Energy conservation and power bonds in co-simulations: non-iterative adaptive step size control and error estimation

Here, we study the flow of energy between coupled simulators in a co-simulation environment using the concept of power bonds. We introduce energy residuals which are a direct expression of the coupling errors and, hence, the accuracy of co-simulation results. We propose a novel energy-conservation-based co-simulation method (ECCO) for adaptive macro step size control to improve accuracy and efficiency. In contrast to most other co-simulation algorithms, this method is non-iterative and only requires knowledge of the current coupling data. Consequently, it allows for significant speed-ups and the protection of sensitive information contained within simulator models. A quarter car model with linear and nonlinear damping serves as a co-simulation benchmark and verifies the capabilities of the energy residual concept: reductions in the errors of up to 93% are achieved at no additional computational cost.