Simultaneous mixed-integer dynamic scheduling of processes and their energy systems

Increasingly volatile electricity prices make simultaneous scheduling optimization desirable for production processes and their energy systems. Simultaneous scheduling needs to account for both process dynamics and binary on/off-decisions in the energy system leading to challenging mixed-integer dynamic optimization problems. We propose an efficient scheduling formulation consisting of three parts: a linear scale-bridging model for the closed-loop process output dynamics, a data-driven model for the process energy demand, and a mixed-integer linear model for the energy system. Process dynamics is discretized by collocation yielding a mixed-integer linear programming (MILP) formulation. We apply the scheduling method to three case studies: a multiproduct reactor, a single-product reactor, and a single-product distillation column, demonstrating the applicability to multiple input multiple output processes. For the first two case studies, we can compare our approach to nonlinear optimization and capture 82% and 95% of the improvement. The MILP formulation achieves optimization runtimes sufficiently fast for real-time scheduling.     

Demand response scheduling under uncertainty: Chance-constrained framework and application to an air separation unit

Recent increases in renewable power generation challenge the operation of the power grid: generation rates fluctuate in time and are not synchronized with power demand fluctuations. Demand response (DR) consists of adjusting user electricity demand to match available power supply. Chemical plants are appealing candidates for DR programs; they offer large, concentrated loads that can be modulated via production scheduling. Price-based DR is a common means of engaging industrial entities; its benefits increase significantly when a longer (typically, a few days) scheduling time horizon is considered. DR production scheduling comes with its own challenges, related to uncertainty in future (i.e., forecast) electricity prices and product demand. In this work, we provide a framework for DR production scheduling under uncertainty based on a chance-constrained formulation that also accounts for the dynamics of the production facility. The ideas are illustrated with an air separation unit case study.     

Integrated scheduling and dynamic optimization of batch processes using state equipment networks

A systematic framework for the integration of short‐term scheduling and dynamic optimization (DO) of batch processes is described. The state equipment network (SEN) is used to represent a process system, where it decomposes the process into two basic kinds of entities: process materials and process units. Mathematical modeling based on the SEN framework invokes both logical disjunctions and operational dynamics; thus the integrated formulation leads to a mixed‐logic dynamic optimization (MLDO) problem. The integrated approach seeks to benefit the overall process performance by incorporating process dynamics into scheduling considerations. The solution procedure of an MLDO problem is also addressed in this article, where MLDO problems are translated into mixed‐integer nonlinear programs using the Big M reformulation and the simultaneous collocation method. Finally, through two case studies, we show advantages of the integrated approach over the conventional recipe‐based scheduling method. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Air separation with cryogenic energy storage: Optimal scheduling considering electric energy and reserve markets

The concept of cryogenic energy storage (CES) is to store energy in the form of liquid gas and vaporize it when needed to drive a turbine. Although CES on an industrial scale is a relatively new approach, the technology is well known and essentially part of any air separation unit that utilizes cryogenic separation. In this work, the operational benefits of adding CES to an existing air separation plant are assessed. Three new potential opportunities are investigated: (1) increasing the plant's flexibility for load shifting, (2) storing purchased energy and selling it back to the market during higher‐price periods, and (3) creating additional revenue by providing operating reserve capacity. A mixed‐integer linear programming scheduling model is developed and a robust optimization approach is applied to model the uncertainty in reserve demand. The proposed model is applied to an industrial case study, which shows significant potential economic benefits. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1547–1558, 2015     

Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed‐integer dynamic optimization problem or a large‐scale mixed‐integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed‐integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2379–2406, 2013     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

A decomposition algorithm for simultaneous scheduling and control of CSP systems

We present a decomposition algorithm to perform simultaneous scheduling and control decisions in concentrated solar power (CSP) systems. Our algorithm is motivated by the need to determine optimal market participation strategies at multiple timescales. The decomposition scheme uses physical insights to create surrogate linear models that are embedded within a mixed‐integer linear scheduling layer to perform discrete (operational mode) decisions. The schedules are then validated for physical feasibility in a dynamic optimization layer that uses a continuous full‐resolution CSP model. The dynamic optimization layer updates the physical variables of the surrogate models to refine schedules. We demonstrate that performing this procedure recursively provides high‐quality solutions of the simultaneous scheduling and control problem. We exploit these capabilities to analyze different market participation strategies and to explore the influence of key design variables on revenue. Our results also indicate that using scheduling algorithms that neglect detailed dynamics significantly decreases market revenues. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2408–2417, 2018     

A discrete-time scheduling model for continuous power-intensive process networks with various power contracts

Increased volatility in electricity prices and new emerging demand side management opportunities call for efficient tools for the optimal operation of power-intensive processes. In this work, a general discrete-time model is proposed for the scheduling of power-intensive process networks with various power contracts. The proposed model consists of a network of processes represented by Convex Region Surrogate models that are incorporated in a mode-based scheduling formulation, for which a block contract model is considered that allows the modeling of a large variety of commonly used power contracts. The resulting mixed-integer linear programming model is applied to an illustrative example as well as to a real-world industrial test case. The results demonstrate the model's capability in representing the operational flexibility in a process network and different electricity pricing structures. Moreover, because of its computational efficiency, the model holds much promise for its use in a real industrial setting.     

Evaluating the demand response potential of ammonia plants

Demand-side management/demand response (DSM/DR) are key strategies for mitigating the inherent variability in electricity generation rates by renewable sources. This article represents—to our knowledge—the first foray into assessing the DR potential of ammonia plants. Ammonia plants are interesting candidates for DR initiatives because of their significant electricity use (for operating compressors driving the synthesis loop) and the ability to store the ammonia product relatively easily and safely. Our approach is based on formulating and solving an optimal DR scheduling problem for an ammonia plant while accounting for the process dynamics. To this end, we introduce a new Hammerstein–Wiener-inspired modeling framework based on injecting linear dynamics in a first-principles static nonlinear model of the process. The results are encouraging; for the cases considered, peak-time power consumption decreases between 3.57% and 7.40%, coupled with 1.39% to 3.70% reductions in operating cost.     

A flexible design framework for process systems under demand-side management

Demand response (DR) has been an appealing strategy for both residential and commercial/industrial customers of electricity due to the increasing penetration of renewable energy resources into the power grid and the deregulation of the energy markets. For industrial DR participants, the management of energy consumption along with the satisfaction of production expectations is generally referred to as demand-side management. Recent research in this area has focused mostly on process scheduling and capacity planning, especially for energy-intensive processes. This article presents a new direction through an optimization-based process design paradigm that allows for the potential reconfiguration of the process flow sheet in real time. Based on a case study of pump network design, a network superstructure is first defined, followed by a two-stage stochastic optimization model. The method of progressive hedging is used to solve the resulting mixed-integer stochastic programming problem. The results demonstrate that, under various scenarios, the reconfigurable design offers significant benefits compared to a fixed network structure in terms of total design cost and expected operating cost.     

考虑需求不确定性的化工生产计划与调度集成

生产计划与调度是化工供应链优化中两个重要的决策问题。为了提高生产决策的效率,不仅要对计划与调度进行集成,而且要考虑不确定性的影响。对于多周期生产计划与调度问题,首先在每个生产周期内,分别建立计划与调度的确定性模型,通过产量关联对二者进行集成。然后考虑需求不确定性,使用有限数量的场景表达决策变量,建立二阶段随机规划模型。最后运用滚动时域求解策略,使计划与调度结果在迭代过程中达到一致。实例结果表明,在考虑需求不确定性时,与传统方法相比,随机规划方法可以降低总费用,结合计划与调度的分层集成策略,实现了生产操作性和经济性的综合优化。     

Integrated design and control of semicontinuous distillation systems utilizing mixed integer dynamic optimization

Semicontinuous distillation systems are notoriously difficult to design and optimize because the structural parameters, operational parameters, and control system must all be determined simultaneously. In the past 15 years of research into semicontinuous systems, studies of the optimal design of these systems have all been limited in scope to small subsets of the parameters, which yields suboptimal and often unsatisfactory results. In this work, for the first time, the problem of integrated design and control of semicontinuous distillation processes is studied by using a mixed integer dynamic optimization (MIDO) problem formulation to optimize both the structural and control tuning parameters of the system. The public model library (PML) of gPROMS is used to simulate the process and the built-in optimization package of gPROMS is used to solve the MIDO via the deterministic outer approximation method. The optimization results are then compared to the heuristic particle swarm optimization (PSO) method.     

New MINLP formulation for the multiperiod pooling problem

The modeling of blending tank operations in petroleum refineries for the most profitable production of liquid fuels in a context of time‐varying supply and demand is addressed. A new mixed‐integer nonlinear programming formulation is proposed that using individual flows and split fractions as key model variables leads to a different set of nonconvex bilinear terms compared with the original work of Kolodziej et al. These are better handled by decomposition algorithms that divide the problem into integer and nonlinear components as well as by commercial solvers. In fact, BARON and GloMIQO can solve to global optimality all problems resulting from the new formulation and test problems from the literature. A tailored global optimization algorithm working with a tight mixed‐integer linear relaxation from multiparametric disaggregation achieves a similar performance. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3728–3738, 2015     

A hierarchical method to integrated solvent and process design of physical CO2 absorption using the SAFT‐γ Mie approach

Molecular‐level decisions are increasingly recognized as an integral part of process design. Finding the optimal process performance requires the integrated optimization of process and solvent chemical structure, leading to a challenging mixed‐integer nonlinear programming (MINLP) problem. The formulation of such problems when using a group contribution version of the statistical associating fluid theory, SAFT‐γ Mie, to predict the physical properties of the relevant mixtures reliably over process conditions is presented. To solve the challenging MINLP, a novel hierarchical methodology for integrated process and solvent design (hierarchical optimization) is presented. Reduced models of the process units are developed and used to generate a set of initial guesses for the MINLP solution. The methodology is applied to the design of a physical absorption process to separate carbon dioxide from methane, using a broad selection of ethers as the molecular design space. The solvents with best process performance are found to be poly(oxymethylene)dimethylethers. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3249–3269, 2015     

A discretization-based approach for the optimization of the multiperiod blend scheduling problem

In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The primary difficulties in solving this optimization problem are the presence of bilinear terms, as well as binary decision variables required to impose operational constraints. An illustrative example is presented to provide unique insight into the difficulties faced by conventional MINLP approaches to this problem, specifically in finding feasible solutions. Based on recent work, a new radix-based discretization scheme is developed with which the problem can be reformulated approximately as an MILP, which is incorporated in a heuristic procedure and in two rigorous global optimization methods, and requires much less computational time than existing global optimization solvers. Detailed computational results of each approach are presented on a set of examples, including a comparison with other global optimization solvers.     

钢铁企业煤气-蒸汽-电力系统耦合优化及应用

煤气、蒸汽和电力是钢铁联合企业能源系统的重要组成部分,其消耗占钢铁企业总能耗的60%左右。合理地制定能源系统的生产以及燃料消耗、电力采购计划,对企业降低成本、减少环境污染有着非常重要的意义。针对煤气-蒸汽-电力系统的燃料结构、设备类型、工况变化等特点,以经济运行成本和环境成本最小为目标函数,建立了针对该系统的耦合优化模型。该模型综合考虑了富余煤气的波动、蒸汽和电力的动态需求、多燃料结构、分时电价等影响因素,并使用GAMS进行优化求解。将模型应用到某大型钢铁联合企业,结果表明该模型能够为钢铁企业煤气-蒸汽-电力系统提供合理的生产计划方案,实现了富余煤气的合理分配以及能源的高效利用,降低了能源系统运行成本,提高了企业的经济效益和环境效益。     

Optimization of grade transitions in polyethylene solution polymerization processes

This study considers the development of optimization models for grade transition of polyethylene solution polymerization processes. A detailed mathematical model is developed to capture the dynamics of the solution polymerization process. This includes time delay models for vapor and liquid recycle streams as well as a reduced, yet accurate, vapor‐liquid equilibrium (VLE) model derived from rigorous VLE calculations. Simultaneous dynamic optimization approach is applied to solve the optimization problem to reduce off‐spec production time and transition time. Two optimization formulations, single stage and multistage, are developed to deal with single‐value target and specification bands of product properties, respectively. The results show significant reductions in grade transition time and off‐spec production time. In addition, the multistage formulation designed for problems with specification bands outperforms its single stage counterpart. It minimizes transition time and off‐spec production directly, and leads to higher performance control profiles. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1126–1142, 2016     

Dynamic predictive scheduling of operational strategies for continuous processes using mixed-logic dynamic optimization

Industrial processes are usually operated in a highly dynamic environment, e.g. with time-varying market prizes, customer demand, technological development or up- and downstream processes. Due to these disturbances, the operational strategies comprising objectives and constraints are regularly adjusted to reflect a change in the environment in order to achieve or maintain optimal process performance. The related operational objectives need not only be of an economical nature, but can also include flexibility, risk or ecological objectives. In this paper, a novel methodology is presented for the modeling and dynamic predictive scheduling of operational strategies for continuous processes. Optimal control actions are computed on a moving horizon employing discrete-continuous modeling and mixed-logic dynamic optimization as introduced by Oldenburg et al. (2003). The approach is successfully demonstrated considering the operation of a wastewater treatment plant.     

General optimization model for the energy planning of industries including renewable energy: A case study on oil sands

A multi‐period optimization model is developed for the energy procurement planning of industries including renewable energy. The model is developed with the objective of identifying the optimal set of energy supply technologies to satisfy a set of demands (e.g., power, heat, hydrogen, etc.) and emission targets at minimum cost. Time dependent parameters are incorporated in the model formulation, including demands, fuel prices, emission targets, carbon tax, lead time, etc. The model is applied to a case study based on the oil sands operations over the planning period 2015–2050. Various production alternatives were incorporated, including renewable, nuclear, conventional and gasification of alternative fuels. The results obtained indicated that the energy optimization model is a practical tool that can be utilized for identifying the key parameters that affect the operations of energy‐intensive industrial operations, and can further assist in the planning and scheduling of the energy for these industries. © 2016 American Institute of Chemical Engineers AIChE J, 63: 610–638, 2017