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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Grid Optimization Competition on Synthetic and Industrial Power Systems

This paper summarizes a grid optimization (GO) competition effort in the United States to find the best solution strategies for up to interconnect-scale power system networks with around 32,000 buses. The optimization problem is a mixedinteger, non-convex non-linear problem, (MINLP) and includes discrete variables such as unit commitment and line switching, control settings (transformer taps and phase shifters with impedance correction tables), and bus shunts. The case study includes six actual industry grids as well as 16 realistic synthetic grids created by three different dataset teams. The winners are selected and ranked based on scoring criteria, which consider the solution quality (such as objective functions) within time limits. Nine winner teams are selected from 26 competitor teams. The results achieved by different teams are described and the performance of different algorithms on synthetic grids and actual industry grids are compared and analyzed.

mixed-integer non-linear programming↗
DOE OSTI2025

Multi-plane moment-of-fluid interface reconstruction in 3D

Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. Here, we present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments. This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess. To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM. Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces. The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values. We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron. Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid. Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.

3D interface reconstruction↗
DOE OSTI2024

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimized finite-build stellarator coils using automatic differentiation

A new stellarator coil design code is introduced that optimizes the position and winding pack orientation of finite-build coils. The new code, called flexible optimized curves in space using automatic differentiation (AD) and finite build (FOCUSADD), performs gradient-based optimization in a high-dimensional, non-convex space. The derivatives with respect to parameters of finite-build coils are easily and efficiently computed using AD. FOCUSADD parametrizes coil positions in free space using a Fourier series and uses a multi-filament approximation to the coil winding pack. The orientation of the winding pack is parametrized with a Fourier series and can be optimized as well. Optimized finite-build coils for a Wendelstein 7-X (W7-X)-like stellarator are found, and compared with filamentary coil results. The final positions of optimized finite-build W7-X-like coils are shifted, on average, by approximately 2.5 mm relative to optimized filamentary coils. These results suggest that finite-build effects should be accounted for in the optimization of stellarators with low coil tolerances.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

An Iterative Approach for Solving the SCOPF Problem Applying LP, SOCP, and NLP Subproblems

We propose to develop efficient algorithms and software for the SCOPF problem. We will employ an iterative approach that will: a) use linear subproblems and other active set filtering techniques to identify the most important contingencies and drastically reduce the SCOPF model size; b) solve SOCP relaxations of the reduced SCOPF to converge to the neighborhood of the global optimal solution and establish a lower bound on the solution, and; c) use a non-convex, nonlinear interior-point solver, Artelys Knitro, to converge quickly to the optimal solution. To identify the most effective approach, we will experiment with several techniques to identify the tradeoffs between contingency subproblem complexity and fast solvability.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Distributed ADMM Using Private Blockchain for Power Flow Optimization in Distribution Network With Coupled and Mixed-Integer Constraints

The optimization problem for scheduling distributed energy resources (DERs) and battery energy storage systems (BESS) integrated with the power grid is important to minimize energy consumption from conventional sources in response to demand. Conventionally this optimization problem is solved in a centralized manner, limiting the size of the problem that can be solved and creating a high communication overhead because all the data is transferred to the central controller. These limitations are addressed by the proposed distributed consensus-based alternating direction method of multiplier (DC-ADMM) optimization algorithm, which decomposes the optimization problem into subproblems with private cost function and constraints. The distribution feeder is partitioned into low coupling subnetworks/regions, which solves the private subproblem locally and exchanges information with the neighboring regions to reach consensus. The relaxation strategy is employed for mixed-integer and coupled constraints introduced in the optimal power flow (OPF) problem by stationary and transportable BESS because DC-ADMM convergence is only guaranteed for strict convex problems. The information exchange and synchronization between subnetworks/regions are vital for distributed optimization. In this work, both of these aspects are addressed by the blockchain. The smart contract deployed on the blockchain network acts as a mediator for secure data exchange and synchronization in distributed computation. The blockchain-based distributed optimization problem’s effectiveness is tested for a 0.5-MW laboratory microgrid for one hour ahead and day-ahead for the IEEE 123-bus and EPRI J1 test feeders, and results are compared with a centralized solution.

25 ENERGY STORAGE↗
DOE OSTI2021

Collaborative Decision Approach for Electricity Pricing-demand Response Stackelberg Game

Demand response programs are considered as a valuable resource in smart grids that provide several advantages of load shifting, peak load reduction, mediating intermittency of renewable energy integration, etc. Flexible price-based incentives have been recognized as a critical strategy in motivating and compensating consumers' load adjustment actions for successful implementation of demand response. Game theoretical approaches, especially Stackelberg games are popularly adopted to model the relationship between electricity price and customers' demand response and solved by the classical centralized backward induction (BI) method. However, the BI method generally requires convexity of the follower's model for necessary optimality conditions, and the computational time of any centralized approach increases sharply with larger problem instances. In this paper, the Stackelberg game of electricity pricing-demand response between a distribution system operator (DSO) and load aggregators (LAs) is decomposed based on a collaborative optimization (CO) framework, where each LA is treated as a discipline with its own domain constraints (e.g. building temperature control), while the DSO at the system level tries to reduce the solution discrepancy and guide the searching towards optimality. Several groups of comparison experiments have demonstrated the effectiveness of the proposed collaborative decision approach in solving the demand response game.

Chen, Yang↗
DOE OSTI2025

Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Local convergence analysis of an inexact trust-region method for nonsmooth optimization

In Baraldi, we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. Furthermore, this algorithm has demonstrated excellent performance and scalability with problem size. In this paper, we enrich the convergence analysis for this algorithm, proving strong convergence of the iterates with guaranteed rates. In particular, we demonstrate that the trust-region algorithm recovers superlinear, even quadratic, convergence rates when using a second-order Taylor approximation of the smooth objective function term.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Relaxations of the steady optimal gas flow problem for a non-Ideal gas

Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.

03 NATURAL GAS↗
DOE OSTI2022

A hybrid architecture for volt-var control in active distribution grids

Modern active distribution grids are characterized by the increasing penetration of distributed energy resources (DERs). The proper coordination and scheduling of a large numbers of these small-scale and spatially distributed DERs is necessary, and warrants the use of novel distributed approaches. In this paper, we propose a hybrid volt-var control architecture for the distribution grid, which leverages existing centralized and local approaches to planning, decision making, and control, and augments it with distributed optimization and distributed control for DER management. First, we propose a convex model to describe the power physics of distribution grids of meshed topology and unbalanced structure, based on current injection and McCormick Envelopes. Second, we employ the distributed proximal atomic coordination (PAC) algorithm to coordinate DERs to provide voltage support. We implement volt-var optimization by optimally coordinating DERs including PV smart inverters and demand response. We present results using the IEEE-34 bus network, using real data from a distribution feeder in Hawaii, to model load and PV generation. Different levels of DER penetration and objective functions are simulated. Finally, our results show the need for the coordination of DERs to improve voltage profiles, even in networks with existing voltage control devices. Further, we show the need for flexible reactive power capabilities to achieve desired grid performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

A time-parallel multiple-shooting method for large-scale quantum optimal control

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Relaxed Multibang Regularization for the Combinatorial Integral Approximation

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. In this work, we consider a class of polyhedral functions that arise particularly as convex lower envelopes of multibang regularizers and show that they have beneficial properties with respect to regularization of relaxations of integer optimal control problems. We extend the algorithmic framework of the combinatorial integral approximation such that a subsequence of the computed discrete-valued controls converges to the infimum of the regularized integer control problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Voltage positioning using co-optimization of controllable grid assets in radial networks

With increasing penetration of solar PV, some distribution feeders are experiencing highly variable net-load flows and even reverse flows. To optimize distribution systems under such conditions, the scheduling of mechanical devices, such as OLTCs and capacitor banks, needs to take into account forecasted solar PV and actual grid conditions. However, these legacy switching assets are operated on a daily or hourly timescale, due to the wear and tear associated with mechanical switching, which makes them unsuitable for real-time control. Therefore, there is a natural timescale- separation between these slower mechanical assets and the responsive nature of inverter-based resources. In this paper, we present a network admissible convex formulation for holistically scheduling controllable grid assets to position voltage optimally against solar PV. An optimal hourly schedule is presented that utilizes mechanical resources to position the predicted voltages close to nominal values, while minimizing the use of inverter-based resources (i.e., DERs), making them available for control at a faster time-scale (after the uncertainty reveals itself). A convex, inner approximation of the OPF problem is adapted to a mixed-integer linear program that minimizes voltage deviations from nominal (i.e., maximizes voltage margins). Here, the resulting OPF solution respects all the network constraints and is, hence, robust against modeling simplifications. Simulation based analysis on IEEE distribution feeders validates the approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

distributionally robust optimization↗
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 OSTI2020

Robust Control of Wave Energy Converters Using Unstructured Uncertainty

In the design of ocean wave energy converters, proper control design is essential to the maximization of the power generation performance for the device. However, in realistic applications, this control design must be undertaken in the presence of model uncertainty. This paper considers the use of robust control theory to optimize the nominal performance for a wave energy converter in stochastic waves, subject to the constraint that the controller be stability-robust to unstructured uncertainties. We formulate the problem as a multi-objective optimal control problem, in which the primary objective is the maximization of power generation for the nominal system, and the competing objective is the norm of the uncertainty input/output channel. This optimal control problem is nonconvex, and we therefore propose an iterative algorithm that can be used to arrive at a local optimal solution. This iterative approach employs the concept of Iterative Convex Overbounding, in the context of the classical Method of Centers. Here, the methodology is demonstrated on a model of a single, buoy- type wave energy converter.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

Here, we demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 38 cases from the PGLib-OPF library, showing that the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 6.2% and 17.5% respectively. The NF relaxation is strengthened in 46.2% of test cases, with average and maximum differences in the optimality gaps of 1.3% and 17.3% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality improvement due to these LNC.

24 POWER TRANSMISSION AND DISTRIBUTION↗