The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the n...The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.展开更多
A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We ...A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We then check the impact of the new deterministic formulation and other two deterministic formulations on the corresponding problem size,nonzero elements and solution time by solving some typical dynamic stochastic programming problems with different interior point algorithms.Numerical results show the advantage and application of the new deterministic formulation.展开更多
分布式能源(Distributed Energy Resources,DER)调度受到许多不确定因素的影响,如可再生能源出力波动和负荷变化。针对传统的随机规划方法忽略不确定变量的时间依赖性的问题,提出了一种求解DER最优运行的随机对偶动态规划(Stochastic Du...分布式能源(Distributed Energy Resources,DER)调度受到许多不确定因素的影响,如可再生能源出力波动和负荷变化。针对传统的随机规划方法忽略不确定变量的时间依赖性的问题,提出了一种求解DER最优运行的随机对偶动态规划(Stochastic Dual Dynamic Programming,SDDP)方法,通过整合n阶自回归(Auto Regressive,AR)模型,将传统的SDDP框架扩展到捕捉不确定风电输出的时间依赖性。与基于场景树的传统随机规划方法相比,该方法在求解效率和计算时间需求之间实现了更好的权衡。展开更多
This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncer...This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncertainty in the observation equation of the LQG problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems. The second solution framework considers a general class of discrete-time LQG problems with unknown parameters in both state and observation equations. The best possible (partial) closed-loop feedback control law is derived by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing the optimal nominal dual control.展开更多
The large-scale integration of renewable energy sources(RES)is the global trend to deal with the energy crisis and greenhouse emissions.Due to the intermittent nature of RES together with the uncertainty of load deman...The large-scale integration of renewable energy sources(RES)is the global trend to deal with the energy crisis and greenhouse emissions.Due to the intermittent nature of RES together with the uncertainty of load demand,the problem of transmission expansion planning(TEP)is facing more and more challenges from uncertainties.In this paper,the TEP problem is modeled as a two-stage formulation,so as to minimize the total of investment costs and generation costs.To ensure the utilization level of the RES generation,the expansion plan is required to provide sufficient transmission capacity for the integration of RES.Also,N-k security criterion is considered into the model,so the expansion plan can meet the required security criteria.The stochastic dual dynamic programming(SDDP)approach is applied to consider the uncertainties,and the whole model is solved by Benders’decomposition technique.Two case studies are carried out to compare the performance of the SDDP approach and the deterministic approach.Results show that the expansion plan obtained by the SDDP approach has a better performance than that of the deterministic approach.展开更多
为实现沿海区域的海上风电场、海上采气平台和陆上热电联供燃气电厂等多种能源生产子单元的协同化运行,考虑可再生能源出力和氢负荷的随机波动,提出沿海区域综合能源生产单元(coastal integrated energy production units,CIEPU)随机优...为实现沿海区域的海上风电场、海上采气平台和陆上热电联供燃气电厂等多种能源生产子单元的协同化运行,考虑可再生能源出力和氢负荷的随机波动,提出沿海区域综合能源生产单元(coastal integrated energy production units,CIEPU)随机优化调度模型。采用参数化代价函数近似(parametric cost function approximation,PCFA)的动态规划算法求解随机优化调度模型。通过一种基于梯度下降的求解方法--Adadelta法,获得策略函数的一阶信息,并计算梯度平方的指数衰减平均值,以更新策略函数的迭代步长;对随机优化调度模型进行策略参数逼近,从而得到近似最优的策略参数,并逐一时段求解出CIEPU的最优调度计划。最后,以某个CIEPU为例,分析计算结果表明,所提出方法获得的优化调度方案可以提高CIEPU运行的经济性并降低碳排放量,验证了所提方法的准确性和高效性。展开更多
文摘The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.
基金This research was partially supported by the Natural Science Research Foundation of Shaanxi Province(2001SL09)
文摘A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We then check the impact of the new deterministic formulation and other two deterministic formulations on the corresponding problem size,nonzero elements and solution time by solving some typical dynamic stochastic programming problems with different interior point algorithms.Numerical results show the advantage and application of the new deterministic formulation.
基金the Research Grants Council of Hong Kong, P.R.China under Grant CUHK 4180/03E
文摘This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncertainty in the observation equation of the LQG problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems. The second solution framework considers a general class of discrete-time LQG problems with unknown parameters in both state and observation equations. The best possible (partial) closed-loop feedback control law is derived by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing the optimal nominal dual control.
基金special project(CEPRI:XT71-12-028)funded by the State Grid of China。
文摘The large-scale integration of renewable energy sources(RES)is the global trend to deal with the energy crisis and greenhouse emissions.Due to the intermittent nature of RES together with the uncertainty of load demand,the problem of transmission expansion planning(TEP)is facing more and more challenges from uncertainties.In this paper,the TEP problem is modeled as a two-stage formulation,so as to minimize the total of investment costs and generation costs.To ensure the utilization level of the RES generation,the expansion plan is required to provide sufficient transmission capacity for the integration of RES.Also,N-k security criterion is considered into the model,so the expansion plan can meet the required security criteria.The stochastic dual dynamic programming(SDDP)approach is applied to consider the uncertainties,and the whole model is solved by Benders’decomposition technique.Two case studies are carried out to compare the performance of the SDDP approach and the deterministic approach.Results show that the expansion plan obtained by the SDDP approach has a better performance than that of the deterministic approach.
文摘为实现沿海区域的海上风电场、海上采气平台和陆上热电联供燃气电厂等多种能源生产子单元的协同化运行,考虑可再生能源出力和氢负荷的随机波动,提出沿海区域综合能源生产单元(coastal integrated energy production units,CIEPU)随机优化调度模型。采用参数化代价函数近似(parametric cost function approximation,PCFA)的动态规划算法求解随机优化调度模型。通过一种基于梯度下降的求解方法--Adadelta法,获得策略函数的一阶信息,并计算梯度平方的指数衰减平均值,以更新策略函数的迭代步长;对随机优化调度模型进行策略参数逼近,从而得到近似最优的策略参数,并逐一时段求解出CIEPU的最优调度计划。最后,以某个CIEPU为例,分析计算结果表明,所提出方法获得的优化调度方案可以提高CIEPU运行的经济性并降低碳排放量,验证了所提方法的准确性和高效性。
