Joint Estimation of Operational Topology and Outages for Unbalanced Power Distribution Systems
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Engineering↗
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Results for “Mixed integer optimization”
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Feedback Control Approaches for Restoration of Power Grids from Blackouts
The automated restoration of power systems with variable energy resources is a timely problem to tackle. Automated restoration advice can support operators in deciding on strategic actions to restore power grids from a blackout with a mix of conventional and renewable generation resources. To this end, this paper frames the restoration process of power grids with solar resources as a nonlinear dynamic model with algebraic constraints in discrete time which is steered by feedback control loops. We discuss two feedback-control strategies based on greedy and reinforcement learning algorithms, and contrast their performance with restoration plans generated by a mixed-integer linear program. We found that the reinforcement learning algorithm infers restoration actions faster than the greedy one. However, the tuning process of the reinforcement learning parameters is slower than for the greedy one.
machine learning↗
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↗
Cooperative Transmission Expansion Planning Experiment Data and Results
GO WEST is an open-source power grid modeling framework for U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It covers 28 balancing authorities (BA) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of U.S. Western Interconnection created by Texas A&M University. Users can try and select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. TEP is an open-source transmission capacity expansion model, built on GO WEST framework. It utilizes linear programming to optimize transmission capacity addition investment on existing lines within GO WEST framework. In this sense, TEP model only increases the thermal capacity of existing transmission lines and does not add new lines to the system, which leaves the topology preserved. TEP minimizes the total cost of the system which comprises the operational cost of satisfying electricity demand (i.e., generation cost), cost of loss of load (i.e., unserved energy), cost of power flow, and cost of new transmission capacity additions (i.e., investment cost). In order to use TEP model, users need to create scenarios with GO WEST framework. In this analysis, outputs from several models are used to create future inputs to GO WEST and TEP models, including GCAM-USA, TELL, CERF and reV. This dataset includes experiment inputs and outputs from three different transmission expansion scenarios (cooperative, intermediate, and individual) for 2019 and 2059. For 2019, a base scenario to illustrate the default (i.e., historical) power grid operations is also included. This study utilizes rcp45hotter_ssp3 scenario from a previous version of GCAM-USA simulations. Sources of the shapefiles in supplementary data are HIFLD Open and U.S. Energy Atlas. Please see the README file for a detailed description of the main and supplementary data.
Capacity Expansion Model↗
IM3 Projected U.S. Western Interconnection Grid Stress Dataset
This dataset provides projected grid stress and reliability results (including all model inputs and outputs from GO WEST and TEP) for Integrated Multisector, Multiscale Modeling (IM3) Phase 2 simulations across eight different scenarios for the U.S. Western Interconnection through 2055. The scenarios include combinations of two Shared Socioeconomic Pathways (SSP3 and SSP5) with four high-resolution climate projections specific to the United States from a set of Thermodynamic Global Warming (TGW) simulations. These climate projections include "hotter" and "cooler" variants for two Representative Concentration Pathways (RCP4.5 and RCP8.5). The resulting eight simulations are: rcp45cooler_ssp3 rcp45cooler_ssp5 rcp45hotter_ssp3 rcp45hotter_ssp5 rcp85cooler_ssp3 rcp85cooler_ssp5 rcp85hotter_ssp3 rcp85hotter_ssp5 GO WEST is an open-source power grid modeling framework for the U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It covers 28 balancing authorities (BAs) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of the U.S. Western Interconnection (ACTIVSg10k). Users can select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. TEP is an open-source transmission capacity expansion model, built on the GO WEST framework. It utilizes linear programming to optimize transmission capacity addition investment on existing lines within the GO WEST framework. The TEP model only increases the thermal capacity of existing transmission lines and does not add new lines to the system, which leaves the topology preserved. In order to use TEP model, users need to create scenarios with the GO WEST framework. Please refer to README file for a detailed description of the dataset including individual files and references.
Capacity Expansion Model↗
Resilient Distribution System Restoration with Equitable Load Shedding
A methodology is proposed for the improvement of electric distribution system resilience to high-impact, low-probability catastrophic events. An approach for dynamic network reconfiguration and coordination of distributed energy resources is introduced to assist in restoration efforts. The problem is formulated as a mixed-integer linear program that minimizes generation costs, the cost of lost load, and costs associated with equitable load shedding, while respecting operational limits of generation, loads, and the network. Constraints are imposed on binary switching variables to ensure equitable load shedding in emergency situations. Numerical validation of the proposed approach is conducted on an example distribution feeder, and case studies are performed to analyze the impact of various parameters in the optimization problem formulation.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Convex Relaxations of Maximal Load Delivery for Multi-Contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks
Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities in gas and power grids, where disruptions can require the curtailment of load in one or both systems. Although typically operated independently, coordination of these systems during severe disruptions can allow for targeted delivery to lifeline services, including gas delivery for residential heating and power delivery for critical facilities. To address the challenge of estimating maximum joint network capacities under such disruptions, we consider the task of determining feasible steady-state operating points for severely damaged systems while ensuring the maximal delivery of gas and power loads simultaneously, represented mathematically as the nonconvex joint Maximal Load Delivery (MLD) problem. To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem. Then, to demonstrate the relaxation’s effectiveness in determining bounds on network capacities, exact and relaxed MLD formulations are compared across various multi-contingency scenarios on nine joint networks ranging in size from 25 to 1191 nodes. The relaxation-based methodology is observed to accurately and efficiently estimate the impacts of severe joint network disruptions, often converging to the relaxed MLD problem’s globally optimal solution within ten seconds.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Battery and backup generator sizing for a resilient microgrid under stochastic extreme events
Owing to the recent power outages caused by extreme events, installing battery energy storage and backup generators is important to improve resiliency for a grid-tied microgrid. In the design stage, the event occurrence time and duration, which are highly uncertain and cannot be effectively predicted, may affect the needed battery and backup generator capacity but are usually assumed to be pre-determined in utility planning tools. This study investigates the optimal battery and backup generator sizing problem considering the stochastic event occurrence time and duration for the grid-tied microgrid under islanded operation. The reliability requirement is quantified by the mean value of the critical customer interruption time in each stochastic islanding time window (ITW), whose length is the duration and the centre is the occurrence time. The stochastic ITW constraint is then transformed to a probability-weighted expression to derive an equivalent Mixed Integer Linear Programming model. Numerical simulations on a realistic grid-tied PV-based microgrid demonstrate that the total cost is reduced by 11.5% considering the stochastic ITW, compared with the deterministic ITW under the same reliability requirement.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Joint Expansion Planning of Power and Water Distribution Networks
This research considers the joint expansion planning of power and water distribution networks, which are interdependent at various levels. We consider the dependency arising through the power consumption of pumps and develop models for integrating new components into existing networks. Then, we formulate the joint expansion planning as a Mixed Integer Nonlinear Program (MINLP). Applying this MINLP to a small-scale test network, we illustrate the advantages offered by joint expansion planning, such as increased flexibility and reduced costs and redundancy, over independently expanding power and water distribution networks.
expansion planning↗
Near-Optimal Solutions for Day-Ahead Unit Commitment
Given the difficulty and the time pressure of solving unit commitment problems, near -optimal solutions (those with 0.1 or 0.001% optimality gaps) are often used in practice. The choice in which of the near -optimal solutions is used, however, is random. We investigate the impact of solution choice on the revenues obtained by generator owners across a variety of pricing schemes and problem instances.
market-clearing↗
Optimal Economic Dispatch and Load-Following Strategies for Nuclear Integrated Energy Systems
The need for distributed and adaptable energy resources that can handle the growing unpredictability in both supply and demand is rising as the power system continues to modernize. In order to satisfy those needs and maintain grid resilience, nuclear power plants can dynamically control their output, despite typically being used as baseload generators. By incorporating energy storage and renewable energy sources, nuclear integrated energy systems are designed to satisfy the electrical and thermal demands of different end-user applications while ensuring flexible power operation. These systems generate revenue by participating in both wholesale and ancillary services electricity markets, as well as commodity markets for various byproducts generated from coupled industrial processes. This study addresses the economic dispatch efficiency of a tightly coupled nuclear integrated energy system comprising a gigawatt-scale light water reactor, commercialized in the U.S., a high-temperature steam electrolysis unit, a district heating network, and specified electrical loads. To demonstrate the nuclear power plant’s flexibility within the day-ahead unit commitment and economic dispatch framework, while maintaining equilibrium even during periods of refueling outages, this paper develops a mixed-integer linear programming framework that models the subsystems and components of its nuclear steam supply system. A systematic comparative analysis of flexible versus baseload nuclear power plant operation under varying levels of renewable energy integration indicates that flexible operation enhances system profitability by more than 18% while also increasing energy storage utilization, improving reactor responsiveness to load fluctuations, and allowing for greater participation across numerous electricity markets.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Managing Power Systems-Induced Wildfire Risks Using Optimal Scheduled Shutoffs
The increasing demands for electricity and the increase in extreme weather conditions are putting unprecedented pressure on our electric grids. Often, this pressure leads to electrical component failures, which might ignite wildfires. This work develops a novel model to balance the reliability of power network operations and the risk of wildfire ignition by opti- mizing the operational schedule of power transmission networks considering time-varying risk measures that include exogenous and operational factors. Energy storage systems are considered to deliver power during peak wildfire hours and enable temporal load shifting. The problem is formulated as a mixed-integer linear program that maximizes a weighted sum of the served power demand and the reduction in grid-induced wildfire risk. The results demonstrate the ability of the model to significantly reduce wildfire risk without considerable load shedding.
power systems operations↗
Resilient Disaster Recovery Logistics of Distribution Systems: Co-Optimize Service Restoration With Repair Crew and Mobile Power Source Dispatch
Repair crews (RCs) and mobile power sources (MPSs) are critical resources for distribution system (DS) outage management after a natural disaster. However, their logistics have not been well investigated. We propose a resilient scheme for disaster recovery logistics to co-optimize DS restoration with the dispatch of RCs and MPSs. A novel co-optimization model is formulated to route RCs and MPSs in the transportation network, schedule them in the DS, and reconfigure the DS for microgrid formation coordinately, etc. The model incorporates different timescales of DS restoration and RC/MPS dispatch, the coupling of transportation and power networks, etc. To ensure radiality of the DS with variable physical structure and MPS allocation, we also model topology constraints based on the concept of spanning forest. The model is convexified equivalently and linearized into a mixed-integer linear programming. To reduce its computation time, preprocessing methods are proposed to preassign a minimal set of repair tasks to depots and reduce the number of candidate nodes for MPS connection. Resilient recovery strategies thus are generated to enhance service restoration, especially by dynamic formation of microgrids that are powered by MPSs and topologized by repair actions of RCs and network reconfiguration of the DS. Case studies demonstrate the proposed methodology.
Disaster recovery logistics↗
Natural gas maximal load delivery for multi-contingency analysis
An increasing dependence on natural gas has amplified existing vulnerabilities to the power grid, including disruptions to gas transmission networks from natural and man-made disasters. To address the operational challenges arising from these disruptions, we, in this study, consider the problem of estimating the steady-state operating capacity of a damaged gas pipeline network while ensuring the maximal delivery of load. Specifically, we formulate the mixed-integer nonconvex maximal load delivery (MLD) problem, which proves difficult to solve on large-scale networks. To address this challenge, we present a relaxation of the MLD problem and use it to determine bounds on the transport capacity of a gas pipeline system. A rigorous computational evaluation over network models ranging in size from 11 to 4,197 junctions shows that the relaxation-based method is suitable for analyzing the impacts of multi-contingency network disruptions, often converging to the optimal solution of the relaxation in less than ten seconds.
03 NATURAL GAS↗
The role of service areas in the optimization of FSS orbital and frequency assignments
An implicit relationship is derived which relates the topocentric separation of two satellites required for a given level of single-entry protection to the separation and orientation of their service areas. The results are presented explicitly for circular beams and topocentric angles. A computational approach is given for elliptical beams and for use with longitude and latitude variables. It is found that the geocentric separation depends primarily on the service area separation, secondarily on a parameter which characterizes the electrical design, and only slightly on the mean orbital position of the satellites. Both linear programming and mixed integer programming algorithms are implemented. Possible objective function choices are discussed, and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed 'ideal' location set. A test problem involving six service areas is examined with results that are encouraging with respect to applying the linear programming procedure to larger scenarios.
Levis, C. A.↗
Efficient Trajectory Options Allocation for the Collaborative Trajectory Options Program
The Collaborative Trajectory Options Program (CTOP) is a Traffic Management Initiative (TMI) intended to control the air traffic flow rates at multiple specified Flow Constrained Areas (FCAs), where demand exceeds capacity. CTOP allows flight operators to submit the desired Trajectory Options Set (TOS) for each affected flight with associated Relative Trajectory Cost (RTC) for each option. CTOP then creates a feasible schedule that complies with capacity constraints by assigning affected flights with routes and departure delays in such a way as to minimize the total cost while maintaining equity across flight operators. The current version of CTOP implements a Ration-by-Schedule (RBS) scheme, which assigns the best available options to flights based on a First-Scheduled-First-Served heuristic. In the present study, an alternative flight scheduling approach is developed based on linear optimization. Results suggest that such an approach can significantly reduce flight delays, in the deterministic case, while maintaining equity as defined using a Max-Min fairness scheme.
Traffic Management Initiative (TMI)↗
SMEX-Lite Modular Solar Array Architecture
For the most part, Goddard solar arrays have been custom designs that are unique to each mission. The solar panel design has been frozen prior to issuing an RFP for their procurement. There has typically been 6-9 months between RFP release and contract award, followed by an additional 24 months for performance of the contract. For Small Explorer (SMEX) missions, with three years between mission definition and launch, this has been a significant problem. The SMEX solar panels have been sufficiently small that the contract performance period has been reduced to 12-15 months. The bulk of this time is used up in the final design definition and fabrication of flight solar cell assemblies. Even so, it has been virtually impossible to have the spacecraft design at a level of maturity sufficient to freeze the solar panel geometry and release the RFP in time to avoid schedule problems with integrating the solar panels to the spacecraft. With that in mind, the SMEX-Lite project team developed a modular architecture for the assembly of solar arrays to greatly reduce the cost and schedule associated with the development of a mission- specific solar array. In the modular architecture, solar cells are fabricated onto small substrate panels. This modular panel (approximately 8.5" x 17" in this case) becomes the building block for constructing solar arrays for multiple missions with varying power requirements and geometrical arrangements. The mechanical framework that holds these modules together as a solar array is the only mission-unique design, changing in size and shape as required for each mission. There are several advantages to this approach. First, the typical solar array development cycle requires a mission unique design, procurement, and qualification including a custom qualification panel. With the modular architecture, a single qualification of the SMEX-Lite modules and the associated mechanical framework in a typical configuration provided a qualification by similarity to multiple missions. It then becomes possible to procure solar array modules in advance of mission definition and respond quickly and inexpensively to a selected mission's unique requirements. The solar array modular architecture allows the procurement of solar array modules before the array geometry has been frozen. This reduces the effect of procurement lead-time on the mission integration and test flow by as much as 50%. Second, by spreading the non-recurring costs over multiple missions, the cost per unit area is also reduced. In the case of the SMEX-Lite procurement, this reduction was by about one third of the cost per unit area compared to previous SMEX mission-unique procurements. Third, the modular architecture greatly facilitates the infusion of new solar cell technologies into flight programs as these technologies become available. New solar cell technologies need only be fabricated onto a standard-sized module to be incorporated into the next available mission. The modular solar array can be flown in a mixed configuration with some new and some standard cell technologies. Since each module has its own wiring terminals, the array can be arranged as desired electrically with little impact to cost and schedule. The solar array modular architecture does impose some additional constraints on systems and subsystem engineers. First, they must work with discrete solar array modules rather than size the array to fit exactly within an available envelope. The array area is constrained to an integer multiple of the module area. Second, the modular design is optimized for space radiation and thermal environments not greatly different from a typical SMEX LEO environment. For example, a mission with a highly elliptical orbit (e.g., Polar, SMEX/FAST) would require thicker coverglasses to protect the solar cells from the more intense radiation environment.
Lyons, John↗
A Configuration Based Pumped Storage Hydro Model in the MISO Day-Ahead Market
Pumped storage hydro units (PSHU) can provide flexibility to power systems. This becomes particularly valuable in recent years with the increasing shares of intermittent renewable resources. However, due to emphasis on thermal generation in the current market practices, the flexibility from PSHUs have not been fully explored and utilized. This paper proposes a configuration based pumped storage hydro (PSH) model for the day-ahead market, in order to enhance the use of PSH resources in the system. A strategic design of incorporating and fully optimizing PSHUs in the day-ahead market is presented. Here, we show the compactness of the proposed model. Numerical studies are presented in an illustrative test system and the Midcontinent Independent System Operator (MISO) system.
13 HYDRO ENERGY↗