Towards Automated Scheduling of NASA’s Deep Space Network: A Mixed Integer Linear Programming Approach
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Johnston, Mark↗
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Mixed-Integer Nonlinear Programming Applications: Pyomo Tools and Tailored Strategies.
Abstract not provided.
Laird, Carl Damon↗
Integration of progressive hedging and dual decomposition in stochastic integer programs
We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. As a result, we report computational results on server location and unit commitment instances.
97 MATHEMATICS AND COMPUTING↗
A Mixed Integer Linear Programming-basedDistributed Energy Management for Three-phaseUnbalanced Active Distribution Network
A mixed integer linear programming (MILP)–baseddistributed energy management for three-phase unbalancedactive distribution network is proposed. Modern distributionnetworks have becoming more and more active with increasingdeployment of microgrids, distributed energy resources (DERs)as well as controllable loads. Considering various ownership andcontrol models of microgrids, DERs and controllable loads, adistributed energy management was formulated using the alternatingdirection method of multipliers (ADMM) algorithm. ByADMM, the distribution management system (DMS) and theseactive components are coordinated through price signals, whichare adjusted according to the generation-load mismatch per nodeper phase. To enable resolution of the ADMM-based distributedoptimization using more accessible and popular MILP solver,different linearization techniques were proposed to linearize theaugmented Lagrangian terms and other nonlinear terms. Resultsof case studies on a three-phase active distribution network withthree microgrids and several DERs and controllable loads validatedthe effectiveness of proposed MILP-based distributed energymanagement. In addition, the capability of proposed method inmitigating phase power unbalance has been demonstrated.
Liu, Guodong↗
Flexible dynamic boundary microgrid operation considering network and load unbalances
Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Further, negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Optimizing design and dispatch of a renewable energy system with combined heat and power
We embellish a mixed-integer program that prescribes a set of renewable energy, conventional generation, and storage technologies to procure, along with a corresponding dispatch strategy. Specifically, we add combined heat and power to this set. The model minimizes fixed and operational costs less incentives for the use of various technologies, subject to a series of component interoperability and system-wide constraints. The resulting mixed-integer linear program contains hundreds of thousands of variables and constraints. We demonstrate how to efficiently formulate and solve the corresponding instances such that we produce near-optimal solutions in minutes. A previous rendition of the model required hours of solution time for the same instances.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Optimal Black Start Allocation for Power System Restoration
Equipment failures, operator errors, natural disasters and cyber-attacks can and have caused extended blackouts of the electric grid. Even though such events are rare, preparedness for them is critical because extended power outages endanger human lives, compromise national security, or result in economic losses of billions of dollars. Since most of the generating units cannot restart without connecting to an energized grid, the system operator relies on a few units with the ability to start autonomously, called Black Start (BS) units, to restore the power system. Allocating and maintaining these units is costly and can severely impact the restoration security and time. We formulate an optimization problem to optimally allocate BS units in the grid, while simultaneously optimizing over the restoration sequence. We extend existing optimal allocation models by including grid considerations such as active power nodal balance, transmission switching, nodal reactive power support and voltage limits. In order to aid the branch and bound tree that solves the resulting large scale mixed integer program, we propose a randomized heuristic that is executed multiple times in parallel on a high-performance computing environment to find feasible solutions. Here, we proceed to solve the IEEE-39, the IEEE-118, and a simplified WECC system with 225 nodes and 136 generators to near optimality.
97 MATHEMATICS AND COMPUTING↗
Optimization of a Mixed Fleet of Aerial Drones for Medical Supplies: A Case Study of Blood Delivery Logistics
Aerial drones have emerged as an innovative solution for faster transportation of time-sensitive items (e.g., emergency medical supplies), potentially reducing the transmission of contagious diseases and enhancing healthcare availability through contactless autonomous delivery. We study fleet sizing and efficient scheduling of a mixed fleet of drones for delivering time-sensitive medical items having distinct release and due times to minimize the required fleet size and fleet composition, the required number of additional batteries, and the total energy consumption. We continuously track the remaining battery energy of drones to determine the optimal timing for battery replacement, rather than replacing the battery at each node. Using actual drone flight test data, we employed a machine learning (ML) method to estimate the energy consumption of different drone types during flight segments for different operating parameters. We present a novel mixed-integer programming model to efficiently formulate the problem that integrates the estimated energy consumption functions from ML. We propose a new greedy heuristic (GH) algorithm and a customized genetic algorithm (GA) for solving large-scale instances of this problem faster. Results demonstrate that the GH algorithm is substantially faster than the accelerated CPLEX and the GA, while sacrificing the solution quality by a small amount. Results based on an actual blood sample delivery case study from Pendleton, Oregon, United States, show that using a mixed fleet of drones reduces the total cost and total energy consumption up to 18.18% and 28.7%, respectively, compared to using a homogeneous fleet.
29 - ENERGY PLANNING, POLICY AND ECONOMY↗
Hybrid Imitation Learning for Real-Time Service Restoration in Resilient Distribution Systems
Self-healing capability is a critical factor for a resilient distribution system, which requires intelligent agents to automatically perform service restoration online, including network reconfiguration and reactive power dispatch. Here, the article proposes the imitation learning framework for training such an agent, where the agent will interact with an expert built based on the mixed-integer program to learn its optimal policy, and therefore significantly improve the training efficiency compared with exploration-dominant reinforcement learning (RL) methods. This significantly improved training efficiency makes the training problem under N-k scenarios tractable. A hybrid policy network is proposed to handle tie-line operations and reactive power dispatch simultaneously to further improve the restoration performance. The 33-bus and 119-bus systems with N-k disturbances are employed to conduct the training. The results indicate that the proposed method outperforms traditional RL algorithms such as the deep-Q network.
42 ENGINEERING↗
Stochastic Optimization for Unit Commitment-A Review
Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC's birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Aerial drone fleet deployment optimization with endogenous battery replacements for direct delivery of time-sensitive products
Aerial drones offer a distinct potential to reduce the delivery time and energy consumption for the delivery of time-sensitive and small products. However, there is still a need in the relevant industry to understand the performance of drone-based delivery under different business needs and drone operating conditions. We studied a drone deployment optimization problem for direct delivery of time-sensitive products with release dates to customers maintaining a specified time window. This paper presents a new mixed-integer programming model, new valid inequalities, a new greedy heuristic algorithm, and a Genetic algorithm to help business owners optimally schedule and route their drone fleet minimizing the required fleet size, the required number of additional batteries, and total energy consumption. A realistic feature of the optimization method is that instead of replacing the drone battery after each return to the depot, it keeps track of the remaining energy in the drone battery and decides on battery replacements accounting for the drone routing and the user-specified minimum required battery energy. Numerical results based on real data from drone flight tests and prepared food delivery industry provide insights into the effect of different practical drone operating parameters on the required fleet size, the required number of battery replacements, and energy consumption. Here, results demonstrate that the proposed heuristic algorithm substantially outperforms the accelerated CPLEX in runtime while sacrificing the solution quality by a small amount. Additionally, results show that using a mixed fleet of hexacopter and quadcopter drones reduces the total energy consumption by 48.52% compared to using a homogeneous fleet of only hexacopters.
Drone energy consumption↗
Alternative mathematical programming formulations for FSS synthesis
A variety of mathematical programming models and two solution strategies are suggested for the problem of allocating orbital positions to (synthesizing) satellites in the Fixed Satellite Service. Mixed integer programming and almost linear programming formulations are presented in detail for each of two objectives: (1) positioning satellites as closely as possible to specified desired locations, and (2) minimizing the total length of the geostationary arc allocated to the satellites whose positions are to be determined. Computational results for mixed integer and almost linear programming models, with the objective of positioning satellites as closely as possible to their desired locations, are reported for three six-administration test problems and a thirteen-administration test problem.
Reilly, C. H.↗
Enhancing Active Distribution Systems Resilience by Fully Distributed Self-Healing Strategy
Distributed restoration can exploit smart grid technologies to enhance the resilience of active distribution networks toward a self-healing smart grid. However, the large number of decision variables, especially the binary ones for reconfiguration, bring challenges to developing scalable distributed distribution service restoration (DDSR) strategies. This paper proposes a fully distributed solution procedure based on the alternating direction method of multipliers (ADMM) for mixed-integer programming problems and applies to develop the DDSR framework. The method consists of relax-drive-polish phases, 1) relaxing binary variables, and applying the convex ADMM as a warm start; 2) driving the solutions toward Boolean values through a proximal operator; 3) fixing the obtained binding binary variables and solving the rest of the problem to polish results and achieve a high-quality suboptimal solution. Then, an autonomous clustering strategy and consensus ADMM are integrated with the proposed method to realize the fully distributed cluster-based framework of DDSR. This framework can first determine DER scheduling and switch status for reconfiguration to energize the out-of-service areas from local faults, and then provide the load restoration solution in a distributed manner for total blackouts in large-scale distribution networks. Furthermore, the effectiveness and scalability of the proposed DDSR framework are demonstrated through testing on the IEEE 123-node, IEEE 8500-node, and synthetic 100k-node test feeders.
24 POWER TRANSMISSION AND DISTRIBUTION↗
A Multi-Parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems
Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. Herein, we present novel algorithms for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-parametric programming theory, the main idea is to recast the lower level problem as a multi-parametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.
42 ENGINEERING↗
A Bi-Level Formulation And Solution Method For The Integration Of Process Design And Scheduling
Design and operation decisions of manufacturing plants can often be expressed within a hierarchical structure, where optimal decisions at lower operating level provide constraints for the decision raking at a higher decision level. In this work, we are addressing the case of a hierarchical design and scheduling optimization problem. The integration of design and scheduling decisions can play a big role in designing economically profitable plants and improving their operational performance. This problem can be expressed as a bi-level problem, where design related decisions occur at the upper level and operational scheduling decisions at the lower level. Since discrete decisions are involved in both optimization levels, the resulting formulation typically corresponds to bi-level mixed-integer programming problems (B-MIP). The solution of B-MIP problems is very challenging, and typically requires the use of global optimization techniques, with many algorithms not able to guarantee feasibility. To overcome the challenges in solving this class of problems we propose the use of a multi-parametric based algorithm for the solution of bi-level mixed-integer linear and quadratic programming problems, capable of providing the exact and global solution. The main idea of this approach is to treat the lower scheduling problem as a multi-parametric programming problem in which the design decisions are considered as parameters. Here, the resulting parametric solutions can then be substituted into the upper level design problem, which can be solved as a set of single-level deterministic programming problems. Through the developed formulation and algorithm we are able to supply the decision makers with the exact solution of the integrated design and scheduling problem.
42 ENGINEERING↗
Utilising demand response for distribution service restoration to achieve grid resiliency against natural disasters
The increased frequency of power outages due to natural disasters in recent years has highlighted the urgency of enhancing distribution grid resilience. The effective distribution service restoration (DSR) is an important measure for a resilient distribution grid. In this work, the authors demonstrate that DSR can be significantly improved by leveraging the flexibility provided by the inclusion of demand response (DR). The authors propose a framework for this by considering integrated control of household-level flexible appliances to vary the load demand at the distribution-grid level to improve DSR. The overall framework of the proposed system is modelled as a three-step method considering three optimization problems to (i) calculate feasible controllable aggregated load range for each bus, (ii) determine candidate buses to perform DR and their target load demand, and (iii) maintain the load level in each house through home energy management during the DSR, considering uncertainties in load and solar generation sequentially. The optimization problems are formulated as linear programming, mixed-integer linear programming, and multistage stochastic programming (solved using the stochastic dual dynamic programming) models. Finally, case studies performed in the IEEE 123-node test feeder show improvements in resilience in terms of energy restored compared to the restoration process without DR.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Mathematical programming formulations for satellite synthesis
The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.
Bhasin, Puneet↗