilinear meshes, and initialization of multi-material simulations. We compare the quadrature scheme to commonly-used quadrature schemes in the literature and show that our scheme is much more efficient in terms of number of quadrature points used. We provide an open-source implementation of the scheme in MATLAB as part of QuaHOG, a software package for Quadrature of High-Order Geometries.

97 MATHEMATICS AND COMPUTING↗

The introspective may achieve more: Enhancing existing Geoscientific models with native-language emulated structural reflection

Geoscientific models manage myriad and increasingly complex data structures as trans -disciplinary models are integrated. They often incur significant redundancy with cross-cutting tasks. Reflection, the ability of a program to inspect and modify its structure and behavior at runtime, is known as a powerful tool to improve code reusability, abstraction, and separation of concerns. Reflection is rarely adopted in high-performance Geoscientific models, especially with Fortran, where it was previously deemed implausible. Practical constraints of language and legacy often limit us to feather-weight, native-language solutions. We demonstrate the usefulness of a structural-reflection-emulating, dynamically-linked metaObjects, gd . We show real-world examples including data structure self-assembly, effortless save/restart and upgrade to parallel I/O, recursive actions and batch operations. We share gd and a derived module that reproduces MATLAB-like structure in Fortran and C++. We suggest that both a gd representation and a Fortran-native representation are maintained to access the data, each for separate purposes. In conclusion, embracing emulated reflection allows generically-written codes that are highly re-usable across projects.

58 GEOSCIENCES↗

Alternating Anderson–Richardson method: An efficient alternative to preconditioned Krylov methods for large, sparse linear systems

Here, we present the Alternating Anderson–Richardson (AAR) method: an efficient and scalable alternative to preconditioned Krylov solvers for the solution of large, sparse linear systems on high performance computing platforms. Specifically, we generalize the recently proposed Alternating Anderson–Jacobi (AAJ) method (Pratapa et al., 2016) to include preconditioning, discuss efficient parallel implementation, and provide serial MATLAB and parallel C/C++ implementations. In serial applications to nonsymmetric systems, we find that AAR is comparably robust to GMRES, using the same preconditioning, while often outperforming it in time to solution; and find AAR to be more robust than Bi-CGSTAB for the problems considered. In parallel applications to the Helmholtz and Poisson equations, we find that AAR shows superior strong and weak scaling to GMRES, Bi-CGSTAB, and Conjugate Gradient (CG) methods, using the same preconditioning, with consistently shorter times to solution at larger processor counts. Finally, in massively parallel applications to the Poisson equation, on up to 110,592 processors, we find that AAR shows superior strong and weak scaling to CG, with shorter minimum time to solution. We thus find that AAR offers a robust and efficient alternative to current state-of-the-art solvers, with increasing advantages as the number of processors grows.

97 MATHEMATICS AND COMPUTING↗

Simulated impedance of diffusion in porous media

This paper describes the use of a frequency domain, finite-difference scheme to simulate the impedance spectra of diffusion in porous microstructures. We investigate both open and closed systems for a range of ideal geometries, as well as some randomly generated synthetic volumes and tomographically derived microstructural data. In many cases, the spectra deviate significantly from the conventional Warburg-type elements typically used to represent diffusion in equivalent circuit analysis. Furthermore, a key finding is that certain microstructures show multiple peaks in the complex plane, which may be misinterpreted as separate electrochemical processes in real impedance data. This is relevant to battery electrode design as the techniques for nano-scale fabrication become more widespread. This simulation tool is provided as an open-source MatLab application and is freely available online as part of the TauFactor platform.

36 MATERIALS SCIENCE↗

Coupling thermal energy storage with a thermally anisotropic building envelope for building demand-side management across various US climate conditions

Here, the thermally anisotropic building envelope (TABE) is a novel active building envelope that enhances energy efficiency and thermal comfort in buildings by transferring heat and cold between building envelopes and hydronic loops. When coupled with thermal energy storage (TES) units, the TABE + TES enables the storage of both heat and cold energy captured by the TABE roof or exterior walls. This stored energy can be later released by the TABE floor for indoor heating and cooling, benefiting both the grid and the end user. This paper evaluates the merits of TABE + TES for building demand-side management across various US climate conditions, focusing on peak load shaving, annual energy savings, and cost savings under time-of-use (TOU) electric rate schedules. Simulations were conducted by integrating time-of-day–informed, rule-based control strategies in MATLAB, TABE components and TES units in COMSOL Multiphysics, and whole-building energy analysis in EnergyPlus. A case study using the US Department of Energy’s prototype single-family detached house model in Birmingham, Alabama; Los Angeles, California; Oak Ridge, Tennessee; and Denver, Colorado, showed that the TABE + TES system achieved (1) 70 % peak load shaving in Los Angeles and Denver and 20 % in Birmingham and Oak Ridge; (2) significant peak electricity savings of 351–497 kWh, reducing peak energy consumption by 38 %–78 %; and (3) annual heating cost savings of 0.79 $\$$/m2–1.17 $\$$/m 2 and cooling cost savings of 0.60 $\$$/m 2 –1.17 $\$$/m 2 using a normal utility rate or low-TOU rate. The benefits of employing the TABE + TES system are even more significant under high TOU rates.

25 ENERGY STORAGE↗