A dynamic programming approach to optimal stochastic orbital transfer strategy
Dynamic programming applications to optimal stochastic orbital transfer strategy, describing computer program
Nishimura, T.↗
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Scalable Energy System Expansion Under Uncertainty Using Multi-Stage Stochastic Optimization
The intermittent nature of power from renewable energy sources poses new challenges for electrical grids. This is due to the variable and uncertain nature of the power output from these resources. These features of renewable generation are becoming more relevant to energy system planning as grids reach higher penetration levels of renewable energy. In this presentation we present approaches for energy system planning based on scalable computational approaches which enable the explicit consideration of operational uncertainties in the planning process. Using multi-stage stochastic programming and the progressive hedging algorithm, we compute energy system expansion decisions on modified versions of the RTS-GMLC test system augmented with large amounts of renewable generation.
MATHEMATICS AND COMPUTING↗
Scalable Energy System Expansion Under Uncertainty Using Multi-Stage Stochastic Optimization
The intermittent nature of renewable energy sources poses challenges for electrical grids. This is due to the variable and uncertain nature of the power output from these resources. These features of renewable generation are more relevant to energy system planning as grids reach higher penetration levels of renewable energy. We present approaches for energy system planning based on scalable computational approaches which enable explicit consideration of operational uncertainties in the planning process. Using multi-stage stochastic programming and the progressive hedging algorithm, we compute energy system expansion decisions on modified versions of the RTS-GMLC test system.
electrical↗
Benders Decomposition Using Graph Modeling and Multi-Parametric Programming
Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A control-inspired approach for energy transition planning under uncertainty
As the global carbon footprint continues to grow, many countries are implementing carbon emission reduction policies which have incentivized the expansion of low-carbon and renewable technologies. However, the speed and scale of deployment falls short of that needed to meet climate goals. Energy system models serve as key tools for guiding investment decisions and helping policymakers evaluate the effects of various policies on the development of an energy system. This study focuses on the energy system of the United States and builds upon prior work by incorporating more geographic granularity to account for the trade of commodities and addresses transmission congestion through electricity price adjustments. Furthermore, real-world characteristics, such as delays in constructing new liquid fuel production and electricity generation facilities, are integrated using a sequential decision-making approach that better reflects how decisions can be updated as uncertainties unfold. Results demonstrate that stochastic programming combined with sequential decision-making produces energy transition pathways that are robust to multiple uncertain futures. Additionally, considering real-world characteristics significantly impacts the deployment of renewable technologies and the ability to meet carbon emission reduction goals while also reliably meeting demand. These findings highlight the importance of accounting for uncertainty and real-world characteristics to avoid overly optimistic projections in energy system planning.
energy systems↗
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↗
Multi-Fidelity Stochastic Economic Dispatch for Operating Low Carbon Power Grids
Grid operators can address the inherently stochastic nature of renewables by solving a two-stage stochastic programming model that minimizes the cost of dispatch decisions while accounting for the complex grid dynamics. It is common to use a sample average approximation to estimate the expectation of the second stage costs in this model. However, the large sample count needed for numerical accuracy makes effective modeling large-scale electric grids computationally intractable. We introduce a control variate multi-fidelity estimator for the second-stage recourse that enables high quality dispatch decisions in real-time with a reduced computational burden. We obtain a hierarchy of model fidelities by linearizing the AC power flow system representation to DC power flow, and by relaxing transmission and voltage network constraints. We evaluate the performance of our proposed method on a synthetic grid with 73 buses against a deterministic baseline with persistence forecast and a high-fidelity reference. Our analysis shows a computational speed-up of 7.62x with a minimal loss in accuracy. The multi-fidelity method is well suited to fidelity combinations that use a simplified network topology in their lower fidelity model and is an attractive option for applications where accurate grid modeling needed on a limited computational budget.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Pyomo.DOE: An open-source package for model-based design of experiments in Python
Predictive mathematical models are a cornerstone of science and engineering. Yet selecting, calibrating, and validating said science-based models often remains an art in practice. Model-based design of experiments (MBDoE) provides a systematic framework to maximize information gain from experiments while minimizing time and resource costs. But MBDoE remains limited to niche application areas, in part because practitioners must integrate expertise in statistics, computational optimization, and modeling. To help reduce this barrier, we introduce Pyomo.DOE, an open-source package for MBDoE. Pyomo.DOE uses a nonlinear sensitivity analysis code k_aug to quickly approximate the Fisher information matrix and leverages a new stochastic programming abstraction. We demonstrate Pyomo.DOE with the first application of MBDoE to fixed-bed breakthrough experiments, which highlights the power of Pyomo.DOE to quantify the value of experimental modifications a priori for large-scale partial differential-algebraic equation (PDAE) models. Here we also provide a mathematical primer on MBDoE targeted at general chemical engineers.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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.↗
A game-theoretic approach to nuclear fuel cycle transition analysis under uncertainty
We present a novel methodology for optimizing nuclear fuel cycle transitions that incorporates a game-theoretic approach and captures interactions among multiple decision makers. The methodology is demonstrated using a two-person sequential game with uncertainty, where the two players represent a policy maker and an electric utility company, though the method generalizes to any number and type of individual decision making entities. Coupled with a sophisticated nuclear fuel cycle simulator, rich transition scenarios may be analyzed to identify robust transition strategies. These strategies explicitly treat uncertainties using a stochastic programming approach, devising optimal near-term hedging strategies that simultaneously consider all possible states of the world, maintaining flexibility to allow for intelligent recourse decisions once uncertainties are resolved. In the demonstration game, reactor technology and fuel cycle scheme adopted by the electric utility are shown to depend on both the policy maker’s decisions and the distributions over uncertain technological and economic outcomes.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Enhancing power grid resilience to winter storms via generator winterization with equity considerations
Here we develop two-stage stochastic programming models for generator winterization that enhance power grid resilience while incorporating social equity. The first stage in our models captures the investment decisions for generator winterization, and the second stage captures the operation of a degraded power grid, with the objective of minimizing load shed and social inequity. To incorporate equity into our models, we propose a concept called adverse effect probability that captures the disproportionate effects of power outages on communities with varying vulnerability levels. Grid operations are modeled using DC power flow, and equity is captured through mean or maximum adverse effects experienced by communities. We apply our models to a synthetic Texas power grid, using winter storm scenarios created from the generator outage data from the 2021 Texas winter storm. Our extensive numerical experiments show that more equitable outcomes, in the sense of reducing adverse effects experienced by vulnerable communities during power outages, are achievable with no impact on total load shed through investing in winterization of generators in different locations and capacities.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Coffee supply chain planning under climate change
The growing demand but uncertain supply makes the sustainability of the coffee industry a shared concern for all participants along the coffee supply chain. This study proposed a decision-making model that comprises the cultivation management, including shade management and annual agriculture management, and the supply chain logistics. A two-stage stochastic program is presented and used within a rolling horizon scheme that periodically updates input data information to deal with uncertainty associated with future climate scenarios. The program minimizes the total expected cost of the entire supply chain of arabica coffee. The study applied the model to the real case study of arabica coffee bean supply to the U.S. market, trying to answer whether arabica coffee supply can meet the U.S. demand from 2022 to 2050 and how to best mitigate any shortage through corporate-farmer partnerships. The results show that the coffee supply will have a 3% shortage in the future; medium-level shade management and more irrigation and fertilization are possible mitigation strategies. These results demonstrate the need for all participants to adopt suitable technologies for the sustainability of global coffee supply chains together.
54 ENVIRONMENTAL SCIENCES↗
Deep Reinforcement Scheduling of Energy Storage Systems for Real-time Voltage Regulation in Unbalanced LV Networks with High PV Penetration
The ever-growing higher penetration of distributed energy resources (DERs) in low-voltage (LV) distribution systems brings both opportunities and challenges to voltage support and regulation. This paper proposes a deep reinforcement learning (DRL)-based scheduling scheme of energy storage systems (ESSs) to mitigate system voltage deviations in unbalanced LV distribution networks. The ESS-based voltage regulation problem is formulated as a multi-stage quadratic stochastic program, with the objective of minimizing the expected total daily voltage regulation cost while satisfying operational constraints. While existing voltage regulation methods are mostly focused on onetime- step control, this paper explores a day-horizon systemwide voltage regulation problem. In other words, the size of action and state spaces are extremely high-dimensional and need to be delicately handled. Furthermore, in order to overcome the difficulty of modeling uncertainties and develop a realtime solution, a learn-to-schedule feedback control framework is proposed by adapting the problem to a model-free DRL setting. The proposed algorithm is tested on a customized 6-bus system and a modified IEEE 34-bus system. Simulation results validate the effectiveness and near-optimality of voltage regulation by ESS in comparison with a deterministic quadratic program solution.
Wang, Shengyi↗
A Multi-Stage Stochastic Risk Assessment With Markovian Representation of Renewable Power
Probabilistic forecasts provide a distribution of possible outputs and so can capture the uncertainty and variability of Variable Renewable Energy (VRE). However, taking advantage of uncertainty information has practical challenges that make it difficult to integrate probabilistic forecasting into control room decision-making. This paper proposes a novel use-case for probabilistic forecasts by incorporating them into the hour-ahead operations for situational awareness via a risk-averse multi-stage stochastic program. We employ a Markovian representation of the probabilistic forecasts that enables the formulation of the multi-stage problem and avoids a scenario generation phase. We test the model on a realistically sized system to assess risk and showcase the capability of using probabilistic renewable forecast as input to produce probabilistic output forecasts of future system states. The results show that the model can capture time consistency in the reserves and Area Control Error (ACE) forecast. The solution times are adequate for risk profiling in hour-ahead timescales.
forecasting↗
Sparow-Examples
SAND2026-16701O SPAROW-Examples software provides a repository of stochastic programming examples designed to demonstrate Sandia's SPAROW optimization library. This resource helps users learn to develop complex applications with SPAROW by offering reference implementations that can be used to test and enhance new optimization solvers. The library offers a diverse range of simple and complex exemplars, including those related to power grid applications such as unit commitment and expansion planning. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Hart, William [Sandia National Lab. (SNL-CA), Live↗
A nonsmooth nonconvex optimization algorithm for two-stage optimization problems
An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties such as prox-regularity assumed in many nonsmooth nonconvex optimization algorithms, (2) the objective can not be analytically expressed and (3) the evaluation of function values and subgradients are computationally expensive. To address these challenges, this report first examines the properties that exist in many two-stage problems, specifically upper-C 2 objectives. Then, we show that quadratic penalty method for securityconstrained alternating current optimal power flow (SCACOPF) contingency problems can make the contingency solution functions upper-C 2 . Based on these observations, a simplified bundle algorithm that bears similarity to sequential quadratic programming (SQP) method is proposed. It is more efficient in implementation and computation compared to conventional bundle methods. Global convergence analysis of the algorithm is presented under novel and reasonable assumptions. The proposed algorithm therefore fills the gap of theoretical convergence for smoothed SCACOPF problems. The inconsistency that might arise in our treatment of the constraints are addressed through a penalty algorithm whose convergence analysis is also provided. Finally, theoretical capabilities and numerical performance of the algorithm are demonstrated through numerical examples.
97 MATHEMATICS AND COMPUTING↗
Performant Optimization Strategies for Multifidelity Stochastic Power Grid Models
This talk goes into the algorithmic work done under the Forest project in order to solve expensive power grid models. We explore multiple fidelities of models that balance accuracy and computational expense. We use bundling strategies and progressive hedging in order to parallelize large stochastic programs.
Alfant, Rachael May [Sandia National Laboratories ↗
Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow
In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.
24 POWER TRANSMISSION AND DISTRIBUTION↗