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A framework for modeling and optimizing dynamic systems under uncertainty

Computers and Chemical Engineering

Nicholson, Bethany L.; Siirola, John D.

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming. We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.

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TYPE Journal Article YEAR 2018
ScopusOSTIDOI

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

Mathematical Programming Computation

Nicholson, Bethany L.; Siirola, John D.; Watson, Jean-Paul W.; Zavala, Victor M.; Biegler, Lorenz T.

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.

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TYPE Journal Article YEAR 2018
ScopusOSTIDOI

A General Framework for Sensitivity-Based Optimal Control and State Estimation

Computer Aided Chemical Engineering

Thierry, David; Nicholson, Bethany L.; Biegler, Lorenz

New modelling and optimization platforms have enabled the creation of frameworks for solution strategies that are based on solving sequences of dynamic optimization problems. This study demonstrates the application of the Python-based Pyomo platform as a basis for formulating and solving Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE) problems, which enables fast on-line computations through large-scale nonlinear optimization and Nonlinear Programming (NLP) sensitivity. We describe these underlying approaches and sensitivity computations, and showcase the implementation of the framework with large DAE case studies including tray-by-tray distillation models and Bubbling Fluidized Bed Reactors (BFB).

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TYPE Conference Poster YEAR 2018
ScopusOSTIDOI

Uncovering New Opportunities from Frequency Regulation Markets with Dynamic Optimization and Pyomo.DAE

Computer Aided Chemical Engineering

Dowling, Alexander W.; Nicholson, Bethany L.

Real-time energy pricing has caused a paradigm shift for process operations with flexibility becoming a critical driver of economics. As such, incorporating real-time pricing into planning and scheduling optimization formulations has received much attention over the past two decades (Zhang and Grossman, 2016). These formulations, however, focus on 1-hour or longer time discretizations and neglect process dynamics. Recent analysis of historical price data from the California electricity market (CAISO) reveals that a majority of economic opportunities come from fast market layers, i.e., real-time energy market and ancillary services (Dowling et al., 2017). We present a dynamic optimization framework to quantify the revenue opportunities of chemical manufacturing systems providing frequency regulation (FR). Recent analysis of first order systems finds that slow process dynamics naturally dampen high frequency harmonics in FR signals (Dowling and Zavala, 2017). As a consequence, traditional chemical processes with long time constants may be able to provide fast flexibility without disrupting product quality, performance of downstream unit operations, etc. This study quantifies the ability of a distillation system to provide sufficient dynamic flexibility to adjust energy demands every 4 seconds in response to market signals. Using a detailed differential algebraic equation (DAE) model (Hahn and Edgar, 2002) and historic data from the Texas electricity market (ECROT), we estimate revenue opportunities for different column designs. We implement our model using the algebraic modeling language Pyomo (Hart et al., 2011) and its dynamic optimization extension Pyomo.DAE (Nicholson et al., 2017). These software packages enable rapid development of complex optimization models using high-level modelling constructs and provide flexible tools for initializing and discretizing DAE models.

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TYPE Conference Poster YEAR 2018
ScopusOSTIDOI
Results 26–50 of 66
Results 26–50 of 66