Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
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Biomedical Science and Engineering

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Label_Title

Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

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Label_Title

Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

Please submit your manuscript via our online submission system:
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Label_Title

Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

Please submit your manuscript via our online submission system:
http://www.sciepub.com/author/signin

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I am looking forward to hearing from you.

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David Rain
Email:join@sciepub.com
Science and Education Publishing (http://www.sciepub.com)

Label_Title

Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

Please submit your manuscript via our online submission system:
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Spatiotemporal Distribution and Efficiency Measurement of Major Global Electricity Export Countries

Mengyao Zhang

School of Economics and Management, Tiangong University, Tianjin, China

Abstract: With the continuous growth of global energy demand and increasing environmental concerns, electricity, as a critical energy carrier, has become increasingly vital in global economic and social development. This study systematically analyzed the spatiotemporal distribution characteristics and efficiency evolution of the top 50 global electricity-exporting countries from 2014 to 2023 using the DEA-BCC model and Malmquist index method. Key findings include: (1) Electricity exports exhibited significant regional agglomeration, with Europe maintaining dominance through its mature transnational grid systems, while China emerged as Asia’s core driver, boosting regional export volumes. (2) Efficiency measurements revealed a decline in the number of DEA-strongly efficient countries (from 4 to 3) and an increase in weakly efficient countries (to 6), primarily due to insufficient scale efficiency. Major exporters such as the U.S. and Italy remained inefficient owing to suboptimal resource allocation. (3) Total factor productivity (TFP) showed an average annual growth of 7.7%, driven by technological progress, but scale efficiency stagnated (index: 0.899), indicating room for scaling optimization.

Keywords: Electricity, Spatiotemporal distribution, Efficiency, DEA-BCC, Malmquist index

Received March 25, 2025; Revised April 28, 2025; Accepted May 05, 2025

Citation: Mengyao Zhang, Spatiotemporal Distribution and Efficiency Measurement of Major Global Electricity Export Countries. Applied Ecology and Environmental Sciences, 13 (1). 27-33. January 2025. doi:10.12691/aees-13-1-4

1. Introduction

With the continuous growth of global energy demand and the continuous transformation of energy structure, electricity, as a clean and efficient form of energy, is becoming increasingly important in international trade. According to data from the International Energy Agency, electricity production accounts for about 40% of the total global energy-related carbon dioxide emissions, a proportion that tops the list of all industries. The export trade in electricity not only reflects the differences in energy resource endowment and energy industry development among countries, but also, to a certain extent, influences the supply and demand balance and price fluctuations in the global energy market.

Current global electricity markets exhibit distinct regional characteristics, with production and exports increasingly concentrated. For instance, Germany, Norway, and China dominate exports due to abundant hydropower, thermal, and nuclear resources [1]. In recent years, research on global energy trade has gradually increased [2], but it mainly focuses on the traditional fossil energy sector, and there are relatively few studies on the export trade of electric power.For example, Ze He et al. [3] explored in detail the evolution characteristics of the global energy trade network and the competitiveness of the international trade from the perspective of complex network, and pointed out that the world energy trade network has the characteristics of "small world" It is pointed out that the world energy trade network has the characteristics of "small world" and scale-free, and that the center of gravity of energy export has gradually shifted from East Asia, the Middle East, Australia and Europe to regions such as Eastern Europe, the Middle East, North America, Australia and West Africa. In addition, based on the fossil energy trade data of the countries along the route from 2000 to 2018, Xia and Du [4] studied the structure of the energy trade of the 21st Century Maritime Silk Road and the evolution of the trade relationship with China, and found that the scale of the trade along the route has been expanded in recent years, but the proportion of the export has declined as a whole. In terms of power trade efficiency measurement, relevant research mainly focuses on the field of renewable energy. Chong Zhaohui et al. [5] explained the trade situation of fossil energy and renewable energy through social network analysis, and found that the renewable energy trade dependence network showed a higher degree of overall dependence, and its dependence on fossil energy trade has a substitution effect. Wang Li et al. [6] studied the geo-factor-driven mechanism of Arctic energy development, pointing out that Arctic countries are mostly energy exporters, while Arctic observer countries are mostly energy importers, and that China's energy imports from Arctic countries are relatively small, but with greater potential.

Although existing studies have provided important perspectives for understanding the global energy trade pattern, systematic studies on the spatial and temporal distribution and efficiency measurement of the world's major power export trade are still insufficient, and the relevant studies have focused on the hierarchical and spatial spheres of power linkages between China and other countries [7], along the "One Belt, One Road" route [8] and the European region [9]. and spatial domains. As a special energy product, the trade of electric power is affected by various factors such as technology, policy and geography, which requires further in-depth exploration of its distribution characteristics and efficiency performance on a global scale. Understanding the spatial and temporal distribution characteristics of foreign power import and export trade can find the center of gravity of international power trade, so that we can better optimize the allocation of power resources, improve the efficiency of energy use and promote the sustainable development of the economy.

2. Research Methods

2.1. DEA-BCC Model

Data Envelopment Analysis (DEA), proposed by Charnes et al. [10] in 1978, evaluates efficiency under variable returns to scale (BCC model). The BCC model decomposes comprehensive efficiency into pure technical efficiency (PTE) and scale efficiency (SE), enabling precise identification of inefficiency sources. Given the diversified and scaling nature of renewable energy development, the BCC model was selected for this study.

The BCC model assumes n decision-making units (DMUs) with m inputs and s outputs. For DMUj, inputs and outputs are denoted as xij and yrj , respectively. The model is formulated as (1):

[picture] | (1)

In the formula, and are relaxation variables, is then the weight of each DMU indicator， represents pure technical efficiency, if , this decision unit is a valid DEA;if but one of the slack variables is not zero, or , SE=1, this decision unit DEA is weakly valid; otherwise it is DEA invalid.

2.2. Malmquist Index

The Malmquist index can be used to describe the change of total factor productivity of decision-making unit in the period before and after, and the reasons leading to this trend of change. When the data to be evaluated DMU is panel data containing observations at multiple time points, the Malmquist Total Factor Productivity Index can analyze the changes in the technical efficiency of decision-making units and the changes in production technology, so it can be used to vertically compare the efficiency values of different time periods from a dynamic point of view. Total factor productivity less than 1 indicates that total factor productivity declined compared with the previous year; total factor productivity greater than 1 indicates that total factor productivity increased compared with the previous year; total factor productivity equal to 1 indicates that there is no change in total factor productivity compared with the previous year. Total factor production index can be further decomposed into technical efficiency index and technical progress index, in which the technical efficiency index reflects the organizational management level of decision-making units, and the technical progress index reflects the level of technological innovation of decision-making units. The details are as in formula (2).

[picture] | (2)

In the formula, MPI is Malmquist Index, Dt and Dt+1 denote the distance function for periods t and t+1, respectively.

3. Empirical Research

3.1. Data Sources

Panel data for the top 50 electricity-exporting countries (2014–2023) were sourced from the World Bank and processed using Excel and DEAP 2.1.

3.2. Spatiotemporal Distribution

In order to have a clearer picture of the spatial and temporal changes in electricity export trade, so with the help of Adobe Illustrator 2021 software, the electricity trade volume of each country in 2014 and 2023 is divided into four echelons from deep to shallow, and plotted as a Lisa diagram, as shown in Figure 1.

Figure 1. Spatial distribution of trade volume of the world's top 50 electricity exporters in 2014 and 2023

As can be seen from Figure 1, the global major electricity export trade in 2014 showed a significant concentration trend, mainly concentrated in Europe, North America and Asia.

In 2014, there were 27 countries in Europe among the top 50 countries in the electricity export trade, and there were even 6 countries in Europe ranked in the top 10, which were Germany, Italy, France, Austria, the Czech Republic and Spain. Specifically, the power exports of European countries not only the number of dominant, and these countries have a certain representative of the power export trade model and development level. This stems from the relatively mature power market reforms in Europe, where cross-border power exchanges and grid interconnections have made intra-regional power supply more stable and efficient. Countries such as Germany, France, and Italy, represented by their strong power production capacity, advanced technological facilities, and well-established power networks, have driven the growth of their power exports.2023 Europe still occupies a dominant position in the global power export market and its power export capacity continues to grow. Although the top 10 countries have changed from 6 in 2014 to 5, the number of top 50 European countries has increased from 27 in 2014 to 30 in 2023, which also indicates a further improvement in Europe's electricity production and export capacity.

In 2014, there were 15 Asian countries in the top 50 and two Asian countries in the top 10, namely China and Japan. Although the number of Asian countries is relatively inferior to that of Europe, China, as the world's top electricity exporter, exports almost as much as the entire European countries' exports combined, which gives Asia a significant advantage in the total electricity export trade.2023 Although the number of Asian countries ranked in the top 50 declines by only one, the number of countries in the top 10 changes from two to three, suggesting that, despite the global electricity market pattern in the changes, Asian countries still maintain a relatively stable position in electricity exports. In particular, China, as the world's largest exporter of electricity, continues to play an important role in promoting electricity exports in Asia. Despite the dominance of European countries in power exports, the Asian region's power export capacity remains highly competitive and has the potential for continued growth. Only a few countries have experienced a decline in power export capacity, while the performance of other countries has been relatively flat, demonstrating the stability and continuity of the Asian region's power exports.

Located in North America, the United States, Mexico and Canada are in the top 50, the first two are in the top 10, which shows that North America also occupies a certain position in the global electricity export market, but compared to Europe and Asia, its electricity export scale and market share is still relatively small, and there is still a lot of room for competitiveness to improve. The remaining continents account for a relatively small number of power exporters and trade volume, in the fourth echelon, indicating that these regions play a relatively weak role in the global power export trade, the market share of power exports is relatively low, and has not yet formed a strong competitiveness. 2023, the power exports of the other continents basically remained unchanged, with a relatively small volume of exports, indicating that these regions are still limited in the capacity of the power exports, and failed to form a strong competitive advantage in global electricity trade.

In summary, from 2014 to 2023, the center of gravity of electricity exports is in Europe, Asia and North America, with the dominant position of Europe further strengthened, while Asian electricity exports also perform more prominently, led by China, especially as its share in total global electricity exports continues to rise. Power exporting countries in other continents have not changed significantly, but are still in a marginal position in global power exports, failing to realize an effective breakthrough.

3.3. Efficiency Evaluation

3.3.1. Data collection and Selection of Indicators

The electricity industry data used in this paper comes from the electricity trade data provided by the World Bank for all countries in the world, and the collected indicator data are organized through EXCEL tables. The decision unit of this paper is the world's top 50 electricity trade exporting countries, and the number of population, land area and GDP of each country's country are selected as input indicators, and the amount of electricity export trade of each country is an output indicator.

3.3.2. Evaluation Results

Using DEAP 2.1 software, this paper evaluated the total factor productivity of electricity exports of the top 50 countries in the world for the period 2014-2023 using equation (1), as shown in Table 1.

Table 1. Evaluation of Total Factor Efficiency in Electricity Export Trade in 2014 and 2023

Figure 2. Electricity export efficiency of the world's major electricity exporting countries in 2014 and 2023

3.3.3. Analysis of Evaluation Results

①Cross-sectional data analysis

In order to make the display of evaluation results more intuitive, so the results will be drawn pyramid diagram, in which the gradient division by efficiency evaluation results, divided into strong effective, weakly effective, ineffective (ineffective but comprehensive efficiency ≥ 0.4) ineffective (ineffective but the comprehensive efficiency in the range of 0.2 to 0.4) very ineffective (ineffective and the comprehensive efficiency < 0.2) five gradients, as shown in Figure 2.

As can be seen from Figure 2, the DEA strongly effective countries change from four in 2014 to three in 2023, of which Singapore and the Czech Republic's electricity export efficiency are both in the strong effective, indicating that they have a greater advantage in the utilization of resources and technical efficiency; Estonia and Austria change from strongly effective to weakly effective and ineffective, respectively, mainly by the impact of the purely technical efficiency, indicating that the ratio of its input factors has become irrational Bulgaria has changed from ineffective to strong effective, and the efficiency of electricity export has improved significantly, indicating that its resource factor ratio and management level have reached a high level, which can provide a reference for other ineffective countries.

Weakly effective countries have changed from 5 to 6, and the reason why these countries are in weakly effective is affected by scale efficiency. Among them, the world's top 2 electricity exports of China and Germany are in the stage of diminishing returns to scale, the comprehensive efficiency in 2023 have declined, are caused by scale efficiency reduction, the reason may be that the scale of electricity exports increased, in the management of negligence, resulting in scale efficiency is low; the rest of the countries are in the stage of diminishing returns to scale, these countries if the increase in the scale of the inputs can increase the total factor productivity of their electricity exports. The number of ineffective countries is 41 in both 2014 and 2023, with the vast majority of ineffective countries in the increasing returns to scale stage.

The top 10 electricity exporting countries, including the United States, Italy, Japan, Spain, Mexico and France, are all ineffective and in the stage of diminishing returns to scale, and the reason for their ineffectiveness is that they are affected by purely technical efficiency, which indicates that the input factor ratios of these countries are irrational and that there is redundancy of input factors. Among the bottom 10 countries, Slovenia, Kyrgyzstan, Ireland and other countries have been in a weakly efficient state, resulting in their failure to achieve strong efficiency due to the influence of scale efficiency; Tunisia, Brazil, Portugal and other countries have been in an ineffective state, which is mainly due to the influence of pure technical efficiency.

②Analysis of changes in time dynamics

Among all the research subjects, 41 countries have been ranked in the top 50 in the world, in order to further understand the sources that affect the changes in the efficiency of each country, so this paper is analyzed with the help of the Malmquist index, and the results of the index for 41 countries, as shown in Table 2.

As can be seen in Table 1, the overall total factor productivity of the world's major electricity exporters grows by about 7.7% between 2014 and 2023, thanks to slight technological advances and improvements in technical efficiency. In particular, the average pure technical efficiency change index reaches 1.146. However, it is worth noting that the change in scale efficiency is not satisfactory, with an average sech of only 0.899, suggesting that most countries have failed to effectively improve their efficiency when expanding their scales, which suggests that more attention should be paid to the rationality of resource allocation and management efficiency.

Table 2. Malmquist Index

Many countries have realized significant improvements in pure technical efficiency by improving internal management and operational processes. For example, the change indices of pure technical efficiency of Bulgaria and Belgium are 3.113 and 1.385 respectively, which are much higher than the average level, showing the great progress in the level of organizational management in these countries. On the contrary, some countries such as Austria and Ukraine are facing the problem of declining pure technical efficiency, which indicates their shortcomings in resource utilization and technology application.

Changes in scale efficiency reveal differences in the effectiveness of scale expansion strategies in different countries. Bulgaria and Belgium not only excel in technical efficiency, but also make significant breakthroughs in scale efficiency, reaching 1.473 and 1.764, respectively.This shows that they successfully combine scale expansion with efficiency improvement. In contrast, large electricity exporters such as China and Germany, despite having large volumes of electricity exports, have experienced challenges in managing scale growth, resulting in lower scale efficiencies. In addition, countries such as Slovakia and Portugal have experienced a marked decline in scale efficiency, reflecting the fact that these countries may have neglected to make the appropriate managerial adjustments and technical support when scaling up.

4. Conclusions

(1) The trend of regional concentration has increased significantly. Global electricity exports show a significant trend of regional concentration. European countries continue to dominate the global power market, thanks to their highly efficient power systems and cross-border grid interconnections, which have boosted the growth of their power exports. Asia has realized a significant increase in total electricity exports, led by China, which plays an important role in the region as the world's largest electricity exporter. In contrast, power exports from North America and other regions, while also in a position to do so, have a small market share and need to improve their competitiveness. Other regions still have limited power export capacity and have failed to develop strong competitiveness in the global market.

(2) In terms of electricity export efficiency, the DEA strongly effective countries change from four in 2014 to three in 2023, and weakly effective countries change from five to six, and these countries are in weakly effective because they are all affected by scale efficiency.There are 41 ineffective countries in both 2014 and 2023, and the vast majority of the ineffective countries are in the stage of incremental scale compensation. The top 10 electricity-exporting countries, including the United States, Italy, Japan, Spain, Mexico and France, are all ineffective and in the stage of diminishing returns to scale, and the reasons for their ineffectiveness are all affected by purely technical efficiency, which suggests that the input factor ratios of these countries are irrational and that there is redundancy of input factors. Ranked in the bottom 10 countries, Slovenia, Kyrgyzstan, Ireland and other countries have been in a weakly effective state, resulting in its failure to reach a strong effective because of the impact of scale efficiency; Tunisia, Brazil, Portugal and other countries have been in an ineffective state, mainly by the impact of pure technical efficiency.

(3) The world's major electricity exporters as a whole have achieved total factor productivity growth, which is largely attributable to technological advances and internal management optimization. However, scale efficiency gains have not kept pace, which is a pressing issue especially for those countries that are trying to increase their electricity exports by scaling up. In order to remain competitive in the global electricity market, countries should focus on the rationalization of resource allocation and the simultaneous improvement of management efficiency, while continuing to promote technological innovation to ensure the sustainable development of electricity exports.

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