Showing papers on "Stochastic programming published in 2021"
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TL;DR: A transactive energy (TE) mechanism-supported energy sharing strategy to coordinate interconnected MECMs in a regional integrated energy system (RIES), where the uncertainty of renewable energy and loads is taken into account via stochastic programming.
Abstract: Multi-energy complementary microgrids (MECMs) provide an important means to accommodate renewable energy sources due to their abundant adjustable resources and flexible operation modes. However, limited capacity and controllability are the main obstacles that prevent MECMs from participating in the market. In this study, we develop a transactive energy (TE) mechanism-supported energy sharing strategy to coordinate interconnected MECMs in a regional integrated energy system (RIES), where the uncertainty of renewable energy and loads is taken into account via stochastic programming. An RIES operator is introduced to trade with the utility grid as an intermediate player between the electricity market and MECMs. For the TE mechanism, we employ alternating direction method of multipliers (ADMM) algorithm to achieve distributed optimization of energy sharing, which is based on the average of the shared energy residual over all MECMs. A clear economic interpretation exists in the method, wherein shared electrical and thermal energy prices can be obtained. Case studies demonstrate the effectiveness of the multi-energy sharing scheme considering integrated demand response (IDR). Moreover, the distributed algorithm can be implemented and converge easily while respecting MECMs’ individual benefits and private information.
80 citations
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TL;DR: In this paper, the authors proposed a new paradigm digital twin network to build network topology and the stochastic task arrival model in IIoT systems, then they formulated the computation offloading and resource allocation problem to minimize the long-term energy efficiency.
Abstract: The rapid development of industrial Internet of Things (IIoT) requires industrial production towards digitalization to improve network efficiency. Digital Twin is a promising technology to empower the digital transformation of IIoT by creating virtual models of physical objects. However, the provision of network efficiency in IIoT is very challenging due to resource-constrained devices, stochastic tasks, and resources heterogeneity. Distributed resources in IIoT networks can be efficiently exploited through computation offloading to reduce energy consumption while enhancing data processing efficiency. In this article, we first propose a new paradigm digital twin network to build network topology and the stochastic task arrival model in IIoT systems. Then, we formulate the stochastic computation offloading and resource allocation problem to minimize the long-term energy efficiency. As the formulated problem is a stochastic programming problem, we leverage Lyapunov optimization technique to transform the original problem into a deterministic per-time slot problem. Finally, we present asynchronous actor-critic algorithm to find the optimal stochastic computation offloading policy. Illustrative results demonstrate that our proposed scheme is able to significantly outperforms the benchmarks.
73 citations
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TL;DR: This work proposes a decision-dependent distributionally robust optimization model, and develops its exact mixed-integer linear programming reformulation after extensively testing problem characteristics and derives valid inequalities to strengthen the formulation.
68 citations
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TL;DR: The results illustrate the efficacy of this model in manipulating market clearing price in favor of the MES, while different case studies show the privileges of utilizing a hybrid RO-SP method.
65 citations
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TL;DR: This work presents SDDP.jl, an open-source library for solving multistage stochastic programming problems using the Stochastic dual dynamic programming algorithm.
Abstract: We present SDDP.jl, an open-source library for solving multistage stochastic programming problems using the stochastic dual dynamic programming algorithm. SDDP.jl is built on JuMP, an algebraic mod...
59 citations
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53 citations
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TL;DR: This research proposes a comprehensive two-stage scenario-based mathematical model to design a resilient food supply chain under demand uncertainty and epidemic disruptions, and covers the special characteristics of FSC, such as products perishability in time and discount prices based on product's age.
47 citations
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TL;DR: In this paper, an optimal framework for the resilience-oriented design (ROD) in distribution networks to protect these grids against extreme weather events such as earthquakes and floods is presented.
47 citations
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TL;DR: In this article, the authors established a three-level supply chain composed of plants, distribution centers, and retailers, and studied the location of distribution centers in the supply chain network and the carbon emissions during processing and transportation.
Abstract: This paper established a three-level supply chain composed of plants, distribution centers, and retailers, and studied the location of distribution centers in the supply chain network and the carbon emissions during processing and transportation. In a random and fuzzy environment, the research objective is to minimize the supply chain’s cost and carbon emission. The multi-objective uncertain equilibrium model of the green supply chain network is established by introducing opportunity constraints, and the stability of the model can be enhanced by using variance function and risk function. Then this research integrated the theory of stochastic programming and fuzzy mathematical programming and employed Monte Carlo simulation; the sample mean approximation, chance-constrained programming and fuzzy expectation to deal with the random parameters and fuzzy parameters in the model so that the uncertain model is clarified. Further, the authors used the hierarchical method, the weighted ideal point method, restriction method, and weighted ideal point method to solve the multi-objective model. Finally, a numerical example is provided to demonstrate the feasibility of the model.
44 citations
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TL;DR: The proposed framework is found to outperform well-established policy baselines and facilitate adept prescription of inspection and intervention actions, in cases where decisions must be made in the most resource- and risk-aware manner.
43 citations
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TL;DR: A stochastic programming model is defined, and a powerful optimization function is used to reach the optimal power received from the main grid to a private microgrid, that is the “LAMBDA lab MG” testbed placed at the Sapienza University of Rome.
Abstract: In this article, a cost-based mathematical optimization is used to evaluate the optimal amount of imported power from the public main grid to a private microgrid (MG), that is the “LAMBDA lab MG” testbed placed at the Sapienza University of Rome. In this regard, this article considers five tests based on using different sources, including a photovoltaic (PV) array, an emergency generator set, a fuel cell, and the main grid, for load satisfaction. The “LAMBDA lab” can be considered as a “multisource multioutput energy hub” with three optional sources and both electrical and heat demands in output. This article considers PV production and load demand as indeterministic parameters and evaluates the problem under uncertainties. As a result, a stochastic programming model is defined, and a powerful optimization function is used to reach the optimal power received from the main grid. Besides, information gap decision theory is used to model the robustness of the problem against uncertainties associated with renewable generation units (PV system) and electricity loads applied on a real case for the first time. In the result section, the contribution of each source in electrical and heat load demands is presented in addition to the cost of each test by evaluating the effect of demand response of 15%. Finally, a comparison between the stochastic programming method and IGDT has been accomplished.
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TL;DR: By implementing the RCGTEP model on an IEEE standard transmission network, the numerical results confirm the capability of this method in improving the economic, operation, angular stability and resiliency indices of the power system simultaneously.
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TL;DR: In this article, a stochastic p-robust optimization method (SPROM) is proposed to guarantee robust operation of the system under the worst-case scenario, which combines both stochiastic programming and robust optimization approaches where minimizes the worstcase cost or regret level.
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TL;DR: The model is formulated as a bi-level stochastic programming problem based on uncertain programming theory, and corresponding equivalent model is also given to solve the problem effectively and can achieve a win-win situation between multi-energy aggregator and consumers.
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TL;DR: This paper proposes a non-accelerated and an accelerated directional derivative method which has a complexity bound which is similar to the gradient-based algorithm, that is, without any dimension-dependent factor.
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TL;DR: A method for coordinated network expansion planning (CNEP) in which the difference between the total cost and the flexibility benefit is minimized and is tested on the IEEE 6-bus and 24-bus test systems using GAMS software.
Abstract: This paper presents a method for coordinated network expansion planning (CNEP) in which the difference between the total cost and the flexibility benefit is minimized. In the proposed method, the generation expansion planning (GEP) of wind farms is coordinated with the transmission expansion planning (TEP) problem by using energy storage systems (ESSs) to improve network flexibility. To consider the impact of the reactive power in the CNEP problem, the AC power flow model is used. The CNEP constraints include the AC power flow equations, planning constraints of the different equipment, and the system operating limits. Therefore, this model imposes hard nonlinearity onto the problem, which is linearized by the use of first-order Taylor’s series and the big-M method as well as the linearization of the circular plane. The uncertainty of loads, the energy price, and the wind farm generation are modeled by scenario-based stochastic programming (SBSP). To determine the effectiveness of the proposed solution approach, it is tested on the IEEE 6-bus and 24-bus test systems using GAMS software.
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TL;DR: This tutorial discusses distributionally robust and risk averse approaches to multistage stochastic programming, and the involved concept of time consistency.
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TL;DR: In this paper, an optimal coordination method for energy dispatch and voyage scheduling is proposed for a renewable energy-integrated hybrid AC/DC multi-energy ship (MES) microgrid under the continuous ship swinging.
Abstract: In this paper, an optimal coordination method for energy dispatch and voyage scheduling is proposed for a renewable-energy-integrated hybrid AC/DC multi-energy ship (MES) microgrid under the continuous ship swinging. In the MES microgrid, all the onboard units are dispatched coordinately with higher flexibility for providing multiple energies. To guarantee the reliable ship operation, diverse uncertainties from solar irradiation, ship swinging angle, and onboard multi-energy demands are managed by an adaptive risk-averse stochastic programming approach to minimize the voyage cost and conditional value-at-risk. Besides, chance constraints are introduced to leverage the quality of thermal service given the thermal inertia. To speed up the solution process, the original nonlinear/nonconvex operation constraints are reformulated to a mixed-integer quadratically constrained programming form by linearization/convexification and scenario generation/reduction methods. Then the problem can be efficiently solved by commercial solvers. Finally, case studies are conducted on a test MES microgrid. The simulation results verify that the proposed method is effective in coordinating multi-energy dispatch and voyage scheduling, minimizing operating cost/risk, and immunizing against diverse uncertainties.
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TL;DR: A regret-matching technique is introduced to model the bounded rationality of PEV owners in deciding the choice to use different charging options for recharging their vehicle, as a dependency with respect to the incentive value and the accessibility of the charging service in long-term horizon.
Abstract: This article proposes a new planning framework for optimal allocation of parking lot (PL)-based charging infrastructures to facilitate the efficient integration of plug-in electric vehicles (PEVs). Unlike existing works, the present article explicitly considers the uncertain implications of incentive policy on PEV owners’ charging behaviors and its effects in PL planning. For this aim, a regret-matching technique is introduced to model the bounded rationality of PEV owners in deciding the choice to use different charging options for recharging their vehicle, as a dependency with respect to the incentive value and the accessibility of the charging service in long-term horizon. Such endogenous uncertainties are considered simultaneously with the inherent exogenous randomness of PEV demand and captured by the proposed PL planning model using a proper scenario generation method. The resulting model turns out to be a two-stage stochastic programming with decision-dependent uncertainties and it is solved by using the genetic algorithm. Numerical studies based on an illustrative test system verify the effectiveness of the proposed model and the approach.
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TL;DR: This research proposes a choice modeling approach embedded in a two-stage stochastic programming model to determine the optimal layout and types of EV supply equipment for a community while considering randomness in demand and drivers’ behaviors.
Abstract: Electric vehicles (EVs) provide a cleaner alternative that not only reduces greenhouse gas emissions but also improves air quality and reduces noise pollution. The consumer market for electrical vehicles is growing very rapidly. Designing a network with adequate capacity and types of public charging stations is a challenge that needs to be addressed to support the current trend in the EV market. In this research, we propose a choice modeling approach embedded in a two-stage stochastic programming model to determine the optimal layout and types of EV supply equipment for a community while considering randomness in demand and drivers’ behaviors. Some of the key random data parameters considered in this study are: EV’s dwell time at parking location, battery’s state of charge, distance from home, willingness to walk, drivers’ arrival patterns, and traffic on weekdays and weekends. The two-stage model uses the sample average approximation method, which asymptotically converges to an optimal solution. To address the computational challenges for large-scale instances, we propose an outer approximation decomposition algorithm. We conduct extensive computational experiments to quantify the efficacy of the proposed approach. In addition, we present the results and a sensitivity analysis for a case study based on publicly available data sources.
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TL;DR: An integrated modeling approach addressing the online channel-driven distribution network deployment (e-DND) problem under uncertainty is presented and an exact solution approach combining scenario sampling and the integer L-shaped method is proposed.
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TL;DR: The proposed SCGTEP is tested on the 6-bus and 118-bus IEEE networks in the GAMS software and can be simultaneously improved operation and security indices about 34.5% and 100%, respectively, compared to the power flow analysis based on the optimal location of generation units and transmission lines.
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TL;DR: This work proposes the use of a two-stage stochastic decision-making approach for designing and operating an MMG considering both the capital cost for installing the electric cables and operating cost.
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TL;DR: In this paper, two mixed-integer linear programming (MILP) methods are proposed to solve the scheduling problem of thermal units and energy storage with uncertainties while ensuring solution robustness and nonanticipativity.
Abstract: Generation scheduling decision-making of power systems with renewable energy and energy storage (ES) is a multistage stochastic programming problem in nature, in which unit commitment (UC) decisions have to be made one day ahead before uncertainties are revealed, and hourly economic dispatch (ED) decisions are successively determined when real uncertainty realizations are observed gradually (i.e., nonanticipativity). To this end, inappropriate ED decisions at current hour may cause infeasibility of future ED decisions (i.e., robustness). Thus, how to properly schedule thermal unit outputs and ES charging/ discharging power against uncertainties becomes an important and urgent issue. In this paper, two mixed-integer linear programming (MILP) methods are proposed to solve the scheduling problem of thermal units and ESs with uncertainties while ensuring solution robustness and nonanticipativity: explicit and implicit decision methods. Specifically, explicit decision method directly assumes affine policies between decision variables and uncertainty realizations; implicit decision method explores safe ranges of thermal unit outputs and ES state-of-charge (SOC) levels to guarantees feasibility of future ED solutions. Both methods can guarantee the nonanticipativity and robustness of multistage solutions. Numerical tests illustrate effectiveness of the proposed methods.
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TL;DR: A bi-level stochastic programming is proposed for the integrated heat-energy and reserve scheduling of the smart MGs in presence of energy storage system (ESS) and demand response (DR) programs based on the maximization of total social welfare as objective function.
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TL;DR: In this article, the authors proposed a hybrid decentralized robust optimization-stochastic programming (DRO-SP) model based on the alternating direction method of multipliers to coordinate the management of entities.
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TL;DR: In this article, a data-driven distributionally robust co-optimization model for the peer-to-peer (P2P) energy trading and network operation of interconnected micro-grids is proposed.
Abstract: This paper proposes a data-driven distributionally robust co-optimization model for the peer-to-peer (P2P) energy trading and network operation of interconnected microgrids (MGs). In particular, three-phase unbalanced MG networks are considered to account for the implementation practices, and the emerging soft open point (SOP) technology is used for the flexible connection of the multi-MGs. First, the energy management in individual MGs is modeled as a distributionally robust optimization (DRO) problem considering the P2P energy trading options and various operational constraints. Later, a novel decentralized and incentive-compatible pricing strategy is developed for P2P energy trading using the alternating direction method of multipliers (ADMM). Furthermore, the uncertainties in load consumption and renewable generation (RG) are taken into account and the Wasserstein metric (WM) is used to construct the ambiguity set of the uncertainty probability distributions (PDs). Consequently, only historical data is needed rather than prior knowledge about the actual PDs. Finally, the equivalent linear programming reformulations are derived for the DRO model to achieve computational tractability. Numerical tests on four interconnected MGs corroborate the advantages of the proposed P2P energy trading scheme and also demonstrate that the proposed DRO model is more effective in handling the uncertainties compared to the robust optimization (RO) and the stochastic programming (SP) models.
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TL;DR: A nested decomposition method is proposed which applies the stochastic dual dynamic integer programming (SDDIP) method to address computational intractabilities of the proposed ADNP approach.
Abstract: This paper presents a multi-period active distribution network planning (ADNP) with distributed generation (DG). The objective of the proposed ADNP is to minimize the total planning cost, subject to both investment and operation constraints. The paper proposes a multi-stage stochastic optimization model to address DG uncertainties over several periods, in which the decisions are made sequentially by only using the present-stage information. A nested decomposition method is proposed which applies the stochastic dual dynamic integer programming (SDDIP) method to address computational intractabilities of the proposed ADNP approach. The presented numerical results and discussions on a 33-bus distribution system and a large-scale 906-bus system verify the effectiveness of the proposed ADNP method and its solution method.
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TL;DR: A new entity called multiple energy distribution company (MEDC) is proposed to meet the electricity, gas, and heat demands of consumers in the presence of renewable energy resources and multi-energy conversion technologies with the lowest operating cost.
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TL;DR: A stochastic optimal energy management and pricing model for LSE with aggregated TCLs and energy storage based on the Stackelberg game and Stochastic programming is proposed.
Abstract: With the development of demand-side management in the smart grid, load-serving entity (LSE) plays a more important role for consumers, which purchases energy from the electricity market and sells it to consumers. Moreover, aggregated thermostatically controlled loads (TCLs) in smart buildings can provide additional demand response capacities and require efficient energy management methods. This article proposes a stochastic optimal energy management and pricing model for LSE with aggregated TCLs and energy storage based on the Stackelberg game and stochastic programming. The energy management and pricing problem are formulated as a bilevel optimization model. The upper level model aims to maximize LSE's expected profit under market price uncertainties and determines the offering prices to consumers. According to the offering price from upper level model, the lower level model optimizes the power purchasing pattern for consumers of two types of buildings with TCLs: factory and office buildings. The nonlinear bilevel model is reformulated and converted into mixed-integer linear programming using a strong duality theory. The proposed model is validated by numerical studies based on real market prices from the PJM electricity market. In addition, the impacts of energy storage, number of buildings, comfortable indoor temperature limits, and offering price limits on LSE's profit are analyzed.