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Results for “Two-stage stochastic programming”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A Stochastic Multi-Commodity Logistic Model for Disaster Preparation in Distribution Systems

In this paper, we propose a stochastic optimization approach for disaster preparation in distribution systems. For an upcoming storm, utilities should have a preparation plan that includes warehousing restoration supplies, securing staging sites (depots), and prepositioning crews and equipment. Pre-storm planning enables faster and more efficient post-disaster deploy ment of crews and equipment resources to damage locations. To assist utilities in making this important preparation, this paper develops a two-stage stochastic mixed integer linear program. The first stage determines the depots, number of crews in each site, and the amount of equipment. The second stage is the recourse action that deals with acquiring new equipment and assigning crews to repair damages in realized scenarios. The objective of the developed model is to minimize the costs of depots, crews, equipment, and penalty costs associated with delays in obtain ing equipment and restoration. We consider the uncertainties of damaged lines, number and type of equipment required, and expected repair times. The model is validated on modified IEEE 123-bus distribution test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Communication-Constrained Expansion Planning for Resilient Distribution Systems

Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances. Therefore it becomes important to study how best to place them on the grid in order to meet a resiliency criteria, while minimizing costs and capturing their dependencies on the associated communication systems that sustain their distributed operations. This paper introduces the Optimal Resilient Design Problem for Distribution and Communication Systems (ORDPDC) to address this need. The ORDPDC is formulated as a two-stage stochastic mixed-integer program that captures the physical laws of distribution systems, the communication connectivity of the smart grid components, and a set of scenarios that specifies which components are affected by potential disasters. The paper proposes an exact branch-and-price algorithm for the ORDPDC that features a strong lower bound and a variety of acceleration schemes to address degeneracy. The ORDPDC model and branch-and-price algorithm were evaluated on a variety of test cases with varying disaster intensities and network topologies. The results demonstrate the significant impact of the network topologies on the expansion plans and costs, as well as the computational benefits of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Stochastic pre-event preparation for enhancing resilience of distribution systems

Extreme weather events are the common causes for power supply interruptions and power outages in electrical distribution systems. Improving the distribution system and enhancing its resilience is becoming crucial due to the increased frequency of extreme weather events. Preparation and allocation of multiple flexible resources, such as mobile resources, fuel resources, and labor resources before extreme weather events can mitigate the effects of extreme weather events and enhance the resilience of power distribution systems. Here, in this paper, a two-stage stochastic mixed-integer linear programming (SMILP) is proposed to optimize the preparation and resource allocation process for upcoming extreme weather events, which leads to faster and more efficient post-event restoration. The objective of the proposed two-stage SMILP is to maximize the served load and minimize the operating cost of flexible resources. The first stage in the optimization problem selects the amounts and locations of different resources. The second stage considers the operational constraints of the distribution system and repair crew scheduling constraints. The proposed stochastic pre-event preparation model is solved by a scenario decomposition method, Progressive Hedging (PH), to ease the computational complexity introduced by a large number of scenarios. Furthermore, to show the impact of solar photovoltaic (PV) generation on system resilience, three types of PV systems are considered during a power outage and the resilience improvements with different PV penetration levels are compared. Numerical results from simulations on a large-scale (more than 10,000 nodes) distribution feeder have been used to validate the effectiveness and scalability of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Optimization under uncertainty of a hybrid waste tire and natural gas feedstock flexible polygeneration system using a decomposition algorithm

Market uncertainties motivate the development of flexible polygeneration systems that are able to adjust operating conditions to favor production of the most profitable product portfolio. However, this operational flexibility comes at the cost of higher capital expenditure. A scenario-based two-stage stochastic nonconvex Mixed-Integer Nonlinear Programming (MINLP) approach lends itself naturally to optimizing these trade-offs. This work studies the optimal design and operation under uncertainty of a hybrid feedstock flexible polygeneration system producing electricity, methanol, dimethyl ether, olefins or liquefied (synthetic) natural gas. A recently developed C++ based software framework (named GOSSIP) is used for modeling the optimization problem as well as its efficient solution using the Nonconvex Generalized Benders Decomposition (NGBD) algorithm. Two different cases are studied: The first uses estimates of the means and variances of the uncertain parameters from historical data, whereas the second assesses the impact of increased uncertain parameter volatility. The value of implementing flexible designs characterized by the value of the stochastic solution (VSS) is in the range of 260–405 M$ for a scale of approximately 893 MW of thermal input. Increased price volatility around the same mean results in higher expected net present value and VSS as operational flexibility allows for asymmetric exploitation of price peaks.

42 ENGINEERING↗
DOE OSTI2020

Scenario Creation and Power-Conditioning Strategies for Operating Power Grids with Two-Stage Stochastic Economic Dispatch

A significant difficulty associated with the use of stochastic programming to solve optimal power flow problems on a 5-minute timescale is the quality of renewable energy scenarios input by the user. This is especially true when considering power systems with high penetrations of renewable energy, e.g. wind power. This paper introduces the use of stochastic programming to solve the DC optimal power flow problem with scenarios drawn directly from high-fidelity data sets. Hence, the proposed method avoids the problem of lost physics by finding high-fidelity analogs that can describe future states of the system. Furthermore, this method can be simply extended to output multi-period scenarios to the stochastic program. We demonstrate the effectiveness of this technique by simulating dispatch operations on a synthetic test system over the course of a week.

94 GMLC - Grid Modernization Laboratory Consortium↗
DOE OSTI2021

Scenario Creation and Power-Conditioning Strategies for Operating Power Grids with Two-Stage Stochastic Economic Dispatch

A significant difficulty associated with the use of stochastic programming to solve optimal power flow problems on a 5-minute timescale is the quality of renewable energy scenarios input by the user. This is especially true when considering power systems with high penetrations of renewable energy, e.g. wind power. This paper introduces the use of stochastic programming to solve the DC optimal power flow problem with scenarios drawn directly from high-fidelity data sets. Hence, the proposed method avoids the problem of lost physics by finding high-fidelity analogs that can describe future states of the system. Furthermore, this method can be simply extended to output multi-period scenarios to the stochastic program. We demonstrate the effectiveness of this technique by simulating dispatch operations on a synthetic test system over the course of a week.

analog forecast↗
DOE OSTI2020

Scenario Creation and Power-Conditioning Strategies for Operating Power Grids with Two-Stage Stochastic Economic Dispatch: Preprint

A significant difficultly associated with the use of stochastic programming to solve optimal power flow problems on a 5-minute timescale is the quality of renewable energy scenarios input by the user. This is especially true when considering power systems with high penetrations of renewable energy, e.g. wind power. This paper introduces the use of stochastic programming to solve the DCOPF problem with scenarios drawn directly from high-fidelity data sets. Hence, the proposed method avoids the problem of lost physics by finding high-fidelity analogs that can describe future states of the system. Furthermore, this method can be simply extended to output multi-period scenarios to the stochastic program. We demonstrate the effectiveness of this technique on simulated dispatch operations of the RTS-GMLC over a week.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Distributionally robust facility location problem under decision-dependent stochastic demand

While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect the willingness of customers to use certain types of services, e.g., carsharing, and therefore they also affect realizations of random demand. Moreover, a decision maker may not know the exact distribution of such endogenous demand and how it is affected by location choices. In this paper, we consider a distributionally robust facility location problem, in which we interpret the moments of stochastic demand as functions of facility-location decisions. We reformulate a two-stage decision-dependent distributionally robust optimization model as a monolithic formulation, and then derive exact mixed-integer linear programming reformulation as well as valid inequalities when the means and variances of demand are piecewise linear functions of location solutions. We conduct extensive computational studies, in which we compare our model with a decision-dependent deterministic model, as well as stochastic programming and distributionally robust models without the decision-dependent assumption. Here, the results show superior performance of our approach with remarkable improvement in profit and quality of service under various settings, in addition to computational speed-ups given by formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Co-optimized trading of hybrid wind power plant with retired EV batteries in energy and reserve markets under uncertainties

To be competitive in the electricity markets, various technologies have been reported to increase profits of wind farm owners. Combining battery storage system, wind farms can be operated as conventional power plants which promotes the integration of wind power into the power grid. However, high expenses on batteries keep investors away. Retired EV batteries, fortunately, still have enough capacity to be reused and could be obtained at a low price. In this work, a two-stage optimization of a wind energy retired EV battery-storage system is proposed. The economic performance of the proposed system is examined concerning its participation in the frequency containment normal operation reserve (FCR-N) market and the spot market simultaneously. To account uncertainties in the wind farm output, various electricity market prices, and up/down regulation status, a scenario-based stochastic programming method is used. The sizing of the equipment is optimized on top of daily operations of the hybrid system which formulates a mixed-integer linear programming (MILP) problem. Scenarios are generated with the Monte Carlo simulation (MCS) and Roulette Wheel Mechanism (RWM), which are further reduced with the simultaneous backward method (SBM) to increase computational efficiency. A 21 MW wind farm is selected as a case study. Here, the optimization results show that by integrating with a retired EV battery-storage system (RESS) and a bi-directional inverter, the wind farm can increase its profits significantly when forwarding bids in both of the aforementioned electricity markets.

17 WIND ENERGY↗
DOE OSTI2020

A Two-Stage Decomposition Approach for AC Optimal Power Flow

The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. Furthermore, this paper proposes a scalable decomposition approach in which the power network is decomposed into a master network and a number of subnetworks, where each network has its own AC-OPF subproblem. This formulates a two-stage optimization problem and requires only a small amount of communication between the master and subnetworks. The key contribution is a smoothing technique that renders the response of a subnetwork differentiable with respect to the input from the master problem, utilizing properties of the barrier problem formulation that naturally arises when subproblems are solved by a primal-dual interior-point algorithm. Consequently, existing efficient nonlinear programming solvers can be used for both the master problem and the subproblems. The advantage of this framework is that speedup can be obtained by processing the subnetworks in parallel, and it has convergence guarantees under reasonable assumptions. The formulation is readily extended to instances with stochastic subnetwork loads. Numerical results show favorable performance and illustrate the scalability of the algorithm which is able to solve instances with more than 11 million buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

A Distributionally Robust Resilience Enhancement Strategy for Distribution Networks Considering Decision-Dependent Contingencies

When performing the resilience enhancement for distribution networks, there are two obstacles to reliably model the uncertain contingencies: 1) decision-dependent uncertainty (DDU) due to various line hardening decisions, and 2) distributional ambiguity due to limited outage information during extreme weather events (EWEs). Here, to address these two challenges, this paper develops scenario-wise decision-dependent ambiguity sets (SWDD-ASs), where the DDU and distributional ambiguity inherent in EWE-induced contingencies are simultaneously captured for each possible EWE scenario. Then, a two-stage tri-level decision-dependent distributionally robust resilient enhancement (DD-DRRE) model is formulated, whose outputs include the optimal line hardening, distributed generation (DG) allocation, and proactive network reconfiguration strategy under the worst-case distributions in SWDD-ASs. Subsequently, the DD-DRRE model is equivalently recast to a mixed-integer linear programming (MILP)-based master problem and multiple scenario-wise subproblems, facilitating the adoption of a customized column-and-constraint generation (C&CG) algorithm. Finally, case studies demonstrate a remarkable improvement in the out-of-sample performance of our model, compared to its prevailing stochastic and robust counterparts. Moreover, the potential values of incorporating the ambiguity and distributional information are quantitatively estimated, providing a useful reference for planners with different budgets and risk-aversion levels.

decision-dependent uncertainty↗
DOE OSTI2023

Incorporation of market signals for the optimal design of post combustion carbon capture systems

Recent studies have shown that fossil generators equipped with post-combustion carbon capture (PCC) systems are needed to reduce the cost of deep decarbonization. Such generators need to be flexible and responsive to grid conditions, particularly in a high variable renewable energy (VRE) environment. In this work, we evaluate the net present value (NPV) of retrofitting an existing natural gas combined cycle (NGCC) unit with a flexible PCC system while incorporating market signals from a high VRE grid. We use our industrial partner’s NGCC configuration as representative of existing NGCC units and Svante’s rapid-temperature swing adsorption (TSA) for PCC. Because of its ability to rapidly startup/shutdown and ramp-up/ramp-down, the chosen capture technology is very attractive for load-following operations. For a given set of market signals, we formulate a two-stage stochastic multi-period optimization problem, under the price-taker assumption, to simultaneously optimize the design of the capture system and operation of the entire plant. Rigorous models for the NGCC unit, PCC system, and compression system are developed using commercial process simulators and validated with either plant or vendor data. For computational tractability, we develop surrogate/reduced-order models for use in the optimization problem. The surrogate model for the NGCC plant is constructed by linearizing the rigorous dynamic model at 75% load, while data-driven nonlinear surrogate models for the capture and compression systems are constructed using simulation data from the rigorous models. The optimization problem, formulated as a mixed integer bilinear program, is implemented in the IDAES® integrated platform and solved to global optimality using Gurobi 9.5. Using this formulation, we determine the profitability of retrofitting an existing NGCC unit with the chosen capture system for multiple regions in the U.S. under two scenarios with different carbon prices. Importantly, the results show that the optimal decision strongly depends on the region and on the carbon price, thereby demonstrating the importance of the inclusion of market signals in the design process.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS2003

Runway Operations Planning: A Two-Stage Heuristic Algorithm

The airport runway is a scarce resource that must be shared by different runway operations (arrivals, departures and runway crossings). Given the possible sequences of runway events, careful Runway Operations Planning (ROP) is required if runway utilization is to be maximized. From the perspective of departures, ROP solutions are aircraft departure schedules developed by optimally allocating runway time for departures given the time required for arrivals and crossings. In addition to the obvious objective of maximizing throughput, other objectives, such as guaranteeing fairness and minimizing environmental impact, can also be incorporated into the ROP solution subject to constraints introduced by Air Traffic Control (ATC) procedures. This paper introduces a two stage heuristic algorithm for solving the Runway Operations Planning (ROP) problem. In the first stage, sequences of departure class slots and runway crossings slots are generated and ranked based on departure runway throughput under stochastic conditions. In the second stage, the departure class slots are populated with specific flights from the pool of available aircraft, by solving an integer program with a Branch & Bound algorithm implementation. Preliminary results from this implementation of the two-stage algorithm on real-world traffic data are presented.

Anagnostakis, Ioannis↗
DOE OSTI2027

Nodal capacity expansion planning with flexible large-scale load siting

We propose explicitly incorporating large-scale load siting into a stochastic nodal power system capacity expansion planning model that concurrently co-optimizes generation, transmission, and storage expansion. The potential operational flexibility of some of these large loads is also taken into account by considering them as consisting of a set of tranches with different reliability requirements, which are modeled as a constraint on expected served energy across operational scenarios. We implement our model as a two-stage stochastic mixed-integer optimization problem with cross-scenario expectation constraints. To overcome the challenge of scalability, we build upon existing work to implement this model on a high performance computing platform and exploit scenario parallelization using an augmented Progressive Hedging Algorithm. The algorithm is implemented using the bounding features of mpisppy, which have shown to provide satisfactory provable optimality gaps despite the absence of theoretical guarantees of convergence. We test our approach and assess the value of this proactive planning framework on total system cost and reliability metrics using realistic testcases geographically assigned to San Diego and South Carolina, with datacenter and direct air capture facilities as large loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1996

Two-stage model of radon-induced malignant lung tumors in rats: effects of cell killing

A two-stage stochastic model of carcinogenesis is used to analyze lung tumor incidence in 3750 rats exposed to varying regimens of radon carried on a constant-concentration uranium ore dust aerosol. New to this analysis is the parameterization of the model such that cell killing by the alpha particles could be included. The model contains parameters characterizing the rate of the first mutation, the net proliferation rate of initiated cells, the ratio of the rates of cell loss (cell killing plus differentiation) and cell division, and the lag time between the appearance of the first malignant cell and the tumor. Data analysis was by standard maximum likelihood estimation techniques. Results indicate that the rate of the first mutation is dependent on radon and consistent with in vitro rates measured experimentally, and that the rate of the second mutation is not dependent on radon. An initial sharp rise in the net proliferation rate of initiated cell was found with increasing exposure rate (denoted model I), which leads to an unrealistically high cell-killing coefficient. A second model (model II) was studied, in which the initial rise was attributed to promotion via a step function, implying that it is due not to radon but to the uranium ore dust. This model resulted in values for the cell-killing coefficient consistent with those found for in vitro cells. An "inverse dose-rate" effect is seen, i.e. an increase in the lifetime probability of tumor with a decrease in exposure rate. This is attributed in large part to promotion of intermediate lesions. Since model II is preferable on biological grounds (it yields a plausible cell-killing coefficient), such as uranium ore dust. This analysis presents evidence that a two-stage model describes the data adequately and generates hypotheses regarding the mechanism of radon-induced carcinogenesis.

NASA Program Radiation Health↗
DOE OSTI2021

Restoration Strategy for Active Distribution Systems Considering Endogenous Uncertainty in Cold Load Pickup

Cold load pickup (CLPU) phenomenon is identified as the persistent power inrush upon a sudden load pickup after an outage. Under the active distribution system (ADS) paradigm, where distributed energy resources (DERs) are extensively installed, the decreased outage duration can induce a strong interdependence between CLPU pattern and load pickup decisions. In this paper, we propose a novel modelling technique to tractably capture the decision-dependent uncertainty (DDU) inherent in the CLPU process. Subsequently, a two-stage stochastic decision-dependent service restoration (SDDSR) model is constructed, where first stage searches for the optimal switching sequences to decide step-wise network topology, and the second stage optimizes the detailed generation schedule of DERs as well as the energization of switchable loads. Further, to tackle the computational burdens introduced by mixed-integer recourse, the progressive hedging algorithm (PHA) is utilized to decompose the original model into scenario-wise subproblems that can be solved in parallel. The numerical test on modified IEEE 123-node test feeders has verified the efficiency of our proposed SDDSR model and provided fresh insights into the monetary and secure values of DDU quantification.

24 POWER TRANSMISSION AND DISTRIBUTION↗