Short-term Scheduling Model Research Articles

Multiple Time Resolution Stochastic Scheduling for Systems with High Renewable Penetration

This paper presents a stochastic unified unit commitment and economic dispatch model for short-term operations scheduling of power systems with high renewable penetration. The model is a unique stochastic real-time tool that performs economic dispatch with up to 36-hour look-ahead capability, providing dispatch instructions for the first time interval and advisory commitment and dispatch schedules for the remaining scheduling horizon. Variable time resolution is used to contain computational requirements, i.e., finer time resolution is used during the first hours and coarser time resolution during the last hours of the scheduling horizon. The mathematical formulation comprises a MILP problem and it is presented as a two-stage scenario-based stochastic, multiple time resolution unit commitment model. The proposed stochastic model is tested against its deterministic counterpart via an annual simulation of Greek power system short-term operations using real 2013 data. Performance indices concerning dispatch costs, energy balances, and unit cycling are calculated and discussed.

耦合电网约束的水电系统短期发电调度研究

电网是水电站电力送出的必经途径，但在输送过程中不可避免地产生一定程度的电力损耗。以往研究大多集中在发电侧的水电站(群)发电量或发电效益最大，未能给予电力损耗充分的重视。因此，本文构建了考虑电网损耗的水电系统发电调度模型，以期实现水电最大化的消纳。同时，针对传统方法的早熟收敛缺陷，提出了耦合遗传算法和离散微分动态规划的离散微分遗传算法(DDGA)，并采用Fork/Join多核框架实现DDGA的并行求解，以求提高算法的搜索性能与求解效率。澜沧江流域梯级应用实例表明：所提模型与DDGA方法能够快速获得计及电网损耗的优化调度结果，有效提高电网水电消纳能力，具有较强的可行性及实用性。 The power grid is the only way of transmitting hydropower generation, and it will inevitably produce a certain degree of power loss in the transport process. Most previous studies focused on the generation side of maximum power out or generation benefits, without giving adequate attention to the power loss. In this paper, a short-term generation scheduling model coupling with power grid constraints is established, with the objective of maximizing the generation at the receiving end. A DDGA algorithm is proposed to solve the model, which combines the advantages of DDDP and GA. Moreover, based on the multi- core computer platform and Fork/Join parallel framework, a parallel processing method is used to improve the efficiency of solving the method. A case study of Lancang River cascade hydropower system proves that the model and DDGA method can quickly obtain optimal scheduling results, and it can improve the absorptive capacity of hydropower grid effectively. The proposed method is reasonability and practicability.

Applying successive linear programming for stochastic short-term hydropower optimization

We present a model for operational stochastic short-term hydropower scheduling, taking into account the uncertainty in future prices and inflow, and illustrate how the benefits of using a stochastic rather than a deterministic model can be quantified. The solution method is based on stochastic successive linear programming. The proposed method is tested against the solution of the true non-linear problem in a principal setting. We demonstrate that the applied methodology is a first-order approximation to a formal correct head-of-water optimization and achieve good results in tests. How the concept of stochastic successive linear programming has been implemented in a prototype software for operational short-term hydropower scheduling is also presented, and the model's ability is demonstrated through case studies from Norwegian power industry. From these studies, improvements occurred in terms of the objective function value and decreased risk of spill from reservoirs.

A dynamic model and an algorithm for short-term supply chain scheduling in the smart factory industry 4.0

Smart factories Industry 4.0 on the basis of collaborative cyber-physical systems represents a future form of industrial networks. Supply chains in such networks have dynamic structures which evolve over time. In these settings, short-term supply chain scheduling in smart factories Industry 4.0 is challenged by temporal machine structures, different processing speed at parallel machines and dynamic job arrivals. In this study, for the first time, a dynamic model and algorithm for short-term supply chain scheduling in smart factories Industry 4.0 is presented. The peculiarity of the considered problem is the simultaneous consideration of both machine structure selection and job assignments. The scheduling approach is based on a dynamic non-stationary interpretation of the execution of the jobs and a temporal decomposition of the scheduling problem. The algorithmic realisation is based on a modified form of the continuous maximum principle blended with mathematical optimisation. A detailed theoretical analysis of the temporal decomposition and computational complexity is performed. The optimality conditions as well as the structural properties of the model and the algorithm are investigated. Advantages and limitations of the proposed approach are discussed.

A multi-objective short term hydropower scheduling model for peak shaving

The short-term scheduling problem of a hydropower system in China Southern Power Grid (CSG) is studied. As one of the largest in China, the system consists of 92 hydro plants with total installed capacity of 41GW occupying 14.7% of the national hydropower capacity at the end of 2013. Abundant hydroelectricity of the system is transmitted from the western provinces to the eastern load centers in CSG. Obvious difficulties of the hydropower scheduling of CSG are large-scale system, complex constraints and multiple power receiving grids of single plants and cascaded systems due to huge capacity. A short-term hydropower scheduling model for peak shaving of multiple power grids is developed for the operations of the hydropower system of CSG. The model is composed of multi-objective optimal peak shaving (MOPS) model, inter grid power distribution (IGPD) model and load fluctuation balance (LFB) model. The MOPS model minimizes the maximum residual loads of each power grid in which the IGPD model is embedded to distribute power of a plant among several power grids. To solve the model, an aggregate function and a multi-objective fuzzy optimization model are combined to establish an alternative objective function, and a proposed constraint successively satisfying (CSS) algorithm is used to address the period coupling constraints in local search. A case study shows that the proposed approach is practicable, adaptable and robust to obtain near optimal results efficiently, and is applicable for large-scale hydropower systems with both multiple and single power receiving grids.

Optimization Model for Scheduling of a Lube-Oil Production Plant

In this paper, a short-term scheduling model is developed for lube-oil production plant using unit-specific event-based continuous time representation and state-task- network (STN) based process representation. Important operational features of a lube-oil production plant such as stream splitting, stream addition, intermediate storage management, product changeover, and continuous feed stream are addressed in much simpler way using STN. The resulting model is a mixed integer linear programming (MILP) model which is solved using GAMS software.

Modeling and Optimization for Short-term Scheduling of Multipurpose Batch Plants

In the past two decades, short-term scheduling of multipurpose batch plants has received significant attention. Most scheduling problems are modeled using either state-task-network or resource-task-network (RTN) process representation. In this paper, an improved mixed integer linear programming model for short-term scheduling of multipurpose batch plants under maximization of profit is proposed based on RTN representation and unit-specific events. To solve the model, a hybrid algorithm based on line-up competition algorithm and linear programming is presented. The proposed model and hybrid algorithm are applied to two benchmark examples in literature. The simulation results show that the proposed model and hybrid algorithm are effective for short-term scheduling of multipurpose batch plants.

Hybrid Model for Short-Term Scheduling of Hydropower Systems

In this paper the authors propose a global–local methodology for optimizing the short-term operation of hydroelectric plants. The authors determine the tradeoffs between minimizing the daily release from the plant and minimizing the number of startups and shutdowns of the generating units. The model is formulated as a mixed integer, nonlinear programming optimization problem with multiple objectives. The authors consider the nonlinearities of the generating units without simplifications or approximations. The authors develop a solution method that combines an evolutionary algorithm for the global search of the integer variables and a gradient-based local optimizer for the continuous variables. The local optimizer is embedded in the global search algorithm. Convergence is achieved by iterating between the global search and the local optimizer. The proposed methodology is applied to a moderately sized Brazilian hydroelectric plant that belongs to the national interconnected system. Additionally, a comparative study was conducted using historical operational records. The results demonstrate that the proposed methodology is feasible for online daily operations and delivers two specific benefits. The first is the efficiency gained, as the model seeks to operate the generating units as close as possible to their most efficient operating points. The second benefit is reduction of the units’ maintenance costs, as the model minimizes switching on/off of the generating units.

Mixed-integer Linear Programming Formulation for Short-term Scheduling of Cascaded Hydroelectric Plants with Pumped-storage Units

In this article, a short-term scheduling model for cascaded hydroelectric chain plants with pumped-storage units is discussed, which considers in detail the various factors of the hydro system and units. A mixed-integer linear programming formulation is established. The main contribution of the article is that a systematic method is established such that the complex multivariable production functions of hydro units can be approximated by a piecewise linear function, and the characteristics of pumped-storage units are described by introducing some ancillary integer variables. Numerical testing results show that the mixed-integer linear programming formulation given in this article is efficient and effective.

Rigorous Unit-Specific Event-Based Model for Short-Term Scheduling of Batch Plants Using Conditional Sequencing and Unit-Wait Times

Continuous-time models have evolved as a promising tool for formulating problems related to short-term scheduling. This article presents an analysis, advantages, and limitations of recent models proposed in the literature for short-term scheduling of batch plants based on unit-specific event-based time representation. The purpose of this study is to generalize and enhance previous unit-specific event-based scheduling models for efficient handling of various issues such as nonsimultaneous material transfers, comprehensive sequencing constraints for handling of different storage policies, unit-wait policies, and utility resources. Accordingly, a rigorous unit-specific event-based model has been proposed that allows for conditional sequencing of each production and consumption task, only if the material produced by a given production task is used by a given consumption task. The proposed approach leads to reduction in number of events, and the model can effectively handle scheduling problems with different storage policies: UIS, FIS, NIS, and ZW. It can can also handle different unit-wait policies. The proposed conditional sequencing concept is also extended for efficient handling of utility resources, thus resulting in further reduction in number of events required compared to the published literature.

Scheduling of displacement batch digesters using discrete time formulation

This paper provides mathematical programming based optimization model and computational results for short-term scheduling of displacement batch digesters in a pulp industry. The scheduling problem involves development of an optimal solution that yields the best sequence of operations in each of the parallel batch digesters sharing common resources. The constraints are imposed on meeting the demand of pulp of different qualities within a specified time horizon. The problem comprises of both fixed-time and variable time durations of the tasks, different storage policies, zero-wait and finite wait times, and handling of shared resources. The scheduling problem is formulated using a state-task-network (STN) representation of production recipes, based on discrete time representation resulting in a mixed-integer linear programming (MILP) problem which is solved using GAMS software. The basic framework is adapted from the discrete-time model of Kondili et al. (Comput. Chem. Eng., 1993, 17, 211–227). Different case studies involving parallel digesters in multiple production lines are considered to demonstrate the effectiveness of the proposed formulation using two different objective functions.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al.2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

Combined Pool/Bilateral Short-Term Hydrothermal Scheduling Model for Day-Ahead Energy Markets

This paper proposes a combined pool/bilateral short term hydrothermal scheduling model (PDC) for the context of the day-ahead energy markets. Some innovative aspects are introduced in the model, such as: i) the hydraulic generation is optimized through the opportunity cost function proposed; ii) there is no decoupling between physical and commercial dispatches, as is the case today in Brazil; iii) interrelationships between pool and bilateral markets are represented through a single optimization problem; iv) risk exposures related to future deficits are intrinsically mitigated; v) the model calculates spot prices in an hourly basis and the results show a coherent correlation between hydrological conditions and calculated prices. The proposed PDC model is solved by a primal-dual interior point method and is evaluated by simulations involving a test system. The results are focused on sensitivity analyses involving the parameters of the model, in such a way to emphasize its main modeling aspects. The results show that the proposed PDC provides a conceptual means for short term price formation for hydrothermal systems.

A mixed integer linear programming model for short-term open pit mine production scheduling

Short-term production scheduling in open pit mines usually generates a scheme to enable mining operations to deliver the budgeted tonnes and grades to the mill while following the long-term mine plan. The goal of this paper is to develop and test an optimisation model for short-term open pit mine production scheduling. A multidestination mixed integer linear programming (MILP) model is proposed, which minimises the overall cost of mining operations including mining, processing, haulage, rehandling and rehabilitation costs. The model is solved by branch-and-cut algorithm using TOMLAB/CPLEX optimiser. The model incorporates buffer and blending stockpiles, horizontal directional mining, and decisions on ramps while controlling technical constraints. A monthly production schedule in an iron ore mine is developed over 12 months to illustrate the practicality of the developed model. Three scenarios with different mining horizontal directions are considered. The scenario with minimum number of drop-cuts is selected as the best practical schedule.

Multi-objective optimization of hydrothermal energy system considering economic and environmental aspects

Along with continuous global warming, the environmental problems, besides the economic objective, are expected to play more and more important role in the operation of hydrothermal power system. In this paper, the short-term multi-objective economic environmental hydrothermal scheduling (MEEHS) model is developed to analyze the operating approach of MEEHS problem, which simultaneously optimize energy cost as well as the pollutant emission effects. Meanwhile, transmission line losses among generation units, valve-point loading effects of thermal units and water transport delay between hydraulic connected reservoirs are taken into consideration in the problem formulation. In order to solve MEEHS problem, a new multi-objective cultural algorithm based on particle swarm optimization (MOCA-PSO) is presented in way of combining the cultural algorithm framework with particle swarm optimization (PSO) to carry though the evolution of population space. Furthermore, an effective constrain handling method is proposed to handle the operational constraints of MEEHS problem. The proposed method is applied to a hydrothermal power system consisting of four hydro plants and three thermal units for the case studies. Compared with several previous methods, the simulation solutions of MOCA-PSO with smaller fuel cost and lower emission effects proves that it can be an alternative method to deal with MEEHS problems. The obtained results demonstrate that the change of optimization objective leads to the shift of optimal operation schedules. Finally, the scheduling results of MEEHS problem offer enough choices to the decision makers. Thus, the operation with better performance of environment is achieved by more energy system cost.

Improved three-index unit-specific event-based model for short-term scheduling of batch plants

Short-term scheduling of batch operations has been an important research area in the past two decades. Recently, Shaik and Floudas (Industrial and Engineering Chemistry Research, 2009, 48, 2947) proposed a novel unified model for short-term scheduling using unit-specific event-based continuous-time representation employing three-index binary and continuous variables. In their comparative study it was shown that the unified model has superior performance among all the models compared in their work. In this work, we present an improved model by taking advantage of the three-index variables and effectively incorporating the concept of active task leading to fewer constraints and big-M terms. We propose improvements in allocation, duration and sequencing constraints, and investigate the effect of big-M terms in several constraints to enable solution of large-scale problems. The computational performance of the proposed formulation is compared with the original three-index model through various examples drawn from literature including Westenberger–Kallrath challenging benchmark problem.

Novel Unified Modeling Approach for Short-Term Scheduling

Unit-specific event-based continuous time models have gained significant attention in the past decade for their advantages of requiring less number of event points, smaller problem size, and hence, a better computational performance. In the literature, different models had been proposed for short-term scheduling problems involving with and without resource constraints using unit-specific event-based formulations. For scheduling problems involving no resource constraints, generally the unit-specific event-based models do not allow tasks to continue over multiple events unlike in models that account for resource constraints explicitly. In this work, we emphasize the necessity for allowing tasks to take place over multiple event points even for simpler scheduling problems involving no resource constraints. We propose a novel short-term scheduling model using three-index binary and continuous variables that efficiently merges both the problems involving resources and no resource constraints into a unified, generic common framework. The proposed approach is based on state-task-network (STN) representation and is suitable for both batch and continuous plants, although we focus only on batch plants in this paper. Detailed computational case studies are presented to demonstrate the efficacy of the proposed model.

Short-term generation scheduling model of Fujian hydro system

The Fujian hydropower system (FHS) is one of the provincial hydropower systems with the most complicated hydraulic topology in China. This paper describes an optimization program that is required by Fujian Electric Power Company Ltd. (FEPCL) to aid the shift engineers in making decisions with the short-term hydropower scheduling such that the generation benefit can be maximal. The problem involves 27 reservoirs and is formulated as a nonlinear and discrete programming. It is a very challenging task to solve such a large-scale problem. In this paper, the Lagrangian multipliers are introduced to decompose the primal problem into a hydro subproblem and many individual plant-based subproblems, which are respectively solved by the improved simplex-like method (SLM) and the dynamic programming (DP). A numerical example is given and the derived solution is very close to the optimal one, with the distance in benefit less than 0.004%. All the data needed for the numerical example are presented in detail for further tests and studies from more experts and researchers.

New approach for scheduling crude oil operations

Scheduling of crude oil operations is crucial to petroleum refining, which includes determining the times and sequences of crude oil unloading, blending, and CDU feeding. In the last decades, many approaches have been proposed for solving this problem, but they either suffered from composition discrepancy [Lee et al. 1996. Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management. Industrial and Engineering Chemistry Research 35, 1630–1641; Jia et al., 2003. Refinery short-term scheduling using continuous time formulation: crude-oil operations. Industrial and Engineering Chemistry Research 42, 3085–3097; Jia and Ierapetritou, 2004. Efficient short-term scheduling of refinery operations based on a continuous time formulation. Computer and Chemical Engineering 28, 1001–1019] or led to infeasible solutions for some cases [Reddy et al., 2004a. Novel solution approach for optimizing crude oil operations. A.I.Ch.E. Journal 50(6), 1177–1197; 2004b. A new continuous-time formulation for scheduling crude oil operations. Chemical Engineering Science 59, 1325–1341]. In this paper, coastal and marine-access refineries with simplified workflow are considered. Unlike existing approaches, the new approach can avoid composition discrepancy without using iterative algorithm and find better solution effectively. In this approach, a new mixed integer non-linear programming (MINLP) formulation is set up for crude oil scheduling firstly, and then some heuristic rules collected from expert experience are proposed to linearize bilinear terms and prefix some binary variables in the MINLP model. Thus, crude oil scheduling can be expressed as a complete mixed integer linear programming (MILP) model with fewer binary variables. To illustrate the advantage of the new approach, four typical examples are solved with three models. The new model is compared with the most effective models (RKS(a) and RKS(b) models) presented by Reddy et al. [2004a. Novel solution approach for optimizing crude oil operations. A.I.Ch.E. Journal 50(6), 1177–1197; 2004b. A new continuous-time formulation for scheduling crude oil operations. Chemical Engineering Science 59, 1325–1341], which proves that the new approach is valid and feasible in most small-size and medium-size problems.

Production scheduling of a large-scale industrial continuous plant: Short-term and medium-term scheduling

In this work, we describe a framework for short-term and medium-term scheduling of a large-scale industrial continuous plant. For medium-term scheduling, two sub-problems are solved using a rolling-horizon based decomposition scheme. An upper-level model is used to find the optimal number of products, and the length of the time horizon to be considered for solving the lower level short-term scheduling problem. At the lower level, we proposed an improved model for short-term scheduling of continuous processes using unit-specific event-based continuous-time representation. The proposed formulation is demonstrated on a large-scale industrial case study comprising up to 100 units with 1/3 processing and 2/3 storage units operating in a continuous-mode for producing more than 100 different products over a one month time horizon.