Flexibility of Integrated Power and Gas Systems: Gas Flow Modeling and Solution Choices Matter

TL;DR

A unified framework for modeling and solution choices on the flexibility provision from gas networks to power systems is developed and one key conclusion is that relaxation-based approaches allow charging and discharging the linepack at physically infeasible high rates, ultimately overestimating the flexibility.

Abstract

Due to their slow gas flow dynamics, natural gas pipelines function as short-term storage, the so-called linepack. By efficiently utilizing linepack, the natural gas system can provide flexibility to the power system through the flexible operation of gas-fired power plants. This requires accurately representing the gas flow physics governed by partial differential equations. Although several modeling and solution choices have been proposed in the literature, their impact on the flexibility provision of gas networks to power systems has not been thoroughly analyzed and compared. This paper bridges this gap by first developing a unified framework. We harmonize existing approaches and demonstrate their derivation from and application to the partial differential equations. Secondly, based on the proposed framework, we numerically analyze the implications of various modeling and solution choices on the flexibility provision from gas networks to power systems. One key conclusion is that relaxation-based approaches allow charging and discharging the linepack at physically infeasible high rates, ultimately overestimating the flexibility.

Figures (6)

• Figure 1: Case Study A: Schematic diagram of the integrated power-gas network.
• Figure 2: Gas load, wind power generation, and electricity load profiles in a 5 time resolution for an illustrative day energinet.
• Figure 3: Case Study A: Change of linepack in pipeline $p_2$ and total electrical load shedding for the $\mathrm{DY}$ (first row), $\mathrm{QD}$ (second row), and $\mathrm{ST}$ (third row) models with a time discretization $\Delta t$ of 1 (first column) and 15 (second column). Red and blue colors refer to the solution of the $\mathrm{NLP}$ and $\mathrm{MISOCP}$ models, respectively. For the latter, the relaxation gap \ref{['eq:def_relaxation_gap']} is shown in light blue. For the $\mathrm{ST}$ model, the linepack change is denoted differently from the $\mathrm{DY}$ and $\mathrm{QD}$ models (i.e., spike instead of continuous line) to indicate that the intertemporal linepack change cannot be exploited. The change of linepack is normalized by the maximum feasible linepack of pipeline $p_2$. The electrical load shedding is the share of the total hourly demand. The change in linepack and load shedding for the models with 15 resolution are aggregated over each hour.
• Figure 4: Comparison of the feasible regions defined by different solution choices $\mathbf{S}$ for an illustrative pipeline and fixed pressure $\pi = \widehat{\Pi}$. The feasible regions of $\mathrm{MILP}$ and $\mathrm{MISOCP}$ are separated by the binary variable $z$ indicating the flow direction. The grey dotted area shows the extension of the feasible regions of $\mathrm{MILP}$ and $\mathrm{MISOCP}$ without the linear overestimator (LO) \ref{['eq:LO_def']}. For illustration purposes, a reduced number of halfspaces is shown for $\mathrm{PELP}$ and $\mathrm{MILP}$. All relaxations include the feasible region defined by the nonconvex constraint $\mathrm{NLP}$.
• Figure 5: Case study B: GasLib 40-node gas network connected to 24-bus IEEE RTS system. Pipeline colors indicate the value of the RMS relaxation gap of each discretized pipeline segment for the optimal solution of model $\mathrm{DY}$-$\mathrm{PELP}$.