On Meeting Energy Balance Errors in Co-Simulations

Abstract

In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters into the subsystems under influence. As executed at fixed time points, this data exchange gives the global method a strong explicite component, and as flows of conserved quantities are passed across subsystem boundaries, it is not ensured that systemwide balances are fulfilled: the system is not solved as one single equation system. These balance errors can accumulate and make simulation results inaccurate. Use of higher-order extrapolation in exchanged data can reduce this problem but cannot solve it. The remaining balance error has been handled in past work with balance correction methods which compensate these errors by adding corrections for the balances to the signal in next coupling time step. Further past work combined smooth extrapolation of exchanged data and balance correction.This gives rise to the problem that establishing balance of one quantity a posteriori due to the time delay in general cannot establish or even disturbs the balances of quantities that depend on the exchanged quantities, usually energy. In this work, a method is suggested which allows to choose the quantity that should be balanced to be that energy, and to accurately balance it.

Dynamic Co-Simulation Methods for Combined Transmission-Distribution System With Integration Time Step Impact on Convergence

“…Together they form the DAE for the transmission system. The model is given by the following equation (19) with x T and y T as the set of transmission system differential and algebraic state variables respectively.…”

“…To couple two or more sub-system solvers in time domain, co-simulation methods are used. In co-simulation the sub-systems are solved separately and the immediate mutual influence of subsystems is replaced by exchanging data at fixed time points [19]. In this section, the co-simulation concept is discussed for series and parallel computation of sub-systems and a convergence analysis of these methods is presented.…”

A Stable but Explicit Cosimulation Coupling Method

“…A solution for these stability issues would be helpful in many applications and is the subject of this contribution. It is important to note that all results and figures herein have been published before in [1]. This contribution is a highly condensed presentation of that content for the purpose of reaching the engineering community rather than novelty.…”