Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper'' 3.5 When is Their Application Beneficial? Given that Power-to-X technologies aim at achieving economic and/or environmental benefits by utilizing renewable electricity, the question arises which approach is favorable under which conditions. In Fig. 4, general trends are given where the decisive factors that affect the economic viability are twofold: the average electricity price and its fluctuations.Herein, the fluctuations indicate the absolute changes in price with time. From the environmental point of view, particularly for mitigating greenhouse gas (GHG) emissions, the Power-to-X applications are evaluated according to the average electricity carbon footprint and its absolute fluctuations over time. E-production in steady-state operation becomes more viable with decreasing average electricity price as this is its major operating cost factor. This way, e-products can become cost-competitive with fossil-based products only if the average electricity price is low. Similarly, e-Production must consume electricity with a low carbon footprint to result in low GHG emissions. By utilizing electricity with a high carbon footprint, GHG emissions might even exceed those of fossil-based products [48]. For steady-state operation, the fluctuations in both factors have no influence on process economics and environmental impact, because the plant does not adapt to those fluctuations. Power-to-X applications for DSM and electricity storage are economically beneficial if the fluctuations in electricity prices are high. In such a case, the capacity of processes operated under DSM and processes for electricity storage can be increased when electricity is available at low costs and the load can be reduced or the energy can be reconverted at high electricity prices, respectively. The benefit needs to recoup the capital investment for gaining operational flexibility. The achievable cost savings do not depend on the average price, because the (absolute) revenue of both buying and reselling electricity and of shifting periods of electricity consumption only depends on the magnitude of fluctuation. Electricity storage facilities and DSM favor a high fluctuation in carbon footprint of the electricity mix in order to exploit the environmental potential. Electricity is used/ stored when the share of RES in the electricity grid is high and reconverted when the share is low [35]. As already stated in Sect. 3.4, combinations of these applications can outperform individual applications. One combination could be DSM for e-Production with an increased production rate when electricity prices are low. Then, equipment oversizing that enables flexible operation should be addressed in process design. The considered fluctuations occur on very different time scales: hourly, daily, or even seasonal.''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper'' 5 Summary and Outlook In this review, Power-to-X technologies are defined more generally than in conventional literature as processes with the goal to exploit the environmental and economic potential of renewable electricity. According to this definition, such technologies comprise DSM, e-Production, and electricity storage. These different approaches for the common goal of utilization of electricity with a high share of RES offer different economic and environmental benefits depending on average electricity prices and fluctuations as well as depending on the electricity average carbon footprint and fluctuations, but they share common challenges. DSM is worthwhile especially for electricity-intensive processes: for CA electrolysis, electricity costs can be saved if variable operation is implemented and oversizing considered. However, the dynamic operation also brings challenges, e.g., limitations on Cl2 storage. It is demonstrated how such a limitation can be overcome by a novel modeswitching operation. For e-Production, two main challenges are identified: technology selection and efficiency improvement. Optimization-based methods give insight into conflicting performance indicators of competing products and processes, e.g., production cost and GWP reduction for e-fuel production, and support decision-making systematically. An additional system-level process analysis using detailed models reveals bottlenecks and can finally lead to significant efficiency improvements as well as GWP and cost reductions. For the ammonia-based electricity storage, optimization-based process design enables a round-trip efficiency of the combined synthesis process that can even exceed the one of electricity storage based on H2 directly. Despite many challenges that have been addressed successfully by PSE methods, there are still open questions and challenges left. Particularly relevant for electrolysis, i.e., a key element of many Power-to-X technologies, the risk of deteriorating equipment lifetime due to flexible operation of Power-to-X processes needs to be investigated. Research regarding this via both experiments and simulations is ongoing; however, long-term compatibility of the material under highly dynamic operation has not been demonstrated conclusively yet. In addition, uncertainties due to external parameters influence decision-making regarding Power-to-X technologies significantly and must be addressed in process design and operation. Especially, uncertainties in future electricity price and carbon footprint in both short and long terms need to be accounted for via prediction methods. This will play a key role for a successful implementation of Power-to-X technologies. All these challenges need to be tackled by further research''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper.''3 Beneficial Utilization of Electricity by Power-to-X Here, Power-to-X processes are defined as processes with the goal to exploit the environmental and economic potential of renewable electricity. This comprises the production of gases and liquids from renewable electricity as well as the provision of heat with the intention to replace fossil-based products, which is called e-Production. Additionally, this definition encompasses the older fields of electricity storage and DSM. With this definition, Power-to-X is not restricted to technologies for the conversion of predominantly electric power into products that are currently based on fossil sources. With DSM, it also incorporates approaches that enable the utilization of renewable electricity for industrial processes that have not been able to utilize such in an effective way until now. We believe that such a broad definition is useful to highlight the relationship and overlap of these fields that become particularly apparent in many Power-to-X technologies falling into more than one of these three categories (gray areas in Fig. 3). We explicitly confine our definition to processes that aim at utilizing renewable electricity and exclude, e.g., general energy management technologies from our definition of Power-to-X. However, contrary to their intended purpose, associated technologies could in principle also utilize other types of energy sources, e.g., for producing synthetic fuels from nuclear power in one country and transport it to another one. In the following, these three main approaches for a beneficial utilization of renewable electricity are briefly introduced, their relations are identified, and their opportunities and common challenges are stated''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper.'' 3.6 Challenges for Successful Implementation of Power-to-X Technologies Power-to-X technologies face a number of challenges for successful implementation, some of which differ from those of classical process systems. Here, technical challenges are discussed and political boundary conditions, e.g., carbon tax or climate targets [49], social acceptance, e.g., preferences for potential Power-to-X products [50], and similar issues are excluded. 3.6.1 Process: Efficient Flexible Operation Power-to-X processes are energy-intensive by definition, and therefore, energy efficiency is of prime importance both for economic and environmental reasons [6, 48, 51]. Beyond high efficiency at a single design point, Power-to-X processes aiming at DSM or electricity storage need to retain high efficiency over a wide range of operating conditions to be able to operate according to electricity price or some other signal for availability of electricity [33] instead of operating at steady-state like today’s process systems. Such changes in operating conditions also need to occur sufficiently fast to follow the changes in electricity supply in the desired time scale. Processes with inherently fast dynamic response can thus easily be used for DSM by appropriate scheduling, e.g., seawater reverse osmosis [41]. Other processes exhibiting slower dynamic response, such as ASU [36], demand advanced control strategies to enable flexible operation for DSM. Additional challenges are associated with the implications of flexible operation on the performance and lifetime of plant equipment and, in particular, catalysts that are not fully understood yet [52].''

Introduction: Describe the purpose and focus of the paper.''1 Introduction On a global scale, the share of renewable energy sources (RES) in electricity production is small but growing continuously. To prevent economic losses and idle green resources caused by energy curtailments, corrective actions need to be taken. Moreover, RES must become accessible for sectors that still heavily rely on fossil resources, i.e., chemical industry, heating, and transportation [1], if global climate targets are to be met. In this context, technologies termed Power-to-[K], such as Power-to-gas, Power-to-chemicals, or Power-to-fuels, have attracted increasing interest in recent years (cf. Sect. 2). The terminology has been used for an ever-increasing number of applications, and the large diversity of applications associated with this terminology has resulted in the term Power-to-X. However, we are not aware of an established definition about what the X may or may not include. Looking at most instances of Power-to-X concepts, these aim at converting electricity into gases, liquids, heat, fuels, or even back from those into electricity [2–7]. We believe that in addition to the new aspect of bringing renewable electricity into production processes to replace fossil-based products, many recently proposed technologies under the term Power-to-X are closely related to the much older concepts of electricity storage and demand side management (DSM). Therefore, a broad definition of Power-to-X as processes with the goal to exploit the environmental and economic potential of renewable electricity is proposed. This explicitly encompasses electricity storage and DSM as well as the newer aspect that we call e-Production. In the following, first, a brief overview of the literature is given (Sect. 2). Then, details on the definition and classification of Powerto-X are provided, before key challenges and benefits for given external conditions are discussed (Sect. 3). Illustrative examples that demonstrate how process systems engineering (PSE) methods support overcoming these challenges are also given (Sect. 4). Finally, the most important findings and still open questions are summarized (Sect. 5).''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper:''Powerto-heat [28], and Power-to-chemicals [7] individually, some of them also collectively [6, 29]. The publications typically consider different performance indicators, i.e., economics, sustainability, efficiency, infrastructure, technology readiness level, etc., as well as a variety of boundary conditions to provide a holistic assessment of the technology. The diversity in boundary conditions and assumptions makes the comparison between the publications difficult. Going through the broad range of different literature on Power-to-X technologies, it is noticeable that their applications in most cases aim at the conversion of predominantly electric power into products that are currently based on fossil energy sources. Therein, the scientific community distinguishes between the product’s state, i.e., Power-to-gas or Power-toliquid, and the product’s intended purpose, i.e., Power-tofuel or Power-to-heat. This product-oriented classification has two shortcomings. First, the notations are ambiguous. Either of the terms Power-to-liquid and Power-to-fuel are used for the same notion. Additionally, ‘‘liquid’’ may refer to fuels, a chemical feedstock, or both, and ‘‘fuel’’ may refer to a liquid, a gas, or both. However, the intended purpose of the product or – even more precisely – of the Power-to-X application is very important for its environmental assessment [6, 29]. Second, the broad usage of the terminology Power-to-[K] and the missing definition lead to the question which technologies to include and which not. For instance, there are DSM endeavors in which some electricity-intensive industrial processes are explicitly operated flexibly to make them utilize renewable electricity effectively (cf. Sect. 3.1). Such approaches are commonly not considered Power-to-X technologies, although flexible operation is a key aspect in many Power-to-[K] processes, and they pursue the same goal of improving the utilization of renewable electricity. This indicates a connection to more established process concepts that were excluded in the keyword search illustrated in Fig. 1. To indicate the increasing interest also in those, Fig. 2 exemplarily shows the number of publications related to some of them using a selection of keywords. In addition to the increasing general interest in these established technologies, the high amount of literature on demand side management with regard to renewable electricity utilization highlights its relevance for Power-to-X processes. Therefore, a broader definition of Power-to-X and a classification based on the way Power-to-X pursues the common goal of a beneficial utilization of renewable electricity are proposed. 3 Beneficial Utilization of Electricity by Power-to-X Here, Power-to-X processes are defined as processes with the goal to exploit the environmental and economic potential of renewable electricity''