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At least 919 records · Page 51

Factorization Machine‐Based Active Learning for Functional Materials Design with Optimal Initial Data

The optimization of functional materials is important to enhance their properties, but their complex geometries pose great challenges to optimization. Data-driven algorithms efficiently navigate such complex design spaces by learning relationships between material structures and performance metrics to discover high-performance functional materials. Surrogate-based active learning, continually improving its surrogate model by iteratively including high-quality data points, has emerged as a cost-effective data-driven approach. Furthermore, it can be coupled with quantum computing to enhance optimization processes, especially when paired with a special form of surrogate model (i.e., quadratic unconstrained binary optimization), formulated by factorization machine (FM). However, current practices often overlook the variability in design space sizes when determining the initial data size for optimization. In this work, we investigate the optimal initial data sizes required for efficient convergence across various design space sizes. By employing averaged piecewise linear regression, we identify initiation points where convergence begins, highlighting the crucial role of employing adequate initial data in achieving efficient optimization. These results contribute to the efficient optimization of functional materials by ensuring faster convergence and reducing computational costs in FM-based active learning.

active learning↗

Optimal control and Galois theory

An important role is played in the solution of a class of optimal control problems by a certain special polynomial of degree 2(n−1) with integer coefficients. The linear independence of a family of k roots of this polynomial over the field Q implies the existence of a solution of the original problem with optimal control in the form of an irrational winding of a k-dimensional Clifford torus, which is passed in finite time. In the paper, we prove that for n≤15 one can take an arbitrary positive integer not exceeding [n/2] for k. The apparatus developed in the paper is applied to the systems of Chebyshev-Hermite polynomials and generalized Chebyshev-Laguerre polynomials. It is proved that for such polynomials of degree 2m every subsystem of [(m+1)/2] roots with pairwise distinct squares is linearly independent over the field Q. Bibliography: 11 titles.

97 MATHEMATICS AND COMPUTING↗

Real-time dispatch optimization for concentrating solar power with thermal energy storage

Concentrating solar power (CSP) plants present a promising path towards utility-scale renewable energy. The power tower, or central receiver, configuration can achieve higher operating temperatures than other forms of CSP, and, like all forms of CSP, naturally pairs with comparatively inexpensive thermal energy storage, which allows CSP plants to dispatch electricity according to market price incentives and outside the hours of solar resource availability. Currently, CSP plants commonly include a steam Rankine power cycle and several heat exchange components to generate high-pressure steam using stored thermal energy. The efficiency of the steam Rankine cycle depends on the temperature of the plant's operating fluid, and so is a main concern of plant operators. However, the variable nature of the solar resource and the conservatism with which the receiver is operated prevent perfect control over the receiver outlet temperature. Therefore, during periods of solar variability, collection occurs at lower-than-design temperature. To support operator decisions in a real-time setting, we develop a revenue-maximizing non-convex mixed-integer, quadradically-constrained program which determines a dispatch schedule with sub-hourly time fidelity and considers temperature-dependent power cycle efficiency. The exact nonlinear formulation proves intractable for real-time decision support. Here we present exact and inexact techniques to improve problem tractability that include a hybrid nonlinear and linear formulation. Our approach admits solutions within approximately 3% of optimality, on average, within a five-minute time limit, demonstrating its usability for decision support in a real-time setting.

14 SOLAR ENERGY↗

Different binding modes of Cu and Pb vs. Cd, Ni, and Zn with the trihydroxamate siderophore desferrioxamine B at seawater ionic strength

The solution speciation in seawater of divalent trace metals (Cd, Cu, Ni, Pb, Zn) is dominated by strong, ostensibly metal-specific organic ligands that may play important roles in microbial metal acquisition and/or detoxification processes. We compare the effective stabilities of these metal-organic complexes to the stabilities of their complexes with a model siderophore, desferrioxamine B (DFOB). While metal-DFOB complexation has been studied in various dilute but often moderately coordinating media, for the purpose of this investigation we measured the stability constants in a non-coordinating background electrolyte at seawater ionic strength (0.7 M NaClO4). Potentiometric titrations of single metals (M) were performed in the presence of ligand (L) at different M:L molar ratios, whereupon the stability constants of multiple complexes were simultaneously determined by non-linear regression of the titration curves with FITEQL, using the optimal binding mode for each metal. Cadmium, Ni, and Zn, like trivalent Fe, sequentially form a bi-, tetra-, and hexadentate complex with DFOB as pH increases, consistent with their coordination number of 6 and regular octahedral geometry. Copper has a Jahn-Teller-distorted square-bipyramidal geometry whereas the geometry of Pb is cryptic, involving a range of bond lengths. Supported by a thermodynamic argument, our data suggest that this impedes binding of the third hydroxamate group and that the hexadentate Cu-DFOB and Pb-DFOB complex identified in earlier reports may instead be a deprotonated tetradentate complex. Absence of the hexadentate complex promotes the formation of a dinuclear (bidentate-tetradentate) complex, M2HL2+, albeit not for Pb in 0.7 M NaCl, evidently due to extensive complexation with chloride. Stabilities of the hexadentate Ni-DFOB, Zn-DFOB, and the tetradentate Pb-DFOB complex are nearly equal, yet about 2 orders of magnitude higher and 4 orders of magnitude lower than those of the hexadentate Cd-DFOB and tetradentate Cu-DFOB complex, respectively. Linear free-energy relations defined by the rare earth elements are able to predict stabilities of the Cd, Zn, and one of the Pb complexes, but underestimate those of the Ni and Cu complexes. The comparison with metal-specific organic ligands detected in seawater yields fair agreement for three of the five metals, implying that they could be siderophore-like. The Cd- and Ni-specific ligands are much stronger and may contain quite different functional groups. Calculations with MINEQL incorporating our new stability constants indicate that very high DFOB concentrations would be required to match the extent of metal-organic complexation observed in seawater, however DFOB may well represent a much broader class of structurally related ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs

This paper considers the linear weighted complementarity problem (denoted by LWCP) introduced by Potra (SIAM J Optim 22:1634–1654, 2012). Based on two weighted smoothing functions, we propose a new nonmonotone smoothing algorithm for solving the LWCP and establish its global and local quadratic convergence without the strict complementarity assumption. Compared to existing nonmonotone smoothing algorithms, the proposed algorithm solves the linear system only approximately which can save the computation work when one solves large-scale LWCPs. Moreover, the nonmonotone line search technique adopted in this paper includes the usual monotone line search and some existing nonmonotone line searches as special cases. Numerical results show that our algorithm is considerably efficient for solving large-scale LWCPs.

97 MATHEMATICS AND COMPUTING↗

Sensitivity Study for Forecasting Variables of WRF-Solar Using a Tangent Linear Approach

Integrating solar generation in recent years has highlighted the need for improved accuracy in predicting solar power. Confidence in solar power forecasting can be achieved by designing an ensemble that provides reliable probabilistic information for solar radiation with reduced uncertainty and error. Ideally, ensemble members are created through the optimized perturbation of the initial conditions in numerical weather prediction (NWP) models. Tangent linear models are capable of efficiently investigating the sensitivity of solar radiation to model input parameters because they do not require individual perturbation of each variable. This sensitivity study using tangent linear models provide us the capability to identify the right variables to perturb in an ensemble prediction system. In this study, we developed tangent linear models for WRF-Solar modules that directly impact the computation of solar radiation and the simulation of cloud formation and dissipation including the Fast All-sky Model for Solar Applications (FARMS), the Noah land surface model (LSM), the Thompson microphysics, the Mello-Yamada-Nakanishi-Niino (MYNN) boundary layer parameterization, and the Deng scheme for a shallow-convection parameterization. A sensitivity analysis was conducted under various scenarios based on satellite observations and model simulations from the National Solar Radiation Data Base (NSRDB) and WRF-Solar, respectively. Critical forecasting variables that are highly sensitive to the forecasting of global horizontal irradiance (GHI), direct normal irradiance (DNI), cloud mixing ratio, cloud tendency, cloud fraction, and sensible and latent heat fluxes were determined using the relevant WRF-Solar module. This study will be used as a guidance on future research leading to high-quality probabilistic solar forecasting. In this presentation, we discuss the validation of tangent linear approach for WRF-Solar modules and illustrate how the sensitivity results are valuable in the improvement of probabilistic solar prediction.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗

Optimization of the beam extraction systems for the Linac4 H{sup −} ion source

The development of the Linac 4 and its integration into CERN’s acceleration complex is part of the foreseen luminosity upgrade of the Large Hadron Collider (LHC). The goal is to inject a 160 MeV H{sup −} beam into the CERN PS Booster (PSB) in order to increase the beam brightness by a factor of 2 compared to the 50 MeV proton linac, Linac 2, that is currently in operation. The requirements for the ion source are a 45 keV H{sup −} beam of 80 mA intensity, 2 Hz repetition rate and 0.5 ms pulse length within a normalized rms-emittance of 0.25 mm· mrad. The previously installed beam extraction system has been designed for an H{sup −} ion beam intensity of 20 mA produced by an RF-volume source with an electron to H{sup −} ratio of up to 50. For the required intensity upgrades of the Linac4 ion source, a new beam extraction system is being produced and tested; it is optimized for a cesiated surface RF-source with a nominal beam current of 40 mA and an electron to H{sup −} ratio of 4. The simulations, based on the IBSIMU code, are presented. At the Brookhaven National Laboratory (BNL), a peak beam current of more than 100 mA was demonstrated with a magnetron H{sup −} source at an energy of 35 keV and a repetition rate of 2 Hz. A new extraction system is required to operate at an energy of 45 keV; simulation of a two stage extraction system dedicated to the magnetron is presented.

43 PARTICLE ACCELERATORS↗

Controlling and Optimizing Photoinduced Charge Transfer across Ultrathin Silica Separation Membrane with Embedded Molecular Wires for Artificial Photosynthesis

Ultrathin amorphous silica membranes with embedded organic molecular wires (oligo( p -phenylenevinylene), three aryl units) provide chemical separation of incompatible catalytic environments of CO 2 reduction and H 2 O oxidation while maintaining electronic and protonic coupling between them. For an efficient nanoscale artificial photosystem, important performance criteria are high rate and directionality of charge flow. Here, the visible-light-induced charge flow from an anchored Ru bipyridyl light absorber across the silica nanomembrane to Co 3 O 4 water oxidation catalyst is quantitatively evaluated by photocurrent measurements. Charge transfer rates increase linearly with wire density, with 5 nm -2 identified as an optimal target. Accurate measurement of wire and light absorber densities is accomplished by the polarized FT-IRRAS method. Guided by density functional theory (DFT) calculations, four wire derivatives featuring electron-donating (methoxy) and -withdrawing groups (sulfonate, perfluorophenyl) with highest occupied molecular orbital (HOMO) potentials ranging from 1.48 to 0.64 V vs NHE were synthesized and photocurrents evaluated. Charge transfer rates increase sharply with increasing driving force for hole transfer from the excited light absorber to the embedded wire, followed by a decrease as the HOMO potential of the wire moves beyond the Co 3 O 4 valence band level toward more negative values, pointing to an optimal wire HOMO potential around 1.3 V vs NHE. Comparison with photocurrents of samples without nanomembrane indicates that silica layers with optimized wires are able to approach undiminished electron flux at typical solar intensities. Combined with the established high proton conductivity and small-molecule blocking property, the charge transfer measurements demonstrate that oxidation and reduction catalysis can be efficiently integrated on the nanoscale under separation by an ultrathin silica membrane.

photocurrent measurements↗

Distributionally robust facility location problem under decision-dependent stochastic demand

While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect the willingness of customers to use certain types of services, e.g., carsharing, and therefore they also affect realizations of random demand. Moreover, a decision maker may not know the exact distribution of such endogenous demand and how it is affected by location choices. In this paper, we consider a distributionally robust facility location problem, in which we interpret the moments of stochastic demand as functions of facility-location decisions. We reformulate a two-stage decision-dependent distributionally robust optimization model as a monolithic formulation, and then derive exact mixed-integer linear programming reformulation as well as valid inequalities when the means and variances of demand are piecewise linear functions of location solutions. We conduct extensive computational studies, in which we compare our model with a decision-dependent deterministic model, as well as stochastic programming and distributionally robust models without the decision-dependent assumption. Here, the results show superior performance of our approach with remarkable improvement in profit and quality of service under various settings, in addition to computational speed-ups given by formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

97 MATHEMATICS AND COMPUTING↗

Open-Loop Control Co-Design of Semisubmersible Floating Offshore Wind Turbines Using Linear Parameter-Varying Models

Here, this paper discusses a framework to design elements of the plant and control systems for floating offshore wind turbines in an integrated manner using linear parameter-varying models. Multiple linearized models derived from aero-elastic simulation software in different operating regions characterized by the incoming wind speed are combined to construct an approximate low-fidelity model of the system. The combined model is then used to generate open-loop, optimal control trajectories as part of a nested control co-design strategy that explores the system’s power production and stability using the platform pitch tilt as a proxy in the context of crucial plant and control design decisions. The radial distance between the central and outer columns and the diameter of the outer columns of the semisubmersible platform are the plant design variables. The platform stability and power production are studied for different plant design decisions. The effect of plant decisions on subsequent power production and stability response of the floating wind turbine is quantified in terms of the levelized cost of energy. The results show that the inner-loop constraints and the plant design decisions affect the turbine’s power and, subsequently, the cost of the system.

17 WIND ENERGY↗

Dynamic Catalysis Fundamentals: I. Fast calculation of limit cycles in dynamic catalysis

Dynamic catalysis—the forced oscillation of catalytic reaction coordinate potential energy surfaces (PES)—has recently emerged as a promising method for the acceleration of heterogeneously-catalyzed reactions. Theoretical study of enhancement of rates and supra-equilibrium product yield via dynamic catalysis has, to-date, been severely limited by onerous computational demands of forward integration of stiff, coupled ordinary differential equations (ODEs) that are necessary to quantitatively describe periodic cycling between PESs. Here, we establish a new approach that reduces, by ≳108×, the computational cost of finding the time-averaged rate at dynamic steady state (i.e. the limit cycle for linear and nonlinear systems of kinetic equations). Our developments are motivated by and conceived from physical and mathematical insight drawn from examination of a simple, didactic case study for which closed-form solutions of rate enhancement are derived in explicit terms of periods of oscillation and elementary step rate constants. Generalization of such closed-form solutions to more complex catalytic systems is achieved by introducing a periodic boundary condition requiring the dynamic steady state solution to have the same periodicity as the kinetic oscillations and solving the corresponding differential equations by linear algebra or Newton-Raphson-based approaches. The methodology is well-suited to extension to non-linear systems for which we detail the potential for multiple solutions or solutions with different periodicities. For linear and non-linear systems alike, the acute decrement in computational expense enables rapid optimization of oscillation waveforms and, consequently, accelerates understanding of the key catalyst properties that enable maximization of reaction rates, conversions, and selectivities during dynamic catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Compression dynamics of quasi-spherical wire arrays with different linear mass profiles

Results of experimental studies of the implosion of quasi-spherical wire (or metalized fiber) arrays are presented. The goal of the experiments was to achieve synchronous three-dimensional compression of the plasma produced in different regions of a quasi-spherical array into its geometrical center. To search for optimal synchronization conditions, quasi-spherical arrays with different initial profiles of the linear mass were used. The following dependences of the linear mass on the poloidal angle were used: m{sub l}(θ) ∝ sin{sup –1}θ and m{sub l}(θ) ∝ sin{sup –2}θ. The compression dynamics of such arrays was compared with that of quasi-spherical arrays without linear mass profiling, m{sub l}(θ) = const. To verify the experimental data, the spatiotemporal dynamics of plasma compression in quasi-spherical arrays was studied using various diagnostics. The experiments on three-dimensional implosion of quasi-spherical arrays made it possible to study how the frozen-in magnetic field of the discharge current penetrates into the array. By measuring the magnetic field in the plasma of a quasi-spherical array, information is obtained on the processes of plasma production and formation of plasma flows from the wire/fiber regions with and without an additionally deposited mass. It is found that penetration of the magnetic flux depends on the initial linear mass profile m{sub l}(θ) of the quasi-spherical array. From space-resolved spectral measurements and frame imaging of plasma X-ray emission, information is obtained on the dimensions and shape of the X-ray source formed during the implosion of a quasi-spherical array. The intensity of this source is estimated and compared with that of the Z-pinch formed during the implosion of a cylindrical array.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Adiabatic quantum linear regression

Abstract A major challenge in machine learning is the computational expense of training these models. Model training can be viewed as a form of optimization used to fit a machine learning model to a set of data, which can take up significant amount of time on classical computers. Adiabatic quantum computers have been shown to excel at solving optimization problems, and therefore, we believe, present a promising alternative to improve machine learning training times. In this paper, we present an adiabatic quantum computing approach for training a linear regression model. In order to do this, we formulate the regression problem as a quadratic unconstrained binary optimization (QUBO) problem. We analyze our quantum approach theoretically, test it on the D-Wave adiabatic quantum computer and compare its performance to a classical approach that uses the Scikit-learn library in Python. Our analysis shows that the quantum approach attains up to $${2.8 \times }$$ 2.8 × speedup over the classical approach on larger datasets, and performs at par with the classical approach on the regression error metric. The quantum approach used the D-Wave 2000Q adiabatic quantum computer, whereas the classical approach used a desktop workstation with an 8-core Intel i9 processor. As such, the results obtained in this work must be interpreted within the context of the specific hardware and software implementations of these machines.

97 MATHEMATICS AND COMPUTING↗

SU-F-J-173: Online Replanning for Dose Painting Based On Changing ADC Map of Pancreas Cancer

Purpose: The introduction of MR-guided radiation therapy (RT), e.g., MR-Linac, would allow dose painting to adapt spatial RT response revealed from MRI data during the RT delivery. The purpose of this study is to investigate the use of an online replanning method to adapt dose painting from the MRI Apparent Diffusion Coefficient (ADC) map acquired during the delivery of RT for pancreatic cancers. Methods: Original dose painting plans were created based on multi-parametric simulation MRI including T1, T2 and ADC, using a treatment planning system (MONACO, Elekta) equipped with an online replanning algorithm (WSO, warm start optimization). Multiple GTVs, identified based on various ADC levels were prescribed to different doses ranging from 50–70 Gy with simultaneous integrated boost in 28 fractions. The MRI acquired after RT were used to mimic weekly MRI, on which the changing GTVs, pancreatic head and other organs-at-risk (OAR) (duodenum, stomach, small bowel) were delineated. The adaptive plan was generated by applying WSO algorithm starting from the deformed original plan based on the weekly MRI using a deformable image registration (DIR) software (ADMIRE, Elekta). The online replanning method takes <10 min. including DIR, target delineation, WSO execution and final dose calculation. Standard IGRT repositioning and full-blown reoptimization plans were also generated to compare with the adaptive plans. Results: The online replanning method significantly improved the multiple target coverages and OAR sparing for pancreatic cancers. For example, for a case with two GTVs with prescriptions of 60 and 70 Gy in pancreatic head, V100-GTV70 (the volume covered by 100% of prescription dose for GTV with 70 Gy)/V100-GTV60/V100-CTV50/V45-duodenum were (95.1/22.2/69.5/85.7), (95.0/97.0/98.6/34.3), and (95.0/98.1/100.0/38.7) for the IGRT, adaptive and reoptimization plans, respectively. Conclusion: The introduced online adaptive replanning method can effectively account for interfractional changes including tumor spatial response during MR-guided RT delivery, allowing precise delivery of dose painting. This study was partially supported by Elekta Inc.

60 APPLIED LIFE SCIENCES↗

SU-E-T-53: Benchmarking a Monte Carlo Model for Patient Plane Leakage Calculations of Low Energy 6MV Unique Linacs

Purpose: To validate the physics parameters of a Monte Carlo model for patient plane leakage calculations on the 6MV Unique linac by comparing the simulations against IEC patient plane leakage measurements. The benchmarked model can further be used for shielding design optimization, to predict leakage in the proximity of intended treatment fields, reduce the system weight and cost, and improve components reliability. Methods: The treatment head geometry of the Unique linac was simulated in Geant4 (v9.4.p02 with “Opt3” standard electromagnetic physics list) based on CAD drawings of all collimation and shielding components projected from the target to the area within 2m from isocenter. A 4×4m2 scorer was inserted 1m from the target in the patient plane and multiple phase space files were recorded by performing a 40-node computing cluster simulation on the EC2 cloud. The photon energy fluence was calculated relative to the value at isocenter for a 10×10cm2 field using 10×10mm2 bins. Tungsten blocks were parked accordingly to represent MLC120. The secondary particle contamination to patient plane was eliminated by “killing” those particles prior to the primary collimator entrance using a “kill-plane”, which represented the upper head shielding components not being modeled. Both IEC patient-plane leakage and X/Y-jaws transmission were simulated. Results: The contribution of photons to energy fluence was 0.064% on average, in excellent agreement with the experimental data available at 0.5, 1.0, and 1.5m from isocenter, characterized by an average leakage of 0.045% and a maximum leakage of 0.085%. X- and Y-jaws transmissions of 0.43% and 0.44% were found in good agreement with measurements of 0.48% and 0.43%, respectively. Conclusion: A Geant4 model based on energy fluence calculations for the 6MV Unique linac was created and validated using IEC patient plane leakage measurements. The “kill-plane” has effectively eliminated electron contamination to patient plane in these simulations.

60 APPLIED LIFE SCIENCES↗

Efficiency in nonequilibrium molecular dynamics Monte Carlo simulations

Hybrid algorithms combining nonequilibrium molecular dynamics and Monte Carlo (neMD/MC) offer a powerful avenue for improving the sampling efficiency of computer simulations of complex systems. These neMD/MC algorithms are also increasingly finding use in applications where conventional approaches are impractical, such as constant-pH simulations with explicit solvent. However, selecting an optimal nonequilibrium protocol for maximum efficiency often represents a non-trivial challenge. This work evaluates the efficiency of a broad class of neMD/MC algorithms and protocols within the theoretical framework of linear response theory. The approximations are validated against constant pH-MD simulations and shown to provide accurate predictions of neMD/MC performance. An assessment of a large set of protocols confirms (both theoretically and empirically) that a linear work protocol gives the best neMD/MC performance. Lastly, a well-defined criterion for optimizing the time parameters of the protocol is proposed and demonstrated with an adaptive algorithm that improves the performance on-the-fly with minimal cost.

97 MATHEMATICS AND COMPUTING↗

Network-Level Optimization for Unbalanced Power Distribution System: Approximation and Relaxation

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. Finally, it is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLPD-OPF model for the same distribution system.

24 POWER TRANSMISSION AND DISTRIBUTION↗