1.1. Motivation
In order to achieve greenhouse gas neutrality, energy policies like the Green Deal of the European Commission aim for energy system integration [
1]. Besides high energy efficiency, integrated energy systems are characterized by a versatile energy mix that includes molecule-based energy carriers in addition to electricity [
2]. These include natural gas transitionally and hydrogen, as well as biogenic and synthetic methane in the long term. Moreover, a coordinated and cross-sectoral operation of the energy infrastructures, hereinafter referred to as integrated energy infrastructures (IEI), is an important property of integrated energy systems [
2].
In renewable energy systems, the electricity infrastructure needs to integrate large amounts of intermittent renewable energy sources (RES). This results in high demand for spatial and temporal flexibility in terms of transport as well as short-term and seasonal storage options [
3]. A bidirectional coupling with the existing gas infrastructure by gas-fired power plants and power-to-gas plants can provide this flexibility [
4]. In addition to the existing natural gas infrastructure, dedicated hydrogen infrastructures are supposed to integrate RES and supply a future hydrogen economy [
5].
In order to derive design principles for the future system, a comprehensive understanding of interactions between these infrastructures in operation is required. For example, cost-benefit analyses can be applied to analyze, evaluate, and compare different concepts of IEI. Such analyses require a dispatch simulation in order to determine key indicators such as costs, emissions or energy not served [
6,
7].
For modeling the dispatch of IEI, different requirements arise. IEI enable raising system-wide synergies to operate the energy system cost-efficiently, sustainably, and securely. However, interdependencies between the coupled infrastructures increase. To adequately address these, an integrated modeling approach rather than a co-simulation approach is necessary [
8]. Furthermore, the provision of temporal flexibility by IEI requires the modeling of a full year in at least hourly resolution [
9]. Besides temporal resolution, the choice of spatial resolution has a strong impact on the results of energy system modeling [
10]. To sufficiently model spatial flexibility, its transmission losses, and operating limits, the physical laws determining the power flows must be considered [
8,
11]. Finally, the modeling should be applicable to real interconnected energy systems, such as the European energy system to draw application-related conclusions. Thus, the following criteria serve as requirements for this paper:
Integrated modeling of multi-energy-infrastructures
Consideration of a full year in at least hourly resolution
Consideration of transmission systems in nodal resolution and the physical laws determining their power flows (electricity and gas flows)
Application on real, large-scale energy systems
1.2. Literature Review on Dispatch Models for IEI
In the following, selected models are analyzed with respect to the raised requirements. They either explicitly or implicitly simulate and optimize the dispatch of energy infrastructures.
Table 1 provides an overview of selected models. The discussed models consider at least two coupled infrastructures and pursue an integrated modeling approach. This list does not claim to be complete but is intended to provide a broad overview of the literature.
Integrated electricity and gas market models represent a model class of dispatch models that focus on simulating the dispatch of power plants (Unit Commitment and Economic Dispatch) and gas supply [
12,
13,
14,
15,
16]. Due to present dependencies on district heating systems, these are mostly modeled as additional boundary conditions for dispatch. Market simulations have a high application orientation and are therefore usually applied to real energy systems such as the European or American energy markets [
12,
14]. These models focus on a full-year consideration with high temporal resolution (1 h or 15 min) as well as a high level of technical detail in the modeling of power plants.
In contrast, the modeling of transmission networks for electricity is often simplified by considering exchange capacities between bidding zones, following the zonal electricity market design [
12,
13,
16]. Transport within a bidding zone is then assumed to be free of congestion. Alternatively, market simulations can model the nodal electricity market design such as the commercial software
PLEXOS [
16].
PLEXOS applies the DC power flow approximation. In market simulations, the transmission networks for gas are usually modeled with a network flow algorithm with linear transfer capacities neglecting fluid mechanics. Market simulations often apply decomposition approaches such as Lagrange relaxation [
17] to solve the resulting linear (LP) or mixed-integer problem (MIP) [
13,
16].
Investment models have similar qualities to market simulations since this model class needs to model the system dispatch to adequately derive investment decisions. In contrast to market simulations, investment models inherently consider the energy system as a whole, so that interactions between all relevant energy carriers are taken into account. In addition to aggregation in the spatial dimension, investment models such as
DIMENSION+ [
18],
REMod-D [
19],
IKARUS [
20], and
PRIMES [
21] often aggregate in the temporal dimension to extrapolate the operating costs from type days or weeks. Other investment models like
TIMES [
22],
REMix [
23,
24], and
PyPSA [
25] increase their spatial resolution by modeling smaller regions or even network nodes and applying a DC power flow (see next paragraph) between its interconnectors. Nemec-Begluk [
26] develops a nested decomposition approach that allows modeling the transmission grid in nodal resolution with a DC power flow. Subsequent to the investment decisions, the total period is sliced into smaller sections. Again, gas infrastructures are not physically modeled in these approaches. Nonetheless,
REMix uses a more detailed representation of the gas infrastructure compared to other investment models. It considers additional operational aspects of gas infrastructure dispatch such as estimations for driving energy of compressors [
24].
Optimal power and gas flow models (OPGF) represent a class of dispatch models, which model the physical laws of power and gas flows in detail. Thus, they consider the physical potentials voltage and pressure. Since the integrated operation of the networks also includes the dispatch of conversion plants such as power-to-gas plants or gas-fired power plants, these models often optimize the dispatch of these plants in addition to network optimization. For these models, modeling the non-linear physical laws resulting from power and gas flows is the main challenge. The AC power flow equations describe the trigonometric and quadratic dependence of active and reactive power flow from voltage magnitude and phase angle. By assuming flat voltage profiles, small voltage angle differences and small resistance to reactance ratios (R/X), linear dependencies arise for modeling the active power flow [
27]. This so-called DC power flow approximation is a permissible and common simplification for planning issues at transmission grid level [
11]. Gas flows are determined by fluid mechanics and described by three differential equations for mass, momentum, and energy conservation [
8]. Thus, transient modeling of dynamic gas flows requires high spatial and temporal resolution. Complexity can be reduced by assuming steady-state conditions, which is a common simplification for planning issues of gas transmission networks [
28]. However, this still results in a non-linear system of equations [
29]. Under so called quasi-steady-state conditions, slow dynamics of mass conservation of gases and linepack flexibility can be simplified considered in hourly resolution [
29,
30,
31,
32].
The commercial software
SAInt [
8,
33] provides an integrated modeling approach with AC power flows and transient gas flows. Source [
30,
34] also model the physical flows in detail. Other approaches like [
31,
35,
36,
37,
38,
39] apply the DC power flow approximation as well as steady-state gas flow assumptions to reduce the complexity of the OPGF problem. Sources [
29,
30,
31,
32] consider simplified gas dynamics by using a quasi-steady-state formulation. The non-linear optimization problem is often solved by applying piecewise linearization approaches like in [
35,
38,
39] or non-linear solvers like in [
30,
34,
37]. The resulting problem is often applied to small test systems and periods of usually 24 h since these approaches are difficult to scale up for large problem sizes [
29]. Chaudry et al. [
36] solve the OPGF problem for large-scale systems and 24 h using a commercial solver based on successive linear programming (SLP). However, they also address problems with further scalability. Löhr et al. [
29] introduce a SLP-based approach showing good scaling properties. It is applied to a power and gas transmission system with over 500 nodes each for a 24 h period.
The OPGF problem commonly considers the electricity and natural gas infrastructure. A bidirectional coupling of electricity and gas infrastructure is a comparatively new aspect. Therefore, power-to-gas plants are only modeled in [
29,
30,
33]. Schwele et al. [
40] additionally consider heat infrastructures with physical thermal power flows. Hydrogen transport grids are a new research topic in energy system analysis and are not considered explicitly in the presented literature. The
Energy Hub Concept by Geidl [
41,
42] basically allows modeling any number of infrastructures and conversion processes between different energy carriers as well as AC power and steady-state gas flows.
Therefore, this literature review shows a research gap. On the one hand, there are energy system models, that can be applied for long periods and large-scale systems but have a low spatial and technical resolution when modeling transmission infrastructures. On the other hand, there are models with high spatial and technical detail, but can only be applied to short periods and small systems. Thus, to the best of the author’s knowledge, no model that meets all listed requirements for dispatch simulation of IEI exists.
Table 1.
Overview of selected existing dispatch models for integrated energy infrastructures.
Table 1.
Overview of selected existing dispatch models for integrated energy infrastructures.
References | Name | Model Class | Energy Carrier | Physics Power/Gas | Spatial Scope/Resolution | Temporal Scope/Resolution |
---|
[12] | Riepin et al. | Market | electricity, gas | network flow | Europe/country | year/1 h |
[13] | Baumann | Market | electricity, gas | network flow | Europe/country | year/1 h (1 d) |
[14,15] | Quelhas et al. | Market | electricity, gas, coal | network flow | USA/US regions | year/1 h |
[16] | PLEXOS | Market | electricity, gas, heat | DC/network flow | USA/Europe/nodal | year/(≥1 min) |
[21] | PRIMES | Invest | total energy system | DC/network flow | Europe /country | years/1 h (type) |
[23,24] | REMix | Invest | total energy system | DC/network flow | Germany/regions | years/1 h |
[25] | PyPSA | Invest | total energy system | DC/network flow | Europe/nodal | years/1 h |
[26] | Nemec-Begluk | Invest | electricity, gas, heat | DC/network flow | Austria/nodal | year/1 h |
[41,42] | Geidl | OPGF | all (modular) | AC/steady state | 3 × 3 test/nodal | day/1 h |
[38] | Correa-P. et al. | OPGF | electricity, gas | DC/steady state | 24 × 20 test/nodal | day/1 h |
[30] | Sun et al. | OPGF | electricity, gas | AC/q.-steady state | 24 × 20 test/nodal | day/1 h |
[40] | Schwele et al. | OPGF | electricity, gas, heat | DC/steady state | 24 × 12 × 3 test/nodal | day/1 h |
[8,33] | SAInt, Pambour | OPGF | electricity, gas | AC/transient | 30 × 25 test/nodal | day/1 h |
[36] | Chaudry et al. | OPGF | electricity, gas | DC/steady state | 16 × 168 UK/nodal | day/1 h |
[29] | Löhr et al. | OPGF | electricity, gas | DC/q.-steady state | 542 × 524 GER/nodal | day/1 h |
1.3. Contribution and Paper Organization
Hence, the purpose of this paper is to introduce a method that enables dispatch modeling for IEI meeting the requirements listed in
Section 1.1. The novelty of this method is the combined capability of modeling non-linear physical power and gas flows while allowing applicability to large-scale systems and long periods.
The introduced model is based on an integrated optimization approach that models electricity, methane, and hydrogen infrastructures “as a whole” integrated energy infrastructure. A DC-power flow and a quasi-steady-state gas flow formulation allow detailed analyses of IEI on grid node level. Thus, network bottlenecks and transport losses can be determined and the temporal flexibility of gas infrastructures through linepacking can be considered. The basic optimization problem describing the dispatch problem for IEI is formulated in
Appendix A.
These specifications result in a complex mathematical problem, that cannot be solved in a closed-loop optimization with currently available solvers and resources. To enable this level of detail, various model reduction and decomposition techniques are applied. The approach of this paper builds on the SLP-based OPGF model introduced in [
29]. This model is integrated into a three-staged nested heuristic. The nested decomposition approach applies successive zooming techniques that focus first on the temporal, then on the spatial, and finally on the technical dimension. Complexity is handled by model reductions of the other dimensions in each stage, which enables scalability to an entire year in hourly resolution and large-scale systems in high technical detail. The main contribution of this paper is to demonstrate the combined application of several model reduction and decomposition techniques to handle application-oriented, large-scale problems. Therefore, it focuses on the methodology presented in
Section 2.
The closing investigations in
Section 3 are intended to prove the applicability of the approach to large-scale systems and illustrate the temporal, spatial, and cross-sectoral interdependencies in IEI and therefore the benefits of the introduced approach. For this purpose, a use case of the future interconnected European energy system in 2040 with a focused analysis of the dispatch in Germany is considered. Application-oriented analyses of European energy infrastructure with the presented spatial, temporal, and technical scope also represent a novelty.
Section 4 concludes the main findings of this paper.