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.     

Optimization of steel production scheduling with complex time-sensitive electricity cost

Energy-intensive industries can take advantage of process flexibility to reduce operating costs by optimal scheduling of production tasks. In this study, we develop an MILP formulation to extend a continuous-time model with energy-awareness to optimize the daily production schedules and the electricity purchase including the load commitment problem. The sources of electricity that are considered are purchase on volatile markets, time-of-use and base load contracts, as well as onsite generation. The possibility to sell electricity back to the grid is also included. The model is applied to the melt shop section of a stainless steel plant. Due to the large-scale nature of the combinatorial problem, we propose a bi-level heuristic algorithm to tackle instances of industrial size. Case studies show that the potential impact of high prices in the day-ahead markets of electricity can be mitigated by jointly optimizing the production schedule and the associated net electricity consumption cost.     

Integrating process and power grid models for optimal design and demand response operation of giga-scale green hydrogen

Electrolysis-based hydrogen production can play a significant role in industrial decarbonization, and its economic competitiveness can be promoted by designing demand response operating schemes. Nevertheless, the scale of industrial supply plants may be significantly large (on the order of gigawatts), meaning that electricity prices cannot be treated as an input for scheduling problems, that is, the “price taker” approach. This article presents a framework for the optimization of a large-scale, electricity-powered hydrogen production facility considering its integration with the power grid. Using a computational case study, we present an iterative scheme for integrating the process model with a model for power grid optimization and capacity expansion, taking the popular GenX model as an example.     

An adjustable robust optimization approach to scheduling of continuous industrial processes providing interruptible load

To ensure the stability of the power grid, backup capacities are called upon when electricity supply does not meet demand due to unexpected changes in the grid. As part of the demand response efforts in recent years, large electricity consumers are encouraged by financial incentives to provide such operating reserve in the form of load reduction capacities (interruptible load). However, a major challenge lies in the uncertainty that one does not know in advance when load reduction will be requested. In this work, we develop a scheduling model for continuous industrial processes providing interruptible load. An adjustable robust optimization approach, which incorporates recourse decisions using linear decision rules, is applied to model the uncertainty. The proposed model is applied to an illustrative example as well as a real-world air separation case. The results show the benefits from selling interruptible load and the value of considering recourse in the decision-making.     

Distributed manufacturing for electrified chemical processes in a microgrid

To alleviate the greenhouse gas emissions by the chemical industry, electrification has been proposed as a solution where electricity from renewable sources is used to power processes. The adoption of renewable energy is complicated by its spatial and temporal variations. To address this challenge, we investigate the potential of distributed manufacturing for electrified chemical processes installed in a microgrid. We propose a multiscale mixed-integer linear programming model for locating modular electrified plants, renewable-based generating units, and power lines in a microgrid that includes monthly transportation and hourly scheduling decisions. We propose a K-means clustering-based aggregation disaggregation matheuristic to solve the model efficiently. The model and algorithm are tested using a case study with 20 candidate locations in Western Texas. Additionally, we define a new concept, “the Value of the Multi-scale Model,” to demonstrate the additional economic benefits of our model compared with a single-scale model.     

基于贝叶斯网络的数据校正方法

精确的物料平衡模型是数据校正技术的基础，但实际上，频繁发生的调度事件动态地改变着物料的流向，目前的研究中往往容易被忽视，为此，从工程实践的角度出发提出一种新的处理方法.依据专家经验选择贝叶斯网络关键变量，利用大量的历史数据学习出贝叶斯网络，继而利用贝叶斯网络的诊断功能实现对调度事件的实时跟踪，最后建立精简模型, 增强了数据校正的可行性.仿真研究证实了该方法的有效性.     

Optimal scheduling of continuous plants with energy constraints

This work addresses the scheduling of continuous single stage multiproduct plants with parallel units and shared storage tanks. Processing tasks are energy intensive and we consider time-dependent electricity pricing and availability together with multiple intermediate due dates, handled as hard constraints. A new discrete-time aggregate formulation is proposed to rapidly plan the production levels. It is combined with a continuous-time model for detailed scheduling as the essential part of a rolling-horizon algorithm. Their computational performance is compared to traditional discrete and continuous-time full-space formulations with all models relying on the Resource-Task Network (RTN) process representation. The results show that the new models and algorithm can generate global optimal schedules much more efficiently than their counterparts in problems involving unlimited power availability. Under restricted power, the aggregate model underestimates the electricity cost, which may cause the rolling-horizon approach to converge to a suboptimal solution, becoming the discrete-time model a better approach.     

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.     

Efficient scheduling method of complex batch processes with general network structure via agent‐based modeling

A novel efficient agent‐based method for scheduling network batch processes in the process industry is proposed. The agent‐based model is based on the resource‐task network. To overcome the drawback of localized solutions found in conventional agent‐based methods, a new scheduling algorithm is proposed. The algorithm predicts the objective function value by simulating another cloned agent‐based model. Global information is obtained, and the solution quality is improved. The solution quality of this approach is validated by detailed comparisons with the mixed‐integer programming (MIP) methods. A solution close to the optimal one can be found by the agent‐based method with a much shorter computational time than the MIP methods. As a scheduling problem becomes increasingly complicated with increased scale, more specifications, and uncertainties, the advantages of the agent‐based method become more evident. The proposed method is applied to simulated industrial problems where the MIP methods require excessive computational resources. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2884–2906, 2013     

Nonlinear scheduling with time-variable electricity prices using sensitivity-based truncations of wavelet transforms

We propose an algorithm for scheduling subject to time-variable electricity prices using nonlinear process models that enables long planning horizons with fine discretizations. The algorithm relies on a reduced-space formulation and enhances our previous work (Schäfer et al., Comput Chem Eng, 2020;132:106598) by a sensitivity-based refinement procedure. We therein expose the coefficients of the wavelet transform of the time series of independent process variables to the optimizer. The problem size is reduced by truncating the transform and iteratively adjusted using Lagrangian multipliers. We apply the algorithm to the scheduling of a multi-product air separation unit. The nonlinear power consumption characteristic is replaced by an artificial neural network trained on data from a rigorous model. We demonstrate that the proposed algorithm reduces the number of optimization variables by more than one order of magnitude, whilst furnishing feasible schedules with insignificant losses in objective values compared to solutions considering the full dimensionality.     

Rolling horizon based planning and scheduling integration with production capacity consideration

The rolling horizon method has been proposed to address the integrated production planning and scheduling optimization problem. Since the method can generally result in small-scale optimization model and fast solution, it has been used in a number of applications in realistic industrial planning and scheduling problems. In this paper, it is first pointed out that the incorporation of valid production capacity information into the planning model can improve the solution quality in the rolling horizon solution framework. A novel method is then proposed to derive the production capacity information representing the detail scheduling model based on parametric programming technique. A heuristic process network decomposition strategy is further applied to reduce the computational effort needed for larger and more complex process networks. Several case studies have been studied, which illustrate the efficiency of the proposed methodology in improving the solution quality of rolling horizon method for integrated planning and scheduling optimization.     

A flexible air separation process: 1. Design and steady-state optimizations

The flexible operation of energy-intensive processes, such as cryogenic air separation, has economic potential due to increasing fluctuations of the electricity markets. Multiproduct air separation processes with high ratios of liquid product are very promising for flexible operation due to storable products. We present a process design with an integrated liquefication cycle and liquid assist operation, that facilitates a high liquid product ratio and a flexible process operation. We use a mechanistic dynamic process model in steady-state process optimizations covering the wide operational range of the proposed process. The optimization results show that the power demand can be varied in a range from 3.5 to 28 MW without violating operational constraints by changing the nitrogen and oxygen production rates. Thus, the proposed process is a promising air separation candidate for flexible operation with respect to fluctuating electricity markets.     

Energy demand management for process systems through production scheduling and control

Demand response (DR) is an integral part of the Smart Grid paradigm, and has become the focus of growing research, development, and deployment in residential, commercial and industrial systems over the last few years. In process systems, energy demand management through production scheduling is an increasingly important tool that has the potential to provide significant economic and operational benefits by promoting the responsiveness of the process operation and its interactions with the utility providers. However, the dynamic behavior of the underlying process, especially during process transitions, is seldom taken into account as part of the DR problem formulation. Furthermore, the incorporation of energy constraints related to electricity pricing and energy resource availability presents an additional challenge. The goal of this study is to present a novel optimization formulation for energy demand management in process systems that accounts explicitly for transition behaviors and costs, subject to time‐sensitive electricity prices and uncertainties in renewable energy resources. The proposed formulation brings together production scheduling and closed‐loop control, and is realized through a real‐time or receding‐horizon optimization framework depending on the underlying operational scenarios. The dynamic formulation is cast as a mixed‐integer nonlinear programming problem based on a proposed discretization approach, and its merits are demonstrated using a simulated continuous stirred tank reactor where the energy required is assumed to be roughly proportional to the material flow. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3756–3769, 2015     

Demand response potential of industrial processes considering uncertain short-term electricity prices

Time-varying electricity prices on the day-ahead and intraday market incentivize demand response of industrial processes. In prior work (Schäfer et al. AIChE J. 2020;66:1-14), we studied the demand response potential with a generalized process model, but neglected the intraday market. Extending our prior investigation, we account for uncertain intraday prices in a mixed-integer linear stochastic programming-based scheduling, that is, we minimize expected cost and conditional value-at-risk in a bi-objective optimization. We find that for very broad variations of the generalized process parameters, the conditional value-at-risk can be reduced significantly without drastically increasing the expected cost. Furthermore, simultaneously improving multiple process parameter leads to synergetic benefits. Moreover, the savings of three electrolysis processes can be more than doubled by marketing flexibility on the intraday market in addition to the day-ahead market. Overall, our model allows for a rapid early assessment of the demand response potential considering the two markets.     

Planning and scheduling of flexible process networks under uncertainty with stochastic inventory: MINLP models and algorithm

The tactical planning and scheduling of chemical process networks consisting of both dedicated and flexible processes under demand and supply uncertainty is addressed. To integrate the stochastic inventory control decisions with the production planning and scheduling, a mixed‐integer nonlinear programming (MINLP) model is proposed that captures the stochastic nature of the demand variations and supply delays using the guaranteed‐service approach. The model takes into account multiple tradeoffs and simultaneously determines the optimal selection of production schemes, purchase amounts of raw materials, sales of final products, production levels of processes, detailed cyclic production schedules for flexible processes, and working inventory and safety stock levels of all chemicals involved in the process network. To globally optimize the resulting nonconvex MINLP problems with modest computational times, the model properties are exploited and a tailored branch‐and‐refine algorithm based on the successive piecewise linear approximation is proposed. To handle the degeneracy of alternative optima in assignment configurations of production scheduling, three symmetry breaking cuts are further developed to accelerate the solution process. The application of the model and the performance of the proposed algorithm are illustrated through three examples with up to 25 chemicals and 16 processes including at most 8 production schemes for each flexible process. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1511–1532, 2013     

聚氯乙烯生产过程全流程调度

研究了电石法制聚氯乙烯(PVC)全流程生产调度问题, 包括从电石生产、盐水电解到氯乙烯(VCM)聚合产品出厂各环节, 其中电石生产和VCM聚合是间歇过程, 其他生产环节是连续过程, 是一个混杂系统调度问题。本文针对过程特性对该问题进行了合理假设, 以包括电耗、库存、产品型号切换、交货延迟等的成本最小为目标, 建立了基于离散时间表示的混合整数线性规划(MILP)调度优化模型, 并针对一个案例进行了调度优化求解和分析, 验证了模型的可行性。     

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.     

Petri-net based scheduling strategy for semiconductor manufacturing processes

Semiconductor manufacturing is a highly automated and capital-intensive industrial process. The operating cost of a wafer processing plant is in general closely related to the design and management of its process flows. Traditionally, the task of production scheduling is performed manually on the basis of past experiences. There are thus real incentives to develop a systematic approach to construct a mathematical programming model in order to reduce the chance of human errors and to ensure operational efficiency in implementing the resulting schedules. To this end, the Petri nets are adopted in this work to accurately model the semiconductor manufacturing activities. The token movements in a Petri net are represented with the well-established scheduling model for batch chemical processes, and the optimal schedule of the given semiconductor process can then be determined accordingly. The feasibility and effectiveness of this scheduling strategy is demonstrated in the present paper with three examples, i.e., the final test process, the re-entrant flow process, and the photolithography-etching process.     

Operating condition diagnosis based on HMM with adaptive transition probabilities in presence of missing observations

A new approach for modeling and monitoring of the multivariate processes in presence of faulty and missing observations is introduced. It is assumed that operating modes of the process can transit to each other following a Markov chain model. Transition probabilities of the Markov chain are time varying as a function of the scheduling variable. Therefore, the transition probabilities will be able to vary adaptively according to different operating modes. In order to handle the problem of missing observations and unknown operating regimes, the expectation maximization algorithm is used to estimate the parameters. The proposed method is tested on two simulations and one industrial case studies. The industrial case study is the abnormal operating condition diagnosis in the primary separation vessel of oil‐sand processes. In comparison to the conventional methods, the proposed method shows superior performance in detection of different operating conditions of the process. © 2014 American Institute of Chemical Engineers AIChE J, 61: 477–493, 2015