Prioritization and Optimal Location of Hydrogen Fueling Stations in Seoul: Using Multi-Standard Decision-Making and ILP Optimization

Abstract

Thus far, the adoption of hydrogen fuel cell vehicles (HCEVs) has been hampered by the lack of hydrogen fueling infrastructure. This study aimed to determine the optimal location and prioritization of hydrogen fueling stations (HFSs) in Seoul by utilizing a multi-standard decision-making approach and optimization method. HFS candidate sites were evaluated with respect to relevant laws and regulations. Key factors such as safety, economy, convenience, and demand for HCEVs were considered. Data were obtained through a survey of experts in the fields of HCEV and fuel cells, and the Analytic Hierarchy Process method was applied to prioritize candidate sites. The optimal quantity and placement of HFSs was then obtained using optimization software, based on the acceptable travel time from intersections of popular roads in Seoul. Our findings suggest that compliance with legal safety regulations is the most important factor when constructing HFSs. Furthermore, sensitivity analysis revealed that the hydrogen supply cost currently holds the same weight as other elements. The study highlights the importance of utilizing a multi-standard decision-making approach and optimization methods when determining the optimal location and prioritization of HFSs and can help develop a systematic plan for the nationwide construction of HFSs in South Korea.

1. Introduction

Global warming is driving the world towards reducing its consumption of fossil fuels. The importance of hydrogen as an energy source is also growing, owing to the adoption of renewable energy generation technologies and the enforcement of regulations aimed at curbing carbon dioxide and nitrogen oxide emissions from energy sources such as natural gas, liquefied petroleum gas, and biogas [1,2,3]. In particular, the significance of hydrogen charging infrastructure is increasing as the world’s production of fossil-fuel-powered vehicles is supposed to cease before 2035, and the transition to electric vehicles or hydrogen cell electric vehicles (HCEVs) accelerates.

The global market for hydrogen fueling infrastructure is in its nascent stage, and owing to the high initial investment costs, a systematic building approach is imperative. In the United States, governmental bodies have devised and implemented a quantization approach to construct a blueprint for building hydrogen fueling infrastructure [4]. Similarly, in Korea, hydrogen industry-related organizations continue to propose comparable initiatives to the government. However, owing to the authorities’ lack of enthusiasm and the immature hydrogen sector for general customers, the need to establish a technique for developing hydrogen fueling stations (HFSs) infrastructure is low [4]. Consequently, there is a pressing need to develop a strategy for constructing an appropriate HFS infrastructure to bolster sales of next-generation HCEVs.

Boo et al. [5] have forecasted the number of HCEVs to be delivered in 2020, 2025, 2030, 2035, and 2040, as well as the number of HFSs that will be required in each city, county, and district in Korea. They have predicted the demand for hydrogen electric cars based on a 0.2% penetration rate in 2020 and a 4.1% penetration rate in 2030 [5]. Furthermore, the demand for hydrogen was assessed by city, county, and district based on the number of cars in each area, and the required base number of HFSs per city, county, and district was computed [5].

To anticipate the demand for hydrogen electric cars, Lawrence and Lawton’s market diffusion model was used, with the starting market characteristics and diffusion rate parameters being the key factors in this model [6].

Lee [7] selected Seoul as a case study target area and proposed a strategy to install HFSs by region based on the number of HFSs forecast by Boo et al. [5]. He suggested using dynamic planning and geographic information systems to select candidate sites for HFSs that are the farthest away from existing HFSs, and to limit candidate sites for HFSs to existing gas stations, LPG fueling stations, and CNG fueling stations [7]. The gap between HFSs was calculated based on the travel time between the existing HFS and HFS candidates, and this criterion was used to prioritize HFS candidates located far from the existing HFS, with consumer convenience being a key consideration [7].

Park et al. [8] conducted a survey on locations in Seoul and metropolitan cities where LPG and HFSs can be built concurrently, while meeting current domestic HCSHFS requirements. Their findings revealed that only six out of Seoul’s 72 LPG charging/fueling stations meet the criteria for concurrent HCSHFS construction. As there is limited available land in the metropolitan city’s downtown area, the authors recommended the implementation of a multi-layered and packed HFS [8].

Melendez and Milbrandt [9] conducted a study on the forecasting and construction of hydrogen demand infrastructure based on regional characteristics, and proposed strategically deploying HFSs in major cities in the United States, where many people live in densely populated regions and are receptive to HCEVs. They identified New York City and Los Angeles as the optimal introduction locations for HFSs and included eight more cities in the second stage of the proposal (2016–2019): Chicago, San Francisco, Philadelphia, Boston, Detroit, Dallas, Atlanta, and Seattle, with plans to construct a total of 3945 HFSs in these areas [9]. The first proposal of deploying HFSs in large cities with dense populations offers the advantage of reducing construction costs while simultaneously increasing the supply scope [9].

Stephens-Romero et al. [10] proposed a model in which regional customers of hydrogen–electric cars determine the ideal quantity and placement of HFSs based on economic efficiency and convenience. They selected Irvine, California as the target location for their case study and designed an affordable HFS that allows HCEV owners in the region to construct a minimum HFS within a defined travel time [10]. Furthermore, the authors identified environmental implications such as greenhouse gas emissions from HFS implementation [10].

The California Hydrogen Infrastructure Tool (CHIT) plans and presents general HFS construction directions for areas in need of hydrogen infrastructure and also evaluates the relative necessity of hydrogen infrastructure via Gap Analysis of current hydrogen infrastructure and future markets [11]. CHIT presented a model that uses optimization techniques and geographic information systems to determine the optimal number and location of HFSs based on traffic volume, demand for HFSs, site analysis of HFSs, travel time to HFSs, and analysis results [11].

Traditional facility placement selection models, such as P-median [12], Set Covering [13], and Maximum Covering [14], seek to identify the ideal site that best meets the needs of the surrounding nodes [11,15]. In contrast, Hodgson [16] noted that in the case of facilities where people buy products or services on the spur of the moment, it is appropriate to examine route-based traffic flowing through the place rather than the demand at nodes around the facility. This comprises LPG and CNG fueling stations as well as gas stations on important highways and arterial routes. In the case of highway gasoline fueling facilities, it is preferable to choose a location that fulfills the largest traffic volume passing through the area rather than a place that optimizes the demand for nearby traffic nodes [16]. Hodgson created the Flow Capacity Location Model (FCLM), a place selection model that is dependent on traffic volume on the route that passes through the location [16]. However, the FCLM model faces a critical issue when optimizing the location of the HFSs [17,18,19,20]. When fueling a hydrogen fuel cell car once, mileage cannot be considered. This is because the FCLM concept is intended to meet the maximum traffic volume flowing through the facility regardless of the vehicle’s maximum range of travel [21].

By incorporating the notion of the maximum mileage of the vehicle into the FCLM, the Flow Refueling Placement Model (FRLM), which is a fueling station location selection model, was suggested in response to the constraints of this FCLM model [19]. The FRLM model created an intuitive linear mathematical model by considering the difficult-to-modify concept of the maximum range of hydrogen fuel cell cars as an external variable [16]. Various extended FRLM models have been presented [18,22,23,24,25,26]. Nonetheless, most of these studies are limited in that they are models that maximize their placement in terms of bias throughout supply and demand [15].

Some studies, such as Wang et al. [27], have proposed a generalized model that can select the optimal location while considering consumer benefits as well as supplier costs; however, it does not adequately reflect the characteristics of HFSs, such as hydrogen supply methods or compliance with laws and regulations.

Previous studies primarily focused on estimating the number of HFSs required to build a hydrogen economy, but this study determined the priority of building HFSs by developing a multi-standard decision-making method that considered major evaluation indicators such as safety, economy, convenience, and demand for HCEVs [11,15,26]. Candidates for new HFSs in Seoul were identified, and the priority of establishing HFS candidates in Seoul was determined through a multi-standard comprehensive evaluation of HFS candidates in Seoul.

Furthermore, the convenience of hydrogen electric car owners was examined by selecting important road crossings in Seoul and evaluating the trip time from major intersections to candidate locations for HFSs. A model was provided using the optimization approach to estimate the ideal location and number of HFSs where the trip time from the intersection of the main highways in Seoul to the HFSs can be achieved within a fixed amount of time.

The primary goal of this research is to create a tool that can create a strategy for constructing an HFS in Seoul, as well as to secure quantification and analysis techniques for constructing an HFS that consider Seoul’s population, traffic volume, number of vehicles, location, and regulations. In particular, the priority for constructing HFSs will be chosen based on the regional demand for hydrogen electric cars in the early phases of the hydrogen economy, considering Seoul’s population, traffic volume, and vehicle count.

Furthermore, the ideal construction foundation and location of HFSs were chosen based on economic efficiency and convenience of use for places that do not infringe building and gas rules. To prioritize the development of HFSs for candidate sites for new sites, a tool and analytical approach were created.

2. Materials and Methods

2.1. Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) was employed in this study to prioritize the construction of HFSs. Saaty pioneered the stratification analysis in the 1970s. AHP is a multi-criteria decision-making (MCDM) approach that selects or prioritizes options by hierarchically categorizing numerous variables to assess the value of each feature (factor) [28]. In recent times, AHP has been adopted by government budget projects, public institutions, universities, and research institutes as an ideal strategy for multi-standard or multi-factor decision-making that involves non-quantitative aspects [28].

AHP employs expert group surveys to evaluate the value of evaluation indicators, and the pairwise comparison approach is used to establish the relative importance of the two evaluation indicators [28].

Table 1. Saaty’s nine-step pairwise comparison scale.

Descriptive Evaluation	Quantification
extreme	9 (9:1)
very strong	7 (8:2)
strong	5 (7:3)
moderate	3 (6:4)
equal	1 (5:5)

presents Saaty’s nine-step pairwise comparison scale.

The step-by-step application technique of AHP consists of four steps, with the first stage deriving crucial characteristics or qualities for the thorough examination of options through expert brainstorming [28]. In the second step, a hierarchical structure of the assessment elements is developed [28]. The assessment elements have a structure that hierarchically produces profoundly connected aspects. The findings of the paired comparison of the respondents received by the survey are verified to be consistent in the third step, and the weights of the assessment elements are computed using the paired comparison results [28]. In Step 4, the total score of each alternative is computed, and the priority of the alternatives is determined by the total score of each alternative [28].

Evaluation for Consistency

Consistency evaluation was used to determine if the pairwise comparison of survey respondents yielded consistent findings. The following symbols are used to describe the consistency evaluation process.

$$\begin{gathered} W_i=\mathrm{Weight} \mathrm{of} \mathrm{evaluation} \mathrm{index} i, \\ {a}_{ij}=\mathrm{relative} \mathrm{importance} \mathrm{of} j \mathrm{compared} \mathrm{to} \mathrm{the} \mathrm{evaluation} \mathrm{index} i, \\ W=(w_1,w_2, \dots ,w_n) \\ A=\mathrm{matrix} a_{ij}, \\ \lambda =\mathrm{an} \mathrm{eigenvalue} \mathrm{of} A \end{gathered}$$

The following are the prerequisites for A to be consistent, according to Saaty [29]:

$$A W=\lambda W$$

(1)

As both sides of Equation (1) are difficult to match perfectly, the following equation is used to compute ${\lambda }_{max}$, which provides an approximation of $\lambda$.

$$A W={\lambda }_{max} W$$

(2)

The following symbols were used to express the consistency ratio, which represents the consistency of the pair-to-pair comparison of the survey respondents.

$$\begin{gathered} CI=\mathrm{Consistency} \mathrm{Index}, \\ RI=\mathrm{Random} \mathrm{Consistency} \mathrm{Index}, \\ CR= \mathrm{Consistency} \mathrm{Ratio} \end{gathered}$$

The following equations are then used to compute CI, RI, and CR.

$$CI=({\lambda }_{max}-n)/\left(n-1\right)$$

(3)

$$RI=1.98\times n/\left(n-1\right)$$

(4)

$$CR=CI/RI$$

(5)

Taha states that if the CR of Equation (5) is less than 0.1, the respondents’ appraisal is assessed to be consistent, whereas if the CR is less than 0.2, the evaluation of consistency is judged to be within an acceptable level [30].

2.2. Integer Linear Programming

Integer Linear Programming (ILP) is a widely used mathematical optimization technique that is commonly used for solving location selection problems. ILP is a mathematical optimization technique that involves minimizing or maximizing a linear objective function subject to a set of linear constraints, where the decision variables are required to be integers. In the context of location selection, the decision variables represent the location of the facility or service, and the objective function represents the cost or profit associated with the location.

The ILP model can be solved using a variety of software packages such as CPLEX, Gurobi, and SCIP. The solution to the ILP model provides the optimal location selection that minimizes the total cost or maximizes the profit, subject to the constraints. The benefits of using ILP for location selection are numerous. First, it provides a rigorous and systematic approach to location selection that takes into account multiple factors and constraints. Second, it allows decision-makers to evaluate a variety of scenarios and trade-offs, and to select the location that best meets their objectives. Third, it can be applied to a wide range of location selection problems, such as facility location, warehouse location, and retail store location.

In this study, the problem of choosing the best foundation and location for an HFS was formalized as an ILP problem under the condition that it can arrive at candidates for the HFS within a given travel time from all major intersections. The installation of a fire station at the lowest possible construction cost falls under the category of set covering problems. Specifically, the problem of determining the best base and location for an HFS can be compared to that of determining the base and location of a fire station such that a fire engine can be dispatched within a specified travel time at the lowest possible cost in the event of a fire. The following symbols were used to formalize as an ILP problem the problem of determining the optimal construction base and location of an HFS under the condition that it can arrive within a given travel time from all the major intersections in Seoul.

$$\begin{gathered} x_j= \mathrm{Existing} \mathrm{or} \mathrm{new} \mathrm{candidate} \mathrm{site} \mathrm{for} \mathrm{HFS}, j=1, 2, \dots , n, \\ {t}_{ij}= \mathrm{Major} \mathrm{intersection} \mathrm{travel} \mathrm{time} \mathrm{from} i \mathrm{to} \mathrm{candidate} \mathrm{HFS} j, i=1, 2, \dots , m, \\ t=\mathrm{Allowed} \mathrm{travel} \mathrm{time} \end{gathered}$$

The ILP problem of 7 determining the optimal construction base and location of HFSs that can arrive within a given travel time was then formulated as:

$$Minimize z={\displaystyle \sum }_{j=1}^n{x}_j$$

(6)

$$subject to {\displaystyle \sum }_{j=1}^n{Y}_{ij}\times x_j\ge 1, i=1, 2, 3, \cdots , m$$

(7)

$$Y_{ij}=\{\begin{array}{c}1, \mathrm{if} \mathrm{the} \mathrm{travel} \mathrm{time} \left(t_{ij}\right) \mathrm{from} \mathrm{intersection} i \mathrm{to} \mathrm{candidate} \mathrm{site} j \mathrm{is} \mathrm{within} \mathrm{the} \mathrm{allowed} \mathrm{travel} \mathrm{time} \left(t\right),\\ 0,\mathrm{otherwise},\end{array}$$

(8)

$$x_j=\{\begin{array}{c}1, \mathrm{when} \mathrm{the} \mathrm{exist} \mathrm{station} j \mathrm{is} \mathrm{selected}\\ 0, otherwise\end{array}$$

(9)

Both the variable j representing the candidate site of the HFS and the variable $Y_{ij}$ representing whether the travel time from the intersection i to the candidate site of the HFS is within the allowed travel time are represented by a binary variable with a value of 0 or 1. The first constraint is that the travel time from intersection i to at least one candidate site for a HFS must be within the allowed travel time.

The objective function determines the best locations for HFSs while simultaneously decreasing the total cost by reducing the total number of HFSs placed.

3. Results and Discussion

3.1. Selection of Research Regions

This study focused on the best site analysis of HFSs based on regional information, utilizing Seoul, Korea as the location for the case study. Seoul is South Korea’s capital and the hub of politics, economy, industry, society, culture, and transportation. Seoul is located at the heart of the Korean Peninsula and is separated into two districts surrounding the Hangang River: south and north. It is divided into 25 regions (gu), and

Table 2. Hydrogen Station data of Seoul by regions.

District (gu)	Population	Household	Land Area (km2)	Vehicles	Passenger Car	EV	HCEV	Average Salary Income (Million Won)
Gangnam	534,103	232,777	40	247,356	226,343	12,176	196	3.55
Gangdong	464,037	202,169	25	152,865	133,027	1294	204	3.27
Gangbuk	297,702	144,313	24	75,252	63,165	514	24	2.2
Gangseo	574,638	273,697	41	206,968	178,730	1777	132	3.15
Gwanak	501,226	283,623	30	118,694	102,859	777	63	2.68
Gwangjin	351,252	169,291	17	98,644	83,994	623	47	2.59
Guro	418,418	183,655	20	147,448	124,837	3799	159	2.86
Geumcheon	242,818	119,583	13	91,398	74,340	561	36	2.84
Nowon	508,014	217,540	35	152,518	134,851	896	63	2.48
Dobong	313,989	138,356	21	95,734	81,651	639	26	2.2
Dongdaemun	353,601	169,873	14	99,130	83,552	659	54	2.82
Dongjak	390,432	185,773	16	106,295	95,087	726	92	3.08
Mapo	375,585	180,084	24	121,739	105,620	1087	143	3.1
Seodaemun	319,554	145,797	18	90,135	79,213	670	85	3.49
Seocho	408,451	167,749	47	176,437	156,015	3497	245	3.73
Seongdong	288,234	133,305	17	105,504	91,300	1461	51	3.04
Seongbuk	441,984	197,082	25	122,686	107,410	926	63	2.77
Songpa	664,514	284,853	34	250,031	213,370	1991	189	3.09
Yangcheon	444,010	181,187	17	151,651	132,101	998	86	2.76
Yeongdeungpo	398,085	188,832	25	144,662	120,956	2388	159	4.29
Yongsan	233,284	109,805	22	75,512	66,949	975	63	3.73
Eunpyeong	470,602	213,876	30	134,245	117,243	901	106	2.43
Jongno	152,211	72,524	24	50,105	41,333	612	72	4.48
Jung	130,785	63,139	10	59,351	48,604	968	38	4.14
Jungnang	390,140	187,413	19	115,748	96,362	778	47	2.46
Seoul	9,667,669	4,446,296	605	3,190,108	2,758,912	41,693	2443	3.09
Korea	51,430,018	23,716,980	100,432	25,556,066	20,999,380	390,403	29,689	3.2

lists the statistics of the HFSs per Seoul region [31].

In 2022, the area of Seoul was 605 km², which is approximately 0.6% of the national land area of 100,432 km² in Korea. The population of Seoul is around 9.66 million, which is 18.8% of the national population of 51.43 million. As of December 2022, the number of registered passenger vehicles in Seoul is approximately 3.19 million, representing 12.5% of the total number of passenger cars in the country, i.e., approximately 25.55 million, which indicates that the number of passenger vehicles in Seoul is lower than the national average. As of December 2022, the total number of registered electric cars in the country was 390,403 [31].

3.2. Current Status of HFSs

According to the construction form, HFSs can be classified as single, side-building, complex, or fusion fueling stations. A side-by-side fueling station is a type of fueling station that utilizes hydrogen and other energy sources along road boundaries, whereas a stand-alone fueling station solely functions as an HFS. A “convergence fueling station” is, according to the Korean government, any installation and operation of a HFS at one business location that uses energy sources like compressed natural gas and liquefied petroleum gas, or any installation and operation of a manufactured HFS.

Currently, there are eight HFSs in Seoul that can be used to refuel privately owned HCEVs. The HFS constructed in Yangjae-dong is a concentrated HFS that uses by-product hydrogen, whereas the HFS constructed in Sangam-dong is a dispersed HFS that creates hydrogen by altering landfill gas (LFG).

However, given the restrictions imposed by the rules, there are few locations in Seoul where HFSs can be built. Therefore, convergence HFSs are being developed as viable alternatives. Convergence HFS construction has the drawback of requiring a business proposal from an existing operator, and is more expensive. However, there is a disadvantage to building a convergence HFS in that it requires a business proposal to the current operator and costs more than a specific amount of rebuilding. Furthermore, because the bulk of LPG and CNG fueling stations are in remote locations, HFSs are less accessible to HCEV owners. There are currently no LPG fueling stations in Mapo-gu, Yongsan-gu, Jongno-gu, or Jung-gu, and none in Dongdaemun-gu, Dongjak-gu, Seodaemun-gu, Yeongdeungpo-gu, Yongsan-gu, or Jongno-gu. Owing to issues with protective facilities, such as military installations and cultural properties, Yongsan-gu and Jongno-gu have no LPG or CNG fueling stations.

3.3. Analysis of a New HFS Location

In Korea, HFSs are governed by the High Pressure Gas Act, Building Act, and School Health Act, and they are subject to stricter regulations than LPG or CNG fueling stations. As the ordinance of the Seoul Metropolitan Government allows the establishment of HFSs in industrial and green areas, this study investigated the location of new HFSs in Seoul to secure the location of HFSs as much as possible. HFSs were based on sites other than those of current LPG and CNG fueling stations, and potential sites were categorized into five tiers through inquiry and analysis. A cadastral map was used during the preliminary stage. The cadastral map was utilized in the preliminary stage to discriminate between locations suitable for the construction of HFSs in industrial and green regions. Candidate sites with an E-class site size of 1540 m² or less were selected in the first stage, D-class sites near protective institutions such as hospitals, schools, children’s facilities, and railways in the second stage, and C-class sites where civil engineering work was unfeasible in the third stage. Step 4 identifies locations that can create HFSs using large-scale civil engineering as B, and step 5 identifies classes that can develop HFSs using basic construction as A. The judgment data collected and analyzed using Seoul Open Lab’s QGIS map are shown in Figure 1a,b and the road-view feature of the Kakao map in Figure 2.

Table 3. Minimum Separation Distance for building HFSs.

Types of Facilities	Separation Distance	Notion
Equipment inspection	1 m	-
Safe explosion	4.5 m	-
School’s borders	200 m	-
Residential facilities	25 m	Apartments, villas, houses under 19 households.
Playgrounds, Hospital, Daycare centers, and kindergartens	50 m	-
railway	30 m	Subway entrance, including outside of the station building

lists the specific separation distance criteria based on various amenities for the construction of HFSs [32].

The HFS Candidate was calculated using Seoul Open Lab (https://openlab.eseoul.go.kr/, accessed on 8 February 2023) data and Daum map sky view, road view, area, and distance measurements, with the scale set to 1:10 m.

The Seoul Real Estate Information Inquiry System (https://kras.seoul.go.kr/, accessed on 8 February 2023) was used to collect data on the land registry site area, building area, land use plan, and official land price. Based on these data, a rating evaluation based on the special criteria, separation distance between the main protective facilities, and maximum area of 780 m² after the special application was undertaken.

The travel time between prospective sites for HFSs and regional (by district) sub-centers was used to determine market accessibility, and districts without distinct sub-centers chose the point with the largest floating population. The travel time between the candidate site of the HFS and the non-core or existing HFS was calculated using the “finding path” function on the following map three times between 10 a.m. and 16 p.m. from Monday to Friday. Figure 3 depicts an estimate of the trip time between two locations using the map shown below.

The traffic volume of potential HFS locations was gathered by searching for the location of each site in the 2021 Seoul Metropolitan Government Traffic Survey data, which were released in March 2022, and the map below. The 2022 Seoul Metropolitan Government Traffic Survey Data were searched for the closest traffic aggregation point at each location, the address of the nearest branch was confirmed, and the total daily average traffic volume data for each branch were utilized. The e-country indicator ‘Registration status as of the end of December 2022 (by kind and usage)’ was used to identify vehicle data, and the income level was computed using year-end income data for each year-end settlement city, county, and district in 2022 [31].

A total of 30 candidate sites located in industrial and green areas that met the minimum area and separation distance requirements were selected, as illustrated in Figure 4. It is feasible to establish 38 HFSs in Seoul, which comprises the existing 8 operational HFSs and 30 new HFSs that can be constructed at potential sites.

3.4. AHP Prioritized HFS Construction Analysis

3.4.1. HFS Construction AHP Model

According to this study, the most important considerations in determining the optimal site for HFSs are safety, affordability, convenience, and the magnitude of the market for HCEVs. Compliance with regulations for HFSs serves as a sub-indicator of their safety, while land rent and hydrogen supply costs serve as sub-indicators of their economic viability. The sub-index of convenience of use is market accessibility and the interval between HFSs, and the sub-index of the HCEV market size was set by traffic volume, income level, and number of vehicles. Land rent cost, a sub-indicator of economic viability, was based on the official land price (1000 won/3.3 m²), which was straightforward because it was desirable to utilize real rent for all candidate locations. The hydrogen supply price is the price of byproduct hydrogen delivered from an HFS (unit: won/kg), and when hydrogen is directly generated at an HFS, it is the price of hydrogen production.

Fueling station accessibility, a sub-indicator of convenience, refers to the temporal distance from the center of each region (former) to the fueling station candidate site, whereas the HFS interval refers to the temporal distance from the existing HFS to the candidate site. The daily traffic volume on roadways near candidate locations for HFSs was chosen as a sub-indicator of demand for hydrogen cars, and the monthly income per family in the region (former) to which candidate sites for fueling stations belonged was chosen.

In addition, the number of vehicles was estimated based on the number of vehicles in the area where the candidate fueling station was located, as well as the number of passenger automobiles per family. The AHP model for determining the priority of constructing HFSs is depicted in Figure 5.

3.4.2. AHP Survey

A survey was conducted among specialists in the disciplines of automotives, energy, and hydrogen fuel cells to compute the weight by comparing pairs of evaluation indicators to identify the weight of evaluation indicators connected to the installation of HFSs. A total of 30 people answered the poll, including representatives from research institutions, automakers, universities, and local government officials from the Ministry of the Environment. The weights of the assessment indicators were derived using the findings of a 22-person survey, eliminating the results of an 8-person survey whose replies were inconsistent.

The geometric average value was used to generate the average value for $a_{ij}$, which indicates the relative significance of two evaluation items i and j through pairwise comparison.

Table 4. Pairwise comparison results on the Level 1 evaluation criteria (i:j is a pairwise comparison between criteria.).

Number	Safety: Economy	Safety: Convenience	Safety: Hydrogen Demand	Economy: Convenience	Economy: Hydrogen Demand	Convenience: Hydrogen Demand
1	0.2	1	1	7	5	0.33
2	0.14	5	0.33	7	5	0.33
3	5	7	9	3	5	0.33
4	7	5	5	1	3	0.33
5	5	7	7	0.33	0.33	1
6	7	9	9	0.2	0.2	1
7	0.33	3	5	7	7	0.33
8	3	0.14	0.2	0.14	0.2	5
9	3	3	1	0.33	1	1
10	3	5	5	0.33	0.33	1
11	0.2	0.2	0.2	1	0.33	1
12	7	7	7	5	5	1
13	9	9	9	3	3	1
14	7	7	5	1	0.33	0.33
15	9	9	9	0.33	0.33	1
16	5	3	5	1	1	3
17	9	9	9	0.2	1	5
18	9	7	7	0.2	0.2	1
19	5	5	7	3	3	1
20	0.2	0.14	3	0.33	3	5
21	0.33	0.33	0.33	1	1	3
22	0.2	0.33	0.2	3	1	1
Geometric mean	2.044	2.545	2.585	1.080	1.064	1.020

summarizes the findings of a survey of respondents on Level 1 assessment indicators, such as safety, economy, ease of use, and desire for hydrogen automobiles, while

Table 5. Pairwise comparison results on the Level 2 evaluation criteria.

Number	Land Rent Cost: Hydrogen Supply Cost	Station Accessibility: Distance to Existing Station	Traffic: Income	Traffic: Number of Vehicles	Income: Number of Vehicles
1	0.2	5	0.14	1	0.14
2	0.14	7	7	0.33	0.11
3	0.14	3	5	1	0.33
4	0.2	0.2	0.33	1	3
5	0.2	5	1	5	5
6	0.2	5	1	0.33	0.33
7	5	0.33	1	5	5
8	0.2	5	5	0.14	0.11
9	0.33	1	5	5	1
10	0.2	0.14	5	5	0.33
11	0.33	1	1	0.33	1
12	7	7	5	5	0.33
13	0.33	3	7	7	0.33
14	5	3	5	5	1
15	0.14	5	3	1	0.2
16	3	7	0.33	1	3
17	1	5	7	1	0.14
18	0.2	7	5	5	3
19	0.33	5	5	5	1
20	0.2	5	5	3	0.33
21	1	7	7	0.2	0.14
22	0.33	0.33	5	3	3
Geometric mean	0.439	2.499	2.578	1.587	0.730

summarizes the results of a survey of respondents on Level 2 evaluation indicators.

The evaluation criteria of Level 1 can be determined by computing the average value of each row based on the standardized matrix A, and W is as follows:

W = (w₁, w₂, w₃, w₄) = (0.44, 0.20, 0.18, 0.18)

Meanwhile, $n=4$ and ${\lambda }_{max}$ = 4.002, as calculated using Equation (2). Using Equations (3)–(5), CI = 0.0007, RI = 2.64, and CR = 0.0003. The respondents’ judgment of the evaluation criteria of Level 1 was judged to be consistent because the CR was less than or equal to 0.1.

The weight ratios of land rent and hydrogen supply costs using the survey data in

Table 6. Raw Data of evaluation of new HFS candidates in Seoul.

Station Number	Legal Conformity	Land Rent Cost (won/3.3 m2)	Hydrogen Supply Cost (won/kg)	Station Accessibility (Minutes)	Distance to Existing Station (Minutes)	Traffic (Vehicles)	Income (10,000 Won/month)	Number of Vehicle (EV Vehicles)
N1	A	1090	8800	15	9	88,638	355	12,176
N2	A	531	8800	21	14	66,463	355	12,176
N3	A	1367	8800	18	13	88,638	355	12,176
N4	A	1260	8800	19	14	116,956	355	12,176
N5	A	570	8800	20	14	116,956	355	12,176
N6	A	416	8800	18	13	88,638	355	12,176
N7	A	590	8800	8	25	30,679	327	1294
N8	A	770	8800	4	28	30,679	327	1294
N9	A	245	8800	9	8	174,491	315	1777
N10	A	127	8800	19	30	54,732	286	3799
N11	A	1634	8800	11	28	146,317	282	659
N12	A	280	8800	11	4	237,956	310	1087
N13	A	315	8800	13	11	237,956	310	1087
N14	A	228	8800	10	4	192,316	373	3497
N15	A	650	8800	8	24	78,989	304	1461
N16	A	710	8800	10	16	67,273	309	1991
N17	A	990	8800	11	22	102,628	309	1991
N18	A	1270	8800	9	22	102,628	309	1991
N19	A	230	8800	9	25	42,373	243	901
N20	A	1020	8800	9	24	69,224	448	612
N21	B	175	8800	23	12	66,463	355	12,176
N22	B	175	8800	20	14	116,956	355	12,176
N23	B	109	8800	14	25	48,117	286	3799
N24	B	45	8800	9	31	60,341	248	896
N25	B	376	8800	8	35	53,892	220	639
N26	B	1200	8800	8	6	68,057	373	3497
N27	B	992	8800	15	4	192,316	373	3497
N28	B	1690	8800	15	20	67,273	309	1991
N29	B	505	8800	16	32	166,143	276	998
N30	B	624	8800	4	22	42,373	243	901

are 0.31 and 0.69, respectively, while the weight ratios of access to fueling stations and fueling intervals are 0.71 and 0.29, respectively. Furthermore, the weight ratio of cars at the traffic and income levels, which are sub-indicators of hydrogen vehicle demand, were determined to be 0.50, 0.20, and 0.30, respectively, and the respondents’ opinions of the evaluation criteria of Level 2 were all consistent. The total weight of the assessment evaluation criteria in Level 2 may be computed by multiplying the weight of Level 1 by the weight of Level 2. If the total weights for compliance, land rent, hydrogen supply price, fueling station access, fueling station spacing, traffic, income level, and vehicle count are expressed as s₁, s₂, s₃, s₄, s₅, s₆, s₇, and s₈, respectively, the set of weights S for the evaluation criteria of Level 2 is as follows.

S = (s₁, s₂, s₃, s₄, s₅, s₆, s₇, s₈) = (0.44, 0.06, 0.14, 0.13, 0.05, 0.09, 0.04, 0.05)

3.4.3. Standardization and Interval Transformation

Table 6 comprises data from important new sites in Seoul that have been examined in accordance with safety legislation by A or B.

Table 7. Standardization data of evaluation of new HFS candidates in Seoul.

Station Number	Legal Conformity	Land Rent Cost (won/3.3 m2)	Hydrogen Supply Cost (won/kg)	Station Accessibility (Minutes)	Distance to Existing Station (Minutes)	Traffic (Vehicles)	Income (10,000 Won/month)	Number of Vehicle (EV Vehicles)
N1	100	62	100	27	26	37	79	100
N2	100	100	100	19	40	28	79	100
N3	100	49	100	22	37	37	79	100
N4	100	53	100	21	40	49	79	100
N5	100	100	100	20	40	49	79	100
N6	100	100	100	22	37	37	79	100
N7	100	100	100	50	71	13	73	11
N8	100	87	100	100	80	13	73	11
N9	100	100	100	44	23	73	70	15
N10	100	100	100	21	86	23	64	31
N11	100	41	100	36	80	61	63	5
N12	100	100	100	36	11	100	69	9
N13	100	100	100	31	31	100	69	9
N14	100	100	100	40	11	81	83	29
N15	100	100	100	50	69	33	68	12
N16	100	95	100	40	46	28	69	16
N17	100	68	100	36	63	43	69	16
N18	100	53	100	44	63	43	69	16
N19	100	100	100	44	71	18	54	7
N20	100	66	100	44	69	29	100	5
N21	80	100	100	17	34	28	79	100
N22	80	100	100	20	40	49	79	100
N23	80	100	100	29	71	20	64	31
N24	80	100	100	44	89	25	55	7
N25	80	100	100	50	100	23	49	5
N26	80	56	100	50	17	29	83	29
N27	80	68	100	27	11	81	83	29
N28	80	40	100	27	57	28	69	16
N29	80	100	100	25	91	70	62	8
N30	80	100	100	100	63	18	54	7

comprises standardization data data of evaluation of new HFS candidates in Seoul.

Owing to the differences in the assessment indicators, the process of integrating them is required if the evaluation indicators of each option (HFS candidate site) comprise quantitative and qualitative variables (scale). The bipolar approach, which assigns 1 to the minimum and 5 to the maximum, was used to translate the qualitative data into quantitative elements in this study. The process of converting the values of items with distinct measuring units into equivalent scales is known as standardization [29].

This study employed linear transformation to standardize, and the maximum value was used for evaluation indicators with a higher preference, while the lowest value was used for evaluation indicators with a lower preference. Compliance with laws, spacing of existing fueling stations, traffic volume, income level, and number of vehicles show higher preferences among the evaluation indicators for prioritizing the establishment of HFSs, and land rent, hydrogen supply price, and access to fueling stations show lower preferences. The score of each HFS candidate site was computed with 100 points for each evaluation index, and the score of the evaluation index with the higher preference was generated using the reciprocal of the evaluation index.

When $x_{ij}$ and $r_{ij}$ are expressed as the evaluation value and evaluation score of the i-th evaluation element of the fueling station j, the connection between $x_{ij}$ and $r_{ij}$ is as follows:

$$r_{ij}=x_{ij}/max x_{ij}, For maximum preference,$$

$$r_{ij}=min x_{ij}/x_{ij}, For minimum preference.$$

(10)

3.4.4. Results of AHP Analysis

The weighted average of the scores, multiplied by the weighted average of each detailed assessment index acquired at Level 2, was used to obtain the total score for each alternative.

Data in

Table 8. Total scores of new HFS candidates in Seoul.

Rank	Station Number	Location Criteria Hangang	Legal Conformity	Land Rent Cost	Hydrogen Supply Cost	Station Accessibility	Distance to Existing Station	Traffic	Income	Number of Vehicle	Total Score
1	N8	South	100	74	100	100	80	13	73	11	84.0
2	N14	South	100	100	100	40	11	81	83	29	81.8
3	N13	North	100	100	100	31	31	100	69	9	81.8
4	N12	North	100	100	100	36	11	100	69	9	81.5
5	N5	South	100	99	100	20	40	49	79	100	81.2
6	N9	South	100	100	100	44	23	73	70	15	81.1
7	N6	South	100	100	100	22	37	37	79	100	80.3
8	N15	North	100	87	100	50	69	33	68	12	79.5
9	N2	South	100	100	100	19	40	28	79	100	79.2
10	N7	South	100	96	100	50	71	13	73	11	78.4
11	N4	South	100	45	100	21	40	49	79	100	78.0
12	N19	North	100	100	100	44	71	18	54	7	77.5
13	N20	North	100	55	100	44	69	29	100	5	77.4
14	N1	South	100	52	100	27	26	37	79	100	77.4
15	N10	South	100	100	100	21	86	23	64	31	77.2
16	N11	North	100	35	100	36	80	61	63	5	77.1
17	N18	South	100	45	100	44	63	43	69	16	77.1
18	N17	South	100	57	100	36	63	43	69	16	76.8
19	N3	South	100	41	100	22	37	37	79	100	76.8
20	N16	South	100	80	100	40	46	28	69	16	76.4
21	N30	North	80	91	100	100	63	18	54	7	74.9
22	N22	South	80	100	100	20	40	49	79	100	72.4
23	N29	South	80	100	100	25	91	70	62	8	72.2
24	N25	North	80	100	100	50	100	23	49	5	71.0
25	N24	North	80	100	100	44	89	25	55	7	70.3
26	N21	South	80	100	100	17	34	28	79	100	69.9
27	N27	South	80	57	100	27	11	81	83	29	68.7
28	N23	South	80	100	100	29	71	20	64	31	68.4
29	N26	South	80	47	100	50	17	29	83	29	66.7
30	N28	South	80	33	100	27	57	28	69	16	63.7

indicates that seven of the top ten HFS candidates with high total evaluation scores were located south of the Hangang River, while the other three were located north of the Hangang River. This shows that there are relatively few new sites north of the Hangang River where HFSs can be built.

According to the total evaluation score, the priority of establishing candidate sites for HFSs is shown in this study for each candidate site. Here, the circled number denotes the number of candidate locations for HFSs, whereas the red number denotes the importance of establishing locations for HFSs. The priorities and locations of the new sites are shown in Figure 6.

3.4.5. Performing Sensitivity Analysis on AHP Results

The final prioritization of alternatives is heavily reliant on the allocation of weights to the primary criteria. Minor variations in the relative weights of these criteria can cause substantial alterations in the final ranking. As these weights are often based on subjective judgments, it is crucial to assess the stability of the ranking under diverse criteria weights. Sensitivity analysis enables this evaluation by utilizing scenarios that reflect diverse views on the relative importance of the criteria. By modifying the weights of individual criteria, we can observe the resultant changes in the priorities and ranking of the alternatives, providing insights into the stability of the ranking. In cases where the ranking is highly sensitive to small changes in the criteria weights, a careful review of the weights is recommended. Furthermore, incorporating additional decision criteria can improve the discrimination potential of the present set of criteria.

The Expert Choice 11 software was employed to evaluate changes in local priority weights of subjective factors. Sensitivity analysis was conducted using the performance graph analysis method. The performance graph displays the performance of alternatives to changes in all parameters. To analyze the performance sensitivity of the alternative, Figure 7, Figure 8, Figure 9 and Figure 10 were used when the main criteria of Level 1 increased and decreased by 20%.

Table 9. Weights of Level 1 criteria when performing sensitivity analysis.

Criteria	Sensitivity	Safety	Economy	Convenience	Hydrogen Demand	Total
Safety	+20%	0.528	0.169	0.152	0.151	1.000
	−20%	0.352	0.232	0.209	0.207	1.000
Economy	+20%	0.420	0.240	0.171	0.169	1.000
	−20%	0.464	0.160	0.189	0.187	1.000
Convenience	+20%	0.422	0.191	0.216	0.171	1.000
	−20%	0.462	0.208	0.144	0.186	1.000
Hydrogen demand	+20%	0.422	0.191	0.171	0.216	1.000
	−20%	0.462	0.208	0.186	0.144	1.000

and

Table 10. Weights of Level 2 criteria when performing sensitivity analysis.

Criteria	Sensitivity	Legal Conformity	Land Rent Cost	Hydrogen Supply Cost	Station Accessibility	Distance to Existing Station	Traffic	Income	Number of Vehicle
Safety	+20%	0.53	0.05	0.12	0.11	0.04	0.08	0.03	0.04
	−20%	0.35	0.07	0.16	0.15	0.06	0.10	0.04	0.06
Economy	+20%	0.42	0.07	0.17	0.12	0.05	0.08	0.03	0.05
	−20%	0.46	0.05	0.11	0.13	0.05	0.09	0.04	0.06
Convenience	+20%	0.42	0.06	0.13	0.15	0.06	0.09	0.04	0.05
	−20%	0.46	0.06	0.14	0.10	0.04	0.09	0.04	0.06
Hydrogen demand	+20%	0.42	0.06	0.13	0.12	0.05	0.11	0.04	0.06
	−20%	0.46	0.06	0.14	0.13	0.05	0.07	0.03	0.04

present the changes in the weight of criteria in Level 1 and Level 2 during that time. The analysis reveals that although the ranking changes when there is a 20% increase or decrease, it is due to the same evaluation score and location of candidate sites clustered in Gangnam-gu.

The hydrogen production technology of HFS used in this study is by-product hydrogen, which is provided at the same supply price. However, constructing an on-site charging station [33] that uses methane reforming and water electrolysis production methods [34,35] may result in different hydrogen supply prices for each candidate HFS, which could change the ranking. Therefore, it is advisable to keep track of and manage rankings using updated data.

3.5. Determination of Optimal Number and Location of HFS

In this study, 259 intersections on major roads in Seoul were selected to investigate the travel time from intersections to candidate sites for HFSs. The main intersections of Seoul subject to the survey were 133 north of the Hangang River and 126 south of the Hangang River. Figure 11 shows the location of the main intersections of Seoul.

Python was used to derive the optimal solution to the problem of minimizing the total construction cost of the hydrogen station under the constraint that the travel time from the main intersection to the HFS candidate site was within the allowed travel time.

The minimum number of HFS constructions and locations when the allowed travel time from the intersection of major roads in Seoul to the HFS candidate site is 30, 20, and 10 min are shown in Figure 12, Figure 13 and Figure 14, respectively.

Figure 12 shows that when the allowed travel time (t) is within 30 min, a total of 15 priority locations determined by AHP are required, and seven additional stations need to be built, in addition to the eight existing stations.

Figure 13 shows that when the allowed travel time (t) is within 20 min, a total of 19 priority locations determined by AHP are required, and 11 additional stations need to be built in addition to the eight existing stations.

Figure 14 shows that when the allowed travel time (t) is within 10 min, a total of 26 priority locations determined by AHP are required, and 18 additional stations need to be built in addition to the eight existing stations.

The points marked with red dots on the map indicate that no nearby HFS candidates can be reached within 10 min of the allowed travel time.

4. Conclusions

HFSs are considered essential for the future of the hydrogen economy, particularly in the transport sector. The principal aim of this study was to determine the priority of constructing an HFS using the stratified analysis method, a multi-standard decision-making technique, while comprehensively considering crucial evaluation indicators such as safety, economy, convenience, and demand for HCEVs. To establish an HFS network that can be charged within 30 min with minimal construction costs, a model was proposed to determine the optimal location and number of HFSs under constraints that meet the travel time from the intersection of major roads in Seoul to the candidate site.

The study showed that compliance with legal safety is the most significant factor in the construction of HFSs. This is because HFSs cannot be built near collective facilities or locations with large floating populations because of the risk of explosion. Furthermore, the hydrogen supply cost, a sub-criteria of the Convenience Criteria, is currently the same, and despite its high weight, we passed the sensitivity analysis. When constructing an on-site charging station that can produce and supply at the same time, the hydrogen supply price changes depending on the supplier. Thus, the priority may change when the market expands in the future. Furthermore, if a HFS is constructed based on the distance priority from the existing HFS, the traffic flow information between the branch and the existing HFSs must be updated.

In the future, it is necessary to apply and implement these techniques nationwide by referring to the research results obtained in Seoul. Considering that some regions may not have data on the detailed indicators used in this study, it is vital to select detailed indicators suitable for each area. The nationwide development plan for hydrogen charging stations should prioritize selecting strategic sales areas for HFSs, and areas where the number of people or HCEVs is expected to be low should be established later.

This study is important because it provides fundamental data necessary to evaluate the economic feasibility of investing in hydrogen infrastructure in the initial stages of investment in the hydrogen economy. Therefore, it is desirable to establish a systematic hydrogen charging station construction plan by conducting an investment analysis of the nationwide HFS construction plan in connection with the nationwide sales strategy of HCEVs.