Numerical Multilinearization of nonlinear models by sparse grids method

Power systems undergo a fundamental shift towards converter-dominated networks, requiring tools that capture the relevant fast phenomena of power converters while maintaining computational efficiency. Some of these dynamics can be described by multilinear models, which can be represented by tensors. Tensor decomposition techniques can then be used to break the curse of dimensionality. Multilinear models allow multiplications of states as well as state and input variables, which occurs for example in the calculation of active and reactive power. This paper presents a method to approximate nonlinear models by multilinear models numerically using a sparse grid method, which enhances the efficiency of numerical integration in the process of evaluatingthe approximation of nonlinear functions. We demonstrate the effectiveness of this approach through an example of the three bus network model, showing that the sparse grids method provides a robust and efficient solution.