Data-driven Wasserstein distributionally robust chance-constrained optimization for crude oil scheduling under uncertainty

Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.

Distributionally robust optimization based chance-constrained energy management for hybrid energy powered cellular networks

Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-mittent,imposing formidable challenges on reliably satisfying users'time-varying wireless traffic demands.In addition,the probability distribution of the renewable energy or users’wireless traffic demand is not always fully known in practice.In this paper,we minimize the total energy cost of a hybrid-energy-powered cellular network by jointly optimizing the energy sharing among base stations,the battery charging and discharging rates,and the energy purchased from the grid under the constraint of a limited battery size at each base station.In solving the formulated non-convex chance-constrained stochastic optimization problem,a new ambiguity set is built to characterize the uncertainties in the renewable energy and wireless traffic demands according to interval sets of the mean and covariance.Using this ambiguity set,the original optimization problem is transformed into a more tractable second-order cone programming problem by exploiting the distributionally robust optimization approach.Furthermore,a low-complexity distributionally robust chance-constrained energy management algo-rithm,which requires only interval sets of the mean and covariance of stochastic parameters,is proposed.The results of extensive simulation are presented to demonstrate that the proposed algorithm outperforms existing methods in terms of the computational complexity,energy cost,and reliability.

Distributionally Robust Newsvendor Model for Fresh Products under Cap-and-Offset Regulation

The cap-and-offset regulation is a practical scheme to lessen carbon emissions.The retailer selling fresh products can adopt sustainable technologies to lessen greenhouse gas emissions.We aim to analyze the optimal joint strategies on order quantity and sustainable technology investment when the retailer faces stochastic market demand and can only acquire the mean and variance of distribution information.We construct a distributionally robust optimization model and use the Karush-Kuhn-Tucker(KKT)conditions to solve the analytic formula of optimal solutions.By comparing the models with and without investing in sustainable technologies,we examine the effect of sustainable technologies on the operational management decisions of the retailer.Finally,some computational examples are applied to analyze the impact of critical factors on operational strategies,and some managerial insights are given based on the analysis results.

Distributed Robust UAVs Formation Control Based on Semidefinite Programming

The formation control of unmanned aerial vehicle(UAV)swarms is of significant importance in various fields such as transportation,emergency management,and environmental monitoring.However,the complex dynamics,nonlinearity,uncertainty,and interaction among agents make it a challenging problem.In this paper,we propose a distributed robust control strategy that uses only local information of UAVs to improve the stability and robustness of the formation system in uncertain environments.We establish a nominal control strategy based on position relations and a semi-definite programming model to obtain control gains.Additionally,we propose a robust control strategy under the rotation setΩto address the noise and disturbance in the system,ensuring that even when the rotation angles of the UAVs change,they still form a stable formation.Finally,we extend the proposed strategy to a quadrotor UAV system with high-order kinematic models and conduct simulation experiments to validate its effectiveness in resisting uncertain disturbances and achieving formation control.

A Distributionally Robust Optimization Method for Passenger Flow Control Strategy and Train Scheduling on an Urban Rail Transit Line

Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestion and further reduce the risk of cross-infection,a novel two-stage distributionally robust optimization(DRO)model is explicitly constructed,in which the probability distribution of stochastic scenarios is only partially known in advance.In the proposed model,the mean-conditional value-at-risk(CVaR)criterion is employed to obtain a tradeoff between the expected number of waiting passen-gers and the risk of congestion on an urban rail transit line.The relationship between the proposed DRO model and the traditional two-stage stochastic programming(SP)model is also depicted.Furthermore,to overcome the obstacle of model solvability resulting from imprecise probability distributions,a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form.A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming(MILP)solver is developed to improve the computational efficiency of large-scale instances.Finally,a series of numerical examples with real-world operation data are executed to validate the pro-posed approaches.

Distributionally Robust Optimal Dispatch of Virtual Power Plant Based on Moment of Renewable Energy Resource

Virtual power plants can effectively integrate different types of distributed energy resources,which have become a new operation mode with substantial advantages such as high flexibility,adaptability,and economy.This paper proposes a distributionally robust optimal dispatch approach for virtual power plants to determine an optimal day-ahead dispatch under uncertainties of renewable energy sources.The proposed distributionally robust approach characterizes probability distributions of renewable power output by moments.In this regard,the faults of stochastic optimization and traditional robust optimization can be overcome.Firstly,a second-order cone-based ambiguity set that incorporates the first and second moments of renewable power output is constructed,and a day-ahead two-stage distributionally robust optimization model is proposed for virtual power plants participating in day-ahead electricity markets.Then,an effective solution method based on the affine policy and second-order cone duality theory is employed to reformulate the proposed model into a deterministic mixed-integer second-order cone programming problem,which improves the computational efficiency of the model.Finally,the numerical results demonstrate that the proposed method achieves a better balance between robustness and economy.They also validate that the dispatch strategy of virtual power plants can be adjusted to reduce costs according to the moment information of renewable power output.

Distributed Robust Optimal Dispatch for the Microgrid Considering Output Correlation between Wind and Photovoltaic

As an effective carrier of integrated clean energy,the microgrid has attracted wide attention.The randomness of renewable energies such as wind and solar power output brings a significant cost and impact on the economics and reliability of microgrids.This paper proposes an optimization scheme based on the distributionally robust optimization(DRO)model for a microgrid considering solar-wind correlation.Firstly,scenarios of wind and solar power output scenarios are generated based on non-parametric kernel density estimation and the Frank-Copula function;then the generated scenario results are reduced by K-means clustering;finally,the probability confidence interval of scenario distribution is constrained by 1-norm and∞-norm.The model is solved by a column-and-constraint generation algorithm.Experimental studies are conducted on a microgrid system in Jiangsu,China and the obtained scheduling solution turned out to be superior under wind and solar power uncertainties,which verifies the effectiveness of the proposed DRO model.

考虑移动氢能存储的港口多能微网两阶段分布鲁棒优化调度

为有效应对海上风电固有的间歇及波动性给港口多能微网带来的不确定性风险,提出一种考虑移动氢能存储的港口多能微网两阶段分布鲁棒优化调度模型。首先,结合Wasserstein距离实现风电出力概率分布模糊集的精确刻画,并通过非参数核密度估计拟合海上风电预测误差概率分布,获得不同置信水平下风电出力区间及场景。其次,分析氢能船舶、汽车等移动氢能存储资源对间歇性风电出力的能源存储潜力,并结合用能心理、交通属性差异,将两者分别建模为激励型、价格型需求响应,实现港口移动氢能存储灵活性资源的高效聚合。再次,针对含移动氢能存储的港口多能微网,构建基于概率分布模糊集的日前-日内两阶段分布鲁棒优化调度模型,并运用线性决策规则与强对偶理论将其转换为混合整数线性规划模型求解。最后,基于海上风电实测数据进行仿真验证。结果证明,移动氢能存储可显著提升港口多能微网的低碳灵活性,所提模型在兼顾港口多能微网经济性的同时,可进一步保证风电不确定性风险下的鲁棒性。

基于分布鲁棒优化的车-站-网日前能量管理与交易

为考虑上级电网电价、光伏出力等多重多层级不确定性对车-站-网互动博弈模型的影响,且充分体现配电网主动管理技术支撑效果,文中提出了一种基于分布鲁棒优化的车-站-网能量管理与交易方法。首先,针对主动配电网内多元主体能量管理与交易问题,建立了配电网运营商、充电站和电动汽车的日前市场互动框架。其次,融合主动网络管理技术和网络约束,在配电网运营商与聚合了电动汽车的多个充电站之间构建了以多主体各自利益最大为目标的双层Wasserstein分布鲁棒互动博弈模型。然后,提出了结合Karush-Kuhn-Tucker条件、对偶原理和大M法的化简方法以解决多层级不确定性造成的求解难题,将双层Wasserstein分布鲁棒模型转化为单层混合整数二阶锥规划模型,并利用商业求解器YALMIP/GUROBI进行了求解。最后,通过算例仿真验证了所提模型和方法的有效性。

基于KL散度距离处理风电不确定性的负荷恢复分布鲁棒优化

在构建以新能源为主体的新型电力系统的背景下,在恢复控制过程中积极利用新能源并充分应对其对运行安全带来的潜在风险对于减小停电损失具有重要意义。首先,为了表征风电出力的不确定性,采用KL散度(Kullback-Leibler)距离作为筛选极端风电出力场景的控制条件,并据此构建模糊集作为风电出力典型场景。在满足相关运行安全约束的前提下,建立了以最大化加权负荷恢复量为优化目标的分布鲁棒优化模型以制定计及风电的负荷恢复方案。经松弛处理和对偶转换所得到的混合整数二阶锥模型可调用商业求解器求解。以接入规模风电场的IEEE 10机39母线系统为例进行仿真,结果表明:相比于传统的鲁棒优化方法,该方法降低了优化结果的保守性,有助于加快负荷恢复,减小停电损失。

含整体煤气化燃料电池-碳捕集电厂的风火储系统分布鲁棒调度方法

整体煤气化燃料电池(integrated gasification fuel cell,IGFC)是与碳捕集技术高度适配的清洁、高效、稳定的绿色煤电技术,有望克服传统碳捕集技术在低浓度CO_(2)环境下产生的高成本、高能耗问题。该文构建含IGFC碳捕集电厂的风火储发电系统。研究IGFC碳捕集电厂的运行机理,对IGFC内部各环节建立数学模型,提出工况匹配时燃烧利用率和阴极空气利用率需要满足的运行条件,并针对该型碳捕集电厂的电碳特性进行分析。为计及风电出力的不确定性,构建风火储系统的两阶段分布鲁棒经济调度模型,引入k阶适应性理论,提出基于正交支撑子集策略的求解方法来获得鲁棒对等式。最后,在改进IEEE-30节点系统中进行算例分析,结果表明,该型碳捕集电厂可利用阳极碳富集的优势,实现系统低碳经济调度的目标,并验证所提优化方法能为可行解提供可解释性。

冷能梯级利用的港口多能微网双层不确定性经济调度

为有效挖掘港口液化天然气(LNG)冷能利用的低碳灵活性潜力,充分发挥多时间尺度协同优化效应,提出一种考虑LNG冷能梯级利用的港口多能微网(MEMG)鲁棒-随机双层不确定性经济调度模型。首先,考虑LNG深冷-中冷-浅冷等各个温区的低碳灵活性潜力,建立低温碳捕集-冷能发电-直接冷却的冷能梯级利用模型,并以此为基础形成捕集-存储-利用协同的碳处理流程。其次,根据等概率逆变换生成考虑预测误差时序相关性的风电场景,并基于Wasserstein距离的0-1规划模型进行场景削减。再次,针对风电预测误差随时间尺度增加而增大的特性,构建多时间尺度优化的鲁棒-随机双层不确定性经济调度模型,上层通过分布鲁棒优化保证日前预调度决策鲁棒性,下层通过随机优化保证日内滚动调度决策经济性。最后,仿真结果表明,所提考虑冷能梯级利用的鲁棒-随机双层调度模型在解决日前长时间尺度预测精度低与日内短时间尺度易陷入局部最优矛盾的同时,可赋予港口MEMG更多经济性、低碳性及供电灵活性。

考虑柔性电/热负荷的综合能源系统分布鲁棒优化调度

综合能源系统(integrated energy system,IES)的效益分析不仅取决于能源供给侧的调度方案,也受到需求侧用能方式的影响。基于此,在IES的需求侧引入柔性负荷响应,以平滑负荷曲线,进一步提升IES的风电消纳能力和经济效益;同时为尽量减小供能侧风电出力不确定性的影响、实现调度方案鲁棒性与经济性的均衡,构建了考虑柔性电负荷和柔性热负荷的IES两阶段分布鲁棒优化调度模型:预调度阶段以IES的日前综合调度成本最低为目标;再调度阶段以风电历史数据为基础,寻找最恶劣风电出力概率分布下的最优机组调节方案,并使用列约束生成算法进行求解。最后,采用算例验证了该模型的有效性。

面向山区铁路工程物流基地选址的分布鲁棒优化模型

山区铁路传统工程建设运输物流基地选址模型较少将未来可能需求纳入考量范畴,忽视了此类临时工程在社会效益方面的可持续发展潜力。针对此问题,在传统工程建设运输物流基地选址模型考虑影响因素及假设基础上,加入永临结合决策变量,构建同时考虑未来社会需求分布的不确定性的工程选址模型。以工程地质条件、建设施工成本、道路情况等多个因素作为评价指标,采用预测未来社会需求并引入波动变量构建非精确机会约束的方式,提出适用于永临结合模式设施选址的“多面体-DRO”二阶段分布鲁棒模型。研究结果表明:服务水平是选址决策的主要影响因素;对于高海拔施工点,选择附近的高海拔设施更加可靠;为尽可能服务高海拔地区,永久设施点更倾向于在高海拔地区修建。建立的模型能够有效抵抗不确定性带来的代价,从而避免决策失误,在山区铁路工程永临结合设施修建方面有着重要理论价值和实际指导意义。

基于分布鲁棒联合机会约束的光储充电站滚动优化调控模型

随着电动汽车的普及和清洁能源装机容量的日益增加,光储充电站展现出广阔的应用前景。针对电动汽车随机接入影响下光储充电站功率难以精准调控的问题,提出基于分布鲁棒联合机会约束(DRJCC)的光储充电站滚动优化调控模型。将基于混合整数规划(MIP)的精确DRJCC模型、基于CVaR-Slim凸松弛的DRJCC模型、基于Bonferroni不等式的DRJCC模型进行对比,通过算例分析验证了所提优化调控模型的有效性。算例分析表明,所提基于CVaR-Slim凸松弛的DRJCC模型能够同时满足更多电动汽车的充电需求。

考虑发用电相似性的海上风电中长期双边协商交易优化决策模型

海上风电是未来最有潜力的可再生能源之一,但其出力具有随机性和波动性。为了更好地促进海上风电的市场化消纳,文中基于海上风电商与负荷聚合商间的中长期双边协商交易构建了优化决策模型。首先,通过时间序列相似性评估方法,为目标海上风电寻找最优的用电负荷组合。其次,考虑需求响应备用容量配置和发用电曲线预测误差,构建了基于两阶段分布鲁棒优化的中长期交易优化决策模型,为海上风电配置适应其未来一段时间内出力特性的需求响应资源,并合理调整中长期交易曲线。最后,通过仿真算例验证了所提模型的有效性和实用性。

考虑风险和碳交易机制的微电网分布鲁棒优化调度

提高微电网风电的消纳能力是实现双碳目标的重要手段。该文构建了一种考虑极限场景和净负荷条件风险价值的微电网低碳分布鲁棒优化模型。首先,针对源-荷不确定性构造基于Wasserstein距离的概率分布模糊集,并考虑极限场景修正该模糊集,以提高模糊集的鲁棒性,减少场景数目,提高求解效率。其次,以包括供能成本、阶梯式碳交易成本和风险成本的微电网日运行成本最小为优化目标,建立分布鲁棒优化调度模型,并利用分段线性近似法和对偶理论将模型转换为线性规划问题求解。最后,通过算例仿真进行验证,结果表明,考虑极限场景的分布鲁棒优化方法具有较强的鲁棒性;引入阶梯式碳交易成本可以有效减少微电网的碳排放量,并提高风电的消纳能力;净负荷条件风险价值可以有效平衡微电网运行的经济性与风险性。

考虑特性分类批处理负荷可调节能力的数据中心微网灵活性设备分布鲁棒容量配置方法

微网灵活性设备主要用于平抑源荷两侧的波动,其容量配置方法应考虑源荷不确定性的影响,而含数据中心微网的灵活性设备容量配置方法还应进一步考虑数据中心负荷的可调节特性。考虑数据中心批处理负荷的可调节能力和源荷不确定性因素,提出一种灵活性设备容量配置方法。根据负荷特性的不同,将批处理负荷划分为2类以更加准确地量化其可调节能力,一类为带宽时序可变限时可平移负荷,另一类为带宽时序不变可中断平移负荷,对这2类批处理负荷进行详细分析并给出一般性的建模方法;构建数据驱动下的min-max-min两阶段分布鲁棒优化容量配置模型,利用1-范数和∞-范数约束场景概率分布模糊集,采用列和约束生成算法对该模型进行化简求解。对某省数据中心微网进行算例分析,验证了所提方法的有效性。

基于LSTM-CGAN的多微网数据驱动分布鲁棒协同优化运行策略

新能源的强烈不确定性给多微网协同运行带来了可靠性和安全性的巨大挑战。为此,提出一种基于长短期记忆(long short-term memory, LSTM)网络和条件生成对抗网络(conditional generative adversarial networks, CGAN)的多微网数据驱动两阶段分布鲁棒协同优化调度模型。首先,为更准确地描述新能源的不确定性,该模型以LSTM-CGAN生成和K-means++聚类算法削减得到的场景集作为分布鲁棒优化集合的初始新能源场景。其中CGAN网络模型使用Wasserstein距离作为判别器损失函数,以新能源日前预测值作为生成对抗网络的条件变量,并采用LSTM构建生成器和判别器。其次,提出一种基于多能点对点交易贡献率的利益分配方法,以实现合作收益的公平分配。然后,为保护各主体隐私并提高求解效率,提出一种耦合可并行计算列与约束生成(columnand constraint generation, C&CG)的交替方向乘子法(alternating direction multiplier method, ADMM)进行求解能量交易问题。算例结果表明,所提场景驱动方法生成的场景集能更准确、更有效地描述新能源的不确定性,能兼顾系统的鲁棒性、经济性和隐私性,并实现每个主体公平合理的利益分配。

考虑碳减排的共燃发电厂鲁棒可信性选址决策优化

基于“碳达峰、碳中和”战略目标,研究考虑碳减排的共燃发电厂选址决策问题.受天气状况、市场环境等外部因素的影响,生物质供应能力和生物质价格等参数具有不确定性,构造一个非精确可能性分布集来描述问题中的不确定参数,进而建立一个分布鲁棒可信性选址优化模型.通过推导鲁棒可信性目标和鲁棒可信性约束的等价形式,将原模型重构为一个可计算的混合整数线性规划模型.最后利用算例分析验证提出方法的有效性.