Distributionally robust model predictive control for constrained robotic manipulators based on neural network modeling

A distributionally robust model predictive control(DRMPC)scheme is proposed based on neural network(NN)modeling to achieve the trajectory tracking control of robot manipulators with state and control torque constraints.First,an NN is used to fit the motion data of robot manipulators for data-driven dynamic modeling,converting it into a linear prediction model through gradients.Then,by statistically analyzing the stochastic characteristics of the NN modeling errors,a distributionally robust model predictive controller is designed based on the chance constraints,and the optimization problem is transformed into a tractable quadratic programming(QP)problem under the distributionally robust optimization(DRO)framework.The recursive feasibility and convergence of the proposed algorithm are proven.Finally,the effectiveness of the proposed algorithm is verified through numerical simulation.

Risk Constrained Self-scheduling of AA-CAES Facilities in Electricity and Heat Markets:A Distributionally Robust Optimization Approach

Advanced adiabatic compressed air energy storage(AA-CAES)has the advantages of large capacity,long service time,combined heat and power generation(CHP),and does not consume fossil fuels,making it a promising storage technology in a low-carbon society.An appropriate self-scheduling model can guarantee AA-CAES’s profit and attract investments.However,very few studies refer to the cogeneration ability of AA-CAES,which enables the possibility to trade in the electricity and heat markets at the same time.In this paper,we propose a multimarket self-scheduling model to make full use of heat produced in compressors.The volatile market price is modeled by a set of inexact distributions based on historical data through-divergence.Then,the self-scheduling model is cast as a robust risk constrained program by introducing Stackelberg game theory,and equivalently reformulated as a mixed-integer linear program(MILP).The numerical simulation results validate the proposed method and demonstrate that participating in multienergy markets increases overall profits.The impact of uncertainty parameters is also discussed in the sensibility analysis.

Distributionally robust optimization of home energy management system based on receding horizon optimization

This paper investigates the scheduling strategy of schedulable load in home energy management system(HEMS)under uncertain environment by proposing a distributionally robust optimization(DRO)method based on receding horizon optimization(RHO-DRO).First,the optimization model of HEMS,which contains uncertain variable outdoor temperature and hot water demand,is established and the scheduling problem is developed into a mixed integer linear programming(MILP)by using the DRO method based on the ambiguity sets of the probability distribution of uncertain variables.Combined with RHO,the MILP is solved in a rolling fashion using the latest update data related to uncertain variables.The simulation results demonstrate that the scheduling results are robust under uncertain environment while satisfying all operating constraints with little violation of user thermal comfort.Furthermore,compared with the robust optimization(RO)method,the RHO-DRO method proposed in this paper has a lower conservation and can save more electricity for users.

A Data-driven Distributionally Robust Operational Model for Urban Integrated Energy Systems

A multi-energy conversion can effectively increase the utilization of renewable energy in the urban integrated energy system(UIES).Meanwhile,the uncertainties of renewable energy resources(e.g.,wind energy)also bring increased challenges to the operation of UIES.In this study,a typical two-stage datadriven distributionally robust operation(DDRO)model based on finite scenarios is proposed for UIES including power,gas and heat networks to obtain a salient strategy from both an economic and robustness perspective.In the first stage,the forecasted information for wind power is especially included to improve the economic aspect of robust decisions.The worst probability distribution for the selected known real-time wind power scenarios can be identified in the second stage where the power differences caused by the real-time uncertainties of wind power can be mitigated by flexible regulation of energy purchasing and coupling units(such as gas turbine,power to gas equipment,electric boiler and gas boiler).Moreover,norm-1 and norm-inf co-constraints are utilized to construct a confidence set for the probability distributions of uncertain wind power.The whole two-stage model is solved by the column-and-constraint generation(CCG)algorithm.Finally,case studies are conducted to show the performance of the proposed model and various approaches.Index Terms-Data-driven methods,distributionally robust optimization,urban integrated energy system,wind power.

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。

考虑灵活爬坡产品的虚拟电厂两阶段分布鲁棒优化运营策略

随着“碳达峰·碳中和”目标的提出,可再生能源大规模并网对电力系统灵活运行提出了更高要求。虚拟电厂(VPP)通过聚合分布式资源,将灵活爬坡产品(FRP)纳入运营策略,参与多类型电力市场以提升运营收益。基于此,提出了考虑FRP的VPP两阶段分布鲁棒优化(DRO)运营策略。首先,考虑高比例可再生能源渗透率下的FRP市场,结合多类型分布式资源运行特性,提出VPP参与多类型电力市场的优化运营框架;其次,结合基于Wasserstein距离的可再生能源出力不确定集和基于场景分析法的电力市场价格典型场景集,构建考虑FRP的VPP日前投标和日内调度两阶段DRO模型;最后,以某VPP为例对所提模型进行有效性验证。算例结果表明,所提VPP运营策略具有较好的调度经济性与风险鲁棒性,在参与多类型电力市场交易中能够实现运营收益最大化。

Distributionally Robust Economic Dispatch Using IDM for Integrated Electricity-heat-gas Microgrid Considering Wind Power

Multi-energy microgrids,such as integrated electricity-heat-gas microgrids(IEHS-MG),have been widely recognized as one of the most convenient ways to connect wind power(WP).However,the inherent intermittency and uncertainty of WP still render serious power curtailment in the operation.To this end,this paper presents an IEHS-MG model equipped with power-to-gas technology,thermal storage,electricity storage,and an electrical boiler for improving WP utilization efficiency.Moreover,a two-stage distributionally robust economic dispatch model is constructed for the IEHSMG,with the objective of minimizing total operational costs.The first stage determines the day-ahead decisions including on/off state and set-point decisions.The second stage adjusts the day-ahead decision according to real-time WP realization.Furthermore,WP uncertainty is characterized through an Imprecise Dirichlet model(IDM)based ambiguity set.Finally,Column-and-Constraints Generation method is utilized to solve the model,which provides a day-ahead economic dispatch strategy that immunizes against the worst-case WP distributions.Case studies demonstrate the presented IEHS-MG model outperforms traditional IEHS-MG model in terms of WP utilization and dispatch economics,and that distributionally robust optimization can handle uncertainty effectively.

分布鲁棒优化方法在电力系统中的理论分析与应用综述

清洁能源、电价等不确定因素对电力系统的规划运行有着重要影响,而分布鲁棒优化(DRO)方法因结合了随机优化和鲁棒优化在处理不确定性方面的优点逐渐受到学者们的关注,文中对DRO方法在电力系统领域的应用情况进行综述。首先,阐述了DRO方法的特点,并与其他不确定性处理方法进行了对比分析。其次,介绍了不同类型的DRO方法在电力系统中的应用现状,并分析了各种DRO方法(包括概率密度、矩信息两大类及基于这两大类的分布鲁棒机会约束方法)的优缺点。最后,对DRO方法在电力系统领域待研究的方向进行了总结与展望。

考虑需求响应的源网荷协调分布鲁棒长期扩展规划

受限于化石能源储量有限性以及环境污染性的特点,在电力系统扩展规划方面需要着重考虑可再生能源的影响。在此背景下,对电力系统进行扩展规划时,考虑发电机组、输电线路与负荷需求响应的协调规划,并探讨采用分布鲁棒方法研究负荷和风电出力的不确定性对系统规划策略的影响。首先,提出一种以最小化投建成本、运行成本以及失负荷弃风惩罚为目标的考虑负荷需求响应的源网荷协调分布鲁棒长期规划模型;然后,针对第二阶段最坏场景,引入数据驱动型模糊集描述不确定性,采用主成分分析法捕获历史数据信息降低模型的保守性,通过对偶原理和仿射决策规则将模型重构为混合整数线性规划模型以便求解;最后,通过算例验证所提扩展规划方法的有效性与通用性。

考虑风电统计特性挖掘的分布鲁棒优化调度方法

提出一种基于数据驱动分布鲁棒优化的电力系统调度方法,以应对考虑风电不确定性的电力系统运行问题。首先,挖掘风电数据统计信息,提出了基于主成分分析与核密度估计的风电概率分布模糊集构建方法,刻画风电随机性以及不同风电机组出力之间的空间相关性;其次,针对含风电的调度问题,建立考虑概率分布模糊集的两阶段分布鲁棒优化问题;然后,将分布鲁棒优化问题变换为其等价可解形式,采用仿射策略以及对偶原理将其转化为线性规划问题进行求解,并且提出了基于样本外测试的概率分布模糊集范围参数选择策略,以保证调度方案的可靠性与经济性。采用6节点与IEEE 118节点系统进行仿真分析,并将所提出的分布鲁棒优化方法与不考虑随机变量相关性的分布鲁棒优化方法以及传统随机、鲁棒优化方法进行对比,以验证所提方法的有效性。

不确定环境下含云计算数据中心的电网韧性增强调度

为解决飓风来临前路径不确定时输电线路随机故障等带来的难题,提出了适用于含云计算数据中心的电网韧性增强日前调度策略,并将其构建为两阶段风险规避的分布鲁棒优化问题。以飓风对输电线路的时空影响为出发点,采用蒙特卡洛模拟获得飓风路径不确定时线路的离散故障集合,并构建基于L1距离度量的分布鲁棒模糊集合。然后,在日前调度中,对机组和数据中心进行优化以平衡经济性和电网韧性,并采用追索问题量化其对日间调度的影响,形成两阶段优化问题。随后,对优化问题进行确定性转换与解耦求解。最后,以含4个数据中心的IEEE-RTS系统为测试算例,验证了所提韧性增强策略应对模糊不确定性的有效性。

基于数据驱动分布鲁棒优化的梯级水光蓄联合优化调度

多种可再生能源互补联合发电技术因其独特优越性正在成为“双碳”背景下电力系统优选供电方案之一,而其不确定性复杂耦合特性下的互补联合调度问题越来越受到人们关注。针对不确定性优化调度问题,本文引入能较好平衡不确定性及鲁棒性的数据驱动分布鲁棒优化理论(data-driven DRO),提出了一种新的基于数据驱动DRO梯级水光蓄联合发电系统协同优化调度方法。首先,考虑系统互补经济调度成本建立两阶段调度模型,制定各电站日前出力调度计划;然后,引入综合范数约束限定概率置信区间,并考虑最恶劣分布下的实时运行调整成本,获取日前调度计划的最优调整方案,日调度计划和调度调整方案形成最优调度计划;最后,本方法采用MP-SP框架,引入CCG算法展开两阶段协同求解。为验证所提方法的性能,引入四川示范区实际运行数据,开展了有效性验证、性能对比分析、计算效率仿真验证等。结果表明:本调度方法的有效性在数据规模、置信度水平两个维度得到了验证;对于SO、RO及本方法鲁棒性及经济性等性能指标的对比,本方法可获得高于SO的鲁棒性及高于RO的经济性;将本调度方法与概率性时序生产模拟方法的计算耗时进行对比,该方法实现了相同计算精度的较高计算效率。基于两阶段调度模型及循环迭代求解的DRO梯级水光蓄联合优化调度方法实现了协同调度结果经济性与保守性的均衡,其高效性能得到验证,为多种可再生能源互补协同调度提供了新思路。