A novel methodology for the planning of charging infrastructure in the scenario of high EV penetration

This article presents a novel methodology for distribution network expansion planning (DNEP) considering the inclusion of electric vehicles (EVs), especially, electric bus (EB) charging loads. The proposed methodology addresses network congestion through an optimum time of charging, cost optimization, new charging infrastructure, and minimization of losses under a set of technical and physical constraints, which represents practical uncertainties. Along with load flow analysis, selection of the number of ports and technology at the host charging station is obtained through the application of response surface methodology. The proposed methodology provides coordinated planning for the development of EB charging station infrastructure that takes into account the effects of both the power dispersion framework and transportation framework. The effectiveness of the proposed methodology is investigated by applying it to the 69-node IEEE modified distribution test system considering three charging technologies, viz. fast charging, ultra-fast charging, and battery swapping. The results of the proposed model are compared with the direct statistical method, and it revealed that the right selection of technology for EB charging and the right planning of the charging infrastructure can effectively optimize the cost of EV charging infrastructure and thereby catalyze the decarbonization of the transportation sector.


List of symbols
For Residual charge in EB (in kWh) connected at mth CP R l Resistance of line l S n;t Load at node n at time t S min;n;t , S max;n;t Minimum and maximum allowable load at node n at time t S b;f ;ss ; S max b;f ;ss Power (and max power) flow in branch b of the network feeder f at substation ss S i Initial state of EB with a full charge and at first stop of the route S iþ ; S kþ State of EB during one-way trip of first/next round S j State of EB at last stop of oneway trip of the first round S jþ ; S lþ State of EB during the returning trip of first/next round T c FCP Charging times taken by FCT port for an SOC of 90% T c UFCP Charging times taken by UFCT port for an SOC of 80% T c BSP Charging times taken by BST port for an SOC of 100% T FC ; T UFC ; T BS Time periods of the day for which each FCT, UFCT and BST port utilized T FCBL , T UFCBL , T BSBL Useful time span of spare battery charged with: FCT port, UFCT port and BST port, respectively TLL TX init , TLL TX max Initial and maximum thermal loading limits of distribution network transformer TLL L init ; TLL L max Initial and maximum thermal loading limits of distribution network line T P Time horizon of planning T OH Outage hours of load node V n;t

Introduction
Electric vehicles (EVs), along with their charging infrastructures, are being deployed at a fast pace by city administrations across the globe to curb greenhouse gas emissions and reverse climate change. However, without proper planning, the introduction of a large number of charging stations will put an additional burden on the grid and thereby impact grid reliability. The optimal location of charging stations to ensure uninterrupted service of public transport and its impact on the distribution system thereof are matters of great concern to energy planners and policymakers today. Charging station (CS) zones will require meticulous and innovative distribution network expansion planning (DNEP) to meet the additional demand due to the increased number of EVs, especially electric buses (EBs) (Xiang et al. 2019). EBs consume considerably higher energy than personal cars, and unplanned penetration of EBs will increase the losses, voltage drop, and overload the distribution network, which will eventually impact the system reliability and power supply quality (Gomez and Morcos 2002). Past studies show that, without adequate focus on DNEP, even a low penetration rate of EBs may lead to distribution transformer overloading (Li and Bai 2011), overshooting of peak load demand (Shao et al. 2009), and higher power losses (Hadley and Tsvetkova 2009). While planning for the charging infrastructure for the EB fleet, three vital strategic elements are essential to consider: where, when, and how to charge the EBs. Literature reveals that the optimal location of charging stations would improve the EB productivity and deliver unwavering quality and intensity of supply (Zhao et al. 2011), which will eventually encourage consumers to opt for this new mode of transport (Karfopoulos and Hatziargyriou 2013;Dong et al. 2018). Hence, it is important to adopt smart charging technologies and positioning and scheduling of charging stations based on real-time data. The distance between the charging stations needs to be strategically maintained so that the EV users are not stressed over the possibility of a loss of energy in transit as well and make the charging stations' locations progressively sensible and predictable in the real world. Many comparisons of planning strategies have been made by researchers in the past. Zhao et al. 2020 compared over 20 research works related to charging station planning, and the review of the past research shows that none of them considered the integration of various types of charging technology, particularly for electric buses. Zeb et al. 2020 have compared normal and fast charging technologies with ultra-fast charging technology (UFCT) utilizing particle swarm optimization (PSO) technique. It has been shown that UFCT, when used along with photovoltaic generation, is more beneficial in all technical aspects as compared to normal and fast charging technologies. The complexity of planning distribution networks and changing infrastructure increases with consideration of renewable energy integration, as the energy yield of those is intermittent and unpredictable Yadav et al. 2021). A review of UFCT has also been done by Wang et al. 2021, which presents the impact of UFCT on battery life and grid. Along with the optimal setup of the charging station, (Nicolaides et al. 2019) compared the heating effects of diesel vs. electric while using the opportunity charging approach. No doubt that the electrification of any public transport route will yield more profit in the long run than conventional diesel buses. Battapothula 2019 has handled the burden on the distribution grid due to the fast charging station load by optimally placing distributed generators in the system. While doing charging station planning, the most important factors considered are location, required load (which in turn depends upon the number and types of chargers), and investment (Chen et al. 2020).
Presently, load-modeling-based investigation and control methodologies are mainly adopted by the researchers to address the issues discussed above, viz. traffic simulation software (Galus et al. 2012), demographic model (Bessa and Matos 2013), parking generation rate model (Zhang et al. 2014), fuzzy logic system (Jingwei et al. 2014), Monte Carlo technique (Yang et al. 2015), trip chain hypothesis (Tang and Wang 2016), Markov chain hypothesis (Wei et al. 2016), and dynamic traffic flow model (Xiang et al. 2016). Zhang et al. (2019) studied the location of charging stations for EVs and built a charging station location model based on the improved whale optimization algorithm. Most of the works found on charging stations and EVs have been brought up with meta-heuristic techniques. While considering several design parameters and output responses for measuring the relative performance of the units, continuous refinements have been performed by the researchers by creating and combining various effective ranking methodologies for DNEP under uncertainty (Ghosh et al. 2017;Verma et al. 2016Verma et al. , 2019. However, traditionally, DNEP is evaluated and executed through static techniques. In the present work, an innovative, dynamic evaluation and optimization technique was employed for siting and sizing of the host charging station (HCS), based on the response surface methodology (RSM) introduced by Box and Wilson 1951. The proposed methodology reconnoiters the relationships between innumerable critical design parameters and multiple response variables. Though numerous response variables increase the complexity because what is optimal for one response may not be so for the others, this problem can be subdued by reducing the variability of a single response (Khuri and Mukhopadhyay 2010).
RSM is an optimization tool that was initially introduced to advance information factors for obtaining maximum yield reaction parameters of any vitality change frameworks. However, due to its versatility and efficiency, its application has been extended to a wide and diverse field of research. While considering design parameters as battery capacity, PV size, and wind turbine rotor swept area, Ekren and Ekren (2008) optimized the hybrid system cost with RSM. Hasanien and Muyeen (2013) obtained the design parameters for the cascaded controller of the power conversion system unit using the Taguchi method, which was then verified by RSM and the genetic algorithm collaboration approach under the grid fault conditions. RSM has also been applied in the field of EV for the optimization of charging infrastructure design (Bayram et al. 2013) in the past. The authors of this work proposed an effective scheme for the optimization of the charging procedure, which also increased the profitability of the CS operators.
RSM has been applied in the field of machine design as well. The shape of the rotor slots of the EV induction motor was optimized by Jeon et al. (2011), in which the authors reported that the dynamic characteristics of the machine obtained through the application of RSM are most suited to EV. RSM has been reported to be effective in voltage stability analysis in power distribution system planning problems (Haesen et al. 2009, Wang et al. 2019and Ren et al. 2016) as well. Two categories of RSMs, viz. the second-order polynomial and the Kriging method, were applied to evaluate reliability and efficiency in transformer cooling system design optimization . To manage the vulnerability of sustainable dispersed generators and the burden under fault conditions of the power distribution system, an assistance rebuilding technique dependent on stochastic RSM is proposed in Wang et al. (2019).
In the present work, a methodology for quantifying the optimal dispatch and charging of EBs is proposed considering three technologies, viz. fast charging technology (FCT), ultra-fast charging technology (UFCT), and battery swapping technology (BST) through the application of RSM as an optimization tool. A comparative analysis of these technologies is carried out while keeping economy, time of utilization, and infrastructure in mind, along with other technical and nontechnical objectives and constraints. The proposed methodology removed decision-makers' subjectivity in weight assignment to the set of near-optimal solutions and relied on the statistical method, which is well proven in other fields of research. The main contributions of this paper are the following.
(a) A novel methodology is proposed for DNEP for the inclusion of charging stations for EBs, considering both technical and commercial aspects of planning. The placement and the sizing of HCS, along with the number of charging ports (CPs) at each HCS, are considered to be the objective functions of the proposed methodology. (b) Comparative analysis of the multiple near-optimal solutions is carried out against a set of criteria, including power losses, voltage deviations, and setup expenses. (c) RSM is employed in the present work for obtaining the most optimal solutions from a set of near-optimal solutions.
The rationale behind the choice of RSM in the present work as the optimization tool is as below.
2. Most of the other techniques provide one of the best solutions from a set of feasible solutions, whereas RSM precisely provides the optimal solution. 3. RSM provides accurate results under probabilistic analysis (Wang et al. 2019).
Therefore, to handle different design variables, the RSM model built with the help of orthogonal arrays is advantageous for obtaining the optimal solution (Hasanien 2013), and hence, RSM is employed in the present work as an optimization tool.
After this introductory section, the rest of the article is organized as follows. Section 2 presents problem formulation comprising of assumptions, objectives, and constraints. Section 3 describes the EB specifications and battery charging optional technologies considered in the present work. The methodology is discussed in Sect. 4. Results and discussions are presented in Sect. 5. Finally, Sect. 6 delineates the conclusions of the present work.

Problem formulation
The main objective of the present work is to derive the placement (location) and sizing (number and capacity of charging ports) of HCS, considering several economic, technical, and nontechnical objective functions, under physical and capacity constraints. Also, several parameters are considered based on the socioeconomic characteristics of the region under study (the city of Delhi, India, in this case) to increase the feasibility of the solution. The complete methodology adopted in the present work is delineated in Fig. 1. In order to make the problem formulation closer to the real-world scenario, in the present work, the parameters and constraints of the city of Delhi, India, are considered. For the present case (i.e., the city of Delhi), the Government of Delhi (GoD) has planned the induction of 1000 EBs and identified six locations for constructing the parent charging stations (PCSs), which will facilitate parking and charging the EBs overnight by normal charging mode. For ensuring equal distribution charging load, about 166 EBs are allotted to each PCS. Further, each PCS will cater to several sub-PCSs (e.g., Rohini PCS is planned to have four sub-PCSs), and, hence, each sub-PCS will be catering to about 40-45 EBs. The schedule and route of plying of EBs are considered to be the same as that of the presently running busses on compressed natural gas (CNG). Practically, the length of all the routes is greater than 50 km, and each bus is required to ply to and fro (from the PCS to the end of the route) at least twice per day. The stoppage time (or idle time) is considered as ten seconds for embarkation and disembarkation of commuters at bus stops, stoppages at traffic signals, and stoppages on-road due to congestion. The maximum speed of the chosen EBs is considered to be 75 km/h, and the maximum distance which can be covered by those is considered to be 151 km per charge (full). 1 Hence, the EB running at any specific route will require midway charging to ensure uninterrupted service to the commuters. Normal charging will require more than two hours for recharge, which will not be a feasible option for charging while the EBs are in transit.
In the proposed solution, a different mode of charging is considered for different times of the day. The EBs shall be charged at their PCS in normal mode and leave the PCS in a fully charged condition. For refresh charging while plying between the PCS and the final stop, the EBs are considered to halt at HCSs and get charged by either FCT, UFCT, or BST. For all EBs as well as for BST spare battery units, the Li-ion battery is considered for the present case.
Assumptions Assumptions on some of the parameters are made regarding the optimization model, information on which is not available in the public domain. These assumptions may vary as per the discretion of the planner, for studies on different cities based on the priorities and objectives to be achieved, equality, and inequality constraints for keeping the pool of solutions under bounded conditions. While considering the overall cost, capital cost for extra batteries and setup cost for HCS is assumed in the present work, as detailed information on the same could not be found. The cost of land required for setting up the charging stations is not considered while estimating the overall cost. It is assumed that excess land available with city public transport authorities shall be used for setting up the charging stations. The EB battery charging process is considered to be continuous, i.e., without any voltage fluctuation and power cut, until the charging state of up to 85% capacity is reached. It is also considered that every EB will get seven hours in the night for a full normal charge, and it will leave PCS with full SOC.
Each fast and ultra-fast charging point is considered to be equipped with smart metering and load control capability. EBs cannot deliver power back to the grid, so the bidirectional flow of electricity is not considered. The EBs battery capacity utilization depends directly upon the actual distance traveled. A safety margin charge reserve is kept for every EB to deal with all odds against running out the power capacity.
DC chargers are considered instead of AC ones, as in the case of AC chargers, high-power rectifiers will be required to be installed in EB, which will consume additional space and will increase the cost of EB. Battery swapping technology consists of a charging system (done with normal charging technology (NCT)) and a robotic swapping mechanism. The charging of spare batteries can be done on-station as well as off-station. Off-station charging may be done to take advantage of the lower tariff in case of space scarcity.
The charging process of spare batteries is considered to be a continuous and cyclical process (24 h). The spare batteries will get charged by NCT in 6-7 h, whereas the swapping process will take place in around 5-min duration. While the EBs will get charged overnight by NCT at PCS, the charging of spare battery packs will happen at HCS. The side-swapping method is considered in the present work for BST operation. Considering one swapping per hour, every HCS must have a minimum of 8 spare charged batteries, and further, if the number of ports is greater than 5, then the number of spare batteries must be equal to the thrice number of ports available at that particular HCS.

Objectives
This section describes various technical and nontechnical objectives taken into consideration for optimizing the charging of EBs with optimal DNEP.
(a) HCS investment (HCSI): The first objective function considered for the optimization model of DNEP is to minimize the total investment for each type of HCS, as noted in (1) where the terms used can be explained with the following equations ((2)-(5)): The first, second, and third terms in (1) represent charging ports' cost of the fast, ultra-fast, and battery swapping technologies, respectively. The fourth term represents capital cost, the fifth and sixth terms represent spare battery cost and robotic arm cost, respectively, and the last term represents the subsidy provided by the Government of India (GoI). All N represent various port quantities.
(b) Number of Charging Points (NCP): As per the GoI guidelines for setting up EV charging infrastructure (under Faster Adoption and Manufacturing of Electric Vehicles (FAME) India Scheme, phase-II), a minimum of five chargers of any one or combination of slow and FCT is mandatory (TGOI 2019; DHI FAME-II 2019). In the present work, all the NCPs are considered to be a combination of BST-, FCT-, and UFCT-based ports. Because of space constraints in the city, the maximum NCP is considered as 25. The number of configurations is a function of N and may be obtained using (6) where a is the initial number of CP considered for any charging technology (i.e., one for all the cases and a minimum of 3). (c) Plug-in period (PIP): The plug-in period is considered as the average time taken by each EBs in the queue to get charged in a scenario when all the charging points in an HCS are occupied (in use). Plug-in period is governed by (7).  (8).
As the sensitivity of the voltage level has a negative correlation with the proximity of additional load to the transformer (Richardson et al. 2012), EBs connected closer to the transformer will get charged at a higher rate, especially in a radial distribution network. To balance the load on the distribution network for maximizing its capacity utilization, the charging rate of each EB must be optimized to maximize the energy delivery to all connected EBs at all times. So, to rank batteries with a low residual charge in battery (RCB), while assuming that the RCB of each EB is known at the commencement of individual optimization time step (a short time interval of 15 min is assumed), the function for maximization of energy delivery to all EBs is expressed as in (9).
This energy delivery optimization will ultimately impact the battery life in the long run; hence, (9) is also considered as the objective for achieving longer battery life. Here, x m which denotes the status of EB connection with CP will be '0' when not connected and is '1' when connected. Hence this energy delivery to all EBs is considered as an integral part of BL.
(e) Power requirement (PR): Total PR (including operational power required for each HCS) is governed by (10).
(g) Tariff (TR): The tariff fluctuates as per the power demand. The demand depends upon the type and number of charging ports. Tariff calculations per month are governed by (12) where

Constraints
At each time interval, the objective functions described in subsection 2.2 can be optimized (minimized or maximized) subject to certain constraints. To obtain optimal values of system losses, power flow, thermal loading, and optimal EB charging, the following constraints are considered in the present work.
(a) The energy-storing system constraints are described as follows. The boundation on the power supply to the battery in any time interval (which cannot exceed the rated charging power) is expressed by (16).
Moreover, the boundation on the energy stored in the battery in any time interval (which cannot exceed the rated capacity) is expressed by (17). A charging rate variation constraint is also imposed by (18) keeping in mind the present battery technology (Hadley and Tsvetkova 2009 where I n;t ¼ I l;t À I lþ1;t ð20Þ s:t: S n;t ! S min;n;t ð21Þ S n;t S max;n;t ð22Þ X t S n;t ¼ E tot;n ð23Þ (c) The constraint for maintaining voltage level and deviation (V dev ) within allocated limits can be summarized as in (24) and (25).
(d) Branch current flow constraints are expressed as (26).
ð26Þ (e) Operational radiality of the distribution network is imposed by (27), which will ensure that the basic rules are obeyed in the planning model (Zhang et al. 2014 (f) The thermal loading constraints for distribution network transformers and lines are summarized in (28) and (29).
(g) Power flow capacity constraints can be quantified by (30).
(i) During DNEP for charging EBs, constraints on charging stations are given by (33), which also ensures that at least five new charging points (term N CP2 ) can be added to the existing station.
(j) The proposed HCSs will exclusively serve the EBs, which will have to be commercially viable and, hence, the least plug-in-period (PIP) is to be ensured to avoid loss of revenue due to waiting time. Hence, a PIP constraint is imposed on every HCS to achieve the financial sustainability of the EB operation, which can be mathematically expressed by (34).
where the minimum duration needed to plug in EB to achieve desirable charging requirements (T min i;t ), which can be mathematically defined as: 3 EBs charging: when, where, and how?
It is considered that the location of the HCS on each route should be such that the EBs reaching the HCS shall have SOC of 10 to 20%, and 80 to 85% while leaving. This is so because the EBs must reach the HCS before complete drain-out and will leave the HCS before 100% SOC as the last 20% of charging is slow and require more time as compared to the time taken to reach 20% to 80% SOC. The charging and discharging state alteration process of EB is shown in Fig. 2, in which the terms shown outside the circle have the following interpretations: represents the driving state of ith EB, a i ¼ 0 represents the ideal state of ith EB, a i ¼ 1þ normal charging or fast charging of ith EB at PCS a i ¼ 1 þ þ ultra-fast charging or battery swapping of ith EB at HCS

Methodology
In the present work, a 69-node IEEE modified distribution test system (Savier and Das 2007) is considered to evaluate the effect of EBs' charging on power quality and reliability. The reconfigured system is modified by utilizing tie switches based on the fuzzy multi-objective approach. The single-line diagram of the 69-node IEEE modified distribution test system, as shown in Fig. 3, has 68 branches with normally closed switches without any tie lines. The current carrying capacity of branches 1-9 is 400 A, of branches 25, 40, 49-51, 53-59, 61-65 is 300 A, and for the rest of the branches is 200 A. The system base voltage and MVA are assumed at 12.66 kV and 100 MVA, respectively. The rest of the section is divided into three parts describing design parameters, output responses, and the methodology used.

Direct statistical method (DSM)
For producing the pool of feasible solutions, a direct statistical method is utilized. The computational region for optimizing the sitting and sizing of HCS is based upon seven objectives. To strengthen the mathematical modeling of various objectives, the considerations are explained below.
(a) Host charging station investment (HCSI): Creating apposite FCT infrastructure is the key to speedy electrification of the bus fleet. However, the following two concerns are typically cited as crucial issues -minimization of the cost of the FCT infrastructure and upgradation of the power system for coordinating the charging load. HCSI is one of the design parameters for the present work. Main terms are considered in (1), and their further classifications are given in (2)- (5)). The capital cost for setting up HCS in India is calculated based on the data given in Table 1.
Three swapping robotic arms are considered for each HCS configuration. An exchange rate of`74 per USD is considered while calculating the capital cost. (b) The number of charging points (NCP): Table 2 shows the number of configurations of charging ports at HCS formed due to various charging technologies (as per (6)), which sum up to 3241 configurations. For example, if the total charging ports to be installed at an HCS are 6 (BST-, FCT-, and UFCTbased ports), the second row (no. of configurations) presents total permutation and combinations of 6 ports.  A subsidy of 70% earmarked by GoI on electrical vehicle supply equipment includes chargers, cable, smart metering, energy meter, breakers, etc. The upstream electrical infrastructure investment (which also includes transformers) is not included under this subsidy. As of now, there is no clarity on subsidy on spare batteries for the swapping process (c) Plug-in period (PIP): PIP is calculated by considering that, for a particular CP configuration, all types of CPs are occupied, and the next EB in the queue will require an average time of all types of CP duration (expressed in (7)). The charging time is considered as 5, 15, and 120 min for BST, UFCT, and FCT, respectively ). In the case of battery swapping, the charging time will be the same as normal charging. However, the time which is considered in the present work is the time that the EB will consume in the swapping process. (d) Battery life (BL): Battery life is considered 'long' for normal charging. Accordingly, the governing equation for average BL, the expression may be represented by (8), and for economic consideration, (8) must be maximized. (e) Power requirement (PR): Total power required (including operational power required) for each HCS is governed by (10). The whole planning revolves around the power required for charging EBs in a minimum time frame. Hence, this response is maximized during optimization compared to other DNEP problems, where the planner targets to minimize this response. (f) Total System losses (TSL): The fundamental objective and constraint equations for total system losses are described in (11) and (19)- (23), respectively, and the calculations are carried out by performing load flow analysis on 69-node IEEE modified distribution test system (see Fig. 3) in MATLAB R2017a environment. It is obvious that the minimization of TSL is targeted in the present work. (g) Tariff (TR): Delhi electricity regulatory commission has introduced a separate energy tariff (substantially lower than the industrial tariff) for EV charging stations, which is`4/kWh for charging from the HT network and &hu20B9; 4.5/kWh for charging from the LT network (DERC 2019). There are no fixed monthly charges applicable as well. The same is considered in the present work. Tariff calculations per month is governed by (12). UFCT port utilization-based consumption is considered 4 h for up to 10 ports, 3 h for 10-20 ports, and 2 h for more than 20 ports. A 20 kW of continuous (for all-day) load is considered for the rest of the power consumed in HCS. As per the guidelines of the Ministry of Power, GOI (GoI-MoP 2018), for normal charging (as well as for battery swapping), 15 kW (model-Bharat DC-001) charger and, for fast charging, 50 kW (CHA-deMO) charger is considered for each charging port. The off-board DC chargers for ultra-fast charging are considered superchargers having 450 kW capacity (Muratori et al. 2019). From a total of 3241 configurations, the maximum and minimum values of the seven objectives are summarized in Table 3.

The optimization model: RSM
Response surface methodology (RSM) is an optimization technique used to acquire the exact models of the design parameters in terms of response factors in the wake of recognizing their relative commitment, utilizing the Taguchi technique. The strategy for steepest ascent/descent can be successfully used to recognize the ideal estimations of the responses. RSM addresses a diverse set of queries, for example:  A novel methodology for the planning of charging infrastructure in the scenario of high EV penetration 5633 (a) How is a specific output influenced by a given arrangement of information factors over some predetermined area of interest? (b) To what extent, the information sources are to be controlled to give an item, fulfilling required details. (c) What estimations of design parameters will yield the greatest for an appropriate response, and what is the idea of response surface near the most extreme?
If the output is very much displayed by a direct capacity of the autonomous factors, at that point, the approximating capacity is the first-order model. If there is a curvature in the framework, at that point, a polynomial of a higher degree must be utilized, for example the second-order model. This model would almost certainly be valuable as a guess to the genuine response surface in generally smaller sections. The second-order model is generally utilized in RSM for the following reasons: (a) The second-order model is truly adaptable. It can take on a wide assortment of practical structures, so it will regularly function admirably as a guess to the genuine response surface. (b) Utilizing the technique for least squares, it is easy to evaluate the parameters in the second-order model.
There is significant handy experience as well as literature available, showing that second-order models function admirably in taking care of genuine response surface issues (Haesen et al. 2009;Ren et al. 2016;Wang et al. 2019). The relationship between a response (y) and of the set of associated design parameters (x 1 ; x 2 ; . . .; x k ) can be mathematically expressed as in (36).
And, for a second-order model, it is expressed as in (37)-(38).
where x ¼ x 1 ; x 2 ; . . .; x k , and f 0 ðxÞ is a vector function of elements p which consists of powers and cross-products of powers of x up to a certain degree represented by the positive integer d, b is a vector of p unknown constant coefficients (parameters), e is random error in the experimental result, n is number of experiments and x ui is the uth setting of the ith control variable. Here, u ¼ 1; 2; . . .; n. Central composite design (CCD): One of the most popular second-order designs: CCD consists of three constituent parts (Khuri and Mukhopadhyay 2010). The first one is a factorial portion, which consists of 2 k factorial design whose factors' levels are coded as À1; 1. The second one is an axial portion consisting of 2k points arranged so that two points are picked on the hub of each design parameter at a distance of a from the design center. And the third segment is n o center focuses. So, the total number of design points in a CCD may be evaluated by (39).
Taguchi's approach: The design parameters of any process can be classified as control parameters (which are easy to control) and noise parameters (which are difficult to control). The noise factors are the reason behind numerous output responses. The fundamental point of parameter configuration is to decide the settings of the control factors for which the procedure reaction is robust to the inconstancy in the framework brought about by the noise factors. To accomplish this objective, Genichi Taguchi advocated the use of crossed arrays by crossing an orthogonal array of control variables (internal array) with an orthogonal array of noise variables (external array) (Khuri and Mukhopadhyay 2010). Taguchi identified three specific goals (minimize, maximize, or achieve the target value of the response) in a process and defined them with a signal-tonoise ratio (S=N). This S=N performance criteria (considering both processes mean and variance) can be expressed as: where y and s 2 are the sample mean and variance, respectively.

Design parameters and responses
As per Taguchi's approach, for the mathematical modeling of the second-order RSM methodology, design parameters are considered as: the number of charging points (NCP), the investment required for setting up HCS (HCSI), energy tariffs (TR), and plug-in period (PIP).
The objective of the proposed charging strategy is to find the optimal location of charging stations along the plying route such that the total travel time, including driving time from the current location to the destination HCS, waiting and charging time at HCS, and the charging cost, is minimized while capacities of the HCSs are fully utilized. To achieve the above objective, the responses considered are: power requirement (PR), total system losses (TSL), and battery life (BL).

Results and discussion
After performing load flow analysis on the 69-node IEEE modified distribution test system in MATLAB R2017a environment and financial analysis on considered configurations for optimal siting of HCS, the results for optimal sizing of HCS using RSM are carried out in the present work. The following subsections present the results of the above analysis, i.e., the calculated results of the impact of design parameters (NCP, HCSI, TR, and PIP) on output responses (PR, TSL, and BL) of the optimization process with RSM and, finally, the results obtained from RSM are verified with those of the calculated results. The results are depicted with the help of surface plots for output responses. These surface plots relate one response with two design parameters (out of four) at a time while keeping the rest of the two design parameters constant. These hold values are the central value of the CCD Table. As per Table 2, after calculation, a total of 3241 responses are obtained, whose summary is presented in Table 3.
The optimized location for sitting of HCS comes out to be nodes 17, 18, or 19. In the following subsections, the results obtained from RSM are discussed.
6.1 Effect of design parameters on power requirement (PR) Figure 4 presents the surface plots of variation in PR with the change in various design parameters. Figure 4a represents the effect of NCP and HCSI on PR while keeping TR and PIP at hold values of`2.736 million and 25 min, respectively, which shows that PR increases with an increase in NCP as well as HCSI. Initially, the change in PR is gradual with the variation of NCP as in the beginning; the charging ports configurations are based on BST ports. BST ports require less power for operation as compared to that of the other two technologies. After NCP reaches a value of 12, the variation in PR increases exponentially because, for a higher value of NCP, the FCT and the UFCT ports dominate over BST ports. It can also be seen from Fig. 3a that the PR varies almost linearly with HCSI. Figure 4b shows the effect of TR and PIP on PR while HCSI and NCP are kept at hold (`48.75 M and 15, respectively). It is evident from the curve that there is an exponential increase in PR with the increase in PIP since, as compared to BST ports, an increase in FCT and UFCT ports will sharply increase PR and also will take more plugin time due to their charging characteristics. Similar relations are obtained when the combinations of design parameters are changes. The trends show that PR has an almost linear and increasing relationship with all four design parameters. This indicates how the power requirement for various technology ports will increase with an increase in all four design parameters.
6.2 Effect of design parameters on total system losses Figure 5 depicts the effect on TSL with variations in design parameters. Figure 5a shows the variation of TSL with NCP and HCSI while keeping the other two design parameters constant (hold). The trend shows a slight reduction in TSL initially and then a considerable increase in losses as NCP increases further. This tendency is validated by the fact that in the beginning, the number of BST ports is less, the FCT and UFCT ports dominate, and hence the PR increases exponentially. Later, with changing configurations, the number of BST ports increases (hence the number of the FCT and UFCT ports decrease), while the PR decreases. The required investment increases when the number of FCT and UFCT ports increases. Along with the investment, losses increase as well, as they consume bulk power, whereas the BST requires normal power for longduration charging of spare battery packs. The plug-in period also increases with higher penetration of these two technologies and, hence, after a slight dip in losses initially, those increase with an increase in PIP (Fig. 5b). These subplots clearly show that TSL value increases with an increase in TR and attains a peak value when all the ports considered are of UFCT type while HCSI and PIP are kept on hold. Total system losses have the same trend as that of power requirement and that is because those have a positive correlation. Figure 6 shows the graphical plot of BL with the change in various design parameters. It may be noted from Fig. 6a that BL value monotonously decreases with an increase in both NCP and HCSI, from an initial peak value, and attains minimum value at maximum NCP and HCSI. The reason behind this nature of the plot is that BL is maximum in the case of BST and minimum in the rest of the two charging technology. The same trend is noted for the variation of BL with PIP (Fig. 6b). Although there is no direct relation between TR and BL, even though indirectly, the BL decreases with an increase in TR. It may be concluded from the results that except for BST ports, all other fast chargers will decrease the life of the battery, whether it is a spare one, or the one mounted on EBs.

Effect of design parameters on battery life
The battery life is observed to decrease with an increase in PIP and with more usage, apart from an increase in the number of FCT or UFCT ports. It is high initially for all the cases because the initial port configuration consists of BST ports that charge spare battery packs with the least charging power and in a maximum allowable time frame.

Optimization reaction
The present study primarily focuses on optimizing the sitting and sizing of HCS through the application of the RSM technique. The results obtained through the analysis are summarized in Fig. 7

Validation of results
The results obtained from RSM are compared with the responses attained from the DSM calculations, and the closest ones are shown in Table 9. Table 10 presents the results justification with percentage variation to the optimized design parameters and output response values obtained from the RSM optimizer. The % variation for the optimal sitting and sizing of HCS response parameters PR (MW), TSL (MW), BL (Yr) are 2.46%, 1.49%, and 3.52%, respectively, and all are well within limits. This indicates that RSM methodology can be adopted for the prediction of best-suited HCS sizing input parameters for optimized performance responses. Out of a total of 3241 calculated responses, the closest and optimal solution provided by RSM is of 16 charging ports (consisting of 3 FCT ports, 4 UFCT ports, and 9 BST ports). The best location for the optimal sitting of HCS comes out to be at nodes 17, 18, and 19 (see Fig. 8) with a minimum voltage of 0.921 p.u. at node 57.

Conclusion
Faster adoption of EVs and EBs will help the global community deal with environmental pollution and climate change. However, this will also put additional stress on the distribution network. Hence, DNEP will be of paramount importance as the penetration of EVs and EBs increases. A novel technique is proposed in this paper for solving the DNEP problem, considering the integration of parent and host charging stations. In the proposed model, various parameters such as the number of charging ports, types of charging technology, and power requirements are optimized under the predetermined constraints of voltage fluctuation, minimization of losses, and plug-in period. It can be concluded from the analysis that BST is the most efficient option in all considered charging port categories' permutations and combinations. However, under practical constraints, when a combination of technologies is to be used, an entwined network of a low number of FCT and UFCT with maximum counts of BST emerges to be best suited. Out of a total of 3241 calculated responses, the closest and optimal solution provided by RSM is 16 charging ports (consisting of 3 FCT ports, 4 UFCT ports, and 9 BST ports). The best location for the optimal sitting of HCS comes out to be nodes 17, 18, and 19 with a minimum voltage of 0.921 p.u. at node 57.
The methodology can be implemented considering the projected requirement to meet future demand. By keeping two out of four design parameters non-variable (fixed at mid-point value), the methodology presents the variation of each response with the other two variable design  parameters. The results provide a vast field of choices for the HCS planner to choose and prioritize design parameters. As a case study, data of the city of Delhi, India, are used in the present work. The proposed methodology will help the planner prioritize and integrate a significant number of charging points of different technologies into the distribution network without adversely affecting its reliability, stability, and performance. As a scope of future work, the proposed model can be further improved by considering the following.
(a) Recompute a fresh power assignment profile during the day itself, considering the personal and commercial EV charging at night. (b) In highly polluted cities like New Delhi, India, to reduce the impact on the environment further, the power generation for charging stations may be from renewable energy sources. (c) The spare capacity of the HCS can be utilized for private and commercial EV charging. (d) The temperature variation factor has not been considered in the present work, which can be included in future work.
Funding The authors have not disclosed any funding.
Data availability Enquiries about data availability should be directed to the authors.

Declarations
Conflict of interest The authors declare that they have no conflict of interest.
Ethical approval The article does not contain any studies with human participants or animals performed by any of the authors.