A direct and analytical method for inverse problems under uncertainty in energy system design: combining inverse simulation and Polynomial Chaos theory

Energy Informatics, vol. 7

Abstract

Abstract This article introduces and formalizes a novel stochastic method that combines inverse simulation with the theory of generalized Polynomial Chaos (gPC) to solve and study inverse problems under uncertainty in energy system design applications. The method is particularly relevant to design tasks where only a deterministic forward model of a physical system is available, in which a target design quantity is an input to the model that cannot be obtained directly, but can be quantified reversely via the outputs of the model. In this scenario, the proposed method offers an analytical and direct approach to invert such system models. The method puts emphasis on user-friendliness, as it enables its users to conduct the inverse simulation under uncertainty directly in the gPC domain by redefining basic algebra operations for computations. Moreover, the method incorporates an optimization-based approach to integrate supplementary constraints on stochastic quantities. This feature enables the solution of inverse problems bounding the statistical moments of stochastic system variables. The authors exemplify the application of the proposed method with proof-of-concept tests in energy system design, specifically performing uncertainty quantification and sensitivity analysis for a Multi-Energy System (MES). The findings demonstrate the high accuracy of the method as well as clear advantages over conventional sampling-based methods when dealing with a small number of stochastic variables in a system or model. However, the case studies also highlight the current limitations of the proposed method such as slow execution speed due to the optimization-based approach and the challenges associated with, for example, the curse of dimensionality in gPC.

Authors 4

1. Sebastian Schwarz corresponding Aachen Institute for Automation of Complex Power Systems

   RWTH Aachen University

   Affiliation as printed

   Institute for Automation of Complex Power Systems, RWTH Aachen University, Mathieustr. 10, 52074, Aachen, Germany

2. Daniele Carta

   Forschungszentrum Jülich

   Affiliation as printed

   Institute of Energy and Climate Research, Forschungszentrum Jülich, Wilhelm-Johnen-Str., 52428, Jülich, Germany

3. Antonello Monti Aachen Institute for Automation of Complex Power Systems

   Fraunhofer Institute for Applied Information Technology · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Fraunhofer Center Digital Energy, Fraunhofer FIT, Hüttenstr. 5, 52068, Aachen, Germany

   Institute for Automation of Complex Power Systems, RWTH Aachen University, Mathieustr. 10, 52074, Aachen, Germany

   JARA-Energy, Wilhelm-Johnen-Str., 52425, Jülich, Germany

4. Andrea Benigni Aachen

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institute of Energy and Climate Research, Forschungszentrum Jülich, Wilhelm-Johnen-Str., 52428, Jülich, Germany

   JARA-Energy, Wilhelm-Johnen-Str., 52425, Jülich, Germany

   RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany