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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Optimization models for integrated biorefinery operations

Variations of physical and chemical characteristics of biomass lead to an uneven flow of biomass in a biorefinery, which reduces equipment utilization and increases operational costs. Uncertainty of biomass supply and high processing costs increase the risk of investing in the US’s cellulosic biofuel industry. We propose a stochastic programming model to streamline processes within a biorefinery. A chance constraint models system’s reliability requirement that the reactor is operating at a high utilization rate given uncertain biomass moisture content, particle size distribution, and equipment failure. The model identifies operating conditions of equipment and inventory level to maintain a continuous flow of biomass to the reactor. Furthermore, the sample average approximation method approximates the chance constraint and a bisection search-based heuristic solves this approximation. A case study is developed using real-life data collected at Idaho National Laboratory’s biomass processing facility. An extensive computational analysis indicates that sequencing of biomass bales based on moisture level, increasing storage capacity, and managing particle size distribution, increases utilization of the reactor and reduces operational costs.

09 BIOMASS FUELS↗
DOE OSTI2024

An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

Applied Probability↗
DOE OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗
DOE OSTI2022

Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not necessarily guaranteed. Here this article analyses the convergence conditions for this fixed point approach, and reports numerical experiments including for large IEEE networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Data-Driven Chance-Constrained Design of Voltage Droop Control for Distribution Networks: Preprint

This paper addresses the design of local control methods for voltage control in distribution networks with high level of distributed energy resources (DERs). The designed control methods adapt the active and reactive power output of distributed energy resources proportional to the deviation of the local measured voltage magnitudes from a reference voltage, which is referred to as droop control. Thus, the design focuses on determining the droop characteristics which satisfy network-wide voltage magnitude constraints. The uncertainty and variability of DERs renders the design of optimal droop controls very challenging. Hence, this paper proposes chance constraints to limit the risk from intermittent DERs, by designing droop control coefficients that guarantee the satisfaction of network operational constraints with a specific probability. In addition, the proposed approach relies entirely on historical data rather than assuming knowledge of the probability distributions that characterize the uncertainty of DERs. The efficacy of the proposed method is demonstrated on a 37-bus distribution feeder.

chance-constrained optimization↗
DOE OSTI2025

Safe Reinforcement Learning-Based Transient Stability Control for Islanded Microgrids With Topology Reconfiguration

This paper proposes a safe reinforcement learning (RL)-based transient stability emergency control (TSEC) method for islanded microgrids. RL requires extensive interaction with the environment to learn control strategies, hence, a data-driven approach is used as a substitute for time-consuming time-domain simulation calculations. Deep sigma point processes (DSPP), which is a Gaussian process model, is utilized to predict the normal distribution of transient stability of microgrids and to construct a transient stability chance constraint. Reward-constrained policy optimization (RCPO) can simultaneously achieve objective prediction, policy learning, and constraint cost coefficient update across multiple timescales. RCPO interacts with the DSPP-based microgrid environment through a multi-process parallel manner, greatly increasing the training speed. Case studies on a real islanded microgrid demonstrate that the proposed method can efficiently and quickly obtain the optimal emergency control strategy while adhering to all hard constraints.

14 SOLAR ENERGY↗
DOE OSTI2022

DNN-based policies for stochastic AC OPF

We report a prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty. Most SOPF formulations consider simple control policies such as affine policies that are mathematically simple and resemble many policies used in current practice. Motivated by the efficacy of machine learning (ML) algorithms and the potential benefits of general control policies for cost and constraint enforcement, we put forth a deep neural network (DNN)-based policy that predicts the generator dispatch decisions in real time in response to uncertainty. The weights of the DNN are learnt using stochastic primal–dual updates that solve the SOPF without the need for prior generation of training labels and can explicitly account for the feasibility constraints in the SOPF. The advantages of the DNN policy over simpler policies and their efficacy in enforcing safety limits and producing near optimal solutions are demonstrated in the context of a chance constrained formulation on a number of test cases.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Drgona, Jan↗
DOE OSTI2024

A safe reinforcement learning algorithm for supervisory control of power plants

Traditional control theory-based methods require tailored engineering for each system and constant fine-tuning. In power plant control, one often needs to obtain a precise representation of the system dynamics and carefully design the control scheme accordingly. Model-free Reinforcement learning (RL) has emerged as a promising solution for control tasks due to its ability to learn from trial-and-error interactions with the environment. It eliminates the need for explicitly modeling the environment’s dynamics, which is potentially inaccurate. However, the direct imposition of state constraints in power plant control raises challenges for standard RL methods. To address this, we propose a chance-constrained RL algorithm based on Proximal Policy Optimization for supervisory control. Our method employs Lagrangian relaxation to convert the constrained optimization problem into an unconstrained objective, where trainable Lagrange multipliers enforce the state constraints. In conclusion, our approach achieves the smallest distance of violation and violation rate in a load-follow maneuver for an advanced Nuclear Power Plant design.

constrained optimization↗
DOE OSTI2021

Efficient Automated Driving Strategies Leveraging Anticipation and Optimal Control

Automated vehicles and advanced driver assistance systems bring computation, sensing, and communication technologies that exceed human abilities in some ways. For example, automated vehicles may sense a panorama all at once, do not suffer from human impairments and distractions, and could wirelessly communicate precise data with neighboring vehicles. Prototype and commercial deployments have demonstrated the capability to relieve human operators of some driving tasks up to and including fully autonomous taxi rides in some areas. The ultimate impact of this technology’s large-scale market penetration on energy efficiency remains unclear, with potential negative factors like road use by empty vehicles competing with positive ones like automatic eco-driving. Fundamentally enabled by historic and look-ahead data, this dissertation addresses the use of automated driving and driver assistance to optimize vehicle motion for energy efficiency. Facets of this problem include car following, co-optimized acceleration and lane change planning, and collaborative multi-agent guidance. Optimal control, especially model predictive control, is used extensively to improve energy efficiency while maintaining safe and timely driving via constraints. Techniques including chance constraints and mixed integer programming help overcome uncertainty and non-convexity challenges. Extensions of these techniques to tractor trailers on sloping roads are provided by making use of linear parameter-varying models. To approach the wheel-input energy eco-driving problem over generally shaped sloping roads with the computational potential for closed-loop implementation, a linear programming formulation is constructed. Distributed and collaborative techniques that enable connected and automated vehicles to accommodate their neighbors in traffic are also explored and compared to centralized control. Using simulations and vehicle-in-the-loop car following experiments, the proposed algorithms are benchmarked against others that do not make use of look-ahead information.

Dollar, Robert Austin↗
DOE OSTI2024

Analytic Neural Network Gaussian Process Enabled Chance-Constrained Voltage Regulation for Active Distribution Systems with PVs, Batteries and EVs

This paper proposes an analytic neural network Gaussian process (NNGP)-based chance-constrained real-time voltage regulation method for active distribution systems with photovoltaics (PVs), batteries, and electric vehicles (EVs). NNGP can utilize historical measurement data to achieve real-time probabilistic node voltage estimation through Bayesian inference. Then, NNGP is fully analytically embedded into the optimal power flow model to perform voltage regulation and adapt to various topological changes. The uncertainties of voltage estimations are easily considered via the chance constraint, and it has been shown that the adoption of this chance constraint can significantly improve the reliability of voltage regulation under various scenarios. The comparison results with other methods, carried out on a real 759-node distribution system located in western Colorado, U.S., show that the proposed method can achieve accurate voltage estimation across different topologies and reliably perform voltage regulation considering PVs, batteries, and EVs.

active distribution systems↗
DOE OSTI2023

Microgrid Tiered Circuits Effects for a Planned Housing Community in Puerto Rico

Puerto Rico faced a double strike from hurricanes Irma and Maria in 2017. The resulting damage required a comprehensive rebuild of electric infrastructure. There are plans and pilot projects to rebuild with microgrids to increase resilience. This paper provides a techno-economic analysis technique and case study of a potential future community in Puerto Rico that combines probabilistic microgrid design analysis with tiered circuits in building energy modeling. Tiered circuits in buildings allow electric load reduction via remote disconnection of non-critical circuits during an emergency. When coupled to a microgrid, tiered circuitry can reduce the chances of a microgrid's storage and generation resources being depleted. The analysis technique is applied to show 1) Approximate cost savings due to a tiered circuit structure and 2) Approximate cost savings gained by simultaneously considering resilience and sustainability constraints in the microgrid optimization. The analysis technique uses a resistive capacitive thermal model with load profiles for four tiers (tier 1-3 and non-critical loads). Three analyses were conducted using: 1) open-source software called Tiered Energy in Buildings and 2) the Microgrid Design Toolkit. For a fossil fuel based microgrid 30% of the total microgrid costs of 1.18 million USD were calculated where the non-tiered case keeps all loads 99.9% available and the tiered case keeps tier 1 at 99.9%, tier 2 at 95%, tier 3 at 80% availability, with no requirement on non-critical loads. The same comparison for a sustainable microgrid showed 8% cost savings on a 5.10 million USD microgrid due to tiered circuits. The results also showed 6-7% cost savings when our analysis technique optimizes sustainability and resilience simultaneously in comparison to doing microgrid resilience analysis and renewables net present value analysis independently. Though highly specific to our case study, similar assessments using our analysis technique can elucidate value of tiered circuits and simultaneous consideration of sustainability and resilience in other locations.

building energy modeling↗
DOE OSTI2024

Optimal celestial bodies for dark matter detection

A wide variety of celestial bodies have been considered as dark matter detectors. Which stands the best chance of delivering the discovery of dark matter? Which is the most powerful dark matter detector? We investigate a range of objects, including the Sun, Earth, Jupiter, Brown Dwarfs, White Dwarfs, Neutron Stars, Stellar populations, and Exoplanets. We quantify how different objects are optimal dark matter detectors in different regimes by deconstructing some of the in-built assumptions in these search sensitivities, including observation potential and particle model assumptions. We find new constraints and future sensitivities across a range of dark matter annihilation final states. We quantify mediator properties leading to detectable celestial-body energy injection or Standard Model fluxes, and show how different objects can be expected to deliver corroborating signals. We discuss different search strategies, their opportunities and limitations, and the interplay of regimes where different celestial objects are optimal dark matter detectors. Deconstructing the assumptions of these searches leads us to point out a new search using the Galactic center stellar population that can provide greater sensitivity to the dark matter-nucleon scattering cross section than the Sun, despite being significantly further away in our Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Secure Control Regions for Distributed Stochastic Systems with Application to Distributed Energy Resource Dispatch: Preprint

With the increasing connectedness and interdependence of systems that are stochastic in nature, the issue of how to manage and coordinate them for safe operation has evidently become more important. In many networked system architectures, the system-wide output has to be delicately managed; often within a prescribed set of bounds. In this paper, a novel control framework is proposed where the bounds on the outputs are translated into independent bounds on the controllable inputs of each subsystem. The main benefit of this framework is that respecting the individual control bounds suffices to guarantee that the system-wide outputs will remain within safe boundaries. Since the systems are assumed to be stochastic, the bounds on the output are introduced as probabilistic chance constraints. The benefits of this framework are demonstrated by applying it to the control of distributed energy resources in a distribution networks where main goal is to keep the voltage magnitudes with their prescribed bounds. The control bounds are evaluated using real data on an IEEE test system.

chance constrained optimization↗
DOE OSTI2022

Secure Control Regions for Distributed Stochastic Systems with Application to Distributed Energy Resource Dispatch

With the increasing connectedness and interdependence of systems that are stochastic in nature, the issue of how to manage and coordinate them for safe operation has evidently become more important. In many networked system architectures, the system-wide output must be delicately managed, often within a prescribed set of bounds. In this paper, a novel control framework is proposed where the bounds on the outputs are translated into independent bounds on the controllable inputs of each subsystem. The main benefit of this framework is that respecting the individual control bounds suffices to guarantee that the system-wide outputs will remain within safe boundaries. Because the systems are assumed to be stochastic, the bounds on the output are introduced as probabilistic chance constraints. The benefits of this framework are demonstrated by applying it to the control of distributed energy resources in a distribution network where the main goal is to keep the voltage magnitudes within their prescribed bounds. The control bounds are evaluated using real data on an IEEE test system.

chance constrained optimization↗
DOE OSTI2023

Renewable electricity capacity planning with uncertainty at multiple scales

Abstract We formulate and compare optimization models of investment in renewable generation using a suite of social planning models that compute optimal generation capacity investments for a hydro-dominated electricity system where inflow uncertainty results in a risk of energy shortage. The models optimize the expected cost of capacity expansion and operation allowing for investments in hydro, geothermal, solar, wind, and thermal plant, as well as battery storage for smoothing load profiles. A novel feature is the integration of uncertain seasonal hydroelectric energy supply and short-term variability in renewable supply in a two-stage stochastic programming framework. The models are applied to data from the New Zealand electricity system and used to estimate the costs of moving to a 100% renewable electricity system by 2035. We also explore the outcomes obtained when applying different forms of CO 2 constraint that limit respectively non-renewable capacity, non-renewable generation, and CO 2 emissions on average, almost surely, or in a chance-constrained setting, and show how our models can be used to investigate the merits of a proposed pumped-hydro scheme in New Zealand’s South Island.

Ferris, Michael C.↗
DOE OSTI2022

High throughput embryonic zebrafish test with automated dechorionation to evaluate nanomaterial toxicity

Engineered nanomaterials pose occupational health and environmental concerns as they possess unique physical and chemical properties that can contribute to toxicity. High throughput toxicity screening methods are needed to address the increasing number of nanomaterials in production. Here we used a zebrafish photomotor response (PMR) test to evaluate a set of fifteen nanomaterials with military relevance. Automated dechorionation of zebrafish embryos was used to enhance nanomaterials bioavailability. Optimal PMR activity in zebrafish embryos was found at 30–31 hours post-fertilization (hpf). Behavioral and toxicological responses were measured at 30 and 120 hpf; behavioral responses were found for thirteen of the fifteen nanomaterials and acute toxicity (LC50) levels for nine of the fifteen nanomaterials below the maximum test concentration of 500 μg/ml. Physico-chemical characterization of the nanomaterials detected endotoxin and bacterial contamination in two of the tested samples, which may have contributed to observed toxicity and reinforces the need for physical and chemical characterization of nanomaterials use in toxicity testing. The zebrafish PMR test, together with automated dechorionation, provides an initial rapid assessment of the behavioral effects and toxicity of engineered nanomaterials that can be followed up by physico-chemical characterization if toxicity is detected, reducing the amount of time and monetary constraints of physico-chemical testing.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗