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Researchers should cite this work as follows:

• Weber, F. (2023). 2018-Weber_Theers_Surmann_Ligges_Weihs-Sensitivity Analysis_of_Ordinary_Differential_Equation_Models. SIMIODE, QUBES Educational Resources. doi:10.25334/0PTZ-0B28

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Weber, Frank, Stefan Theers, Dirk Surmann, Uwe Ligges, and Claus Weihs. 2018. Sensitivity Analysis of Ordinary Differential Equation Models.

See https://d-nb.info/1160443556/34 .Accessed 8 March 2023.

Introduction The goal of sensitivity analysis is to examine how sensitive a mathematical model responds to variations in its input variables (Confalonieri et al., 2010). This incorporates, according to Confalonieri et al. (2010), the identification of relevant model inputs, model balance, model simplification and general model building. Two major approaches to sensitivity analysis can be distinguished: local and global sensitivity analysis. Local sensitivity analysis investigates the model response when only one parameter is varied when holding all other parameters at constant central values. Global sensitivity analysis investigates the model response when every existing parameter in the model is varied (see Saltelli et al., 2010 or Confalonieri et al., 2010). Although local methods are easier to implement, today global sensitivity analysis techniques are more common as their results do not depend on central values. Confalonieri et al. (2010) list three classes of global sensitivity analysis techniques: regression, screening and variance-based methods. The most well-known representatives of the two latter ones will be treated here.

This report will focus on the sensitivity analysis of ordinary differential equation (ODE) models since they can be used to model so-called Low Frequency Oscillations (LFOs). LFOs are permanent complex valued voltage oscillations with a frequency of up to 2 Hz occurring in electrical systems like the European electrical transmission system. As an energy network is an “electro-mechanical system” with power produced and consumed by mechanical systems, Surmann et al. (2014) point out that a mechanical system of connected harmonic oscillators is suitable for modeling LFOs. Mathematically, this model is based on a system of ordinary differential equations.

Keywords: sensitivity, parameter, system, regression