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1. Cleaner Energy Systems 4 (2023) 100048
Contents lists available at ScienceDirect
Cleaner Energy Systems
journal homepage: www.elsevier.com/locate/cles
Multiobjective optimal operation strategy for electric vehicle battery
swapping station considering battery degradation
Astha Aroraa
, Mohit Murarkaa
, Dibakar Rakshita,∗
, Sukumar Mishrab
a
Department of Energy Science and Engineering, Indian Institute of Technology Delhi 110016, India
b
Department of Electrical Engineering, Indian Institute of Technology Delhi 110016, India
a r t i c l e i n f o
Keywords:
Electric vehicles
Charging infrastructure
Battery swapping
Cost optimization
a b s t r a c t
The study aims to analyze a futuristic view of the automobile industry conducive to the much-needed penetration
of Electric Vehicles (EVs) as per the current environmental and economic scenario. The study suggests the roll-out
of EVs in tandem with the supporting Charging Infrastructure, which is a prerequisite for adopting the former.
Although transport electrification is a much-accentuated and researched solution to the deteriorating environment
and plummeting conventional resources, the design, production, manufacturing, use, degradation, and disposal of
an exponential number of lithium-ion batteries for the same have environmental, economic, and social impacts.
Thus, emphasis has been made on the sustainable use of charging infrastructure that curbs unnecessary and early
battery aging from fast charging technology. Battery swap requests at a Battery Swapping Station (BSS) can be
served via batteries from either available battery stock or by charging previously incoming discharged batteries.
The study suggests an optimal strategy for the same via a mathematical model representing the operation cost of
a BSS consisting of three components, namely, cost of battery utilization, damage cost associated with different
charging methods, and dynamic electricity cost. The solution to the multiobjective optimization problem gave the
optimum number of batteries that should be used from the battery stock and the charging decision for incoming
discharged batteries, given the possible charging options and the constraints on demand satisfaction. Finally, the
results from two different optimization tools, Solver in MS Excel and Lingo software, were compared.
Introduction
An exponential surge in population and economic standards has
given rise to a proportionate swell in energy demand. Global final en-
ergy consumption has been observed to increase by 1.5 times in 20 years
from 2000-2019. The transport sector alone accounts for 29% of the final
energy consumption as of 2019, as depicted in Fig. 1 (Data & Statistics
- IEA [WWW Document]).
Considering the geopolitical trends and uneven distribution of fi-
nite resources across the globe, there is a substantial increase in gas
prices, causing numerous nations to switch from gas to coal. This,
in turn, leads to increased emissions. The trend has been observed
to mount due to the current geopolitical unrest surrounding Ukraine
(Energy Agency, 2022). 44% of the total CO2 emissions can be at-
tributed to coal as the primary energy source, followed by oil and
natural gas. The transport sector contributes 25% of these emissions
Abbreviations: E-mobility, Electric Mobility; EV30@30, 30% EV sales in 2030 globally; INR, Indian National Rupee; DISCOMS, Distribution Companies; HPC,
High Power Charging; LP, Linear Programming; IEX, Indian Energy Exchange Ltd.; SoC, State of Charge; PM2.5, Particulate Matter 2.5 micrometer; GHG, Green
House Gas; MINLP, Multi-Integer NonLinear Programming; IEA, International Energy Agency; XFC, Extreme Fast Charging; QoS, Quality of Service; GST, Goods and
Services Tax; ToD, Time of Day; GRG, Generalized Reduced Gradient; NEMMP, National Electric Mobility Mission Plan.
∗
Corresponding author.
E-mail address: dibakar@iitd.ac.in (D. Rakshit).
(Data & Statistics - IEA [WWW Document]). With the exponentially
multiplying transportation sector (road transport in particular) and no
considerable change in the carbon intensity of road transport energy
consumption, this is expected to worsen. As per the Global Air Quality
ranking based on average annual PM2.5 concentration in (μg/m3), 46 of
the world’s 50 most polluted cities belonged to Central and South Asia.
Transportation constitutes one of the leading PM2.5 emission sources,
which is responsible for emitting pollutants and resuspending road dust
in most regions like Central and Southern Asia, North America, China
Mainland, Columbia, and South Africa (Abbafati et al., 2020). The afore-
mentioned poses a significant challenge to rampant global warming, pol-
lution, declining air quality, and scaling average earth temperature. As
a result, the countries look forward to a clean and sustainable energy
transition for an efficient and effective solution.
EV, an early invention from the mid-19th century, offers to change
the alpha and omega of the automobile industry. It has advantages like
https://doi.org/10.1016/j.cles.2022.100048
Received 24 September 2022; Received in revised form 14 November 2022; Accepted 4 December 2022
Available online 5 December 2022
2772-7831/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

2. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
Fig. 1. Time trend of total final energy consumption by sector in the world.
Fig. 2. Time trend of global EVs sale.
higher propulsion efficiency than the conventional Internal Combustion
Engines (ICE) in a wide range of speed and torque and smoother speed
control. Empirical studies also depict the impact of the introduction of
EVs on the mitigation of pollutant emissions and the reduction of emis-
sions of sulfur dioxide (SO2), nitrogen oxide (NOx), and inhalable parti-
cles by substantial percentages (Yu and Li, 2019). With considerable ad-
vancement in research and technology, EV adoption trends are picking
up pace. The global electric car stock touched the 16.5 million mark in
2021, with China, Europe, and the United States as the EV market’s key
players, as depicted in Fig. 2. In China alone, 3.3 million EVs were sold in
2021, more than that in the entire world in 2020 (Energy Agency, 2022).
While in countries like Brazil, India, and Indonesia, fewer than 0.5% of
car sales are electric. Specific barriers to EV proliferation, such as range
anxiety, high upfront cost, extended charging periods, and lack of suffi-
cient and all-congruent charging infrastructure, still requires prominent
solution (Online Document).
The charging infrastructure is not yet adequate to accommodate the
impending automobile transition. The global stock of publicly accessi-
ble charging stations stood at 1.3 million as of 2020, of which 30% were
fast chargers. Thus the global public Charging Station (CS) or Electric
Vehicle Supply Equipment (EVSE) to EV ratio was 0.13, surpassing the
set target (0.1 EVSE/EV or 10 EV/EVSE) for publically accessible charg-
ers by the Alternative Fuel Infrastructure Directive (AFID). But most
individual nations like Europe (0.09 EVSE/EV), the United States (0.06
EVSE/EV), India (0.04 EVSE/EV), and New Zealand (0.02 EVSE/EV)
were not able to achieve this target (Report). While most charging
occurs at home/work, deploying publically accessible fast chargers is
critical to facilitating longer journeys and encouraging EV adoption.
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3. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
Although extensive R&D is deployed to look into DC fast, extreme fast,
and high-power charging, technological and economic barriers exist.
Thus, there is a need for substantial investment and promotion of envi-
ronmentally and socially sustainable practices for EV market expansion.
Hence, BSSs have drawn considerable attention as a faster, more conve-
nient, cheaper, and safer solution. But BSSs come with their unique chal-
lenges like the need for standardization of batteries, vehicles, and swap-
ping infrastructure, an operation model to address ownership, mainte-
nance, and payment of shared batteries, expensive initial BSS construc-
tion cost, and reduced efficiency of the system due to low congestion at
swapping stations.
The proposed study attempts to address a few of these challenges.
Literature review shows that no previous research has suggested a ver-
satile, real-time decision-making model for serving incoming battery
swap requests at a BSS using the same approach. Previous researchers
have worked on some algorithms for the deployment of BSS. Still, most
of them are either computationally extensive with many variables and
constraints or location and vehicle fleet specific. The novelty of our pro-
posed multiobjective model is its simplicity and the utilization of com-
prehensive and commercially viable tools for optimization. Moreover,
the model is flexible to any changes in its input parameters, like differ-
ent costs associated with a BSS and geographic location.
Literature review
Still in a nascent stage, the global EV market needs an exhaustive
study of the potential challenges to the e-mobility industry so they can
be addressed effectively. Many countries have less than 1% market share
for EVs despite the plethora of initiatives and policies toward the col-
lective goal of EV30@30 (Report). Although automobile manufacturers
promote EVs as ‘the future of mobility,’ along with a bunch of govern-
ment incentives, EV diffusion into the transport sector is scant.
Potential barriers to EV adoption
Critical insights have been obtained via empirical analysis regarding
EV adoption in India (Bhattacharyya and Thakre, 2020). On the sup-
ply (stakeholder) side, the critical factor identified was the choice of
charging technology (electric charging/battery swapping) followed by
charger configuration. On the demand (consumer) end, the most influ-
ential factors were high upfront cost and availability of charging sta-
tions. Similarly (Foley et al., 2020) investigate why some nations fall
behind in the EV market. The study uses Australia’s EV market share
of 0.4% and compares different variables against EV sales through sec-
ondary and descriptive analysis. The high initial cost is identified as the
primary barrier, followed by a lack of adequate charging infrastructure.
One of the key obstacles to adopting EVs is the limited capacity of
batteries, which necessitates frequent charging. Although a larger bat-
tery capacity would reduce the charging requirement, it would sub-
stantially increase the weight of EVs, minimize efficiency and lengthen
charging times (Chen et al., 2021). EV users suffer from range anxiety
despite range extension because of infrastructure scarcity. The same is
not true for Internal Combustion Engine Vehicle (ICEV) users, as ample
refueling stations exist. The ‘detachable’ nature of fuel (oil/gas) from
vehicles relieves users’ anxiety. While a level-2 AC CS takes several
hours to charge, a DC or fast CS can bring an EV’s battery up to 80%
of its rated capacity in around 30–60 min, depending on battery capac-
ity and environmental temperature. An extreme fast charger (XFC) and
high power charger (HPC) offering 350kW power and higher, respec-
tively, can recharge an EV with a 200-mile range in less than 10 min
(Brenna et al., 2020). But fast charging negatively impacts battery life
and may lead to instability and insecurity problems for the power grid.
Various literature (Rezvanizaniani et al., 2014; Tomaszewska et al.,
2019; Yang and Wang, 2018) mention the effect of charging rates on
battery health. High charging or discharging rates can accelerate battery
degradation resulting from electrolyte decomposition and Solid Elec-
trolyte Interphase (SEI) formation on graphite anode. This may ulti-
mately lead to capacity fade through the loss of active lithium and other
active materials (Pelletier et al., 2017). Another study based out of China
proposes a comprehensive environmental analysis of the types of elec-
tric vehicle chargers and the associated energy consumption, emissions
during manufacturing, use, and end-of-life stages (Zhang et al., 2019).
The results depicted that the home charger had the lowest cumulative
energy demand and global warming potential. In contrast, the public
mix chargers (integrating both AC and DC) were found to be the worst
of all charger types compared. Some studies even suggest that the life
cycle assessment of EV charging infrastructure had higher energy con-
sumption and CO2 emissions than ICEVs.
A comparative study between ICEVs and battery vehicles based
on life cycle assessment presents a review of sustainability challenges
linked to alternative technologies that are often missed in the environ-
mental debate (Lavrador and Teles, 2022). The sensitivity of EV technol-
ogy to the availability of finite mineral resources like lithium, graphite,
cobalt, dysprosium, terbium, praseodymium, and neodymium poses sig-
nificant supply risks for this industry. Moreover, 70% of the battery-
producing capacity is in China, and most of the supply chain might re-
main Chinese till 2030 (Global Supply Chains of EV Batteries – Analysis
- IEA 2022 [WWW Document]). The increasing EV sales and the war in
Ukraine have collectively exacerbated the prices of critical raw mate-
rials like cobalt, lithium, and nickel surging. As the emphasis on road
transport electrification increases to achieve the net zero ambitions, the
demand for EV batteries and the consequent need for critical materials
is expected to mount. This gives rise to environmental challenges like
possible damage from mining and battery leaking.
Moreover, there are challenges in structuring markets for recycling,
reusing, repurposing, and adequate final battery disposal in the national
chain. The rapid growth and innovation in the Lithium-ion Battery in-
dustry give rise to uncertainty regarding investment for future growth,
hence, calls for regulations that create a framework for stable operation.
But stringent regulations and constraints on battery sourcing and man-
ufacturing can lead to reduced innovation and lower EV adoption rates
(Melin et al., 2021).
Battery swapping
Although CSs can be deployed in populated areas providing charging
access to EVs, there can be long queues during peak occupancy of CSs.
The high upfront cost, the requirement of a dedicated space for instal-
lation, grid constraints, etc., make CS a less feasible solution. BSSs are
being looked up for a faster EV energy supply solution wherein service
time can be comparable to or even beat ICEV refueling. Battery swap-
ping is an old concept finding its roots in 1896 to overcome the limited
range of electric cars and trucks. EV users can barter their discharged
batteries with charged ones at a BSS. It decouples the EV charging pro-
cess from the vehicle, both temporally and spatially. Its advantages over
traditional charging are multifold (You et al., 2022). One, battery swap-
ping time is less than that of a top-up charge. Second, the aggregation
of charging loads reduces the demand uncertainty, simplifying power
operation. Third, the fact that all loads are clustered in one place al-
lows flexible battery charging scheduling and ancillary services, if any
(Sun et al., 2018). Fourth, the cost of EVs can be tremendously reduced
when the battery is leased rather than purchased, as it is the core of a
vehicle’s cost. Fifth, swapping offers longer battery life because batteries
are charged independently and optimally as per the maximum battery
life (Chen et al., 2021). Considering the many benefits of BSSs, attempts
worldwide are being made to deploy the technology successfully.
A study based out of China proposes an optimized BSS scheme for
Suzhou’s urban electric taxicab fleet, mindful of maintaining the Quality
of Service (QoS) of the vehicle fleet by incentivizing charging schedul-
ing to avoid congestion at BSS (Wang et al., 2018). They consider the
historical demand trends and traffic data for real-time battery swapping
scheduling. Moreover, a comparative study between CS and BSS based
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4. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
on earnings, operating revenue, and service capacities depicted the lat-
ter to have greater potential over the former for taxi and bus fleets.
Another study presents a cost-minimization-based solution for an opti-
mal plan of a BSS with multistakeholder involvement in its operation
(Wu, 2021). The cost of utilization of batteries from available stock has
been proposed to be linked with both the initial purchase price of the
batteries and their life cycle. Infante and Ma (2021) suggest a multi-
stakeholder planning and operational strategy involving BSS owners,
EV users, and DISCOM operators. Based on a multiobjective optimiza-
tion framework, insights on trade-offs between battery swapping and EV
shifting visit decisions are provided, given the flexibility on load con-
straint by DISCOM operators Jordehi et al. (2020) in their study suggest
an energy management model that tries to minimize the cost of a micro-
grid by integrating it with a BSS. BSSs are connected to power grids. In
addition to the various benefits mentioned, they act as responsive loads
for grids and reduce their operation cost by scheduling such loads. An-
other similar study by Xu et al. (2022) identifies battery swapping as a
more economical and efficient system than plug-in charging. They sug-
gest an energy management problem that integrates BSS with renewable
energy. Even if renewable energy is not brought into picture, an opti-
mized charging model can facilitate the deployment of a sustainable
BSS, given the scarcity of finite resources.
Like other developing nations, India also looks forward to deploy-
ing charging infrastructure as a pathway for EV proliferation. With se-
rious considerations from the government on the same through vari-
ous schemes, incentives, and a recent draft policy on battery swapping
(Policy Document), the future of EVs seems bright for reinforcing the
e-mobility game in the nation. Battery swapping falls under the big-
ger umbrella of Battery as a Service (BaaS) which involves purchasing
an EV without the battery, hence lowering the upfront costs. During
the budget 2022-23, the Indian government announced plans to intro-
duce a battery-swapping policy and interoperability standards as a step
towards the deployment of an efficient battery-swapping system. The
overall objective of the policy is to incentivize large-scale EV adoption
by being mindful of the efficient use of scarce resources like land, public
funds, and finite raw material for battery manufacturing and delivering
customer-centric services. Hence, the policy addresses the technical, reg-
ulatory, institutional, and financial challenges to India’s wide-scale EV
proliferation.
Battery swapping is currently technologically more feasible for two
and three-wheelers than for four-wheelers and e-buses. And the fact that
global EV sales are presently driven by two and three-wheeler fleets
favors the deployment of battery-swapping technology.
Optimization tools
Planning and configuring BSS is a challenge as it involves numer-
ous factors to consider, including the number of batteries, chargers,
employees, and other entities that are required to be decided before-
hand and are dependent on the nature of the fleet to be managed.
Since the resources at each end, either for investment or operation, are
limited, a multiobjective optimization model must be deployed involv-
ing multiple stakeholders to present an all-inclusive BSS design. Plan-
ning and optimization problems in the energy field, like resource allo-
cation/allotment or cost minimization, are regularly encountered. Nu-
merous commercial and open-source platforms used in the areas of fi-
nance, marketing, logistics, production, manufacturing, etc., have also
been analyzed for the problems in the field of engineering like RE plan-
ning (Horasan and Kilic, 2022), optimization in the public transport
network (Kiciński, 2021), optimal design of battery storage systems
(Massaro et al., 2021), etc. Horasan and Kilic suggest constructing a
multiobjective decision-making model for renewable energy planning
to determine the most appropriate resource diversity for the different
regions of Turkey. With the escalating global population, exponential
increase in energy consumption, and a significant depletion of conven-
tional resources, it is more than urgent to change the current energy
mix. The problem statement focuses on five renewable energy sources:
solar, wind, geothermal, hydroelectric, and biomass. The four objective
functions of the proposed model include maximization of the technical
score of regions, job creation, environmental score, and cost minimiza-
tion. The problem is solved using LINGO software as a comprehensive
optimization tool.
Massaro et al., in their study, employ MS Excel environment to ad-
dress the integration of Battery Energy Storage Systems (BESS) in En-
ergy Communities (ECs) to improve EC efficiency. ECs are open, vol-
untary, collective, and citizen-driven initiatives toward cleaner energy
transition. They help decentralize the energy system where the grid is
owned by a group of local people with solar/wind plants installed in
close vicinity of the residence. But an EC faces multiple issues due to
the inconsistency of renewable energy production if deployed without
BESS. Moreover, with the impending explosion of EVs in the energy sec-
tor, the modeling of BESS in ECs can not be ignored. The study intends to
find the optimal size of BESS under various conditions, maximize shared
energy and the revenues of EC actors. The multiobjective problem is op-
timized through the GRG non-linear algorithm of MS Excel Solver.
Methodology
Mathematical formulation
The study proposes a multiobjective business and operating model
to deploy BSS successfully. It is a concoction of majorly the following
components.
(a) Number of batteries pulled out from stock to serve the arriving swap-
ping EV orders
(b) Potential charging damage from the use of higher-rating chargers
(c) Electricity costs for different periods of the day
A mathematical model incorporating the following as the operation
cost of a BSS is put forward. Due to its high initial cost and associated
lifespan, the battery is one of the most expensive parts of an EV. With
the Battery as a Service (BaaS) model in the picture, EV owners are ex-
empted from this massive crunch of investment as batteries are now the
responsibility of the service providers. A cost is incurred on the part of
the BSS operator pertaining to the purchase of an initial battery stock
and maintenance of the same. Battery life is not only determined by
its chemistry but also by the charging technology and equipment used.
Also, the price of electricity used to charge the incoming discharged bat-
teries is on the station operator’s account. Thus, from the BSS operator’s
point of view, it has to minimize its cost of operation while deciding the
optimal charging schedule for the incoming batteries. The decision is to
assign the charging method to each battery such that incoming swap re-
quests can be met. Hence, the operation cost of a BSS consists of multiple
stakeholders: the BSS operators, the EV drivers, and the DISCOM oper-
ators. The BSS operators have the charging decision authority. The EV
drivers come in with swap requests and declare the vehicle specifications
in advance, like arrival time and remaining battery charge. This helps in
devising an optimal charging schedule for batteries. The DISCOM opera-
tors declare the day-ahead price of electricity on a daily/hourly/15 min
basis.
The mathematical formulation for the following model is presented
below:
Minimize
{
𝐶bat × Ba𝑡max +
𝑛
∑
𝑖=1
DC(𝑖) +
𝑛
∑
𝑖=1
𝐸𝑑(𝑖)𝐸𝑡(𝑖)
}
(1)
Where,
Cbat = Normalized cost of battery per charging
Batmax = Maximum number of batteries used from stock to serve every
demand
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5. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
DC(i) = Damage cost associated with ith
battery charging configuration
Ed(i) = Energy demanded by 𝑖𝑡ℎ
battery = Batcap(1 − SoC(i))
Et(i) = Cost of energy per unit for the time at which ith
battery arrives
n = Total number of batteries in decision
Batcap = Battery capacity in kWh
SoC(i) = State of charge of incoming battery i
The different components of operation cost can be defined as follows:
Cost of Batteries: A normalized cost for a battery per charge cycle,
given by its initial purchase and life cycle.
Damage cost: The charging damage caused by different charging
rates and technologies.
Electricity cost: ToD (Time of Day) tariff specified in India by IEX
(Indian Energy Exchange)
Calculations for normalized battery cost and damage cost are men-
tioned in Appendix. The operator bears a cost for using batteries from
stock when they are charged. To reduce this cost, it would try to min-
imize the batteries pulled out from its initially available stock. But to
meet the swap requests, the operator will have to make the charging
decision such that it does not lose a potential customer. To do so, it will
fast charge a few batteries to serve the swap request and incur an addi-
tional cost pertaining to the damage cost associated with fast charging.
Lower the batteries pulled out from stock, more the chances of assigning
a fast charger to an incoming discharged battery, and vice-versa.
Assumptions
For ease of calculation, the model has made some assumptions:
• EV drivers declare the arrival time and SoC of incoming battery swap
requests beforehand.
• Incoming discharged batteries are put to charge as soon as they ar-
rive for swap.
• Discharged batteries are charged up to maximum capacity, i.e., SoC
equal to 1.
• All swap demands are met, i.e., no customer goes out from the BSS
without a fully recharged battery.
• If, at the time of arrival of a discharged EV, a previously discharged
battery has been completely recharged and is available, the EV is
given that battery. Else if a battery is available in stock, it is pulled
out.
• EVs are considered only consumers and not providers, as frequent
charging-discharging cycles reduce the battery’s lifespan.
• Batteries maintain the same state of health throughout life and can
be charged up to maximum capacity, i.e., SoC equal to 1.
• Batteries are homogeneous, i.e., all batteries have the same capacity
and other technical specifications except arriving time and SoC.
Only two modes of charging have been considered, slow and fast.
Model specifications and data
The decision is to assign one of the two charging modes to a set of
N incoming discharged batteries. Hence, there are 2N solutions to the
problem. The aim is to optimize the number of batteries pulled out from
stock and the charging decision to maintain the QoS and minimize the
operation cost. The Mixed-Integer Non-Linear Programming (MINLP)
optimization is performed on the same mathematical formulation men-
tioned above but across two different platforms. The data consists of
random arrival times of 15 discharged EVs on a particular day between
8:56 and 11:44 h. It is considered that time of arrival of swap demands
is known in advance. The remaining SoC and cost of energy to charge
them at the time of arrival are also known. The SoC values are randomly
generated between 0.2 and 0.5. Batteries, homogenous in nature, have
a battery capacity equal to 3 kWh. Slow chargers provide a full charge
in 5 h or 300 min, and fast chargers require 1 h or 60 min. Data is
mentioned in Appendix.
Model 1
The optimization problem is solved using Solver in MS Excel. Solver
is an add-in for Excel developed for Windows by Frontline Solvers Inc.,
which allows one to build and solve optimization models in Excel. Ex-
cel’s wide-scale popularity and familiarity make it an ideal platform for
formulating and optimizing linear, non-linear, and integer programming
models. It can be used to find the optimal (maximum/minimum) value
for a formula in one cell, which is the objective cell subject to con-
straints/limits on the other formula cells on the worksheet. Solver finds
its use for allocating scarce resources, maximizing or minimizing prof-
its/costs/risks in finance, investment, marketing, manufacturing and
production, distribution and logistics, human resources, science, and en-
gineering. The constraints to the problems can be integer or binary, or
all different. An evolutionary algorithm based on the Theory of Natural
Selection has been used for this particular situation. It uses mechanisms
inspired by biological evolution, like mutation, reproduction, and selec-
tion. It often gives well-approximated solutions to problems. The solver
starts with a random “population,” i.e., a set of input values fed into
the model, and results are evaluated compared to the target value. The
ones closest to the target are selected to create a second population of
“offspring,” which are a “mutation” of the best set of input values from
the first population. Further, second population is evaluated, and the
best of that is chosen to create a third population, and so on. A stepwise
approach to the evolutionary algorithm is also mentioned in Fig. 3.
For the Evolutionary algorithm, the default values of convergence,
mutation rate, population size, random seed, and maximum time with-
out improvement are 0.0001, 0.075, 10, 0, and 30 s. The values have
been modified for better results to 0.0000001, 0.9, 1000, 0, and 300 s.
The values were further tried to be changed, but the results remained
the same. Table 1 below also lists these specifications.
Formulae and equations
s = decision variable for slow charging, 1 if slow charged, 0 if not
f = decision variable for fast charging, 0 if s = 1 & 1 if s = 0
b = f + s
(
to ensure that it always equals 1, i.e., a swap request is always
served
)
br = battery required at each swap request
tch = time required to charge an incoming discharged battery
bs = remaining batteries in stock
Table 1
Model 1 specifications.
Parameters Values
Battery capacity 3 kWh
Slow charge (time required) 5 h/300 min
Fast charge (time required) 1 h/60 min
Decision variables s, Bat𝑚𝑎𝑥
Other variables f, b, br, tch , bs, bi, t, At, Ac, SoCr, tr, Ec,
Tc
Constant/Known parameters Cbat , DC, Batcap, Et (i), SoC(i)
Constraints s = binary, 1 ≤ bs ≤ n, 1 ≤ Batmax ≤ n,
Batmax = integer
Objective Min (Tc, Bat𝑚𝑎𝑥)
Solving method Evolutionary
Convergence 0.0000001
Mutation Rate 0.9
Population size 1000
Maximum time without improvement 300 s
5

6. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
Fig. 3. A general representation of the evolu-
tionary algorithm.
bi = incoming discharged batteries recharged
t = arrival time
At = inter arrival time
Ac = cumulative arrival time
SoCr = required SoC
tr = ready time
Ec = energy cost
Tc = total cost
tch (in minutes) = [60∗ f + 300∗ s](1 − SoC)
SoCr(i) = 1 − SoC(i)
At = time difference between the arrival of two consecutive swap requests
tr = tch + At
Et(i) = ToD Tariff (in INR∕MWh)
Ec(i) = (1 − SoC(i)) × Batcap × Et(i) (2)
Tc = Cbat × Batmax +
n
∑
i=1
DC (i) +
n
∑
i=1
Ec(i) × 0.001 (3)
Battery stock condition. The battery stock condition at any time is gov-
erned by the variable bs(t). It is dependent on Batmax, bi(t) and br(t). It
is important to monitor it as we must ensure that each swap request is
met. The following equations will take care of that.
br(t) = battery required at each swap request = 1 (one swap at a time)
bi(t) = COUNTIF
(
𝑡𝑟 ≤ 𝐴𝑐
)
bs(t) = bs(t − 1) + bi(t) − br(t − 1) ∀ t, battery swaps
bs(t = 0) = Batmax (at the arrival of the first swap request)
Model 2. Considering the limits to the free add-in in MS Excel,
another commercially available operations research software tool is
used. “Lingo” is a comprehensive tool designed by Lindo Systems Inc.
to build and solve problems across linear, non-linear (convex/non-
convex/global), quadratic, stochastic, integer, and various other do-
mains in a concise manner. It provides an integrated platform for con-
venient problem formulation using its Algebraic Modeling Language
and fast built-in solvers. It can easily be embedded in spreadsheets
and import data from the same, making it even more user-friendly.
Lingo has been used to solve various optimization problems across sev-
eral fields in data-driven research. It is a powerful and well-established
tool for solving problems on inventory and allocation/assignment of re-
sources like machinery, staff, money, time, etc. It is found to outperform
other solution techniques like evolutionary algorithms, GRG algorithm,
Monte Carlo non-deterministic method, etc. The study uses a trial ver-
sion of the same with certain limitations on the number of constraints
for some solver options. From a bunch of solvers available, viz., non-
linear, global, general, integer, stochastic programming, etc., if options
are set to default, the tool will automatically identify the type of problem
and pass it on to the suitable solver. This further minimizes compatibil-
ity problems between the modeling language and solver components.
While other local search solvers stop at the first local optimum found,
a global solver searches until the global optimum is found. A global
solver converts a non-convex, non-linear problem into convex, linear
sub-problems. Lingo solves the problem using the Branch and Bound al-
gorithm for solving a discrete and combinatory optimization problem.
It consists of several stepwise enumerations of potential solutions by ex-
ploring the entire search space. Further, a rooted decision tree is built
using all possible solutions in which the root node represents the whole
search space. This tree is constructed by checking for solutions that com-
ply with the bounds/constraints set to the problem. The decision to add
a node is further made based on the same, and the aim is to form smaller
subsets until no more solutions can be found. Every child node is a par-
tial solution and part of the solution set. The node with the best bound
is explored at each level; thus, the best and optimal solution is found. A
general stepwise approach of the Branch and Bound algorithm is men-
tioned in Fig. 4.
The specifications for solving the optimization problem are listed
below in Table 2. Other formulae and constraints remain the same as in
Model 1.
Other variables denoting cumulative time, required SoC, incoming
batteries recharged, and ready time are the same as in Model 1. And the
same data-sheet can be used for Model 2. The other options are set to
default so that the model can choose the best possible one.
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7. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
Fig. 4. A general representation of the branch and bound algorithm.
Table 2
Model 2 specifications.
Parameters Details
Decision variable(s) Fast, AS
Other variables Electricity, Recharged Battery, Cum_Time,
Ready Time, Req_SoC, BS, IC, B
Initial non-feasibility tolerance 0.001
Final non-feasibility tolerance 0.000001
NLP Solver Version 3.0
Threads 20
Mode Prefer concurrent
Generator memory limit (MB) 32
Derivatives Second order
Electricity = price of electricity at the time of arrival of swap request
BS = batteries remaining in stock
AS = initially available stock or maximum batteries that can be used from stock
Fast = 1 if the battery is fast charged, 0 if slow charged
B = maximum(BS) = AS
IC = normalized cost of battery per charging
Results and discussion
The operation cost for providing service to 15 swap requests after
optimization is INR 584.79, and the optimum value of the maximum
number of batteries that need to be pulled out from available stock to
serve all demands is 8, as shown in Fig. 5. The problem was initiated by
assigning random values to slow charge and other parameters adjusted
according to their respective formulas. The number of batteries that re-
quired fast and slow charging was 7 and 8, respectively, as depicted
in Fig. 6. These results were obtained from Model 1 and solved using
Evolutionary Algorithm from Solver in Excel.
The battery stock condition is depicted in Figs. 7 and 8. At the ar-
rival of the last swap request, the battery stock is one and the incoming
discharged batteries recharged at the end of the evaluation period is 7.
All the incoming discharged batteries are recharged till 15:30 h. Thus,
the available battery stock for serving swap demand is also restored,
i.e., equal to Batmax. Till 10:29 h, the battery stock decreases at a con-
stant rate. Only after the battery that came in at 9:58 h is recharged to
its full capacity does battery stock reduction slow down. From 11:10 h
to 11:38 h, the battery stock witnesses an increase, as a few incoming
discharged batteries have been charged. After 11:44 h, when there are
no swap requests to be served, the incoming discharged batteries previ-
ously on charge will be recharged to total capacity and added up to the
battery stock to restore it to the initial value, i.e., 8.
Model 2 using Lingo software gives local optima in all its solutions
and is not found to improve further with the best parameter modifica-
tions. Only two of the many solutions are taken into account for the
reader’s reference. The two solutions are represented by 1 and 2, and
both have two parts, ‘a’ and ‘b.’ Part ‘a’ depicts the solution for opera-
tion cost and the maximum number of batteries used from stock. Part
‘b’ depicts the solution for the number of batteries recharged, battery
charging decision, battery ready time, and remaining batteries in stock.
The first solution for operation cost and the maximum number of batter-
ies used from stock for serving 15 swap demands are INR 584.82 & 12,
depicted as (1a) and (1b) in Fig. 9 and Table 3, respectively. The second
solution for operation cost and the maximum number of batteries used
from stock is INR 615.96 & 10, depicted as (2a) and (2b) in Fig. 9 and
Table 4, respectively. The number of batteries requiring fast charge was
3 and 6, respectively, in the second solution.
Since more batteries are assigned slow charging in the two solutions
obtained from Lingo, the incoming batteries will be recharged slowly,
and to serve swap requests, more batteries from stock need to be pulled
Fig. 5. Optimization results from solver in excel (1).
7

8. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
Fig. 6. Optimization results from solver in excel (2).
Fig. 7. Status of incoming recharged batteries.
Fig. 8. Status of batteries available in stock with respect to Batmax.
8

9. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
Fig. 9. Optimization results (1a) and (2a), as obtained from software.
Table 3
Optimization results from Lingo (1b).
# Number of batteries
recharged
Fast charge
status
Ready time Remaining
batteries in stock
1 0 0 223.59 10
2 0 0 296.05 9
3 0 0 269.19 8
4 0 0 291.01 7
5 0 1 171.99 6
6 0 1 176.32 5
7 0 1 183.52 4
8 0 1 192.72 3
9 0 1 189.88 2
10 0 0 384.12 1
11 4 1 237.41 4
12 5 0 417.16 4
13 5 0 398.86 3
14 5 0 444.01 2
15 6 0 428.00 1
Table 4
Optimization results from Lingo (2b).
# Number of batteries
recharged
Fast charge
status
Ready time Remaining
batteries in stock
1 0 1 88.72 12
2 0 0 296.05 11
3 1 1 148.23 11
4 1 1 156.60 10
5 1 0 331.97 9
6 1 0 349.61 8
7 1 0 361.62 7
8 2 0 367.61 7
9 2 0 349.43 6
10 3 0 384.12 6
11 3 0 427.04 5
12 3 0 417.17 4
13 3 0 398.87 3
14 3 0 444.01 2
15 3 0 428.00 1
out. All batteries will be recharged up to full capacity by the same time,
i.e., 15:30 h, and the initial battery stock will be restored. While Solver
in MS Excel, even after several iterations, is stuck on the first local opti-
mum, Lingo keeps looking for solutions. Also, Lingo, with its powerfully
integrated optimization solvers, suggests a solution that is more favor-
able to our requirement regarding battery degradation. In the second so-
lution from Lingo, only 3 batteries are assigned fast charging compared
to 7 in the solution obtained from Solver in MS Excel. This implies that
fewer batteries are exposed to wear and tear from faster-charging rates
in the second solution suggested by LINGO.
Both models yield feasible and similar solutions to the problem.
There can be several local optima solutions to minimize cost, and no
global optima to such a problem exist. But, considering the damage as-
sociated with the influence of fast charging of batteries on their state of
health and lifespan, one could go with solutions where fast charging is
less utilized, i.e., the one suggested by Model 2.
Future of battery swapping in India
Although India is a new entrant into the EV market, its transportation
sector is on the cusp of electrification. India stands in the third position
regarding global greenhouse gas emissions only after the world’s two
most significant contributors, China and the United States, respectively.
And, with the announcement of the magnanimous goal of net-zero emis-
sions by 2070 at the recent COP-27 meet in Egypt and also at COP26
meet in Glasgow, India must expedite its work towards the same. Taking
a huge step towards cleaner mobility, the Faster Adoption and Manu-
facturing of hybrid and Electric Vehicles (FAME) scheme was launched
in two phases as a part of the National Electric Mobility Mission Plan
(NEMMP) in 2015 to incentivize EV adoption. But despite an upscale in
environmental awareness, affordability & technology advancement, and
the aid of various government schemes, campaigns & subsidies, the lack
of adequate supporting infrastructure for the same and extended charg-
ing periods remain a crucial barrier holding back the projected growth
of the EV market. Hence, EV users suffer from range anxiety because
of infrastructure scarcity. The same is not true for ICEV users, as ample
refueling stations exist. The ‘detachable’ nature of fuel (oil/gas) from
vehicles relieves users’ anxiety. Consequently, an alternate, more con-
venient, cheaper, and safer solution must be considered. This is where
Battery Swapping Stations come into the picture for providing a faster
EV energy supply solution wherein service time can be comparable to
or even beat ICEV refueling.
Because the country’s vehicle composition is such that two and three-
wheeler public vehicles are the primary dominants like many other de-
veloping nations, there is an opportunity for a substantial social and en-
vironmental impact (Jhunjhunwala et al., 2018). With limited charging
infrastructure availability, high investment cost, and expansion of the
same in tandem with the obsolete distribution infrastructure in India,
battery swapping looks more deployable. Also, the fact that EVs can now
be bought without batteries under the BaaS model favors the Indian sce-
nario hugely, as it is economically more viable. Currently, batteries con-
stitute a substantial crunch of the total EV cost, and the lithium that is
majorly used to manufacture these batteries is imported from China and
Hong Kong (Lithium Import And Production [WWW Document]). Thus,
battery-swapping technology offers increased affordability and creates
an opportunity for the circular economy of vehicles (online document).
Since huge investments are being made into the emerging e-mobility sys-
tems, it is more than called-for to consider refurbishing, recycling, and
9

10. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
repurposing materials from the electric automotive sector to reduce the
overall carbon footprints and unit costs with the elimination of sourcing
to an extent.
Conclusions and scope of further work
The future of mobility is electric, and many countries like China,
Europe, and the United States are progressively on the path to welcom-
ing this transition in the conventional automotive sector. Lack of ad-
equate charging infrastructure, longer charging periods, technical and
economic issues with fast charging, and dependence of the electric au-
tomobile industry on finite resources remain significant challenges that
are difficult to address. Hence, the study attempts to determine the next
best choice to promote EV adoption. Battery Swapping is emerging as
one of the more convenient solutions. An optimized strategy for deploy-
ing a successful BSS model is proposed that minimizes the operation cost
in tandem with the maintenance of QoS and sustainability in the battery
chain by checking on battery degradation. The multiobjective optimiza-
tion problem gave the solution for the optimum number of batteries that
should be used from the battery stock, given the possible charging op-
tions that could be used for incoming discharged batteries and the con-
straints on demand satisfaction. However, the model considers the var-
ious costs of battery use, battery degradation, and electricity consistent
with the perspective of India; its application is not limited to India alone.
With the release of the draft policy on battery swapping in India, the
study suggests an analysis of various models of BSS deployment as a pre-
requisite to the success of the swapping technology and EV proliferation
in India, where the EV adoption rate falls below 1%. The multiobjective
model is flexible to the change in arrival time, SoC of swap requests, and
other costs. Hence it is entirely versatile and adjustable to geographical
changes.
Model 1 and Model 2 were representations of the same mathemati-
cal model solved using two different optimization tools, MS Excel Solver
and Lingo. Some variables were same and some different for both mod-
els but the input parameters, namely, arrival time, arrival SoC, and ToD
tariff, remained the same. In Model 1, the optimization began by as-
signing random initial values to the different variables. The evolution-
ary algorithm was then applied, and the optimum solution for operation
cost, maximum number of batteries used from stock, and charging deci-
sion for incoming batteries was found. In Model 2, the input parameters,
namely, arrival time, arrival SoC, and ToD tariff in the form of an excel
sheet were fed into the model, wherein the objective and variables were
defined. After applying the Branch and Bound algorithm, the optimum
solution was found. The two optimization tools were concurrent on the
solution for the operation cost, i.e., INR 584.82, which also appears to
be the minimum possible value of operation cost. But from both tools,
the values for the maximum number of batteries used from the stock
differ. Both tools give local optima because the damage cost associated
with assigning a fast charger to an incoming battery and the cost of
utilization of a battery from the stock are the same. To reinforce the
model, a charging schedule can also be brought into the picture, given
ToD tariffs such that operating costs can be better optimized. It would
also relieve the grid of the potential burden imposed by the charging
load. Moreover, strict constraints on the frequency of use of fast charge
at different time periods in a day can be imposed to prevent unnecessary
and premature aging of batteries. Finally, the model attempts to address
the inherent problem of planning and strategy for any new technology
or change.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
CRediT authorship contribution statement
Astha Arora: Conceptualization, Methodology, Software, Writing –
original draft. Mohit Murarka: Formal analysis, Validation, Writing –
review & editing. Dibakar Rakshit: Supervision, Project administration.
Sukumar Mishra: Supervision, Project administration.
Data availability
Data will be made available on request.
Acknowledgment
The authors would also like to thank the Department of
Science and Technology, Government of India, "Different En-
ergy Vector Integration for Storage of Energy" - Grant number-
TMD/CERI/MICALL19/2020/03(G).
Appendix
Normalized cost of battery
For a battery cost of INR 10380/kWh (Dash and Bandi-
vadekar, 2021), an EV with battery capacity 3kWh and average battery
life of 1000 cycles, the normalized cost per charging will be:
𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑐𝑜𝑠𝑡 =
𝑏𝑎𝑡𝑡𝑒𝑟𝑦 𝑐𝑜𝑠𝑡∕𝑘𝑊 ℎ × 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (𝑖𝑛 𝑘𝑊 ℎ)
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 𝑐𝑦𝑐𝑙𝑒𝑠
=
10380 × 3
1000
= 𝐼𝑁𝑅 31.14
Damage cost
The normalized damage cost for fast charging is the additional cost
incurred by BSS for fast charging the incoming discharged batteries.
Two charging modes have been considered: slow charging of 1.5 kW
output and fast charging of 7 kW output. For charge rates of 0.2C
and 1C, the corresponding battery life is 1000 cycles and 500 cy-
cles (Rezvanizaniani et al., 2014). Hence, the normalized damage costs
(Wu, 2021) for them will be INR 31.14 and INR 62.28, respectively. If
a slow charger is taken as a reference, the additional cost of using a fast
charger will be INR 31.14.
Data
Table 5
Battery swapping data.
S.No. Arrival time (t) Arrival soc (SoC) ToD tariff (INR/MWh)
1 8:56 0.44 3359.84
2 9:03 0.22 3298.23
3 9:58 0.50 3525.67
4 10:03 0.44 3749.22
5 10:12 0.33 3749.22
6 10:13 0.28 3749.22
7 10:19 0.26 3749.43
8 10:29 0.27 3749.43
9 10:30 0.34 3749.43
10 10:39 0.25 3760.06
11 11:10 0.21 3999.35
12 11:20 0.28 4009.72
13 11:31 0.37 4279.74
14 11:38 0.25 4279.74
15 11:44 0.32 4279.74
10

11. A. Arora, M. Murarka, D. Rakshit et al. Cleaner Energy Systems 4 (2023) 100048
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