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

Abstract

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 EnergyConservation-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 noniterative 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.

Virtual prototyping of maritime systems and operations: applications of distributed co-simulations

“…The accuracy of the simulation results can be discussed from the power residuals too, since low power residuals means high accuracy in simulation results due to the discrete communication point. The simulation results from the control systems and the vessel motion in this case study are also converging to the simulation results in [37] where almost the same system is simulated as a continuous system except that the power plant model and the electrical motors 14 also argue for stable thruster control systems since the energy residuals seem to be bounded, in contrast to the uncontrolled quarter-car cosimulation system studied in [34] where the energy residuals keep growing during the co-simulation. Hence, co-simulations can also be used as a tool for tuning the control systems before being installed in real processes, which are also affected by sampling characteristics and sampling delays.…”

“…Hence, a subsystem would either receive/transmit too much power or too little power to the submodel environment in transient simulation regions, due to the fundamentals in the co-simulation strategy, and this affects the accuracy of the simulation results as well as the stability of the system. This is thoroughly studied in [34], which proposes an energyconservation-based co-simulation method (ECCO) that aims to reduce the power discrepancy between submodels.…”

“…This makes it ideal for practical use, as re-stepping is often not supported by models, especially the custom-made models commonly used in industrial and research settings. For more details about ECCO, the reader is referred to [34]. Stability and accuracy in co-simulations have been minor research topics in the ViProMa project and more research should be devoted to these topics in the future.…”

“…This is one of the drawbacks by using co-simulations. However, by applying suited co-simulation algorithms that minimize these sampling characteristics, such as the ECCO algorithm presented in [34], or by manually setting the communication time step small in comparison to the smallest dynamical time constant in the co-simulation [41], the related numerical simulation errors and the corresponding power residuals can be reduced. However, in this particular case study the idea is to mimic the sampling characteristics and the sampling delays that are present in realistic controlled systems.…”

An empirical survey on co-simulation: Promising standards, challenges and research needs

“…Impact of coupled error controlled algorithms [12,28] 5.7 6.0 5.8 Uncertainty quantification/propagation [7,39] 5.6 6.0 5.8 Impact of updating inputs (and the discontinuity it introduces) in the subsystems [10,20]. 5.6 6.0 5.7 Acausal approaches for co-simulation [59] 5.6 6.0 5.7 Impact of using different tolerances in a sub-component on the overall simulation [3] 5.3 6.0 5.5 Numerical stability [11,22,21] 5. Most research needs (all except simulator black boxing and IP protection) are assessed by the experts with a interpolated median value greater 4.5, corresponding to at least "Somewhat agree".…”