Analysing the Cost-Effectiveness of Charging Stations for Electric Vehicles in the U.K.’s Rural Areas

While U.K. authorities have attempted to tailor measures to boost sales of electric vehicles (EVs) and support citizens through different schemes, the size and geographic coverage of the existing charging network are insufficient, which undermines electromobility promotion. There are 15,853 public charging points installed in the U.K. as of 3 August 2021, and the demands for public EV charging are rising. For rural areas, there is little support from local authorities or private companies. To identify how a charging station can be installed and work, this study researches existing charging stations nationwide. Generally, most Public Charging Stations (PCS) in rural areas have unsatisfactory cost-effectiveness due to their long payback period. This paper presents how many rural PCS are able to afford the cost in the first eight years. Based on the ever-increasing demands of the market, EV producers are switching their business strategies. Meanwhile, the rural areas may become urban with the same definition. When it comes to the analysis of cost-effectiveness, it is possible for the PCS to bring more elements into the calculation. For Capital Expenditure (CAPEX) and Operation Expenditure (OPEX), the unnecessary cost leaves more profit space, like the possibility of unplanned maintenance costs.


Introduction
Greenhouse gases, including carbon dioxide, mainly originate from the transportation sector [1]. It carries on growing as the key factor in the economy and quality of life index, though global climate change and warming brings a big challenge to the development of human civilisation [2,3]. To reduce transport emissions, many European countries have adopted policy measures for clean power to transport [2]. The U.K. authorities have attempted to tailor measures to boost sales of electric vehicles (EVs) and support citizens through different schemes, for example, the U.K. government offers customers incentives in investing the EVs supply equipment (EVSE) [2].
EVs can resolve the greenhouse emission issue and the fossil fuel scarcity problem [4]. EVs are more economically affordable and environmentally friendly [5] compared to internal combustion engine vehicles (ICEV). The US Department of Energy reports that EVs convert 77% of electrical energy to power at the wheels, which differs from fuel-based vehicles that convert approximately 12-30% of the energy stored in gasoline [6]. EVs impact local and regional electricity grids as well [7]. EVs bring a socioeconomic development opportunity for islands and remote locations due to the reduction of fuel imports [8].
In Norway, drivers are willing to purchase EVs due to their financial viability rather than their environmental conscience [9]. Goldin et al. [10] found that EV owners can save 40% of annual maintenance costs. There are no tailpipe emissions, which plays a central role in pollution emission reduction [5].
The U.K. government strongly supports EV owners for sustainable development [11]. The local authorities are required to meet the various travel needs of individual and

Literature Review
User-friendly and economical charging stations increase the acceptance of electric mobility [18]. Data show EVs have lower annual maintenance costs compared to traditional petrol and diesel vehicles [10]. The electric car market has expanded rapidly in recent years [13]. The development of EV markets has raised the interest of investors in the EV charging stations [2,19]. Charging stations enable EV drivers to travel far [21]. Studies have shown the current main types of chargers with statistical supports [23,24]. Furthermore, three levels of charger need to be installed according to the local demands to achieve high net profit [4]. The energy issues for islands and remote locations were considered in a previous study [8], with the energy consumption in charging stations estimated using machine learning and relative methods [6]. The site selection of PCS and how it influences users' daily life was developed in [5].
Different types of charging strategies serve many groups of people and various businesses. Investing in rapid-charging infrastructure was researched in [2] by listing parameters and structure of cost and revenue in the U.K. The authors developed a business model for this kind of charging station. They suggested the only revenue for charging stations is selling electricity. Bibby [25] demonstrates that the definitions of urban and rural classify all regions in the U.K. Both rural and urban locations have different types, and the U.K. government releases a definite list for rural and urban locations. Municipalities have the majority of EVs on U.K. roads [16] and there is little uptake of EVs in rural areas according to data from previous years.
Due to EV users' various charging behaviours, most EV owners prefer to recharge their cars at home [7,8,11,26]. Surveys show that a small portion of charging events occur in public charging points [20].
Both CAPEX and OPEX have been applied to the financial analysis of charging stations [2,27]. A few articles generally estimate the common payback periods for PCS. Typically, the reasonable payback time is more than three years and up to seven years [1].
The above studies have investigated the development of EVs and how charging stations work. The majority of charge point-related details have been referred to, including calculating cost and revenue. Those studies have been reviewed in this project before analysis. There is a research gap for rural PCS, especially their cost-effectiveness.
This paper analyses the cost-effectiveness of installing and running a PCS network in rural areas. Compared to the PCS in the urban city, there are few advantages in investing in rural PCS, considering the differences between PCS in cities and rural areas [26]. Based on the parameters of charging infrastructure and data on EVs in the U.K., this paper forecasts electricity demands and calculates their payback periods, including making suggestions on increasing cost-effectiveness. Furthermore, the mathematical models in this paper can be swiftly applied in different situation with corresponding data.

Data and Methodology
The methodology of this project was developed for multidimensional analysis of the financial elements of charging stations in the U.K., especially in rural areas. Suitable business models have been developed for public charging infrastructures in suburban regions due to the distinct functions of charging stations in city centres and these areas. Listing the advantages and drawbacks of those business models contributes to the selection of the right one.
After confirming the corresponding business model, this paper analyses its cost and revenue. As for the cost of the charging station, it can be calculated through capital expenditure (CAPEX) and operational expenditure (OPEX). The CAPEX is required before operations begin and the OPEX is related to the operation and maintenance of chargers [2]. The parameters of CAPEX and OPEX mainly refer to information released by the U.K. government.
Before calculating the revenue of public charging stations, the equation requires electricity demands. It is less likely to search the definite electricity data due to the charging events varying a lot. Moreover, there are few surveys on how frequently EV drivers use their cars and into their various charging behaviours. Thus, this paper uses the average electric car range and the average electricity consumption per 100 miles. The relationship between EVs number and electricity demands is represented below in the equation. It is vital to identify the percentage of charging events happening in public charging stations since this project mainly focuses on them. The equation is as follows: In this equation, E d is electricity demands for public charging points. E v is the number of electric vehicles.
Yurday [28] reports the average electric car range is 193 miles in the U.K. at the beginning of 2021, but the range in summer is different from that of winter. To reduce the margin of error, this paper has calculated it in years. EV manufacturers should include the numbers for the whole year. For different EV types, the number of kilowatt hours (kWh) an electric car uses is not the same. An electric car is supposed to use approximately 30 kWh every 100 miles, which can be used in calculating electricity consumption [29]. Muzi [20] points out that 5% of charging events happen in public charging points, including chargers on the street, in car parks and along road corridors.

Urban and Rural Area Definition
An explicit classification method is required in analysing PCS in the U.K.'s rural areas. Rural-urban definition for small-area geographies (RUC) is an essential fundamental principle in this paper. The grid of hectare cells is a standard for the identification of settlements within RUC [25]. Classifying rural and urban areas requires a few steps due to profiles and files. Two files are mentioned in this paper, (RUC2011) and (RUC2001), which are the updates of the past two decades.
As is shown in Figure 1, this flow chart demonstrates how the government classifies areas. Several elements should be considered, including former files, residence, and population, etc. RUC has another dimension, which involves context in the physical settlement. A two-level typology of rural areas is shown below: In Figure 2, sparseness represents the local density, and both rural and urban areas have been generally split into two parts. Each part still contains three settlement types.
On the other hand, urban is the same in segregation, but the branches in sparseness are different. A conurbation consists of a large area with grown and joined towns, usually near a city. According to their scale, conurbations can be separated into major and minor.
The map in Figure 3 clearly displays urban and rural areas with colours. Regions in urban areas are marked in four different shades of grey. It is evident that rural areas dominate the U.K., and play a vital role in connecting cities. In this project, rural areas consist of three types: 'largely rural', 'mainly rural', and 'urban with significant rural'. After selecting the corresponding codes, according to Table 1,  in Table 2, we collected licensed EVs numbers of 138 rural areas. The 138 groups of data are the basis for the cost-effectiveness analysis. After distinguishing where the rural areas are, this paper seeks business strategies for PCS. As presented in Table 2, the lines in Bold are rural area data. In the U.K., London is the municipality with the highest number of battery-electric and plug-in hybrid cars [16]. Steps in the identification of settlements [25] In Figure 2, sparseness represents the local density, and both rural and urban areas have been generally split into two parts. Each part still contains three settlement types.  Steps in the identification of settlements [25] In Figure 2, sparseness represents the local density, and both rural and urban areas have been generally split into two parts. Each part still contains three settlement types. On the other hand, urban is the same in segregation, but the branches in sparseness are different. A conurbation consists of a large area with grown and joined towns, usually near a city. According to their scale, conurbations can be separated into major and minor.
The map in Figure 3 clearly displays urban and rural areas with colours. Regions in  In this project, rural areas consist of three types: 'largely rural', 'mainly rural', and 'urban with significant rural'. After selecting the corresponding codes, according to Table  1, in Table 2, we collected licensed EVs numbers of 138 rural areas. The 138 groups of data are the basis for the cost-effectiveness analysis. After distinguishing where the rural areas are, this paper seeks business strategies for PCS. As presented in Table 2, the lines in Bold are rural area data. In the U.K., London is the municipality with the highest number of battery-electric and plug-in hybrid cars [16].

Business Model Selection
Before selecting business models, this paper researched charging behaviours among EV consumers. Approximately 50% to 80% of all charging events happen at home, based on the average number of charging events [7]. Fifteen to twenty-five percent of charging events occur at work [7,26], and the remaining 5% of charging events happen in a PCS, including on-street city charging, chargers in car parks, and fast charging along road corridors [7,20].
In Figure 4, home charge dominates the charging events. Serradilla et al. [2] suggest that credible business models are developed, which will bring more private investment to the PCS market. The companies lack motivation due to insufficient innovative business models [18]. Thus, a suitable business model for PCS in rural areas is required in this project. This section lists several popular business models for EVCSs, analysed and compared in a multidimensional way.  Three ways were introduced to build a charging station business profitably and sustainably [32]. Table 3 presents three models' characteristics and what groups of people they are suitable for.

Home 80%
Workplace 15% Public 5% Three ways were introduced to build a charging station business profitably and sustainably [32]. Table 3 presents three models' characteristics and what groups of people they are suitable for. Both Model 1 and Model 2 have other purposes before being installed. In other words, investors do not expect to be profitable through charging customers or users. They find the business opportunities from attracting EV owners, rather than charging them. Those who have additional or unplanned space where they can install EVCSs prefer Model 1 because EVCSs bring more functions to their buildings and properties. The revenue from EVCSs are just a tiny part of their business, but they indeed play an essential role in attracting more people and gaining popularity.
The EVCS in Model 2 is similar to parking lots for specific areas or property. As a facility, EVCSs serve those who live or work in the area for business purposes. The hotels, complexes, and centres with EVCSs have a higher value. Thus, landlords or business people could set a higher rent than those that do not have EVCSs.
As for Model 3, it takes advantage of the local sustainability programs. The incentives include funding them with a tax credit [32]. It is a win-win for the government and companies to stimulate the EV market and promote their ecoconscious brands.
In conclusion, the three proposed models [32] take advantage of the potential value of EVCSs. However, they do not suit PCS in rural areas because the cost of installation and running is unaffordable for private investors.
In Table 4, five different business models for EVCSs are presented [33], which massively consider most of the situations in regions, firms, and local authorities. There are some initial conditions in Models 1 and 3, like off-street parking or sufficient internal resources. Managers and investors recognise EVCSs as tools rather than as a core business element in Model 1. For corporations whose employees are EV owners, installing an EVCS is a necessary and cost-effective way to meet charging demands. Governments are encouraging enterprises, firms, and councils to invest in EVCSs with running programs or incentives. As for those who plan to invest in EVCSs in rural areas, Model 2 could be considered. Rural areas contain towns, urban fringe, and villages where population density is relatively low. The study showed less than 0.1% EV uptake in rural areas, which means those regions are less likely to attract investors due to the risk in installation and management of EVCSs. However, rural areas do not just connect regions but attract tourists with their visitor attractions. Thus, Model 2 can bring business opportunities to EVCSs in those places with lower risk and higher ROI compared to other models. Furthermore, the other business models can be applied in this project since the advantages somehow fit the conditions of rural charging stations. For example, if there is an available space for parking, companies or landlords can also apply commercial EV charging. A reliable fast-charging network is required in the PCS business, which involves a long-term partnership and resources from companies or governments. Judging from the business models mentioned above, the installation of PCS vary by region, EV uptake, and local policy, etc. When this paper sought a business model for rural PCS, it found no unique model that can be perfectly applied. Investors of small business groups may install more than one PCS in rural areas with a fast charge network, commercially billing customers and users. The many business models for EVCS cannot all be analysed in this paper. This paper discusses the drawbacks of four classical business models. The levels of revenue can be seen in Table 5. In Models 1 to 3, a regulation can be designed so that the higher price of an EVCS, the less attractive it is. Thus, the price for EV owners is a deciding factor in commercial EV charging. As for price setting, it depends on how much profit investors plan to achieve. Dynamic spike pricing (DSP) policy was introduced, which was proposed to reduce the charging cost of EVs [11]. The competitiveness in a region impacts the development of charging stations, while the current charging price is generally fixed or related to the different periods [17]. Business investors who cannot be fully funded by governments or charging infrastructure providers are more likely to be concerned about its cost-effectiveness.
In this section, the business models play a central role in deciding how businesses allocate costs and make a profit for rural PCS. In the following sections, we analyse the expenses and revenues of PCS in rural areas.

Results and Discussions
To analyse cost-effectiveness, this paper refers to several parameters in the cost and revenue of PCS. The cost of EVCSs include construction, maintenance, and operating costs [5]. In terms of costs, there are two terms-capital Expenditure (CAPEX) and operational Expenditure (OPEX).

CAPEX
In this paper, CAPEX contains five models as shown in Figure 5, and the details of the models are elaborated in Table 6. revenue of PCS. The cost of EVCSs include construction, maintenance, and operating costs [5]. In terms of costs, there are two terms-capital Expenditure (CAPEX) and operational Expenditure (OPEX).

CAPEX
In this paper, CAPEX contains five models as shown in Figure 5, and the details of the models are elaborated in Table 6.   Figure 5. Models of CAPEX [2]. Table 6. Summary of CAPEX parameters [2].

Element Definition Parameter
Charger purchase and delivery As is listed in Table 6, some of the models have parameters that vary by country or area. For management, site preparation, and commission, there is no relative statistical support. The U.K. government announced that it contributes 350 GBP per charger towards workplace EV charging stations. Moreover, a general commercial PCS installation costs around 1000-1500 GBP plus VAT (1118-1675 EUR) in total. Expected investments are 36,500 GBP per charger in CAPEX, and rising to £42,000 with a new power connection. Figure 6 shows that the majority of CAPEX is the cost of purchasing, delivering, and installing chargers. About 60-80% of the cost of a public EV charger is the installation [35]. The way investors distribute funds to those models depends on the type of charger, site, and budget, etc. Even if the total CAPEX has a parameter, its branch data are still necessary for the following calculation because some of the parameters are related to OPEX. For instance, maintenance cost and unplanned maintenance cost are according to the cost of charger purchase and delivery. Furthermore, installing a grid-connected charging station is not just related expenditure but also construction permits, local unity and time [36].
• Power connection, limited communication test, function and safety checks As is listed in Table 6, some of the models have parameters that vary by country or area. For management, site preparation, and commission, there is no relative statistical support. The U.K. government announced that it contributes 350 GBP per charger towards workplace EV charging stations. Moreover, a general commercial PCS installation costs around 1000-1500 GBP plus VAT (1118-1675 EUR) in total. Expected investments are 36,500 GBP per charger in CAPEX, and rising to £42,000 with a new power connection. Figure 6 shows that the majority of CAPEX is the cost of purchasing, delivering, and installing chargers. About 60-80% of the cost of a public EV charger is the installation [35]. The way investors distribute funds to those models depends on the type of charger, site, and budget, etc. Even if the total CAPEX has a parameter, its branch data are still necessary for the following calculation because some of the parameters are related to OPEX. For instance, maintenance cost and unplanned maintenance cost are according to the cost of charger purchase and delivery. Furthermore, installing a grid-connected charging station is not just related expenditure but also construction permits, local unity and time [36].

OPEX
OPEX consists of five models just like CAPEX. Table 7 explains the models in Figure  7 with parameters and resources. Unlike Table 6, the models in Table 7 have relative parameters which are related to CAPEX.  Figure 6. Cost breakdown as a percentage of the total CAPEX in all sites [2].

OPEX
OPEX consists of five models just like CAPEX. Table 7 explains the models in Figure 7 with parameters and resources. Unlike Table 6, the models in Table 7 have relative parameters which are related to CAPEX.  In 2020, the U.K. electricity price per kWh according to the Department for Business, Energy and Industrial Strategy was 0.172 GBP. Tenants need to pay £50,000 or above per year. However, the charging stations in rural areas are less likely to reach this kind of site rent. In this project, the site rent will be £1000 (per year) because tenants do not have to rent so much land.

Revenue
Electricity sales are a unique way that charging points can raise revenue. The daily charger usage costs contribute to 80% of EV charging [34]. Thus, the electricity demands, cost of electricity, and price for EV drivers are required parameters in calculations. These parameters change dynamically. For instance, the electricity purchase cost rises 5.2% annually [2]. The price for EV drivers to recharge will rise simultaneously. Thus, this project assumes that the gap between electricity cost and the price is the same.
A total annual profit of around 200 GBP is achievable when "selling" electricity at a profit of 0.04 GBP per kWh [37]. But the price of recharging varies by region, type of charger, car brand, etc. Pod Point rapid chargers cost 23 p/kWh at Lidl and 24 p/kWh at Tesco [38]. According to Tesla, EV owners are charged at 26.4 p per kWh [38].
Current types of charging stations include Level 1, Level 2, and DC fast chargers (DCFC) [24]. There are three types of charger in the U.K.-slow chargers, fast chargers, and rapid chargers. The features and parameters of these chargers are displayed in Table  8.  In 2020, the U.K. electricity price per kWh according to the Department for Business, Energy and Industrial Strategy was 0.172 GBP. Tenants need to pay £50,000 or above per year. However, the charging stations in rural areas are less likely to reach this kind of site rent. In this project, the site rent will be £1000 (per year) because tenants do not have to rent so much land.

Revenue
Electricity sales are a unique way that charging points can raise revenue. The daily charger usage costs contribute to 80% of EV charging [34]. Thus, the electricity demands, cost of electricity, and price for EV drivers are required parameters in calculations. These parameters change dynamically. For instance, the electricity purchase cost rises 5.2% annually [2]. The price for EV drivers to recharge will rise simultaneously. Thus, this project assumes that the gap between electricity cost and the price is the same.
A total annual profit of around 200 GBP is achievable when "selling" electricity at a profit of 0.04 GBP per kWh [37]. But the price of recharging varies by region, type of charger, car brand, etc. Pod Point rapid chargers cost 23 p/kWh at Lidl and 24 p/kWh at Tesco [38]. According to Tesla, EV owners are charged at 26.4 p per kWh [38].
Current types of charging stations include Level 1, Level 2, and DC fast chargers (DCFC) [24]. There are three types of charger in the U.K.-slow chargers, fast chargers, and rapid chargers. The features and parameters of these chargers are displayed in Table 8. The parameters are related to how much it costs per charger per year. There is little literature about the relationship between EV owners and the number of chargers in one charging station. This paper assumes that one PCS in the rural area typically provides two chargers. The CAPEX and OPEX can be estimated in the following section.
To summarise, the electricity purchase cost is 0.172 GBP per kWh, and sales price is 0.264 GBP per kWh, which is applied in cost-effective analysis combined with electricity demands.
The parameters and equation in Sections 3 and 6 will be applied in this part. Based on Table 7, this project firstly calculates the CAPEX of the charging station.
As is assumed in the end of Section 6.3, there are two chargers in this station. Thus, the amount of CAPEX can be easily calculated (Table 9). This number is less likely to influence the following analysis once a PCS has been installed.

Electricity Usage Forecast
OPEX is highly related to the number of existing EVs according to Equation (1). The unique variable in Table 10 is Ed. To demonstrate the method for dealing with OPEX, this project predicts the electricity demands of County Durham in Table 11. Before calculating Ed, this paper applies linear programming in an Ev forecast. Judging from the statistical information in Table 2, the number of licensed vehicles experienced an increasing trend.
To accurately forecast electricity demands in the next four quarters, this paper uses ten groups of EVs, which have not been shown in Table 11, with the help of the 'FORECAST' function in Excel. The numbers in the second line are presented. The reason that this paper predicts future EVs is to estimate payback time. Through this method, future data can be addressed. The trend of Ed and Ev can be seen in Figures 8 and 9.  However, not all groups of data have a constant growing tendency. For example, Figure 10 shows that the number of licensed vehicles in the Isles of Scilly increases and decreases during this period, but it moderately begins to rise from 2020. So, this project chooses to make the prediction based on the latest data from quarter 1 2020 to quarter 1 2021.    However, not all groups of data have a constant growing tendency. For example, Figure 10 shows that the number of licensed vehicles in the Isles of Scilly increases and decreases during this period, but it moderately begins to rise from 2020. So, this project chooses to make the prediction based on the latest data from quarter 1 2020 to quarter 1 2021.   However, not all groups of data have a constant growing tendency. For example, Figure 10 shows that the number of licensed vehicles in the Isles of Scilly increases and decreases during this period, but it moderately begins to rise from 2020. So, this project chooses to make the prediction based on the latest data from quarter 1 2020 to quarter 1 2021.   However, not all groups of data have a constant growing tendency. For example, Figure 10 shows that the number of licensed vehicles in the Isles of Scilly increases and decreases during this period, but it moderately begins to rise from 2020. So, this project chooses to make the prediction based on the latest data from quarter 1 2020 to quarter 1 2021.   The more recent data is shown in the first quarter of 2021. This paper selects the first quarter in the following years to represent the corresponding Ev of this year. The selected data are printed in yellow in Table 12. After refining and simplifying the tables, this section finally collects Ev in Table 13.  Combining Equation (1) and Table 12, Ed in the rural areas can be calculated, as is shown in Table 13. This paper predicts the data of the next thirty-two quarters because the further a prediction is made, the more error it has. This project selected eight numbers from those thirty-two prediction numbers to prevent the error from influencing the accuracy and dependency in the following calculations.

ISLES OF SCILLY
After calculating the Ed, all columns in Table 14 have a definite value. This paper displays some of the data that are used in the following research.

Revenue Calculation
Filling the column with values completes Table 10. Then, the OPEX of the next eight years have their own value. Table 15 lists the detailed data of OPEX in County Durham in the first year. Based on the results, in the next few years in County Durham, investors do not need to spend money on CAPEX, but the OPEX will change as time goes by due to the dynamic variable Ed.
The revenue also needs the data of Ed. Ed plus price for EV drivers equals total revenue. The net revenue can then be calculated by minimising the CAPEX and OPEX.
As is shown in Table 16, for the whole eight years the net income for the PCS is negative, meaning no profit was made from this charging point during this period.  To observe dynamic changes, the data were inputted into line graphs.
As shown in Figure 11a, the cost has a more dramatic increase trend compared to that of revenue. The Figure 11b shows how net revenue change in years. The revenue cannot cover its cost, and the gap between cost and revenue is growing, which means this PCS cannot make a profit if investors do not adjust in time. The actual cost-effectiveness of setting up charging infrastructures is very poor. It is necessary to identify the reasons why there is no rising tendency in net revenue.

Reasons and Solutions
OPEX plays a vital role in the increase of total cost once installation has been completed. Thus, the factors that influence the speed of increase feed into OPEX. The factors are listed below.
The unchangeable factors in Table 17 are 'Site rent' and 'Electricity cost'. There is no change in site rent, except that other bodies can fund PCS. Furthermore, businesses are unable to boost Ed-the unique variable in electricity cost. The cost of electricity purchase is a national standard measured by the government. The last three elements are related to the number of chargers. Therefore, reducing the number of chargers is an available method to slow down the speed of total OPEX. Moreover, CAPEX declines at the same time. After changing one factor, this paper analyses the effectiveness of one charger in County Durham. Table 18 lists the details of novel OPEX, and Table 18 updates its cost and revenue in County Durham. However, the net revenue remains the same, negative.

Elements
Parameter (

Reasons and Solutions
OPEX plays a vital role in the increase of total cost once installation has been completed. Thus, the factors that influence the speed of increase feed into OPEX. The factors are listed below.
The unchangeable factors in Table 17 are 'Site rent' and 'Electricity cost'. There is no change in site rent, except that other bodies can fund PCS. Furthermore, businesses are unable to boost Ed-the unique variable in electricity cost. The cost of electricity purchase is a national standard measured by the government. The last three elements are related to the number of chargers. Therefore, reducing the number of chargers is an available method to slow down the speed of total OPEX. Moreover, CAPEX declines at the same time. After changing one factor, this paper analyses the effectiveness of one charger in County Durham. Table 18 lists the details of novel OPEX, and Table 18 updates its cost and revenue in County Durham. However, the net revenue remains the same, negative. During these eight years, the total cost in PCS with one charger still outnumbers that of revenue. Nevertheless, there is an apparent minimal decrease trend closing to the end of the year. It means the speed of increase in revenue exceeds that of cost. With the ever-decreasing gap between cost and revenue, charging stations in County Durham will profit in the following years.
It is a fact that can be seen in Table 19 and Figure 12 that the decreasing trend gradually slows down. Cost of the year. It means the speed of increase in revenue exceeds that of cost. With the everdecreasing gap between cost and revenue, charging stations in County Durham will profit in the following years.
It is a fact that can be seen in Table 19 and Figure 12 that the decreasing trend gradually slows down.
It seems that the investment in rural PCS is likely to pay back after eight years. However, the lifespan of payback is long for investors who cannot afford this tremendous loss. It seems that the investment in rural PCS is likely to pay back after eight years. However, the lifespan of payback is long for investors who cannot afford this tremendous loss. It is essential to seek other methods of boosting net revenue.
As we mentioned before, profit is related to electricity demands. The decision variables used in our model are as follows: x Revenue in this year f (x) Annual net revenue Both Equations (2) and (3) share the same variable-E d . The total amount of site rent, back office running costs, maintenance costs, and unplanned maintenance costs is 1274.50 GBP. Equation (3) minus Equation (2) equals annual revenue.
When f "(x) is a positive value, there is no loss in that year. If f "(x) remains negative, the net revenue will not be positive anymore.
The minimal number of chargers is one. Currently, the cost cannot be cut by reducing the number of chargers. Fortunately, there is one last parameter that has not been changedthe profit gap. If investors plan to make a profit as soon as possible, they can bill EV drivers more in electricity price.
For instance, this paper assumes that investors increase rates from 0.264 GBP per kWh to 0.50 GBP per kWh. It can easily be predicted that the trend of total revenue is sharper than before.
As is shown in Table 20, the PCS in County Durham starts to make a profit in year 6. Figure 13 shows that the total revenue covers the total cost and rises dramatically in the following years. When f″(x) is a positive value, there is no loss in that year. If f″(x) remains negative, the net revenue will not be positive anymore.
The minimal number of chargers is one. Currently, the cost cannot be cut by reducing the number of chargers. Fortunately, there is one last parameter that has not been changed-the profit gap. If investors plan to make a profit as soon as possible, they can bill EV drivers more in electricity price.
For instance, this paper assumes that investors increase rates from 0.264 GBP per kWh to 0.50 GBP per kWh. It can easily be predicted that the trend of total revenue is sharper than before.
As is shown in Table 20, the PCS in County Durham starts to make a profit in year 6. Figure 13 shows that the total revenue covers the total cost and rises dramatically in the following years.   Based on the data in Table 21, the internal rate of return (IRR) can be calculated in Excel. The IRR in Table 22 is 27%, which means it will earn a 27% compound annual growth rate. The IRR is positively related to revenue, once the CAPEX is confirmed. There is no standard for PCS to have a certain IRR. The businesses can opt to adjust parameters and compare them to select the highest one.
The different levels of sales price correspond to different levels of IRR shown in Table 22. The IRR shares positive relationships with the sales price. The precondition is that the electricity demands do not impact sales price. The private investors can compare the IRR of different rural PCS and go for the most profitable one.
The sales price of 0.50 GBP per kWh cannot guarantee that all rural PCS are able to pay back in these eight years. Equation (4) can be applied to calculate how many electricity demands it needs. The first parameter in Equation (4) switches to 0.328.
When f "(x) exceeds 0, it requires E d to achieve 3770.71. It means the annual revenue of this PCS can cover the OPEX when its electricity demands reach 3770 during these eight years. There is no standard or reference timeline for investors to pay back the fund. This section suggests two ways to shorten the payback period. One is reducing the cost where possible and another one is raising the price for EV drivers. As for cost-saving, it has a bottom line since the necessity of management and hardware. The conditions of PCS are the basement of future development and running. On the contrary, there is no maximum for charging electricity, but, the high price of recharging for EV drivers is likely to negatively impact electricity demands, public reputation, and EV development, etc. Even though the price for EV drivers doubled and it ignores the CAPEX, there are still 30 rural regions that cannot make any profit during these eight years due to insufficient electricity demands. The 30 rural regions include North Devon, Scarborough, Rutland, Redcar and Cleveland, the Isles of Scilly and others. Figure 14 shows that the regions with insufficient E d account for 22% of PCS in all rural regions. Predictably, those PCS with not enough E d will suffer from consistent losses over eight years.
demands. The 30 rural regions include North Devon, Scarborough, Rutland, Redcar and Cleveland, the Isles of Scilly and others. Figure 14 shows that the regions with insufficient Ed account for 22% of PCS in all rural regions. Predictably, those PCS with not enough Ed will suffer from consistent losses over eight years. Meanwhile, the PCS with sufficient E d may still make losses for many years. Compared with those regions with insufficient E d , they just have a capability of recovering costs.
This paper highly recommends that investors consider cost-reduction first because rising prices may raise complaints among EV drivers. If there is little effect in making profits, then the business begins to manage the price according to the revenue they want to produce.

Payback Period
There are 138 groups of data regarding current vehicle numbers and predictions. It is difficult to calculate them one by one but this paper calculates how much electricity demand they need in those eight years to cover the cost. In other words, the latest payback period is eight years.
With the assistance of Equations (2) and (3), this paper accumulates those eight groups of data to list an equation of total cost.
The decision variables used in our model are as follows: x Year F Total OPEX of 8 years F Total revenue of 8 years When the gap between F and F is 3650-CAPEX, the PCS eventually covers all the costs with sufficient revenue. Then this equation could be: After simplifying Equation (7), the results should be the integer: This point represents that the total cost of PCS equals that of total revenue. After calculating the amount of Ed, this project accumulates 138 groups of Ed to select those regions whose payback times are less than 8 years.
Forty-six regions can reach this line. As shown in Figure 15, one-third of PCS in rural areas can pay back what they invest from 2021 to 2028, according to the sequences of total electricity demands. Those regions include Wiltshire, Glasgow City, Northumberland, and Central Bedfordshire, etc. The eight years' payback period is a bottom line in this project. Spirit (n.d.) suggests that the payback period is typically five to eight years [39]. If these rural PCS are unable to reach this bottom line, the risk of it is high for investors. The cost-effectiveness of most investments in rural PCS is relatively low.

Summary
In this chapter, the parameters and methodology mentioned are applied. The calculation of Ed is elaborated in Section 3, but the prediction of Ev is completed in this section. The U.K. government's data of licensed EVs strongly supports the prediction in this project. Enough statistical support can make the forecast more accurate. Mostly Ev experienced a moderate increase from 2011 to 2020, and fluctuations were seen in a few regions. Linear programming is a reasonable choice because the regulation can be easily spotted through the trends inside. However, the prediction is a mathematical result that cannot symbolise the authentic statistic. Based on the average car range, average electricity consumption per kilometre as well as the predicted Ev directly contribute to the Ed data from 2022 to 2028. The equations in this model are highly relative. Due to the closing relationship among equations, the results are more accurate and dependable with low error. Moreover, the cost-effectiveness analysis process is displayed in the flow chart below.
Through the process in Figure 16, net revenue can be calculated step by step. After calculating OPEX each year, this project has to add CAPEX in the first year and accumulate one by one. In other words, the total cost of a particular year contains CAPEX and all previous OPEX. The way of accumulating revenue is the same. Then, the total accumulated cost in that year minus that of revenue equals to current net revenue. The net revenue results in the tables mean how much net revenue the PCS gains or loses that year. If this result turns the negative number into a positive number, it means that this PCS starts to make a profit. However, the results show that there is no profit. The elements that influence the changes in net revenue have been identified in this project. Thus, two parts can be adjusted by investors. Figure 17

Summary
In this chapter, the parameters and methodology mentioned are applied. The calculation of Ed is elaborated in Section 3, but the prediction of Ev is completed in this section. The U.K. government's data of licensed EVs strongly supports the prediction in this project. Enough statistical support can make the forecast more accurate. Mostly Ev experienced a moderate increase from 2011 to 2020, and fluctuations were seen in a few regions. Linear programming is a reasonable choice because the regulation can be easily spotted through the trends inside. However, the prediction is a mathematical result that cannot symbolise the authentic statistic. Based on the average car range, average electricity consumption per kilometre as well as the predicted Ev directly contribute to the Ed data from 2022 to 2028. The equations in this model are highly relative. Due to the closing relationship among equations, the results are more accurate and dependable with low error. Moreover, the cost-effectiveness analysis process is displayed in the flow chart below.
Through the process in Figure 16, net revenue can be calculated step by step. After calculating OPEX each year, this project has to add CAPEX in the first year and accumulate one by one. In other words, the total cost of a particular year contains CAPEX and all previous OPEX. The way of accumulating revenue is the same. Then, the total accumulated cost in that year minus that of revenue equals to current net revenue. The net revenue results in the tables mean how much net revenue the PCS gains or loses that year. If this result turns the negative number into a positive number, it means that this PCS starts to make a profit. However, the results show that there is no profit. The elements that influence the changes in net revenue have been identified in this project. Thus, two parts can be adjusted by investors. Figure 17 displays how this project works in case the net revenue remains negative during this period. Firstly, a dramatic decrease occurs in net revenue, meaning the revenue of PCS cannot cover its cost every year. On the contrary, the net revenue starts to climb, representing that the revenue of PCS is able to cover its annual cost, even if it is negative. This process can help investors gradually boost the revenue of PCS. Reducing the number of chargers to the minimum can cut the CAPEX and basement of OPEX, which directly decreases the total cost of PCS. However, it can slow down the growth rate of the total cost.  If there is a slight improvement in profit-making, it is reasonable for the business to speed up the growth rate of total revenue by raising the price. The rising price for EV drivers may bring other issues to PCS. As is suggested in Figure 16, the price could be changed more than once. So, investors have opportunities to change the price depending on the facts. For example, managers can slightly adjust the price at the beginning. Based  If there is a slight improvement in profit-making, it is reasonable for the business to speed up the growth rate of total revenue by raising the price. The rising price for EV drivers may bring other issues to PCS. As is suggested in Figure 16, the price could be changed more than once. So, investors have opportunities to change the price depending on the facts. For example, managers can slightly adjust the price at the beginning. Based If there is a slight improvement in profit-making, it is reasonable for the business to speed up the growth rate of total revenue by raising the price. The rising price for EV drivers may bring other issues to PCS. As is suggested in Figure 16, the price could be changed more than once. So, investors have opportunities to change the price depending on the facts. For example, managers can slightly adjust the price at the beginning. Based on the evaluation of the growth rate in net revenue, another price adjustment could be considered. Before investing in PCS in rural areas, the business could estimate the revenue in the following years. This project gives an accessible model for evaluation. It is available for businesses to forecast their financial situation with this model. For managers running their PCS, the model can help them predict how many years they need to pay back, what they invest in or how much they can raise the electricity price. Meanwhile, for investors or companies who plan to install a PCS in rural areas, this analysis process references how many chargers they need, what a reasonable price is, and the possible payback period. Using line charts in this model shows the trend and compares cost and revenue in a onetime line. For example, the point where the total cost meets total revenue represents when this PCS turns loss into net profit. A gap exists after putting two lines into one chart: the value of net revenue. This paper uses two colours, blue and orange, to distinguish them. If an orange line is on top of the blue one, the PCS will make a profit.
This project assumes the same conditions-charger numbers, CAPEX, special electricity price. Once the charger number is confirmed, the only variable is Ed, as presented in Equation (7).
So long as this model presumes the latest payback time is eight years, the minimal total electricity demands of a PCS comes out. This number could be called the 'electricity demands threshold'. In other words, if its total electricity demands reach this 'threshold', the PCS will pay back before 2028.
Investors can adjust this threshold. For instance, if businesses plan to pay back investments in five years, it changes the eight into five based on the Equations (5) and (6): x Year F 1 Total OPEX of 5 years F 1 Total revenue of 5 years The other parameters remain the same. The gap between Equations (8) and (9) equals the value of CAPEX. However, this 'threshold' cannot be changed by random. The lower the 'threshold' is, the less likely the charging stations can pay back their investments. Moreover, the purpose of the 'threshold' is to examine whether the PCS pays back in time.
Even though this model improves the cost and price, most rural PCS are less likely to gain any net profit before 2028.

Conclusions
This chapter aims to summarise all the results given in the whole paper and discuss the limitations and further research.
As listed in Figure 18, the content structure concludes the main tasks done in the project. Firstly, the environmental issues are threatening people, and the transport sector has to be responsible for air pollution, global warming and resource shortages, etc. Governments and authorities, therefore, encourage EVs as an alternative to traditional cars. Due to ever-expanding global EV markets, more charging stations are required to serve EV drivers and meet their electricity demands. Installing a public charging point involves many incentives, from policy to management. To identify how a charging station is installed and works, this project researches existing charging stations nationwide. Although the charger types, charging speed, and cables varied by region, the design concept of the charging infrastructure is the same. The many charging points are suitable for different groups of EV drivers due to their various charging behaviours.
After completing all the preparation tasks, this project has all the critical data and tools. It lists cost and revenue step by step. The data collected were processed with linear programming to forecast quarterly EV numbers from 2021 to 2028, with County Durham used as an example. The first groups of net revenue show no profit over the period. The case of County Durham exposes the intrinsic problems.
After identifying the problems, this paper aimed to identify reasons and provide solutions. According to the calculation processes, two elements can help investors prevent the losses. Furthermore, after addressing issues with those two elements-charger number and sales price-we showed they have a logical relationship, as presented in a flow chart.
Generally, most PCS in rural areas have unsatisfactory cost-effectiveness due to their long payback period. This paper reveals how many rural PCS are able to afford the cost in the first eight years.
It is a dependable reference for businesses, investors, or companies to evaluate the cost-effectiveness of installing charging stations for EVs. Meanwhile, this paper suggests a brand new way of gaining cost-effectiveness for those who experience a negative trend in net revenue.
According to the results of this paper, managing a PCS plays a supporting role in Installing a public charging point involves many incentives, from policy to management. To identify how a charging station is installed and works, this project researches existing charging stations nationwide. Although the charger types, charging speed, and cables varied by region, the design concept of the charging infrastructure is the same. The many charging points are suitable for different groups of EV drivers due to their various charging behaviours.
After completing all the preparation tasks, this project has all the critical data and tools. It lists cost and revenue step by step. The data collected were processed with linear programming to forecast quarterly EV numbers from 2021 to 2028, with County Durham used as an example. The first groups of net revenue show no profit over the period. The case of County Durham exposes the intrinsic problems.
After identifying the problems, this paper aimed to identify reasons and provide solutions. According to the calculation processes, two elements can help investors prevent the losses. Furthermore, after addressing issues with those two elements-charger number and sales price-we showed they have a logical relationship, as presented in a flow chart.
Generally, most PCS in rural areas have unsatisfactory cost-effectiveness due to their long payback period. This paper reveals how many rural PCS are able to afford the cost in the first eight years.
It is a dependable reference for businesses, investors, or companies to evaluate the cost-effectiveness of installing charging stations for EVs. Meanwhile, this paper suggests a brand new way of gaining cost-effectiveness for those who experience a negative trend in net revenue.
According to the results of this paper, managing a PCS plays a supporting role in installation and operations. A well-managed PCS with high cost-effectiveness not only benefits local EVs users, but also travellers. This study has flexibility in its calculations. Based on the results of this study, managers are able to select a rational payback period for their PCS with sufficient data of local EVs. Moreover, cost-control can be applied here by listing related CAPEX and OPEX. Automation and localised renewable energy sources for PCS like solar, wind, hydrokinetic could help standalone charging stations, especially those in the rural areas, to increase their cost-effectiveness.

Limitations
The parameters and variables in those equations have some limitations. The number of E v forecasts vastly exceeds its sample number, which may cause unexpected errors among predictions of later years. Since E d directly corresponds to E v , the error will be added to the whole calculation process. Moreover, the average car range has dynamic changes, which impacts the speed of revenue growth rate.
As aforementioned, the profit gap between sales and electricity consumption remains the same as revenue directly involves E d . Further, the relationship between the sales price and E d is less likely to be expressed in the equation. If investors seek more profit by raising prices dramatically, they may suffer from decreasing sales due to negative reputation.
In fact, before installing a PCS in a certain place, investors need to confirm how many chargers a PCS should have based on local population or EV uptakes. There is little literature material in researching the relationship between charger number and local EV drivers. PCS do not just serve the people in the region as visitors and travellers who pass by may recharge their cars as well. Therefore, the 5% share of public charging events is not accurate in rural areas.

Further Research
The current literature briefly mentions the chicken-and-egg relationship between EVs and charging infrastructure. To what extent they influence each other is unknown, despite the complicity in modelling and constraints. The recharging issues cannot be discussed separately because the charger types and charging speed were standardised by EV manufacturers. Based on the demands of the market, EV producers are switching their business strategies. As the providers, charging stations have to take action to cater to EV markets. The inherent risk is an inevitable factor for private investors, businesses, and companies. The U.K. government is concerned about the whole EV industry. Incentives and policy encourage manufacturers as well as consumers. Meanwhile, the rural areas may become urban. The research on charging points in rural areas has to consider these regulation changes and urban classifications.
When it comes to the analysis of cost-effectiveness, it is possible to bring more elements into the calculation. For the CAPEX and OPEX, the unnecessary cost leaves more profit space, like the possibility of unplanned maintenance costs. In conclusion, the analysis needs more references and more dimensions in order to have a more comprehensive business model. Funding: This research received no external funding from funding agencies in the public, commercial or not-for-profit sectors.

Conflicts of Interest:
The authors declare no conflict of interest.