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DOE OSTI2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Substation-Level Grid Topology Optimization Using Bus Splitting

Operations of substation circuit breakers are important for maintenance needs and topology reconfiguration in power systems. Bus splitting is one type of topology change where the two bus bars at a substation can become electrically disconnected under certain actions of circuit breakers. Because these events involve detailed substation modeling, they are typically not considered in routine power system operation and control. In this paper, an improved substation-level topology optimization framework is developed by expanding traditional line switching decisions by breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bilinear terms in the resultant optimization problem to linear inequality constraints. Thus, a tractable mixed-integer linear program reformulation is attained that allows for efficient solutions in real-time operations. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the computational performance and economic benefits of the proposed topology optimization approach.

bus split↗

DOE OSTI2021

Per-Phase and 3-Phase Optimal Coordination of Directional Overcurrent Relays Using Genetic Algorithm

Penetration of the power grid by renewable energy sources, distributed storage, and distributed generators is becoming increasingly common. Increased utilization of these distributed energy resources (DERs) has given rise to additional protection coordination concerns, particularly where they are utilized in an unbalanced manner or where loading among phases is unbalanced. Digital relays such as the SEL-751 (produced by Schweitzer Engineering Laboratories, Pullman, WA, USA) series have the capability of being set on a per-phase basis. This capability is underutilized in common practice. Additionally, in optimization algorithms for determining relay settings, the time-overcurrent characteristics (TOCs) of relays are generally not treated as variables and are assigned before running the optimization algorithm. In this paper, TOC options themselves are treated as discrete variables to be considered in the optimization algorithm. A mixed integer nonlinear programming problem (MINLP) is set up where the goal is to minimize relay operating times. A genetic algorithm (GA) approach is implemented in MATLAB where two cases are considered. In the first case, the TOC and Time dial setting (TDS) of each relay is set on a three-phase basis. In the second case, per-phase settings are considered. Relay TDSs and TOCs are both considered as simultaneous discrete control variables. Despite the stochastic nature of using per-phase settings for unbalanced systems is found to generally allow for shorter operating times. However, for relatively balanced systems, it is best to use three-phase settings if computation time is of importance.

Matthews, Ronald C.↗

DOE OSTI2021

Improved Air-Conditioning Demand Response of Connected Communities over Individually Optimized Buildings

Connected communities potentially offer much greater demand response capabilities over singular building energy management systems (BEMS) through an increase of connectivity. The potential increase in benefits from this next step in connectivity is still under investigation, especially when applied to existing buildings. This work utilizes EnergyPlus simulation results on eight different commercial prototype buildings to estimate the potential savings on peak demand and energy costs using a mixed-integer linear programming model. This model is used in two cases: a fully connected community and eight separate buildings with BEMS. The connected community is optimized using all zones as variables, while the individual buildings are optimized separately and then aggregated. These optimization problems are run for a range of individual zone flexibility values. The results indicate that a connected community offered 60.0% and 24.8% more peak demand savings for low and high flexibility scenarios, relative to individually optimized buildings. Energy cost optimization results show only marginally better savings of 2.9% and 6.1% for low and high flexibility, respectively.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage

Variable renewable energy availability has increased the volatility in energy prices in most markets. Nuclear power plants, with a large ratio of capital to variable costs, have historically operated as base load energy suppliers but the need for more flexible operation is increasing. We simulate the techno-economic performance of a 950 MWt nuclear power plant, based on the Westinghouse lead-cooled fast reactor, coupled with molten salt thermal storage as a method for flexible energy dispatch. We use the System Advisor Model to model the nuclear reactor thermal power input and power cycle operating modes. We combine this robust engineering model with a mixed-integer linear program model for optimized dispatch scheduling. We then simulate the coupled nuclear and thermal storage system under different market scenarios with varying price volatility. We find that the coupled plant outperforms the base plant under markets where energy price peaks fluctuate by a factor of two or more about the mean price. We show that a calculated power purchase agreement price for the plant improves by up to 10% when operating under California energy market conditions. Sensitivity analysis on the thermal storage cost shows that the optimal design remains unchanged even when doubling costs.

25 ENERGY STORAGE↗

DOE OSTI2023

Series FACTS Devices for Increasing Resiliency in Severe Weather Conditions

Severe weather conditions are low-probability, high-impact events that affect grid operations. The majority of power outages are caused by severe weather conditions. Grid resiliency to weather events can be enhanced by decreasing the reliance on its affected sections. One way to do this is to reduce the power flow through lines vulnerable to severe weather. If a line is disconnected, its initial power flow is distributed through the neighbor lines, which may cause congestion in the grid. FACTS devices can be used to control the power flow of lines that have a higher chance of power outages. Most previous works do not consider weather events in power flow control. In this work, a linearized optimal power flow (OPF)–based algorithm is developed to minimize the real power flow of vulnerable lines considering the thermal limits of lines to prevent infeasible solutions; the simulation is fast, making it suitable for large-scale systems. The proposed optimization problem is presented as a mixed-integer linear program (MILP), making it capable of using short-term load forecasting due to its high solution speed. The proposed optimization problem considers multiple lines with different outage probabilities and the uncertainties of the weather forecast. Moreover, it estimates the power reduction in vulnerable lines due to changes in the series FACTS devices. The performance of the proposed optimization problem is tested on IEEE 14-, 30-, and 118-bus systems for several scenarios. The results are validated with the AC power flow results from MATPOWER.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Model for Collaboration among Carriers to Reduce Empty Container Truck Trips

In recent years, intermodal transport has become an increasingly attractive alternative to freight shippers. However, the current intermodal freight transport is not as efficient as it could be. Oftentimes an empty container needs to be transported from the empty container depot to the shipper, and conversely, an empty container needs to be transported from the receiver to the empty container depot. These empty container movements decrease the freight carrier’s profit, as well as increase traffic congestion, decrease roadway safety, and add unnecessary emissions to the environment. To this end, our study evaluates a potential collaboration strategy to be used by carriers for domestic intermodal freight transport based on an optimization approach to reduce the number of empty container trips. A binary integer-linear programming model is developed to determine each freight carrier’s optimal schedule while minimizing its operating cost. The model ensures that the cost for each carrier with collaboration is less than or equal to its cost without collaboration. It also ensures that average savings from the collaboration are shared equally among all participating carriers. Additionally, two stochastic models are provided to account for uncertainty in truck travel times. The proposed collaboration strategy is tested using empirical data and is demonstrated to be effective in meeting all of the shipment constraints.

42 ENGINEERING↗

DOE OSTI2020

Dynamic Optimal Dispatch of Energy Systems with Intermittent Renewables and Damage Model

With the increasing penetration of intermittent renewable energy sources into the grid, there is a growing need for process systems-based strategies that integrate dispatchable and variable energy systems for supplying the demand while maintaining grid reliability. The proposed framework corresponds to a dynamic mixed-integer linear programming optimization approach that integrates coal-fired and natural gas-fired power plants, NaS batteries for energy storage, and solar/wind energy to supply the demand. This optimization approach considers an economic goal and constraints to provide power balance while maintaining the overall damage of the natural gas combined cycle (NGCC) power plant drum under a maximum stress as well as avoiding the overheating of the NGCC superheater and reheater. Renewable curtailment levels are also retained at minimum levels. Case studies are analyzed considering different loads and renewable penetration levels. The results show that the demand was met for all cases. Grid flexibility was mostly provided by the NGCC, while the batteries were used sparingly. In addition, considering a CO 2 equivalent analysis, the environmental performance was intrinsically connected to grid flexibility and the level of renewable penetration. Stress analysis results reinforced the necessity for an equipment health-related constraint.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A Scalable Approach to Minimize Charging Costs for Electric Bus Fleets

Incorporating battery electric buses into bus fleets faces three primary challenges: a BEB’s extended refuel time, the cost of charging, both by the consumer and the power provider, and large compute demands for planning methods. When BEBs charge, the additional demands on the grid may exceed hardware limitations, so power providers divide a consumer’s energy needs into separate meters even though doing so is expensive for both power providers and consumers. Prior work has developed a number of strategies for computing charge schedules for bus fleets; however, prior work has not worked to reduce costs by aggregating meters. Additionally, because many works use mixed integer linear programs, their compute needs make planning for commercial-sized bus fleets intractable. This work presents a multi-program approach to computing charge plans for electric bus fleets. The proposed method solves a series of subproblems where the solution to the charge problem becomes more refined with each problem, moving closer to the optimal schedule. The results demonstrate how runtimes are reduced by using intermediate subproblems to refine the bus charge solution so that the proposed method can be applied to large bus fleets of 100+ buses. Not only will we demonstrate that runtimes scale linearly with the number of buses but we will also show how the proposed method scales to large bus fleets of over 100 buses while managing the monthly cost of energy.

Mortensen, Daniel (ORCID:0000000276494452)↗

DOE OSTI2020

Optimal Equilibrium Selection of Price-Maker Agents in Performance-Based Regulation Market

This paper analyzes the oligopolistic equilibrium of multiple price-maker agents in performance-based regulation (PBR) markets. In these markets, there are price-maker agents representing some frequency regulation (FR) providers and a number of independent price-taker FR providers. An equilibrium problem with equilibrium constraints (EPEC) model is employed in this paper to study the equilibria of a PBR market in the presence of price-maker agents and pricetaker FR providers. Due to the incorporation of the FR providers' dynamics, the proposed model is reformulated as a mixed-integer linear programming (MILP) problem over innovative mathematical techniques. An optimal equilibrium point is also selected for the market, where none of the agents is unique deviator and the dynamic performance of power system is improved simultaneously. The effectiveness of proposed optimal equilibrium point is evaluated in the numerical results section by comparing the outputs with conventional optimal dispatches of the FR providers.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Mitigation-Aware Bidding Strategies in Electricity Markets

Market power exercise in the electricity markets distorts market prices and diminishes social welfare. Many markets have implemented market power mitigation processes to eliminate the impact of such behavior. The design of mitigation mechanisms has a direct influence on investors' profitability and thus mid-/long-term resource adequacy. In order to evaluate the effectiveness of the existing market power mitigation mechanisms, this paper proposes a mitigation-aware strategic bidding model and studies the bidding strategies of the market participants under current practice. The proposed bidding model has a bilevel structure with strategic participant's profit maximization problem in the upper level and the dispatch problem for market operators in the lower level. In particular, the consideration of potential offer mitigation is incorporated as upper-level constraints based on the conduct and impact tests. This bilevel problem is reduced to a single-level mixed-integer linear program using the KKT optimality conditions, duality theory, and linearization. Numerical results illustrate how a strategic player can exercise market power to achieve a higher profit even under the current market power mitigation process and we analyze the social impact that the market power exercise results.

Wu, Yiqian↗

DOE OSTI2024

Optimal Design of Food Packaging Considering Waste Management Technologies to Achieve Circular Economy

Plastic packaging plays a fundamental role in the food industry, avoiding food waste and facilitating food access. The increasing plastic production and the lack of appropriate plastic waste management technologies represent a threat to the environmental and human welfare. Therefore, there is an urgent need to identify sustainable packaging solutions. Circular economy (CE) promotes reducing waste and increasing recycling practices to achieve sustainability. In this work, we propose a CE framework based on multi-objective optimization, considering both economic and environmental impacts, to identify optimal packaging designs and waste management technologies. Using mixed-integer linear programming (MILP), techno-economic analysis (TEA), and life cycle assessment (LCA), this work aims to build the first steps in packaging design, informing about the best packaging alternatives and the optimal technology or technologies to process packaging waste. For the economic analysis, we consider the minimum increase in price (MIP) when adding recycling to the cost of each packaging solution, while for the environmental analysis, the greenhouse gas emissions impact was considered. A case study on ground coffee packaging is used to illustrate the proposed framework. The results demonstrate that the multilayer bag option is the most convenient when considering both the chosen economic and environmental impacts.

Life Cycle Analysis↗

DOE OSTI2020

REopt Lite Overview & Training Exercise

This training exercise provides users with an introduction to and hands-on, interactive exploration of REopt Lite's capabilities. REopt Lite is a free, publicly available techno-economic optimization web tool for distributed energy systems, developed at the National Renewable Energy Laboratory (NREL). REopt Lite helps organizations evaluate the economic viability of grid-connected solar photovoltaics (PV), wind turbines, and battery storage; identify system sizes and battery dispatch strategies to minimize energy costs; and estimate how long a system can sustain critical load during a grid outage. The model is formulated as a mixed-integer linear program based in an underlying application programming interface (API) that is also free and publicly available. This training activity is structured as a group exercise. Participants split into eight groups and each group is assigned a different hypothetical site to model and assess the opportunity for solar PV + battery storage. Groups work together to develop results for their site and then re-convene to compare and discuss results, inputs/drivers of the analysis, and other factors impacting the decision-making process for behind-the-meter solar PV and battery storage.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

Examining the Net Revenue and Downstream Flow Impact Trade-Offs for a Network of Cascading, Small-Scale Hydropower Facilities: Preprint

In this work, we used a price-taker model to investigate the trade-offs between net revenue and downstream flow impacts for a network of small, cascading hydro facilities. The network consisted of 36 facilities, each with a small amount of local storage (between 2 and 45 minutes). Generator sizes ranged between 0.5 and 1 MW, nominal, and the total capacity of the network was 33.5 MW. We used a multi-integer linear programing model to maximize the net revenue of the combined network subject to operating and environmental constraints. Net revenue optimizations relied on historic price data, and dry, typical, and wet years were studied to help ensure robustness. Energy and ancillary service sales were included in the net revenue calculations, and both unit commitment and dispatch simulations were performed. We found that limiting the downstream flows to ±50% of the river’s natural flows had a negligible impact on net revenues (<1% reduction), irrespective of hydrologic conditions, and even when downstream flows were limited to ±5%, net revenues were only impacted by 4%. These outcomes are significant because they demonstrate how an array of small-scale hydropower facilities can be operated to have minimal impact on natural stream flows—addressing a critical environmental concern.

downstream flow↗

DOE OSTI2020

DER Planning with Resilience Analysis Using REopt Lite: A Behind-the-Meter Techno-Economic Analysis Tool

REopt Lite is a techno-economic decision support model for behind-the-meter energy systems design and dispatch modeling. REopt Lite is used to optimize energy systems for buildings, campuses, communities, and microgrids. It is based on a Mixed Integer Linear Programming (MILP) optimization model. It is a fully automated and streamlined energy modeling tool that can be used off-the-shelf for a wide variety of distributed generation integration analyses and at the same time is architected to be extensible for user-specific customizations for advanced users and subject matter experts. It is publicly available as a webtool as well as has an Application Programming Interface (API). The API functionality enables programmatic access to the model facilitating smooth integration with other distribution systems modeling tools, and automated multiple scenarios/sensitivity studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy: Preprint

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoltaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2021

Coordinated Optimization and Control of Residential Solid State Power Substations in Electrical Distribution Network

This paper proposes a computationally efficient mixed integer linear programming (MILP) model for the coordinated optimization of solid-state power substations (SSPSs) in a feeder considering the full unbalanced three-phase structure of the distribution grid and its characteristics. The proposed model determines the optimal real and reactive power of each SSPS at the point of common coupling (PCC) that minimizes the operating cost and maximizes the system performance, e.g., voltage regulation and phase balancing. To improve the computational efficiency, an inscribed octagon is introduced to approximate the quadratic capacity constraints of components. Numerical simulation results show the effectiveness of the proposed model and significant improvements in voltage profiles and power imbalance between phases.

Liu, Guodong↗

DOE OSTI2021

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy

61 RADIATION PROTECTION AND DOSIMETRY↗