Conference article

Optimization-friendly thermodynamic properties of water and steam

Marcus Åberg
Department of Automatic Control, Lund University, Sweden

Johan Windahl
Modelon AB, Ideon Science Park, Lund, Sweden

Håkan Runvik
Modelon AB, Ideon Science Park, Lund, Sweden

Fredrik Magnusson
Department of Automatic Control, Lund University, Sweden

Download article

Published in: Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017

Linköping Electronic Conference Proceedings 132:51, p. 449-458

Show more +

Published: 2017-07-04

ISBN: 978-91-7685-575-1

ISSN: 1650-3686 (print), 1650-3740 (online)


This paper describes the development of an optimization-friendly thermodynamic property model of water and steam that covers liquid, vapor, 2-phase as well as the super-critical region. All equations are at least twice continuously differentiable with respect to all model variables and can be used in dynamic optimization problems solved by efficient derivative-based algorithms. The accuracy has been verified against the industry standard IAPWS 97 and performance and robustness has been tested by solving a trajectory optimization problem where the start-up time of a gas power plant has been minimized while satisfying constraints on temperature gradients, pressure and flows. Simulations of various plant models have also been performed to verify and benchmark the implementation. The results show that the new media can be used in both solving dynamic optimization and simulation problems yielding reliable results. The new media has been integrated into Modelon’s Thermal Power library 1.13.


Dynamic optimization, Thermodynamic properties, Power plant start-up, ThermalPower library, WaterIF97, Optimica,


Andersson, J. (2013). A general-purpose software framework for dynamic optimization. Ph. D. thesis. Faculty of Engineering, KU Leuven, Leuven, Belgium.

Aute, V., & Radermacher, R. (2014). Standardized polynomials for fast evaluation of refrigerant thermophyiscal properties. International Refrigeration and Air Conditioning Conference at Purdue. Purdue, Indiana.

Casella, F., Donida, F., & Åkesson, J. (2011). Object-Oriented Modeling and Optimal Control: A Case Study in Power Plant Start-Up. 18th IFAC World Congress.

Griewank, A., & Walther, A. (2008). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, second edition. ISBN: 978-0-89871-659-7.

International Association for the Properties of Water and Steam. (2015). Guideline on the Fast Calculation of Steam and Water Properties with the Spline-Based Table Look-Up Method (SBTL) .

Kretzschmar, H.-J., & Wagner, W. (2008). International Steam Tables. [electronic resource] : Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg.

Kumar, S., & Mathur, T. (2014). Dynamic Load Scheduling of Optimization of Power Plants. Advanced Control of Industrial Processes (AdCONIP). Hiroshima University, Hiroshima, Japan.

Larsson, P.-O. (2015, October). Report from the modelon tutorial at the 2015 modelica conference. Retrieved from

Magnusson, F. (2016). Numerical and symbolic methods for dynamic optimization. PhD thesis, Lund University, Department of Automatic Control, Lund, Sweden.

Magnusson, F., & Åkesson, J. (2015). Dynamic Optimization in Processes, 3(2), 471-496.

Nocedel, J., & Wright, S. (2006). Numerical Optimization. New York, NY: Springer New York.

Parini, P. (2015). Object Oriented Modeling and Dynamic optimization of energy systems with application to combined-cycle power plant start-up. Msc thesis, Politechnico di Milano, Milano.

Petzold, L. R. (1982). A Description of DASSL: A Differential Algebraic System Solver. Presented at IMACS World Congress, Montreal, Canada, August 8-1 3, 1982.

Runvik, H. (2014). Modelling and start-up optimization of a coal-fired power plant. Master’s thesis, Lund University, Department of Automatic Control, Lund.

Schulze, C. (2014). A Contribution to Numerically Efficient Modeling of Thermodynamic Systems. PhD thesis, Technische Universität Braunschweig, Fakultät für Maschinenbau.

Thorade, M., & Saadat, A. (2013). Partial derivatives of thermodynamic state properties for dynamic. Environmental Earth Sciences, 70, 8, 3497-3503.

Wagner, W., Cooper, J., Dittmann, A., Kijima, J., Kretzschmar, H.-J., Kruse, A., . . . Trübenbach, J. (2000). The IAPWS Industrial Formulation 1997 for the Thermodynamic propertiies of Water and Steam. J. Eng. Gas Turbines Power 122, 150-182.

Velut, S., Larsson, P.-O., Runvik, H., Funqvist, J., Bohlin, M., Nilsson, A., & Modarrez Razavi, S. (2014). Production Planning for Distributed District Heating Networks. 11th International Modelica 2015 Conference. Versailles, France.

Windahl, J., Prölss, K., Bosmans, M., Tummescheit, H., van Es, E., & Sewgobind, A. (2014). MultiComponentMultiPhase - A framework for thermodynamics in Modelica. Proceedings of the 11th International Modelica Conference. Versailles, France.

Zimmer, D., Otter, M., Elmqvist, H., & Kurzbach, G. (2014). Custom Annotations: Handling Meta-Information in Modelica. Proceedings of the 10th International Modelica 2014 Conference. Lund, Sweden.

Åberg, M. (2016). Optimisation-friendly modelling of thermodynamic properties of media. Master’s thesis, Lund University, Department of Automatic Control, Lund. Retrieved from

Åkesson, J. (2008). Optimica - An Extension of Modelica Supporting Dynamic Optimization. Proceedings of the 8th International Modelica 2008 Conference. Bielefeld, Germany.

Citations in Crossref