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Applied Energy
journal homepage: www.elsevier.com/locate/apen
A review on electric vehicle charging station operation considering market
dynamics and grid interaction
Saheb Ghanbari Motlagh
∗
, Jamiu Oladigbolu
, Li Li
Faculty of Engineering and IT, University of Technology Sydney, Sydney, Australia
HIGHLIGHTS
∙ This paper reviews EV charging station operation with market and grid interactions.
∙ The study examines smart charging, bidirectional charging, and pricing models.
∙ The study explores various optimization methods for EV scheduling.
∙ The study identies gaps in pricing, uncertainty management, and market design.
AR T I C L E I N F O
Keywords:
Electric vehicle
Electric vehicle charging station
Power system
Optimization
Operation management
A B S T R A C T
The growing adoption of Electric Vehicles (EVs) presents pressing challenges and opportunities for power systems
and market dynamics. This paper comprehensively reviews state-of-the-art operational optimization techniques
for EV charging, including model predictive control, reinforcement learning, and distributed approaches. The
study examines strategies to address uncertainties in renewable generation, market pricing, and EV charging
behavior. Advanced pricing schemes like distribution locational marginal pricing and game-based methods are
explored to align protability with system stability. The signicance of bidirectional charging in reducing peak
loads, supporting ancillary services, and balancing battery degradation with user satisfaction is also discussed.
Finally, emerging challenges in privacy, multi-energy coupling, and regulation are presented, emphasizing re-
search directions to enhance grid resilience, economic viability, and sustainability. This review oers valuable
insights for policymakers, energy utilities, and EV stakeholders to facilitate a smooth and cost-eective transition
toward an electried and decarbonized transportation and power sector.
1. Introduction
1.1. Importance and motivation
In recent decades, global warming, environmental problems, and the
urgent need to reduce carbon emissions have increased the share of re-
newable energy worldwide [1]. In recent years, many countries have
started to reduce their dependency on fossil fuels, optimize their demand
[2], and prepare themselves for the day without fossil fuel resources
[3]. Increasing fossil fuel prices and problems in the fossil fuel sup-
ply chain due to the war in Ukraine accelerated this trend even more
[4]. Economic thrift, reducing the operation costs of power systems [5],
diversifying energy sources [6], enhancing the system security against
cyber-attacks [7], creating jobs, and encouraging societies to build smart
infrastructures to support sustainable development have also promoted
renewable resources in many countries [8].
Meanwhile, the transportation system also did not remain un-
changed, and many countries started to decarbonize their transporta-
tion systems. Electric Vehicles (EVs) and Hydrogen Fuel Cell Vehicles
(HFCVs) are both being used in many countries [9]. As is evident from
their names, HFCVs use hydrogen as their fuel and have no emissions.
Their refueling time is 3–5 min, and their range is 500–650 km [10],
which is counted as their benet compared to EVs. Their more extended
range makes them well-suited for heavy trucks and buses. However,
there are some drawbacks to HFCVs, such as limited hydrogen refueling
stations, high costs of hydrogen, and less accessibility to hydrogen [11].
Moreover, since hydrogen is still mainly produced using natural gas
and fossil fuel resources, the environmental impact of HFCVs is highly
∗ Corresponding author.
Email address: Saheb.ghanbarimotlagh@student.uts.edu.au (S. Ghanbari Motlagh).
https://doi.org/10.1016/j.apenergy.2025.126058
Received 8 March 2025; Received in revised form 24 April 2025; Accepted 3 May 2025
Applied Energy 392 (2025) 126058
0306-2619/© 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
dependent on the real source of hydrogen [12]. Like HFCVs, EVs produce
no emissions, but their real environmental impact depends on the source
of the electricity they are charged with [13].
On the other hand, EVs have a higher recharging time, and
their driving range is 320–480 km [14]. However, EVs also oer
notable advantages that make them superior to HFCVs. These ad-
vantages include lower vehicle costs and economies of scale in bat-
tery production compared with the high costs and limited production
of fuel cell technology [15]. EVs further benet from higher en-
ergy eciency and widespread charging networks, which continue
to expand. They also require minimal maintenance and can uti-
lize cheaper renewable electricity in public and residential parking
lots [16].
These benets have caused a wide variety of EVs, mainly produced
by Tesla, Nissan, BMW, etc, compared to HFCVs in many countries.
In China, from 2015 to 2019, the average annual growth rate of EV
sales was 45.7 % [17]. In the United States (USA), EV sales surged
from 0.3 million in 2020 to 0.7 million in 2021, more than dou-
bling within a year; this growth brought EVs to a 4.5 % share of
total vehicle sales [18]. European Union has set the ambitious goal
of achieving 60 % EV sales of total vehicles by 2030 [19]. In com-
parison, Australia has a relatively lower EV adoption rate and reached
2 % of whole on-road vehicles in 2021 [20]. Globally, EV sales soared
from 0.8 million (≤1 % of total vehicle sales) in 2016 to 6.6 million
(8.3 %) in 2021 [18]. These numbers are forecasted to increase sharply
in the coming years, as governments use various economic levers and
policies such as subsidies, discounts, tax incentives, exemption pro-
grams, and purchasing and driving incentives to motivate people to use
EVs [21].
However, regardless of social, environmental, economic, and trans-
portation aspects of EV adoption, increasing the number of EVs can
directly aect power systems. Simultaneous charging of EVs, especially
during peak hours, can lead to sharp demand spikes, and this can cause
problems such as voltage uctuations and instability, frequency insta-
bility, and transformer overloading [22]. Increased peak demand due to
improper charging of EVs can sharply increase power system costs due to
the rapid need for upgrades [23]. Since many countries have been trying
to decarbonize their energy sector, the share of renewable energy re-
sources in these countries, which are mainly uncertain, intermittent, and
non-dispatchable, has been increasing [24]. Adding EVs to these highly
penetrated renewable power systems is like a double-sided razor. EVs
can help absorb excess renewable energy generation. Still, if the charg-
ing process is not well-scheduled, it can also cause huge mismatches
between generation and consumption during peak and non-peak hours.
Unpredictable charging behaviors of EVs highlight the need for ad-
vanced load forecasting and real-time management of EV/renewable
penetrated power systems [25]. Large-scale EV charges can introduce
non-linearity from power electronics in chargers and harmonic distor-
tion or result in lower power factors and require the power system to
use compensation devices such as capacitors [26]. Clustering EVs in an
area can cause local congestion and overloading of transmission lines
[27]. Increasing reliance on digital platforms and smart charging pro-
grams can increase the risks of cyberattacks and natural disaster impacts
on power systems [28]. These factors show that the improper charging
regime of EVs can increase the nancial costs of power systems and their
reliability and security risks. They emphasize the importance of schedul-
ing optimization of EVs and state-of-the-art management strategies for
new power systems.
This paper aims to review the most cutting-edge operation and
scheduling optimization methods and management strategies for EV-
penetrated power systems, including power quality and Vehicle-to-Grid
(V2G) integration, smart charging and real-time scheduling, Articial
Intelligence (AI) and Machine Learning (ML) roles in EV charging opti-
mization, pricing strategies and market operations for EV charging, and
revenue optimization in EV infrastructure.
1.2. Related papers
EVs are becoming an essential part of the transportation sector in
many countries. In the meantime, EV Charging Stations (EVCSs) are
the connection point between the transportation and power systems.
Therefore, EVCSs are the levers that can be used to optimize the charging
process of EVs with various policies, such as cost minimization, revenue
maximization, incentivizing EV users, congestion management, etc. In
the last two decades, numerous research papers have been published
on EV charging optimization. Moreover, many researchers have put ef-
fort into reviewing these works from various perspectives. To the best
of the author’s knowledge, the main repetitive subjects that review pa-
pers considered are EV integration and power system impacts, EVCS
planning and grid upgrade impacts, V2G impacts on power systems
and users, smart charging, scheduling, and optimization techniques,
Dynamic Pricing (DP) and demand response programs, and AI and ML
in EV optimization.
Some review papers focused on EV integration in power systems. Ref.
[29] covered several topics such as power quality, scenario study, elec-
tricity markets, demand response and management, V2G, power system
stability, and battery swapping. Ref. [30] focused more on technical as-
pects of EV integration in power systems, such as converter topology,
power quality, voltage proles, load curves, and power ows. Ref. [31]
focused mainly on V2G and its applications in voltage and frequency reg-
ulation, peak shaving, load management, and its benets for EV users.
In [32], topics such as large-scale EV penetration impacts on power sys-
tems and their economic dispatch strategy, joint scheduling of EVs with
renewable energy resources, and EV-penetrated power systems risk man-
agement were reviewed. Ref. [33] discussed EVs’ impacts on the power
grid, the role of V2G, and economic and regulatory challenges. Ref. [34]
concentrated on power systems’ exibility in the case of large-scale pen-
etration of EVs. Ref. [35] reviewed the same research area for existing
low-voltage distribution systems. Ref. [36] was mainly focused on V2G
impacts on the power system and electricity markets.
Some review papers tried only to cover research related to V2G and
its social, technical, and economic impacts on both power systems and
EV users. In [37], Sovacool et al. put an eort to discuss the neglected
social aspects of the transition to V2G and highlight the community’s
need for cross-competitiveness of V2G and human and social considera-
tions of this new technology. They also discussed the economic aspects
of V2G, such as EVs, operators, stakeholders, business models, the main
innovation in applying this technology in power systems, and policy
implications in [38], and concluded that business models could play an
essential role in V2G implication than technical aspects such as batteries,
EVs, and power systems. Ref. [39] reviewed the mentioned challenges
regarding V2G in published research and concluded that the main chal-
lenges that can endanger V2G implications could be battery degradation,
aggregation and communication, eciency, and the charger. Ref. [40]
also reviewed advances and challenges regarding the V2G. The main in-
novation of this work was covering wireless V2G technology. Ref. [41]
discussed charging topology, communication standards, and operation
strategies for V2G and Vehicle-to-Home (V2H).
In recent years, smart charging, real-time scheduling, and opti-
mization techniques have been the most repeated topics in EV-related
research papers. Ref. [42] was focused on DP methods with applications
in optimal charging strategies and suggested that real-time DP, critical
peak pricing, and Time-of-Use (ToU) programs can eectively optimize
the charging schedule, reduce the overall prices, and compensate for the
negative impacts of random charging. Ref. [43] reviewed charging meth-
ods, ancillary services provided by smart EV charging platforms, and
possible eects of smart charging strategies on charging and operational
costs. Ref. [44] discussed the scheduling methods for discharging and
charging EVs. Based on their results, real-time smart charging methods
like Reinforcement Learning (RL) can eciently schedule EV charging,
manage power systems, and enhance waiting time.
Applied Energy 392 (2025) 126058
2
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Table 1
Summary of previously published reviews.
References Operation optimization Economic considerations
Model predictive
control (MPC)
RL and real-time
optimization
V2G Smart charging Pricing and market dynamics Cost optimization
[29] * * * *
[30,33,35,36,38,43,50] * * * *
[31,51] * * * * *
[34] * * * *
[22,52] * * *
[53,54] * * * *
[37,40,55,56] * * *
[41] * * *
[42,57,58] * * *
[44] * * * *
[59] * * *
[49,60] * * * * *
[61] * *
[45–48] * * *
This review * * * * * *
Like every engineering area, AI and ML play critical roles in the EV
domain. EV optimization, predicting EV driver charging behavior, EV
load forecasting, and renewable resources output forecasting are some
of the main utilizations of AI and ML in this domain. Ref. [45] reviewed
the research on AI and ML applications in EV charging behavior analysis
using historical charging patterns and real-world factors such as weather
and trac. Ref. [46] reviewed papers on AI and ML usage in optimizing
EV charging through prediction models that forecast charging behavior,
considering the weather, user habits, and charging station availability.
Ref. [47] focused on AI and ML applications to predict critical battery
health metrics in EVs, including State of Charge (SoC), remaining use-
ful life, and knee points. It highlights the eectiveness of ML models
like Support Vector Machines, Neural Networks, and Recurrent Neural
Networks in monitoring battery degradation and enhancing real-time
battery management. Ref. [48] discussed the advances of ML and AI in
EV security enhancement, such as detecting and responding to cyber
threats, including intrusion detection, authentication, and attack pre-
vention. Ref. [49] highlights the use of various ML techniques, including
supervised, unsupervised, and RL, to address challenges in optimizing
EV charging and discharging strategies, managing uncertainties in EV
behavior, optimizing charging schedules, and improving grid interaction
through V2G services. The paper also explores strategic frameworks such
as game theory, auctions, and economic incentives like pricing models,
demonstrating how ML can provide innovative solutions to encourage
EV participation in energy markets.
1.3. Research gaps and contributions
Based on the explanation presented in the last section, an analysis
of the previously published papers on EV charging optimization and
scheduling is summarized in Table 1. Although some of these papers
signicantly reviewed a broad range of topics, the table still exhibits
specic gaps and limitations.
Table 1 can better exhibit the concentration of previous review pa-
pers on various EV charging and scheduling topics. Based on Table 1
and Fig. 1, the limitations can be outlined below:
1. There is no study covering all operation-EV-related elds, such
as various optimization techniques and economic aspects. Some
literature, such as [29,51,53,54], were comprehensive review pa-
pers that covered a wide range of areas but still ignored or did
not comprehensively discuss some optimization techniques, cost
minimization, and real-time optimization.
2. MPC is an approach that allows dynamic decision-making over
time and can help address uncertainties regarding renewable re-
sources, prices, and EV drivers’ behaviors. Through this approach,
the optimization is solved in limited time windows. The optimiza-
tion process continues as time progresses and new data become
available. In recent years, many research papers have used this
approach in their methodologies, but still, a few review papers
have addressed this method.
3. Another optimization approach that can address uncertainties in
real-time is RL. Many studies used RL for DP and revenue opti-
mization, smart charging and load balancing, V2G optimization,
demand response, etc. However, there is a gap in review papers
that address real-time RL-based optimization studies.
This study reviews numerous papers on EV integration in power sys-
tems to cover the mentioned limitations. The main contributions of this
study are listed below:
1. This review paper thoroughly investigates all aspects of EVCSs,
such as optimization approaches and economic considerations.
2. To cover the limitations of review papers on real-time optimization
approaches, precisely the MPC and RL-based methods, this study
reviews previously published research papers focusing on real-
time optimization for energy management in EVCS-penetrated
power systems.
3. This study reviews methods for optimization of EV-integrated
power systems under uncertainties in EV charging and driving
behaviors, renewable energy generation, and market uctuations.
What sets this review apart is vefold. First, we introduce a unied
classication framework that tags every surveyed study by its optimiza-
tion approach, uncertainty treatment, and pricing mechanism. Second,
we provide side-by-side comparison tables for all major method fam-
ilies (MPC, stochastic programming, RL, bilevel, ADMM, RO/DRO),
highlighting each one’s real-time readiness, scalability, and practical
constraints. Third, we systematically catalog the handful of existing eld
pilots for DLMP and game-theoretic pricing, revealing where theory has
begun to move into practice and challenges in their practical imple-
mentation. Fourth, we distill these ndings into a concise regulatory
roadmap, charting the path from today’s static taris through dynamic,
V2G-enabled markets to standardized cybersecurity and data privacy.
Fifth, we identify key open challenges and outline concrete research di-
rections, grounded exclusively in publications from the last ve years,
to serve as a reference for future studies on EV charging operations.
Even though other reviews have noted broad future work items, this
survey’s challenge analysis and research agenda reect today’s state of
the art, ensuring its insights fully align with the most recent advances.
These contributions give our paper a fresh literature update and the most
integrated, practice-oriented, and policy-aware synthesis.
Applied Energy 392 (2025) 126058
3
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Fig. 1. Summary of previously published reviews.
The rest of the paper is organized as follows. Section 2 is focused on
operation optimization. This section includes modeling considerations
and optimization methods used in EV-integrated power systems and EV
charging. Section 3 discusses the limitations and research directions re-
lated to EV charging and EV-integrated power systems. Finally, Section 4
presents the most essential ndings of this work and concludes this work.
2. Operation optimization
With the increasing number of EVs on the roads and the need for
ecient energy supply, operation optimization is becoming more crit-
ical. Since utilizing advanced smart charging programs and optimizing
the charging process is less expensive than the unlimited increment of
EVCSs, in most of the literature, the main concentration is on operation
optimization rather than planning. Eective operation optimization can
help the energy system operators handle higher demands and variabil-
ities, help grid stability and management, save energy, and delay the
upgrades in power systems and EVCS infrastructures.
This study divides operation optimization into modeling consid-
erations and optimization techniques for EV charging. The modeling
consideration focuses on pricing schemes and markets, revenue and
benet maximization methods, and smart charging solutions for bidirec-
tional charging. In contrast, the optimization techniques section focuses
on various strategies to optimize EV charging, such as the MPC, model-
free optimizations using RL, real-time optimization, and distributed
optimization techniques.
2.1. Modeling considerations
Carefully formulated modeling frameworks are the initial steps for
developing an operational strategy for EV charging infrastructure. These
models are foundational tools that capture technical, economic, and
behavioral complexities that inuence charging operations. These mod-
els usually consider network topology, EVCS available capacity, energy
availability, user preferences, and regulatory constraints. They enable
stakeholders to assess trade-os, predict outcomes under diverse sce-
narios, and identify viable pathways to improve eciency and user
satisfaction.
A robust modeling consideration oers a reliable platform for ap-
plying optimization and decision-making. Whether focusing on DP, load
balancing, renewable integration, or V2G interactions, a well-structured
model helps ensure that the resulting strategies are data-driven and
context-aware. In the following, pricing schemes and market dynam-
ics are discussed rst, then methods of benet maximization and cost
minimization are reviewed. These two sections explore how practical
model considerations can guide the protability of EV charging for op-
erators, EVCSs, and EV drivers. Lastly, bidirectional charging and smart
charging solutions are presented, exploring the role of adequate model
consideration in power system resilience and prot optimization.
2.1.1. EV pricing models and market dynamics
Pricing schemes are the most eective tools to shape user behavior,
inuence demand, and balance the power system’s performance regard-
ing EVs and the whole power system. These mechanisms are levers of the
power system operators to motivate people for o-peak demand, inte-
grate renewables more eectively, and reduce the overall system costs.
Pricing impacts the economic viability of power systems and ensures
equitable access for users and sustainable grid operation. Various pric-
ing schemes have been developed, ranging from static pricing models
to more complex dynamic frameworks, each tailored to address specic
challenges in grid management.
Based on the reviewed literature, pricing mechanisms in EV-related
publications can be divided into ve groups. The rst and simplest one
is static pricing, a at fee or at rate not noticed in many works. In
most studies, at rates are used as a benchmark model to show the ef-
fectiveness of the other schemes [62,63]. In the second group, the prices
are not at, meaning that the prices are dierent at dierent hours but
are not being determined by any algorithm during an optimization or
real-time process. Most real-world pricing schemes, such as ToU pricing,
demand charges, and demand response programs, can be categorized
into this group [64]. The third group consists mainly of AI-based real-
time pricing models, such as RL pricing, which use forecasts to determine
prices during the optimization process [65]. DP using game theories,
mainly applied using bi-level optimization and quasi-pricing mecha-
nisms, is the other group. These schemes can eectively consider the
interaction and benets of various parties, such as grid operators, EVCSs,
and EV users [66]. Finally, the last category is Distribution Locational
Marginal Pricing (DLMP), which focuses on cost-reective pricing based
on localized demand–supply dynamics.
Fig. 2 compares the mentioned pricing schemes. This gure illus-
trates that at fee pricing is the most straightforward scheme that cannot
satisfy grid operators, EVCS operators, and EV drivers. Pre-determined
dynamic prices are more advanced and can fulll some operators’ con-
siderations. Since it’s predictable for users, they can adapt to the prices
and reduce costs. In contrast, forecasted prices are more based on the
data and preferences of operators rather than users, and following the
prices is more complicated for end users. However, in game-based mod-
els, the interaction of multiple parties is considered. Still, there is a
Applied Energy 392 (2025) 126058
4
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Fig. 2. Pricing schemes for EV charging.
possibility of dissatisfaction and unfair prot sharing, and some play-
ers might be able to dominate the market. At last, DLMP prioritizes the
preferences of the power system, and it is hard for end users to inuence
prices, but it is more likely to guarantee a stable supply for end users.
Table 2 summarizes some of the most recent works on game-based
pricing of EV-integrated power systems. Based on this table, Stackelberg
games are widely used for game-based pricing, especially for their capa-
bility for hierarchical decision-making, where followers can respond to
the leader’s moves during optimization. Cooperative games and Nash-
based games are other widely used methods. These methods maximize
collective benets and fair allocation and maintain system stability.
Moreover, some dierent approaches are categorized in this section,
like the double auction mechanism that can provide a participatory
framework in energy trading. Economic optimization, like maximiz-
ing the benets, keeping system balance and fairness, and considering
real-world constraints such as power distribution system constraints,
battery costs and degradation, and trac and routing considerations,
are the most repetitive objectives in most of these studies. Analyzing
these works shows that balancing economic eciency with user satis-
faction and fairness, and expanding the use of hybrid games are some
of the potential future work options. Moreover, game-based optimiza-
tion methods cannot solely address the uncertainties. Therefore, other
alternatives, such as AI and ML-based methods, can be incorporated into
these works.
Moreover, Table 3 presents the summary of works on EV-integrated
power systems that used DLMP as a part of their pricing scheme. This
table shows the widespread use of advanced optimization models, such
as bi-level and tri-level models, with advanced mathematical program-
ming for linearization and essential constraints for convex relaxation.
Voltage limits, line capacity, transformer capacity, active and reactive
power balances, and consideration of OPF are the main consistent core
constraints across all these works. This shows that in DLMP-incorporated
models, the safe operating limits are more important than in game-based
optimization models. Regarding the EVs, SoC limits, charging and dis-
charging limits, and charging behavior considerations such as arrival
and departure times are the main factors that can be used to couple
electric mobility demand to power systems operation.
Moreover, most studies consider the impacts and limitations of dis-
tributed energy resources and demand response limits. Consideration
of all these constraints with DLMP as a pricing tool is to guide the
behavior of EV aggregators and users and all other participants, not
only to compete and make a prot but also to transition toward a
more exible, sustainable, and reliable power system with high inte-
gration of EVs and renewables. Another conclusion from Table 3 is that
many studies have attempted to incorporate multi-dimensional consid-
erations, such as multi-energy systems or the simultaneous integration
of transportation and power system constraints. These models can help
us to go toward more robust and realistic models; however, they also
result in problems with high complexity. The use of methodologies
ranging from simpler linearized OPF models to multi-period AC-OPF,
second-order conic relaxations, and large-scale mixed integer linear
programming formulations shows the eorts of researchers to balance
the computational tractability with modeling delity in increasingly
complex power-transport and multi-energy systems.
One of the main questions about game-based pricing and DLMP is
their applicability to real-world EV-integrated projects. Research shows
that these methods in the EV area remain in the simulation phase.
However, some cases tried to validate their results using real-world data
for game-based pricing [99,100] and DLMP [101]. Moreover, some stud-
ies tried to model the pricing schemes accurately rather than assuming
perfect rationality and considering the static, individual-level competi-
tion. This makes these schemes more applicable and closer to real-world
scenarios. For example, [102] used real-time bidirectional communica-
tion, explicitly handled information asymmetry and bounded rational-
ity, and employed an evolutionary game formulation combined with
trac equilibrium models to more realistically capture the complex
Applied Energy 392 (2025) 126058
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S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Table 2
Summary of the recent paper on game-based pricing.
Reference Year Game type Main objective Players involved
[67]
[66]
[68]
[69]
[70]
[71]
[72]
[73]
[74]
[75]
[76]
[77]
[78]
[79]
[80]
[81]
2021
2022
2023
2022
2023
2020
2022
2021
2024
2024
2024
2023
2023
2024
2023
2022
Two stages, game-based pric-
ing in each stage, stage 1:
Noncooperative game, Stage 2:
Generalized Nash Equilibrium
Cooperative game (Asymmetric
Nash Bargaining Method)
Stackelberg game (non-
cooperative)
Nash-Harsanyi Bargaining
game (cooperative game)
Stackelberg game
Generalized Nash Equilibrium
problem
Bilevel optimization (non-
cooperative)
Nash-type game
Stackelberg game
Double auction mechanism
(not traditional game theory,
but closely related due to its
competitive and participatory
structure)
Cooperative game
Stackelberg game
Nash-Stackelberg game
Stackelberg game
Multi-leader common-follower
game formulated as a non-
cooperative Nash game
Non-cooperative game, solved
at the Rosen-Nash normalized
equilibrium point
Stage 1: optimal power allocation among Photovoltaic (PV), battery,
and grid to maximize utility and ensure system balance, stage 2:
ecient and fair EV charging coordination under limited power
resources while considering individual EV preferences.
Maximize the economic payo of EVCSs and their respective EVs,
fairly allocate benets among EVCSs and EVs while satisfying power
distribution network constraints.
Optimize hydrogen trading prices and quantities between the hydro-
gen provider and Hydrogen Fueling Stations (HFSs), maximize the
hydrogen provider’s revenue while ensuring incentive compatibility
and rationality for HFSs
Facilitate fair energy trading between wind farms and HFSs, maxi-
mize mutual benets while addressing uncertainties in wind power
output and electricity prices.
Minimize the distributed energy station’s operational costs, includ-
ing energy transactions and emissions, optimize hydrogen vehicles
refueling strategies to reduce costs while considering trac and
routing.
Maximize the utility of active load aggregators while ensuring fair
energy pricing under network constraints and maintaining the
safety of the distribution network.
Upper level (distribution company): maximize distributed genera-
tion hosting capacity and minimize operation costs while interacting
with the EV aggregator and rival distribution company, lower level
(EV aggregator): maximize prot by trading electricity with the
upper-level distribution company, rival distribution company, and
EV owners.
Minimize the operational costs of both the power transmission net-
work and the electried highway network through coordinated
charging-driving navigation and Location Marginal Pricing (LMP)
interactions
Achieve a win-win economic scenario between EV retailers and
EV users, maximize EV retailers’ prots while minimizing EV
users’ costs and dissatisfaction through hybrid demand response
mechanisms.
Enable secure and ecient energy trading between prosumers while
respecting network constraints, Incorporate EVs’ charge-discharge
schedules and preferences to optimize the desired SoC at departure.
Develop a real-time charging price strategy for fast charging stations
based on DLMP and service fees, maximize the prots of the fast
charging stations cooperative alliance while addressing demand
response preferences of EV users.
Upper level: EVCSs formulate bidding strategies and expected
charging/discharging schedules, middle level: DSO clears the
distribution-level market, determines DLMP, and allocates re-
sources, lower level: transmission system operator optimizes
wholesale market operations, including power and reserve
schedules.
EV aggregators: maximize revenue from bidding in the energy-
frequency regulation market while considering EV battery costs,
wind power producers: maximize revenue from wind power par-
ticipation in the same market, factoring in penalties for output
deviations.
Stage 1: maximize the prots of the DSO, EVCS operators, and EV
users while ensuring optimal energy allocation and reducing costs.
Stage 2: Establish a hierarchical pricing mechanism to balance retail
electricity prices between EVCS operators and EV users and clear
prices between EVCS operators and the distribution network.
Enable EVCS providers to maximize their prots through strategic
pricing of EV charging at fast charging stations, guide EV users’
routing and charging decisions based on these prices to achieve
equilibrium in the coupled power-transportation network.
Facilitate ecient and fair energy pricing for Peer-to-Peer (P2P) en-
ergy trading among prosumers, optimize energy exchange between
prosumers and the grid while considering DLMP.
Stage 1: PV, battery, and grid, stage 2: EVs
competing for charging resources
At the upper level: EVCSs, at the lower level:
Individual EVs within the EVCSs.
Leader: hydrogen auctioneer (on behalf of
hydrogen providers), followers: HFSs
Wind farms, HFSs
Leader: distributed energy station operator,
followers: hydrogen vehicles
Active load aggregators (like EV aggregators)
competing for energy resources
Upper-level distribution company, EV aggre-
gator, rival distribution company, EV owners
(indirectly through the aggregator)
Transmission system operator: manages power
ow and optimizes electricity prices based on
system constraints, trac highway operator:
optimizes EV charging-driving decisions to min-
imize travel costs while responding to electricity
prices.
Leader: EV retailers setting electricity prices and
schedules. Followers: EV users determine their
charging and discharging behaviors in response
to prices.
Prosumers equipped with EVs and PV systems,
Distribution System Operators (DSO), and dis-
tribution market operators facilitate the trading
framework.
Fast charging stations forming a cooperative
alliance, EV users responding to charging prices
and road conditions.
Leaders: EVCSs, followers: DSO clearing the
market and coordinating with the transmission
system operator
EV aggregators, wind power producers, power
trading center
Leader: EVCS operators, followers: EVs
Leaders: EVCS providers competing in pricing
strategies; followers: EV users who respond by
optimizing their routing and charging behaviors.
Prosumers acting as energy buyers and sellers,
DSO
interplay between charging station pricing, EV user behavior, and trans-
portation network constraints. In [103], unlike traditional static or
solely DLMP models, this scheme adjusts charging prices dynamically
in real-time, combining the prot motives of EVCS operators with de-
mand response incentives from the DSO so that charging prices reect
market competitiveness and help maintain grid stability. Finally, while
Applied Energy 392 (2025) 126058
6
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Table 3
Summary of the recent paper on DLMP.
Reference Year Methodology/Approach Considered constraints
[82]
[83]
[84]
[85]
[86]
[87]
[88]
[74]
[89]
[90]
[91]
[92]
[76]
[77]
[93]
[78]
[94]
2021
2022
2022
2021
2024
2024
2023
2024
2023
2023
2021
2023
2024
2023
2023
2023
2022
Mathematical programming with equilibrium
constraints reformulated as mixed-integer linear
programming
Lagrangian dual decomposition theory to calculate
DLMP, congestion prices are derived as part of the
lagrangian multipliers associated with power ow and
transformer capacity constraints
Bi-level optimization to minimize the EV charging costs
and DSO operational costs, DLMP calculated using a
linearized Optimal Power Flow (OPF) model
The bi-level model considers EV aggregators as lead-
ers and the DSO as followers. DLMP was calculated
using actual DistFlow equations in the lower-level
optimization problem of a bi-level framework.
Active power DLMP derived from the rst-order partial
derivatives of the Lagrangian function for the active
load demand. Multi-period Alternating Current (AC)
OPF accounts for power losses, voltage constraints, and
the radial topology of distribution networks.
DLMP are derived using a decentralized bi-level op-
timization model and convex second-order conic
programming
DLMP calculated using AC-OPF in the integrated
power-transportation system.
DLMP is determined through a bi-level optimization
framework considering the OPF
DLMP calculated using a two-stage OPF framework
DLMP calculated using bi-level optimization frame-
work transformed to single-level mixed-integer linear
programming considering OPF in the lower level
DLMP calculated using a market-based multi-period
AC-OPF model.
DLMP calculated using a Lagrange dual decomposition
approach
DLMP calculated using a Lagrange function
DLMP calculated in the middle level of a tri-level op-
timization framework using distribution-level market
clearing
DLMP determined based on the Lagrange dual
decomposition approach
The DLMP values computed as part of a two-tier
market model employing a Nash-Stackelberg game
framework
DLMP determined in a two-stage transactive energy
system
Voltage magnitude limits, power balance for active and reactive components, load exibil-
ity and thermal comfort constraints for Heating, Ventilation, and Air Conditioning (HVAC),
SoC and charging limits for EVs, aggregator-driven DLMP step changes and power loss
considerations.
Voltage magnitude limits, transformer capacity limits, bidirectional power ow constraints
to manage network congestion, EV aggregator constraints, such as SoC, charging/discharg-
ing power limits, and uncertainty in arrival/departure times.
Voltage magnitude and angle limits, active and reactive power ow limits in branches,
aggregated EV SoC and charging/discharging limits, transformer and line capacity, balance
constraints for active and reactive power at nodes.
Voltage magnitude limits, power balance equations for active and reactive power, line ow
and transformer capacity limits, EV aggregator constraints, including charging/discharg-
ing power limits, SoC dynamics, arrival and departure times of EVs, and minimum and
maximum energy levels.
Voltage magnitude and angle limits, active and reactive power balance equations, line ow
and transformer capacity limits, EV charging constraints including charging/discharging
power limits, temporal charging exibility, SoC dynamics.
Active and reactive power ow equations, voltage magnitude limits for the distribution
system and microgrids buses, line capacity and transformer capacity constraints, SoC limits
and charging/discharging rates for EVs in EVCSs, renewable generation limits for PVs and
wind turbines in microgrids and EVCSs, constraints for robust operation under renewable
energy uncertainty using distributionally Robust Optimization (RO).
Voltage magnitude limits, power ow constraints (active and reactive), line and trans-
former capacity constraints, EV constraints, such as SoC limits, parking duration and
charging rate (fast/slow modes), driving schedules for routine and long-distance trips,
aggregator-level constraints to balance regional loads and prevent congestion.
Voltage magnitude limits, power ow constraints (active and reactive), line and trans-
former capacity limits, EV constraints, SoC dynamics, charging and discharging power
limits, temporal and spatial distribution of EV loads, renewable energy and storage
constraints for wind, PV, and advanced adiabatic compressed air energy storage
Voltage magnitude limits, power ow constraints (active and reactive), line and trans-
former capacity constraints, EVCS constraints load shifting for optimal charging schedules,
SoC dynamics, distributed energy resources constraints, including renewable energy limits
for PVs, Energy Storage System (ESS) operational limits, cost balancing between energy
procurement and distributed energy resources bids.
Voltage magnitude and angle limits, active and reactive power ow limits, line and trans-
former capacity limits, aggregated load constraints, time-shifting availability, minimum
on-time and operational limits of individual loads, day-ahead market constraints for
exibility provision by load Aggregators.
Voltage magnitude and current limits on the distribution network, power ow equations
(active and reactive) based on the AC-OPF model, line and transformer capacity limits,
EV constraints like charging power limits, SoC dynamics, arrival and departure schedules,
renewable generation, and battery energy storage constraints.
Voltage magnitude limits, line and transformer capacity constraints in the local distribu-
tion system, energy balance constraints for EVCSs operators, EV-specic constraints SoC
dynamics, bidirectional charging and discharging power limits, time-varying charging and
discharging utility functions.
Voltage magnitude limits, active and reactive power balance equations, line and trans-
former capacity constraints, EV constraints such as travel time preferences, selection of
fast charging stations based on charging price and road network conditions, cooperative
alliance constraints for fast charging stations like fair income allocation using the Shapley
value, dynamic adjustment of service fees.
Voltage magnitude and power ow limits, line and transformer capacity limits, EV con-
straints like charging and discharging, power limits, SoC dynamics, arrival and departure
schedules of EVs at charging stations, renewable energy generation limits and uncertainty
constraints, transmission and distribution boundary power consistency conditions.
Voltage magnitude limits, active and reactive power balance constraints, line and trans-
former capacity constraints, EV constraints such as charging power limits, SoC limits and
dynamics, arrival and departure schedules, renewable energy generation constraints for PV
and storage operation limits for ESS, road network constraints, including congestion and
travel time minimization.
Voltage magnitude and current ow limits for all nodes, line and transformer capacity
limits, EV constraints like charging/discharging power limits, SoC dynamics, arrival and
departure schedules, wind power output uncertainty and ramp rate constraints, energy
balance and market equilibrium conditions for power generation and demand.
Voltage magnitude limits at all nodes, line, and transformer capacity constraints, active
power ow equations based on branch ow models, EV constraints including charging
and discharging power limits, SoC limits and dynamics, arrival and departure schedules,
renewable energy constraints for PV and ESS, maximum curtailment limits for demand
response, energy procurement limits from the upstream grid, ESS charging/discharging
rates and SoC limits.
(continued on next page)
Applied Energy 392 (2025) 126058
7
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Table 3 (continued)
Reference Year Methodology/Approach Considered constraints
[79]
[95]
[96]
[97]
[80]
[98]
[81]
2024
2023
2021
2024
2023
2020
2022
Least-Squares tting used to predict day-ahead and
real-time DLMP based on linear relationships with
EVCS operator power transactions.
DLMP calculated from an AC-OPF model using second-
order cone programming for relaxation and further
linearized using a polyhedral global approximation.
DLMP determined using a linearized AC power ow
model, considering active and reactive power coupling.
DLMP are determined using an extended OPF model
with a social welfare optimization framework.
DLMP calculated as part of a second-order conic pro-
gramming formulation for the power distribution
network
DLMP calculated using a multi-objective optimization
framework
DLMP derived as part of an OPF formulation for the
distribution network
Voltage magnitude limits, power ow constraints (active and reactive), line and trans-
former capacity constraints, EV constraints like charging/discharging power limits, SoC
dynamics, arrival and departure schedules, renewable energy generation limits for PV and
wind, aggregate feasible regions for EVCS operators as virtual energy storage devices.
Power grid constraints including active and reactive power balance equations, voltage
magnitude limits, line and transformer capacity constraints, EV operational constraints
including charging/discharging power limits, SoC dynamics, relocation costs for vehicles
to balance rental and charging demands, economic constraints including budget limitations
for investment in EVs, chargers, and EVCSs, revenue and cost trade-os for both the e-
carsharing company and the DSO
Power system constraints like active and reactive power balance equations, voltage mag-
nitude limits, line and transformer capacity constraints, energy hub constraints such as
capacity limits for ESSs, eciency constraints for energy conversions, trading limits be-
tween energy hubs, market Constraints like fair trading benets using Nash Bargaining,
coordination between distributed generation and demand response based on DLMP.
Voltage magnitude limits at buses, line and transformer capacity constraints, active and
reactive power ow equations, EV charging/discharging power limits, SoC dynamics, park-
ing schedules, and travel patterns, capacity limits for PV, wind turbines, and combined
heat and power units, cryogenic energy storage charging/discharging eciency and SoC
limits.
Voltage magnitude and thermal limits, line and transformer capacity constraints, active
and reactive power ow balance equations, EV-specic routing and charging constraints
based on SoC dynamics, elastic origin-destination travel demands, trac congestion con-
straints, competitive pricing strategies among EVCSs, equilibrium conditions for Nash
game solutions.
Voltage limits at all buses, line and transformer capacity constraints, active and reactive
power ow equations, EV and battery energy storage charging and discharging power lim-
its, SoC dynamics for batteries and EVs, EV scheduling for coordinated charging during
o-peak hours, participation limits in demand response programs, wind and solar genera-
tion limits based on stochastic models, curtailment and ramping constraints for renewable
resources
Voltage magnitude limits, line and transformer capacity limits, active and reactive power
balance equations, charging/discharging limits for battery ESSs, SoC dynamics, EV-specic
exible load scheduling constraints, pricing bounds to ensure fair transactions between
prosumers and the grid
traditional game-based pricing in EV charging often relies on dynamic
price signals alone, such as ToU or bidding strategies based on sup-
ply/demand, in [104], fast charging right is considered as an additional,
transferable asset that allows for a more nuanced control.
Implementation of DLMP and game-based pricing faces several prac-
tical challenges and implementation issues in real-world cases and
within the existing electricity market. Current market structures are
built on simpler pricing models and lack the real-time, high-resolution
data infrastructure required for real-time implementation of DLMP.
At the same time, the computational complexity of solving dynamic,
multi-agent optimization problems poses signicant scalability concerns
[105]. Additionally, integrating these models into established whole-
sale and retail markets demands extensive upgrades to clearing and
settlement systems. It requires substantial regulatory reform to ensure
fairness, transparency, and consumer protection [106]. The uncertainty
of market participant responses and potential trust issues further com-
plicate adoption, making coordinated eorts among regulators, utilities,
and stakeholders essential to mitigate systemic risks and manage the
high cost of overhauling existing frameworks [107].
2.1.2. Revenue and cost optimization for EV charging networks
Prot optimization is critical for the sustainability and scalability of
the EV charging network, and all involved sides, such as power sys-
tem operators, EVCSs, and end-users, make their eorts to increase
protability. Specically, the nancial challenges for EVCS operators,
like high infrastructure costs, energy procurement, and maintenance ex-
penses, intensify the importance of this optimization procedure and rep-
resent the importance of innovative optimization strategies to improve
the protability of the EV charging network.
Generally, benet maximization includes minimizing costs and max-
imizing the system’s revenue. Cost reduction can be achieved by opti-
mizing infrastructure costs, minimizing energy procurement, optimizing
maintenance and operational costs, and minimizing battery degradation,
especially in models considering bidirectional charging. Eq. (1) shows
the general objective function of V2G-integrated optimization problems.
The rst term in this equation, ℜ
𝑉 2 𝐺 (𝑡), shows the revenues of the EV re-
lated to the sold energy or other ancillary services provided to the power
systems through V2G. The second term, Δ
𝑉 2 𝐺 (𝑡), shows the degradation
costs due to the V2G process.
max 𝑇
𝑡=0
ℜ
𝑉 2𝐺 (𝑡) −
𝑇
𝑡=0
Δ
𝑉 2𝐺 (𝑡)
𝑆𝑢𝑏𝑗 𝑒𝑐𝑡 𝑡𝑜 𝐶𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠
(1)
In the context of V2G, degradation is primarily driven by the in-
creased cycling intensity and depth of discharge associated with energy
exchanges between the EV battery and the grid. This accelerated wear
can shorten battery lifespan, raising concerns about the long-term eco-
nomic viability of V2G participation. To address this, many studies
incorporate degradation cost functions. For instance, in [87], revenue
from oered energy to the grid and costs related to calendar degra-
dation, which is associated with SoC and the working temperature of
the battery, are considered. In [108], in addition to calendar degrada-
tion, cycle degradation, which is related to the number of charged and
discharged cycles, is considered. It is worth noting that many of the
degradation cost functions, particularly those incorporating both cycle-
based and calendar-related terms, are inherently nonlinear. For instance,
cycle degradation typically varies with depth of discharge and charg-
ing rate, while calendar aging depends on factors such as temperature
and resting SoC. As a result, optimization models seeking to capture
these detailed eects may become non-convex [109]. Consequently, lin-
ear or piecewise-linear approximations of the degradation cost are often
used to maintain tractable computational complexity. By carefully cal-
ibrating these linearized models against empirical battery data, it is
Applied Energy 392 (2025) 126058
8
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Fig. 3. Protability for EV charging network.
possible to preserve a reasonable level of accuracy while still ensuring
the optimization problem can be solved eciently [108].
Energy procurement minimization is one of the most conventional
considerations for cost minimization. Employment of ToU pricing to
shift the loads from peak demand hours is a common approach to mini-
mizing costs [110]. Implementation of demand response programs and
DP schemes to move the EV load and maximize the usage of renewable
energy resources are the other considerations discussed in many studies
[111]. Ecient handling of uncertainties in energy prices, EV loads, and
renewable generation is another essential point that can inuence the
cost of the EV charging network [112]. Minimization of infrastructure
costs is mainly related to planning optimization. However, some opera-
tional and maintenance costs can also be categorized as infrastructure-
based. These costs can be reduced by minimizing renewable generation
costs and EVCS maintenance costs by implementing smart schedul-
ing strategies [113]. Reducing the transformer’s congestion and annual
losses are the other critical considerations in some studies for optimizing
the maintenance and operation costs [114]. In most papers that consider
bidirectional charging for EVs, battery degradation is regarded as one of
the main costs, and many studies tried to minimize battery degradation
by implementing smart charging strategies, reconguration optimiza-
tion [115], and integrating advanced battery aging and health models
[116,117].
Revenue maximization in EV charging networks can be achieved by
optimizing charging fees and participating in grid services. Advertising
and partnerships, data services, and data sharing with other entities, like
the power grid, to assist in analyzing end-user behavior, are dierent
approaches for revenue maximization. However, they are not discussed
in studies. The main reason for overlooking data services is the privacy
concerns that can arise from sharing private data. Revenue maximization
based on charging fees can be done using ToU pricing, implementing de-
mand response programs, and various pricing schemes discussed before
[63,118,119]. Besides bidirectional charging, other ancillary services,
like voltage droop control, active power transfer [120], and exibility
services for power systems [121], can maximize the revenue of EVCSs
(Fig. 3).
Table 4 reviews some of the key works in prot maximization in
EV-related studies. As presented in the table, the main objectives range
from maximizing operators’ revenue and minimizing the costs to bal-
ancing the power system operation stability and optimizing resource
allocation. EV drivers’ behaviors for accurate modeling of the charg-
ing demand, multi-energy system dynamics, uncertainties in prices, data
privacy, and components and power system constraints are the primary
considerations of most of the works presented in this table. Various
methods are used to solve these optimization problems. Analytical
Target Cascading hierarchically decomposes complex issues into man-
ageable sub-problems and addresses privacy in competitive pricing
scenarios. Moreover, distributed multi-agent coordination facilitates
localized decision-making and enables EV aggregators and charging
stations to optimize pricing and scheduling while maintaining system
reliability. Heuristic methods, such as adaptive algorithms, prioritize
real-time charging coordination by balancing resource utilization and
minimizing user inconvenience. Convex decomposition techniques and
convex–concave approximations eciently handle non-linearities in en-
ergy ow scheduling, particularly in joint power-hydrogen networks.
Other approaches, like bi-level optimization frameworks, integrate mul-
tiple objectives at various levels and can be used to balance protability
with grid stability.
2.1.3. Smart charging solutions and bidirectional charging
As the adoption of EVs continues, incorporating smart charging
strategies and integrating bidirectional charging into the charging and
discharging plans are becoming critical to ensure power system stability
and enhance renewable penetration and prot. Smart charging strate-
gies provide advanced scheduling and real-time optimization to align the
power system conditions with charging demand, renewable penetration,
and other end-users’ demands, and integrating bidirectional ow can in-
crease exibility. Fig. 4 shows the most critical considerations for smart
charging strategy frameworks. Most works on smart charging strategies
emphasize cost reduction and enhance the system’s renewable energy in-
tegration and eciency, incorporating dynamic factors such as demand
exibility (by analyzing the stochastic behavior of the EV users), con-
sidering EVs, power systems, and user constraints. ML-based methods,
heuristic and meta-heuristic algorithms, and advanced techniques such
as distributed optimization methods, MPC, and RO are usually used to
handle these problems’ uncertainties, scalability, and privacy.
Table 5 highlights the most recent and relevant studies on smart
charging strategies. Based on this table, techniques such as RL, bi-level
programming, and consensus-based decentralized optimization are used
for dynamic scheduling problems of EVs, considering the scalability of
the problem and user-centric adaptability. Moreover, in some studies,
technologies such as V2G and Vehicle-to-Building (V2B) help balance
the power system and enhance protability. These studies use optimiza-
tion techniques such as quadratic programming, mixed-integer linear
programming, and distributionally RO (DRO) to handle the problems
and address the uncertainties. Renewable resource constraints, EV bat-
tery SoC constraints, and power grid constraints are the main constraints
in almost all smart charging strategies. Privacy is the other issue that
arises in centralized systems, and methods like the Alternating Direction
Method of Multipliers (ADMM) and the implementation of P2P energy
trading have been alternatives for addressing this issue. Moreover, clus-
tering techniques can be used to group users’ behavior based on their
demand for more ecient handling of the uncertainties and produce
more realistic and practical scenarios for advanced smart charging tech-
niques. These advancements illustrate the critical role of smart charging
strategies in optimizing the power system’s operation and securing the
charging network’s resilience, eciency, and scalability. The impor-
tance of these strategies will be revealed increasingly with the increasing
trend of EV adoption worldwide.
2.2. Optimization techniques for EV charging
As the penetration of EVs steadily increases in many countries,
their charging patterns become more unpredictable. Coupling this un-
predictable load with intermittent renewable generation reveals the
need for robust and ecient optimization methods. Traditional, static
methods usually fail to address the dynamic nature of generation and
load. Moreover, dynamic prices, user mobility, congestion issues, and
evolving system constraints complicate the situation. Consequently, this
section discusses denitions such as day ahead, real-time scheduling,
and optimization methods such as the MPC, model-free optimiza-
tion, multi-objective approaches, RO methods, and distributed privacy-
preserving optimization methods. These methods provide continuous
Applied Energy 392 (2025) 126058
9
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Table 4
Recent studies on prot optimization in EV charging.
Reference Year Objective Key considerations Optimization approach
[122] 2023 Maximizing the prot using competitive
pricing method
DLMP for distribution system, and competition
management among EVCSs considering the privacy
Analytical Target Cascading and equilibrium
problem formulation for upper-level problem
[123] 2023 Maximizing the revenue of the EV-to-EV
charging operator
Decentralized framework for matching EVs
considering the battery constraints
Highly acceptable pair decision algorithm for
optimizing the revenue and minimizing waiting
time
[124] 2023 Minimizing the costs by optimizing the
energy purchase of an integrated elec-
tricity charging and hydrogen refueling
stations
Considerations of bounded rationality for EV
drivers, constraints for exchanging electricity and
hydrogen, and self-price and cross-price elasticity to
enhance the exibility
DP strategy for multi-energy system and choice
theory for optimize resource allocation
[125] 2024 Maximizing the prot by minimizing the
charging costs of EVs
Considerations of realistic EV demand by model-
ing the driver behavior and travel times, and grid
stability constraints
Bi-level optimization with DLMP in higher level and
EV demand response for EVs in the lower level
[126] 2021 Minimizing the costs and balance the
system stability
Considering the bidding by EV drivers, grid relia-
bility constraints, and privacy addressing by only
sharing limited data
Distributed multi-agent coordination algorithm for
local aggregators to optimize the pricing, minimize
the charging costs and ensure the power system
reliability
[127] 2022 Minimizing the operational costs of EV
aggregators
Integrating the energy, reserve, and balanc-
ing market, and addressing the uncertainties of
prices, reserve market (both up and down reserve
capacity), and EV demand
Two-stage linear optimization strategy with Monte
Carlo and k-means clustering to handle uncertainty
[128] 2021 Minimizing the costs by maximizing the
resource utilization
EVCS, power system constraints, and EV battery
constraints
Adaptive heuristic algorithm for charging
scheduling
[129] 2022 Maximizing the operational prot of
residential carpark
Joint constraints of power-hydrogen networks, and
consideration of storage and grid dependency
Convex decomposition with convex–concave ap-
proximation with bilinear and second order terms
for computational eciency
Fig. 4. Modeling consideration for smart charging optimization.
Applied Energy 392 (2025) 126058
10
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Table 5
Recent studies on smart charging strategies in EV charging.
Reference Year Objective Methodology/Approach Considered factors/Constraints Bidirectional
charging
[130] 2020 Coordinate the power and trac network
using EV charging services
RL Trac equilibrium, power grid
operation, charging fees
–
[131] 2021 Minimize the charging cost considering the
limited number of chargers
Bi-level programming model Charging station capacity, ToU pricing,
EV demands
–
[132] 2024 Enhance the operation of the power system
and balance the load
Convex optimization problem for
decentralized scheduling
EV attributes, grid constraints, renewable
energy integration
V2G
[133] 2020 Minimize the cost and enhance the per-
formance of the power system using
reconguration and bidirectional charging
Mixed-integer programming Battery degradation, grid stability,
renewable energy integration
V2G
[134] 2024 Reduce EV charging cost and enhance user
experience
Deep RL for real-time decision-making User preferences, PV self-consumption,
electricity pricing
–
[135] 2023 Minimize the load variance while maximizing
the PV usage using V2G
Quadratic programming PV generation limits, EV constraints,
voltage stability constraints
V2G
[136] 2020 Optimize the overall energy consumption of
a building and grid load using smart charging
strategy and V2B
Mixed-integer linear programming Building load, EV availability, grid
demand
V2B
[137] 2024 Enhance the charging network eciency using
optimal clustering and optimization
K-means clustering algorithm combined
with heuristic optimization
Charging station density, grid capacity,
user demand patterns
–
[138] 2023 Assess the EV charging management on grid
stability and eciency
Real-world pilot study with demand
response strategies
Grid constraints, user demand proles,
renewable integration
–
[114] 2024 Assess the impact of smart charging on grid
stability and storage usage
Linear programming Battery storage capacity, EV charging
demand, grid load balancing
V2G
[139] 2024 Optimize EV smart charging Consensus-based decentralized opti-
mization with priority clustering to
accelerate convergence
User preferences, charging capacity
constraints, scalability, privacy
–
[140] 2022 Balance the load using smart EVCS selection Load-Balancing matching strategy Distance to charging stations, microgrids
load demand
–
[87] 2024 Minimize the cost in a distribution system
connected to microgrids and smart parking
lots
DRO, ADMM, and convex second-order
cone programming optimization
Renewable energy resources uncertainty,
SoC limits, privacy
V2G
adaptation to evolving conditions, exploit decentralized computing ar-
chitectures to mitigate communication overhead and privacy concerns,
and balance competing objectives like grid stability, cost minimization,
and user satisfaction. Fig. 5 illustrates various categories of optimiza-
tion methods, their use cases, advantages, and drawbacks. The following
subsections explore these state-of-the-art optimization strategies, high-
lighting their methodological foundations and practical implications for
modern EV charging ecosystems.
2.2.1. Scheduling and control
• MPC
MPC (also known as Receding Horizon Control or Rolling Horizon) is
an advanced control tool used in various applications, such as indus-
trial processes, autonomous vehicles, and other dynamic systems that
require real-time decision-making, including energy systems. MPC is
used to predict the future behavior of a system based on the present
state and control inputs over a prediction horizon. It is also appli-
cable to linear, non-linear, or hybrid systems. MPC determines the
optimal sequence of control actions by minimizing the formulated
cost function of the optimization problem. MPC incorporated the re-
ceding horizon principle, which applies only the rst control input
of the optimized sequence and repeats the process using updated
measurements and system states at each time step. MPC can also ef-
fectively handle the system’s state, input, and output limits to ensure
feasible and safe operation. For instance, Eqs. (2) and (3) represent
the simple linear system’s model [141].
𝑥
𝑘+1 = 𝐴𝑥
𝑘 + 𝐵𝑢
𝑘 , (2)
𝑦
𝑘 =𝐶𝑥
𝑘 ,(3)
Generally, Eqs. (2) and (3) are state and output equations, re-
spectively. In these equations, 𝑥
𝑘 is the state vector, 𝑢
𝑘 is the control
input, and 𝑦
𝑘 is the output at time step 𝑘. Moreover, matrices 𝐴,
𝐵, and 𝐶 dene the system dynamics. Eq. (4) represents a common
quadratic cost function used in MPC problems. MPC seeks to min-
imize this cost function over a nite prediction horizon of 𝑁
𝑝 (5)
[141].
𝐽 =
𝑁
𝑝−1
𝑖=0
(𝑟𝑘+𝑖 − 𝑦
𝑘+𝑖)
𝑇𝑄(𝑟
𝑘+𝑖 − 𝑦
𝑘+𝑖) + Δ𝑢
𝑇
𝑘+𝑖𝑅Δ𝑢
𝑘+𝑖
, (4)
minimize
𝑢
𝑘 ,…,𝑢
𝑘+𝑁𝑝−1
𝐽 , (5)
Moreover, MPC incorporates various constraints for optimization.
Eqs. (6), (7), and (8) represent the control input constraint, output
constraint, and state constraint, respectively [141].
𝑢
min ≤ 𝑢
𝑘≤ 𝑢
max ,(6)
𝑦
min ≤ 𝑦
𝑘≤ 𝑦
max,(7)
𝑥
min ≤ 𝑥
𝑘≤ 𝑥
max .(8)
MPC can predict the system’s future behavior and take proac-
tive rather than reactive corrections. Applying constraints on control
parameters ensures feasibility and safety. The main drawbacks of
MPC are the high computational demand for systems with long hori-
zons and complex dynamics, high dependence of the accuracy on
modeling quality, and implementation complexity. These features
make MPC suitable for process control, energy and power systems,
transportation, and robotics applications. Table 7 shows some works
on EV-integrated power systems that used MPC for optimization
and system control. Based on this table, MPC is used for various
cost-minimization purposes, peak load minimization, and congestion
management in power systems, considering various demand re-
sponses and demanded charges, uncertainties, and real-world system
constraints.
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Fig. 5. Categories of optimization methods.
• Bilevel programming model
Bilevel programming or optimization is a specialized approach in
mathematical programming for modeling decision-making and op-
timization problems. This method includes a hierarchical structure
involving two levels. Bilevel optimization can be categorized as a
sub-category of game theory, specically the Stackelberg game, be-
tween upper and lower-layer players. In contrast, game theories
apply to problems with more than two players. Eqs. (9), (10) and
(11) show a basic formulation of the upper-level problem in bilevel
optimization. In this formulation, Eq. (9) shows the objective func-
tion of the upper level (also called leader), Eq. (10) represents the
general form of upper-level constraint, 𝑥 is the decision variable con-
trolled by upper-layer player, and 𝑋 is the upper-level’s feasible set
of decision variables [72].
minimize
𝑥∈𝑋𝐹 (𝑥, 𝑦) (9)
subject to 𝑔(𝑥, 𝑦) ≤ 0 (10)
𝑦 ∈ arg min{𝑓 (𝑥, 𝑦) ∣ ℎ(𝑥, 𝑦) ≤ 0, 𝑦 ∈ 𝑌 }(11)
Moreover, Eqs. (12) and (13) represent the lower-level (also
called follower) objective functions and the general constraint format
for the lower level, respectively. In these equations, 𝑦 is the decision
variable controlled by the lower-level player, and 𝑌 is the feasible
set for the lower-level decision variable.
minimize
𝑦∈𝑌𝑓 (𝑥, 𝑦) (12)
subject to ℎ(𝑥, 𝑦) ≤ 0 (13)
In cases where the lower-level problem is convex, the prob-
lem can be reformulated into a single-level optimization using the
Karush–Kuhn–Tucker theorem [84], which makes it easier to solve.
In non-convex lower-level problem cases, methods like global op-
timization techniques, branch and bound methods, or heuristic
approaches may be used. The special structure of bilevel optimiza-
tion makes it suitable for hierarchical decision-making, modeling
the interactions between the layers, and realistic strategic planning
where players respond to the decisions. However, computational
complexity, limited solution methods without guaranteed global op-
timality, high sensitivity to parameter changes, and implementation
challenges are some drawbacks of this method. Bilevel optimization
is widely used in transportation and network design, supply-chain
management, revenue management, and energy markets. The appli-
cations of this method in EV-integrated power systems encompass
a broad spectrum of objectives, including cost optimization, social
welfare maximization, maximizing renewable energy usage, opera-
tional cost minimization, prot maximization, and maximizing the
hosting capacity. This approach allows for the structured optimiza-
tion of multiple objectives and constraints, carefully considering
Applied Energy 392 (2025) 126058
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S. Ghanbari Motlagh, J. Oladigbolu and L. Li
ToU prices, charger limitations, battery degradation, renewable inte-
gration, bidirectional charging, hydrogen generation, P2P markets,
demand uncertainties, DLMP, and the stability of power systems.
• Stochastic programming
Stochastic programming is a widely used optimization method un-
der uncertainty. This method is practical when deciding before the
actual scenarios of uncertain parameters are realized. Like the other
optimization methods, stochastic programming tries to minimize or
maximize the expected value of a function, considering the uncer-
tainties of one or more decision variables. The basic formulation of
an objective function using stochastic programming is shown in (14)
[142].
min
𝑥≥0
{𝑐
𝑇 𝑥 + E[𝑞
𝑇 𝑦(𝜉)]} (14)
In the above equation, 𝑥 is the decision variable, 𝜉 is the ran-
dom variable, and E is the expectation over the distribution of 𝜉.
Moreover, 𝑐 and 𝑞 are cost coecients for 𝑥 and 𝑦, respectively. In
this formulation, 𝑐
𝑇 𝑥 is minimized by choosing 𝑥 in the rst-stage
decision. In the second stage, after realizing the random variable
𝜉, 𝑞
𝑇 𝑦(𝜉) is minimized by choosing 𝑦(𝜉). Some constraints may also
contain random variables when modeling a problem using stochas-
tic programming. Constraints can be hard or soft, meaning always
satised or satised with a certain probability. A general constraint
format involving uncertain variables in stochastic programming is
represented in (15) and (16) [142].
𝐴𝑥 = 𝑏(15)
𝑇 (𝜉)𝑥 + 𝑊 (𝜉)𝑦(𝜉) ≥ ℎ(𝜉),∀𝜉(16)
In these equations, 𝐴 and 𝑇 (𝜉) are matrices, while 𝑏 and ℎ(𝜉)
are vectors. Moreover, 𝑦(𝜉) is the second-stage decision variable
that adapts to the realized uncertainty. At the same time, 𝑊 (𝜉)
is the recourse matrix that denes the constraints governing 𝑦(𝜉)
based on the realization of 𝜉. The presented formulation is only the
most basic two-stage stochastic programming model. However, other
models, such as multi-stage stochastic programming and chance-
constrained programming, have more complicated formulations and
can be implemented based on the needs. Stochastic programming
can help control risks and is exible in modeling uncertainties and
decision timing. However, it can be computationally expensive, and
as the number of scenarios and depth of decision stages increases,
the size of the problem grows exponentially. The other drawback
of stochastic programming is the oversimplication and assump-
tion, such as considering normal distribution for data, which might
not always represent real-world complexity. However, the main is-
sue with stochastic programming may be that the eectiveness of
this method is highly dependent on the availability and accuracy
of the probability distribution for uncertain variables. Stochastic
programming is widely used in nance, supply chain management,
healthcare, agriculture, public policy, and the energy sector planning
and operation.
2.2.2. ML and AI-based optimization
• Model-free RL (MFRL)
MFRL is a method that can handle the problem without explicit
knowledge of an environment’s dynamics. MFRL can learn the poli-
cies by getting feedback from its interactions with the environment,
aiming to nd the best policies to maximize cumulative reward. The
core of MFRL can be described by elements such as the set of possible
states, the set of actions, policies, feedback signals that indicate the
quality of actions for specic states or rewards, and the value func-
tion that estimates how good the state is for an agent or how good it
is to perform a particular action in a given state. Eq. (17) represents
the general format of the value function in an MFRL problem, which
maximizes the expected cumulative reward.
𝑉
𝜋 (𝑠) = E[𝑅
𝑡∣ 𝑠
𝑡 = 𝑠, 𝜋] (17)
In the above equation, 𝑉
𝜋 (𝑠) is the state value function for policy
𝜋, 𝑠 is the state, 𝑠
𝑡 is the state at time 𝑡, and 𝑅
𝑡 is the reward at time
𝑡. Moreover, Eq. (18) represents the expected return 𝑄
𝜋 (𝑠, 𝑎)when
action 𝑎 is taken under policy 𝜋 at time 𝑡.
𝑄
𝜋 (𝑠, 𝑎) = E[𝑅
𝑡 ∣ 𝑠
𝑡 = 𝑠, 𝑎
𝑡 = 𝑎, 𝜋] (18)
Finally, (19) shows the cumulative reward (𝑅
𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 ), which is
the rewards obtained by an agent over a sequence of time steps in
an environment. In this equation, 𝑇 is the time horizon.
𝑅
𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 =
𝑇
𝑡=0
𝑅
𝑡(19)
MFRL methods can be value-based and policy-based, like Q-
learning and State-Action-Reward-State-Action (SARSA). Q-learning
is an o-policy learner, which means it can directly approximate the
optimal value and action functions independently from the policy
being followed. At the same time, SARSA is an on-policy learner,
which means it can update its action and value function based on
the action taken by the current policy. In contrast, policy-based
methods directly optimize the policy without using a value func-
tion as an intermediate. Gradient ascent and actor-critic methods
are policy-based methods widely used for nding optimal policy
parameters.
MFRL methods can handle high-dimensional and continuous ac-
tion spaces, and since there is no need for modeling the environment,
they are easier to implement compared to other optimization meth-
ods. MFRL methods often achieve better results in learning optimal
policies than human-level performance in many tasks, making them
a strong optimization tool. Requiring many interactions with the en-
vironment, high variance in some cases, and a lack of theoretical
foundation for stochastic dynamics or incomplete state information
are the main drawbacks of MFRL methods. The main use cases of
these methods include gaming, robotics, nance, and autonomous
vehicles. They are also used in some EV-integrated power system
optimization problems. Table 7 shows some related works that used
MFRL for optimization problems. Reviewed works demonstrate that
MFRL can be eectively employed for optimizing various prob-
lems with diverse objectives, such as minimizing load variance,
costs, and emissions, maximizing prots and social welfare, while
addressing critical considerations like bidirectional charging, elec-
tricity price uctuations, EV charging behavior, battery degradation,
renewable energy integration, DP, and driving path optimization in
multi-energy systems.
As discussed, MFRL and MPC can handle uncertainties of re-
newables, EV behaviors, and grid conditions. Table 6 compares
their uncertainty handling performance, adaptability, implementa-
tion complexity, and computational requirements. Based on this
comparison, MPC can only handle known uncertainties, while MFRL
can handle various uncertainties through learning. Due to this dif-
ference, the main computational burden of MPC is in the solving
process of the real-time optimization problem. Meanwhile, MFRL is
more ecient and faster in real-time and computationally intensive
during training. A few studies have compared these two methods in
EV-related problems. Based on [143], the performance of the meth-
ods in solving uncertain optimization problems is quite comparable.
However, MPC is easier to adapt to new settings and new models.
Moreover, MFRL needs more hyperparameter tuning, which makes
it more time-consuming. MFRL is quite slow during training, but can
quickly produce control decisions when trained. In comparison, MPC
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S. Ghanbari Motlagh, J. Oladigbolu and L. Li
Table 6
Comparison between MPC and MFRL.
Method MPC MFRL
Adaptability [145] Limited by model accuracy and prediction horizon High adaptability to changing environments and uncer-
tainties
Computational requirements [146] Requires solving optimization problems in real-time Computationally intensive during training and ecient
at runtime
Handling uncertainties [147] Manages known uncertainties through forecasts Learns to handle both known and unknown uncertain-
ties
Implementation complexity [148] Requires detailed system modeling and tuning Requires large datasets and careful design of learning
algorithms
is slow in solving optimization, but does not require a separate train-
ing process. Furthermore, based on [144], data and forecast errors in
real-world operation, such as out-of-order PV data or missed EV ar-
rivals, cause MPC to exceed its intended peak demand and incur extra
costs compared to a scenario with perfect forecasts. MFRL naturally
adapts over time through online learning but experiences short-term
costs while rening its policy.
2.2.3. Distributed computing and optimization methods and privacy issues
With the increasing complexity of power systems and the integra-
tion of renewables and EVs, there is a signicant need for advanced
optimization and computation frameworks that can handle optimiza-
tion problems in a distributed manner and address the computational
complexity with decentralized decision-making and system-wide solu-
tions. Besides decreasing the computational demand and initial costs
for central computational systems, these approaches can address pri-
vacy issues. Because the need for information sharing decreases, at least
a portion of computations can happen in the outer layers of the sys-
tem. This section discusses edge computing and ADMM as methods for
decentralized decision-making and distributed optimization.
• Edge computing
Edge computing is a distributed computing paradigm. In edge com-
puting, the processes happen close to the data generation sources,
and the dependence on centralized and cloud infrastructures de-
creases. Moreover, the need to transfer large amounts of data across
the network decreases, resulting in latency reduction and bandwidth
usage. Edge computing usually involves optimizing the placement
and execution of tasks in the distributed edge devices and locations.
Based on edge computing, assigning tasks to edge devices can be
structured as an optimization problem. This optimization problem
can contain objectives and constraints such as computational costs,
latency, communication or synchronization costs among edge de-
vices, energy usage, computational capacity, or quality of service
[149].
The main advantages of edge computing are low latency, band-
width eciency, enhanced privacy and security, and scalability. It
also has drawbacks, like insucient computational power in some
edge devices, complexity in management, higher initial costs, and
data exchange issues between edge devices. The main use cases
of edge computing are autonomous vehicles, healthcare, industrial
Internet of Things, telecommunications, smart grids, and power sys-
tems. As evident from Table 7, the number of works on EV-integrated
power systems with edge computing approaches is limited compared
to other approaches. Compared to dierent methods, where cost,
benet, and load optimization are the primary focuses, studies in-
volving edge computing also prioritize computational eciency as
a key objective. Moreover, these studies’ most widely used con-
siderations are bidirectional charging, renewable integration, EV
charging behavior, EV battery constraints, hydrogen generation,
demand uncertainty, demand response programs, and DP.
• ADMM
ADMM is an optimization method for large-scale problems with
separable objective function structures. It implements the features
of augmented Lagrangian and dual decomposition methods and
transforms the original optimization problem into a distributed and
parallel optimization problem. ADMM can solve a convex optimiza-
tion problem with the following separable format, represented in
(20) and (21) [87].
min
𝑥∈𝑋,𝑧∈𝑍𝑓 (𝑥) + 𝑔(𝑧) (20)
s.t. 𝐴𝑥 + 𝐵𝑧 = 𝑐 (21)
In the above equations, 𝑓 and 𝑔 are the objectives, 𝑥 and 𝑧 are
the decision variables, and 𝑋 and 𝑍 represent the feasible regions
for the variables 𝑥 and 𝑧. The augmented Lagrangian method can be
applied to the above equations as shown in (22). In this equation, 𝜆
is the lagrangian coecient and
𝜌
2𝐴𝑥 + 𝐵𝑧 − 𝑐 is the penalty term.
Moreover, Eqs. (23)–(25) represent the iterative process of an ADMM
algorithm. In these equations, 𝑘 is the iteration index. Finally, Eq.
(26) shows the convergence criterion of an ADMM algorithm, and 𝜀
is the convergence threshold [87].
𝐿(𝑥, 𝑧, 𝜆) = 𝑓 (𝑥) + 𝑔(𝑧) + 𝜆
𝑇 (𝐴𝑥 + 𝐵𝑧 − 𝑐) +
𝜌
2𝐴𝑥 + 𝐵𝑧 − 𝑐2
2(22)
𝑥(𝑘 + 1) = arg min
𝑥∈𝑋𝐿(𝑥, 𝑧(𝑘), 𝜆(𝑘)) (23)
𝑧(𝑘 + 1) = arg min
𝑧∈𝑍𝐿(𝑥(𝑘 + 1), 𝑧, 𝜆(𝑘)) (24)
𝜆(𝑘 + 1) = 𝜆(𝑘) + 𝜌
𝐴𝑥(𝑘 + 1) + 𝐵𝑧(𝑘 + 1) − 𝑐
(25)
𝜆(𝑘 + 1) − 𝜆(𝑘) ≤ 𝜀(26)
Decomposability, scalability, robustness, ease of implementation,
and exibility are the main reasons for the popularity of ADMM
among distributed optimization methods. However, ADMM still
suers from slow convergence, global communication issues in dis-
tributed systems, weak performance for non-convex problems, and
parameter tuning requirements for the penalty parameter 𝜌. ADMM
is usually used in areas like ML, signal processing, distributed opti-
mization, statistics, control, robotics, nance, and energy systems.
As shown in Table 7, ADMM is widely used compared to other
optimization techniques. It is applied to various optimization prob-
lems, including cost optimization, load optimization, and renewable
resource optimization.
Some other concepts can be used for distributed decision-making and
are less discussed in the EV area. For instance, federated learning is
a distributed ML paradigm that enables local training on end devices,
such as EVs or smart meters, ensuring that raw charging records remain
private. At the same time, only aggregated model updates are transmit-
ted to a central server. This minimizes data exposure by sharing only
model gradients instead of sensitive raw data and allows for person-
alized local models tuned to individual behaviors. Also, its scalability
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Table 7
Optimization methods used in recently published papers on EV-integrated energy systems.
Method Reference Main objective Main consideration
MPC [63,116,127,164–
172]
Minimize the cost, minimize the congestion, minimize the
peak load, minimize the generation cost, minimize the
net present cost, minimize the EV charging costs, emis-
sion reduction, atten the load, minimize the operational
cost, minimize the grid dependency
Demand charge, EV related uncertainties, multi-energy sys-
tem, islanded energy systems, demand response programs,
renewable uncertainties, battery storage constraints, user
comfort, P2P transactions between microgrids, multi markets,
EV related constraints, charging power limits, grid constraints,
EV behavior constraints, bidirectional charging, market un-
certainties, hydrogen generation, DP, transportation system,
renewable integration
Bilevel optimization [72,74,84,85,90,
131,172–180]
Minimize the cost, maximize the social welfare, maximize
the renewable energy usage, minimize the operational
cost, maximize the prot, maximize the hosting capacity,
reduce the carbon emission
ToU prices, limited chargers, battery degradation, renewable
integration, bidirectional charging, hydrogen generation, P2P
market, hydrogen demand uncertainties, DLMP, EVs uncer-
tainties, power system stability constraints, trac system, EV
routing, demand response program, renewable uncertainties,
multi-energy systems
Stochastic programming [115,180–187] Minimize the operational cost, minimize the loss, min-
imize the total cost associated with the provision of
exibility, maximize the social welfare, maximize the
prot, minimize the emission
Reconguration decision making, EV uncertainties, renewable
resources uncertainties, bidirectional charging, EV battery
constraints, power system constraints, power losses, EVCS
congestion, energy hub, hydrogen generation, hydrogen
demand uncertainties, price uncertainties, trac ow
MFRL [65,88,119,188–
197]
Minimize the load variance, maximize the prot, mini-
mize the charging price, reduce the emission cost, reduce
the range anxiety, minimize the operating cost, maxi-
mize the social welfare, maximize station prot while
guaranteeing customer demand
Bidirectional charging, electricity price variation, EV charging
behavior, battery degradation, renewable energy, DP, driving
path selection, multi-energy system
Edge computing [185,198–200] Improve the computational eciency of EVCSs, atten
the load prole, increase renewable usage, minimize the
cost, maximize the benet
Bidirectional charging, renewable integration, EV charging be-
havior, EV battery constraints, hydrogen generation, demand
uncertainty, demand response program, DP
ADMM [81,87,91,117,170,
185,186,201,202,
202–206]
Flatten the load, minimize the cost, minimize the
wind spillage, minimize the long-term average total
cost, minimize the operational cost, minimize the grid
dependency
Network congestion, battery aging, EV driver behavior,
demand response programs, hydrogen generation, renew-
able integration, price uctuation, trac ow, P2P market,
hydrogen transfer and delivery time, DLMP, renewable uncer-
tainties, price uncertainties, DP, OPF, double auction-based
trading mechanism, operational constraints of the power
system, line congestion
RO [69,74,83,85,108,
180,185,207]
Minimize the operational costs, maximize the prot, min-
imize the congestion, minimize the EV aggregators cost,
maximize the social welfare, minimize the emission
Storage systems constraints, EV batteries constraints, bidirec-
tional charging, demand response, RO for price uncertainties,
hydrogen generation, RO for wind power generation uncer-
tainties, RO for PV power generation, DLMP, congestion
management, RO for EV aggregators uncertainties, OPF,
multi-energy system
DRO [87,172] Maximize the real-time prots, minimize the operational
costs
Multi-energy systems, hydrogen generation, P2P market, EV
driver behavior, DRO for PV power uncertainty, DRO for wind
power uncertainty
Multi-objective
optimization
[132,171,180,188,
208–213]
Minimize the cost-emission, minimize the EV charging
cost-V2G cost, minimize the operational cost-EV charging
costs-loss, optimize the load variance-prot-EV charg-
ing cost-emission, optimize the costs-SoC level-charging
ramps, optimize the hydrogen sell revenue-electricity
purchase cost-operating cost-feeder congestion, opti-
mize the operational costs-power quality, operational
costs-emission
Bidirectional charging, renewable integration, OPF, grid re-
silience, hydrogen generation, multi-energy systems, DP,
renewable uncertainty, demand response program
Heuristic and meta-
heuristic optimization
methods
[113,169,188,204,
214–218]
Minimize the load variance, minimize the EV charg-
ing cost, minimize the carbon emissions, reduce the
peak load, maximize the prot, minimize the long-term
average total cost
EV battery constraints, Charge/discharge power limits,
transformer capacity limits, Bidirectional charging, de-
mand response program, multi-energy systems, hydrogen
generation, EV charging behavior
makes it well-suited for real-time applications in dynamic EV ecosystems
[150]. Blockchain technology also enhances decentralized charging in-
frastructures by providing a tamper-proof ledger that securely records
every transaction or data exchange, anonymized. Its immutable log-
ging guarantees that each event is cryptographically secured, ensuring
auditability and transparency. In addition, smart contracts automate
data handling protocols, enforcing user consent and strict adherence
to privacy policies [151]. Incorporating zero-knowledge proofs further
strengthens privacy, allowing the validation of transactions without ex-
posing any underlying sensitive information [152]. In V2G interactions,
these blockchain features work cohesively to conrm that charging ses-
sions comply with contractual requirements while keeping individual
energy usage data condential [153].
Emerging standards and protocols are essential for harmonizing
security and privacy across the V2G ecosystem. In this context, ISO
15118 is evolving to facilitate robust V2G communication with en-
hanced authentication and cryptographic key management and address
more stringent privacy requirements [154]. Concurrently, IEC 63110 is
being developed to dene secure communication protocols between EVs
and charging systems [155], while Extended Open Charge Point Protocol
incorporates advanced security measures such as mutual authentication
and secure session management [156].
Methods discussed in this section collectively oer promising ap-
proaches for managing the complexity of modern power systems with
renewables and EV integration, while enhancing privacy and security.
However, concerns remain, such as heterogeneous security across de-
vices, communication overhead vulnerabilities, limited computational
power, and risks of inference and cyber attacks. By processing data
locally, edge computing reduces dependency on centralized systems,
lowering latency, communication costs, and the risk of data breaches
Applied Energy 392 (2025) 126058
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S. Ghanbari Motlagh, J. Oladigbolu and L. Li
[149]. ADMM facilitates the decomposition of large-scale optimization
problems into parallel tasks across distributed nodes, although its
need for secure inter-node communications remains challenging [91].
Federated learning minimizes raw data exposure by enabling local
model training and sharing only aggregated updates, yet it also requires
safeguards against inference attacks [150]. Meanwhile, blockchain tech-
nologies provide a tamper-proof, decentralized ledger for secure data
exchanges reinforced by smart contracts that automate protocol enforce-
ment [153].
2.2.4. Robustness and uncertainty management
As it is obvious from all reviewed works in this study, uncertainties
are one of the signicant issues with EV/renewable-integrated power
systems, and many approaches have been used to address these issues.
RO and DRO are advanced optimization methods designed to handle
the uncertainties during the optimization process. These methods suit
applications involving renewable energy integration, DP, and demand
response programs, ensuring system stability and cost-eectiveness un-
der unpredictable conditions. By incorporating these approaches, mod-
ern EV charging systems can achieve higher reliability and adaptability
to real-world operational challenges.
• RO
RO is a mathematical formulation method for uncertain optimiza-
tion problems. RO diers from traditional methods as it does not rely
on deterministic assumptions but considers solving the optimization
problem while uncertain decision variables are in the worst-case sce-
nario. Therefore, RO can ensure resilience in decision-making in the
presence of uncertainties. A general RO problem can be formulated
like (27) [157].
min
𝑥∈𝑋max
𝜉∈Ξ 𝑓 (𝑥, 𝜉) (27)
In the above equation, 𝑥 is the decision variable, 𝑋 is the fea-
sible set of decision variables, 𝜉 is the uncertain parameter, Ξ is
the uncertainty set containing all possible realizations of 𝜉, and 𝑓
is the objective function. The inner maximization ensures that the
model accounts for the worst-case scenario of the uncertain parame-
ter, which makes the decisions robust. Eq. (28) represents a general
formulation of constraints in an RO model [157].
𝑔(𝑥, 𝜉) ≤ 0 ∀𝜉 ∈ Ξ (28)
RO can guarantee the feasibility of the decisions under all realiza-
tions of uncertainty within the predened uncertainty set. Moreover,
compared to many methods, RO does not require precise probability
distributions for uncertain parameters. It only considers the range
of the uncertain parameter. The other advantages of RO are sim-
pler formulation and better computational eciency compared to
methods like stochastic programming. These advantages make RO
well-suited for real-world applications. In contrast, conservatives,
due to concentrating on worst-case scenarios for uncertain parame-
ters, and high dependence of the results on the uncertainty set design,
are the main drawbacks of the RO method. RO’s main use cases are
in the energy market, transportation and logistics, grid congestion
management, renewable integration, and EV charging optimization.
Based on Table 7, in EV-integrated power systems, RO is usually used
to optimize the operational cost, prot, emissions, social welfare,
and congestion by addressing price, wind, and PV generation and
EV behavior uncertainties.
• DRO
While RO focuses on optimizing the decision for the worst-case
scenario, considering a predened uncertainty set, DRO takes a
probabilistic view and optimizes the decision based on a range of
probability distributions called ambiguity sets, rather than xed sets.
DRO is like a bridge between stochastic programming and RO. Eq.
(29) represents a general formulation of a DRO problem [158].
min
𝑥∈𝑋sup
P∈
E
P [𝑓 (𝑥, 𝜉)] (29)
In this formulation, 𝑥 is the decision variable, 𝑋 is the feasible
set of decision variables, 𝜉 is the uncertain parameter, P is the prob-
ability distribution belonging to the ambiguity set , which contains
all plausible distributions for 𝜉, and E
P [𝑓 (𝑥, 𝜉)] is the expected value
of the objective function under the distribution P. The ambiguity
set is the heart of DRO and denes the range of distributions
over which the optimization is performed. Moment, distance, and
support-based sets are the common ways to dene ambiguity sets.
Flexibility, risk mitigation, and balance between conservativeness
and performance are the advantages, while ambiguity set design,
computational complexity for complex and high-dimensional am-
biguity sets, and dependency on probabilistic information are the
drawbacks of DRO. Healthcare, supply chain management, and -
nance are the areas in which DRO is widely used. In regions of EV
charging and energy systems, DRO can address the uncertainties of
renewables, markets, and EV charging behavior.
Stochastic programming, RO, and DRO can all address uncertain-
ties in EV and renewable-penetrated power systems. However, there
are dierences in their approaches, performance, and requirements.
Moreover, uncertainties in renewable generation, market prices, and
EV behavior in modern energy systems require methods to cap-
ture interdependencies. Stochastic programming uses full probability
distributions to accurately model these correlations, making it vul-
nerable to inaccuracies in distributional assumptions. RO takes a
more conservative route by preparing for the absolute worst-case
scenario within a pre-specied uncertainty set, often assuming that
all variables hit their extreme values simultaneously, a rarely real-
istic condition. In contrast, DRO constructs an ambiguity set of all
probability distributions whose rst and second moments are esti-
mated from historical data and constrained to match the empirical
means and covariance matrix of renewable output, market prices and
EV behavior, ensuring that the observed interdependencies, namely
the pairwise correlations, are enforced in every candidate scenario.
This, in turn, enables more ecient risk management in scenarios
where uncertainties are strongly interrelated.
2.2.5. Multi-objective optimization
Unlike the ordinary optimization methods that focus on optimizing
a single objective, the objective function in multi-objective optimization
problems might include two or more conicting objectives, and multi-
objective optimization seeks a set of Pareto optimal solutions. These
solutions are the trade-os among the objectives, while no other so-
lutions in the search space are superior in all objectives. Eqs. (30) and
(31) represent the general formulation of a multi-objective optimization
problem with two objectives. In this formulation, 𝑓
1 and 𝑓
2 are the ob-
jectives, 𝑔
𝑖 are the constraints for 𝑖 = 1, … , 𝑚, 𝑥 is the decision variable
vector, and 𝑋 is the feasible set dened by the constraints [159].
Minimize 𝐹 (𝑥) = [𝑓
1 (𝑥), 𝑓
2 (𝑥)] (30)
Subject to 𝑔
𝑖 (𝑥)≤ 0, 𝑖 = 1,…, 𝑚
𝑥 ∈ 𝑋
(31)
Although multi-objective optimization methods can be complex to
implement and have a heavy computational burden for decision-making
between Pareto optimal solutions, they are still more exible and pro-
vide more comprehensive solutions considering various perspectives.
Engineering design, economics, and resource management are the use
cases of these methods. Fuzzy Pareto optimality, epsilon-constraint, and
augmented epsilon-constraint are the most popular multi-objective op-
timization methods used in EV-integrated power systems. Fuzzy Pareto
optimality seeks solutions that balance objectives in a soft optimal sense
rather than strict Pareto dominance [160]. In the epsilon-constraint
method, one primary objective is put in the objective function, while
Applied Energy 392 (2025) 126058
16
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
others are placed in the constraints list [161]. In contrast, in the aug-
mented epsilon-constraint method, all objectives are out in the objective
function [162], and compared to the simple epsilon-constraint method,
the augmented epsilon-constraint method provides better feasibility
handling due to the augmentation term.
2.2.6. Heuristic and meta-heuristic optimization methods
Heuristic and meta-heuristic optimization methods are strategies to
solve large-scale and complex problems in a reasonable time frame.
Heuristics are usually faster and simpler methods that can be used to
solve problems by making educated guesses. However, these methods
cannot guarantee the nding of optimal global solutions. The greedy
algorithm, local search, simulated annealing, and tabu search are pop-
ular heuristic methods. In contrast, meta-heuristics are higher-level
approaches that can be adapted to various optimization tasks, explore
large search spaces eciently, and escape local optima to nd near-
global solutions. Popular meta-heuristic approaches include genetic
algorithms, particle swarm optimization, and ant colony optimization.
The origin of most heuristic and meta-heuristic optimization methods is
the natural processes, behaviors, or phenomena, and the formulation for
each is dierent. Therefore, the formulation of these methods is not pro-
vided in this study, but it can be easily found in the literature. Moreover,
in some cases, ML can be used to optimize EV-integrated power systems.
For instance, in [163], unsupervised learning is used for distributing EV
charging loads and trac ows in coupled power and transportation
systems. However, these methods cannot be categorized as heuristic or
metaheuristic.
Flexibility, scalability, high speed, and robustness are the main
advantages of heuristic and meta-heuristic methods. However, as men-
tioned before, these methods cannot guarantee global optimality.
Moreover, the performance of these methods is highly dependent on
parameter settings. Furthermore, many meta-heuristic methods utilize
random processes, and each run might produce dierent outcomes.
Engineering design, telecommunication, nance, scheduling problems,
transport and logistics, and energy systems are the primary areas of use
for these methods. Based on the summary of the reviewed papers on
EV-integrated power systems in Table 7, particle swarm optimization,
genetic algorithm, whale optimization algorithm, greedy algorithm, and
ordinal optimization are the most common heuristic and meta-heuristic
optimization methods.
Each optimization approach mentioned in this section incorporates
a distinct balance between computational complexity and scalability,
which is critical when considering real-world, large-scale deployments
for EV charging. For example, MPC and bilevel optimization provide
rigorous frameworks for dynamic decision-making and hierarchical con-
trol. Yet, they involve solving complex optimization problems at each
time step or nested level, which can become computationally prohibitive
as the system size grows [72,166]. Stochastic programming, while pow-
erful in accommodating uncertainty through scenario analysis, often
suers from an explosion in computational demands with increasing
scenarios. Mitigation strategies such as decomposition or scenario re-
duction can help, but scalability remains challenging [219]. In contrast,
MFRL typically incurs high computational costs during its training phase
but oers fast, near-instantaneous decision-making during deployment.
However, ensuring convergence and generalization over large heteroge-
neous charging networks may require distributed training frameworks
[189]. Edge computing enables scalability by decentralizing compu-
tations and reducing latency, provided that coordination among dis-
tributed nodes is eciently managed [149]. Algorithms like ADMM
are desirable for large-scale problems because they decompose a large
optimization task into smaller sub-problems that can be solved in par-
allel. However, they may converge more slowly compared to tailored
solvers [91]. RO and DRO trade o computational intensity against
conservatism. In many cases, RO can yield tractable solutions by fo-
cusing on worst-case scenarios, while DRO introduces a more rened
uncertainty model at the expense of additional complexity [87]. Multi-
objective optimization further complicates the landscape by seeking
Pareto-ecient solutions across conicting performance measures such
as cost, reliability, and environmental impact [161]. Finally, heuristic
and meta-heuristic approaches provide valuable practical exibility by
yielding good enough solutions within a reasonable time frame. They
are naturally amenable to parallelization, though they sacrice global
optimality guarantees [214]. Ultimately, the choice among these meth-
ods should reect the specic requirements of a large-scale EV charging
infrastructure, including the available computational resources, real-
time response demands, and the acceptable trade-os between solution
optimality, accuracy, and computational feasibility.
3. Challenges, research directions, and policy gaps for
EV-integrated systems
The rapid increase in EV adoption places enormous pressure on exist-
ing power infrastructures, necessitating strategic upgrades, expansions
of distribution networks, and smart charging strategies. Although build-
ing additional transmission lines and enhancing transformer capacities
can support the growing demand, the associated costs are substantial. As
a result, there is a need to combine and prioritize advanced management
strategies, such as smart charging, demand response, and integrated
energy storage, to defer capital-intensive investments. Models that si-
multaneously account for uncertainties in renewable energy generation,
load forecasts, and EV arrival patterns are essential to ensure reliability
while controlling costs.
Controlling such complex systems in real-time requires robust
scheduling and optimization frameworks. Receding horizon or MPC
strategies can dynamically update decisions based on evolving forecasts,
yet their computational requirements grow signicantly for large-scale
deployments. Bilevel and multi-objective formulations and distributed
optimization methods like ADMM enable multiple stakeholders to coor-
dinate while maintaining local autonomy and privacy. MFRL and other
data-driven methods promise adaptive pricing and scheduling, but en-
suring their stability and interpretability remains an open challenge.
Better approaches are also needed to capture various sources of uncer-
tainty, ranging from sporadic charging behaviors and rapidly changing
load proles to stochastic renewable generation, in ways that balance
model tractability with real-world accuracy.
Bidirectional charging and V2G integration add a new layer of op-
portunities and challenges. While V2G can substantially reduce peak
demand and provide ancillary services, battery degradation expenses
and user convenience must be balanced by proper incentive mecha-
nisms. Regulatory frameworks in many regions have not yet caught up
with the complexities of two-way power transfer, raising questions about
suitable pricing, aggregator business models, and standardized commu-
nication protocols. Researchers are exploring how exible local markets,
real-time carbon signals, and carefully structured taris can encour-
age EV owners to oer grid services without incurring excessive risks
or costs. More detailed battery-aging models and fair benet-sharing
schemes will be crucial to support widespread adoption.
Safeguarding data privacy and cyber-physical security is another
concern, as charging services and aggregators collect sensitive driver
and grid information. Decentralized and distributed optimization ap-
proaches can reduce the need for central data aggregation, but com-
munication channels remain vulnerable. Edge computing oers near-
real-time responses and potentially lower data transfer volumes, yet
it must integrate robust intrusion detection and secure communication
protocols to prevent breaches or manipulation. Increased digital inter-
connectivity requires more comprehensive risk assessments, coordinated
detection systems, and standardized guidelines to ensure operational
eectiveness and user trust.
Ongoing research into multi-energy system coupling underscores the
need to handle electricity, hydrogen, heat, and other energy carriers in
the same planning environment. Hybrid refueling stations are already
Applied Energy 392 (2025) 126058
17
S. Ghanbari Motlagh, J. Oladigbolu and L. Li
appearing in some regions, bringing additional synergies and trade-
os between hydrogen production, energy storage, and EV charging.
Deploying these systems at scale will require advanced models that si-
multaneously address technical, economic, and environmental aspects.
Pilot projects remain essential for validating theoretical frameworks, im-
proving user acceptance, and informing the policy environment. Moving
forward, collaboration among utility companies, EVCS operators, auto-
motive manufacturers, and government agencies will be instrumental
in guiding infrastructure expansions and operation management, coor-
dinating ecient real-time control, and ensuring that EV systems scale
sustainably and securely.
Analysis of the recently published works reveals regulatory gaps.
Many reviewed studies propose advanced pricing schemes, such as dy-
namic pricing (e.g., DLMP, game-based pricing), that better reect grid
conditions and optimize EV charging behavior. Existing electricity mar-
ket regulations and tari structures are primarily based on static or
simple ToU models. They do not yet accommodate the complexity of
real-time pricing and bidirectional energy ows inherent in innovative
EV charging operations. While bidirectional charging can provide grid
support and revenue streams, its potential is hindered by uncertainties
surrounding battery degradation and user inconvenience. There is a lack
of clear regulations or nancial incentives that address the cost–benet
balance for EV owners participating in V2G. For instance, in the case
of Australia, which has a growing EV market, V2G is still not being
used comprehensively due to a lack of proper regulation [220]. Most
EV manufacturers, except Nissan, omit V2G in their battery warranties,
leading to consumer hesitancy due to potential warranty voiding [221].
The reviewed literature emphasizes the increasing role of data-driven
methods (like MFRL) and distributed optimization frameworks, which
require extensive collection and real-time processing of user and grid
data. Current policies may not adequately provide clear guidelines on
cybersecurity measures for smart EV charging systems.
4. Conclusions
The rapid advancement of EVs necessitates robust smart charging
that addresses cost, eciency, and grid reliability. Recent studies high-
light the signicance of meticulous optimization for the charging process
and power dispatch in EV-integrated power systems, which can mitigate
grid bottlenecks and reduce infrastructure expenses. Equally important
is integrating renewable energy resources with EVCSs, which require
comprehensive methods to handle generation and user demand un-
certainties. Techniques such as MPC and MFRL demonstrate strong
adaptability to real-time uctuations in power availability and charging
requirements, thus enhancing system resilience.
Pricing strategies form a key element of operational optimization.
Methods ranging from DLMP to game-based schemes can incentivize
users to adopt o-peak charging and participate in ancillary services,
strengthening reliability and economic viability. Bidirectional charg-
ing/discharging further augments this exibility by enabling EVs to
feed power back into the grid. However, practical adoption depends
on carefully structured compensation models that account for battery
degradation and user preferences. Advances in multi-energy integration,
particularly hydrogen, heat, and electricity coupling, oer additional
synergies for ecient and sustainable operations.
Future eorts are expected to focus on policy frameworks and stan-
dardization, ensuring that data privacy and system integrity remain
intact in a digitized, interconnected environment. Greater collaboration
among utilities, EV manufacturers, government agencies, and tech-
nology providers is critical to accelerating widespread EV adoption.
This collective approach will facilitate more robust modeling, eective
real-time control, and integrated planning, ultimately creating a sus-
tainable, ecient, and resilient transportation ecosystem. Although a
few works mentioned in this review paper slightly mentioned infras-
tructure investment or operational and maintenance costs, this work
only focuses on the operation optimization of EVCSs and EV-integrated
power systems. Evaluation of the long-term economic sustainability of
the proposed operational optimization strategies, considering factors
such as initial investment costs, amortization, maintenance and oper-
ational costs, components’ lifetime, long-term energy price uctuations,
economic variations, lifecycle assessment, internal rate of return, and
payback period falls within the scope of future works.
CRediT authorship contribution statement
Saheb Ghanbari Motlagh: Writing – review & editing,
Writing – original draft, Visualization, Methodology, Investigation,
Conceptualization. Jamiu Oladigbolu: Methodology, Writing – review
& editing. Li Li: Writing – review & editing, Supervision.
Funding
This research received no specic grant from funding agencies in the
public, commercial, or not-for-prot sectors.
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
No data was used for the research described in the article.
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