Large-scale empirical study on the momentum equation’s inertia term

Optimal coordinated operation of integrated natural gas and electric power systems: A review of modeling and solution methods

“…Although the difference between DY and QD models is still negligible, it slightly increases with the finer time discretization from 0.72 % to 0.91 %. This is in line with the findings presented in [34], which show that the effect of the inertia term increases with finer time discretization.…”

“…Looking at the first two rows, the QD and DY models achieve very similar linepack profiles, supporting the results found in [34] on the negligible impact of the inertia term. In the ST model, the linepack flexibility cannot be exploited.…”

“…It has been shown, e.g., in [32] and [33], that the contribution of the inertia term to the pressure drop in the conservation of momentum equation ( 3) is relatively low compared to the friction force (less than 1 %). In [34], the magnitude of the inertia term in real-world situations is assessed using a large set of historical data for the German gas network with a high temporal resolution of 3 minutes. The contribution of the inertia term becomes relevant (> 0.5 bar) only when very fast dynamics occur (e.g., sudden shut-down or start-up of a large gas-fired generator), which happens very rarely [34].…”

“…In [34], the magnitude of the inertia term in real-world situations is assessed using a large set of historical data for the German gas network with a high temporal resolution of 3 minutes. The contribution of the inertia term becomes relevant (> 0.5 bar) only when very fast dynamics occur (e.g., sudden shut-down or start-up of a large gas-fired generator), which happens very rarely [34]. As shown in Section OC.2 of the online companion [30], one can verify their empirical findings with the solutions of the optimal gas flow problem.…”

Optimizing transient gas network control for challenging real-world instances using MIP-based heuristics

“…For pipes, we use the friction-dominated model given as (ISO3) in [9]. It is based on the Euler equations modeling the one-dimensional gas flow in straight cylindric pipes and can be derived by assuming a constant temperature (isothermal conditions), gas composition, and compressibility factor, as well as gas velocities much smaller than the speed of sound and a negligible inertia term, which both are usually given in real-world conditions, see [35,9] and [21]. Note that while we assume a constant gas temperature over time, we may consider different temperature levels for different parts of the network to represent changing soil structure or varying depth levels of the pipelines.…”