Research on Risk Evaluation of Transnational Power Networking Projects Based on the Matter-Element Extension Theory and Granular Computing

Abstract

In project management, risk assessment is crucial for stakeholders to identify the risk factors during the whole life cycle of the project. A risk evaluation index system of a transnational networking project, which provides an effective way for the grid integration of clean electricity and the sustainable development of the power industry, is constructed in this paper. Meanwhile, a combination of granular computing and order relation analysis (G1 method) is applied to determine the weight of each indicator and the matter-element extension evaluation model is also employed to seek the global optimal decision during the risk assessment. Finally, a case study is given to validate the index system and evaluation model established in this paper by assessing two different investment schemes of a transnational high voltage direct current (HVDC) transmission project. The result shows that the comprehensive risk level of Scheme 1 is “Low” and the level of Scheme 2 is “General”, which means Scheme 1 is better for the stakeholders from the angle of risk control. The main practical significance of this paper lies in that it can provide a reference and decision support for the government’s power sectors, investment companies and other stakeholders when carrying out related activities.

1. Introduction

As the source of country’s development, the power industry plays a vital role in the economic development of society and it is a basic industry for the promotion of people’s standard of living. In China, electrical energy’s share of the total energy consumption was 25.8% in 2015 and it is expected to reach 27% in 2020, which should help reduce the carbon emissions effectively [1,2,3]. Under the support of China’s Belt and Road Initiative and the strategy of Building the Global Energy Network, transnational networking projects also contributes to the balance of different countries’ power industry development and the decrease of the population without electricity. Meanwhile, it also provides an effective way to promote the integration of clean electricity sources, such as wind power, solar power, hydropower and so on, which significantly promotes the clean energy efficiency and the sustainable development of the power industry. Now the construction of transnational networking projects in China is still at its preliminary stage, but it is growing rapidly. On the basis of the original projects, a series of transnational networking projects have already been proposed since the promulgation of the Belt and Road Initiative, aiming at exploring the potential international power industry market and achieving the common development of regional economies along the line.

Table 1. Transnational networking projects in recent years.

Year	Project	Status
2015	The 500 kV HVDC project between Thailand and China	In Planning
2015	The 500 kV HVDC project between Vietnam and China	In Planning
2015	China State Grid’s Extra High Voltage (EHV) projects plan based on the Belt and Road Initiative (Transmission corridor along the Silk Road economic belt)	In Planning
2016	The 500 kV Direct Current (DC) networking project between Ethiopia and Kenya	Under Construction
2016	The ±250 kV DC networking project between Malaysia and Indonesia	Under Construction
2016	The 400 kV Alternating Current (AC) networking project between Nepal and India	Under Construction
2016	Northeast Asia power interconnection project	Under Preparation

enumerates a series of transnational networking projects proposed in recent years [4,5].

Considering the development trends of the power industry, it is necessary to construct a scientific risk assessment index system and a practical evaluation model for transnational networking projects, which contributes to identifying the risk factors faced by the project and providing decision support for the stakeholders [6]. As a new research subject, studies about risk evaluation of transnational networking project are still insufficient, but researches concentrated on risk assessment of domestic ordinary projects are relative mature at present. Based on the concept of Work Progress Status (WPS) and Weighted Sum Method, Muriana and Vizzini [7] proposed a new technique for risk management of each WPS of the project rather than the evaluation of entire project, which was devoted to updating the risk degree of the project continually and providing managers preventive and corrective actions in project management. Zhao and Guo [8] used the Analytic Hierarchy Process (AHP) and the fuzzy synthetic evaluation method to carry out the risk assessment of the Zhejiang-Fuzhou EHV distribution networking project. In Kang’s research [9], the fuzzy multiple objective linear programming (FMOLP) model was constructed to provide references for the management of project and then, a wind turbine construction project in Taiwan was employed for empirical analysis to validate the model established in this paper. Fu [10] applied the expert scoring method to identify the risk factors in the construction process of power grid projects on the basis of life cycle theory. The risk factors of power grid projects under the Engineering Procurement Construction (EPC) mode were divided into six categories in Wang’s paper [11], and the Analytic Network Process (ANP) and Interpretative Structural Modeling Method (ISM) were employed to determine the risk level of the whole power grid project. Based on Monte Carlo method, Long [12] carried out the risk assessment of an UHV power system and a comprehensive index system was constructed to evaluate the risk level of a regional power system. Meanwhile, researches on risk evaluation of transnational projects mainly focus on the area of international investment and oil projects. Yang [13] analyzed the influence of political risks in transnational investment and the “political index” was employed to measure the political risks faced by the project. Wang [14] constructed a risk framework for transnational oil and gas investment projects by using the scenario planning method. The Value at Risk (VaR) method was utilized in Zhang’s paper [15] to identify the risk factors that Chinese oil companies may face in overseas mergers and acquisitions. In Jin’s research [16], five risk features of Peer-Peer Protocol (PPP) project were analyzed and then, the multiple linear regression technique was applied to deal with the original data. The fuzzy AHP-Based risk assessment methodology was also employed to carry out the risk evaluation of PPP projects in Li’s [17] research. Through the analysis of the relevant literature, a brief comparison of different risk evaluation methods is listed in

Table 2. The comparison of different risk evaluation methods.

Method	Advantages	Disadvantages
Expert evaluation method	A simple subjective method. Make full use of experts’ experience and knowledge.	Lack objectivity. Result is greatly influenced by the experts’ attitude.
AHP	A systematic analytic technique. Make a combination of qualitativeanalysis and quantitative analysis.	Qualitative analysis plays a key role in weight determination. Too many indicators make it difficult to obtain the exact eigenvalues and eigenvectors.
Fuzzy synthetic evaluation method	Fuzzy problems or objects can be effectively analyzed. The result contains plenty of information.	Qualitative analysis plays a key role in weight determination. Too many indicators make it hard to determine the Membership.
ANP	Take the interactions between various factors or adjacent levels into consideration.	Inconsistency may exist in determining the relative importance of each factor.
The Monte Carlo method	Strong adaptability in dealing with complex problems or systems.	A large amount of quantitative data is needed. A certain degree of randomness.

.

As an application of the extension theory, the matter-element extension evaluation model is been widely used in scientific research in recent years. Compared with other methods, the matter-element extension evaluation model can effectively seek the global optimal decision when dealing with complex systems based on the comparison of a variety of known decisions. The concept of interval number is introduced in the extension model in the process of determining the classical domain and joint domain of the object to be evaluated, which provides an effective way for handling uncertain problems. He [18] used the matter-element extension model to evaluate the risk level of urban power networking planning. Wu and Peng [19] employed the multi-level extension assessment method to carry out a comprehensive benefit evaluation of a power distribution network project. The matter-element extension evaluation model was also used to evaluate the quality of water in Sun’s research [20], and the normalization of the classical domain was introduced to avoid the phenomenon that the value of the indicator exceeds the range of the joint domain. Xu and Niu [21] carried out a comprehensive evaluation of renewable energy generation grid-connecting systems, where the matter-element extension model was applied in the empirical analysis.

As mentioned above, researches on risk evaluation of networking project are mainly concentrated on domestic projects, in other words, studies on risk evaluation of transnational networking projects are relatively uncommon at present. Compared with domestic projects, one of the main characteristics of transnational networking projects is that the networking project is carried out in different countries, which means there are more risk factors to be identified during the implementation of the project, such as the geopolitics, cultural differences, state relations, etc. Based on the facts above, a comprehensive risk evaluation index system and the corresponding judging criteria of transnational power networking project are constructed in this research, which can provide a certain reference and decision support for the government’s power sectors, construction units, investment companies and other stakeholders. The main contributions of this paper are as follows:

• A risk evaluation index system and the corresponding judging criteria of transnational networking projects are established in this paper. Based on the characteristics of transnational networking projects, a comprehensive risk evaluation index system, including four first-level indicators and eleven secondary indicators, and the corresponding judging criteria are established.
• The Global Peace Index and the National Governance Index are employed during the quantization of the related qualitative indexes. The Global Peace Index and the National Governance Index are respectively introduced in this paper during the quantization of “War or terrorist attack” and “Change of government or statute”, which are two important qualitative indicators in the index system.
• A combination weighting method is proposed in the weight determination part. This paper employs a combination of granular computing and the order relation analysis method to determine the weight of each indicator, aiming at improving the reliability of the results, which can finally help to improve the rationality of the evaluation result.

The rest of this paper is structured as follows: Section 2 introduces the research procedure and the method employed in this paper; Section 3 describes the risk index system and the corresponding judging criteria of transnational networking project. A case analysis is proposed in Section 4 to validate the index system and the evaluation model established in this paper. The conclusions of this research are drawn in Section 5.

2. Method

2.1. Research Procedure

As a systematic project, a transnational networking projects is a kind of infrastructure project with advanced technology and substantial investment, which involves a series of risk factors during the whole life cycle of the project, including political, social, natural, economic and technical risks, so it is necessary to carry out a comprehensive risk evaluation of the investment scheme before the implementation of the project, which can partly reduce the waste of social resources and help stakeholders identify the internal and external risk factors faced by the project. The research procedure of this paper is shown in Figure 1.

2.2. Weight Determination

The indicator weight reflects the importance of the index to the object to be evaluated. As a key link during the risk evaluation process, the weight of each indicator has a massive impact on the assessment results. The method used to determine the weight can be roughly divided into three categories: subjective, objective and the combination weighting methods [22]. The granular computing and the G1 Method are combined to determine the weight of each indicator in this research, which can effectively improve the rationality of the result.

(1) Granular Computing

The concept of information granules, which is the basic theory of granular computing, was firstly proposed by Zadeh [23] in 1979. It is usually used to handle problems with uncertainty by dividing a complex object into several parts, which can effectively reduce the problem complexity. As a new topic, the application of granular computing at the present stage mainly includes two aspects: dealing with uncertainty problems and multi-granular computing. In this paper, the main idea of granular computing is to reckon the importance of different indicators by calculating the quotient space with different granularity based on the rough set theory [24]. Compared with other weighting methods, granular computing can solve problems with incomplete and small samples, and on the basis of making full use of available information, it employs an objective method to process the original data. The steps of granular computing are as follows:

Step 1:

Providing the index system and the evaluation criteria for the experts. All members of the expert group will assign a mark to each index independently to indicate the importance of each indicator. Suppose there are “n” experts and “m” indicators, the original data “X” can be obtained, where X = {x₁, x₂, ..., x_n}, x_i = {y_i1, y_i2, ..., y_im}, i = 1, 2, ..., n.

Step 2:

Calculating the similarity relation between x_i and x_j, where i and j represent different experts. Then, as shown in Equation (1), the fuzzy similarity matrix of the samples can be obtained:

$$R={\left(r_{ij}\right)}_{n\times n}=\left[\begin{array}{ccc}1& & \\ ⋮& \ddots & \\ r_{n1}& \cdots & 1\end{array}\right]$$

(1)

Step 3:

The quotient space family with inclusion relation, $\left\{X\left(\phi \right)|0\le \phi \le 1\right\}$, can be calculated and different values of $\phi$ stand for different granular spaces.

Step 4:

Calculating the importance of each index in different granular spaces. The importance can be gained by:

$$\mathrm{sig}(a_k,C,D)=\gamma (C,D)-\gamma \left(C-\left\{a_k\right\},D\right)$$

(2)

where $a_k$ is the kth indicator; C is the condition attribute set; D is the decision attribution set; $\gamma \left(C-\left\{a_k\right\},D\right)$ stands for the condition attribute set’s dependence on decision index set when the $a_k$ is dropped from C.

Step 5:

The comprehensive importance can be calculated by Equation (3):

$$\mathrm{sig}(a_k,C,D)=\frac{1}{q}{\displaystyle \sum }_{p=1}^q{\mathrm{sig}}^{X\left({\phi }_p\right)}\left(a_k,C,D\right)$$

(3)

where q is the number of total quotient space families; ${\mathrm{sig}}^{X\left({\phi }_p\right)}\left(a_k,C,D\right)$ is the importance of $a_k$ in the quotient space family of X(${\phi }_p$).

(2) The G1 Method

As a subjective method, the G1 Method, which usually uses the scores provided by experts to determine the weight of indicators, is a visual and effective method in weight determination. During the process of this link, experts’ experience has been fully utilized, which can provide scientific guidance for practice. Based on the marks delivered by the expert group, the order of all indicators can be obtained to calculate the importance ratio of the adjacent index. The steps are as follows:

Step 1:

Obtaining the order relation. According to the available information, experts give marks to the indicators based on his own experience, the original order relation can be obtained as follows:

$$x_1<x_2<\cdots <x_m$$

(4)

where x represents different indicators; m is the number of the indicator.

Step 2:

Calculating the importance ratio. On basis of the order relation obtained in step 1, the importance ratio of two adjacent indicators can be calculated according to the original marks provided by the expert:

$$r_k=w_{k-1}/w_k (k=m, m-1, 2)$$

(5)

where $r_k$ refers to the kth importance ratio; w_k−1 is the score of the (k − 1)th indicator; w_k is the score of the kth indicator.

Step 3:

Determining the weight of each indicator:

$${\omega }_m={(1+{\displaystyle \sum }_{k=2}^m{\displaystyle \prod }_{i=k}^m{r}_i)}^{-1}$$

(6)

$${\omega }_k=r_i\times {\omega }_{k-1}$$

(7)

where ${\omega }_k$ is the weight of the kth indicator determined by the G1 method.

Step 4:

Results integration. Differences may exist between the weights determined by different experts and it is essential to make a comprehensive analysis of the results obtained from different experts. The final result of the weight can be calculated by:

$$W_K=\frac{1}{L}\left({\omega }_{1k}+{\omega }_{2k}+\cdots +{\omega }_{Lk}\right)$$

(8)

where L is the number of the expert; $W_K$ is the final weight of the kth indicator.

2.3. Matter-Element Extension Evaluation Model

Extension theory, which is the theoretical basis of the matter-element extension evaluation model, was firstly proposed in Cai’s research [25]. The main idea of the matter-element extension theory is that dividing the object to be evaluated into different grades, the conclusion will be obtained according to the correlation degrees between the object and different grades, and the implementation of matter-element extension evaluation model can effectively solve complex and fuzzy problems. With the development of the theory, some improvements have been proposed to avoid the defects existing in the original model. For example, the normalization of classical domain can effectively avoid the phenomenon that the value of indicator exceeds the range of the joint domain, which may make the correlation functions impossible to calculate. The processed model is described as the improved matter-element extension evaluation model [26,27]. Taking the characteristics of transnational networking projects into account, the matter-element extension evaluation model is employed to carry out the risk evaluation in this research. The steps in detail are as follows:

Step 1:

Determine the classical domain, joint domain and the object to be evaluated:

$$R_{\mathit{j}}=(N_j,C_i,V_{ji})=\left[\begin{array}{ccc}{N}_j& c_1& v_{j1}\\ & \cdots & \cdots \\ & c_n& v_{jn}\end{array}\right]=\left[\begin{array}{ccc}{N}_j& c_1& <a_{j1},b_{j1}>\\ & \cdots & \cdots \\ & c_n& <a_{jn},b_{jn}>\end{array}\right]$$

(9)

where ${\mathrm{R}}_j$ stands for the jth grade of the matter-element model; $N_j$ represents the jth grade of the object in classical domain; c₁, ..., c_n are the features of N_j; V_ji and $<a_{ji},b_{ji}>$ are the range of c_i under the jth grade, i = 1, 2, ..., n (Classical domain):

$$R_{\mathit{p}}=(p,C_i,V_{pi})=\left[\begin{array}{ccc}p& c_1& v_{p1}\\ & \cdots & \cdots \\ & c_n& v_{pn}\end{array}\right]=\left[\begin{array}{ccc}p& c_1& <a_{p1},b_{p1}>\\ & \cdots & \cdots \\ & c_n& <a_{pn},b_{pn}>\end{array}\right]$$

(10)

where p stands for the level of the object to be evaluated; v_pi and $<a_{pi},b_{pi}>$ are the range of c_i under all grades, i = 1, 2, ..., n (Joint domain):

$$R_{\mathbf{0}}=\left[\begin{array}{ccc}{p}_0& c_1& v_1\\ & \cdots & \cdots \\ & c_n& v_n\end{array}\right]$$

(11)

where p₀ is the object to be evaluated; v_i is the observed value of indicator c_i, i = 1, 2, ..., n.

Step 2:

Obtain the weight of indicator. This paper employs a combination of granular computing and G1 Method to determine the weight of each indicator.

Step 3:

Normalization. The way of normalization is shown in Equations (12) and (13):

$$R_{\mathit{j}}{}^{\prime }=(N_j,C_i,V_{ji}{}^{\prime })=\left[\begin{array}{ccc}{N}_j& c_1& <\frac{a_{j1}}{b_{p1}},\frac{b_{j1}}{b_{p1}}>\\ & \cdots & \cdots \\ & c_n& <\frac{a_{jn}}{b_{pn}},\frac{b_{jn}}{b_{pn}}>\end{array}\right]$$

(12)

$$R_{\mathbf{0}}{}^{\prime }=\left[\begin{array}{ccc}{p}_0& c_1& \frac{v_1}{b_{p1}}\\ & \cdots & \cdots \\ & c_n& \frac{v_n}{b_{pn}}\end{array}\right]$$

(13)

Step 4:

Calculate the correlation degree:

$$D(v,V_{ji}^{\prime })=\left|v_i-\frac{a_{ji}+b_{ji}}{2}\right|-\frac{b_{ji}-a_{ji}}{2}$$

(14)

$$K_{\mathit{j}}(p_0)=1-{\displaystyle \sum }_{i=1}^n{\omega }_i{D}_{ij}$$

(15)

where D is the distance from the object to the classical domain; K is the correlation degree, i = 1, 2, ..., n.

Step 5:

Draw the conclusions. According to the principle of maximum relevance, the level of the object to be evaluated can be determined based on the results obtained in Step 4.

3. Index System

Based on the characteristics of transnational networking projects, the internal and external risk factors faced by the project are systematically identified before the establishment of the index system. Through the comparison of different risk factors and the review of the expert group, a comprehensive risk evaluation index system, including four first-level indicators and eleven secondary indicators, is established to support the further risk evaluation. Meanwhile, the criteria for ranking the risks of each indicator is also constructed in this part, which is a core part of this research. The index system is shown in

Table 3. The risk evaluation index system of transnational networking projects.

First-Level Indicator	Secondary Indicator
Political Risk (A)	State relation (A1) War or terrorist attack (A2) Change of government or statute (A3)
Social and Natural Risk (B)	Public acceptance (B1) Extreme weather or natural disaster (B2)
Economic Risk (C)	Net present value rate (C1) Internal rate of return (C2) Exchange fluctuations (C3)
Technical Risk (D)	Parameters of power network (D1) Reliability of power supply (D2) Construction risk (D3)

and the corresponding judging criteria of different risk indicators are shown in

Table 4. Evaluation criteria of the political risk.

Index	Criteria and the Score
A1	Type Score	Union (0,2]	Strategic Partnership (2,4]	Partnership (4,6]	Friendship (6,8]	Diplomatic Relations (8,10]
	Rank	Extremely Low	Low	General	High	Extremely High
A2	Score	(0,2]	(2,4]	(4,6]	(6,8]	(8,10]
	Rank	Extremely Low	Low	General	High	Extremely High
A3	Score	(0,2]	(2,4]	(4,6]	(6,8]	(8,10]
	Rank	Extremely Low	Low	General	High	Extremely High

,

Table 5. Evaluation criteria of the social and natural risk.

Index	Criteria and the Score
B1	Acceptance	100% ≤ PA < 90%	90% ≤ PA < 80%	80% ≤ PA <6 0%	60% ≤ PA < 40%	40% ≤ PA ≤ 0%
	Score	(0,2]	(2,4]	(4,6]	(6,8]	(8,10]
B2	Rank	Extremely Low	Low	General	High	Extremely High
	Score	(0,2]	(2,4]	(4,6]	(6,8]	(8,10]
	Rank	Extremely Low	Low	General	High	Extremely High

,

Table 6. Evaluation criteria of the economic risk.

Index	Criteria and the Score
C1	NPVR	NPVR ≥ 0			NPVR < 0
	Score	(0,6]			(6,10]
	Rank	Acceptable			Unacceptable
C2	IRR	IRR ≥ 7%			IRR < 7%
	Score	(0,6]			(6,10]
	Rank	Acceptable			Unacceptable
C3	Range	0 ≤ F < 1%	1% ≤ F < 2%	2% ≤ F < 3%		3% ≤ F < 5%	5% ≤ F < 10%
	Score	(0,2]	(2,4]	(4,6]		(6,8]	(8,10]
	Rank	Extremely Low	Low	General		High	Extremely High

and

Table 7. Evaluation criteria of the technical risk.

Index	Criteria and the Score
D	Score	(0,2]	(2,4]	(4,6]	(6,8]	(8,10]
	Rank	Extremely Low	Low	General	High	Extremely High

.

3.1. Political Risk

(1) State relations

As a transnational networking project is carried out in two or more different countries at the same time, it means the relationship between the two countries involved in the project has a significant impact on the development of the project [28].

(2) War or terrorist attack

A peaceful and stable social environment is an important foundation for the smooth development of transnational projects, but a series of instabilities, such as wars or terrorist attacks will produce certain risks to the construction of the transnational networking project. Thus, this factor is involved in the risk index system and the quantization of this indicator is shown in Equation (16):

$$\mathrm{SI}=\left(\max \left\{r_a,r_b\right\}-1\right)/\left(n/10\right)$$

(16)

where SI stands for the Stable Index; r_a, r_b represent the ranking of the two countries in the Global Peace Index (GPI); n is the number of the countries listed in GPI; the range of SI is [0,10].

(3) Change of government or statute

As a skill-intensive and capital-intensive project, a transnational networking project usually has a longer construction period and larger quantities of work. Changes of government or statute may occur during the period of construction, which sometimes will lead to the situation that policies of different governments are discontinuous and this brings risks to the implementation of the project. The quantization of this indicator is shown in Equation (17):

$$\mathrm{PS}=\alpha \times \left(\max \left\{k_a,k_b\right\}-1\right)/\left(n/10\right)+\beta \times E^{\prime }$$

(17)

where PS represents the political stability; k_a, k_b are the ranking of the two countries in the National Governance Index (NGI); n is the total number of countries in NGI; $E^{\prime }$ stands for the mean value of experts’ scores; $\alpha$ = 0.5, $\beta$ = 0.5.

3.2. Social and Natural Risk

(1) Public acceptance

Land requisition for the substation and the transmission line corridor is an essential activity before the construction of a transnational networking project, which usually includes land acquisition, relocation, crop compensation, etc. There may be some conflicts during the implementation of this part. Meanwhile, during the construction period, the project will inevitably have some influences to the local environment along the line, such as noise, environmental pollution, electromagnetic radiation and so on, so the public acceptance, which can be obtained by the way of questionnaires, is proposed to measure the social risk faced by the project.

(2) Extreme weather or natural disaster

The long construction period and the project site sometimes will expose the networking project to extreme weather or natural disasters, which may cause economic losses and bring certain risks to the implementation of the project, so it is necessary to take the weather and natural factor of the areas within the scope of the project into account when carrying out the risk evaluation.

3.3. Economic Risk

(1) Net present value rate

The net present value rate of investment (NPVR) refers to the ratio of a cash flows’ present value to the investment’s present value, which is a dynamic index to measure the profitability of the project. A higher NPVR means better potential profitability, thus this factor is used to measure the economic risk in this paper and the calculation formula is shown in Equation (18):

$$\mathrm{NPVR}=\mathrm{NPV}/\mathrm{PVI}$$

(18)

where NPV is the net present value of the cash flow; PVI is the present value of the investment; NPVR is usually used for the comparison of different schemes.

(2) Internal rate of return

As an index for measuring the effect of investment, Internal Rate of Return (IRR) reflects the project’s ability to repay the initial investment [29]. In this paper, IRR is employed to measure the economic risk of the project, and it can also be used for the comparison of different schemes. As shown in Equation (19), the trial method can be used to calculate the value of IRR:

$$i^{\ast }={\mathrm{NPV}}_n(i_{n+1}-i_n)/{\mathrm{NPV}}_n+\left|{\mathrm{NPV}}_{n+1}\right|+i_n$$

(19)

where i* stands for IRR; i_n and i_n+1 are two trial discount rates; NPV_n is the net present value under the discount rate of i_n, NPV_n+1 is the net present value under the discount rate of i_n+1; constraint condition: i_n+1 − i_n ≤ 2%; the benchmark yield of power networking industry is 7% [30].

(3) Exchange fluctuations

For transnational projects, the fluctuation of exchange rates, influenced by the balance of payments and inflation, has a great impact on the cost of the project [31,32].Therefore, the exchange fluctuation is employed in this paper to measure the economic risk of transnational networking projects. Equation (20) shows the calculation of this indicator:

$$F=\left(\left|S^{\prime }-S\right|/S\right)\times 100\text{\%}$$

(20)

where F is the degree of exchange rate volatility; $S^{\prime }$ is the expected exchange rate between the countries involved in the project; S is the current exchange rate.

3.4. Technical Risk

(1) Parameters of power network

As a skill-intensive project, power networking projects often involve a series of advanced technologies and facilities, including intelligent transformers, intelligent sensors, relay-protection equipment and so on [33], so the technical parameters of the key technology and equipment involved in the project are essential to ensure the stable operation of the resulting power grid.

(2) Reliability of power supply

Unexpected situations, such as overloads and power outages, will have a great impact on the operation of the project. As a key indicator of power projects, the power supply reliability is an important indicator to measure the technical risk of a transnational networking project. The capacity-load ratio and the power supply ability are introduced in this paper to determine the value of this risk indicator:

$$R_s=T/P$$

(21)

$$RS=\left[1-n/N\right]\times 100\text{\%}$$

(22)

where R_s is the capacity-load ratio; RS stands for the power supply stability; T is the total capacity of substation equipments; P is the load of the network; N is the observation time; n is the average interruption time.

According to the result obtained above, the value of this risk indicator can be calculated by using the following formulas:

$$y_1=\{\begin{array}{c}1, 1.8\le R_s\le 2.2\\ 10, \mathrm{others} \end{array}$$

(23)

$$y_2=\{\begin{array}{c}1-\left(RS-a\right)/\left(1-a\right)\times 10 , a\le RS\le 100\\ 10, \mathrm{others} \end{array}$$

(24)

$$R=\alpha y_1+\beta y_2$$

(25)

where R is the final value of this indicator; y₁ is the score of “capacity-load ratio”; y₂ is the score of “power supply stability”; the value of “a” is determined by the voltage level [34]; $\alpha$ = 0.5, $\beta$ = 0.5.

(3) Construction risk

During the construction of transnational networking projects, a series of professional operations have certain risks for construction units, such as aloft work, live wire working and so on. Time delays are another kind of risk factors faced by the project, which mean the project cannot be delivered in time. Based on the facts above, the construction risk is employed to measure the technical risk of the project. The expert group or the independent evaluation agency can often be invited to carry out the evaluation of this indicator.

4. Case Study

Based on the works carried out in previous sections, this part provides a comprehensive risk evaluation of a transnational HVDC transmission project introduced in [35], and the evaluation model and risk index system established above are employed to carry out the empirical analysis. The comprehensive risk level of two different construction schemes can be respectively drawn based on the index system and evaluation model established above. Furthermore, according to the evaluation result, the analysis of two different schemes will be carried out from different stakeholders’ perspectives, which can provide a certain reference and decision support for the project decision makers. Carrying out the comprehensive risk evaluation of transnational networking project helps to identify risk factors faced by the project and improve the rationality of the decision-making process, which is of great practical significance in project management and project planning.

4.1. Basic Information of the Project to Be Evaluated

Table 8. The basic information of two different investment schemes.

Item	Scheme 1	Scheme 2
Total investment (Million USD)	4471.80	3095.81
Project life cycle	28 years	28 years
Transmission line capacity	8000 MW	4400 MW
Voltage level	±800 kV	±660 kV
Cable type	6 × 1250 mm2	6 × 720 mm2
Annual Transmitted Power	35,449 GWh	35,449 GWh
Interruption time/Observation time	0.0144 h/1000 h	0.0352 h/1000 h
On-grid price (Supply-side)	47.23 USD/MWh	47.23 USD/MWh
Free on board	51.89 USD/MWh	51.02 USD/MWh
On-grid price (Receive-side)	68.0 USD/MWh	68.0 USD/MWh
Net present value of the project (Million USD)	3092.76	3715.77
Net present value rate (NPVR)	73.6%	97.4%
Internal rate of return (IRR)	12%	13.55%
Public acceptance	78%	65%
Benchmark yield	7%
Composite depreciation rate	4.46%
Import value-added tax	8.5%

shows the basic information and data of two different investment schemes of a transnational HVDC transmission project, which is the foundation to launch the risk evaluation and the comparison of different schemes. Through the collection of the available materials, the value of each indicator can be calculated, which is used to conduct the risk evaluation in the next steps. In addition to the information listed in Table 8, a series of extra information should also be provided before evaluating the risk level of each investment scheme. The extra information is listed as follows: the relationship of the countries involved in this project is “Strategic partnership”; there are 121 countries in the GPI and 192 countries in the NGI; the ranking of two countries in GPI are 35 and 48; the ranking of two countries in NGI are 75 and 109; the exchange fluctuation is expected to be 1.6%; some qualitative indicators cannot be directly quantified, and the value of these indicators are determined by the expert group, such as the “extreme weather or natural disaster”, “parameters of power network” and the “construction risk”.

Table 9. The measurement and standardization of each indicator.

Indicator	Scheme 1		Scheme 2
	Ob	St	Ob	St
A1 (State relation)	3	0.3	3	0.3
A2 (War or terrorist attack)	3.9	0.39	3.9	0.39
A3 (Change of government or statute)	5.3	0.53	5.3	0.53
B1 (Public acceptance)	78%	0.22	65%	0.35
B2 (Extreme weather or natural disaster)	4.5	0.45	4.5	0.45
C1 (NPVR)	73.6%	0.4	97.4%	0.3
C2 (IRR)	12%	0.4	13.55%	0.3
C3 (Exchange fluctuations)	1.6%	0.3	1.6%	0.3
D1 (Parameters of power network)	3.3	0.33	6.2	0.62
D2 (Reliability of power supply)	2.3	0.23	4.9	0.49
D3 (Construction risk)	7.2	0.72	5.8	0.58

Note: Ob = observation value; St = standardized value.

shows the value of each indicator after standardization.

4.2. Weight Determination

According to the characteristics of transnational networking project, setting up a related expert group remains fundamental during the process of weight determination. All the relevant materials are available to the group member and the Delphi law is adopted in this section. Each indicator will be marked by the expert group, ranging from 0 to 100, and the higher score means the greater importance. The initial data for determining the weight can be obtained in this section.

(1) Granular Computing

Step 1:

Standardizing the original data. According to the scores of the first-level indicators, distance between different samples can be calculated by using the MATLAB. Different kinds of distance between classes, including “ward”, “complete”, “average”, “centroid” and “single”, are employed for clustering according to the characteristics of the original data. Then, the composite coefficient “Q” can be calculated to determine the optimal distance between classes, and the closer Q is to 1, the better the clustering is. The composite coefficient of first-level indicators can be calculated by using MATLAB and the results are as follows: Q = {0.8355, 0.8501, 0.8607, 0.7960, 0.7692}. The maximum value of Q is “0.8607”, which means the distance of “average” between classes is much more appropriate (the distance between samples is Euclidean distance). The result of clustering is shown in Figure 2, and the families of quotient space can also be obtained according to the clustering result (shown in

Table 10. Quotient space families.

Space Family	Clustering Result	Clustering Number
1	[{x1},{x2},{x3},{x4},{x5},{x6},{x7},{x8},{x9},{x10}]	10
2	[{x1},{x2,x6},{x3},{x4},{x5},{x7},{x8},{x9},{x10}]	9
3	[{x1},{x2,x6,x10},{x3},{x4},{x5},{x7},{x8},{x9}	8
4	[{x1},{x2,x6,x10},{x3},{x4},{x5,x7},{x8},{x9}]	7
5	[{x1},{x2,x6,x10},{x3,x4},{x5,x7},{x8},{x9}]	6
6	[{x1},{x2,x6,x10},{x3,x4,x8},{x5,x7},{x9}]	5
7	[{x1},{x2,x6,x9,x10},{x3,x4,x8},{x5,x7}]	4
8	[{x1},{x2,x5,x6,x7,x9,x10},{x3,x4,x8}]	3
9	[{x1},{x2,x3,x4,x5,x6,x7,x8,x9,x10}]	2
10	[{x1,x2,x3,x4,x5,x6,x7,x8,x9,x10}]	1

).

Step 2:

The discrete interval provided by the expert group is applied in data discretization and then, the corresponding equivalence class can be obtained when one of the indexes is deleted:

U/ind (S-{A}) = [{x1},{x2},{x3},{x4},{x5},{x6,x9,x10},{x7},{x8}]

U/ind (S-{B}) = [{x1,x4},{x2,x6,x10},{x3},{x5},{x7},{x8},{x9}]  

U/ind (S-{C}) = [{x1},{x2},{x3},{x4},{x5},{x6,x7,x9,x10},{x8}]  

U/ind (S-{D}) = [{x1},{x2},{x3},{x4,x7},{x6,x10},{x8},{x9}]   

Step 3:

On the basis of the results obtained above, the importance of each first-level index in different granularity spaces can be calculated and at the same time, the weight of first-level indicators can be determined after normalization.

Table 11. The attribute significance of the first-level index.

Family/Index	A	B	C	D
1	3/10	5/10	4/10	4/10
2	3/10	5/10	4/10	4/10
3	3/10	2/10	4/10	2/10
4	3/10	2/10	4/10	2/10
5	3/10	2/10	4/10	2/10
6	3/10	2/10	4/10	2/10
7	0	2/10	4/10	2/10
8	0	2/10	0	2/10
9	0	2/10	0	0
10	0	0	0	0
Importance	0.18	0.24	0.28	0.2
Weight	0.2	0.267	0.311	0.222

shows the attribute significance and the weight of the first-level index.

Step 4:

Calculation of the weight of the secondary indicators. The process of determining the weight of secondary indexes by granular computing is the same as the steps above, and due to the length limitation, no more details will be repeated.

Table 12. Weight obtained by using granular computing.

First-Level Indicators	Secondary Indicators	Comprehensive Weight
A (0.200)	A1 (0.298)	0.0596
	A2 (0.319)	0.0638
	A3 (0.383)	0.0766
B (0.267)	B1 (0.571)	0.1525
	B2 (0.429)	0.1145
C (0.311)	C1 (0.260)	0.0809
	C2 (0.466)	0.1449
	C3 (0.274)	0.0852
D (0.222)	D1 (0.339)	0.0753
	D2 (0.268)	0.0595
	D3 (0.393)	0.0872

shows the weight of indicators obtained by using granular computing.

(2) G1 Method

Step 1:

Determining the order relation. The order of first-level indexes can be obtained in the light of the scoring results.

Step 2:

Calculating the importance of each index. For example, an order of the four first-level indexes can be determined according to expert’s scores: B$<$D$<$C$<$A. “R” represents the relative importance of two adjacent indicators, and then a series of results can be calculated according to the original data: R₂ = A/C = 1.12, R₃ = C/D=1.06, R₄ = D/B = 1.11; w(B) = 1/(1 + R₂ × R₃ × R₄ + R₃ × R₄ + R₄) = 0.217, w(D) = 0.217 × 1.11 = 0.241, w(C) = 0.241 × 1.06 = 0.256, w(A) = 0.256 × 1.12 = 0.286.

Step 3:

Repeating the previous steps to gain the weight determined by all experts. Each expert will determine an order relation between the first-level indicators according to their own experience, and it is necessary to repeat the steps above to obtain the weights determined by different experts.

Step 4:

Obtaining the comprehensive weight of the first-level indicator. The comprehensive weight can be obtained directly by seeking the arithmetic mean of the data obtained in Step 3. And the results are as follows:

w(A) = 0.258, w(B) = 0.237, w(C) = 0.249, w(D) = 0.256.

(26)

Step 5:

Repeating the steps above to gain the weight of each secondary indicator. And the weights calculated by G1 Method are listed in

Table 13. Weights obtained by using the G1 Method.

First-Level Indicators	Secondary Indicators	Comprehensive Weight
A (0.258)	A1 (0.346)	0.0893
	A2 (0.321)	0.0828
	A3 (0.333)	0.0859
B (0.237)	B1 (0.523)	0.1239
	B2 (0.477)	0.1131
C (0.249)	C1 (0.322)	0.0801
	C2 (0.342)	0.0853
	C3 (0.336)	0.0836
D (0.256)	D1 (0.339)	0.0867
	D2 (0.351)	0.0900
	D3 (0.310)	0.0794

.

4.3. Risk Evaluation of Two Investment Schemes

(1)

Classifying the risk level of the system. In this paper, the risk level of the transnational HVDC transmission project is divided into five different grades, including “Extremely Low”, “Low”, “General”, “High” and “Extremely High”.

(2)

Determining the classical domain of each index. The classical domain of each indicator is listed as follows (except indicator “B1”): the classical domain of “Extremely Low” is (0,0.2); “Low” is (0.2,0.4); “General” is (0.4,0.6); “High” is (0.6,0.8); “Extremely High” is (0.8,1). The classical domain of different risk levels and the matter-element to be evaluated are shown as follows:

$$\begin{gathered} R_1=\left[\begin{array}{c}{N}_1{\mathrm{A}}_1\left(0,0.2\right)\\ {\mathrm{A}}_2\left(0,0.2\right)\\ {\mathrm{A}}_3\left(0,0.2\right)\\ {\mathrm{B}}_1\left(0,0.1\right)\\ {\mathrm{B}}_2\left(0,0.2\right)\\ {\mathrm{C}}_1\left(0,0.2\right)\\ {\mathrm{C}}_2\left(0,0.2\right)\\ {\mathrm{C}}_3\left(0,0.2\right)\\ {\mathrm{D}}_1\left(0,0.2\right)\\ {\mathrm{D}}_2\left(0,0.2\right)\\ {\mathrm{D}}_3\left(0,0.2\right)\end{array}\right]R_2=\left[\begin{array}{c}{N}_2{\mathrm{A}}_1\left(0.2,0.4\right)\\ {\mathrm{A}}_2\left(0.2,0.4\right)\\ {\mathrm{A}}_3\left(0.2,0.4\right)\\ {\mathrm{B}}_1\left(0.1,0.2\right)\\ {\mathrm{B}}_2\left(0.2,0.4\right)\\ {\mathrm{C}}_1\left(0.2,0.4\right)\\ {\mathrm{C}}_2\left(0.2,0.4\right)\\ {\mathrm{C}}_3\left(0.2,0.4\right)\\ {\mathrm{D}}_1\left(0.2,0.4\right)\\ {\mathrm{D}}_2\left(0.2,0.4\right)\\ {\mathrm{D}}_3\left(0.2,0.4\right)\end{array}\right]R_3=\left[\begin{array}{c}{N}_3{\mathrm{A}}_1\left(0.4,0.6\right)\\ {\mathrm{A}}_2\left(0.4,0.6\right)\\ {\mathrm{A}}_3\left(0.4,0.6\right)\\ {\mathrm{B}}_1\left(0.2,0.4\right)\\ {\mathrm{B}}_2\left(0.4,0.6\right)\\ {\mathrm{C}}_1\left(0.4,0.6\right)\\ {\mathrm{C}}_2\left(0.4,0.6\right)\\ {\mathrm{C}}_3\left(0.4,0.6\right)\\ {\mathrm{D}}_1\left(0.4,0.6\right)\\ {\mathrm{D}}_2\left(0.4,0.6\right)\\ {\mathrm{D}}_3\left(0.4,0.6\right)\end{array}\right]R_4=\left[\begin{array}{c}{N}_4{\mathrm{A}}_1\left(0.6,0.8\right)\\ {\mathrm{A}}_2\left(0.6,0.8\right)\\ {\mathrm{A}}_3\left(0.6,0.8\right)\\ {\mathrm{B}}_1\left(0.4,0.6\right)\\ {\mathrm{B}}_2\left(0.6,0.8\right)\\ {\mathrm{C}}_1\left(0.6,0.8\right)\\ {\mathrm{C}}_2\left(0.6,0.8\right)\\ {\mathrm{C}}_3\left(0.6,0.8\right)\\ {\mathrm{D}}_1\left(0.6,0.8\right)\\ {\mathrm{D}}_2\left(0.6,0.8\right)\\ {\mathrm{D}}_3\left(0.6,0.8\right)\end{array}\right] \\ {R}_5=\left[\begin{array}{c}{N}_5{\mathrm{A}}_1\left(0.8,1\right)\\ {\mathrm{A}}_2\left(0.8,1\right)\\ {\mathrm{A}}_3\left(0.8,1\right)\\ {\mathrm{B}}_1\left(0.6,1\right)\\ {\mathrm{B}}_2\left(0.8,1\right)\\ {\mathrm{C}}_1\left(0.8,1\right)\\ {\mathrm{C}}_2\left(0.8,1\right)\\ {\mathrm{C}}_3\left(0.8,1\right)\\ {\mathrm{D}}_1\left(0.8,1\right)\\ {\mathrm{D}}_2\left(0.8,1\right)\\ {\mathrm{D}}_3\left(0.8,1\right)\end{array}\right]R^{\prime }=\left[\begin{array}{c}{\mathrm{P}}^{\prime }{\mathrm{A}}_1\left(0.30\right)\\ {\mathrm{A}}_2\left(0.39\right)\\ {\mathrm{A}}_3\left(0.53\right)\\ {\mathrm{B}}_1\left(0.22\right)\\ {\mathrm{B}}_2\left(0.45\right)\\ {\mathrm{C}}_1\left(0.40\right)\\ {\mathrm{C}}_2\left(0.40\right)\\ {\mathrm{C}}_3\left(0.30\right)\\ {\mathrm{D}}_1\left(0.33\right)\\ {\mathrm{D}}_2\left(0.23\right)\\ {\mathrm{D}}_3\left(0.72\right)\end{array}\right]R^{″}=\left[\begin{array}{c}{\mathrm{P}}^{″}{\mathrm{A}}_1\left(0.30\right)\\ {\mathrm{A}}_2\left(0.39\right)\\ {\mathrm{A}}_3\left(0.53\right)\\ {\mathrm{B}}_1\left(0.35\right)\\ {\mathrm{B}}_2\left(0.45\right)\\ {\mathrm{C}}_1\left(0.30\right)\\ {\mathrm{C}}_2\left(0.30\right)\\ {\mathrm{C}}_3\left(0.30\right)\\ {\mathrm{D}}_1\left(0.62\right)\\ {\mathrm{D}}_2\left(0.49\right)\\ {\mathrm{D}}_3\left(0.58\right)\end{array}\right] \end{gathered}$$

(27)

where R represents the classical domain of five different risk levels; N stands for the different risk level; R′ and R″ represent the matter-element to be evaluated.

(3)

Determining the weight of each indicator. Utilizing the weights obtained above, the final comprehensive weight of each secondary indicator can be calculated by synthesizing the results obtained in Section 4.2., which can effectively improve the rationality of the final result. The final comprehensive weight is listed in

Table 14. The weight of each index obtained by different methods.

First-Level Indicator	Secondary Indicator	Granular Computing	G1 Method	Comprehensive Weight
A	A1	0.0596	0.0893	0.0745
	A2	0.0638	0.0828	0.0733
	A3	0.0766	0.0859	0.0813
B	B1	0.1525	0.1239	0.1381
	B2	0.1145	0.1131	0.1138
C	C1	0.0809	0.0801	0.0805
	C2	0.1449	0.0853	0.1150
	C3	0.0852	0.0836	0.0844
D	D1	0.0753	0.0867	0.0810
	D2	0.0595	0.0900	0.0748
	D3	0.0872	0.0794	0.0833

.

(4)

Calculating the distance between indicators and the classical domain. The distance of each indicator from the matter-element to the classical domain (Dij) can be calculated directly according to the formula listed in Section 2, and the results are shown in

Table 15. Distance between the matter-element to be evaluated and classical domain.

Indicator	R′ (Scheme 1)					R″ (Scheme 2)
	d1i	d2i	d3i	d4i	d5i	d1i	d2i	d3i	d4i	d5i
A1	0.10	−0.10	0.10	0.30	0.50	0.10	−0.1	0.10	0.30	0.50
A2	0.19	−0.01	0.01	0.21	0.41	0.19	−0.01	0.01	0.21	0.41
A3	0.33	0.13	−0.07	0.07	0.27	0.33	0.13	−0.07	0.07	0.27
B1	0.12	0.02	−0.02	0.18	0.38	0.25	0.15	−0.05	0.05	0.25
B2	0.25	0.05	−0.05	0.15	0.35	0.25	0.05	−0.05	0.15	0.35
C1	0.20	0	0	0.20	0.40	0.10	−0.10	0.10	0.30	0.50
C2	0.20	0	0	0.20	0.40	0.10	−0.10	0.10	0.30	0.50
C3	0.10	−0.1	0.10	0.30	0.50	0.10	−0.10	0.10	0.30	0.50
D1	0.13	−0.07	0.07	0.27	0.47	0.42	0.22	0.02	−0.02	0.18
D2	0.03	−0.03	0.17	0.37	0.57	0.29	0.09	−0.09	0.11	0.31
D3	0.52	0.32	0.12	−0.08	0.08	0.38	0.18	−0.02	0.02	0.22

.

(5)

Computing the correlation degree. According to the results obtained above, the correlation degree of two schemes with different risk levels can be calculated, respectively.

The correlation degree of R′ (Table 15, Scheme 1):

$$\begin{gathered} K_1=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.803 \\ {K}_2=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.979 \\ {K}_3=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.969 \\ {K}_4=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.807 \\ {K}_5=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.611 \end{gathered}$$

(28)

The correlation degree of R″ (Table 15, Scheme 2):

$$\begin{gathered} K_1=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.773 \\ {K}_2=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.960 \\ {K}_3=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.989 \\ {K}_4=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.840 \\ {K}_5=1-{\displaystyle \sum }_{\mathrm{i}=1}^{11}{\omega }_i{d}_{ij}=0.640 \end{gathered}$$

(29)

(6)

Determining the risk level. According to the correlation degree calculated above, the comprehensive risk level of two investment schemes can be determined: the risk level of Scheme 1 is “Low” since K₂ is the maximum value among the five correlation degrees of R′; the risk level of Scheme 2 is “General” because K₃ is the maximum value among the five correlation degrees of R″.

4.4. Analysis of the Evaluation Result

Based on the index system and evaluation model established in this paper, the risk evaluation of two different investment schemes of a transnational HVDC transmission project is carried out in this section. As listed in Table 14, the weight of “Public acceptance” is 0.1381, which is the maximum value of the eleven secondary indicators, and it means that the public acceptance has a great impact on the risk level of the project. In addition, based on the weights listed above, “Extreme weather or natural disaster” and “IRR” are the other two important risk factors faced by the transnational networking project. According to the results obtained above, the comprehensive risk level of scheme 1 is “Low” and the risk level of Scheme 2 is “General”, which means Scheme 1 is better for the decision makers from the perspective of risk control. However, due to the lower voltage level and transmission capacity of Scheme 2, the original investment of Scheme 2 is significantly lower than that of scheme 1, and during the process of evaluation it is not hard to find that the NPVR of Scheme 2 is 97.4% and the IRR is 13.55%, both of which are better than that of Scheme 1, which makes it has more economic advantages. In other words, Scheme 2 is much more attractive and profitable for those enterprises who are investment-oriented and risk-preferred, even though they may face higher overall risks, but at the same time, the limitation of technical parameters of Scheme 2 also leads to the result that its transmission capacity cannot meet the further development of the local power system, hence the “Parameters of power network”, “Reliability of power supply”, “Public acceptance” of Scheme 2 are worse than Scheme 1. As listed in Table 9, taking the reliability of power supply for example, Scheme 1 scores 2.3 points and Scheme 2 scores 4.9, which finally makes the comprehensive risk level of Scheme 1 is lower than that of Scheme 2.

5. Conclusions

As a new subject in power industry, the construction of transnational networking projects provides an effective way for the utilization of clean electricity. Taking the development trends of the power industry into consideration, a comprehensive risk evaluation index system and the corresponding judging criteria of transnational networking projects are established in this paper. Based on analyzing the characteristics of the project, a risk evaluation index system, including four first-level indicators and eleven secondary indicators, is constructed in this paper and the matter-element extension evaluation model is applied to seek the global optimal result of risk evaluation. In the process of weight determination, the granular computing and the G1 method are combined to improve the rationality of the result. On the basis of the works above, two different investment schemes of a transnational HVDC transmission project case study are evaluated by using the risk evaluation index system and the matter-element extension evaluation model established in this paper, which aims at validating the risk index system and the evaluation model constructed in this paper. According to the results obtained in Section 4, the maximum value of the degree of correlation of Scheme 1 is 0.979 (K₂), which means the comprehensive risk level of Scheme 1 is “Low”, and similarly, the maximum value of the degree of correlation of Scheme 2 is 0.989 (K₃), indicating that the risk level of Scheme 2 is “General”. From the perspective of risk control, the final result shows that Scheme 1 is more appropriate for a government’s power sectors or investment companies because the comprehensive risk level of Scheme 1 is lower than that of Scheme 2. Meanwhile, during the process of risk evaluation, we can also find that the NPVR and IRR of Scheme 2 are better than that of Scheme 1 due to its lower original investment, reaching 97.4% and 13.55%, respectively. This it means Scheme 2 has more economic advantages than Scheme 1, which makes it an attractive selection for those who are investment-oriented and risk-preferred. In summary, the construction of transnational networking project provides an effective way to address the challenges faced by the global energy industry, and it is in this context that a comprehensive risk evaluation index system and a risk evaluation model are established in this paper, which helps to identify the risk factors and carry out corresponding measures for the decision makers. The practical significance of this paper lies in that an intuitive method is proposed in this research to measure the risks faced by a project, including political, social, natural, economic and technical risks, which can provide a certain reference and decision support for power sectors, investment companies and other stakeholders when carrying out related activities.