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GRACE Final Technical Report

The GRACE project (Grid that is Risk-Aware for Clean Electricity) was a five-year research initiative funded by the U.S. Department of Energy's Advanced Research Projects Agency- Energy (ARPA-E) under the PERFORM program. Led by Duke University's Nicholas School of the Environment, with contributions from The Ohio State University, North Carolina State University, Dartmouth College, and Pacific Northwest National Laboratory, the project addressed a fundamental challenge in grid management: conventional software plans for a single most-likely outcome and relies on reserves as a buffer, leaving utilities poorly equipped for the growing variability introduced by renewable energy. GRACE demonstrated a better approach: explicitly representing thousands of plausible future scenarios and choosing operating schedules that perform well across all of them.

14 SOLAR ENERGY↗

Quantum Stochastic Programming [SWR-26-040]

The Quantum Stochastic Programming tool contains quantum computing algorithms for two-stage stochastic optimization, with a focus on the Unit Commitment (UC) problem in power systems. The algorithms combine Discrete Quantum Annealing (DQA) with Quantum Amplitude Estimation (QAE) to compute expected-value objective functions over a probability distribution of wind-power scenarios. Based on: arXiv 2402.15029 - "Quantum algorithms for the two-stage stochastic unit commitment problem"

Maack, Jonathan [National Laboratory of the Rockie↗

STOCHASTIC OPTIMAL POWER FLOW FOR REAL-TIME MANAGEMENT OF DISTRIBUTED RENEWABLE GENERATION AND DEMAND RESPONSE (Final Report)

To meet the grand challenge of a sustainable energy future, there has been a surge of interest in renewable energy. Today, the uncertainty associated with renewable resources is handled by using operating reserves. The high penetration of renewable resources, however, introduces difficult-to-control dynamics and challenges for power system operation. Decision support tools are necessary at the bulk system operational level to recognize and efficiently utilize renewable resources and distributed demand response products in concert with traditional grid resources. It is envisaged that responsive load can potentially have very significant cost advantages over either spinning or non-spinning ramping reserve. Critical decisions are made during hour(s)-ahead and real-time power system operation regarding the commitment and dispatch of generators to ensure power delivery is both reliable and economic. These decisions are typically made by a security constrained optimal flow, which determines future generator commitments, dispatches, and ensures adequate reserves are available in the event of a contingency (unexpected outage) or if future system conditions deviate from forecasts. However, security has been always based on a pre-specified subset of contingency constraints whose enforcement does not guarantee security under all possible future possibilities while also giving little or no weight to the likelihood of each contingent event or the severity of its consequences. Existing tools, which are based exclusively on deterministic optimization models, do not yield optimal operational decisions to address these new challenges, in terms of both reliability and cost-effectiveness. This project has focused on developing a stochastic optimal power flow (SOPF) framework, which integrates renewable resource uncertainty, load uncertainty, distributed storage (DS), demand response (DR) products, in a holistic manner to address the uncertainty associated with ever-increasing renewable resources, along with the inclusion of distributed demand response products in future power systems. A proof-of-concept problem was created using the Pennsylvania-Jersey-Maryland (PJM) power system network. Synthetic wind generation was added to the system to simulate 50% wind penetration. A 1-hour test of SOPF operation indicated more than 6% operational cost savings. The project continued by adding the Midwestern Independent System Operator (MISO) as a partner, with focus shifting from SOPF to Stochastic Look-Ahead Unit Commitment (SLAC). Unlike PJM, MISO is faced with significant renewable energy resources within its footprint and is challenged with substantial uncertainty in its operations. The SLAC distinguishes itself from existing tools that operators use. At best, today’s tools solve two to three cases independently, where one or two system parameters, such as forecasted load level (e.g., a low, base, and high forecast), are varied and the resulting scenarios are analyzed independently. The stochastic-based optimization of SLAC leverages statistical information from an ensemble of potential operational scenarios and their respective likelihood. The SLAC output can be translated into valuable information to the operator such as suggested commitments, optimal scheduling and dispatch of resources, reserve requirements at both locational and zonal resolutions, ramping availability and requirements, availability of demand response including operational guidance concerning the near-term and real-time coordination between distributed energy resources, and utilization of distributed storage resources. The developed SOPF/SLAC tool, a stand-alone tool compatible with existing EMSs, will provide system operators with unprecedented visibility, flexibility and predictability to these resources and operational guidance concerning the real-time coordination between DERs and DR/DS products. The game changing and practical impact of this disruptive technology will be dramatic and will usher in a new era in the electric power industry, wherein green energy concepts are fully embraced, and electric power costs are lowered throughout the nation.

42 ENGINEERING↗

Stochastic Look Ahead Commitment: A Computational Perspective

This presentation gives an overview of a stochastic look ahead commitment (SLAC) problem for managing transmission grid uncertainty in the near- to medium-term (15 minutes to a few hours). We discuss formulation and solution methods, as well as application to transmission system operations.

27 ARPA - Advanced Research Projects Agency-Energy↗

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty

Practical solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We report computational experiments that demonstrate the ability to solve very large stochastic programming problems - including mixed-integer variants - in minutes of wall clock time, efficiently leveraging significant parallel computing resources. We report results for the largest publicly available instances of stochastic mixed-integer unit commitment problems, solving to provably tight optimality gaps. In addition, we introduce a novel software architecture that facilitates combinations of methods for accelerating convergence that can be combined in plug-and-play manner. Finally, the mpi-sppy package is written in Python, leverages the widely used Pyomo (http://www.pyomo.org) library for modeling mathematical programs, builds on existing MPI implementations to ensure efficiency and scalability, and is available via http://github.com/Pyomo/mpi-sppy.

97 MATHEMATICS AND COMPUTING↗

Modeling transmission line constraints in two-stage robust unit commitment problem

Integration of renewable energy sources and demand response poses new challenges to system operators as they increase the uncertainty of the power supply and demand. Recently, robust optimization techniques are applied to the unit commitment problem with uncertainty as an alternative to the stochastic programming approaches. However, it remains challenging to solve the robust unit commitment model with full transmission line constraints. In this paper, we propose novel acceleration techniques for solving two-stage robust unit commitment problem with consideration of full transmission line constraints. We use 1) the cutting-plane algorithm for the master problem, which dynamically includes critical transmission line constraints, and 2) column-generation methods, including the branch-and-price-and-cut algorithm and heuristic approaches, for the subproblems, which add only necessary transmission line dual variables on the fly. Furthermore, computational results for the modified IEEE 118-bus system show that the combination of the cutting-plane algorithm and the heuristic column-generation approach greatly reduces the total solution time of the two-stage robust unit commitment problem.

Heuristic algorithms↗

Assessment of wind power scenario creation methods for stochastic power systems operations

Probabilistic scenarios of renewable energy production, such as wind, have been gaining popularity for use in stochastic variants of power systems operations scheduling problems, allowing for optimal decision-making under uncertainty. The quality of the scenarios has a direct impact on the value of the resulting decisions, but until now, methods for creating scenarios have not been compared under realistic operational conditions. Here, we compare the quality of scenario sets created using three different methods, based on a simulated re-enactment of stochastic day-ahead unit commitment and subsequent dispatch for a realistic test system. We create scenarios using a dataset of forecasted and actual wind power values, scaled to evaluate the effects of increasing wind penetration levels. We show that the choice of scenario set can significantly impact system operating cost, renewable energy use, and the ability of the system to meet demand. This result has implications for the ability of system operators to efficiently integrate renewable production into their day-ahead planning, highlighting the need for the use of performance-based assessments for scenario evaluation.

17 WIND ENERGY↗

mpi-sppy: Optimization Under Uncertainty for Pyomo

We introduce a new Pyomo extension for optimization under uncertainty, mpi-sppy. This extension allows for the mixing of, and sharing of information between, various algorithmic approaches for optimization under uncertainty. We will discuss the underlying architecture and assess the performance and scalability of mpi-sppy on various systems, including HPC clusters.

27 ARPA - Advanced Research Projects Agency-Energy↗

Stochastic robust mathematical programming model for power system optimization

We present a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with different uncertainty sets. In addition, a case study of unit commitment shows the effectiveness of the proposed model and algorithms.

97 MATHEMATICS AND COMPUTING↗

Data-Driven Unit Commitment Refinement - a Scalable Approach for Complex Modern Power Grids

Integration of renewable generation, which is often intermittent and decentralized, substantially increases the stochasticity and complexity of power grid operations. Future power systems planning will require significant computational capability to evaluate balance between demand and supply under varying conditions, both temporally and spatially. The standard approach for generation unit commitment is to use mixed-integer linear programming to find the optimal generation schedule considering ramping and generator constraints. In the future grid this poses computational scalability challenges because generation and demand are not known with certainty due to stochasticity in weather and complexity of the grid. To address this challenge, we present a data-driven unit commitment approach that can efficiently include stochastic weather impacts and contingency considerations to improve unit commitment. Our approach uses graph-based data analytics techniques on solutions to the security constrained (and possibly stochastic) economic dispatch problem to identify potential improvements to a given unit commitment. Recent breakthroughs in fully-parallel stochastic economic dispatch software allow this approach to be scalably deployed. Simulations on synthetic South Carolina and Texas grids show this method can improve grid reliability with security constraints over a set of contingencies, while also meaningfully lowering total generation cost.

Holt, Timothy↗

Constructing probabilistic scenarios for wide-area solar power generation

Optimizing thermal generation commitments and dispatch in the presence of high penetrations of renewable resources such as solar energy requires a characterization of their stochastic properties. In this study, we describe novel methods designed to create day-ahead, wide-area probabilistic solar power scenarios based only on historical forecasts and associated observations of solar power production. Each scenario represents a possible trajectory for solar power in next-day operations with an associated probability computed by algorithms that use historical forecast errors. Scenarios are created by segmentation of historic data, fitting non-parametric error distributions using epi-splines, and then computing specific quantiles from these distributions. Additionally, we address the challenge of establishing an upper bound on solar power output. Our specific application driver is for use in stochastic variants of core power systems operations optimization problems, e.g., unit commitment and economic dispatch. These problems require as input a range of possible future realizations of renewables production. However, the utility of such probabilistic scenarios extends to other contexts, e.g., operator and trader situational awareness. Finally, we compare the performance of our approach to a recently proposed method based on quantile regression, and demonstrate that our method performs comparably to this approach in terms of two widely used methods for assessing the quality of probabilistic scenarios: the Energy score and the Variogram score.

14 SOLAR ENERGY↗

Stochastic Methods Applied to Power System Operations with Renewable Energy: A Review

Renewable energy resources have been rapidly integrated into power systems in many parts of the world, contributing to a cleaner and more sustainable supply of electricity. Wind and solar resources also introduce new challenges for system operations and planning in terms of economics and reliability because of their variability and uncertainty. Operational strategies based on stochastic optimization have been developed recently to address these challenges. In general terms, these stochastic strategies either embed uncertainties into the scheduling formulations (e.g., the unit commitment [UC] problem) in probabilistic forms or develop more appropriate operating reserve strategies to take advantage of advanced forecasting techniques. Other approaches to address uncertainty are also proposed, where operational feasibility is ensured within an uncertainty set of forecasting intervals. In this report, a comprehensive review is conducted to present the state of the art through Spring 2015 in the area of stochastic methods applied to power system operations with high penetration of renewable energy. Chapters 1 and 2 give a brief introduction and overview of power system and electricity market operations, as well as the impact of renewable energy and how this impact is typically considered in modeling tools. Chapter 3 reviews relevant literature on operating reserves and specifically probabilistic methods to estimate the need for system reserve requirements. Chapter 4 looks at stochastic programming formulations of the UC and economic dispatch (ED) problems, highlighting benefits reported in the literature as well as recent industry developments. Chapter 5 briefly introduces alternative formulations of UC under uncertainty, such as robust, chance-constrained, and interval programming. Finally, in Chapter 6, we conclude with the main observations from our review and important directions for future work.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Uncertainty Quantification for Capacity Expansion Planning

This report quantifies the uncertainty in output decisions from a Capacity Expansion Planning (CEP) model. The need to understand how uncertainties within CEP models and modeling assumptions affect Quantities of Interest (QoIs) such as expansion and operating costs, as well as expansion decisions remains an ongoing challenge in scientific research and industrial operations. This area of research is particularly important for models which seek to capture how large networks will evolve and operate under increased sources of variable generation, i.e., higher penetration of renewable technologies such as solar and wind generators. Uncertainty quantification (UQ) of CEP models which estimate expansion costs and decisions, and production cost models which estimate operating costs and dispatch decisions, is a key focus of research at NREL. The Regional Energy Deployment System (ReEDS) represents a state-of-the-art CEP model and considers a range of possible grid evolutions in an attempt to identify key drivers, ramifications, and decisions which contribute to better informed investment and policy decisions. However, research to quantify how uncertainties and model assumptions, such as unit commitment (UC), within ReEDS may be affecting its outputs remains challenging due to to size and complexity of the model

24 POWER TRANSMISSION AND DISTRIBUTION↗

Stochastic Models, Indices & Optimization Algorithms for Pricing & Hedging Reliability Risks in Modern Power Grids: Data Plan - Princeton

We collected and cleaned the synthetic grid data produced by NREL for the Texas and New York synthetic grids. We developed a high dimensional joint stochastic model for load at the zone level, and solar and wind power productions at the asset level, capturing the spatial and temporal dependencies between all the variables, and demonstrated how such a model could be fitted to historical data. We designed and implemented a simulation engine which can produce Monte Carlo scenarios for the hourly day-ahead values of load, and solar and wind power productions at the spatial and temporal resolutions of the historical data used to fit the model. Finally we developed an open-source Python package which can, from an input grid model, efficiently use forecasts and large numbers of Monte Carlo scenarios to provide unit commitment and economic dispatch for each of these scenarios. The high dimensional stochastic model and the subsequent Monte Carlo simulation engine were implemented in the package PGscen and the corresponding UC and ED optimization programs in the package Vatic.

14 SOLAR ENERGY↗

Stochastic Continuous-time Flexibility Scheduling and Pricing in Wholesale Electricity Markets

Large-scale integration of intermittent renewable energy sources (RES) is calling for additional flexibility resources as well as more advanced modeling and optimization techniques to account for the increasing uncertainty and variability in power systems operation. As the RES integration gains momentum, the magnitude and frequency of their variations increase, which may trigger ramping scarcity events in real-time power systems operation. This necessitates revisiting the present definition of power systems flexibility and reserve services to reflect their robustness and adequacy towards sub-interval variations of the load and RES, as well as adjusting the operation models to accommodate the new reserve services. This project took a fundamental approach and aimed at developing continuous-time scheduling and pricing model that accurately models the continuous-time variations of load and RES and efficiently deploys the ramping capability of flexible resources to compensate the sources of variability and uncertainty in the market. In this regard, this project pursued the following goals: Developing stochastic multi-fidelity continuous-time optimization models for scheduling of energy storage (ES) systems and flexible loads in wholesale energy markets; Developing the theory and practices of continuous-time locational marginal pricing for valuating energy storage systems and flexible loads in wholesale energy markets; Developing function space solution approach to convert the proposed stochastic multi-fidelity continuous-time optimization models into tractable mixed-integer linear optimization models; and Defining flexibility reserve as a new type of reserve in markets that would enable ultimate participation of energy storage devices in provision of services to compensate the variability and uncertainty of RES in electricity markets. This project successfully completed all five major tasks defined in the SOPO, and produced 8 high-impact journal papers, 6 conference papers, 3 published U.S. patents, and one web-based software for continuous-time operation optimization of power systems. The application of the proposed flexibility reserve and the stochastic multi-fidelity continuous-time operation scheduling models would modify the forward commitment and schedule of generating units, ES devices and flexible loads, and would line up the resources in such a way that the composition of available resources is better prepared to respond to the sub-hourly variations of the load and renewable resources in real-time operation. Therefore, this project paves the way to sustainable, reliable, and economic integration of renewable energy resources in power system, supporting the progress towards reaching the national targets on energy independence. Even if the proposed models offers a radically different point of view as compared to existing models, it does not alter fundamentally the architecture of power systems operations, nor the complexity of the scheduling problem, so the integration of this project in power systems is extremely practical.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Power System Resilience Enhancement in Typhoons Using a Three-Stage Day-Ahead Unit Commitment

In this work, we propose a three-stage resilient unit commitment model which considers uncertain typhoon paths and line outages to improve the power system resilience against typhoon events. The proposed solution coordinates resources in response to the worst-case scenario for each possible typhoon path. The optimal decision is based on the characterization of the power system schedule into three stages of preventive control, emergency control, and restoration. Preventive control is performed before the typhoon occurs by quickly adjusting the three-stage resilient unit commitment schedule; emergency control is conducted during the typhoon by shedding local loads to meet the power balance, while other control strategies are assumed to be unavailable due to possible interruptions in the communication system; restoration is realized after the typhoon, when resources are optimally dispatched to repair the outages of critical devices and recover the normal operation state of the power system quickly. Considering the typhoon path uncertainty, we have introduced a stochastic model for possible typhoon paths where all possible affected lines along each typhoon path are assumed to be on outage during the typhoon. Accordingly, we explore the strategy for co-optimizing the three stages in unit commitment. The proposed model is tested on the IEEE 118-bus system and the real-world provincial system to verify its effectiveness.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Integration of progressive hedging and dual decomposition in stochastic integer programs

We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. As a result, we report computational results on server location and unit commitment instances.

97 MATHEMATICS AND COMPUTING↗

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↗