Determination of operability limits using simplicial approximation

Goyal, Vishal; Ierapetritou, Marianthi G.

doi:10.1002/aic.690481217

Cited by 58 publications

(35 citation statements)

References 7 publications

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“…The constructed convex hull is guaranteed to be inscribed in the actual feasible region, however, only if the feasible region is convex. To evaluate the feasibility of nonconvex processes, Goyal and Ierapetritou (2003) develop an approach in which the feasible region is approximated by subtracting outer polytopes around the infeasible regions from an expanded convex hull obtained by simplicial approximation (Goyal and Ierapetritou 2002). Sung and Maravelias (2007) propose an attainable region approach that determines the feasible production levels of the underlying MILP production scheduling model and an underestimation of the production cost in an integrated planning and scheduling framework.…”

Section: Introductionsupporting

confidence: 40%

Data-driven construction of Convex Region Surrogate models

et al. 2015

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As we strive to solve more complex and integrated optimization problems, there is an increasing demand for process models that are sufficiently accurate as well as computationally efficient. In this work, we develop an algorithm for the data-driven construction of a type of surrogate models that can be formulated as mixed-integer linear programs yet still provide good approximations of nonlinearities and nonconvexities. In such a surrogate model, which we refer to as Convex Region Surrogate, the feasible region is given by the union of convex regions in the form of polytopes and for each region, the objective function can be approximated by a linear function. In this paper, we present the proposed two-phase algorithm and demonstrate its effectiveness with a real-world case study.

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Section: Introductionsupporting

confidence: 40%

Data-driven construction of Convex Region Surrogate models

et al. 2015

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“…In constraint (14), the product demand d t,s,h g is met on an hourly level by either own production or external product purchases, B t,s,h g , for each time period t and scenario s. In the particular case of an air separation plant, liquid oxygen and nitrogen are commodity products that can also be shipped from a different plant or be procured from a competitor if the plant is not able to meet demand. The latter case is covered by so-called product-swap agreements that allow to pick up product at a competitor's plant for a pre-set price.…”

Section: Mass Balances and Demand Satisfaction Constraintsmentioning

confidence: 42%

Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part I: Modeling

Mitra

Pinto²,

Grossmann

2014

Computers & Chemical Engineering

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With the advent of deregulation in electricity markets and an increasing share of intermittent power generation sources, time-sensitive electricity prices (as part of so-called demand-side management in the smart grid) offer potential economical incentives for large industrial customers. These incentives have to be analyzed from two perspectives. First, on an operational level, aligning the production planning with the electricity price signal might be advantageous, if the plant has enough flexibility to do so. Second, on a strategic level, investments in retrofits of existing plants, such as installing additional equipment, upgrading existing equipment, or increasing product storage capacity, facilitate cost savings on the operational level by increasing operational flexibility.In part I of this paper, we propose an MILP formulation that integrates the operational and strategic decision-making for continuous power-intensive processes under time-sensitive electricity prices. We demonstrate the trade-off between capital and operating expenditures with an industrial case study for an air separation plant. Furthermore, we compare the insights obtained from a model that assumes deterministic demand with those obtained from a stochastic demand model. The value of the stochastic solution (VSS) is discussed, which can be significant in cases with an unclear setup, such as medium baseline product demand and growth rate, large variance or skewed demand distributions. While the resulting optimization models are very large-scale, they can mostly be solved within up to three days of computational time. A decomposition algorithm that allows solving the problems faster is described in part II of the paper.

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“…5), Goyal & Ierapetritou (2002) presented an approach based on the ideas of inner and outer approximation of the feasible region in order to measure the entire feasible region. However, they restricted themselves to the case of no control variables.…”

Section: Simplicial Approximation To Feasibility Limitsmentioning

confidence: 42%

“…Steps in simplicial approximation. Initial convex hull (1,2,3) and the resulting convex hull (1,2,3,4) after one iteration (Goyal & Ierapetritou, 2002). …”

Section: Flexible Design With Confidence Intervals and Process Variabmentioning

confidence: 45%

Evolution of concepts and models for quantifying resiliency and flexibility of chemical processes

Grossmann

Calfa

García-Herreros

2014

Computers & Chemical Engineering

117

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This paper provides a historical perspective and an overview of the pioneering work that Manfred Morari developed in the area of resiliency for chemical processes. Motivated by unique counter-intuitive examples, we present a review of the early mathematical formulations and solution methods developed by Grossmann and co-workers for quantifying Static Resiliency (Flexibility). We also give a brief overview of some of the seminal ideas by Manfred Morari and co-workers in the area of Dynamic Resiliency. Finally, we provide a review of some of the recent developments that have taken place since that early work.1

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Determination of operability limits using simplicial approximation

Cited by 58 publications

References 7 publications

Data-driven construction of Convex Region Surrogate models

Data-driven construction of Convex Region Surrogate models

Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part I: Modeling

Evolution of concepts and models for quantifying resiliency and flexibility of chemical processes

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