This article has been accepted for publication in IEEE Access.

This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2025.3582189

fDate of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2024.Doi Number

Optimal Operation of Electric Vehicle

Supply Equipment by Aggregators in
Local Energy Community
Ali Esmaeelnezhad1, Graduate Student Member, IEEE, Toktam Tavakkoli Sabour1, and Ravi
P. Joshi1, Fellow, IEEE, Mohammad Sadegh Javadi2, Senior Member, IEEE, Pedro H. J.
Nardelli3, Senior Member, IEEE
1
Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX 79409, USA
2
Institute for Systems and Computer Engineering, Technology and Science (INESC TEC), 4200-465 Porto, Portugal
3
Department of Electrical Engineering, School of Energy Systems, LUT University, 53850 Lappeenranta, Finland

Corresponding author: P. H. J. Nardelli (e-mail: Pedro.Nardelli@lut.fi).

This paper has been partly funded by EU MSCA project COALESCE (n. 101130739), and by the Research Council of Finland via X-
SDEN (n. 349965), and ECO-NEWS (n. 358928).

ABSTRACT This paper proposes a centralized energy management system for low voltage (LV) distribution
networks. The main contribution of this model is to manage the energy serving at the local energy
communities in the presence of electric vehicle supply equipment (EVSE). Unlocking the demand response
potential by the EVSE at the distribution network with the contribution of the active residential prosumers
has been investigated in this study under different operational planning scenarios. The developed model is
based on the multi-temporal optimal power flow (MTOPF) concept while the unbalanced nature of LV
networks has been addressed using unbalanced power flow equations. The aggregator can effectively manage
the optimal charging of electric vehicles (EVs) by home and public chargers available at the distribution
network. Simulation results on a modified unbalanced LV network illustrate that the optimal operation of
EVSE minimizes the electricity costs of end-users. The simulation results show that the operating costs and
systems losses reduce by 9.22% and 43.45%, respectively. These results have been obtained considering the
switching actions and 100% PV power generation index using the presented MV-LV coordinated operational
model. Besides, the energy storage systems improve the peak-to-average (PAR) ratio by 9.87%.

INDEX TERMS Centralized Energy Management, Unbalanced Power Flow, Coordinated MV-LV
Networks, Electric Vehicle Supply Equipment.

Indices/Sets PkG,i ,t Active power generation of unit i (kW)

i, N L Index/total number of nodes G
Q k ,i ,t Reactive power generation of unit i (kVAr)
t , NT Index/total number of time intervals
k, Nk Index/total number of phases
PkDisch
,i ,t
.
Discharging power of ES (kW)
Ch .
v, N EV Index/total number of EVs P k ,i ,t Charging power of ES (kW)
Variables Pk ,ij ,t Transmitted active power by line ij (kW)
PGsG,t2 H Grid to home power at time t, scenario s (kW) Qk , ji , t Transmitted reactive power by line ij (kVAr)
PkVH
, v ,i ,t Charge power of EVs at home (kW) I SQ
Square of transmitted current by line ij (pu)
k ,ij ,t
PvVC
, i ,t Charge power of EVs at EVSEs (kW) P Loss
Active power loss of line ij (kW)
k ,ij ,t
LS
P k ,i ,t Curtailed load at phase k at time t (kW) QkLoss Reactive power loss of line ij (kW)
, ij , t
V
ST v ,t Plugging of EV to the charger V SQ
Square of nodal voltage (pu)
k ,i ,t
V
SD v ,t Unplugging of EV from the charger y ij , t Status of line ij
LS k , i , t Load shedding status

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EkES,i ,t Stored energy in ES (kWh) PvVC

,i ,t Maximum charging power at EVSE (kW)
V Av ,VH
E v ,t Energy stored in EV (kWh) I k , v ,i ,t EV’s availability at home
Av ,VC
IkCh,i,.t I EV’s availability at EVSE
Charging status of ES v ,i ,t

PkContract Contracted power (kW)

I kDisch
,i ,t
.
Discharging status of ES
,i

Pt Agg Aggregator’s transaction power (kW)

PvTr,t Travel power consumption by EV (kW)
I kVH,v ,i ,t Connection status of EV to home’s charger I. INTRODUCTION
Coordinated operation of low-voltage (LV) distribution
IvVC,i,t Connection status of EV to EVSE’s charger systems and medium-voltage (MV) electric networks is of
ij ,t Auxiliary variable in the directional graph the utmost importance. This is particularly important in the
Parameters presence of electric vehicles (EVs) and parking
tTOU TOU Tariff for the residential sector ($/kWh) infrastructure, given the dynamic nature of the energy
sector. The adoption of EVs into existing power
tEVSE Cost of charging EV at EVSE ($/kWh)
distribution networks emerges as a critical issue as this rate
 tFIT Feed-in-tariff for PV panels ($/kWh) continues to increase. The increasing penetration rate of EV
 t
LS
Load shedding cost ($/kWh) chargers and their associated demands impose challenging
 V
EV’s connection fee ($) issues on the operational planning of distribution networks
D due to the high demand for power and energy in this sector.
P Residential active power demand (kW)
k ,i ,t
Proposing an efficacious coordinated LV-MV systems
D
Q k ,i ,t Residential reactive power demand (kVAr) operation model will result in a reliable energy supply to
PkPV
,i ,t PV active power injection (kW) EVs, optimizing resource utilization, mitigating operating
QkV,v,t costs, and easing grid congestion as well. This topic is
EV’s reactive power demand (kVAr)
regarded as one of the most significant in supporting
Rij Resistance of line ij (Ω) resilient and sustainable energy systems [1]. It addresses
X ij Reactance of line ij (Ω) the challenges posed by increased EV penetration levels
Z ijSQ Square of the impedance of line ij (Ω2) and helps to achieve smart distribution systems in the long
term. EV charging and discharging cause a varying load
M Big number
SQ demand across the distribution system supplying
S Square of the apparent power of line ij
k , ij
residential, commercial, and EV parking lots. A good,
S kG,i ,t Rated power of generation unit G optimal solution to this overall situation requires the
V kSQ
,i Minimum squared voltage at node i integration of modern energy management systems with
V SQ
Maximum squared voltage at node i (p.u.) LV distribution networks (LVDNs) to prevent overloading
k ,i
SQ conditions and preserve power quality. Besides, the MV
I Maximum squared current of line ij (p.u.)
k , ij
system which is supposed to supply several LVDNs, must
 kDisch
,i
.
Discharging efficiency accommodate the aggregated load of EVs. Different
 kCh, i . Charging efficiency methods like real-time monitoring, load forecasting, and
t Time interval installing energy storage devices are needed to meet the
E kES, i
desired operation requirement of the MV and LV systems
Minimum energy stored in ES (kWh)
at high efficiency and stability. Furthermore, the smart grid
EkES,i ,t Maximum energy stored in ES (kWh) facilitates the communication required between different
Ch .
P k ,i Maximum charging power (kW) devices in the system and the system operator. This will
P Disch .
k ,i Maximum discharging power (kW) enable deploying demand response programs and smart
QkES,i
charging protocols. Some short-term power regulation
Minimum reactive power (kVAr)
strategies for distribution networks facing critical
QkES,i Maximum reactive power (kVAr) faults/disturbances have been presented and studied [2]. A
ES
E k , i , Initial Initial energy stored in ES (kWh) cost-based pricing scheme for load response and
E ES
k , i , Final Final energy stored in ES (kWh) investigation into the impact of distributed generation
fluctuations on subsystems’ operations, optimization of
E vV Minimum energy stored in EV (kWh)
economic scheduling, and load controllability were
E vV Maximum energy stored in EV (kWh) introduced. The study utilized numerical results from the
V
E v , Initial Initial energy stored in EV (kWh) PG&E-69 distribution system. It also demonstrated the
E V
v ,Target Target energy stored in EV (kWh) model’s effectiveness in managing radial structure load
PkVH
clusters and its applicability to transmission switching and
, v ,i ,t Maximum charging power at home (kW)
microgrid applications.

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The congestion problem occurring in LVDNs has been and distribution system operator (DSO) coordinated
addressed [2][3] using a combinatorial technique including framework was developed and discussed [12]. It employed
soft open points (SOPs) and flexible power electronic a multi-port, multi-period feasible region formulation, a
devices together with a market-based strategy to account two-stage robust planning model, and a distributed
for the consumption pattern of flexible loads like EVs. The coordination algorithm. A technology-neutral technique for
impacts of distributed energy resources (DERs) and voltage ancillary services provision through TSO-DSO
community energy trading (CET) on LVDNs were studied coordination and DER aggregation has also been presented
[4]. In that work, the performance of CET and home energy [13]. It aimed at voltage stability by using distributed
management systems (HEMSs) were compared from the generation which minimized investment in reactive
operating and grid impact points of view. The effect CET equipment. Validated by dynamic studies and hardware
may have on the phase unbalance, transformer, and line testing, it effectively improved system flexibility cost.
loadings, as well as voltage deviation, were addressed and Bakhtiari et al. [14] devised a stochastic inference-dual-
analyzed. Then, it was shown that a centralized CET model based decomposition method to handle the TSO–DSO-
will successfully mitigate the community energy costs and Retailer coordination problem, vital for grid stability
promote self-consumption of renewable energy and self- amidst increasing embedded energy resources. An iterative
sufficiency as well. A modern extended dynamic market method that integrates distributed flexibility into
programming (EDP) technique to optimize the operation of TSO-DSO coordinated electricity markets while employing
radial LVDNs was also developed [5]. It addressed the an effective scheduling/forecasting grey-box agent for
optimal power flow problem. The proposed methodology consumer integration by discussed by Tsaousoglou et al.
substantially eases the computational load and guarantees [15]. This technique facilitates seamless market inclusion
optimality. Load balancing issues in LVDNs have been of flexible loads, indicating significant convergence
investigated [6] by raising the penetration level of rooftop features and operational efficiency taking into
PVs. A new technique to control phase reconfiguration consideration uncertainties due to renewable power
devices (PRDs) for changing the phase positions of generation. Marques et al. [16] used five TSO-DSO market
residential end-users dynamically based on measurable models for electricity flexibility procurement, addressing
data from such devices and the controller was discussed. coordination efficiency and minimum sharing of
The challenges and opportunities in local energy trading information. A look-ahead multi-interval framework for
markets (LETMs) for prosumers with solar PV systems optimizing TSO-DSO coordination, focusing on
have been handled in the literature [7]. In this respect, the integrating DERs and flexibility resources has also been
effects uncertainties due to solar power generation may discussed [17]. This work compared two models:
have on market operations have been addressed and a exogenous DSO, which uses statistical anticipation of DSO
centralized strategy was developed for optimizing such actions by TSOs. Besides, an embedded DSO was used,
operations and maximizing the economic benefits for all proposing a new TSO-DSO coordination mechanism
players. Independent per-phase control capabilities of 3- involving a flexibility market operator.
phase, 4-wire PV inverters can be utilized to upgrade the Recently, the penetration level of EVs has been
efficiency of LVDNs [8]. Such studies leverage the dramatically increased, bringing severe challenges as well
inverters’ ability to inject different active and reactive as golden opportunities to the power system. In this respect,
powers into each phase to minimize system phase multiple fast-charging EV charging stations should be
unbalance. The parallel transformers existing in the planned to be constructed within the distribution system
distribution systems can also be deployed for providing zone. In this connection, a mixed-integer linear
reactive power absorption functionality through staggered programming (MILP) model was developed [18] for
tap operations [9]. This strategy will economically optimally locating and sizing EV fast-charging stations
outperform conventional reactive power compensators. within coupled transportation and electrical distribution
The impact of different voltage control strategies on the systems. It optimized road congestion, travel time, and
photovoltaic hosting capacity in low-voltage distribution power losses while improving power quality by taking into
networks has also been assessed [10]. A novel transactive consideration various load profiles and demands. A multi-
energy system design managed by an independent period model has been presented [19] for planning the sites
distribution system operator for unbalanced distribution and capacities of public EV charging stations, leveraging
networks has been reported [11]. The study aimed to align real-world EV operation data from Beijing, China. It
customer power decisions with network constraints while addresses the dynamic spatiotemporal distribution of
preserving customer privacy through a consensus-based charging loads by evaluating multi-scenario predictions of
negotiation process before each operating period [11]. charging demands. Finally, a methodology has been
A method and framework for promoting power distribution developed [20] to identify and allocate public charging
network flexibility through DERs and energy storage zones for EVs while focusing on urban environments with
investments, under a transmission system operator (TSO) varying EV travel patterns.

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On the one hand, the increase in the number of EVs and the empower DNOs to efficiently orchestrate energy
high demand for energy needed for EV charging requires transactions, reduce operational expenses, and enhance the
strengthening the infrastructure in the power distribution renewable power generation utilization index during the
networks. In addition, optimal utilization of network daily operational horizon, resulting in a sustainable energy
equipment and energy production in MV and LV networks supply chain. The prominent research gap is: 1) how to
can significantly reduce the stress on power transmission coordinate the load balance at the MV-LV networks
networks. Therefore, the management of distribution without techno-economic constraint violations; 2) how to
networks when facing the ever-increasing challenge of the maintain the least operational planning at MV-LV networks
need for clean energy and the use of EVs should be in the presence of a high penetration rate of renewable
effectively considered. The proposed solution entails power generation and EV charging needs. Table I
employing aggregators as intermediaries bridging represents a detailed comparison between recently
distribution network operators (DNO), end-users, and EV published research works and this paper.
owners. By assuming a managerial role, aggregators
TABLE I
REVIEW OF EXISTING RESEARCH
MV-LV Unbalanced Aggregator DR/Incentive Curtailment
Reference EV Charging Stationary ES
Coordination PF Modeling Role Model Handling
[21] × ×  ×  × ×
[22] × ×  ×  × ×
[23] × ×  × ×  ×
[24] × ×  ×  × ×
[25] × ×  ×   ×
[26] × ×    × ×
[27] ×   × × × 
[28] ×   × × × 
[29] × ×    × ×
[30] ×     × ×
[31] × ×    × 
[32] × ×     ×
[33] ×     × ×
[34] ×     × 
[35]  ×     ×
[36] × ×  ×  × ×
[37] × ×  ×  × ×
[38] × ×  ×  × ×
[39] × ×  ×  × 
[40] × ×  ×  × 
[41] × ×  ×  × ×
[42] × ×  ×  × ×
Present paper       

Assessing the references cited in-depth makes it abundantly Second, it is sometimes disregarded the unbalanced
evident the unique and significant contributions the current character of LV networks, which is crucial in realistic home
study brings about. Although a lot of studies on EV and prosumer environments. Although Ref. [30] noted
integration into distribution networks have been conducted, unbalanced distribution networks, it did not systematically
major constraints still exist in most of the current work that include unbalanced power flow constraints into the
the proposed model addresses holistically. optimization model. This work carefully integrates
Above all, the idea of coordinated MV-LV network unbalanced three-phase power flow equations at the LV
operation stays either completely lacking or only partially level, integrated within a centralized mixed-integer
investigated in earlier research. References [21], [22], [25], quadratically constraint programming (MIQCP)
[31] focused just on local LV effects or simplified MV framework, so presenting a much more accurate and useful
network considerations without including the dynamic operational planning model.
interdependencies across voltage levels. On the other hand, Third, previous studies either absently or superficially
using network switching techniques and multi-temporal handled aggregator-based management of EV charging and
optimization to improve general system efficiency and energy trading. Studies including [23], [26], [31], [32]
resilience, the present work pioneers a detailed, scalable addressed individual EV or station-level charging strategies
framework for coordinated MV-LV operational planning. without regard to the function of an intermediary
aggregator coordinating residential and public charging

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behaviors under system-level constraints. The present work base case scenario is identical to the first tier of TOU,
introduces dynamic load engagement TOU and incentive- which is 0.15$/kWh, which means that the end-user should
based ("Happy Hour") pricing mechanisms, so creatively not pay any additional fees if they charge their EVs outside
formalizing the aggregator's role in optimizing both private the home. It convinces the EV owners to charge their
and public EV charging schedules. Under increasing vehicles during the ‘Happy Hour’ time.
penetration scenarios, the scalable deployment of EVSEs The MV-LV coordinated operation concept is introduced
depends critically on this aggregator-centric approach. and described in Section II. Section III includes the
Moreover, it is still mostly overlooked how stationary mathematical modeling of the problem. The simulation
energy storage (ES) systems could be included into results are presented and discussed in Section 4, and lastly,
coordinated EV and network operation. Although some the concluding remarks are included in Section V.
research studies addressed renewable energy management,
i.e. Refs. [23], [27], [31], they hardly linked EV operations II. OPERATIONAL PLANNING OF MV-LV NETWORKS
with stationary storage in a consistent optimal strategy. The general scheme for coordinated operational planning
Specifically modeling stationary ES systems at the MV-LV problems at MV-LV networks is illustrated in Fig. 1. This
substations, the current work shows their efficiency in conceptual framework underscores the interaction between
reducing operational costs, increasing the peak-to-average each sector in power system operational planning
Ratio (PAR) by 9.87%, and improving network loadability. processes. In particular, the DSO will coordinate the
Finally, the current literature did not sufficiently address operational planning with the TSO using a secure data
curtailment handling, especially minimizing PV generation exchange stream. On the other hand, the DSO is responsible
curtailment during surplus periods. Through adaptive for monitoring and operating the MV-LV network. In this
public EVSE incentives, directly responding to PV generalized scheme, the operational planning problem at
generation availability, and so efficiently lowering the MV network will address the multi-temporal optimal
renewable energy curtailment while preserving system power flow (MTOPF) problem considering the balanced
stability, the proposed model uniquely incorporates three-phase operation of the MV network. The network
renewable-aware EV charging management. switching actions can be executed at this level to
By means of coordinated MV-LV operational planning, appropriately reconfigure the MV network with the aim of
rigorous unbalanced power flow modeling, aggregator- loss reduction, voltage profile enhancement, or due to
based EVSE management, grid-scale stationary storage seasonal operation strategies or planned maintenance. It
deployment, and renewable energy curtailment mitigating should be noted that the operating topology of the network
within a centralized, computationally tractable should remain radial, considering the network switching
optimization framework, the present work advances the actions. The voltage stability issue should be adequately
field. To the best of the authors' knowledge, no current handled at this level, maintaining the LV network’s voltage
research concurrently addressed all these important profile within the standard range. Accordingly, the
aspects, so supporting the originality and thorough capacitor banks are typically installed on the MV side of
contributions of this work. the distribution network. These capacitor banks help
Accordingly, this paper covers several novelties and improve power factor correction and voltage regulation,
contributions in the domain of operational planning of local thereby enhancing the efficiency and stability of the
energy communities. The main contributions are as distribution system. The grid-scale ES systems will be
follows: TSO MV Network
 Developing a multi-temporal optimal power flow (HV Network)
- Balanced OPF
problem for MV-LV networks dealing with unbalanced - Network Switching
- Power Loss Management
power flow constraints. - Voltage Profile Control
 Proposing an integrated model for the optimal operation - Radial Network Operation
(MV-LV Network)

of public charging stations to enhance the load transition

DSO

and loading factor of distribution networks.

 Leveraging the consumer engagement level by
Aggregator
LEC

considering different hourly tariffs, in particular for EV LV Network

- Unbalanced OPF
chargers at home and in the public sector using the - ES Energy Management
‘Happy Hour’ mechanism. - Hosting PV-EV
- Load Priority Management
The ‘Happy Hour’ mechanism, an incentive energy pricing
EVSE

- Aggregator Energy Trading

- Phase Balancing
mechanism, has been introduced in this paper to reduce
stress and congestion on the network. In this mechanism,
the cost of EV charging at the public EVSEs is dynamically FIGURE 1. General scheme of the coordinated operation planning.
changing while the local PV power generation is
increasing. It should be noted that the energy cost at the

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installed on the LV side of MV-LV substations. Such ES with executing functions at the edge (i.e., at the EVSEs).
systems will be controlled and operated by the DNO to This centralized approach requires a coordinated model to
support the network operation strategies in normal and accommodate drivers’ preferences: target state-of-charge
contingent operational planning. On the LV side, the and departure hour. Additionally, forecasting the charging
network is distributed more extensively with a diverse requirements of electric vehicles proves challenging due to
range of consumers with different load profiles. Hence, irregular time series data, requiring the prediction of
operational planning management in a network with multiple parameters to quantify flexibility in EV charging
unbalanced load distribution is more challenging than in the accurately.
MV network. In addition, in the presence of highly
penetrated PV power generations, the LV feeders face III. PROBLEM FORMULATION
exceeding power generations, resulting in over-voltages, This section provides the mathematical model of the
network congestion, and, in worst-case scenarios, centralized operation management model for MV-LV
damaging LV feeders by overheating the cables. On the networks as an optimization problem. It should be noted that
other hand, increasing the number of EVs and their the MTOPF problem is represented as a standard MIQCP
corresponding charging needs impose other issues on LV model and CPLEX solver has been used for solving the
networks. problem. The main concept of MTOPF has been tested and
It should be noted that the operating topology of the verified in [43]. The main objective of this problem is to
minimize the aggregated energy cost of the end-users
network should remain radial, considering the network
within the local energy community. The objective function
switching actions. The voltage stability issue should be
is provided in (1). The aggregator’s objective function
adequately handled at this level, maintaining the LV
includes three main terms, the first term reveals the cost of
network’s voltage profile within the standard range. energy consumption by each individual, including the cost
Accordingly, the capacitor banks are typically installed on of residential power consumption, ܲ௞,௜,௧ ஽
, charging EVs at
the MV side of the distribution network. These capacitor ௏ு ௏஼
home, ܲ௞,௩,௧ , charging of EVs at the EVSE, ܲ௞,௩,௧ , and the
banks help improve power factor correction and voltage ௉௏
benefits achieved by injecting power of PV panels, ܲ௞,௜,௧ .
regulation, thereby enhancing the efficiency and stability of
the distribution system. The grid-scale ES systems will be The time-of-use (TOU) tariff is applied to the energy
installed on the LV side of MV-LV substations. Such ES consumption at home, ߣ்ை௎ ௧ , while the public chargers’ cost
systems will be controlled and operated by the DNO to is represented by ߣா௏ௌா
௧ and feed-in-tariff for PV panels is
support the network operation strategies in normal and modeled as ߣிூ் ௧ . The second term is related to the load
௅ௌ
contingent operational planning. On the LV side, the shedding, ܲ௞,௜,௧ , and the corresponding cost, ߣ௅ௌ ௧ , should be

network is distributed more extensively with a diverse selected big enough to avoid load curtailment in the
range of consumers with different load profiles. Hence, operational planning problem in normal operating
operational planning management in a network with conditions. The last term in the objective function is the
plugging cost of EVs to the chargers, either at home or
unbalanced load distribution is more challenging than in the
public EVSE. This term is added to the objective function
MV network. In addition, in the presence of highly
to avoid any possible interruptions during the charging
penetrated PV power generations, the LV feeders face
period. For the sake of simplicity, the corresponding term
exceeding power generations, resulting in over-voltages, for both home and EVSE chargers are modeled by index ܸ.
network congestion, and, in worst-case scenarios, In some EVSEs, there is a fixed connection fee that should
damaging LV feeders by overheating the cables. On the be paid by the EV owners while their EVs are plugged into
other hand, increasing the number of EVs and their the charging stations. In this case, the corresponding cost
corresponding charging needs impose other issues on LV can be considered by dividing the corresponding cost by the
networks. coefficient of ߱′௏ , while ߱′௏ = 0.5߱௏ . Eqs. (2) and (3)
Simultaneous charging of multiple EVs poses a potential indicate the active and reactive power balance equations,
challenge to the LV networks, diminishing their hosting taking into account the branch flows, respectively. Active
capacity and creating a bottleneck in decarbonizing the and reactive power losses are calculated using Eqs. (4) and
mobility sector. This issue necessitates a coordinated (5), respectively. Furthermore, voltage drop constraints
approach with other resources tied to the electrical grid, considering the switching actions are also stated in (6) and
such as local PV panels and grid-scale and small-scale (7) using the big-M method. It is noteworthy that M should
storage units. Hence, coordinated EV charging strategies be sufficiently big to guarantee this set of equations while
become imperative to effectively manage charging rates representing the switching actions. More details are
and schedules, utilizing local data from EV supply provided in [43]. The power flow of the feeders is also
equipment (EVSE) and taking into account grid operating restricted as shown in (8) while the rated capacity of
conditions, electricity tariffs, and the expectations of EV generating units is indicated in (9). The voltage limit and
drivers. Optimal control of smart charging is typically line current rating are also stated in (10) and (11),
centralized due to high computational demands associated respectively. The active and reactive load curtailments are

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shown in (12) and (13), respectively where they can vary Min
from 0% to 100%. Expression (14)-(21) are used to model  NT N L N K D TOU NT N L N EV N K VH TOU 
the stationary energy storage system. Eq. (14) states the   Pk ,i ,t t     Pk ,v ,i ,t t 
energy available in the storage system at each time slot and  t 1 i 1 k 1 t 1 i 1 v 1 k 1  t
it is restricted as (15). The active charge and discharge  NT N L N EV VC EVSE NT N L N K PV FIT 
powers are limited to the maximum values as stated in (16)     Pv ,i ,t t  Pk ,i ,t t  (1)
 t 1 i 1 v 1 t 1 i 1 k 1 
and (17), respectively. Constraint (18) avoids the NT N L N K NT N EV

, i , t t t     STv , t  SDv , t  
  PkLS
conflicting operation modes of the stationary energy LS V V V

storage system. The reactive power of the electrical energy t 1 i 1 k 1 t 1 v 1

storage system is shown in (19). Eq. (20) shows that the P G
  P Disch.
P Ch.
 
k ,i ,t k ,i ,t k ,i ,t
storage system starts the scheduling period with an initial
 P  Rij I kSQ,ij ,t  PkD,i ,t  PkV,v ,t
(2)
value of Eq. (21) emphasizes that the amount of energy P k , ji , t  k , ij , t
available in the storage system at the end of the scheduling ji L ij L

period must be equal to the initial value. The EV’s state of

energy constraint considering charging at home using
QkG,i ,t  QkES,i ,t  Q
ji L
k , ji , t   Q
ij L
k , ij , t  X ij I kSQ,ij ,t 
(3)
single-phase chargers and public chargers with a 3-phase  QkD,i ,t  QkV, v ,t
charger is indicated in Eq. (22). Eq. (23) states that the
, ij ,t  Rij I k ,ij ,t
PkLoss SQ
amount of energy available in the battery must be within (4)
the permitted range and at the beginning of the day must be
௏ Q Loss
k ,ij ,t X I SQ
ij k , ij ,t (5)
equal to the initial value shown by ‫ܧ‬௩,௜௡௜௧௜௔௟ as shown in
,i ,t  Vk , j ,t   2  Rij Pk ,ij ,t  X ij Qk ,ij ,t   Zij I k ,ij ,t 
(24). Besides, at the end of the day the amount of energy VkSQ SQ
 SQ SQ

available in the battery of EV must be equal or greater than (6)
the initial value as stated in (25). Eq. (26) shows that at the  1  yij ,t  M
home level, the charging power is a function of the
,i ,t  Vk , j ,t   2  Rij Pk ,ij ,t  X ij Qk ,ij ,t   Zij I k ,ij ,t 
contracted power phase, for example the charger is installed VkSQ SQ
 SQ SQ

at the same phase of the contracted power of home, A, B, or (7)
 1  yij ,t  M
C. The charging power at the EVSE can be done through a
three-phase charger. According to (28) the EV can be 0  PkSQ
, ij ,t  Qk ,ij ,t  yij ,t Sk ,ij
SQ SQ
(8)
charged at home if the car is available at home. The
0   PkG,i ,t    QkG,i ,t    SkG,i ,t 
SQ SQ SQ
availability parameter should be defined by the EV owner (9)
as one of the parameters. Constraint (29) states that the
charging at public EVSE is applicable if the EV can plug-
V SQ
k ,i V SQ
k ,i ,t V SQ
k ,i (10)
in to the EVSE. The connection to the charger and 0 I SQ
k ,ij ,t y I SQ
ij ,t k ,ij (11)
disconnection from the charger at home and EVSE are
modelled in (30) and (31), respectively. Eq. (32) shows the P LS
k ,i ,t  P LSk ,i ,t
D
k ,i ,t (12)
contracted power considered for each customer considering Q LS
k ,i ,t Q D
k ,i ,t LSk ,i ,t (13)
the instant power transactions due to the presence of PV
panels, stationary storage, and EV chargers installed at  P Disch.

EkES,i ,t  EkES,i ,t 1  kCh,i . PkCh
,i ,t 
. k ,i ,t
 t (14)
home. Eq. (33) states that the aggregator’s capacity for   Disch.
 k ,i 
participating in the market should be respected. Radiality
operation of the MV-LV network constraints are expressed EkES,i  EkES,i ,t  EkES,i ,t (15)
in (34)-(36). The auxiliary binary variables in (34), i.e., 0 P Ch.
P I Ch. Ch.
(16)
k ,i ,t k ,i k ,i ,t
‫ݒ‬௜௝,௧ and ‫ݒ‬௝௜,௧ , deal with the direction of the network
topology. The links’ direction to substation is not possible 0P Disch.
k ,i ,t P Disch. Disch.
k ,i I
k ,i ,t (17)
since it is injecting power to the network (35). Equation 0 I Ch.
I Disch.
1 (18)
k ,i ,t k ,i ,t
(36) confirms that the number of links bringing power to
each node is limited to only 1 link to avoid any possible Q ES
k ,i Q ES
k ,i ,t Q ES
k ,i (19)
loops in the graph. This constraint guarantees there is no E ES
E ES
(20)
ீ k ,i ,t 1 k ,i , Initial
loop in the graph. It should be noted that ܲ௞,௜,௧ includes PV
and power injection by grid and DG units to phase, k, at E ES
k , i , t  24 E ES
k , i , Final (21)
node i and time t. E EV
v ,t
V
v ,t 1 P P Tr
v ,t
VH
|
k , v ,i ,t k  k (VH ),i  i (VH ) P VC
|
v , i , t i  i ( EVSE ) (22)
E E E
V
v
V
v ,t
V
v (23)
E V
v ,t 1 E V
v , Initial (24)
E V
v , t  24 E V
v ,Target (25)

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, v , i , t  Pk , v , i , t I k , v , i , t
PkVH VH VH
(26) solving the problem. The main concept of MTOPF has been
tested and verified in [43]. The balanced and unbalanced
,i ,t  Pv ,i ,t I v ,i ,t
PvVC VC VC
(27) optimal power flow models used in this paper have been tested
I VH
k , v ,i ,t I Av ,VH
k , v ,i ,t (28) and verified in [44] and [45], respectively. In addition, optimal
scheduling of distribution networks in the presence of
I VC
I Av ,VC
(29)
v ,i ,t v ,i ,t
renewable resources, stationary batteries and EV’s have been
I VH
|
k , v ,i ,t i  i (VH ) I VH
|
k , v ,i ,t 1 i  i (VH )  ST VH
k , v ,t  SD VH
k , v ,t (30) examined in [44].
I VC
|
v ,i ,t i i ( EVSE ) I VC
|
v ,i ,t 1 i i ( EVSE )  ST VC
v ,t  SD
VC
v ,t (31)
N EV
PkD,i ,t   PkVH PV
 Ch. Disch .

, v , i , t  Pk , i , t   Pk , i , t  Pk , i , t   Pk , i
Contract
(32)
v 1
NL NK N ES N K

  P
i 1 k 1
D
k ,i ,t ,i ,t     Pk , i ,t  Pk ,i , t  
 PkPV   Ch.
i 1 k 1
Disch.

N L N EV N K N L N EV
(33)
 PkVH,v,i,t   PvVC,i,t  Pt Agg
i 1 v 1 k 1 i 1 v 1
 ij , t   ji , t  yij , t  (ij )   L (34)

j N
ji , t 0 i   S , (ij )   L
(35)

 ji , t 1 (ij )   L
(36)
j N FIGURE 2. The interface between the MT-OPF engine and the input
parameters.
The operational model is based on the multi-temporal optimal
power flow engine. The MTOPF engine calls the input data,
solving the problem. The main concept of MTOPF has been
including hourly energy tariff (λTOU), load shedding cost (λLS),
tested and verified in [43]. The balanced and unbalanced
feed-in-tariff (λFIT), and the dynamic energy price at the public
optimal power flow models used in this paper have been tested
EVSEs (λEVSE). In addition, the forecasted loads and PV power
and verified in [44] and [45], respectively. In addition, optimal
productions at each specific node will be sent to the MTOPF
scheduling of distribution networks in the presence of
engine. It should be noted that the happy hour mechanism is a
renewable resources, stationary batteries and EV’s have been
dynamic incentive mechanism which is designed to engage the
examined in [44]. The single-line diagram of the test
EV owners to connect their vehicles to charge during the
network is depicted in Fig. 3 including the connection of
period with high PV power production. The MTOPF engine
the LV and MV networks, distribution, and sub-
then calls the CPLEX solver to run the model and the optimal
transmission transformers, switching and load transfer
scheduling of the MV-LV network will be determined
points, public EVSEs, and grid-scale batteries.
accordingly. The decision variables are power flow results,
Furthermore, as can be observed, various LV loads with
optimal network configuration and switching actions, optimal
different power consumption and priorities are distributed
management of stationary ES units and charging of EVs using
across the network. It should be noted that the type of
home or public chargers. The interaction between the MTOPF
chargers has not been considered; however, they can be
engine and the input-output are presented in Fig. 2. It should
either AC or DC. Indeed, the efficiency of inverters and
be noted that the MTOPF model developed in this paper
rectifiers have not been considered in this study. The data
handles balanced and unbalanced power flow equations,
used in this paper are available in [46]. It should be noted
which have inherently non-linear terms. It will result in a non-
that the main core of the model is the MIQCP model for
linear optimization problem with several decision variables
running the optimal power flow problem in the MTOPF
that should be determined. Thus, the overall optimization
engine, which has been tested in the previous research [44].
problem is complex and should determine the direction of
The optimal solutions for standard benchmarks with
power flow in the presence of local power generations as well
different sizes have been compared with the existing
as units and public EV charger management systems. One of
literature [44].
the contributions of this paper is to present the optimization
First, the simulation analysis has been conducted to assess
problem into a standard MIQCP framework which can be
the performance of the coordinated MV-LV network
solved using any proper solver.
operation considering the impacts of network switching
actions at the MV side to network operation planning
IV. SIMULATION RESULTS
The proposed model is implemented and evaluated using a strategy. In this regard, two scenarios have been
MV-LV test network considering different scenarios. It is investigated to evaluate the impact of load transfer and
noteworthy that the MTOPF problem is represented as a participation of different sectors of the MV network on
standard MIQCP model and CPLEX solver has been used for minimizing cost. As the connection of two networks

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between nodes 1 and 2 can be controlled through a

maneuver switch, operation with the open and closed
switch scenarios is studied. It is worth noting that the
network capacity in areas 1 and 2 faces no limitation in
supplying the LV load demands and switching is done for
the sake of minimizing the losses and operating costs. The
operating costs and total system losses for PV power
generation index taking into consideration the switching
action are illustrated in Figs. 4 and 5, respectively. In this
study, no load curtailment was observed. However, load
prioritization was incorporated into the model to serve as a
comprehensive benchmark for scenarios where curtailment
may occur. Specifically, priority coefficients of 1, 10, and 100
were assigned to low-, medium-, and high-priority loads,
respectively. While there is no PV power generation, the
difference between the operational costs in Fig. 4 is related
to the power losses before and after switching actions. As
can be observed, the decrease in the operating costs is
considerable with the increasing solar power generation
thanks to cheap solar power generation during hours with
the highest TOUs. Connecting the two MV networks using
the maneuver switch between nodes 1 and 2 for the PV
power generation index 100% has led to 9.22% decrease in
the operating costs while it is 7.18% when the switch is
open. Under identical conditions, when the switch is
closed, there’s a 43.45% decrease in total system losses,
compared to a 40.16% reduction when the switch is open,
as illustrated in Fig. 5.
These findings underscore the significance of both the
switching actions and solar power generation in the
operational planning problem. Fig. 6 provides the TOU and
happy hour electricity prices at EVSEs for different PV
power generation indexes. The electricity consumption cost
at EVSEs is subject to the PV power generation level and FIGURE 3. MV-LV network topology.
will be reduced while the PV power injection is increasing.
The TOU has three tiers; between 11:00 and 17:00, the
price is 0.25$/kWh, while during the off-peak hours, the
electricity price is 0.15$/kWh. It should be noted that the
connection fee, ߱௏ , is 0.2$. The electricity demand per
phase with PV=0% with and without EV loads when the
maneuver switch is closed is indicated in Fig. 7. According
to this illustration, EV owners prefer to charge their EVs at
home using domestic chargers during the off-peak period.
In this case, there is no waiting time for plugging EVs into
the chargers, while there is no difference in energy FIGURE 4. Operational system costs with network switching action.

consumption costs for charging at home or using EVSEs.

FIGURE 5. Total system losses considering network switching action.

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The PAR has been selected as a key performance indicator

(KPI) because it effectively captures the efficiency of the
energy management strategy in both reducing peak demand
stress on the network and utilizing off-peak periods. This
helps moderate power losses, lower total operational costs,
and alleviate congestion in the MV and potentially high-
voltage (HV) networks. PAR serves as a critical metric for
evaluating the effectiveness of demand response programs
and energy management strategies, particularly at the MV
and LV levels. Furthermore, in the present study, even in
scenarios where public EVSEs are unavailable, as outlined
FIGURE 6. TOU and happy hour energy costs at EVSEs for different PV in Table III, no load curtailment occurs. The power
power.
curtailment terms are included in the objective function
solely to demonstrate the model’s capability to perform load
shedding if necessary. However, such actions are heavily
penalized to ensure they are avoided under normal
operational planning conditions. The transferability of
public chargers has been assessed through a sensitivity
analysis and the results obtained are given in Table III. The
transferability matrix provides the EVSE’s load transfer to
other adjacent public chargers while one of the EVSEs is
not available.
It is noteworthy that S0 refers to the scenario where all
EVSEs are available and the numbers in the associated row
FIGURE 7. Electricity demand per phase for PV=0%.
indicate the hosted EVs in the mentioned points. For
Fig. 8 displays the impact of solar power generation on the example, the number of hosted EVs at the EVSE located at
charging behavior of EV owners using home chargers and N10 is 1. Scenarios S1-S7 show the unavailability of EVSEs.
EVSEs. The simulation results show that the increased For instance, the EV’s load demand will be transferred to N18
renewable power generation in the LV side results in in case no charger is available at N10, as it is stated in S1. In
modifying the charging behavior of EV owners according addition, an EV is transferred from N49 to N111 to alleviate
to the proposed happy hour incentive. Furthermore, with the cost. It is worth mentioning that Table III represents only
the increased tendency toward charging EVs at EVSEs, the the number of hosted EVs at each node and no information
amount of load demand at the beginning and final hours of regarding the charging schedules is included.
the day reduces. This issue points out the performance of The simulations were performed using the CPLEX solver
the proposed happy hour incentive and changing the energy within the GAMS 24.1 environment, running on a laptop
tariff for EVs where the renewable power injection is equipped with AMD R7 4800H processor, 16 GB of RAM,
substantial. and a 64-bit operating system. For the case study presented in
In another case study, the performance of ES on system this paper, the average convergence time was approximately 8
operation is investigated. In this case, the PV power seconds.
generation is ignored to assess the contribution of ES to the
grid operation. The grid power injections with and without
Power

ES, as depicted in Fig. 9 confirm that the load profile is

(kW)

changed with the contribution of the three grid-scale ES

systems installed in the network. The total energy
consumption with and without ES systems is 2.376 MWh
and 2.322 MWh, respectively. The difference is due to the
efficiency of the ES systems in charging and discharging
Power
(kW)

mode operations. In this study, PAR is enhanced from 1.52

to 1.37 which is a tangible achievement. It should be noted
that in this case, the MV networks are not connected
through maneuver switches and there is no PV power FIGURE 8. EV charging demand for PV=0% and PV=100%.
generation from the residential sector to the grid. A
comparative case study has been conducted for different
operating scenarios in Table II considering the impacts of
PV, MV Link, and ES on operational planning case studies,
C1-C8.

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is capable of effectively adapting to network topology

changes. These features contribute to enhanced operational
performance by reducing losses and congestion under normal
conditions, while also improving loadability and system
resiliency in the face of outages, hazards, and other network
disturbances. The functionality of the presented model to
manage local energy communities with public EVSEs has
been tested and verified. Moreover, deploying the potential
impact of demand response programs through EVSEs in LV
distribution networks has been addressed. In this regard, the
FIGURE 9. Grid power injection with and without ES systems without
PV. Happy Hour strategy for engaging EV owners into charging
their vehicles at EVSEs has been simulated in this study. The
TABLE II performance of the MV-LV network in the presence of EV,
COMPARATIVE ANALYSIS FOR DIFFERENT CONDITIONS PV, and network switching actions has been studied. The
Energy Max Min Average
Case PV Link ES
(MWh) (kW) (kW) (kW)
impact of switching two MV networks has been investigated
C1 0 0 0 2.322 147.02 37.48 96.73
where it is found that in the case the two MV networks are
connected through the maneuver switch, the operating cost
C2 0 0 1 2.376 135.83 61.6 98.98
will decrease by 9.22%. On the other hand, when the
C3 0 1 0 2.329 142.98 37.48 97.05 maneuver switch is open, increasing the PV index to 100%
C4 0 1 1 2.384 134.37 61.71 99.33 led to 7.18% reduction in the costs. In addition, the total
C5 1 0 0 1.206 143.02 -40.18 50.26 system losses were mitigated by 43.45% in the case of closed
C6 1 0 1 1.257 121.21 -12.59 52.39
switch while it was 40.16% with the open switch. Then, the
performance of the transferability of public chargers in the
C7 1 1 0 1.222 147.05 -40.06 50.94
case of unavailability of public chargers has been simulated.
C8 1 1 1 1.260 116.62 -11.64 52.49 Using this approach, in case no charger is available at one
node, the EV will be transferred to another node to be
TABLE III
TRANSFERABILITY MATRIX FOR EVSES’ UNAVAILABILITY charged. Furthermore, the PAR ratio was enhanced using the
N10 N18 N49 N64 N81 N111 N123 energy storage systems by 9.87%, i.e. from 1.52 to 1.37.
S0 1 2 2 3 1 2 0
The model developed in this paper was based on a standard
MIQCP optimization problem. The model addressed several
S1 0 3↑ 1↓ 3 1 3↑ 0
concerns, including the optimal operation of MV-LV assets,
S2 4↑ 0 1↓ 3 2↑ 1↓ 0 grid-scale energy storage units, private and public EV
S3 2↑ 2 0 3 2↑ 2 0 chargers, local renewable power generations, and fluctuating
S4 1 3↑ 4↑ 0 2↑ 2 0
single-phase loads at the LV side. The model extensively
considers the load balance equation at both LV and MV sides.
S5 1 2 1↓ 5↑ 0 2 0
Such a complex optimization problem needs powerful solvers
S6 1 2 1↓ 3 1 0 2↑ to guarantee the global optimum results. Scalability is still a
S7 1 2 2 3 1 2 0 big challenge that should be further examined considering
decomposition or decentralized approaches, which are the
V. CONCLUSION next steps in this research.
In this paper, the operational planning problem of
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MOHAMMAD SADEGH JAVADI (Senior

ALI ESMAEEL NEZHAD received his BSc Member, IEEE) received the B.Sc. degree from
and three MS degrees in electrical engineering Shahid Chamran University of Ahwaz, Iran in
in 2011 and 2013, 2020, and 2024 respectively. 2007, M.Sc. in Power System from University of
He is currently pursuing a Ph.D. in Electrical Tehran in 2009 and the Ph.D. degree in the field
Engineering at Texas Tech University. He is a of Electrical Power Engineering from Shahid
reviewer of more than 98 prestigious journals Chamran University of Ahwaz, Iran in 2014. He
including IEEE Transactions on Smart Grid, is an Associate Professor at IAU, Shiraz, Iran and
IEEE Transactions on Power Systems, IEEE currently is a Researcher at INESC TEC, Porto,
Transactions on Industrial Informatics, IEEE Portugal. He is the author of three book chapters,
Systems Journal, Applied Energy. His current and more than 150 journal and conference papers.
research interests include smart homes, energy He is author and co-author in high-quality journals like IEEE
hubs, planning in restructured power systems, TRANSACTIONS ON INDUSTRIAL INFORMATICS, IEEE
power market, plug-in electric vehicles, and renewable energy sources. TRANSACTIONS ON Smart Grids, Applied Energy, Sustainable Cities
and Society, Energy, International Journal of Power and Energy Systems,
IEEE ACCESS, IET Generation, Transmission & Distribution, Electric
TOKTAM TAVAKKOLI SABOUR received
Power Component and Systems, and International Transactions on
her bachelor’s and master’s degrees in electrical
Electrical Energy Systems. He is serving as an Associate Editor in IEEE
engineering from Sadjad University, Iran, and
Transactions on Systems, Man, and Cybernetics: Systems, IEEE Internet of
Texas Tech University, US, in 2016 and 2024,
Things, and E-Prime Journal. He received the Best Reviewer Awards from
respectively. Her current research interests
IEEE TRANSACTIONS ON SMART GRID and IEEE TRANSACTIONS ON
include renewable energy sources, power system
POWER SYSTEM in 2019. His research interests include Power System
operation and control, microgrid, and energy
Operations and Planning, Multi-Carrier Energy Systems, Islanding
hubs.
Operation of Active Distribution Networks, Distributed Renewable
Generation, Demand Response and Smart Grid.

RAVI P. JOSHI (Fellow, IEEE) received the

B.Tech. and M.Tech. degrees in electrical PEDRO H. J. NARDELLI received the
engineering from IIT Bombay, India, and the B.S. and M.Sc. degrees in electrical
Ph.D. degree from Arizona State University, engineering from the State University of
Tempe, AZ, USA, in 1983, 1985, and 1988, Campinas, Brazil, in 2006 and 2008,
respectively. He is currently a Full Professor respectively. In 2013, he received his
with Texas Tech University, Lubbock, TX, doctoral degree from University of Oulu,
USA. He has authored more than 220 journal Finland, and State University of Campinas
publications. His current research interests following a dual degree agreement. In 2017,
include the modeling of charge transport, electric breakdown, he received the Title of Docent from
nonequilibrium phenomena, semiconductor physics, and bioelectrics. He is University of Oulu. In 2018, he started
a Licensed Professional Engineer in Texas. He is also a fellow of the working at LUT, where he is currently Full
American Association for the Advancement of Science (AAAS), Institute Professor. More information:
of Physics (FInstP), Institution of Engineering and Technology (FIET), the https://sites.google.com/view/nardelli/.
Institution of Electronics & Telecommunication Engineers; and an IEEE
Distinguished Lecturer. He also received the 2017 IEEE-NPSS Merit Award
and the 2022 IEEE-IPMHVC Dunbar Award. He has served as a Guest
Editor for five special issues for IEEE Transactions on Plasma Science, and
is now a senior editor.

VOLUME XX, 2017 13

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