Energy conservation and coupling error reduction in non-iterative co-simulations

Abstract

When simulators are energetically coupled in a co-simulation, residual energies alter the total energy of the full coupled system. This distorts the system dynamics, lowers the quality of the results, and can lead to instability. By using power bonds to realize simulator coupling, the Energy-Conservation-based Co-Simulation method (ECCO) [Sadjina et al. 2016] exploits these concepts to define non-iterative global error estimation and adaptive step size control relying on coupling variable data alone. Following similar argumentation, the Nearly Energy Preserving Coupling Element (NEPCE) [Benedikt et al. 2013] uses corrections to the simulator inputs to approximately ensure energy conservation. Here, we discuss a modification to NEPCE for when direct feed-through is present in one of the coupled simulators. We further demonstrate how accuracy and efficiency in non-iterative co-simulations are substantially enhanced when combining NEPCE with ECCO's adaptive step size controller. A quarter car model with linear and nonlinear damping characteristics serves as a co-simulation benchmark, and we observe reductions of the coupling errors of up to 98 % utilizing the concepts discussed here.

Assessment of Methods for the Real-Time Simulation of Electronic and Thermal Circuits

“…However, this approach to obtainẋ suffers from two shortcomings. First, only the derivative-level expression of the algebraic constraints is explicitly enforced by Equation (5). Accordingly, the accumulation of integration errors causes the solution to drift away from the exact satisfaction of Φ = 0.…”

“…Such simulation processes often describe multiphysics systems of great complexity, composed by subsystems with very different behavior and physical properties. This task can be performed in an efficient way by means of co-simulation schemes, integrating the dynamics of each subsystem with its own dedicated solver, and coupling these through the exchange of a limited set of input and output variables [2][3][4][5]. This is the case of test benches in the automotive industry, in which physical components of a vehicle are interfaced to an RT simulation of the overall system, which may include mechanical, thermal, electronic, or hydraulic effects, as well as interactions with the driving environment.…”

Towards the Verification of Hybrid Co-simulation Algorithms

“…This property is not preserved in näive co-simulation algorithms because of the input approximations, and the non-negligible communication step size. The work in [4], extended in [27], demonstrates a co-simulation algorithm that monitors the power flow between simulators and employs a correction scheme to account for the artificial energy introduced by the co-simulation. The work in [26] complements the above work by showing how the energy residual can be used as an error indicator to control the communication step size.…”

A Novel Approach for Handling Discontinuities in Non-iterative Co-simulation

“…In (Drenth, 2016) the benefit of filtering techniques is demonstrated along very stiff system integration. Recently, in (Sadjina and Pedersen, 2016), an extension of NEPCE for incorporation of direct feedthrough was done. For handling stiff systems linearly-implicit schemes are proposed (Arnold et al, 2007).…”