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At least 37 records · Page 2

MULTI-LEADER: MULTI-source LEarning-Accelerated Design of high-Efficiency multi-stage compRessor (Final Technical Report)

The objective of MULTI-LEADER is to cut design costs by 80% while generating more energy-efficient designs of multi-stage compressors by developing and implementing novel machine learning (ML) techniques, which enable faster and fewer design iterations, improved solver performance, and concurrent multi-disciplinary design. Current industrial practices for the design of multi-stage compressors involve simulation-based design optimization with successive levels of model fidelity, iteratively evaluated between distinct disciplines, one stage at a time to tackle the high dimensional design variations. This project addresses these key design challenges: (1) concurrent optimization of multiple stages under many non-linear constraints; (2) multitude of evaluation of high-fidelity and expensive solvers and their gradients during optimization convergence in high-dimensional design; (3) multi-disciplinary design to maximize aerodynamic performance while guaranteeing structural integrity and additive manufacturability; (4) utilization of multiple fidelity of solvers with disparate parameterization and modeling assumptions. MULTI-LEADER achieved more than 5x speed up in detailed design of more energy-efficient compressors via these machine learning (ML) innovations: (i) rapid design surrogates by multi-source learning from diverse fidelities across multiple disciplines, (ii) physics-constrained data-augmented modeling for improved empiricism, (iii) generative manifold embedding for high dimensional concurrent design without gradient information; (iv) budget-constrained fidelity-adaptive sampling towards fewer design iterations.

33 ADVANCED PROPULSION SYSTEMS↗

A Sequential Quadratic Programming Algorithm for Nonsmooth Problems with Upper- \({\boldsymbol{\mathcal{C}^2}}\) Objective

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objective functions is proposed and analyzed. Upper- \({\boldsymbol{\mathcal{C}^2}}\) is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems e.g., recourse of stochastic programming and projection onto closed sets. The algorithm can be viewed as an extension of sequential quadratic programming (SQP) to nonsmooth problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objectives or a simplified bundle method. It is globally convergent with bounded algorithm parameters that are updated with a trust-region criterion. The algorithm handles general smooth constraints through linearization and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. In conclusion, the capabilities of the algorithm are demonstrated by solving both simple upper- \({\boldsymbol{\mathcal{C}^2}}\) problems and a real-world optimal power flow problem used in current power grid industry practices.

97 MATHEMATICS AND COMPUTING↗

Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends

Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, in this work, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τ d,R for rings of length N R blended with linear chains of length N l to scale as τ d,R ~ N$^2_R$N$^{3.4}_L$.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimal Network Reconfiguration and Scheduling With Hardware-in-the-Loop Validation for Improved Microgrid Resilience

With the increased occurrence of various major extreme weather events, power outages and prompt power system restorations have recently drawn more attention to the resilience and recovery of power systems. From the perspective of a more resilient power delivery at the distribution grid, system restoration using network topology reconfiguration together with optimal scheduling of distributed energy resources are adopted in this paper. The proposed optimization model aims at minimizing the total load shedding cost and other operational costs, in which linearized topological constraints borrowed from graph theory and linearized DistFlow models are respectively used to maintain the radial network topology and power flow balance after system contingencies. To demonstrate the applicability of the proposed strategy, a real-world case study of a networked three-microgrid system in Adjuntas, Puerto Rico, is used with the consideration of different independent/interconnected microgrid scenarios, contingencies, and fairness settings. Furthermore, hardware-in-the-loop testing is conducted for the same three-microgrid network, where the closely matched results with the simulated ones have validated the effectiveness of the proposed restoration strategy, which is now ready to move one step forward towards field deployment. Finally, to test the proposed restoration strategy in a larger networked system, the modified IEEE-33 bus test distribution system is considered, and the results show a more resilient power delivery for critical loads under three and four line outages.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Substation-Level Grid Topology Optimization Using Bus Splitting

Operations of substation circuit breakers are important for maintenance needs and topology reconfiguration in power systems. Bus splitting is one type of topology change where the two bus bars at a substation can become electrically disconnected under certain actions of circuit breakers. Because these events involve detailed substation modeling, they are typically not considered in routine power system operation and control. In this paper, an improved substation-level topology optimization framework is developed by expanding traditional line switching decisions by breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bilinear terms in the resultant optimization problem to linear inequality constraints. Thus, a tractable mixed-integer linear program reformulation is attained that allows for efficient solutions in real-time operations. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the computational performance and economic benefits of the proposed topology optimization approach.

bus split↗

Incorporating physical constraints into Gaussian process surrogate models (LDRD Project Summary)

This report summarizes work done under the Laboratory Directed Research and Development (LDRD) project titled "Incorporating physical constraints into Gaussian process surrogate models?' In this project, we explored a variety of strategies for constraint implementations. We considered bound constraints, monotonicity and related convexity constraints, Gaussian processes which are constrained to satisfy linear operator constraints which represent physical laws expressed as partial differential equations, and intrinsic boundary condition constraints. We wrote three papers and are currently finishing two others. We developed initial software implementations for some approaches. This report summarizes the work done under this LDRD.

97 MATHEMATICS AND COMPUTING↗

Uncertainty-Informed Operation Coordination in a Water-Energy Nexus

The widespread deployment of smart heterogeneous technologies and the growing complexity in our modern society calls for effective coordination of the interdependent lifeline networks. In particular, operation coordination of electric power and water infrastructures is urgently needed as the water system is one of the most energy-intensive networks, an interruption in which may quickly evolve into a dramatic societal concern. This paper develops a novel analytic for uncertainty-aware day-ahead operation optimization of the interconnected power and water systems (PaWS). Joint probabilistic constraint (JPC) programming is employed to capture the uncertainties in wind resources and water demand forecasts. The proposed integrated stochastic model is presented as a non-linear non-convex optimization problem, where the non-linear hydraulic constraints in the water network are linearized using piece-wise linearization technique, and the non-convexity is efficiently tackled with a solution methodology to convert the proposed model with JPCs to a tractable mixed-integer linear programming (MILP) formulation that can be quickly solved to optimality. Here, the suggested framework is applied to a 15-node commercial-scale water network jointly operated with a power transmission system using a modified IEEE 57-bus test system. The numerical results demonstrate the of the proposed stochastic framework, resulting in cost reduction (13% on average when compared to the traditional setting) and energy saving of the integrated model under different realizations of uncertain renewable energy sources (RESs) and water demand scenarios. Additionally, the scalability of the proposed model is tested on a modified IEEE 118-bus test system connected to five water networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Mixed integer linear programming‐based distributed energy management for networked microgrids considering network operational objectives and constraints

Abstract Mixed integer linear programming (MILP)–based distributed energy management for networked microgrids embedded modern distribution systems is proposed. Considering the diverse ownership of microgrids, distributed energy resources (DERs) that interface directly with utilities and responsive loads, an alternating direction method of multipliers–based distributed framework was formulated for the scheduling of networked microgrids embedded modern distribution systems by adjusting nodal price signals iteratively. In addition, to make the formulated optimization problems resolvable through more accessible and popular MILP solvers, different linearisation techniques were employed to transform the nonlinear terms into linear or mixed integer linear formats. The proposed MILP‐based distributed method preserves all participants' autonomy (e.g., microgrids, DERs that interface directly with utilities and responsive loads), while incentivising them to actively participate in the distribution system operation with price signals. The proposed method is validated with results of numerical simulation using a modern distribution system consisting of multiple networked microgrids, DERs that interface directly with utilities, as well as responsive loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Survey of Constrained Gaussian Process: Approaches and Implementation Challenges

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a larger effort in scientific machine learning, many recent works have incorporated physical constraints or other a priori information within Gaussian process regression to supplement limited data and regularize the behavior of the model. We provide an overview and survey of several classes of Gaussian process constraints, including positivity or bound constraints, monotonicity and convexity constraints, differential equation constraints provided by linear PDEs, and boundary condition constraints. We compare the strategies behind each approach as well as the differences in implementation, concluding with a discussion of the computational challenges introduced by constraints.

97 MATHEMATICS AND COMPUTING↗

Power Grid Reliability Estimation via Adaptive Importance Sampling

Electricity production currently generates approximately 25% of greenhouse gas emissions in the USA. Thus, increasing the amount of renewable energy is a key step to carbon neutrality. However, integrating a large amount of fluctuating renewable generation is a significant challenge for power grid operating and planning. Grid reliability, i.e., an ability to meet operational constraints under power fluctuations, is probably the most important of them. In this letter, we propose computationally efficient and accurate methods to estimate the probability of line overflow, i.e., reliability constraints violation, under a known distribution of renewable energy generation. To this end, we investigate an importance sampling approach, a flexible extension of Monte-Carlo methods, which adaptively changes the sampling distribution to generate more samples near the reliability boundary. The approach allows to estimate overload probability in real-time based only on a few dozens of random samples, compared to thousands required by the plain Monte-Carlo. Our study focuses on high voltage direct current power transmission grids with linear reliability constraints on power injections and line currents. Herein, we propose a novel theoretically justified physics-informed adaptive importance sampling algorithm and compare its performance to state-of-the-art methods on multiple IEEE power grid test cases.

power system faults↗

An ℓ 0 ℓ 2 -norm regularized regression model for construction of robust cluster expansions in multicomponent systems

In this work we introduce ℓ 0 ℓ 2 -norm regularization and hierarchy constraints into linear regression for the construction of cluster expansions to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The ℓ 2 -norm regularization is used to suppress intrinsic data noise, while the ℓ 0 -norm is used to penalize the number of nonzero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged set of effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of ℓ 0 ℓ 2 -norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation, convergence speed, and the reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional ℓ 1 -norm regularized cluster expansion models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs

We study solution sensitivity for nonlinear programs (NLPs) whose structures are induced by graphs. These NLPs arise in many applications such as dynamic optimization, stochastic optimization, optimization with partial differential equations, and network optimization. We illustrate that for a given pair of nodes, the sensitivity of the primal-dual solution at one node against a data perturbation at the other node decays exponentially with respect to the distance between these two nodes on the graph. In other words, the solution sensitivity decays as one moves away from the perturbation point. This result, which we call exponential decay of sensitivity, holds under the strong second-order sufficiency condition and the linear independence constraint qualification. We also present conditions under which the decay rate remains uniformly bounded; this allows us to characterize the sensitivity behavior of NLPs defined over subgraphs of infinite graphs. The theoretical developments are illustrated with numerical examples.

97 MATHEMATICS AND COMPUTING↗

MPC4CLR (Model-Predictive-Control-for-Critical-Load-Restoration-in-Power-Distribution-Systems) [SWR-22-24]

Model predictive control (MPC) is a system or process control technique for making decisions under uncertainty via rolling look-ahead optimizations at each control step where only the current step decisions are applied, and the rest are discarded. In this work, we developed an MPC for a critical load restoration (CLR) in power distribution systems to recover system service (electricity delivery) following an extreme event-triggered substation outage. The method considers the problem of controlling distributed energy resources (DERs) of the distribution system with the objective of achieving maximum load pick up while satisfying distribution network flow and voltage constraints. A linearized optimal power flow (OPF) model is employed to represent the physics of the network. The problem formulation is augmented with a ramping (up) reserve product for the DERs to ensure improved and upward monotonic load restoration as time evolves. Simulation analysis and performance tests are performed using a modified IEEE 13-bus test feeder integrated with wind, solar, microturbine, and energy storage battery. The software is developed using various software packages in Julia and Python. The MPC model is implemented using the JuMP optimization language in Julia while the data analytics including renewable generation and load demand forecasts, running the MPC simulation and visualizations is performed in Python.

Eseye, Abinet Tesfaye↗

Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints

Here, we propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate of the active set. The algorithm enforces descent on the objective function to promote global convergence to B-stationary points. We provide a convergence analysis and preliminary numerical results on a range of test problems. We also study the effect of fixing the active constraints in a bound-constrained quadratic program that can be solved on each iteration in order to obtain fast convergence.

97 MATHEMATICS AND COMPUTING↗

Gradient-based constrained optimization using a database of linear reduced-order models

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential Equation (PDE). A key component of this methodology is the construction, during an offline phase, of a database of pointwise, linear, Projection-based Reduced-Order Models (PROM)s associated with a design parameter space and the linear PDE(s). A parameter sampling procedure based on an appropriate saturation assumption is proposed to maximize the efficiency of such a database of PROMs. A real-time method is also presented for interpolating at any queried but unsampled parameter vector in the design parameter space the relevant sensitivities of a PROM. The practical feasibility, computational advantages, and performance of the proposed methodology are demonstrated for several realistic, nonlinear, aerodynamic shape optimization problems governed by linear aeroelastic constraints.

97 MATHEMATICS AND COMPUTING↗

Semidefinite programming algorithm for the quantum mechanical bootstrap

Here, we present a semidefinite programming algorithm to find eigenvalues of Schrödinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the variables (expectation values of operators in an energy eigenstate), plus positivity constraints (unitarity) that need to be satisfied. By fixing the energy we linearize all the constraints and show that the feasibility problem can be presented as an optimization problem for the variables that are not fixed by the constraints and one additional slack variable that measures the failure of positivity. To illustrate the method we are able to obtain high-precision, sharp bounds on eigenenergies for arbitrary confining polynomial potentials in one dimension.

97 MATHEMATICS AND COMPUTING↗

Cosmological Constraints from Combining Photometric Galaxy Surveys and Gravitational Wave Observatories

Spatial variations in survey properties due to selection effects generate substantial systematic errors in large-scale structure measurements in optical galaxy surveys on very large scales. On such scales, the statistical sensitivity of optical surveys is also limited by their finite sky coverage. By contrast, gravitational wave (GW) sources appear to be relatively free of these issues, provided the angular sensitivity of GW experiments can be accurately characterized. We quantify the expected cosmological information gain from combining the forecast LSST 3$\times$2pt analysis (combination of three 2-point correlations of galaxy density and weak lensing shear fields) with the large-scale auto-correlation of GW sources from proposed next-generation GW experiments. We find that in $\Lambda$CDM and $w$CDM models, there is no significant improvement in cosmological constraints from combining GW with LSST 3$\times$2pt over LSST alone, due to the large shot noise for the former; however, this combination does enable a $\sim6\%$ constraint on the linear galaxy bias of GW sources. More interestingly, the optical-GW data combination provides tight constraints on models with primordial non-Gaussianity (PNG), due to the predicted scale-dependent bias in PNG models on large scales. Assuming that the largest angular scales that LSST will probe are comparable to those in Stage III surveys ($\ell_{\rm min}\sim50$), the inclusion of next-generation GW measurements could improve constraints on the PNG parameter $f_{\rm NL}$ by up to a factor of $\simeq6.6$ compared to LSST alone, yielding $\sigma(f_{\rm NL})=8.5$. These results assume the expected capability of a network of Einstein Telescope-like GW observatories, with a detection rate of $10^6$ events/year. We investigate the sensitivity of our results to different assumptions about future GW detectors as well as different LSST analysis choices.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraining primordial non-Gaussianity from DESI quasar targets and Planck CMB lensing

We detect the cross-correlation between 2.7 million DESI quasar targets across 14,700 deg 2 (180 quasars deg -2 ) and Planck 2018 CMB lensing at ~30σ. We use the cross-correlation on very large scales to constrain local primordial non-Gaussianity via the scale dependence of quasar bias. The DESI quasar targets lie at an effective redshift of 1.51 and are separated into four imaging regions of varying depth and image quality. We select quasar targets from Legacy Survey DR9 imaging, apply additional flux and photometric redshift cuts to improve the purity and reduce the fraction of unclassified redshifts, and use early DESI spectroscopy of 194,000 quasar targets to determine their redshift distribution and stellar contamination fraction (2.6%). Due to significant excess large-scale power in the quasar autocorrelation, we apply weights to mitigate contamination from imaging systematics such as depth, extinction, and stellar density. We use realistic contaminated mocks to determine the greatest number of systematic modes that we can fit, before we are biased by overfitting and spuriously remove real power. We find that linear regression with one to seven imaging templates removed per region accurately recovers the input cross-power, f NL and linear bias. As in previous analyses, our fNL constraint depends on the linear primordial non-Gaussianity bias parameter, b Φ = 2(b - p)δ c assuming universality of the halo mass function. We measure f NL = -26 +45 -40 with p = 1.6 (f NL = -18 +29 -27 with p = 1.0), and find that this result is robust under several systematics tests. Future spectroscopic quasar cross-correlations with Planck lensing can tighten the f NL constraints by a factor of 2 if they can remove the excess power on large scales in the quasar auto power spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗