Batch Based Modeling And Lagrangian Relaxation Algorithms For Energy Units Scheduling Problems

Scheduling problem on energy units is the key issue in operation management of energy enterprise,of which the key task is to determine the schedule of start-up,turn-off,and economical dispatch of energy units during a given time horizon,subjecting to system demand and production technological constraints.Scientific scheduling of units can reduce the operational cost of units,improve energy efficiency and optimize the operation of units while satisfying the energy demand.Therefore,research on modeling and optimization of energy units scheduling problem is a hot topic in both industrial and academic communities.For the general energy unit scheduling problem arising from the units operation management in both electric power system and oil production system,we propose unified batch based modeling methods to describe the problem in order to reduce the dimension of models.Based on the proposed modeling method,integer programming models are established for the electric power unit scheduling problem with wind turbines and oil production units scheduling problem,respectively.The complex structures and the strong NP-hardness of the models motivate us to design Lagrangian relaxation algorithms and corresponding acceleration strategies to solve the problems.Furthermore,the decision support system of energy units scheduling is developed.Major research contents are summarized as follows:1)Scheduling strategy based on batch modeling of unitsFor the practical scheduling of energy units,the number of wind turbines and oil wells are so large that it will lead to models with high dimensions,which are difficult to be solved.According to the proximity in spatial distribution,physical location and working mode,the units are grouped into different batches in this paper.Based on the analysis on the common features of the two kinds of energy units,the unified batch based modeling strategy is derived.Based on the analysis of the specific features between the two kinds of the units,the batch based modeling and its parameter aggregation methods are proposed,respectively.2)Modeling of generating unit scheduling with wind turbines batchTaking into consideration the battery embedded to reduce the instable supply fluctuation of wind turbines in electric grid,the scheduling problem of large-scale wind power integrated power system is to minimize the total operation cost of the system by determining the optimum start-up/shut-down status and power generation of each wind turbine and thermal power generating unit during a given planning period,while satisfying the technical requirements such as system load,spinning reserve,minimum start-up and start-down time and the ramping constraint of the wind turbines.Since that the large-scale models constructed by traditional single-unit modeling method are difficult to solve due to the large amount of wind turbines,the mixed integer programming model based on batch modeling strategy is established,and parameter aggregation method based on batch model is proposed through batching wind turbines with similar physical location.The effectiveness of the proposed model is verified by extensive experiments based on randomly generated data.3)The solution method for the power unit scheduling problem with wind turbine batch characteristicsSince the batching model is NP-hard,CPLEX software cannot obtain an near optimal solutions as the problem size increases.For this problem,a Lagrangian relaxation algorithm is proposed to obtain suboptimal solutions.By relaxing coupling constraints,including the power balance constraints,spinning reserve constraints and turbine-battery-coordinated into the objective function,the original problem is decomposed into three sub-problems,which corresponds to wind turbines,thermal power and battery parts,respectively.For thermal power unit sub-problem,a dynamic programming algorithm is constructed,and optimal solution property is derived to accelerate the algorithm.In the LR algorithm,surrogate subgradient method is designed to simplify the complexity of sub-problems in the subgradient algorithm,and the corresponding multiplier updating strategy.The experimental results show that the proposed Lagrangian relaxation algorithm based on batching model performs better than the commercial software CPLEX,and it can obtain an near optimal solutions in a relatively short time.4)Batch scheduling problem of oil well in oilfield productionThe batch scheduling of oil wells in oilfield production is to determine the optimum work ways of oil well in oilfield production in a given planning horizon,which includes the start-up and shut-down status in each time period and the yield of production so that the total production operation cost of oil wells is minimized while satisfying the demand of oil recovery and considering the impact of the bottom pressure variation of the oil well on its start-up/shut-down status and minimum start up and start down time of oil well and so on.Since the large scale models constructed by the modeling method of traditional single model is difficult to solve,batch modeling strategies and methods are put forward.The mixed integer programming model based on batch is established,and the parameter aggregation method of batching model is also proposed.The LR algorithm is designed for obtaining approximate optimal solutions.Randomly generated extensive experiments demonstrate that the batching model is superior to the single-unit model,and the performance of proposed LR algorithm is better than CPLEX.5)Batch scheduling problem of oil well considering ramping constraints in oilfield productionIn the practical oilfield production scheduling of oil wells,in order to avoid the damage to equipments caused by large variation of oil pumping in adjacent periods,ramping constraints need to be taken into consideration to ensure that the oil pumping changes smoothly in adjacent periods.For batch scheduling problem of oil well considering ramping constraints in oilfield production,by regarding the machine switching condition and the oil production as decision variables duriing a given scheduling period,and the minimized oil well running and operating costs as objective function,a nonlinear integer programming model is established based on batch modeling strategies and methods.Through linear transformation,the model is converted into a linear integer programming model,and enabling small-scale problems to be solved by CPLEX directly.For the medium and large scaled problems,since that CPLEX cannot solve the problem effectively,LR algorithm is proposed to solve the problem.Due to the inefficiency of dynamic programming method in solving the decomposed single unit sub-problems with ramping constraints,the state space reduction strategy is put forward by taking the feature states as the representatives of all states that have the same stage,thus the complexity of the proposed dynamic programming can be reduced from O(n4)to O(n2).The efficiency of the algorithm can be significantly improved.Experiments results illustrate that the proposed LR algorithm can obtain the near optimal solutions for small scale problems,and the algorithm can obtain high-quality solutions in a reasonable computing time for the medium and large scale problems.6)Dss for energy unit schedulingTaking the proposed batching models and optimization algorithms for energy unit scheduling problems as the core,the decision support system of the energy scheduling is developed.The system can not only work out the power generation unit scheduling which includes thermal power,wind turbines and battery,but also can realize production scheduling of oil well.The system functions modules include data management,generation of model parameters configuration,optimization algorithm running module and the result analysis module,and so on.This system has realized the friendly interface of user operation and flexible function of human interaction,and also multiple scheme evaluation.It establishes the foundation of software platform for the further application of energy unit scheduling.