1 Introduction

Since 2005, Europe’s energy transition has been notably oriented towards renewable sources, particularly wind and solar energy [1]. However, the supply of these energy sources remains unpredictable, characterized by substantial intermittency. This trait gives rise to challenges, including imbalances between supply and demand such as generation congestion and excess demand at distinct time intervals. These issues, in turn, contribute to fluctuating and declining electricity prices, which do not promote the attraction of further investments [2, 3]. To address these issues, expanding and developing the electricity grid and network infrastructure is vital. This infrastructure enables efficient transfer of electricity from areas with surplus power to those with shortages, effectively stabilizing supply. As Europe increasingly relies on volatile renewable energy, this infrastructure becomes even more critical, making it a field of research that is likely to maintain and receive increasing interest in the years to come.

Grid expansion and development constitutes a complex field. It encompasses a range of facets, including political considerations surrounding cross-regional connections (e.g., [4]), social factors like public acceptance (e.g., [5]), equitable allocation of benefits among stakeholders (e.g., [6]), technical challenges tied to high-voltage transmission and storage equipment (e.g., [7]), and the selection of nodes and expansion pathway (e.g., [8]). Additionally, optimizing societal welfare, entailing aspects such as system costs and market efficiency, also forms an integral part of this domain (e.g., [9]).

Considering the contemporary relevance of grid-related research, and the complexity of the field, our goal is to offer a comprehensive overview of recent research, covering the period from 2013 to 2023, and to pinpoint promising areas for future investigations. We select literature from the past ten years for review, aiming to confine our time frame to a period which saw a surge in relevant research. Overall, we hope this may serve as a useful resource for both newcomers and seasoned researchers in the field. To achieve our objective, we conduct a structured search and categorize recent research based on geographical scope, grid expansion strategies, research focus, and the methodologies employed. Based on the categorized search results, we uncover and analyze emerging trends in the field. Furthermore, we delve into recurring frameworks found in the selected literature, pinpointing associated references for documentation. Drawing from our analysis of the literature, we also outline potential directions for future research in this field.

Existing review articles concerning grid expansion mainly focus on comparative analyses of centralized grid extension and decentralized off-grid node creation models, primarily targeting solutions for electricity access challenges in deficient or rural regions, particularly within Africa and South Asia [10,11,12,13,14]. Meanwhile, there are not many review articles on grid expansion regarding power system stability in response to climate change and increased renewable generation share, and the studied time range is only up to 2015 [15], highlighting the need for an updated review.

In recent years, the urgency of climate change and the transition to renewable energy has grown, leading to increased attention. Seasoned researchers, as well as new ones, have contributed with new and valuable studies. These studies look into new and updated research questions, motivated by the growing need for a green transition, while considering changes in political circumstances and technological development. For instance, the inclusion of recently published protocols from European Commission, like the agreement about the interconnection of offshore power grids among coastal countries [16], has reduced the need for political risk assessment, shaping both research focus and state of the art modeling and analysis. Additionally, the innovation and evolution of related technologies, such as hydrogen as storage facility, has progressively broadened the horizons of expansion strategies, and shaped grid-related research. Moreover, pre-existing models have undergone modifications and further development, and new models have appeared. The culmination of this underscores the necessity for an up-to-date review and synthesis of recent literature.

The reminder of this paper is organized as follows. Section  explains the approach of searching the references analyzed in this paper. Section  outlines the criteria employed herein for the classification of grid expansion. Section  presents the overview and methodological results of the retrospective analysis. Section  discusses the trends in research focus and state of art and the reasons behind them, as well as the future research opportunities. Section  presents the summarizing remarks.

2 Search methodology

To identify relevant articles, we performed a structured search in Scopus, a widely employed database for academic research and various other applications [17]. An article can be considered a search hit if its title, abstract, or keywords contained the following elements:

  1. 1.

    Research Topic: At least one of the terms “energy” or “power”, in conjunction with “transmission” or “grid”, along with “expansion” or “extension”.

  2. 2.

    Geographical Scope: At least one of the terms “Europe”, “EU”, or “European Union”.

  3. 3.

    Methodology: At least one of the terms “optimization”, “simulation”, “statistical”,“regression”, or “analysis”.

  4. 4.

    Publication Year: Ranging from “2013” to “2023”.

This search resulted in an initial pool of 162 articles. Subsequently, we refined the selection by narrowing down the subject area. Specifically, we only retained articles from subject areas: “energy”, “environmental sciences”, “engineering”, “mathematics”, “economics and econometrics”, “business management”, “computer sciences”, “social sciences”, “decision sciences”, “materials sciences”, “earth sciences”, and “agricultural and ecological sciences”. Following this selection, the number of articles was reduced to 148.

Next, we conducted a manual abstract-based screening. During this phase, we eliminated articles, such as [18, 19], that primarily focus on the initial construction rather than the expansion of the grid. Additionally, we excluded articles that consider the grid merely as a research constraint. For example, some articles such as [20] study how to increase the stability of electricity system with high renewable generation share under the condition that the grid expansion is restricted or not allowed. Moreover, we omitted papers that only use grid expansion as a comparison to study other unrelated topics. For instance, certain articles suggest that addressing the supply–demand mismatch resulting from the volatility of renewable energy can be achieved through sector coupling, offering a viable alternative to traditional grid expansion approaches [21, 22]. We also removed certain overview articles from consideration. As an illustration, specific articles such as [15] undertake reviews of the advancements and plans pertaining to offshore grid expansion in recent years. Following this screening phase, the number of articles was reduced from 148 to 76.

Finally, we conducted a manual article content screening. Following a thorough review of the content within the pool of 76 articles, we proceeded to refine the selection based on the degree of relevance and applicability of their contents to the specific topic under investigation. Ultimately, the final count was settled at 59 articles.

3 Categories

Our search procedure, including abstract and content screening, revealed several useful categories which can be used to group and analyze the papers, including geographical scope, the expansion strategy/strategies studied, and the methodology employed. In this section, we outline these criteria.

Firstly, distinguishing whether the grid expansion’s geographical scope occurs solely within a single country or involves cross-border transmission between nations holds significant relevance (Table 1). This is because such a distinction pertains to cooperative arrangements and the distribution of responsibilities among diverse stakeholders. Secondly, grid expansion can manifest through varied approaches, encompassing the interlinking of existing nodes with transmission lines, the establishment of new nodes for connectivity, and the connection of nodes in farther places. Hence, it is crucial to ascertain the precise approach adopted in a grid expansion study, as this enables the expansion strategy to function as another key classification determinant (Table 2). Lastly, the methodology embraced by the research also stands as a vital criterion, as the attributes of modelling frameworks can significantly impact the accuracy, sensitivity, and applicability of the results (Table 3).

Table 1 Definition of three common geographical scopes for grid expansion
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Table 2 Definition of three common grid expansion strategies
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Fig. 1
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Interlinking strategy. The thickness of the lines can signify either the voltage level or the flow capacity

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Fig. 2
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Node Creation strategy

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Fig. 3
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Zone Extension strategy

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Table 3 Definition of various model attributes for studying grid expansion
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4 Results

In this section, we present the search results and their categorization. First, we provide a descriptive overview of when and where the articles were published. Second, we provide both a high level and detailed overview of the categorized search results, including the employed geographical scope, expansion strategy/strategies studied, research focus, and employed methodology/methodologies. Finally, we provide an overview and insight to nine established and recurring frameworks.

4.1 High-level overview

Fig. 4
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Summary of publication year of selected articles

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Fig. 5
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Summary of journals in which selected articles were published (This figure only includes 57 articles, which is two less than the 59 articles we examined in total. This discrepancy is due to the fact that two of the articles we discussed (reference [47] and [67]) are not journal articles, but rather chapters from a book.)

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Figure 4 shows the number of publications by year. 2022 boasts the highest number of publications pertaining to power grid expansion, totaling at 12. This is closely followed by 8 publications in the year 2018. The figure indicates a possible upward trend in the number of relevant publications by year, with 21 articles published in the period 2013–2017, and the remaining of the 59 articles published in the period 2018–2023. Although this may be credited to random fluctuations, it may also reflect an increasing interest in the topic at hand.

Regarding journals in which the articles were published (Fig. 5), four journals, namely Energy, Energy Policy, IEEE, and Applied Energy, exhibit a high frequency. Following this, there are six journals displaying a moderate frequency, encompassing Energy Economics, Energies, Frontiers in Energy Research, Energy Research & Social Science, Journal of Cleaner Production, and International Journal of Electrical Power Energy Systems. Conversely, the remaining journals are singular occurrences. Overall, it can be deduced that the target journals of articles related to power grid expansion are relatively concentrated. And the scientific field of the main target journal is mainly “energy”, supplemented by “economics” and “engineering”.

Fig. 6
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Summary of geographical scope

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Fig. 7
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Heat map indicating the number of times European countries have been studied as subjects of grid expansion

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In terms of geographical scope, while studies on grid expansion that focus on a single country or regions within a country make up only about 19% and 3% of the cited literature respectively, research with a multinational focus constitutes a significant 78% (Fig. 6). As indicated by Fig. 7, Europe as a whole predominates as the primary coverage region within the multinational category, as almost all European countries have been studied more than 29 times, with a notable concentration on the North Sea countries such as Germany, France, Netherlands, the United Kingdom, and the Nordic countries.

Regarding the classification of grid expansion strategies (Fig. 8), the majority of research considers one or two distinct expansion strategies. Among these, establishing new transmission lines between nodes emerged as the prevailing strategy (62%). However, this approach frequently coincides with the establishment of new nodes (12%) or the enlargement of the grid’s scope to encompass additional nodes for connectivity (12%). The overlap between Zone Extension and Node Creation strategies remains relatively low, constituting only 2%. Only one paper undertakes a comprehensive analysis of all three expansion strategies concurrently.

Fig. 8
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Summary of expansion strategy

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Fig. 9
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Summary of the applied methodology

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Considering the methodology aspect (Fig. 9), over 71% of the cited references employ optimization models, followed by approximately 14% utilizing statistical models. Simulation models are applied only seven times out of the 59 references. Analyzing the model characteristics (Fig. 10), deterministic models are observed more frequently than stochastic models, with the former being over twice as common. A substantial majority of the models adopt a linear structure (52 out of 53) and exhibit dynamic behavior (50 out of 53). Models incorporating mixed-integer attributes constitute less than 14%.

Fig. 10
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Methodology attributes summary

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4.2 Detailed overview

Table 4 provides a detailed overview of the categorized search results. Besides serving as a comprehensive overview of the relevant literature, which could be useful as a reference guide, its contents are also helpful in analyzing trends in research and state of the art, and in conceiving further research ideas, which we will discuss later.

Several observations can be made from the table. First, regarding expansion strategies, the Node Creation strategy primarily entailed the incorporation of renewable energy farms as novel nodes in the early phase between 2013 and 2023. However, in subsequent years, the Node Creation strategy shifted towards integrating energy storage facilities like hydrogen as additional nodes within the grid. While the Zone Extension strategy increasingly centered around offshore wind as its prime research focal point, there has been a noticeable trend towards combining the enhancement of solar energy nodes with a concurrent increase in energy storage nodes in recent times, indicative of growing interest within the field.

Second, in terms of the focus aspect, an observation arises that early references on grid expansion primarily delved into strategies for mitigating project delays, alongside methodologies for computing and distributing costs and benefits associated with cross-border grid connections. Subsequently, the later literature after 2018 shifted its attention to optimizing the expansion path of the power grid across various scenarios, all while prioritizing either the utmost efficiency or minimal cost.

Third, regarding the methodology perspective, during the initial phase after 2013, the methodology predominantly centered around statistical analysis and empirical demonstration. In the subsequent period, there was a shift towards optimization methodologies, often supplemented by simulation approaches. Post-2020, the landscape of optimization models became increasingly diverse, with numerous researchers incorporating new constraints or additional layers into existing models from previous literature, thus enhancing the models’ sophistication. In addition, a substantial proportion of the optimization models in the later period from 2013 to 2023 are equipped with publicly available software, allowing researchers direct usability.

The categorized search results also reveal some interesting connections between the geographical scope and expansion strategy/strategies studied. First, the analysis of Table 4 reveals that Interlinking emerges as the predominant expansion strategy when the research pertains to a single country (e.g., [8, 23, 24]). In essence, investigations into power grid expansion within a specific country are oriented towards the interconnection of nodes across diverse regions, thereby forging an expansive power grid spanning the country’s scope. Such studies often aim to decipher the optimal selection of existing nodes that can help to strike a balance between minimal investment costs and the attainment of heightened energy efficiency across the overarching grid.

In terms of the Node Creation expansion strategy, the geographical scope of the research topic exerts insignificant influence. Both national and multi-national type are common in investigating the optimal locations for establishing various energy nodes (e.g., [25, 26]). It is noteworthy that, irrespective of whether an article pertains to a national or multi-national context, emissions serve as a common constraint in most of the Node Creation research (e.g., [25, 27]). This constraint stems from the inherent objective of new nodes establishment, which typically revolves around increasing the share of clean energy power generation, often complemented by storage facilities that synergize with renewable energy sources, to meet environmental goals.

In the context of the Zone Extension strategy, a tendency emerges for research to encompass multiple countries as the focal point (e.g., [4, 28]), with limited instances of this expansion approach being adopted in national-focused articles. This is because Zone Extension often entails complicated cross-connections. For instance, in a scenario where country A links to country B, country B extends its connection to countries C and D, and country D establishes transmission lines with both countries A and C concurrently, it is better to use these four countries as a whole to conduct research. As a result, when pursuing the strategy of Zone Extension as the primary research avenue, the inclination has been to encompass the broadest possible array of regions, reflecting a prevailing choice within prior investigations.

Table 4 Overview table
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4.3 Established and recurring frameworks

Through our review process, we identified several established and recurring frameworks. Figure 11 provides an overview of these frameworks along with common inputs and outputs. Table 5 provides more detailed information about the frameworks, including their characteristics and purposes.

Fig. 11
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General structure of energy system planning models

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Broadly speaking, the motivations behind these models all align with a common goal: to accommodate the incorporation of a greater share of renewable energy sources as a crucial response to the imperative of combating climate change. The intermittency and unpredictability inherent to wind and solar generation pose a challenge in incorporating higher shares of these technologies within the energy mix, necessitating effective supply–demand balancing mechanisms and the development of optimization models. Central to these models, the objective function aligns with the maximization of social welfare, operationalized through the minimization of system costs. Given that European-wide multi-country joint regions are the most common research subjects for grid expansion, ENTSO-E, which is the European association for the cooperation of transmission system operators for electricity, serves as a main data resource for obtaining a substantial repository of information pertaining to grid expansion in Europe. The output of these models commonly encompasses generation, costs, storage, and transmission aspects. However, it’s crucial to underscore that a shared issue encountered in these models pertains to their computational complexity, resulting in extended running times.

Regarding the models themselves, among the nine methodologies frequently encountered in grid expansion literature, only three (EMPIRE, TIMES, and FlexPlan) belong to the category of stochastic models. Stochastic models embrace uncertainty by utilizing probability distributions of parameters, rather than fixed parameter values. The uncertainty often comes from fluctuating energy generation and volatile energy consumption. Among these three common stochastic models, EMPIRE and TIMES share a considerable degree of similarity. Both models account for short-term and long-term dynamics, culminating in a shared presentation as two-stage stochastic programs. In congruence with EMPIRE’s multi-horizon tree formulation, TIMES employs a here-and-now decision mechanism to encompass various time slices. However, a notable distinction between EMPIRE and TIMES is that EMPIRE demonstrates smoother behavior when accommodating stable energy sources like natural gas and nuclear energy.

Deterministic models hold a more significant presence when exploring energy system and grid expansion, constituting six out of the nine commonly used models. These models prioritize capturing correlations and anti-correlations between fixed values of electricity demand and generation potential, deeming the consideration of uncertainty a reasonable trade-off. ELMOD and REMix are among the frequently employed deterministic models, with ELMOD even can offer a specialized variant capable of integrating uncertainty considerations after being applied many times. Balmorel, developed in 2001, stands as the pioneering model addressing energy systems and transmission expansion. Its application, however, faces limitations due to the constraints of its data, confined to the North Sea and Baltic Sea regions. In contrast, the AnyMOD model distinguishes itself by targeting macro energy systems across expansive regions, rendering it more suitable for intercontinental grid expansion studies. Similarly, REMix proves suitable for investigating power transmission over extensive areas, given its data sources spanning Europe and North Africa. The uniqueness of the LIMES model lies in its emphasis on policy-level constraints, in contrast to other models that prioritize economic analysis. ELMOD, REMix, and PyPSA adopt a continuous 24-hour time-frame to simulate variable demand and wind/solar input. This enables them to more accurately mirror the dynamics of the European electricity market and depict changing trends of the energy system within a year. However, this attribute may render these models less responsive to trends occurring in the same time-frame across the long term. Finally, EMPIRE, AnyMOD, FlexPlan, PyPSA, and Balmorel all boast open-source status, offering accessible and user-friendly options for researchers and analysts alike.

Table 5 Established framework table
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4.4 Strengths and weaknesses of established frameworks

Table 6 further provides a comparative analysis of the advantages and disadvantages of above models in Table 5, based on four selected measures. These measures include: the model’s ability to account for uncertainties in electricity demand and variable renewable energy generation; the adoption of sufficiently granular hourly data in the model’s time resolution; the accuracy of the model’s power flow calculation mechanism; and the model’s suitability for macro-level research on cross-border, large-scale power grids versus micro-level research within specific countries. The reason we also consider the transmission formulations in the model as an evaluation index is because they determine the optimal operating levels for different generators within a transmission network. The two main types of OPF are ACOPF and DCOPF, with each has its own distinct advantages and disadvantages that can significantly impact the model structure. ACOPF considers both active and reactive power flows and voltage angles, making it more accurate but also more computationally intensive. Conversely, DCOPF simplifies the problem by only considering active power flows and neglecting the resistance of transmission lines. This makes it less accurate but also less computationally intensive. Lastly, our criterion for determining the model’s scope of application is based on the nodes in the model. If the node is country-based, we believe the model is suitable for studying cross-border power grids. If the nodes are specific to each power plant, we believe the model is more suitable for research within a country or a limited region.

According to Table 6, it can be found that the advantages of the ELMOD and EMPIRE models are that they both take into account the uncertainties that can affect the energy system in the short and long term, and utilize hourly data for their analyses. These can result in a high degree of accuracy in their predictions regarding energy system costs and the generation mix. However, both models employ DCOPF for power transmission, which will lead to a certain degree of reduction in the accuracy of the transmission-related portions of the model output. The AnyMOD model boasts two primary advantages. Firstly, its temporal resolutions are flexible. Secondly, despite being a deterministic model, it allows for variations in energy carriers. However, a notable disadvantage of this model is the relative complexity of its power flow sub-model, which results in high computational complexity. In contrast, the LIMES model’s main advantages lie in its low model complexity and short runtime. Its primary drawback, however, is its inability to analyze uncertainty, despite its capacity to supplement short-term fluctuations. In essence, the LIMES model is best suited for large-scale models with a long-term focus. The TIMES model excels in accurately supplementing the heterogeneous impact of various types of uncertainties on both operational and investment decisions in the long and short term. However, its transmission formula solely focuses on the transmission path of energy commodities from original resources to terminal demand, neglecting to consider energy storage nodes in the process.

The FlexPlan model’s strength lies in its ability to consider various uncertainties and support both ACOPF and DCOPF. This results in more reliable output regarding the energy mix, cost, and transmission. However, this also leads to a high level of model complexity. On the other hand, the PyPSA and REMix models fall short in capturing the uncertainty in electricity demand and variable renewable energy production. Despite this, they can consider both AC and DC transmission. Consequently, while the accuracy of the energy mix portion of these two models’ results is relatively low, the accuracy of the transmission part is largely assured. The Balmorel model’s primary advantage is the specificity and precision of its nodes, making it well-suited for studying the expansion of connections between power plants within a country.

Table 6 Comparison of advantages and disadvantages of various optimization models
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5 Discussion

Commencing this section, we analyze the rationales behind the noticeable shift in research focus within the literature concerning European grid expansion. Subsequently, an examination of the developmental trajectory and prevalent issues related to model application is presented. In the final subsection, we highlight potential avenues for future research.

5.1 Research focus and trends

As previously mentioned in Sect. 4.1, the countries along the North Sea and the Baltic Sea are studied significantly more than the rest of the countries. We also pointed out in Sect. 4.5   that over the course of nearly a decade, research papers on grid expansion within the context of energy system stability under climate change and the growing share of renewable energy production exhibit three distinct characteristics: an increasing emphasis on offshore wind power expansion as the primary research subject, a growing focus on hydrogen energy for new node construction, and the gradual inclusion of the interlinking between solar energy and energy storage equipment. In the following section, we discuss why the research focus on this topic presents a geographically concentration and why it shows such changing trends.

There are two primary reasons why offshore wind power expansion has emerged as a main research subject in European grid expansion in recent years. Firstly, offshore wind energy, compared to onshore wind, offers vast development space and potential. Secondly, offshore wind projects has garnered collective policy support from many European countries. As a result, the proliferation of offshore wind projects has led to countries surrounding the North Sea and Baltic Sea, where these projects are concentrated, being more frequently discussed in the context of European grid expansion than other regions.

Wind energy has held a central role in the renewable energy capacity expansion since renewable energy became the backbone of Europe’s energy transition [96]. However, the main focus across all countries has centered on onshore wind power. According to 2022 data from Wind Europe, 87% of Europe’s wind power capacity expansion originates from onshore wind energy [97]. Despite the United Kingdom having the largest number of offshore wind farms, its cumulative installed capacity by 2022 remains notably smaller, standing at around 15GW, in stark contrast to the nearly 60GW of installed capacity generated by onshore wind power [97]. Germany follows with approximately 9GW, trailed by the Netherlands, Denmark, and Belgium, in where the collective installed capacity of offshore wind power falls below 4GW [97]. This underscores the substantial potential for further development within the realm of offshore wind power.

In the aforementioned context, the European Commission took further steps to support wind power development by issuing a directive in 2020 aimed at propelling offshore wind power expansion to aid in achieving climate neutrality by 2050 [98]. This document proposes to increase Europe’s installed offshore wind capacity to 60GW by 2030 and 300GW by 2050. To facilitate this, European nations subsequently forged a cooperative agreement for the expansion of the European energy network, seeking to reduce procedural hurdles and permitting timeframes [99]. The agreement includes five main sea basins: the North Sea Offshore Grid, the Baltic Sea Offshore Grid, the Southwest European Offshore Grid, the Atlantic Offshore Grid, and the Southeast European Offshore Grid. The introduction of these policies and agreements has prospered research focused on offshore wind within the realm of grid expansion.

Consequently, the emphasis on constructing new nodes in grid expansion has shifted from onshore renewable energy plants to offshore wind farms. This transformation has then directed greater attention to coastal European countries, including the United Kingdom, Germany, France, and Denmark, turning them into focal points for researchers. This explains the clear regional concentration observed in the geographical scope of the studies cited in the literature.

The growing mention of hydrogen energy as a storage device in grid expansion studies is also largely attributed to the expansion of offshore wind power. As the offshore wind grid expands, addressing its instability issues becomes increasingly critical. Thus, with the technological advancements in hydrogen since 2015 [100, 101], the application of this technology within energy systems has emerged as an intriguing topic [102]. Consequently, from 2018 onward, there has been a surge in research papers exploring the economic feasibility of using hydrogen as a carrier to connect offshore and onshore nodes, potentially replacing traditional submarine cables.

Finally, the widespread discussion about the role of energy storage facilities in enhancing supply stability in energy systems with a large proportion of renewable energy has sparked interest in determining which type of renewable energy is most efficient for cooperation with energy storage nodes. In particular, the connections between hydrogen and offshore wind power nodes, onshore wind power nodes, and solar energy nodes have become focal points of discussion. This is why there has been a recent increase in comparative studies examining the collaboration between solar energy and hydrogen energy, as well as the partnership between wind energy and hydrogen energy.

5.2 State of the art

Based on the findings presented in Sect. 4.2 , power grid expansion studies were predominantly characterized by the utilization of statistical models during the initial phase of our research period. However, as we progressed into the latter half of the research period, the main focus shifted towards optimization models. This section delves into the reasons for this trend in applied methodologies and outlines how optimization models for this topic have evolved over time. Finally, we summarize and discuss common problems with these optimization models and possible solutions.

Firstly, the shift in state of art from statistical methodology to optimization methodology is related to the evolving research focus. As mentioned in the previous Sect. 5.1 , the surge in offshore wind adoption, spurred by intergovernmental cooperation agreements within Europe, and the expanding role of hydrogen in grid expansion, driven by technological advancements, initiated a preliminary exploration phase concerning the integration of offshore grids and energy storage nodes into the energy system. During this phase, the research questions mainly revolved around the feasibility of embedding these two components within energy systems, thus emphasizing the “how” aspect. For example, once the offshore grid is established, how it can be economically connected with the onshore energy system. Similarly, the establishment of offshore power grids often involves the cooperation of multiple neighboring countries, so how to allocate costs and benefits in the cooperation is another common question in the initial stage. Furthermore, exploring the establishment of new onshore hydrogen energy nodes confronted construction delays and public opposition, posing further “how” questions. To address these initial “how” inquiries, methodologies like regression analysis and cost-benefit analysis, manifesting as statistical models, were deemed suitable. Subsequently, as these preliminary questions yielded affirmative outcomes, researchers transitioned to the subsequent phase, evolving from “how” to “how better/best” investigations. This type of problem usually includes optimal concerns such as how to select the optimal node location of the offshore power grid and how to plan the optimal expansion path. The optimal questions naturally align with the employment of optimization methodologies. So far, research into the realm of European grid expansion continues to revolve around refining objective functions of various optimization models, while accommodating a growing array of constraints.

Secondly, we discuss the process of developing the optimization model. Through the coordinated efforts of numerous researchers, the optimization models aimed at studying the expansion of the European power grid have evolved, incorporating a wider array of constraints and uncertainties, thus becoming more intricate and better capable of simulating real-world scenarios. A significant improvement is that subsequent scholars have extended their investigations beyond the foundational models that were established earlier, distinguishing between short-term and long-term dynamics. This entails delving into short-run operational uncertainties and long-run demand fluctuations. In the succeeding iterations of models, the incorporation of seasonal energy capacity constraints alongside environmental impact considerations become evident, representing a refinement that effectively captures the intermittent nature of renewable energy sources. Furthermore, these later models integrate provisions for curtailing the excess renewable energy that cannot be fed into the grid. Another noteworthy advancement lies in the heightened recognition of the growing demand for hydrogen energy and the potential for its associated infrastructure reuse. Consequently, the evolution toward multi-stage models ensued in the later iterations of optimization models regarding grid expansion. Moreover, the subsequent models transcend mere pursuit of total system cost minimization, striving to explore configurations that achieve the dual objectives of minimizing investment and operational costs, along with optimizing the efficiency of transmission and storage units across diverse power generators.

Finally, we turn to the challenges associated with these optimization models. As optimization models concerning the expansion of the European power grid have progressively evolved and matured, these have also caused a marked increase in computational complexity and execution time. Avoiding binary variables is a common technique which can mitigate models’s computational complexity while maintaining result accuracy. This rationale underlies the findings in Sect. 4.1 , which indicate that models featuring mixed integer attributes constitute a relatively small portion of all optimization models. Specifically, within the realm of European grid expansion, important questions such as whether a node should be integrated into the grid are typically formulated as decision variables expressed through binary outputs. Nevertheless, in order to avert the escalation of complexity caused by mixed integers, researchers often opt for an alternative approach: they assume that all nodes can be connected while designating capacity of nodes as a continuous decision variable. In this way, nodes whose capacity is determined to be zero by the final optimal result can be seen as nodes not requiring connection, whereas other nodes can be interpreted as affirmatively answering the question “whether it needs to be connected with the grid.” This method has been widely adopted by researchers in the literature to expedite model execution time, though it still falls short of significantly mitigating overall model complexity. In pursuit of this objective, researchers have undertaken further efforts.

To further grapple with the computational complexity challenge inherent to extensive macro energy system models, researchers have advanced two more solutions: time series reduction and spatial dimension reduction. In order to capture the uncertainty brought about by the mismatch of supply and demand at different times of the day, the data for the optimization model of grid expansion is inputted in units of hours. Subsequently, to mitigate computational complexity while retaining the time span, a method entails re-scaling time steps to group them into discrete time periods, thereby modeling representative spans instead of the entire time series, can be adopted [103]. This temporal aggregation can be achieved by hierarchical clustering and k-means approaches. However, while this strategy reduces computation time, it also introduces varying degrees of distortion, potentially underestimating or overestimating investment and system costs [104,105,106]. An alternative method for managing computational complexity within macro energy system models is spatial aggregation. This involves consolidating neighboring regions sharing similar attributes into larger and more homogeneous clusters [107,108,109]. Yet, such integration can also negatively impact the precision of the model outcomes [110]. Currently, advanced schemes for temporal and spatial aggregation in energy system optimization models are still under active investigation, aiming to strike a balance between computational efficiency and result accuracy.

5.3 Research opportunities

Based on our review, we have discovered some possible avenues for future research. These are outlined below.

5.3.1 Adapting geographical focus to recent geopolitical development

The results in Sect. 4.1 show that the North Sea region is by far the most frequently studied area within the domain of European grid expansion. However, exploring the Central and Eastern European region as a future focal point for grid expansion study will hold significant interest. The conflict between Russia and Ukraine in 2022 has led to countries that were previously dependent on oil and gas supplies from Russia, such as Hungary, Slovakia, and the Czech Republic, experiencing energy and power shortages now. Therefore, for countries in this region, increasing the proportion of renewable energy in the energy system and expanding the cross-border grid could be an appropriate and urgent response. This imperative presents a compelling and immediate motivation for future researchers to study the topic of European grid expansion with Central and Eastern Europe as the main subject.

5.3.2 Imperfect competition

Existing models for grid-expanded energy system rely on the assumption of a perfect market. However, the reality is that numerous countries’ energy markets involve powerful producers. Research indicates that enlarging cross-border grids would not notably diminish the power of these predominant players [61]. Consequently, investigating grid expansion within imperfect markets featuring influential market participants presents another interesting avenue for research.

5.3.3 Merging the study of grid development with sector coupling

Common models to investigate grid expansion mainly focus on macro energy systems, many of which solely encompass the electricity sector. The limited models incorporating additional sectors, such as heat and transportation, primarily center on enhancing overall system flexibility through multi-sector considerations, while lacking the consideration of inter-sector interactions (i.e., sector coupling) [30]. However, sector coupling presents another important method for enhancing energy system stability, an aspect frequently explored by researchers as an alternative of grid expansion [21, 22]. Nevertheless, the literature usually treats grid expansion and sector coupling as two independent solutions of energy system stability for separate research. Consequently, merging these two aspects - exploring grid expansion within the context of sector-coupled energy systems - constitutes a more complicated yet invaluable research trajectory.

5.3.4 New technologies

In light of the growing popularity of hydrogen as novel nodes in grid expansion, the research related to European grid expansion only incorporates green hydrogen. However, hydrogen can be divided into green hydrogen and blue hydrogen according to the energy source of the electricity required for hydrogen’s production [111]. Green hydrogen denotes hydrogen generated using electricity derived from renewable energy sources, resulting in low carbon emissions throughout the entire process [111]. However, the production cost for this variant of hydrogen remains relatively high. Conversely, blue hydrogen derives from electricity sourced by blending fossil gas, resulting in a process that emits a notable amount of carbon dioxide. Nonetheless, the production of blue hydrogen is accompanied by carbon capture technology to curtail carbon emissions [112]. In addition, the main infrastructure of blue hydrogen can later be used for the green hydrogen [7]. Hence, while blue hydrogen might not attain the same environmental friendliness as green hydrogen today, it remains a viable option from a developing perspective, due to its economic advantage stemming from lower production costs [7]. Consequently, contemplating both green and blue hydrogen as new node options presents a further avenue for reducing system costs of grid expansion - a prospect worthy of deeper exploration in the future.

Existing energy system planning models, which study grid expansion, generally incorporate nuclear energy. However, in addition to large traditional nuclear power plants, another technology known as Small Modular Nuclear Reactors (SMRs), has gained popularity in recent years within the field of energy transition and can also be regarded as a potential candidate for inclusion in these models. Compared to traditional nuclear power plants, SMRs offer several advantages including smaller capacity, lower initial investment cost, higher safety, flexible location requirements, and shorter construction periods [113]. Consequently, many researchers believe that SMRs could serve as a stable backup energy choice in future energy systems with a large proportion of renewable energy [114]. From this perspective, SMRs have the potential to compete with energy storage nodes such as hydrogen energy. However, it’s important to note that SMR technology is still in its infancy worldwide, leading to that there is significant uncertainty surrounding the actual construction costs and operating costs [115]. Despite this, the consideration of incorporating SMRs into the generation mix of the energy system remains a topic worthy of study.

5.3.5 Scalability

In Sect. 5.2 , it was noted that the optimization models for power grid expansion commonly encounter challenges related to computational complexity. Some existing solutions, in turn, lead to varying degrees of result distortion. Consequently, a continuing subject of interest pertains to minimizing the computational complexity of the model while upholding result precision. This also can stand as a prospective avenue for future researchers to explore.

5.3.6 Beneficiaries and financiers among grid expansion connectors

It is a universally recognized conclusion that grid expansion can effectively help reduce the total cost of the energy system [13, 14, 44]. However, in the context of transnational grid expansion, the challenge lies in ensuring that the benefits can be equitably distributed among various countries while maximizing the overall revenue, to ensure the sustainability of the cooperation [6, 63, 66]. Currently, literature that primarily studies a single country’s cross-border power grid connection with neighboring countries has proposed expansion suggestions that can maximize the interests of that particular country [20, 54, 59]. However, it is evident that the plans for maximizing returns in various countries are not always in agreement with each other. In addition, studies that focus on the entire EU region confirm the the asymmetric economic impact of grid expansion on the internal countries [43, 45, 53, 55, 65]. However, potential solutions are not provided yet. Thus, this could also be an interesting direction for future researchers.

5.3.7 Social impact of grid expansion

The social impact of grid expansion, along with its subsequent influence on public acceptance, are agreed by researchers to be challenges that cannot be ignored, as whether grid expansion can proceed without delays is consistently believed can affect implementation effectiveness [5, 46, 64]. The literature concurs that submarine cables are a more socially acceptable alternative compared to onshore overhead transmission lines [9, 27]. Additionally, while grid expansion has been demonstrated to significantly aid the energy system in reducing carbon emissions, the construction of transmission lines and the establishment of more nodes have also been proven to negatively impact the local environment [116]. However, even though researchers agree that the positive environmental impact from decarbonizing the energy sector following successful grid expansion implementation outweighs the negative environmental impact during the expansion process [117, 118], the extent is still uncertain and waiting for further research.

6 Summary

This paper examines 59 references relevant to the the European grid expansion based on studies concerning energy system stability under the energy mix with increased renewable generation share spanning from 2013 to 2023. Throughout this period, owing to advancements in associated energy storage technologies like hydrogen, the endorsement of the EU cooperation agreement on offshore wind energy, and the growing urgency to address the issue of unstable renewable energy supply under the energy transition, an increasing amount of attention and research effort has been directed towards this area. As a result, the research content within the literature regarding European grid expansion has undergone significant updates during the recent decade, thus warranting the necessity of categorization and synthesis of the evolving trends and the dissection of the underlying rationales. This paper principally conducts a comprehensive and detailed analysis of the referenced literature across four dimensions: the geographical scope of the research subject, the principal strategies concerning power grid expansion, the focal points of the investigations, and the applied research methodologies. The aspiration is for this paper to facilitate emerging researchers entering the realm of grid expansion in swiftly assimilating the essential contextual information, keeping up-to-date with recent advancements in the field, and identifying potential trajectories of future development.

This paper reveals that the primary focus of research regarding European grid expansion revolves around multi-national collaborative areas. Among these, the “Europe” category, encompassing all European nations, emerges as the most common research subject, with particular emphasis on countries bordering the North Sea and the Baltic Sea. In instances where individual countries serve as the focal point, Germany, the United Kingdom, France, and the Nordic countries exhibit the highest frequency of occurrence.

We categorize grid expansion strategies into three principal types: the Interlinking strategy, which pertains to enhancing inter-connectivity between existing nodes; the Node Creation strategy, entailing the establishment of new nodes; and the Zone Extension strategy, which involves enlarging the grid’s coverage area. Notably, the research articles that focus on power grid expansion within a single country predominantly explore the Interlinking strategy. In contrast, references encompassing multi-national research subjects frequently incorporate a combination of two or more of the aforementioned strategies. Additionally, we observe a significant transformation in the literature’s Node Creation strategy from primarily establishing additional renewable nodes to a greater concentration on creating hydrogen storage nodes. Similarly, the main focus of the Zone Extension strategy evolves from cross-border connections between onshore power grid systems in different nations to interconnections among countries surrounding offshore wind power grids.

The paper also identifies a clear trend in the methodology employed within articles addressing European grid expansion, transitioning from statistical models to optimization models. This shift is primarily driven by the evolving focus of research literature. In the initial phase of this paper’s research time-frame, offshore grid expansion and hydrogen energy storage nodes emerged as novel considerations in grid expansion. During this period, research mainly utilized statistical models such as regression, cost-benefit analysis, and game theory to explore how to integrate these hot aspects into the energy system. Subsequently, as the foundational “how” challenges of the early stage were essentially resolved, researchers proceeded to delve deeper into the pursuit of better results. Consequently, the prevalent methodology adopted by researchers in the later stages transitioned to optimization models, aligning with the altered research emphasis centered on devising optimal grid expansion pathways. Furthermore, we undertake an in-depth analysis of the distinctive attributes and applicable scenarios associated with nine common optimization models (comprising three stochastic and six deterministic models) regarding European grid expansion research. The analysis uncovers a significant similarity between EMPIRE and TIMES within stochastic models which consider the renewable generation flexibility and the energy demand uncertainty. Additionally, it is found that ELMOD and REMix as the most frequently employed deterministic models. Notably, AnyMOD and REMix exhibit enhanced suitability for examining large-scale power grid expansion, whereas LIMES proves more apt for policy-focused research inquiries. Considering four metrics - the model’s consideration of uncertainty, the granularity of its time resolutions, the type of optimal power flow it uses, and its appropriate application range - it appears that ELMOD, EMPIRE, TIMES, and FlexPlan produce relatively more accurate outputs in terms of energy system costs and optimal generation mix, while the reliability of the transmission part of the results from FlexPlan, PyPSA, and REMix is comparatively higher. Nevertheless, these models still grapple with unresolved challenges concerning computational complexity and lengthy execution time.

We finally point out some potential research opportunities for the future researchers. Studying grid expansion in sector-coupled macro energy systems, examining cross-border power transmission in imperfect energy markets with powerful players, and exploring multi-country node connections in the context of increasing renewable generation within Central and Eastern European countries facing emergency energy and power shortages due to the Ukraine war, are all interesting future research directions. Additionally, including more technologies such as hydrogen as energy storage facilities and small modular nuclear as backup energy resource in the model, discussing the asymmetric economical impact of grid expansion among connectors, and investigating the social influence of grid expansion on public acceptance, would also be worthy of further study.

7 Declaration of Generative AI and AI-assisted technologies in the writing process

During the final preparations of this article the authors used Grammarly (https://www.grammarly.com/) and ChatGPT 3.5 (https://chat.openai.com/) in order to improve sentence structure, language, and grammar. The authors want to assure readers that these tools have been exclusively used for the specific purposes mentioned and no others. After using these tools, the authors carefully reviewed the AI-suggested improvements and made desirable adjustments before implementation. The authors take full responsibility for the content of the publication.