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Results for “successive convex approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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14 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

A QCQP Approach for OPF in Multiphase Radial Networks with Wye and Delta Connections: Preprint

This paper examines the AC Optimal Power Flow (OPF) problem for multiphase distribution networks featuring renewable energy resources (RESs). We start by outlining a power flow model for radial multiphase systems that accommodates wye-connected and delta-connected RESs and non-controllable energy assets. We then formalize an AC OPF problem that accounts for both types of connections. Similar to various AC OPF renditions, the resultant problem is a non convex quadratically-constrained quadratic program. However, the so-called Feasible Point Pursuit-Successive Convex Approximation algorithm is leveraged to obtain a feasible and yet locally-optimal solution. The merits of the proposed solution approach are demonstrated using two unbalanced multiphase distribution feeders with both wye and delta connections.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successive convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Beyond Relaxation and Newton–Raphson: Solving AC OPF for Multi-Phase Systems With Renewables

This paper focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with high integration of renewables, where adjustments of the real and reactive output powers from renewable sources of energy are necessary in order to enforce voltage regulation. The AC OPF problem is known to be nonconvex (and, in fact, NP-hard). Convex relaxation techniques have been recently explored to solve the OPF task with reduced computational burden; however, sufficient conditions for tightness of these relaxations are only available for restricted classes of system topologies and problem setups. Identifying feasible power-flow solutions remains hard in more general problem formulations, especially in unbalanced multi-phase systems with renewables. To identify feasible and optimal AC OPF solutions in challenging scenarios where existing methods may fail, this paper leverages the Feasible Point Pursuit - Successive Convex Approximation algorithm - a powerful approach for general nonconvex quadratically constrained quadratic programs. The merits of the approach are illustrated using single- and multiphase distribution networks with renewables, as well as several transmission systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Distributed Optimal Power Flow Using Feasible Point Pursuit

The AC Optimal Power Flow (OPF) is a core optimization task in the domain of power system operations and control. It is known to be nonconvex (and, in fact, NP-hard). In general operational scenarios, identifying feasible (let alone optimal) power-flow solutions remains hard. This paper leverages the recently proposed Feasible Point Pursuit algorithm for solving the OPF problem to devise a fully distributed procedure that can identify AC OPF solutions. The paper considers a multi-area setting and develops an algorithm where all the computations are done locally withing each area, and then the local controllers have to communicate to only their neighbors a small amount of information pertaining to the boundary buses. The merits of the proposed approach are illustrated through an example of a challenging transmission network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2014

Shape transition of unstrained flattest single-walled carbon nanotubes under pressure

Single walled carbon nanotube's (SWCNT's) cross section can be flattened under hydrostatic pressure. One example is the cross section of a single walled carbon nanotube successively deforms from the original round shape to oval shape, then to peanut-like shape. At the transition point of reversible deformation between convex shape and concave shape, the side wall of nanotube is flattest. This flattest tube has many attractive properties. In the present work, an approximate approach is developed to determine the equilibrium shape of this unstrained flattest tube and the curvature distribution of this tube. Our results are in good agreement with recent numerical results, and can be applied to the study of pressure controlled electric properties of single walled carbon nanotubes. The present method can also be used to study other deformed inorganic and organic tube-like structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
DOE OSTI2015

Spatial Ecology of Blanding’s Turtles (Emydoidea blandingii) in Southcentral New Hampshire with Implications to Road Mortality

Understanding the spatial ecology and habitat requirements of rare turtle species and the factors that threaten their populations is important for the success of long-term conservation programs. We present results on an eight-year field study in which we used radiotelemetry to monitor the activity and habitat use of 23 adult (male, n = 7; female, n = 16) Blanding’s turtles in southcentral New Hampshire. We found that females occupied home ranges (as defined by minimum convex polygons) that were approximately two times larger than the home ranges of males. Despite the sex difference in home range size, we found no sex difference in core area size (defined as the 50% kernel density estimate). We found that activity patterns varied by season, with increased activity each month after hibernation, and peak activity coinciding with the late spring-early summer nesting season. We observed sex-based and seasonal differences in wetland use. Males appeared to prefer emergent and scrub-shrub wetlands in each season, whereas females preferred scrub-shrub wetlands in spring and ponds in summer and fall. We identified road mortality risk as a potentially important threat for this population because females crossed roads ten times more frequently than males (based on proportion of observations). The preservation of wetland networks, as well as the implementation of measures to minimize road mortality, are important considerations for the long-term persistence of this population.

Activity↗
DOE OSTI2019

Inner Approximation of Minkowski Sums: A Union-Based Approach and Applications to Aggregated Energy Resources: Preprint

This paper develops and compares algorithms to compute the inner approximation of Minkowski sum of convex polytopes. We consider flexibility from distributed re- sources, such as solar photovoltaic (PV) inverters, demand side resources, etc. A polytopic representation of a single inverter's feasible operating region is proposed first. The aggregate flexibility can be computed using the Minkowski sum. Homothet and Zonotope-based approaches have been explored in literature. We show that as heterogeneity increases, such approaches lead to conservative estimates. Hence, we show how to exploit union-based Minkowski sum computation through successive homothetic decomposition of polytopes. While the union-based approach can lead to dimensionality issues, we show how to limit the complexity by predefining a candidate set. Efficiency, accuracy and trade-offs have been analyzed. Numerical examples have been presented to illustrate the effectiveness of the proposed algorithm.

14 SOLAR ENERGY↗
DOE OSTI2022

Resilient Operating Constraints for Power Distribution Systems under Setpoint Attacks

Integration and operation of distributed generation (DG) and energy storage (ES) in power distribution systems are enabled by communication networks and embedded sensor and control devices that increase the vulnerability of the systems to cyber-threats, broadening the attack surface and making adversary actions more unpredictable. This paper proposes a methodology that uses ellipsoidal approximations to quantify the potential damage caused by successful attacks that affect, directly or indirectly, the desired operation setpoints and may drive the power distribution operation to unsafe states by violating the limits of voltage or line flows. More specifically, a new methodology is introduced to find the optimal non-symmetric operating constraints that can be imposed to each DG and ES in order to guarantee that the power distribution system is resilient to any malicious setpoints. The proposed method takes as inputs the system topology, DG and ES capabilities, and load limits to solve a convex optimization problem formulated using linear matrix inequalities (LMIs) and the power flow equations. The proposed solution is agnostic to the attacker's action or load profile and it does not require any assumption about the location or means of the attack. The numerical results on a test distribution feeder with several DG and ES illustrate how the proposed resilient operating constraints guarantee the security of the power distribution system under setpoint attacks.

Giraldo, Jairo↗
DOE OSTI2020

Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation

This work explores the application of the recently developed Koopman operator approach for model identification and feedback control of a hydraulic fracturing process. Controlling fracture propagation and proppant transport with precision is a challenge due in large part to the difficulty of constructing approximate models that accurately capture the characteristic moving boundary and highly-coupled dynamics exhibited by the process. Koopman operator theory is particularly attractive here as it offers a way to explicitly construct linear representations for even highly nonlinear dynamics. The method is data-driven and relies on lifting the states to an infinite-dimensional space of functions called observables where the dynamics are governed by a linear Koopman operator. Here this work considers two problems: (a) fracture geometry control, and (b) proppant concentration control. In both cases, an approximate linear model of the corresponding dynamics is constructed and used to design a model predictive controller (MPC). The manuscript shows that in the case of highly nonlinear dynamics, as observed in the proppant concentration, use of canonical functions in the observable basis fails. In such cases, a priori system knowledge can be leveraged to choose the required basis. The numerical experiments demonstrate that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired target values maximizing the oil and gas productivity. Additionally, due to its linear structure, the Koopman models allow convex MPC formulations that avoid any issues associated with nonlinear optimization.

42 ENGINEERING↗
DOE OSTI2012

Modified semi-classical methods for nonlinear quantum oscillations problems

We develop a modified semi-classical approach to the approximate solution of Schroedinger's equation for certain nonlinear quantum oscillations problems. In our approach, at lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. With suitable smoothness, convexity and coercivity properties imposed on its potential energy function, we prove, using methods drawn from the calculus of variations together with the (Banach space) implicit function theorem, the existence of a global, smooth 'fundamental solution' to this equation. Higher order quantum corrections thereto, for both ground and excited states, can then be computed through the integration of associated systems of linear transport equations, derived from Schroedinger's equation, and formal expansions for the corresponding energy eigenvalues obtained therefrom by imposing the natural demand for smoothness on the (successively computed) quantum corrections to the eigenfunctions. For the special case of linear oscillators our expansions naturally truncate, reproducing the well-known exact solutions for the energy eigenfunctions and eigenvalues. As an explicit application of our methods to computable nonlinear problems, we calculate a number of terms in the corresponding expansions for the one-dimensional anharmonic oscillators of quartic, sectic, octic, and dectic types and compare the results obtained with those of conventional Rayleigh/Schroedinger perturbation theory. To the orders considered (and, conjecturally, to all orders) our eigenvalue expansions agree with those of Rayleigh/Schroedinger theory whereas our wave functions more accurately capture the more-rapid-than-gaussian decay known to hold for the exact solutions to these problems. For the quartic oscillator in particular our results strongly suggest that both the ground state energy eigenvalue expansion and its associated wave function expansion are Borel summable to yield natural candidates for the actual exact ground state solution and its energy. Our techniques for proving the existence of the crucial 'fundamental solution' to the relevant (inverted-potential-vanishing-energy) Hamilton-Jacobi equation have the important property of admitting interesting infinite dimensional generalizations. In a project paralleling the present one we shall show how this basic construction can be carried out for the Yang-Mills equations in Minkowski spacetime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography

Purpose: This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ{sub 0} pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ{sub 1}-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

The GCT camera for the Cherenkov Telescope Array

The Gamma Cherenkov Telescope (GCT) is one of the designs presented for the Small Sized Telescope (SST) section of the Cherenkov Telescope Array (CTA). The GCT uses dual-mirror optics, resulting in a compact telescope with good image quality and a large field of view with a smaller, more economical, camera than is achievable with conventional single mirror solutions. The photon counting GCT camera is designed to record the flashes of atmospheric Cherenkov light from gamma and cosmic ray initiated cascades, which last only a few tens of nanoseconds. The GCT optics require that the camera detectors follow a convex surface with a radius of curvature of 1 m and a diameter of ~35 cm, which is approximated by tiling the focal plane with 32 modules. The initial camera prototype is equipped with multi-anode photomultipliers, each comprising an 8×8 array of 6×6 mm 2 pixels to provide the required angular scale, adding up to 2048 pixels in total. Detector signals are shaped, amplified and digitised by electronics based on custom ASICs that provide digitisation at 1 GSample/s. The camera is self-triggering, retaining images where the focal plane light distribution matches predefined spatial and temporal criteria. The electronics are housed in the liquid-cooled, sealed camera enclosure. LED flashers at the corners of the focal plane provide a calibration source via reflection from the secondary mirror. The first GCT camera prototype underwent preliminary laboratory tests last year. In November 2015, the camera was installed on a prototype GCT telescope (SST-GATE) in Paris and was further used to successfully record the first Cherenkov light of any CTA prototype, and the first Cherenkov light seen with such a dual-mirror optical system. A second full-camera prototype based on Silicon Photomultipliers is under construction. Up to 35 GCTs are envisaged for CTA.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)

Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗