http://cepac.cheme.cmu.edu/pasilectures/sahinidis/NVSpaperthree.pdf

Optimization under uncertainty: state-of-the-art and opportunities

Simultaneous approaches for dynamic optimization problems are surveyed and a number of emerging topics are explored. Also known as direct transcription, this approach has a number of advantages over competing dynamic optimization methods. Moreover, a number of industrial applications have recently been reported on challenging real-world applications. This study provides background information, summarizes the underlying concepts and properties of this approach, discusses recent advances in the treatment of discrete decisions and, finally, illustrates the approach with two process case studies.

An overview of simultaneous strategies for dynamic optimization

Chance constrained programming approach to process optimization under uncertainty

On-line optimization via off-line parametric optimization tools

Flexibility is a widely used term in planning process and real-time operation. The existing research on flexibility uses different techniques to study flexibility property from different aspects. While studying a property from various viewpoints increases the understanding on the subject, we need a consistent theoretical framework to consolidate the ideas generated in the field, compare and contrast results, and build on for future analysis. Based on the insights of the nature of flexibility, this paper proposes a unified framework for defining and measuring flexibility in power system. Under the proposed framework, we propose a flexibility metric which evaluates the largest variation range of uncertainty that the system can accommodate. Such a metric takes into account transmission network and system operations constraints, which are critical to assessing flexibility, but are often ignored in literature. A robust optimization technique is used to calculate the proposed metrics. While the illustrative example presented in this paper focuses on the flexibility in real-time system operation in the presence of wind and load uncertainty, this framework can generally be applicable to long-term studies such as system planning.

A Unified Framework for Defining and Measuring Flexibility in Power System

This article presents an in-depth case study that demonstrates (i) how the process and control design, involving both discrete and continuous decisions, can be simultaneously optimized for systems described by realistic dynamic models and that (ii) mixed-integer dynamic optimization problems, involving thousands of differential−algebraic equations, can now be solved using state-of-the-art algorithms and technology. The study in question involves a distillation column that is subject to time-varying disturbances and time-invariant uncertainty. A new, multicomponent, mixed-integer dynamic distillation model is developed and used to simultaneously determine the number of trays, feed tray location, column diameter, reboiler and condenser surface areas, 5 × 5 control structure, PI-gains, reset times, and set-points, to obtain an economically optimal system that is also guaranteed to give feasible dynamic operation over all uncertainty scenarios.

A case study in simultaneous design and control using rigorous, mixed-integer dynamic optimization models

New algorithms for mixed-integer dynamic optimization

Simultaneous design and control optimisation under uncertainty

A new, unified theory and algorithms, based on multiparametric programming techniques, for the solution of flexibility analysis and design optimization problems in linear process systems are presented. They are used for the flexibility test and index problems in systems with deterministic parameters, and for the stochastic and expected stochastic flexibility evaluation problems in systems with stochastic parameters. They are computationally efficient and give the explicit dependence of various flexibility metrics on the values of the continuous design variables. The latter feature enables the easy and efficient comparison of design alternatives. It also allows for the compact formulation of design optimization problems that can be solved parametrically to yield the exact algebraic form of the trade-off curve of economics against flexibility. Key features of the proposed approach are demonstrated through both mathematical and process examples.

Flexibility analysis and design of linear systems by parametric programming

This article presents a new framework, based on parametric programming, that unifies the solution of the various flexibility analysis and design optimization problems that arise for linear, convex, and nonconvex, nonlinear systems with deterministic or stochastic uncertainties. This approach generalizes earlier work by Bansal et al. It allows (1) explicit information to be obtained on the dependence of the flexibility characteristics of a nonlinear system on the values of the uncertain parameters and design variables; (2) the critical uncertain parameter points to be identified a priori so that design optimization problems that do not require iteration between a design step and a flexibility analysis step can be solved; and (3) the nonlinearity to be removed from the optimization subproblems that need to be solved when evaluating the flexibility of systems with stochastic uncertainties.

/pdf/flexibility-analysis-and-design-using-a-parametric-2769pvz7qf.pdf

V. Bansal

Papers

A case study in simultaneous design and control using rigorous, mixed-integer dynamic optimization models

New algorithms for mixed-integer dynamic optimization

Simultaneous design and control optimisation under uncertainty

Flexibility analysis and design of linear systems by parametric programming

Flexibility analysis and design using a parametric programming framework