Object-Oriented Modeling and Optimal Control: A Case Study in Power Plant Start-Up

Casella, Francesco; Donida, Filippo; Åkesson, Johan

doi:10.3182/20110828-6-it-1002.03229

Cited by 26 publications

(30 citation statements)

References 9 publications

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“…Furthermore, even if the tearing residuals and full system are well-conditioned, the numerical computation ofz i through (21) after having computed the solution of (22) may be numerically unstable. Another potential drawback is that (22) is significantly more dense than (19), which may cause it to actually be more expensive to solve if sparsity is exploited in the computations. This topic is discussed further below.…”

Section: Tearingmentioning

confidence: 99%

“…The benefits of this approach over solving the full diagonal block (19) numerically is that (22) has fewer variables and equations, equal to the number of tearing variables, often allowing it to be solved more efficiently. But a perhaps more important benefit is that a sufficiently good initial guess for convergence is only needed forẑ i , whereas solving the full system would also require a sufficiently good guess forz i .…”

Section: Tearingmentioning

confidence: 99%

“…This problem has become highly industrially relevant during the last decade, due to an increasing need to improve power-generation flexibility due to the unpredictable output of renewable energy sources such as solar and wind power. The model was first developed by Casella et al [19] but has since been further developed. The objective is a quadratic penalty from reference values, with an important upper bound on the turbine thermal stress.…”

Section: Ccppmentioning

confidence: 99%

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Symbolic elimination in dynamic optimization based on block-triangular ordering

Magnusson

Åkesson

2017

Optimization Methods and Software

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We consider dynamic optimization problems for systems described by differential-algebraic equations (DAEs). Such problems are usually solved by discretizing the full DAE. We propose techniques to symbolically eliminate many of the algebraic variables in a preprocessing step before discretization. These techniques are inspired by the causalization and tearing techniques often used when solving DAE initial value problems. Since sparsity is crucial for some dynamic optimization methods, we also propose a novel approach to preserving sparsity during this procedure.The proposed methods have been implemented in the open-source JModelica.org platform. We evaluate the performance of the methods on a suite of optimal control problems solved using direct collocation. We consider both computational time and probability of solving the problem in a timely manner. We demonstrate that the proposed methods often are an order of magnitude faster than the standard way of discretizing the full DAE, and also significantly increase probability of successful convergence.

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Section: Tearingmentioning

confidence: 99%

Section: Tearingmentioning

confidence: 99%

Section: Ccppmentioning

confidence: 99%

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Symbolic elimination in dynamic optimization based on block-triangular ordering

Magnusson

Åkesson

2017

Optimization Methods and Software

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“…The resulting nonlinear model has nine state variables and 127 algebraic variables. A more detailed discussion on the physical modelling of the plant can be found in [11].…”

Section: Physical Model Setupmentioning

confidence: 99%

“…The JModelica.org platform has been used in several industrial applications, including [28,5,35,31,23,11] The JModelica.org compilers generate C-code intended for compilation and linking with numerical solvers. While this is a well established procedure for compiling Modelica models, it suffers from some drawbacks.…”

Section: Jmodelicaorgmentioning

confidence: 99%

Integration of CasADi and JModelica.org

Andersson

Åkesson²,

Casella

et al. 2011

Linköping Electronic Conference Proceedings

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This paper presents the integration of two open source softwares: CasADi, which is a framework for efficient evaluation of expressions and their derivatives, and the Modelica-based platform JModelica.org. The integration of the tools is based on an XML format for exchange of DAE models. The JModelica.org platform supports export of models in this XML format, wheras CasADi supports import of models expressed in this format. Furthermore, we have carried out comparisons with ACADO, which is a multiple shooting package for solving optimal control problems.CasADi, in turn, has been interfaced with ACADO Toolkit, enabling users to define optimal control problems using Modelica and Optimica specifications, and use solve using direct multiple shooting. In addition, a collocation algorithm targeted at solving largescale DAE constrained dynamic optimization problems has been implemented. This implementation explores CasADi's Python and IPOPT interfaces, which offer a convenient, yet highly efficient environment for development of optimization algorithms. The algorithms are evaluated using industrially relevant benchmark problems.

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