Hard uncertainties in multiobjective layout optimization of photovoltaic power plants

Abstract

This paper describes how to treat hard uncertainties defined by so-called uncertainty maps in multiobjective optimization problems. For the uncertainty map being set-valued, a Taylor formula is shown under appropriate assumptions. The hard uncertainties are modeled using parametric set optimization problems for which a scalarization result is given. The presented new approach for the solution of multiobjective optimization problems with hard uncertainties is then applied to the layout optimization of photovoltaic power plants. Since good weather forecasts are difficult to obtain for future years, weather data are really hard uncertainties arising in the planning process. Numerical results are presented for a real-world problem on the Galapagos island Isabela.

Keywords:

• Multiobjective optimization
• parametric set optimization
• uncertainties
• photovoltaic power plants

Acknowledgements

We would like to express our gratitude to Karl-Heinz Küfer, Kai Plociennik and colleagues of the Department Optimization, Fraunhofer ITWM (Germany), for the great and close cooperation with Siemens AG over multiple years in the PVplanet project. Without this photovoltaic layout planning software (cf. [17]), the extensive evaluation in this paper would not have been possible. The authors thank two anonymous referees for their valuable suggestions.

Notes

1 http://meteonorm.com/de/.