Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mixed Integer 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

Optimal Sizing and Dispatch of Solar Power with Storage

Designers of utility-scale solar plants with storage, seeking to maximize some aspect of plant performance, face multiple challenges. In many geographic locations, there is significant penetration of photovoltaic generation, which depresses energy prices during the hours of solar availability. An energy storage system affords the opportunity to dispatch during higher-priced time periods, but complicates plant design and dispatch decisions. Solar resource variability compounds these challenges, because determining optimal system sizes requires simultaneously considering how the plant will be operated under the imposed market and weather conditions. We develop an approach to analyze the economic performance of hybrid and single-technology solar power plants, which incorporates optimal dispatch, and considers the expected electricity market and weather conditions. We utilize the System Advisor Model software package to simulate the operation of multiple renewable generation and energy storage technologies, in conjunction with hourly-fidelity generation decisions determined by a revenue-maximizing, mixed-integer linear program. We show that, under our assumed market and weather conditions, the lifetime benefit-to-cost ratio can be improved by 6 to 19 percent, relative to a baseline design without optimizing, and that a concentrating solar power with thermal energy storage design produces significantly more energy per year, but is less profitable under our cost assumptions.

black-box optimization↗

Designing a drone delivery network with automated battery swapping machines

Drones are projected to alter last-mile delivery, but their short travel range is a concern. In this study, we propose a drone delivery network design using automated battery swapping machines (ABSMs) to extend ranges. The design minimizes the long-term delivery costs, including ABSM investment, drone ownership, and cost of the delivery time, and locates ABSMs to serve a set of customers. We build a mixed-integer nonlinear program that captures the nonlinear waiting time of drones at ABSMs. To solve the problem, we create an exact solution algorithm that finds the globally optimal solution using a derivative-supported cutting-plane method. To validate the applicability of our program, we conduct a case study on the Chicago Metropolitan area using cost data from leading ABSM manufacturer and geographical data from the planning and operations language for agent-based regional integrated simulation (more commonly known as POLARIS). A sensitivity analysis identifies that ABSM service times and costs are the key parameters impacting the long-term adoption of drone delivery.

25 ENERGY STORAGE↗

Effective restoration strategies of interdependent power system and communication network

The power system is continuously evolving towards a smarter grid by adding intelligent electrical devices that leverage communication technologies to provide visualisation, control and automation. The integration of power system and communication network has brought challenges into the resilience of interdependent networks. Following an outage or blackout, system operators cannot only restore one network while simply ignoring the interconnection with the other network. Effective restoration strategies that involve co‐ordination between power system and communication network have become critical in enhancing the resilience. An optimisation‐based restoration strategy is developed to coordinate the restoration actions between two networks. The problem is modelled as a mixed integer linear programming problem, with the objective of activating every node in both networks with the minimum number of activation/energisation of branches. The developed strategies are tested on the modified IEEE 14‐bus system incorporating communication network. Simulation results demonstrate that the coordinated restoration strategies are effective and critical in the successful recovery of interdependent networks. The developed model could also provide insights in network design and planning to enhance the resilience of interdependent power system and communication network.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Robust trajectory-constrained frequency control for microgrids considering model linearization error

Grid supportive modes integrated within inverter-based resources can improve the frequency response of renewable-rich microgrids. The synthesis of grid supportive modes to guarantee frequency trajectory constraints under a predefined disturbance set is challenging but essential. To tackle this challenge, a numerical optimal control (NOC)-based control synthesis methodology is proposed. Without loss of generality, a wind-diesel fed microgrid is studied, where we aim to design grid supportive functions in the wind turbine. In the control design, linearized models are used, and the linearization-induced errors are quantitatively analyzed by reachability and interval arithmetics and represented in the form of interval uncertainties. Then, the NOC problem can be formulated into a robust mixed-integer linear program. The control structure is strategically configured into two levels to realize online deployment. The proposed control is verified on the modified 33-node microgrid with a full-order three-phase nonlinear model in Simulink. In conclusion, the simulation results show the effectiveness of the proposed control paradigm and the necessity of considering linearization-induced uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Distributed biomass supply chain cost optimization to evaluate multiple feedstocks for a biorefinery

Conventional practices of siting all biomass preprocessing operations at the biorefinery is widely believed to be the most cost-effective solution for feedstock supply because of economies of scale. Yet, biomass preprocessing operations could be decentralized by moving the preprocessing operations to distributed biomass preprocessing centers, also known as “depots” located near biomass sources. We present a comparative case study with multiple biomass resources to analyze biorefinery feedstock supply logistics designs having distributed depots and a primary depot co-located with the biorefinery. A mixed-integer linear programming model was developed to simultaneously optimize feedstock sourcing decisions, and optimal preprocessing depot locations and size, utilizing biomass resources from agricultural residue, energy and municipal solid waste to meet carbohydrate specifications and feedstock demand for a biochemical conversion process. Findings from a case study in the US showed that a biorefinery could increase its feedstock supply draw area and supply volume by 57.3%, 177.4% respectively without increasing the feedstock delivered cost by adopting distributed depot-in the feedstock supply chain design. A distributed-depot-based supply chain can be more economical by selecting optimal mix of biomass resource, optimal siting and depot scales during feedstock supply chain design. The results from this study indicate that a biorefinery can utilize dynamic blending to meet the feedstock quality specifications as well as larger supply radius in the distributed depot-based supply chain design to access more available biomass to handle potential feedstock supply uncertainty.

09 BIOMASS FUELS↗

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real–world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. Herein we present a novel deterministic mixed–integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics–based constraints on the first and second derivatives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data-Driven Energy Resilience Assessment and Enhancement in Urban Communities: A Case Study in Detroit

This paper presents a data-driven framework for assessing and enhancing energy resilience in urban communities. The resilience assessment is based on two datasets: 1) annual aggregated power outage data and 2) 15-minute interval outage data. High-impact, low-probability (HILP) events are identified within these datasets to evaluate community resilience under extreme conditions. To enhance resilience, an optimization framework utilizing mixed integer linear programming is developed to determine the optimal sizing and placement of solar photovoltaic (PV) systems and battery energy storage systems (BESS). This method offers a cost-effective and practical solution for improving energy resilience in vulnerable communities. Furthermore, a case study of the City of Detroit in Michigan demonstrates the effectiveness of the framework through simulation and validation.

Energy resilience assessment↗

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↗

Bidding strategy for microgrid in day-ahead market based on hybrid stochastic/robust optimization

In this paper, we propose an optimal bidding strategy in the day-ahead market of a microgrid consisting of intermittent distributed generation (DG), storage, dispatchable DG and price responsive loads. The microgrid coordinates the energy consumption or production of its components and trades electricity in both the day-ahead and real-time markets to minimize its operating cost as a single entity. The bidding problem is challenging due to a variety of uncertainties, including power output of intermittent DG, load variation, day-ahead and real-time market prices. A hybrid stochastic/robust optimization model is proposed to minimize the expected net cost, i.e., expected total cost of operation minus total benefit of demand. This formulation can be solved by mixed integer linear programming. The uncertain output of intermittent DG and day-ahead market price are modeled via scenarios based on forecast results, while a robust optimization is proposed to limit the unbalanced power in real-time market taking account of the uncertainty of real-time market price. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator, a battery and a responsive load show the advantage of stochastic optimization in addition to robust optimization.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Design and dispatch optimization of packaged ice storage systems within a connected community

The traditional implementation of cool thermal energy storage (CTES) must be reimagined within the context of a dynamic grid and smart buildings operating as connected communities. As most buildings do not operate central chillers or connect to district cooling loops, this necessitates a broader use of packaged CTES. Our objective is to begin answering the question of how such packaged CTES should be implemented within a connected community. We do so by presenting a simulation–optimization workflow employing building energy modeling software and a mixed-integer linear program to design and dispatch a packaged CTES technology to achieve minimum total annual cost. We demonstrate this methodology on a seven-building case study using current utility rates and find that total annual cooling energy costs can be reduced by 17.8% compared to baseline, after accounting for the cost of storage. We perform three parametric sensitivity studies to evaluate modeling assumptions and obtain the prioritization of storage procurement as a function of annualized life-cycle cost of storage. We find that a community optimization approach provides significantly different results than individual building optimizations and provides greater savings compared to baseline.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Non-Exhaustive Search Algorithm to Identify Distribution Grid Operational Topology

Distribution grid, in general, is constructionally loopy but a radially operated network. Opening and closing of suitable tie-switches allow transition from one topology to another. Identifying the operational topology of a distribution system is essential for accurate control actions. This paper proposes a non-exhaustive search approach to detect the operational topology of the distribution feeder by estimating the switch statuses. In this work, a mixed-integer linear programming approach is proposed that finds the correct operational topology by identifying the system load demand and power flow variables that are closest to the corresponding measured values. The problem is constrained by distribution power flow and radial structure of the feeder. This formulation allows the inclusion of errors in power/line flow measurements making it more suitable for a practical distribution system. The proposed approach finds the correct operational topology without exhaustively searching for all possible topologies. We thoroughly validate the accuracy and effectiveness of the proposed approach in identifying correct operational topology using IEEE 123-node feeder with the help of numerous simulations studies. It is observed that the approach performs well even at very high percentages of load and flow measurement errors.

Missed detection ratio (MDR), Mixed-integer linear↗

Resilient Distribution System by Microgrids Formation After Natural Disasters

Microgrids with distributed generation provide a resilient solution in the case of major faults in a distribution system due to natural disasters. This paper proposes a novel distribution system operational approach by forming multiple microgrids energized by distributed generation from the radial distribution system in real-time operations, to restore critical loads from the power outage. Specifically, a mixed-integer linear program (MILP) is formulated to maximize the critical loads to be picked up while satisfying the self-adequacy and operation constraints for the microgrids formation problem, by controlling the ON/OFF status of the remotely controlled switch devices and distributed generation. A distributed multi-agent coordination scheme is designed via local communications for the global information discovery as inputs of the optimization, which is suitable for autonomous communication requirements after the disastrous event. The formed microgrids can be further utilized for power quality control and can be connected to a larger microgrid before the restoration of the main grids is complete. Numerical results based on modified IEEE distribution test systems validate the effectiveness of our proposed scheme.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Exploiting Identical Generators in Unit Commitment

Here, we present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down-time, and cost curves) into a single unit reduces redundancy in the search space induced by both exact symmetry (permutations of generator schedules) and certain classes of mutually non-dominated solutions. We study the impact of aggregation on two large-scale UC instances, one from the academic literature and another based on real-world operator data. Our computational tests demonstrate that when present, identical generators can negatively affect the performance of modern MILP solvers on UC formulations. Further, we show that our reformation of the UC MILP through aggregation is an effective method for mitigating this source of computational difficulty.

97 MATHEMATICS AND COMPUTING↗

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. Next, we introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

97 MATHEMATICS AND COMPUTING↗

Coordinated platooning with multiple speeds

In a platoon, vehicles travel one after another with small intervehicle distances; trailing vehicles in a platoon save fuel because they experience less aerodynamic drag. This work presents a coordinated platooning model with multiple speed options that integrates scheduling, routing, speed selection, and platoon formation/dissolution in a mixed-integer linear program that minimizes the total fuel consumed by a set of vehicles while traveling between their respective origins and destinations. The performance of this model is numerically tested on a grid network and the Chicago-area highway network. We find that the fuel-savings factor of a multivehicle system significantly depends on the time each vehicle is allowed to stay in the network; this time affects vehicles’ available speed choices, possible routes, and the amount of time for coordinating platoon formation. For problem instances with a large number of vehicles, we propose and test a heuristic decomposed approach that applies a clustering algorithm to partition the set of vehicles and then routes each group separately. When the set of vehicles is large and the available computational time is small, the decomposed approach finds significantly better solutions than does the full model.

33 ADVANCED PROPULSION SYSTEMS↗

Optimal blending management of biomass resources used for biochemical conversion

This research develops an optimization model to describe the tradeoff among blend components in the least-cost biomass blend, based on resource availability, quality requirements, and logistics cost for a biochemical conversion. A mixed-integer linear programming model is developed to determine the least-cost blend from a set of candidate feedstocks. A case study – based on a biorefinery located in western Kansas that uses three-pass corn stover, two-pass corn stover, switchgrass, miscanthus, and municipal solid waste fractions to meet biochemical conversion specifications and feedstock demand – shows that the delivered cost of an optimal blend that meets carbohydrate and ash specifications is 12.12% higher than the delivered cost of optimal blend that meets a carbohydrate specification only. The results indicate that a least-cost blend that meets both carbohydrate and ash specifications consists of miscanthus (48.2%) and switchgrass (29.4%) whereas the least-cost blend meeting carbohydrate specification only comprises three-pass corn stover (55.4%) and two-pass corn stover (20.4%). Here an optimal blend uses a low-cost municipal solid waste fraction in all cases, implying that blending could be a potential strategy to reduce delivered feedstock cost.

09 BIOMASS FUELS↗