# On meeting Energy Balance Errors in Cosimulations

## TL;DR

This paper addresses the challenge of energy balance errors in coupled simulations, proposing a method to accurately balance energy across subsystems to improve simulation accuracy.

## Contribution

It introduces a novel method to precisely balance energy in co-simulations, overcoming limitations of previous balance correction techniques.

## Key findings

- The proposed method effectively reduces energy balance errors.
- It improves the accuracy of coupled simulation results.
- The method maintains system-wide energy consistency.

## 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 explicit 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.