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At least 325 records · Page 18

Power Flow Solution Methods for Combined Transmission and Distribution Systems

High distributed PV penetration makes the distribution systems more active and increases their impact on the upstream transmission grid. To facilitate the studies on this area, this paper proposes a power flow (PF) model and formulation of combined transmission and distribution (T&D) power systems. The formulation is based on the physical coupling of transmission and distribution grids. The unbalanced nature of distribution feeders and voltage regulators are modeled so that the resulting PF balance equations in distribution systems are similar to those in the interconnected transmission system. The formulated nonlinear PF equations are solved using the proposed unified and sequential methods. Both methods are verified and compared with each other using several combined T&D power systems. A multi-period PF simulation is also included to demonstrate the capability of the proposed formulation and solution methods in capturing the influences of high distributed PV penetration on transmission level.

Nguyen, Quan H.↗

Partner with a Third-Party Delivery Service or Not? A Prediction-and-Decision Tool for Restaurants Facing Takeout Demand Surges During a Pandemic

Amidst the COVID-19 pandemic, restaurants become more reliant on no-contact pick-up or delivery ways for serving customers. As a result, they need to make tactical planning decisions such as whether to partner with online platforms, to form their own delivery team, or both. In this paper, we develop an integrated prediction-decision model to analyze the profit of combining the two approaches and to decide the needed number of drivers under stochastic demand. We first use the susceptible-infected-recovered (SIR) model to forecast future infected cases in a given region and then construct an autoregressive-moving-average (ARMA) regression model to predict food-ordering demand. Using predicted demand samples, we formulate a stochastic integer program to optimize food delivery plans. We conduct numerical studies using COVID-19 data and food-ordering demand data collected from local restaurants in Nuevo Leon, Mexico, from April to October 2020, to show results for helping restaurants build contingency plans under rapid market changes. Our method can be used under unexpected demand surges, various infection/vaccination status, and demand patterns. Here, our results show that a restaurant can benefit from partnering with third-party delivery platforms when (i) the subscription fee is low, (ii) customers can flexibly decide whether to order from platforms or from restaurants directly, (iii) customers require more efficient delivery, (iv) average delivery distance is long, or (v) demand variance is high.

97 MATHEMATICS AND COMPUTING↗

Enhanced Light Outcoupling from OLEDs Fabricated on Novel Low-Cost Patterned Plastic Substrates of Varying Periodicity

OLEDs continue to make strides in display applications, but their commercial utilization in solid-state lighting (SSL) is lagging. An ongoing challenge, in particular for manufacturing, is the need for enhanced efficiency and hence the necessity to increase in an inexpensive approach the extraction of the light generated inside the OLED into the forward (viewing) hemisphere. In conventional OLEDs fabricated on a transparent flat anode coated on glass, the external quantum efficiency (EQE) is only ~20%. About 50% of the light is lost to internal waveguiding in the high refractive index (RI) organic + ITO anode layers and to surface plasmon polaritons (SPPs) at the organic/metal cathode interface. Another ~30% of the light is externally waveguided in the substrate to its edges. While extraction of the externally waveguided light is commonly addressed by adding a microlens array (MLA) or a scattering layer at the substrate’s air-side, light outcoupling increases by only ~1.6-1.7x (vs up to 2.5x in improving from ~20% to ~50%). The use of a hemispherical lens or an index matching fluid (IMF) at the substrate/photodetector (PD) interface increases the outcoupling by at least 2x; these approaches however, are not viable industrially, and even a MLA is sometimes undesirable due to its non-planar, scattering structure. In multi-stack tandem OLEDs, where the metal cathode is far from the emitting zone(s), the impact of photons loss to SPPs decreases. Our project addressed the ~50% loss to the internally waveguided light and SPPs. We evaluated OLEDs fabricated on patterned or planarized plastic substrates manufactured in a cost-effective approach compatible with a roll-to-roll (R2R) process. The OLEDs were either (i) patterned to various degrees depending on the pitch a and height or depth h of the pattern features or (ii) planar, with a pattern buried under a flat high RI planarization layer. We demonstrated that the outcoupling from green patterned OLEDs reaches ~50% by mitigating plasmon–related loss and internal waveguiding, even without the addition of a MLA, a hemispherical lens, or IMF. Simulations conducted in parallel with the experimental effort demonstrated how diffraction by conformally corrugated OLEDs increases the outcoupling to >60%. Structures with varying pitch values were also simulated indicating that combining domains of varying pitch could increase outcoupling to 55-60%. Experimentally, we additionally assessed the role a and h in determining not only the OLED efficiencies, but also their structural properties, i.e., the uniformity and conformality throughout the OLED stack. As planar OLEDs are preferred over corrugated devices, we studied different patterns in plastic substrates that were planarized by a high RI formulation. Planar green OLEDs on such structures showed enhanced efficiencies with EQEs larger than 60% with the addition of an IMF (to extract the substrate mode) at the substrate/Si PD interface. White OLEDs showed EQEs of 45.5%. Plastic substrates are currently less attractive than glass substrates due to drawbacks such as permeability to water vapor and oxygen, and in some cases thermal instability. Plastic substrates however, are flexible and easy to handle unlike thin flexible glass, and once transparent thin barrier films are available, they will become more attractive; they are already of interest in medical applications. Importantly, as it is easy to generate various patterns in different plastic materials, they provide excellent means for assessing and optimizing enhancing extracting structures. Such structures can also be transferred to glass substrates with some process modifications. The technical effectiveness and economic feasibility of the project lie in the patterning of the extracting plastic substrates in an approach that is scalable to R2R manufacturing. R2R processes are of drastically lower-cost than batch or single-unit fabrication. The patterned plastic can be a part of an integrated substrate either plastic or glass, which includes also a MLA or a planar layer with embedded scattering particles, as well as a conductive metal mesh/electrode design. SSL is environmentally-friendly and as OLED SSL becomes more efficient it will reduce electricity consumption, and hence lighting cost, as well as produce less expensive attractive lighting fixtures. Our university-industry collaboration is hence of major benefit to the public as it demonstrates the feasibility of manufacturing optimized extracting substrates for highly efficient OLEDs for SSL in a future R2R process, which would drastically reduce the manufacturing cost and increase production in the USA. Moreover, newly developed methods by our team allow low-cost roll manufactured substrates to be transferred to flexible or rigid glass substrates, which solves the plastic substrate barrier issues, and when combined with device encapsulation will increase the OLEDs’ environmental stability.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Assessment of Cementitious Composites for High-Temperature Geothermal Wells

High-temperature (HT) geothermal wells can provide green power 24 hours a day, 7 days a week. Under harsh environmental and operational conditions, the long-term durability requirements of such wells require special cementitious composites for well construction. This paper reports a comprehensive assessment of geothermal cement composites in cyclic pressure function laboratory tests and field exposures in an HT geothermal well (300–350 °C), as well as a numerical model to complement the experimental results. Performances of calcium–aluminate cement (CAC)-based composites and calcium-free cement were compared against the reference ordinary Portland cement (OPC)/silica blend. The stability and degradation of the tested materials were characterized by crystalline composition, thermo-gravimetric and elemental analyses, morphological studies, water-fillable porosity, and mechanical property measurements. All CAC-based formulations outperformed the reference blend both in the function and exposure tests. The reference OPC/silica lost its mechanical properties during the 9-month well exposure through extensive HT carbonation, while the properties of the CAC-based blends improved over that period. The Modified Cam-Clay (MCC) plasticity parameters of several HT cement formulations were extracted from triaxial and Brazilian tests and verified against the experimental results of function cyclic tests. These parameters can be used in well integrity models to predict the field-scale behavior of the cement sheath under geothermal well conditions.

15 GEOTHERMAL ENERGY↗

Ultrasound Characterization of Plastic Bonded Explosives With Varied Binder Content and Density

Advanced explosive formulations and methods of production require rapid characterization for both processes and materials. Here, we present results for ultrasound characterization of a plastic bonded explosive (PBX) formulation as a function of binder weight percent and pressing density using through-transmission sound speed measurements. The explosive in this study was composed of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) combined with the fluoropolymer binder Kynar Ultraflex B. Binder content ranged from 2.6 wt.% to 11.5 wt.% with associated explosive formulation densities from 1.69 g/cc to 1.89 g/cc. We find linear and nonlinear changes in longitudinal and shear sound speeds, peak frequencies, and measured elastic properties for the different PBX formulations. These measured changes can differentiate the tested formulations, highlighting the potential for ultrasound as a nondestructive characterization method for newly-formulated PBXs. We also demonstrate through-transmission measurements using different coupling media and present results from an ultrasound technique called resonant ultrasound spectroscopy (RUS). Both transmission and RUS approaches may allow for rapid and even automated characterization of PBX components suitable for high-throughput manufacturing operations.

Engineering↗

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

In this work, we present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Eulerian thermo-mechanical simulations of heterogeneous solid propellants using an approximate projection method

We present a mathematical model that describes thermo-mechanical deformations and thermal gradients on the unsteady burning of a heterogeneous solid propellant. A scaling study shows that the deformations in solid at combustion timescales can be treated as quasi-static. The resulting thermo-mechanical formulation is formulated on a Cartesian grid and makes use of a weak form of Chorin-type projection method to deal with large difference in shear modulus of constituent materials. Further, a one-dimensional verification study is carried out by comparing numerical simulations with those of an analytical model. In addition, convergence studies for a two-dimensional propellant sandwich configuration are presented for the stress, velocity, and reference map components. Finally, simulations are carried out for a two-dimensional random propellant pack and the time-averaged burn rate and strains are reported.

42 ENGINEERING↗

Rich Dynamics of a General Producer–Grazer Interaction Model under Shared Multiple Resource Limitations

Organism growth is often determined by multiple resources interdependently. However, growth models based on the Droop cell quota framework have historically been built using threshold formulations, which means they intrinsically involve single-resource limitations. In addition, it is a daunting task to study the global dynamics of these models mathematically, since they employ minimum functions that are non-smooth (not differentiable). To provide an approach to encompass interactions of multiple resources, we propose a multiple-resource limitation growth function based on the Droop cell quota concept and incorporate it into an existing producer–grazer model. The formulation of the producer’s growth rate is based on cell growth process time-tracking, while the grazer’s growth rate is constructed based on optimal limiting nutrient allocation in cell transcription and translation phases. We show that the proposed model captures a wide range of experimental observations, such as the paradox of enrichment, the paradox of energy enrichment, and the paradox of nutrient enrichment. Together, our proposed formulation and the existing threshold formulation provide bounds on the expected growth of an organism. Moreover, the proposed model is mathematically more tractable, since it does not use the minimum functions as in other stoichiometric models.

59 BASIC BIOLOGICAL SCIENCES↗

LDRD Abbreviated report: High-Order General-Discrete-Ordinates Method Enabling Efficient Deterministic Transport in Hydrodynamic Simulations

Deterministic transport simulations for national-security and energy applications often operate in high-dimensional phase-space, where accuracy and cost both become major challenges. A common numerical artifact in such problems is the “ray-effect,” which appears as unphysical streaks. Beyond misinterpretation, these artifacts can contaminate tightly coupled physics, such as fluid dynamics, radiation-hydrodynamics, and laser-plasma interactions, eroding the predictive capability of entire multiphysics workflows. Our objective was to make high-dimension studies practical on modern hardware while mitigating the ray-effect without relying on prohibitively expensive sampling approaches such as Monte Carlo methods. We developed the Generic Discretization Library (GenDiL), a Graphics Processing Unit (GPU)-first framework that uses high-order Discontinuous Galerkin (DG) methods and matrix-free algorithms to reduce memory usage and improve computational efficiency, critical for phase-space simulations. GenDiL supports phase-space adaptivity in both mesh size and polynomial order (hp-adaptivity) to place resolution only where it is needed. A central capability is Local Dimensional Refinement (LDR), which couples lower-dimension continuum models to higher-dimension kinetic models through stable and conservative interfaces, so that high-fidelity physics is applied only in regions where it is essential. Building on the GenDiL framework, we developed the General SN (GSN) family of algorithms as a true generalization of the polar SN approach (discrete ordinates, often denoted SN). Rather than tying discrete ordinates to a specific polar change of coordinates, GSN formulates transport on an arbitrary change of coordinates chosen to reduce ray-effect. We studied two complementary variants: an analytic variant, where the coordinate map is prescribed in advance by a closed-form function; and a data-driven variant, where a quantity of interest, such as the net flux, guides the coordinate system. GenDiL provides the library infrastructure for efficient GPU execution, but the GSN concept is algorithmic and independent of any one library. Across representative high-dimension tests, including non-symmetric solutions, both variants delivered strong ray-effect mitigation at practical cost, moving four- to six-dimensional analysis toward repeatable, routine studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations

The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

B-spline↗

New procedure for evaluation of U(3) coupling and recoupling coefficients

A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group–subgroup chains is presented. While the canonical U(3) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and in so doing provides a faster and more accurate determination of any and all required results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(3).

Cross-Coupling Reaction↗

Mechanical separations of corn stover anatomical fractions in an integrated feedstock preprocessing system: An experimental and data-driven modeling study

High variabilities of material attributes in lignocellulosic biomass present risks for biofuel and biochemical productions and must be mitigated via preprocessing. Since almost no mechanical device is originally designed for processing biomass, how to operate existing apparatuses with efficient performance has not been investigated extensively. This work presents a study on an integrated screening and air classification to separate cobs and stalks from husks and leaves in corn stover. Prototype machine learning models were developed to assess the feasibility of predicting the process outcome based on the measurable parameters. The models trained upon limited experimental data rendered decent predictive accuracy of yield and purity. The experimental data and modeling results collectively suggest decreasing throughput leads to a higher purity. To the contrary, if throughput increases, a lower purity is likely. A possible trade-off between yield and purity of the separated streams indicates the need for optimal combinations of feedstock size, moisture, and throughput to achieve optimized separations. The results of this study also suggest the need to further improve model predictability by developing more accurate formulations for physics governing the integrated unit operations. To accomplish this, additional experimental data needs to be generated for model training.

09 - BIOMASS FUELS↗

Optimizing and Exploring Untapped Micro-Hydro Hybrid Systems: a Multi-Objective Approach for Crystal Lake as a Large-Scale Energy Storage Solution

Increasing electricity demand and concerns about climate change and fossil fuel consumption have highlighted the importance of renewable energy resources and storage systems. This paper proposes a method for exploring untapped pumped hydro storage potentials to accommodate intermittent renewable energy generation profiles. Hourly measured data from 2022 in Benzie County, Michigan, United States, were gathered for system sizing and a thorough, realistic analysis. By employing the multi-objective grey wolf optimization algorithm, we formulated optimal sizing and energy-management strategies for three different scenarios. Unlike similar studies, the 3rd with triple objective functions (OFs) scenario aims to maximize both reliability and ecological OFs while minimizing the cost OF. It has shown promising results with multiple solutions, considering economic, environmental, and reliability factors. A case study conducted in Crystal Lake, Michigan, revealed that although Crystal Lake would function only as a micro-hydro power facility, it is a promising and huge storage unit with a substantial storage capacity of around 14.9734GWh. The system investigated is significant in the USA due to its rapid deployment capabilities, minimal construction requirements, and ease of integration with the distribution grid. The fuzzy logic method was employed to identify the best non-dominant solution among the other solutions. Furthermore, these outcomes include a notably low levelized cost of energy at 0.046147$/kWh, a robust index of reliability of 99.705%, and a significant reduction in CO₂ emissions amounting to 7.9142×10 3 tons/year, when considering the triple OFs. The paper’s methodology provides valuable insights for regions aiming to utilize renewable energy from untapped storage sources.

13 HYDRO ENERGY↗

Assessment of rhizosphere bacterial diversity and composition in a metal hyperaccumulator (Boehmeria nivea) and a nonaccumulator (Artemisia annua) in an antimony mine

Abstract Aims Heavy metal hyperaccumulators are widely used in mining restoration due to their ability to accumulate and transport heavy metals, compared to nonaccumulators. Rhizosphere bacteria in metal hyperaccumulators play a key role in the uptake of heavy metals from soil; however, assessments of the differences of rhizosphere bacteria between metal hyperaccumulators and nonaccumulator are scarce. Methods and results To understand the difference of bacterial composition between hyperaccumulator and nonaccumulator in rhizosphere, the diversity and composition of rhizosphere bacteria in a metal hyperaccumulator (Boehmeria nivea) and a nonaccumulator (Artemisia annua) grown in the same field in Xikuangshan were evaluated using Illumina Miseq high-throughput sequencing technology. Boehmeria nivea and A. annua had 3926 overlapping OTUs, 19,736 and 17,579 unique OTUs, respectively. Boehmeria nivea had lower Chao1 index, Shannon index and Pielou index than A. annua. The dominant phyla and genera of rhizosphere bacteria in B. nivea and A. annua were similar, but some rhizosphere bacterial communities with heavy metal remediation ability mainly appeared in the rhizosphere of the hyperaccumulator. Compared to A. annua, B. nivea showed a significantly higher relative abundance of rhizosphere bacteria, such as Acidobacteria and Bacteroidete at the phylum level and RB41 at the genus level. Some specific rhizosphere bacteria with the ability to bind metal, such as Leifsonia and Kibdelosporangium, were only found in the rhizosphere of B. nivea. Conclusion Results indicated that B. nivea, as a metal hyperaccumulator, has a key function in governing metal-resistant rhizosphere bacteria in response to antimony compound pollution stress. Significance and Impact of Study Understanding the diversity of rhizosphere bacteria between hyperaccumulators and nonaccumulators is beneficial to formulate strategies to improve metal uptake efficiency by selecting specific plant species and rhizosphere bacteria grown on polluted soil.

Lin, Yuxiang↗

Support of domain decomposition-based solvers in Chroma

In multilevel integration, the correlation functions are decomposed into factors that depend only on fields localized into lattice subdomains so that they can be independently integrated. Although the standard formulation of the LQCD action is not local in the presence of fermions, past studies have shown approximations of the quark propagator and the fermionic determinant dependent on the gauge fields within specific subdomains can still be effective. We will present our current progress in supporting domain decomposition within Chroma, which is necessary for multilevel integration approaches. The efforts are focused on extending the code base to efficiently manipulate subdomains for lattice fields and operators and performing inversions and eigendecompositions within domains.

Alcalde, Eloy Romero↗

Penetration through Slots in Cylindrical Cavities Operating at Fundamental Cavity Modes in the Presence of Electromagnetic Absorbers

Placing microwave absorbing materials into a high-quality factor resonant cavity may in general reduce the large interior electromagnetic fields excited under external illumination. In this study, we aim to combine two analytical models we previously developed: 1) an unmatched formulation for frequencies below the slot resonance to model shielding effectiveness versus frequency; and 2) a perturbation model approach to estimate the quality factor of cavities in the presence of absorbers. The resulting model realizes a toolkit with which design guidelines of the absorber's properties and location can be optimized over a frequency band. Analytic predictions of shielding effectiveness for three transverse magnetic modes for various locations of the absorber placed on the inside cavity wall show good agreement with both full-wave simulations and experiments, and validate the proposed model. This analysis opens new avenues for specialized ways to mitigate harmful fields within cavities.

36 MATERIALS SCIENCE↗

Hydrophobic Lightweight Cement with Thermal Shock Resistance and Thermal Insulating Properties for Energy-Storage Geothermal Well Systems

This study assessed the possibility of using polymethylhydrosiloxane (PMHS)-treated fly ash cenospheres (FCS) for formulating a thermally insulating and thermal shock (TS)-resistant cementitious blend with calcium aluminate cement. To prevent FCS degradation in an alkaline cement environment at high temperatures, the cenospheres were pre-treated with sodium metasilicate to form silanol and aluminol groups on their surface. These groups participated in a dehydrogenation reaction with the functional ≡Si–H groups within PMHS with the formation of siloxane oxygen-linked M-FCS (M: Al or Si). At high hydrothermal temperatures of 175 and 250 °C, some Si–O–Si and SiCH 3 bonds ruptured, causing depolymerization of the polymer at the FCS surface and hydroxylation of the raptured sites with the formation of silanol groups. Repolymerization through self-condensation between the silanol groups followed, resulting in the transformation of siloxane to low crosslinked silicon-like polymer as a repolymerization-induced product (RIP) without carbon. The RIP provided adequate protection of FCS from pozzolanic reactions (PR), which was confirmed by the decline in zeolites as the products of PR of FCS. Cements with PMHS-treated FCS withstood both hydrothermal and thermal temperature of 250 °C in TS tests, and they also showed improved compressive strength, toughness, and water repellency as well as decreased thermal conductivity. The lubricating properties of PMHS increased the fluidity of lightweight slurries.

15 GEOTHERMAL ENERGY↗

Substation-Level Grid Topology Optimization Using Bus Splitting: Preprint

Operations of substation circuit breakers are of high significance for performing system maintenance and topology optimization. Bus splitting is one type of topology changes where the two bus-bars at a substation become electrically disconnected after certain actions of circuit breakers. As these events involve detailed substation modeling, they are not typically considered in power system routine operation and control. In this paper, an improved substation-level topology optimization is developed by expanding traditional line switching with breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bi-linear terms in the resultant topology optimization model. Thus, a tractable mixed-integer linear program formulation is presented which can be efficiently solved for real-time control. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the performance and economic benefits of the proposed topology optimization approach.

bus split↗