Investigation of the Dynamic Behavior of Brayton Batteries for Coupled Generation of Electricity, Heat, and Cooling

Abstract

This study presents a comprehensive dynamic system analysis of air-based Brayton batteries for the coupled generation of electricity, heat, and cooling. Building upon a previously published structural concept study, the most promising system architectures were modeled and evaluated using quasi-stationary simulations with dynamically designed thermal energy storage (TES) in Ebsilon Professional^®. The results show round-trip efficiencies (RTEs) of up to 50% for pure electricity generation and round-trip utilizations (RTUs) exceeding 85% for combined heat and power. Integration of waste heat further increases RTU to more than 100%, albeit at the expense of electrical efficiency. Dynamic simulations demonstrate stable operation with load gradients up to 2 MW min⁻¹, highlighting suitability for flexible industrial and grid applications. Regenerator-based TES exhibits the most favorable trade-off between efficiency and cost, while hybrid configurations of solid and liquid media offer additional optimization potential. The estimated investment costs range between 200 and 800 EUR/kWh_el, comparable to other large-scale Carnot battery systems. The findings provide a validated framework for the techno-economic design and control of next-generation Brayton battery systems and lay the foundation for experimental validation and pilot-scale implementation.

1. Introduction

In [1], the methodology and results of a comprehensive analysis of different concepts for Brayton batteries for the combined generation of electricity, heat, and cooling were presented. Based on a systematic structural analysis, over 200,000 concepts were examined and the efficiency and performance of different configurations were evaluated. The study identified lead concepts for different applications and showed that low-pressure air-driven systems with heat input or removal at different points of the process deliver the most promising results. The results provide important insights into the optimization of Brayton batteries for efficient and sustainable energy production. These investigations formed the basis for this publication. Here, the lead concepts defined in [1] will be examined in more detail using dynamic system simulations, including the design of the components, with a focus on the thermal energy storage (TES).

The state of the art and research on Brayton batteries was described in detail in [1].

Therefore, this paper provides further information on publications that have been released since then. In addition, it provides an overview of the literature on dynamic system considerations and the state of the art in storage technologies suitable for integration into Brayton battery systems.

1.1. Overview of Current Relevant Publications on Brayton Batteries

Brayton batteries remain an active and fast-developing area of research, with current efforts aimed at improving their efficiency, adaptability, and cost-effectiveness. In contrast to electrochemical storage systems such as lithium-ion batteries, they present several noteworthy advantages:

• Scalability: They are well-suited for energy storage on medium-to-large scales.
• Versatile energy output: These systems can deliver not only electrical power but also heating and cooling.
• Long service life and reduced material expenses: Their design avoids the use of rare or degradable materials, offering favorable long-term economic prospects.

Nonetheless, various technical and financial obstacles must still be addressed:

• Suboptimal round-trip efficiency: Present implementations reach efficiencies between 20% and 50%, depending on system architecture [2,3].
• Challenging thermal control: Enhancing performance requires efficient integration of heat exchangers and waste heat recovery systems [2,4].

Several research strategies are being pursued to optimize these systems:

• Broadening the functional scope: Shifting from solely generating electricity to delivering combined electricity, heat, and cooling is a key area of exploration [5,6].
• Investigating alternative working fluids: Gases such as air, carbon dioxide, or argon are being assessed to increase energy conversion efficiency [7,8].
• Integrating waste heat utilization: Capturing and reusing thermal losses offers an avenue for improving overall system performance [6,7].

While thermodynamic analyses remain central [9,10], economic considerations are becoming increasingly relevant. Efforts to lower capital expenditures [11,12] and conduct comprehensive techno-economic assessments [5,13] are critical for enhancing the competitiveness of this technology.

Particular attention is being paid to Brayton cycles operating with CO₂, which show strong potential as an energy storage solution [14,15]. Their compatibility with renewable energy systems—especially solar thermal power plants—could significantly broaden their application range [16,17].

Future advancements are expected to revolve around novel system architectures and material innovations [9,18], as well as hybrid concepts that combine different storage methods [19,20]. Moreover, emerging approaches aim to link Brayton battery systems with chemical processes such as hydrogen production or CO₂ conversion [14,21].

Despite the significant progress made, further technological developments are necessary for Brayton batteries to achieve commercial competitiveness relative to established storage technologies. Continued research must focus on refining both their technical performance and economic viability to fully realize their potential as a promising energy storage option.

1.2. Literature Review on Dynamic System Analyses of Brayton Batteries

The dynamic simulation of Brayton batteries is an increasingly important field of research in the context of the energy transition. In view of the increasing share of fluctuating renewable energies, the ability of these systems to provide load flexibility, operation under off-design conditions, and safe transient behavior are becoming the focus of scientific attention.

A central aspect of dynamic simulation is the mapping of transient processes such as starting processes, load changes, or faults. For example, studies on the DLR CoBra system, a prototype Brayton heat pump with a target temperature above 250 °C, show that the start-up process is subject to special requirements for temperature management and the avoidance of compressor instabilities [22,23]. Modeling the thermal inertia of heat exchangers and pipelines is essential to avoid critical temperature gradients and mechanical resonances. The control strategy used must take this into account as well as the requirements for fast controllability to minimize start-up times.

The ability to react to load changes has also been intensively investigated, for example in the simulation of Brayton heat pumps in partial load operation [24] or in the discharge operation of Carnot battery systems for grid stabilization [25]. This shows that so-called inventory control strategies—i.e., the targeted regulation of the working fluid quantity in the cycle—are an effective method of flexibly adapting the net rated output to the load demand without significantly impairing the thermal quality of the storage temperatures [26,27].

The need to take thermal inertia into account also becomes clear in Carnot battery systems with packed bed storage or latent heat storage. These exhibit slow temperature adjustments, which in turn can lead to delayed performance responses [28,29]. Dynamic modeling that couples heat transfer as well as flow and cycle process dynamics is therefore essential for a realistic assessment of system stability and efficiency. Corresponding models show, among other things, that the design of the particle size, the ratio of storage length to diameter and the compression ratios are decisive for efficiency and stability in discharge operation [28,30].

At the same time, the influence of external thermal influences is also being investigated, for example in solar thermal integrated Carnot battery systems. Here, studies demonstrate that a relatively constant system efficiency can be achieved despite seasonal fluctuations in the solar supply, provided that the components (e.g., heat pumps and Rankine cycles) can be stably controlled in off-design operation [31,32]. In particular, it is shown that variable pressure operating modes in the discharge process can offer advantages in terms of efficiency if the load is in the upper partial load range.

Frate et al. [33] focuses explicitly on the dynamic modeling of a Brayton battery system: thermodynamic models are combined with inventory control. The results show a high dynamic responsiveness and partial load capability with minimal efficiency reduction—a sign that Brayton battery can realistically be used in grid storage.

The large number of different model approaches—from continuous 1D solid models [34] to FEM-based thermodynamic models [29] and detailed Modelica simulations [22,35]—shows that the modeling depth and numerical methods depend heavily on the application context. For industrial high-temperature heat pumps based on CO₂ cycles, such as the 35 MW system developed by MAN ES, it has been shown that realistic dynamic models are capable of mapping rapid performance jumps of up to 80% within 30 s [35].

Another field of research concerns the integration of innovative mechanical concepts to increase efficiency. For example, Wang et al. [36] propose a Carnot battery system with liquid pistons that achieves a significant improvement in round-trip efficiency (up to 70.4%) and storage density through optimized heat transfer in hot and cold storage tanks. This work also shows the need for dynamic simulations to evaluate the transient system behavior and the control strategies over several charge–discharge cycles.

In summary, it can be stated that the dynamic simulation of Brayton batteries is an essential part of system development and design. Whether for the evaluation of starting processes [37], for the analysis of control strategies in partial load operation [25,33], for the integration of renewable heat sources [38], or for the optimization of components and storage [29,30], all studies emphasize that the full potential of these technologies can only be exploited by taking a holistic, dynamic approach.

1.3. Technology Overview of Heat Storage for Brayton Batteries

Heat storage plays a central role in Brayton batteries, as it enables the temporal decoupling of the charging and discharging phases. Systems based on sensible heat storage, i.e., the temperature-dependent storage of thermal energy in the storage medium, are particularly well established. Within this group, three classes of materials are particularly relevant: liquid media such as salts or organic oils, solids in packed or compact form and hybrid concepts that combine features of both approaches.

Liquid storage media are used indirectly in Brayton batteries: The heat from the primary circuit is transferred to a separate storage circuit via heat exchangers. In practice, molten nitrate salts are often used, which are known from concentrated solar thermal power (CSP), where they have decades of operating experience. Their usable temperature range is typically between around 290 °C and 565 °C; below this temperature, the phase change to solid takes place, above this limit thermal decomposition sets in. However, newer material and tank concepts indicate that stable operating conditions around 600 °C are also possible. Thermal oils offer easier handling and are suitable for temperature ranges up to around 400 °C, but are more critical in terms of long-term stability and fire behavior.

Solid media thermal energy storage are characterized by high temperature resistance, comparatively low material costs, and a large selection of available storage materials (ceramics, natural stone, and refractory bricks). In many concepts, the working fluid flows directly through the storage bed, whereby direct heat transfer is achieved without an additional heat exchanger. However, this design can mean that the storage tanks have to be designed for process pressure, which could increase the investment costs. A characteristic feature of such storage tanks is the formation of a temperature profile along the direction of flow. As a result, the outlet temperature changes during the charging and discharging phases, which can have an impact on the downstream process. Various measures are being discussed to limit these effects, including bypass lines to mix flows of different temperatures, additional electrical heating, or targeted heat dissipation to smooth out temperature fluctuations.

Hybrid or mixed systems combine solid and liquid storage materials in order to utilize the advantages of both technologies. One approach, for example, is to flow a liquid such as salt or oil through a solid media bed, which serves as a heat transfer and storage medium at the same time. Such concepts can achieve a more homogeneous temperature distribution in the storage tank and increase heat transfer rates while maintaining the high thermal stability and cost-effective mass of the solids. However, the design requirements increase here, for example with regard to material compatibility, corrosion protection, and flow control.

• Conclusion: Comparison and System Integration

Liquid media enable more uniform temperature control and often more compact storage tanks, but require a complex selection of materials for heat exchangers and pipes. Solid media energy storage scores points for robustness and low material costs, but reacts more slowly to load changes, and generates greater temperature fluctuations at the outlet. Mixed systems can represent a compromise here, but are more complex in terms of design and have been less widely tested to date. In Brayton batteries, the choice of storage medium not only determines the achievable storage capacity, but also the control behavior of the overall system, especially in partial load and off-design operation.

• Novelty Statement

Although various long-duration energy storage (LDES) technologies such as liquid–air energy storage (LAES), compressed air energy storage (CAES), and Rankine-based Carnot batteries have been widely investigated, the majority of published work focuses on steady-state performance and single-energy-output operation. In contrast, this study provides the first systematic dynamic analysis of air-based Brayton battery systems for combined generation of electricity, heat, and cooling. The key novel contributions compared to the state-of-the-art LDES literature are as follows:

• A fully time-resolved system-level dynamic simulation of 15 Brayton battery architectures, including the transient evolution of regenerator-based TES;
• The assessment of hybrid system performance (electricity and heat and cooling) under realistic load changes, which is largely absent in existing LAES, CAES, and high-temperature thermal storage studies;
• A unified techno-economic comparison framework enabling direct benchmarking of Brayton batteries against other LDES technologies;
• The identification of operating regimes in which Brayton batteries achieve competitive round-trip utilization (RTU > 85%) despite lower peak electrical RTE, demonstrating system advantages in multi-energy applications.

These contributions extend the predominantly steady-state literature on LDES and provide the first detailed basis for control and design of multi-output Brayton Carnot batteries under real operating conditions.

2. Methods

The results of the stationary system simulations for the lead concepts from [1] are summarized in

Table 1. Results of the stationary system simulations and definition of the technologies of the components and their technical requirement profiles.

Option	ID	Cooler/ Heater	Essential Data	Thermal Energy Storage (TES)	Compressor/ Expander	Recu
Pure electricity generation (PEG)	PEG1	CbC_Dis	Air ϑmax = 625 °C П = 2.6 RTE = 49.5%	HT-TES: Reg (2.6 bar; 601–155 °C) LT-TES: Reg o. Oil (1 bar; 82–409 °C)	Ch: Turbo blower, air turbine; PC/PT = 2.74 Dis: Turbo blower, air turbine; PC/PT = 0.58	-
	PEG2	CbT_Ch	Air; ϑmax = 450 °C П = 2.6 RTE = 42.9%	HT-TES: Reg (2.6 bar; 431–85 °C) LT-TES: Reg o. Oil (1 bar; −23–269 °C)	Ch: Turbo blower, air turbine; PC/PT = 3.15 Dis: Turbo blower, air turbine; PC/PT = 0.61	-
Coupled generation of electricity and heat (CHP)	CHP1	CbT_Dis	Air ϑmax = 450 °C П = 8.1 RTU = 86.8% RTE = 10.3% Q/Wel = 7.45 (Dis.)	HT-TES: Reg (8.1 bar; 433–121 °C) LT-TES: Reg (1 bar; −82–39 °C)	Ch: Turbo compressor, air turbine; PC/PT = 2.87 Dis: Turbo compressor, air turbine; PC/PT = 0.88	Fixed head tube bundle
	CHP2	CaC_Dis	Air ϑmax = 625 °C П = 2.0 RTU = 81.2% RTE = 19.0% Q/Wel = 3.27 (Dis.)	HT-TES: Reg (2.0 bar; 607–279 °C) LT-TES: Reg o. Salt (1 bar; 205–460 °C)	Ch: Turbo blower, air turbine; PC/PT = 2.12 Dis: Turbo blower, air turbine; PC/PT = 0.87	-
Coupled generation of electricity and heat with waste heat integration (CHP+WHI)	CHP+WHI1	HbT_Ch + CbT_Dis	Air ϑmax = 625 °C П = 12.3 RTU = 103.1% RTE = 0.9% Q/Wel = 119.32 (Dis.)	HT-TES: Reg (12.3 bar; 602–175 °C) LT-TES: Reg (1 bar; −78–11 °C)	Ch: Turbo compressor, air turbine; PC/PT = 3.26 Dis: Turbo compressor, air turbine; PC/PT = 0.99	Fixed head tube bundle
	CHP+WHI2	HaLTTES_Ch + CbT_Dis	Air ϑmax = 450 °C П = 6.1 RTU = 94.2% RTE = 2.5% Q/Wel = 36.73 (Dis.)	HT-TES: Reg (6.1 bar; 435–155 °C) LT-TES: Reg (1 bar; −38–62 °C)	Ch: Turbo compressor, air turbine; PC/PT = 2.56 Dis: Turbo compressor, air turbine; PC/PT = 0.97	Fixed head tube bundle
	CHP+WHI3	HaT_Ch + CaC_Dis + CaT_Dis	Air ϑmax = 625 °C П = 5.5 RTU = 84.6% RTE = 19.4% Q/Wel = 3.37 (Dis.)	HT-TES: Reg (5.5 bar; 607–279 °C) LT-TES: Reg o. Oil (1 bar; 89–251 °C)	Ch: Turbo compressor, air turbine; PC/PT = 2.19 Dis: Turbo compressor, air turbine; PC/PT = 0.86	Fixed head tube bundle
Coupled generation of electricity and cooling (CCP)	CCP1	CbT_Ch + HaT_Ch	Air ϑmax = 625 °C П = 2.8 RTU = 53.2% RTE = 42.4% Q/Wel = 0.20 (Ch.)	HT-TES: Reg (2.8 bar; 601–154 °C) LT-TES: Reg o. Oil (1 bar; 18–394 °C)	Ch: Turbo blower, air turbine; PC/PT = 3.92 Dis: Turbo blower, air turbine; PC/PT = 0.58	-
	CCP2	CbT_Ch + HbC_Dis	Air ϑmax = 450 °C П = 2.7 RTU = 51.7% RTE = 38.3% Q/Wel = 0.34 (Dis.)	HT-TES: Reg (2.7 bar; 433–289 °C) LT-TES: Reg o. Oil (1 bar; −22–273 °C)	Ch: Turbo blower, air turbine; PC/PT = 3.15 Dis: Turbo blower, air turbine; PC/PT = 0.65	-

Note: The designations in the Heater/Cooler column are made up of H or C for heater or cooler; b or a for before or after; T or C or LTTES for turbine or compressor or low-temperature TES; Ch or Dis for charging or discharging line.

. The definition of the component technologies and their technical requirement profiles are also listed there.

Please refer to the explanations in [1] (Section 2.1: Boundary Conditions and Assumptions) for a complete description of the modeling assumptions and parameter definitions. In the present work, dry air with temperature-dependent ideal-gas properties as implemented in Ebsilon Professional^® is used as the working fluid. Turbomachinery is modeled using ideal isentropic efficiencies without transient shaft dynamics, and heat exchangers are calculated using ε–NTU relations. Nominal operating conditions are defined through the compressor outlet temperature (COT) and turbine inlet temperature (TIT), which are varied depending on the operating mode. No environmental heat losses are considered.

Round-trip efficiency (RTE) is defined as

$$RTE={\displaystyle \frac{W_{\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b},\mathrm{d}}-W_{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p},\mathrm{d}}}{W_{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p},\mathrm{c}}-W_{\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b},\mathrm{c}}}}$$

where $W_{\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b},\mathrm{d}}$ stands for work of the turbine in the discharging line and $W_{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p},\mathrm{c}}$ for the work of the compressor in the charging line, etc. The RTE represents the conversion efficiency of stored electrical energy during a complete charge–discharge cycle.

Round-trip utilization (RTU) extends this definition by also accounting for useful heat or cooling delivered during discharge:

$$RTU={\displaystyle \frac{W_{\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b},\mathrm{d}}-W_{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p},\mathrm{d}}+Q_{\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r},\mathrm{d}}+Q_{\mathrm{C}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{r},\mathrm{d}}}{W_{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p},\mathrm{c}}-W_{\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b},\mathrm{c}}-Q_{\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r},\mathrm{c}}-Q_{\mathrm{C}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{r},\mathrm{c}}}}$$

where $Q_{\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r},\mathrm{d}}$ is the useful heat supplied during discharging and $Q_{\mathrm{C}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{r},\mathrm{c}}$ the cold supplied during the charging phase, etc. This metric is commonly used in hybrid Carnot battery systems to quantify overall energy recovery including thermal co-products.

2.1. Modeling/Design of Components

Table 1 shows the power ratios of the turbomachinery for the charging and discharging lines. The absolute values are obtained by specifying one of the outputs. Here, the output of the turbine in the discharging train is selected and the system is set in the steady state so that 100 MW_el is generated at the generator during the discharging process.

Based on this output and the system requirements for the supply of the respective form of energy (see Tables 1 and 2 in [1]), the charging and discharging times for the thermal energy storage systems and their design are determined.

For pure electricity generation, this results in a charging duration of 8 h and a discharging duration of 16 h. For the combined generation of electricity and cooling, this is 12 h in each case. For the combined generation of electricity and heat, the conditions are much more complicated. The requirement profiles defined for process heat for a permanent (24/7) heat supply require either the installation of an additional storage system on the user side, i.e., outside the Carnot battery system, or a system of alternately operated high-temperature and low-temperature heat storage on the supplier side, i.e., within the Carnot battery system, in order to enable parallel operation of the charging and discharging lines at the same time. The second approach is chosen here in order to consider a complete system at this point, which covers the requirements without additional components on the user side. However, this requires four storage tanks at the high temperature level and four storage tanks at the low temperature level.

Table 2. Alternating operating mode of the TES in the case of process heat supply.

Phase	Hour	HT-TES1	HT-TES2	HT-TES3	HT-TES4	LT-TES1	LT-TES2	LT-TES3	LT-TES4
Charging	1.–8.	Charging	Charging	Charging	Discharging	Discharging	Discharging	Discharging	Charging
Discharging	9.–16.	Discharging	Standstill	Standstill	Standstill	Charging	Standstill	Standstill	Standstill
	17.–24.	Standstill	Discharging	Standstill	Standstill	Standstill	Charging	Standstill	Standstill
Charging	25.–32.	Charging	Charging	Discharging	Charging	Discharging	Discharging	Charging	Discharging
Discharging	33.–40.	Discharging	Standstill	Standstill	Standstill	Charging	Standstill	Standstill	Standstill
	41.–48.	Standstill	Discharging	Standstill	Standstill	Standstill	Charging	Standstill	Standstill

Color legend: Blue = Charging, Red = Discharging, Green = Standstill.

shows the alternating operating mode over 48 h; the sequence then starts from the beginning.

The individual storage units are thus designed for 8 h of charging and 8 h of discharging, which is not the same as the charging and discharging time of the Brayton battery. During 8 h, three out of four HT-TESs are charged and three out of four LT-TESs are discharged via the charging line. At the same time, the remaining HT-TES is discharged and the remaining LT-TES is charged via the discharge line. Although the discharge line is operated simultaneously, the system is net charged during these 8 h. During the following 8 h, one HT-TES of four is discharged via the discharge line and one LT-TES of four is charged. After this, another HT-TES is discharged and another LT-TES is charged for a further 8 h. During these 16 h, the remaining TESs are not flowed through and the charging line is not operated. The process during the following 8 h is similar to that of the first 8 h, with another HT-TES of the four being discharged and another LT-TES of the four being charged. The next 16 h, which complete the 48 h, are identical to the first 16 h block (9th to 24th hours).

As can be seen in Table 1, all concepts on the high-temperature side and many concepts on the low-temperature side require a regenerator-based TES, i.e., a direct-flow solid media heat storage. The discharge characteristic of such a TES is transient, which must be taken into account in the thermal design and also in the implementation of the designed TES in the quasi-stationary system models. The design is carried out using a MATLAB^® (Version R2020a) script, which is described in Section 2.1.2.

By specifying the boundary conditions for charging and discharging the storage tank from the results of the stationary system simulations, such as mass flows, temperatures, pressures, and permissible temperature drop at the end of the discharging process, as well as the desired cycle durations and the inventory material, a storage tank design is calculated that meets all specifications. The inventory material used for this study is a ceramic sphere bed, with the diameter of the spheres being kept variable. This results in a solution field of possible designs. It is advisable to limit this solution field by restricting the permissible pressure drop across the storage bed. Figure 1 and Figure 2 show an example of such a solution field for an HT-TES and an LT-TES for the lead concept PEG1, with each marker representing a possible design.

A solution was selected on the basis of the inventory parameters of mass, height, diameter, and particle diameter. The solution with the lowest mass is usually selected, as this has a significant impact on the investment costs of regenerator-based TESs. Furthermore, care was taken to ensure that the height and number of storage tanks required were kept as small as possible. Based on experience from other storage projects, a maximum diameter of 18 m was selected for the inventory, which in turn leads to seven or eight storage tanks in the case shown.

The procedure shown was carried out for all the required regenerator-based TESs in the various concepts.

The design of thermal energy storage systems based on liquids such as oil or molten salt is based on simple energy balancing. Details on this can also be found in [39]. These systems require a heat exchanger that transfers heat from the secondary circuit to the primary circuit and vice versa. By specifying the calculated air temperatures at the LT-TES and the air mass flows, the required mass flows of the storage fluids are obtained by specifying the material data for the oil and the molten salt. The required masses for the storage liquids and the dimensions of the two-tank storage system are calculated on the basis of time-series calculations, assuming 10% additional inventory as a safety buffer and a height-to-diameter ratio of the tanks of 2.

Simplified component models are required for integration into quasi-stationary system models in Ebsilon Professional^®. As with the stationary system models, the modeling of the turbomachinery is realized with standard components for turbomachinery implemented in the software, which are based on the isentropic state change approach. The standard components from Ebsilon Professional^®, which use the NTU approach, are also used for the required heat exchangers. The liquid storage tanks are modeled using the energy and mass balancing of the heat exchanger, as previously described in the design. The dynamic modeling of the regenerator-based TES is implemented using the indirect storage module available in Ebsilon Professional^®, which describes the thermal behavior of a pipe, and some user-defined functions for internal heat transfer and pressure loss, see Figure 3. The detailed procedure can again be found in [39]. The calculation results for the thermal behavior, which were obtained with this simplified component model for regenerator-based TES, were compared with those from a calculation tool in MATLAB^® and found to be in good agreement.

Dynamic requirements for the other components of the concepts can be derived from the quasi-stationary system modeling with integration of the dynamic regenerator-based TES models. This is dealt with in the simulation of complete systems at the end of the next section.

2.1.1. Numerical Methods

The dynamic simulations were performed using a quasi-stationary time-step scheme in Ebsilon Professional^®, in which all component models (compressor, turbine, heat exchangers, regenerator-based TES, and piping) are evaluated at each time step under transient boundary conditions. A fixed simulation time step of 60 s was applied, which was found to ensure numerical stability while capturing the evolution of thermal fronts within the TES.

Ebsilon’s internal Newton–Raphson solver was used to converge each time step, with a relative convergence tolerance of 1 × 10⁻⁷ for temperature, mass flow rate, and pressure variables. The discretization of the regenerator-based TES was implemented using a finite-volume lumped capacity model consisting of 100 axial segments, in which energy balances for solid and fluid nodes were solved sequentially by the Crank–Nicolson algorithm. Axial heat conduction was neglected, while convective heat transfer between fluid and storage material was modeled.

The design of the regenerator-based TES (including the pressure losses and the geometric sizing of the container and the particles) was carried out externally in MATLAB^® prior to the Ebsilon simulations. The resulting parameters were then imported into Ebsilon as fixed model constants. No runtime coupling between the two software environments was performed. Thus, MATLAB was used solely for design and pre-processing, while Ebsilon Professional^® executed the full dynamic time-resolved cycle simulation within the system models.

• Clarification of quasi-stationary vs. dynamic simulation:

In this study, the term quasi-stationary simulation refers to a time-step approach in which each time step is solved as a steady-state operating point, while transient evolution is captured by updating component boundary conditions between time steps. The term dynamic simulation refers to the overall time-dependent behavior resulting from this stepwise progression. Thus, while individual time points are steady-state solutions, the combined sequence reproduces the transient system response with high numerical stability and significantly reduced computational cost compared to full transient PDE-based simulations.

2.1.2. Regenerator-Based TES Model

The thermal energy storage was designed using a simplified π–λ regenerator model according to [40], implemented in MATLAB^® within a dedicated design tool. Based on this design, the regenerator was modeled in the system simulation as a packed-bed heat storage unit with axial discretization. A one-dimensional finite-volume approach was applied assuming constant thermophysical properties within each time step, no axial heat conduction, and counterflow heat exchange between fluid and storage material.

Convective heat transfer between solid storage material and fluid was calculated using standard packed-bed heat transfer correlations (e.g., Wakao–Kaguei type) within each axial control volume. Pressure losses were evaluated using the Ergun equation. The governing energy balances and the associated discretization scheme follow standard formulations for packed-bed regenerators and are therefore not repeated here for brevity. All geometric and thermophysical parameters (porosity, specific heat capacity, particle size, regenerator length, and flow area) were obtained from the MATLAB^® design calculation and subsequently imported into Ebsilon Professional^®, where the dynamic system simulation was performed.

2.2. Modeling/Simulation of Complete Systems

The defined lead concepts for the respective purposes were mapped in quasi-stationary system models in the Ebsilon Professional^® simulation environment. Taking into account the different options for the storage technology (regenerator vs. liquid salt vs. oil) at the cold end for some of the concepts (see Table 1), a total of 15 different overall system models results. It is not possible to present and discuss all of these here; instead, representative examples are used. The flow diagrams of the other lead concepts then only differ with regard to the position of the heaters or coolers. The actual models, on the other hand, differ significantly for each lead concept due to other parameters for the components and fluid flows, other temperature fields of the regenerator-based TES, and different time series and had to be taken into account individually in the models.

Figure 4 shows the overall system model for the PEG1 lead concept with the regenerator-based TES as an LT-TES. The flow diagram for the lead concept PEG2 in the case of the regenerator-based TES as an LT-TES is identical except for the position of the cooler, which is not upstream of the compressor in the discharging train, but upstream of the turbine in the charging train. The flow diagrams of the CCP1 and CCP2 lead concepts are also identical to the flow diagram shown, apart from this difference and the additional heater downstream of the turbine in the charging train and upstream of the compressor in the discharging train.

Figure 5 shows the overall system model for the lead concept PEG2 with an oil storage system as an LT-TES.

The flow diagram for the lead concept PEG1 in the case of the oil storage tank as an LT-TES is identical except for the position of the cooler, which is not upstream of the turbine in the charging line but upstream of the compressor in the discharging line. The flow diagrams of the lead concepts CCP1 and CCP2 in the case of the oil storage tank as an LT-TES are also identical to the flow diagram shown, except for the additional heater after the turbine in the charging train and before the compressor in the discharging train.

Figure 6 shows the overall system model for the CHP1 lead concept with the regenerator-based TES as an LT-TES.

The flow diagrams for the CHP+WHI1 and CHP+WHI2 lead concepts are identical to the flow diagram shown, except for the additional heater upstream of the turbine in the charging train or downstream of the LT-TES in the charging train. The flow diagram for CHP2 in the case of the regenerator-based TES as an LT-TES can be formed from this by removing the recuperator and moving the cooler to the position after the compressor in the discharging train instead of before the turbine in the discharging train.

Figure 7 shows the overall system model for the CHP+WHI3 lead concept with the regenerator-based TES as an LT-TES.

The flow diagram for the CHP2 lead concept in the case of the regenerator-based TES tank as an LT-TES can be formed from this by removing the recuperator, the heater downstream of the turbine in the charging line, and the cooler downstream of the turbine in the discharging line.

Figure 8 shows the overall system model for the CHP+WHI3 lead concept with an oil storage system as an LT-TES.

The flow diagram for the lead concept CHP2 in the case of the liquid salt storage tank as an LT-TES can be formed from this again by removing the recuperator, the heater after the turbine in the charging line, and the cooler after the turbine in the discharging line.

The following methodology was used to model and simulate the overall systems: First, the boundary condition (temperatures, pressures, mass flows, and permissible temperature drop) for the components at the design point under full load was determined using simplified system simulation in Ebsilon Professional^® at a discharge capacity of 100 MW_el. These boundary conditions were then used to design the storage tanks in MATLAB^® (see previous section), model these designed storage tanks in Ebsilon Professional^®, simulate until the steady state was reached (in the case of regenerator-based TES tanks), and verify the storage tank performance using existing MATLAB^® models. The steady-state and verified storage models were then integrated into the system models. These system models were then used to calculate time series that represent a daily cycle (or a 2-day cycle in the case of alternating regenerator-based TES systems) at minute resolution in off-design mode. At the end, the evaluation was carried out with regard to round-trip efficiency, round-trip utilization, oil and salt quantities, and storage utilization rate (see next section).

These overall models can also be used to carry out variation studies with regard to component specifications and process parameters. Since the parameters of the working fluids and compressor outlet temperatures (and thus also indirectly the pressure in the charging train) were already covered by the concept matrix in the first step of the concept study, only the pressure in the discharging train, i.e., the turbine discharge pressure, remains open as an essential parameter. The results are discussed in the next section.

For economic evaluation of the overall systems, cost models were developed for the central components of the Brayton batteries. These are largely based on specific individual costs, calculated using power functions for cost degression. This was based either on literature data or on empirical values from previous projects and, where necessary, price escalation was carried out using price indices in order to obtain costs for a uniform calculation point in time.

The respective source of the cost basis for the individual components is as follows:

• Regenerator-based TES: (pressurized) container, inventory, thermal insulation inside (if applicable) and outside, liner to protect the inner insulation of the container if applicable, foundation: DLR internal cost models.
• Heat storage based on liquids:

  -

  Mineral oil-based heat transfer oil “FRAGOLTHERM Q-32-N”: DLR internal cost models.

  -

  Salt “Solar Salt”: DLR-internal cost models.

  -

  Tanks [41].

  -

  External thermal insulation: DLR internal cost models.

  -

  Heat exchangers [41].

• Compressors [41,42,43,44,45].
• Turbines [41,42,44].
• Heat exchangers [41].

The cost models mentioned are of course subject to uncertainties, so that the calculated investment costs should be understood as an estimate only. The uncertainty of the cost models is particularly high for turbomachinery, as no data is available for large turbomachinery in the large output range (≥100 MW_el). However, the costs calculated on the basis of the various literature sources also vary considerably for the small output range (<5 MW_el), even after the aforementioned harmonization of the calculation basis.

3. Results

Using the models for the overall systems explained in the previous section, time-series calculations were carried out in off-design mode to map a daily cycle (or a 2-day cycle in the case of alternating regenerator-based TES systems) at minute resolution. The evaluation of these time-series results in values for RTE and RTU that take into account the dynamic effects of the regenerator-based TES systems. Furthermore, the simulations were calculated with regenerator-based TES designs that were designed for the existing boundary conditions. Accordingly, there are deviations from the values calculated with the stationary system model. The results of the quasi-stationary system simulations are summarized in

Table 3. Results of the quasi-stationary system simulations: pure electricity generation (PEG).

ID	Essential Data	Thermal Energy Storage (TES)	Compressor/ Expander	Recu	Cooler/ Heater
PEG1—Reg	ϑmax = 625 °C П = 2.6 RTE = 50.0% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 1073.4 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 536.7 kg/s	HT-TES: ϑmax = 625 °C, ϑmin = 155 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 67,615 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 42 mm, 8 tanks (H = 25 m, D = 17.1 m), η = 45% LT-TES: ϑmax = 427 °C, ϑmin = 63 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 81,442 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 81 mm, 7 tanks (H = 27 m, D = 18.1 m), η = 36%	Charging line: Turbo blower (PN = 265 MWel); air turbine (PN = 98 MWel) Discharging line: Turbo blower (PN = 58 MWel); air turbine (PN = 101 MWel)	-	CbC_Dis (AHEX = 91,301 m2)
PEG1—Oil	ϑmax = 625 °C П = 2.6 RTE = 50.0% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 1073.4 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 536.7 kg/s	HT-TES: ϑmax = 625 °C, ϑmin = 155 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$s = 67,615 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 42 mm, 8 tanks (H = 25 m, D = 17.1 m), η = 45% LT-TES: ϑmax = 427 °C, ϑmin = 63 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 20,033 t, $V_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 22,259 m3, 12 tanks (each cold and hot, H = 21.1 m, D = 10.6 m), AHEX = 696113 m2	Charging line: Turbo blower (PN = 265 MWel); air turbine (PN = 98 MWel) Discharging line: Turbo blower (PN = 58 MWel); air turbine (PN = 101 MWel)	-	CbC_Dis (AHEX = 91,301 m2)
PEG2—Reg	ϑmax = 450 °C П = 2.6 RTE = 47.1% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 1318.2 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 659.1 kg/s	HT-TES: ϑmax = 450 °C, ϑmin = 65 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 79,101 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 41 mm, 8 tanks (H = 27.2 m, D = 17.8 m), η = 46% LT-TES: ϑmax = 285 °C, ϑmin = −40 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 94,089 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 75 mm, 7 tanks (H = 27.8 m, D = 18.1 m), η = 38%	Charging line: Turbo blower (PN= 264 MWel); air turbine (PN = 98 MWel) Discharging line: Turbo blower (PN = 58 MWel); air turbine (PN = 101 MWel)	-	CbT_Ch (AHEX = 1,265,181 m2)
PEG2—Oil	ϑmax = 450 °C П = 2.6 RTE = 44.5% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 1318.2 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 659.1 kg/s	HT-TES: ϑmax = 450 °C, ϑmin = 65 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 79,101 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 41 mm, 8 tanks (H = 27.2 m, D = 17.8 m), η = 46% LT-TES: ϑmax = 285 °C, ϑmin = −40 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 22,523 t, $V_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 25,024 m3, 13 tanks (each cold and hot, H = 21.4 m, D = 10.7 m), AHEX = 839,975 m2	Charging line: Turbo blower (PN = 264 MWel); air turbine (PN = 98 MWel) Discharging line: Turbo blower (PN = 58 MWel); air turbine (PN = 101 MWel)	-	CbT_Ch (AHEX = 1,265,181 m2)

,

Table 4. Results of the quasi-stationary system simulations: Coupled generation of electricity and heat (CHP).

ID	Essential Data	Thermal Energy Storage (TES)	Compressor/ Expander	Recu	Cooler/ Heater
CHP1	ϑmax = 450 °C П = 8.1 RTU = 85.6% RTE = 6.4% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 1408.3 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 469.4 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 469.4 kg/s	HT-TES (4x): ϑmax = 450 °C, ϑmin = 104 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 27,546 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 39 mm, 3 tanks (H = 24.6 m, D = 18 m), η = 48% LT-TES (4x): ϑmax = 46 °C, ϑmin = −82 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 46,408 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 160 mm, 3 tanks (H = 39,7 m, D = 18,4 m), η = 27%	Charging line: Turbo compressor (PN= 516 MWel); air turbine (PN = 182 MWel) Discharging line: Turbo compressor (PN = 88 MWel); air turbine (PN = 101 MWel)	Fixed head tube bundle (AHEX= 92,702 m2)	CbT_Dis (AHEX = 18,904 m2)
CHP2—Reg	ϑmax = 625 °C П = 2.0 RTU = 61.2% RTE = 13.0% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 2087.5 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 695.8 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 695.8 kg/s	HT-TES (4x): ϑmax = 625 °C, ϑmin = 260 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 49,480 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 48 mm, 6 tanks (H = 22.1 m, D = 18 m), η = 41% LT-TES (4x): ϑmax = 474 °C, ϑmin = 190 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 52,438 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 27 mm, 6 tanks (H = 23.1 m, D = 18.1 m), η = 38%	Charging line: Turbo blower (PN = 397 MWel); air turbine (PN = 190 MWel) Discharging line: Turbo blower (PN = 87 MWel); air turbine (PN = 101 MWel)	-	CaC_Dis (AHEX = 12,266 m2)
CHP2—Salt	ϑmax = 625 °C П = 2.0 RTU = 83.2% RTE = 9.8% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 2087.5 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 695.8 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 695.8 kg/s	HT-TES (4x): ϑmax = 625 °C, ϑmin = 260 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 49,480 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 48 mm, 6 tanks (H=22.1 m, D=18 m), η = 41% LT-TES: ϑmax = 474 °C, ϑmin = 190 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 54,534 t, $V_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 31,341 m3, 16 tanks (each cold and hot, H = 21.5 m, D = 10.8 m), AHEX = 608,966 m2	Charging line: Turbo blower (PN = 397 MWel); air turbine (PN = 190 MWel) Discharging line: Turbo blower (PN = 87 MWel); air turbine (PN = 101 MWel)	-	CaC_Dis (AHEX = 12,266 m2)

,

Table 5. Results of the quasi-stationary system simulations: coupled generation of electricity and heat with waste heat integration (CHP+WHI).

ID	Essential Data	Thermal Energy Storage (TES)	Compressor/ Expander	Recu	Cooler/ Heater
CHP+WHI1	ϑmax = 625 °C П = 12.3 RTU = 106.9% RTE = 1.4% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 1239.0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 413.0 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 413.0 kg/s	HT-TES (4x): ϑmax = 625 °C, ϑmin = 150 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 22,868 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 28 mm, 4 tanks (H = 17.2 m, D = 17 m), η = 52% LT-TES (4x): ϑmax = 16 °C, ϑmin = −83 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 26,653 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 41 mm, 4 tanks (H = 18 m, D = 17.9 m), η = 42%	Charging line: Turbo compressor (PN = 644 MWel); air turbine (PN = 201 MWel) Discharging line: Turbo compressor (PN = 99 MWel); air turbine (PN = 101 MWel)	Fixed head tube bundle (AHEX = 82,287 m2)	HbT_Ch (AHEX = 144,178 m2) + CbT_Dis (AHEX = 23,538 m2)
CHP+WHI2	ϑmax = 450 °C П = 6.1 RTU = 94.4% RTE = 0.8% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 1570.0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 523.3 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 523.3 kg/s	HT-TES (4x): ϑmax = 450 °C, ϑmin = 139 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 28,172 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 28 mm, 4 tanks (H = 18.5 m, D = 18.2 m), η = 52% LT-TES (4x): ϑmax = 68 °C, ϑmin = −44 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 58,223 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 40 mm, 4 tanks (H = 23.7 m, D = 17.5 m), η = 24%	Charging line: Turbo compressor (PN = 519 MWel); air turbine (PN = 205 MWel) Discharging line: Turbo compressor (PN = 97 MWel); air turbine (PN = 101 MWel)	Fixed head tube bundle (AHEX = 103,621 m2)	HaLTTES_Ch (AHEX = 61,281 m2) + CbT_Dis (AHEX = 21,228 m2)

and

Table 6. Results of the quasi-stationary system simulations: coupled generation of electricity and cooling (CCP).

ID	Essential Data	Thermal Energy Storage (TES)	Compressor/ Expander	Recu	Cooler/ Heater
CCP1—Reg	ϑmax = 625 °C П = 2.8 RTU = 57.7% RTE = 46.9% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 501.9 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 501.9 kg/s	HT-TES: ϑmax = 625 °C, ϑmin = 128 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 52,625 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 65 mm, 5 tanks (H = 29 m, D = 17.8 m), η = 41% LT-TES: ϑmax = 414 °C, ϑmin = −4 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 54,917 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 68 mm, 7 tanks (H = 22.9 m, D = 17.2 m), η = 38%	Charging line: Turbo blower (PN = 132 MWel); air turbine (PN = 34 MWel) Discharging line: Turbo blower (PN= 58 MWel); air turbine (PN = 101 MWel)	-	CbT_Ch (AHEX = 144,658 m2) + HaT_Ch (AHEX = 13,456 m2)
CCP1—Oil	ϑmax = 625 °C П = 2.8 RTU = 55.8% RTE = 44.9% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 501.9 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 501.9 kg/s	HT-TES: ϑmax = 625 °C, ϑmin = 128 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 52,625 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 65 mm, 5 tanks (H = 29 m, D = 17.8 m), η = 41% LT-TES: ϑmax = 414 °C, ϑmin = −4 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 13043 t, $V_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 14,491 m3, 8 tanks (each cold and hot, H = 21 m, D = 10.5 m), AHEX = 432,998 m2	Charging line: Turbo blower (PN = 132 MWel); air turbine (PN = 34 MWel) Discharging line: Turbo blower (PN = 58 MWel); air turbine (PN = 101 MWel)	-	CbT_Ch (AHEX = 144,658 m2) + HaT_Ch (AHEX = 13,456 m2)
CCP2—Reg	ϑmax = 450 °C П = 2.7 RTU = 60.7% RTE = 39.6% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 674.5 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 674.5 kg/s	HT-TES: ϑmax = 450 °C, ϑmin = 88 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 63,420 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 52 mm, 7 tanks (H = 24.5 m, D = 17.9 m), η = 45% LT-TES: ϑmax = 289 °C, ϑmin = −38 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 73,543 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 71 mm, 8 tanks (H = 25.3 m, D = 17.8 m), η = 37%	Charging line: Turbo blower (PN = 132 MWel); air turbine (PN = 43 MWel) Discharging line: Turbo blower (PN= 65 MWel); air turbine (PN = 101 MWel)	-	CbT_Ch (AHEX = 123,245 m2) + HbC_Dis (AHEX = 11,188 m2)
CCP2—Oil	ϑmax = 450 °C П = 2.7 RTU = 54.2% RTE = 40.0% Charging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 674.5 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s Discharging: ${\dot{m}}_{\mathrm{C}\mathrm{h}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 0 kg/s, ${\dot{m}}_{\mathrm{D}\mathrm{i}\mathrm{s}.\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ = 674.5 kg/s	HT-TES: ϑmax = 450 °C, ϑmin = 88 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 63,420 t, $d_{\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}}$ = 52 mm, 7 tanks (H = 24.5 m, D = 17.9 m), η = 45% LT-TES: ϑmax = 289 °C, ϑmin = −38 °C, $m_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 17226 t, $V_{\mathrm{I}\mathrm{n}\mathrm{v},\mathrm{t}\mathrm{o}\mathrm{t}}$ = 19,139 m3, 10 tanks (each cold and hot, H = 21.4 m, D = 10.7 m), AHEX = 576,587 m2	Charging line: Turbo blower (PN = 132 MWel); air turbine (PN = 43 MWel) Discharging line: Turbo blower (PN = 65 MWel); air turbine (PN = 101 MWel)	-	CbT_Ch (AHEX = 123,245 m2) + HbC_Dis (AHEX = 11,188 m2)

.

For the CHP+WHI3 lead concept calculated with the simplified system model, a quasi-stationary system model was also set up, but no error-free calculation could be made here. The reason for this is that the temperature gradients at the internal recuperator are too low, which also makes the economic viability of such a concept appear questionable.

The variation study carried out with regard to the pressure in the discharge line, i.e., the turbine outlet pressure, showed for the PEG1 and PEG2 lead concepts that there is already an optimum when the turbine outlet pressures of the two turbines are the same. If both values for the turbine outlet pressure are reduced or increased at the same time, the height of the RTE remains the same; only the overall pressure level shifts. This is also the case with the lead concepts for coupled generation.

The techno-economic evaluation of the variation studies provides the following estimate of the investment costs, summarized in

Table 7. Estimation of the investment costs for the lead concepts including exemplary distribution to the main individual components.

Lead Concept ID	Estimated Investment Costs in EUR Million	Capacity-Related Investment Costs in EUR/kWhel	Power-Related Investment Costs in EUR/kWel	Exemplary Distribution in %
				HT-TES	LT-TES *	Compressor	Turbines	HEX *
PEG1—Reg	175–317	241–436	3853–6975	31	30	26	10	4
PEG1—Oil	213–355	302–503	4827–8051	26	39	23	9	3
PEG2—Reg	198–263	274–363	4385–5810	32	33	16	9	9
PEG2—Oil	246–311	383–484	6133–7737	27	44	14	8	8
CHP1	351–619	2289–4037	36,624–64,597	28	34	29	7	2
CHP2—Reg	436–704	1674–2703	26,787–43,255	38	34	21	6	0
CHP2—Salt	481–749	2818–4387	45,080–70,185	35	39	20	6	0
CHP+WHI1	380–832	8273–18,116	132,369–289,850	27	19	44	6	4
CHP+WHI2	416–627	18,158–27,396	290,534–438,340	26	41	23	7	3
CCP1—Reg	136–206	194–294	3111–4700	33	30	19	10	8
CCP1—Oil	154–223	219–319	3510–5098	29	36	18	9	8
CCP2—Reg	157–194	264–326	4220–5221	34	37	13	9	7
CCP2—Oil	180–217	302–365	4840–5841	30	44	11	8	6

* The investment costs for the salt and oil heat exchangers are allocated to the low-temperature storage system, LT-TES.

, including distribution to the main individual components.

To categorize the data, it should be noted that the entire efficiency chain, including motors and generators with realistic individual efficiencies, was taken into account in the system simulations. Furthermore, individual components were selected from the state of the art (or those that could be developed in the near future) in order to demonstrate the short-term—but also realistic—potential. This also includes very moderate compressor outlet temperatures of 450 and 625 °C, respectively. However, this also results in a relatively low RTE, which has an indirect negative effect on the cost data. The fact that there are no publicly available precise cost figures for large turbomachinery also contributes to a high level of uncertainty in the cost figures.

In some concepts, solid media storage, liquid salt storage, and oil storage can all be considered LT-TESs. A comparison in terms of RTE or RTU and costs is useful here in order to define a preferred variant in each case. With the PEG1 and PEG2 concepts for pure electricity generation, a regenerator-based TES with the same or better RTE values is also the more favorable variant. This is also the case for the combined generation of electricity and cooling, whereby a slightly higher RTU is also recorded for the regenerator variant. In the CHP2 variant, the salt storage system is preferable for the combined generation of electricity and heat despite slightly higher costs compared to the regenerator-based TES system due to the significantly higher value for RTU.

After the evaluation with regard to the TES technology, a selection of a lead concept for each purpose is envisaged based on the RTE and RTU values and the estimated investment costs. However, this only makes sense for the combined generation of electricity and cooling, as the concept with the lower compressor outlet temperatures of 450 °C performs better in all respects compared to 625 °C. For all other purposes, the concepts are equally viable at both low and high compressor outlet temperatures.

The time-series calculations carried out in off-design mode, which map a daily cycle (or a 2-day cycle in the case of regenerator-based TES systems to be operated alternately) at minute resolution, can be evaluated with regard to the performance curves over time, which is exemplified below for four of the favored lead concepts.

Figure 9 shows the power characteristics of the PEG1-Reg lead concept over 24 h, with the charging line operating in the first 8 h and the discharging line operating for the last 16 h. The decreasing electrical power during discharging and all other sliding changes are due to the characteristic temperature curves at the outlet of the regenerator-based TES tanks.

Figure 10 shows the performance characteristics of the CHP1-Reg lead concept over 48 h, whereby the first 8 h are spent operating the charging line, followed by 16 h for the discharging line, followed by another 8 h of charging and 16 h of discharging. The regenerator-based TES characteristics can also be seen here, with the 8 h cycle for charging and discharging the individual storage tanks also becoming clear in the heat output.

Figure 11 shows the performance characteristics of the CHP+WHI2 lead concept over 48 h. The operating sequence and the 8 h cycle mentioned is the same as described for the CHP1 lead concept. In addition, there is the temporal progression of the waste heat supply.

Figure 12 shows the power characteristics of the CCP2-Reg lead concept over 24 h, which are very similar to those of the PEG1-Reg lead concept, see Figure 9, whereby the charging train is operated for 12 h, followed by 12 h of discharging. In addition, there is also the course of the cooling discharge, which is 0 MW during charging and then drops from around 23 MW to around 2.2 MW over the 8 h of discharging due to the regenerator-based TES characteristics.

Dynamic requirements for the turbomachinery and heat exchangers of the concepts can be derived from the quasi-stationary system modeling with integration of the dynamic regenerator-based TES models. Apart from switching processes between the charging and discharging lines, maximum load gradients of around 2 MW/min result. This gradient is not imposed as a boundary condition but follows directly from the analysis of the simulated time evolution of the operating point. It arises from the thermal dynamics of the TES and the achievable change in mass flow within the 60 s step resolution of the simulation.

4. Discussion

4.1. Comparison of Calculated Efficiencies with Literature Data

The round-trip efficiencies (RTEs) of up to 50% calculated in this work for pure electricity generation and round-trip utilizations (RTUs) of over 85% for coupled electricity and heat generation are in the upper range of the values reported in the literature. Vandersickel and Ludwig [2] and Tang et al. [3] state RTE values of between 20% and 50% for current Brayton battery systems, depending on the working fluid and process topology. The results of this study thus confirm that air-based systems at moderate compressor outlet temperatures (450–625 °C) can be competitive with CO₂₋ based concepts if the thermal energy storage is integrated in an optimized manner.

With an RTU of 83% and an RTE of 9.8%, the CHP2-Salt concept shows that liquid storage systems enable a higher utilization rate if heat is supplied as a product in addition to electricity. This observation is consistent with the studies by Neises and McTigue [5] and Huang et al. [6], which emphasize the trade-off between electrical efficiency and overall energy utilization in hybrid Brayton systems. Particularly high RTU values above 100%, as achieved with CHP+WHI1 and CHP+WHI2, make it clear that waste heat integration (WHI) can achieve almost complete energetic utilization of the process potential—albeit at the expense of electrical efficiency (RTE < 2%).

This confirms the assessment formulated in the latest literature [13,14] that modern Brayton systems should be designed for maximum overall energy utilization and not primarily for electrical efficiency.

4.2. Dynamic Behavior and Transient System Characteristics

The implemented quasi-stationary models with dynamic regenerator-based TES systems realistically reproduce transient effects such as temperature curves, storage discharge, and load changes. The simulated load gradients of around 2 MW/min show stable and controllable behavior in off-design operation.

These results are consistent with the dynamic investigations by Oehler et al. [22], Pettinari et al. [23], and Yang et al. [25], who described similar reaction speeds for CO₂ and air cycles. The characteristic decrease in discharge power over time—visible in Figure 9, Figure 10, Figure 11 and Figure 12—is due to the temperature fronts in the solid regenerator-based TES, as also observed by Frate et al. [33] and McTigue and Neises [26] in their dynamic studies.

The regenerator-based TES ensures smooth mass-flow transitions by damping temperature oscillations through its thermal inertia. Even under rapid load steps, the compressor mass flow stabilizes within seconds due to the quasi-stationary solver structure, while turbine inlet temperature evolves more slowly following the thermal front. This intrinsic stability is a key advantage of Brayton-based Carnot batteries.

Although the dynamic simulations indicate stable operation, several turbomachinery risks must be considered in real systems. Rapid changes in mass flow may reduce the compressor surge margin, particularly during transitions between charging and discharging. Turbine overspeed events may occur if the thermal front in the TES shifts more rapidly than expected. Additionally, thermal gradients during fast load changes can introduce transient thermal stresses in turbine blades and regenerator-based TES walls. These effects require advanced control strategies and will be considered in future research.

The good agreement between the simplified storage models in Ebsilon Professional^® used in this work and the results from MATLAB^® reference models proves that the selected modeling method is suitable for precisely describing the transient behavior of large-scale Brayton battery systems.

4.3. Evaluation of Thermal Energy Storage Technologies

The variants with regenerator, oil, and salt storage systems show that regenerator-based TES systems with the same or higher efficiency are usually also the most cost-effective option. This observation is in line with the results of Sava [28] and Xue and Zhao [29], who emphasize the high temperature resistance and low material costs of solid media heat storage systems.

However, liquid and hybrid concepts—as described in Ayadi et al. [19] and Sharma et al. [20]—offer advantages in terms of temperature homogeneity and controllability, which is particularly advantageous for frequent load changes. The power drops observed in this study during the discharge phases make it clear that the thermal inertia of solid media heat storage remains a key design criterion.

The present results confirm the assessments of Perez-Gallego [34] and Wolscht et al. [35], according to which hybrid storage concepts—combinations of solid and liquid media—have the potential to improve both thermal stability and economic efficiency.

4.4. System Architecture and Operating Strategies

The efficiency of the concepts investigated depends significantly on the pressure ratio and the compressor outlet temperature. A higher temperature level (625 °C) increases the RTE, but requires more complex materials and cooling strategies. Lower temperatures (450 °C), on the other hand, lead to more stable operation and lower material requirements. This trade-off relationship is also emphasized by Lu et al. [8] and Shamsi et al. [14].

It is noteworthy that no physically stable concepts for the simultaneous generation of electricity, heat, and cooling could be identified. This is in line with the analysis of Neises and McTigue [5], according to which triple-generation systems can only be realized with extended storage architectures or alternative working fluids.

The alternating TES mode of operation simulated in this work (e.g., CHP1) proves to be a suitable strategy for ensuring a continuous heat supply (24/7 operation). Such control approaches were also recommended by Pettinari et al. [23] and Wolscht et al. [35] for industrial high-temperature heat pumps.

4.5. Techno-Economic Assessment

The techno-economic analysis (Table 7) shows that thermal storage (30–40%) and turbomachinery (20–30%) account for the largest share of costs. The calculated capacity-related investment costs of 200–800 EUR/kWhel correspond to the orders of magnitude reported in Ben-Venuti et al. [11] and Guccione and Guedez [13].

This confirms that Brayton batteries are particularly economically attractive when cost-effective solid media heat storage systems are used and added value is created by supplying heat or cooling. The results also underline the need to consider technical optimization and cost development together—a central topic of current work by Liu et al. [15] and McTigue et al. [18].

4.6. Summary of Discussion

The dynamic simulations carried out confirm the trends described in the literature, but extend them to include a quantitative, systematic evaluation of real large-scale Brayton battery concepts. In summary, the following can be stated:

• Air-based systems achieve RTEs of up to 50%, with RTUs achieving over 85% in combined heat and power.
• RTU values of over 100% can be achieved by integrating waste heat.
• Regenerator-based TES systems are currently the most efficient and economical storage solution for Brayton batteries.
• The dynamic behavior is largely determined by temperature fronts in regenerator-based TESs.
• Economic competitiveness depends primarily on storage and turbine costs.

This work thus closes the gap between the conceptual analyses of Krüger [1] and realistic dynamic system simulations. It provides a sound basis for demonstration and scaling projects for the further development of thermal energy storage technologies.

5. Conclusions

In the previously published study by Krüger [1], lead concepts for Brayton batteries for different applications were defined on the basis of a broad-based systematic structural analysis.

In this study, these concepts were examined in detail using dynamic system simulations, including component-based design and thermal energy storage. The focus was on the evaluation of system efficiency, transient behavior, and techno-economic performance.

5.1. Summary of Key Findings

• The calculated round-trip efficiencies (RTEs) reach up to 50% for concepts with pure electricity generation.
• For combined electricity and heat generation, round-trip utilizations (RTUs) of over 85% are achieved.
• With additional waste heat integration, RTU values of over 100% are possible—albeit at the expense of RTE.
• For combined electricity and cooling generation, RTUs of up to 60% are achieved with continued high RTEs of around 40%.
• The dynamic simulations show a stable control behavior with load gradients of up to 2 MW/min, which underlines the suitability for flexible energy and industrial applications.
• The investment cost estimate shows that the largest cost drivers are the heat storage (30–40%) and turbomachinery (20–30%), whereby the total system costs are in the range of other large-scale Carnot battery concepts.

5.2. Identified Optimization Potentials

The defined lead concepts can be further improved in terms of energy efficiency, cost efficiency, and system flexibility.

The following optimization potentials were identified:

1.

Variable operating conditions

To increase system flexibility, future analyses should include variable boundary conditions with different temperature and load profiles. A parameter study on sliding compressor outlet temperatures (COTs) can help to determine optimum operating windows and increase economic efficiency.

2.

Configuration of the heat storage tanks

As outlined in Section 3, the permanent (24/7) provision of process heat requires either an additional storage system on the user side (outside the car-not-battery) or an alternating high/low-temperature storage system on the producer side to enable parallel charging and discharging operation. In this study, the second approach was chosen, which allows autonomous operation but requires eight thermal storage units. For cost reasons, the first variant—a central user storage system—could be more economical in the long term.

3.

Bidirectional turbomachinery

The development of compressors and expanders that work in both directions could halve the amount of equipment required. In techno-economic terms, this would be evaluated against a potentially lower RTE.

4.

Hybrid and multi-storage concepts

Future developments should combine solid media and liquid storage to improve both thermal stability and economics.

5.

System integration and control strategies

Further optimization should include an integrated view of control, storage management, and process coupling. The modeling of sliding COT values in particular offers potential for a more realistic representation of dynamic operating conditions.

5.3. Outlook

The results of this work provide a sound basis for the further development of air-based Brayton batteries.

Future work should focus on the following:

• Experimental validation of the model assumptions and simulation results;
• Evaluation of hybrid storage architectures under real operating conditions;
• Integrated optimization of efficiency, control and economy;
• Overall ecological and systemic assessment of the use of the technology.

To support practical deployment, targeted experimental investigations would be required to confirm the predicted system-level behavior under realistic cycling conditions, including the off-design operation of compressors and turbines, long-term thermal stability of the storage material, and the achievable round-trip efficiencies (RTE/RTUs). Such studies would also form the basis for the development of robust control strategies that ensure stable operation, protect turbomachinery surge margins, and enable online optimization of operating points in multi-energy applications.

Brayton batteries thus make a promising contribution to the decarbonized, flexible energy supply of the future—especially in applications with simultaneous use of electricity, heat, and cooling.