Received 3 April 2023, accepted 13 April 2023, date of publication 18 April 2023, date of current version 24 April 2023.
Digital Object Identifier 10.1109/ACCESS.2023.3268028
EV Parking Lots for Flexible Energy Sourcing
KHASHAYAR MAHANI, FARHAD ANGIZEH , (Graduate Student Member, IEEE),
AND MOHSEN A. JAFARI, (Member, IEEE)
Department of Industrial and Systems Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA
Corresponding author: Farhad Angizeh (farhad.angizeh@rutgers.edu)
This work was supported in part by the Qatar National Research Fund (a member of the Qatar Foundation) through the National Priorities
Research Program (NPRP) Award under Grant NPRP13S-0206-200272.
ABSTRACT Energy storage is inherently a flexible asset that can be used to reduce renewable energy
curtailment and the congestion at its host network, enhance system resilience, and provide ancillary services
at peak times. But the cost of technology still hampers the large-scale adoption of storage in power
distribution networks. With EV parking lots included in its asset portfolio, a city can take advantage of the
power stored in the parked EVs without major capital investments. In this article, we formulate the operation
of an EV parking lot from the viewpoint of its owner (i.e., a city or a private entity). The lot works as a market
aggregator with operational uncertainties stemming from: (i) random arrival and departure of vehicles, (ii)
the SoC of EV batteries at the times of arrival and departure, and (iii) willingness of EV owners to participate.
The risks from these uncertainties and market prices of ancillary services impact the bottom line of the lot
owner’s revenue. For EV owners the excessive up and down cycles of battery is offset by discount offered
by the lot owner. We provide an illustrative example and a roadmap to extend this model to take the holistic
view of a power distribution network.
INDEX TERMS EV parking lot, V2G control, energy storage system, dynamic capacity, queueing model,
market participation, mix-integer linear programming (MILP).
j
NOMENCLATURE
t
t0
i
v
St
G
K
λi
1ti
n
m
Ni
µi
µ′i
Index of time.
Initial time slot of the planning horizon.
Index of time interval number.
Index of electric vehicle (EV).
Number of occupied spaces at t.
General Distribution.
Number of parking spaces.
Parameter of inter-arrival time exponential
distribution.
Duration of time interval i.
Auxiliary variable for number of arriving
EVs.
Auxiliary variable for number of departing
EVs.
Number of EVs arriving in ith interval.
Parameter of time-to-stay exponential dist.
EVs departure rate during ith interval.
wi
Li
Pv
Ev
λt
FRCR
t
SoCvInt
SoCvFnl
fp (.)
Regt
PVt 2G
PG2V
t
ϕ
ρ
RMCCPt
RMPCPt
The associate editor coordinating the review of this manuscript and
approving it for publication was Xiaofeng Yang
38770
.
βt
Expected number of EVs arrived in jth interval and stayed in parking lot till ti−1 .
Number of EVs departing in ith interval.
Rated power of EV v.
Energy capacity of EV v.
Locational marginal price (LMP) at t.
FR credit at t.
Initial SoC of EV v.
Desired final SoC of EV v.
Day-ahead stochastic planning function.
Aggregated planned FR commitment at t.
Aggregated planned discharge to grid at t.
Aggregated planned charge from grid at t.
Discount factor for V2G enabled EVs.
Performance score.
Regulation market capacity clearing price
at t.
Regulation market performance clearing
price at t.
Mileage ratio at t.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
FRv,t
N
PVv,t2G
SBRev
t
EVvChCst
tvInt
tvFnl
ϑvV 2G
Dv
PEtCst
EVvSve
DegCst
EVv
γv
TvXtr
CapCst
EVv
Cyc
Nv
τ
2G
PPV
t
NEV
ξv,t
2V
PPV
v,t
c
η
ηd
PPV
t
ϕ∗
α
Prα
λ̂ACap
λ̂OSpc
Committed FR capacity of EV v at t.
Number of time steps.
Planned discharge power of EV v at t.
Parking lot owner’s sell back revenue at t.
Charging cost of EV v.
Arrival time of EV v.
Departure time of EV v.
Binary variable equal to 1 if EV v gives the
V2G permission to the lot owner; and 0 otherwise.
Demand of EV v.
Cost of power purchased from grid to charge
EVs at t.
Cost-saving of EV v.
Degradation cost of EV v.
Fraction of time that battery of EV v is
deployed by the lot owner.
Extra parking time of EV v.
Capital cost of battery of EV v.
Maximum number of cycles that battery of
EV v can be charged and discharged.
Planning time horizon.
Power flow from PV to grid at t.
Total number of EVs using parking lot during τ .
Binary parameter equal to 1 if EV v is parked
in lot at t; and 0 otherwise.
Power flow from PV to EV v at t.
Battery charging efficiency.
Battery discharging efficiency.
PV output power at t.
Optimal discount factor.
Planning risk.
Probability that actual FR capacity becomes
less than planned capacity at t given α.
Weighted LMP by aggregated battery capacity.
Weighted LMP by percentage of occupied
spaces.
ˆ CR,ACap
FR
Weighted FR credit by aggregated battery
capacity.
ˆ CR,OSpc
FR
Weighted FR credit by percentage of occupied spaces.
Aggregated capacity of EV batteries parked
in lot at t.
Percentage of occupied parking spaces at t.
ACapt
OSpct
farms and clean Hydrogen) to achieve the net zero goal [1].
The intermittent nature of these renewable sources, however,
requires adoption of energy storage in a power grid (both at
the distribution and bulk levels). Energy storage is a flexible
asset that can help a network to reduce renewable power curtailment and the congestion at peak times, enhance resilience,
and be a clean power source for ancillary services [2], [3].
Reduced peak demand and congestion at a network lead to
reduced or deferred infrastructure investments, thus helping reduce the overall cost of energy. However, the cost of
energy storage of almost every existing technology exceeds
its economic benefits, unless the economics of resilience and
deferred investments are accurately quantified and included
in the cost and benefit analysis [4]. With massive penetration
of Electric Vehicles (EVs), cities will allow the construction
of public and private EV parking lots. For EV charging, these
lots can be sourced by the grid or be co-located with wind or
solar farms. In either case, these lots can be valuable sources
of flexibility in cities’ energy asset portfolios, without major
capital investments. These benefits, however, come with challenges too. In particular, a lot owner (which can be public or
private) must deal with several sources of uncertainties.
Vehicle to Grid (V2G) technology and FERC order 841 [5]
allow large facilities, such as EV parking lots, to participate in
the wholesale energy and ancillary service markets [6]. This
can generate tangible financial incentives and benefits for EV
parking lot industry which is expected to substantially grow
with many smart city initiatives around the world. An EV
lot follows a Modular Energy Storage Architecture (MESA1 )
where the energy modules are EVs, and each EV space is
equipped with a V2G unit. The total energy stored at the
parking lot for a duration of time depends on the number
of parked vehicles, and varies randomly with arrivals and
departures of vehicles and their State of Charge (SoC). The
participation of vehicle owners is driven by economic benefits
and the risk-averseness of vehicle owners. Thus, not every
parked EV will participate, and for the participating ones
there may be uncertainties due to unexpected departures or
other factors. Technically speaking, we are dealing with an
aggregated Energy Storage System (ESS) with total capacity
changing randomly over the course of a day. This translates to market risks if the aggregator engages in arbitrage
or other ancillary services. This article contributes: (i) by
formulating these business risks and (ii) incorporating them in
day-ahead planning and operation of the lot. Our formulation
covers the economic perspectives of the lot owner and the
EV owners.
B. LITERATURE REVIEW
I. INTRODUCTION
A. BACKGROUND AND PROBLEM DESCRIPTION
Cities around the world are slowly transforming to clean
energy and targeting net zero residential and commercial
communities for 2050. A clear trend is to use a mixed
portfolio of renewable energy assets (e.g., solar farms, wind
VOLUME 11, 2023
EV integration studies in the literature mainly explore the
impacts of EV adoption on demand and the required upgrades
in generation, transmission and distribution systems to meet
1 MESA is an open set of specifications and standards to accelerate interoperability, scalability, safety, quality, availability, and affordability in energy
storage systems [7].
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
the demand [8]. The increased peak load due to plugged-in
EVs may overload service transformers causing transformer
overheating and subsequent deterioration [9]. EV charging
is likely to cause power quality problems, including, undervoltage conditions, voltage and current harmonics, etc. [10],
[11], [12]. To mitigate the negative impacts of EV charging, Time-Of-Use (TOU) pricing scheme is proposed in [13]
where the utilities incentivize customers to charge their EVs
during off-peak hours. Utility-owned smart controls aiming
at maximize utility and costumers’ benefits are proposed
in [14] and [15]. The authors in [16] address the problem of
maximizing the profits for the EV owners by selling excess
energy to the grid, while in [17] and [18] control algorithms
to maximize EV owner’s profit from selling power to the grid
and participating in the frequency regulation (FR) market are
proposed. Yao et al. analyze the EV charging coordination
based on price- and incentive-based demand response (DR)
programs [19]. Also, the aggregated capacity of batteries in
the EV parking lots can be used in the ancillary market. The
impact of unit unavailability on system capacity depends on
the configuration and series/parallel connections of individual batteries or storage units [20], [21].
Apart from that, the authors in [22] propose a robust algorithm based on a receding horizon linear problem for the EV
aggregator considering EV constraints, price uncertainties,
and battery aging that is compensated by a utilization index.
By employing a real travel database, Giordano et al. propose
a day-ahead optimization of EVs fleet charge in [23], while
considering the arrival and departure times forecasts and the
energy required for the next trip. Moreover, in [24], a linear
optimization model to maximize the revenues obtained by a
V2G EV aggregator is developed considering grid services
in the UK electricity market, while in [25], a linear planning
model that aids EV aggregation investors for the purpose
of ancillary service markets is proposed where the number
of targeted EVs and the best incentives to the EV owners
are also determined. An aggregate of EVs is modeled as
a virtual battery in [26] considering the stochastic number
of connected EVs and their initial SoCs. Further, the economic behavior of an EV aggregator is evaluated in [27],
where wholesale electricity market participation impacts on
locational marginal prices and power dispatch patterns are
explored. A multi-timescale response capacity evaluation
model of EV aggregator is proposed in [28], where EV
owners’ responsive willingness based on psychology model,
as well as charge-discharge states and SoCs are established.
In [29], Wang et al. propose a state-space method to develop a
reduced EV aggregator model at the system level to describe
the response characteristics of many EVs and to realize frequency regulation.
To the best of our knowledge, there is a major gap in
understanding how an EV aggregator facility should operate
in a distribution network. Moreover, the cost and benefit of
such a facility for its owner, EV owners, and distribution
network requires investigation.
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C. CONTRIBUTION AND PAPER STRUCTURE
Our proposed model integrates multiple revenue streams
stemming from the dynamic aggregated capacity achieved
from the EV batteries, which turns the parking lot to be an
aggregated dynamic ESS while characterizing the stochasticities of the EVs behaviors. Moreover, the cost and benefit
analysis of such a facility for its operator/owner, EV owners, and distribution network requires more investigations.
The technical approach presented here for an EV aggregator
behaving as an ESS is sufficiently generic as long as the
following system-level assumptions are met:
• The parking lot is owned and operated by an independent
entity.
• One or more storage modules may be owned by a single
individual.
• Modules become available and unavailable according to
independent and time-dependent stochastic processes.
• SoC for a module at the time of availability is random,
and a required level of charge must be met prior to its
unavailability.
• The parking lot owner has full access to the modules
during the time periods that they are available as long
as the SoC at the time of unavailability is met.
There are also assumptions with respect to modules
including:
• Type and size of modules might be different.
• Each storage module is stochastically degradable, and
the parameters for the degradation processes are known
a priori.
Finally, there are financial assumptions to be considered as
well, including:
• The parking lot owner acts as an aggregator in the market
and can offer market products, such as FR and/or peak
load shaving. These transactions are hidden from the
module owners and are between utility and the parking
lot owner.
• A module owner decides to engage in a transaction
with the parking lot owner based on compensation and
degradation risks.
• Individual owners must pay a premium to participate.
In summary, the main contributions of this paper can be
listed as follows:
• Developing a comprehensive, integrated day-ahead
planning model for a parking lot owner who uses a
queueing formulation to compute EV population at different times and a stochastic optimization model with
objectives of maximizing the stacked up revenue streams
from the FR market, energy arbitrage, and EVs charging
fees constrained by EV owners’ compensation agreements for degradation costs.
• Driving the stochastic behavior of the aggregated storage by random arrivals and departures of EVs, random arrivals and firm departures SoCs, and whether
an EV owner is willing to participate by compromising
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
TABLE 1. Summary of literature review highlighting the scope and contribution of this paper.
between the optimized discount received and the cost
of overstaying in the parking lot that is reflected as the
battery degradation cost.
The rest of the paper is structured as follows. Section II
includes preliminaries and Section III gives the day-ahead
planning and operational model. Section IV gives experimental results and summarizes our findings. Finally, conclusions
are drawn in Section V followed by the future extensions.
II. PRELIMINARIES
A. THE HOLISTIC VIEW OF THE FRAMEWORK
The facility owner aims at maximizing his/her revenue by
optimally controlling bi-directional power flow in the facility, constrained by vehicle owners’ permissions. A vehicle
owner’s decision is partially dependent on what s/he receives
in return, either as a discount for the use of the facility
or as an expedited payback. The vehicle owner needs to
weigh this return against battery degradation. For the lot
owner to participate in the market, the facility must plan
in day-ahead depending on vehicle queues. Here, a queueing model is developed that explains vehicle arrivals and
departures, and the number of vehicles in the facility. The
results from this model are fed into a day-ahead planning
model which also takes into account day-ahead and regulation market capacity and performance clearing prices, i.e.
RMCCP and RMPCP respectively (see Fig. 1; Day-ahead
stochastic planning block). The day-ahead model assumes
optimal operational control for each of the multiple scenarios
that are generated according to the stochastic inputs. We also
formulate planning risks and risks to the distribution network
due to the underlying stochasticity of the facility (Fig. 1;
Distribution network impact-assessing model block). The
optimal operational control model governs bi-direction power
flow in the facility and works closely with the facility and
vehicle owner’s revenue model. Fig. 1 illustrates the holistic
view of the proposed approach.
B. THE QUEUEING MODEL
The initial SoC of an EV battery is a random variable that
follows truncated normal distribution bounded from below,
with mean and variance as functions of the vehicle’s arrival
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time. EVs that arrive earlier have higher mean value and
lower variance. It is assumed that EVs should reach to the
owner-defined SoC upon departure. Between arrival and
departure times, an EV can be part of the lot’s modular
energy storage system if the V2G permission is granted by
the EV owner. The facility has a finite number of parking
spaces for EVs. We assume that the facility is empty at the
beginning of the day when t0 = 0, i.e. St0 = 0. EVs arrive
according to a general stochastic process and occupy parking
spots for a random period each; this time also follows a general probability distribution. Underlying arrival distributions
change with time of the day, and time-to-stay distributions
vary from one EV to another. Further SoC levels at arrival and
departure times depend on individual vehicles characteristics.
From a queueing point of view, this parking facility works
as a G/G/K /0 queue, where the first two G’s are general
distribution designations for inter-arrival time and time-tostay of vehicles, respectively. K is the number of parking
spaces and the capacity of the facility. We assume an exponentially distributed inter-arrival times with a time-dependent
parameter λi for the ith time interval. The probability of n
vehicle arrivals during the ith time interval is then given by:
P{Ni = n} =
[λi .1ti ]n −λi .1ti
e
n!
∀n = 0, 1, . . . , K
(1)
and the expected umber of arrivals during this interval is:
E[Ni ] =
K
X
[λi .1ti ]n
n=0
(n − 1)!
e−λi .1ti
(2)
where 1ti is the duration of ith interval. Moreover, the time
to stay of any EV, which arrives during the ith interval,
is assumed to be a random variable that follows an exponential distribution with the mean value 1/µi . Let µ′i be the vehicle departure rate from the facility during the ith interval from
the perspective of an outside person. This time-dependent
departure rate is the function of time to stay of EVs, which
arrived during prior intervals. µ′i can be calculated by the
weighted average of the times to stay of all vehicles that are
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
FIGURE 1. Schematic diagram of the proposed framework.
at the facility, and is given by:
Pi−1
µ′i =
i
j=1 wj .µj
Pi−1 i
j=1 wj
∀i
(3)
where weight wij is the expected number of vehicles which
arrived in the jth interval and remained in the facility till ti−1 :
wij = λj .1tj .e−µj .(ti−1 −tj )
∀i, j
(4)
Then the probability of n vehicles departing the facility during
the ith interval given m vehicles are in the parking lot at the
time ti−1 is:
P{Li = n|Sti−1 = m} =
[m.µ′i .1ti ]n
′
.e−m.µi .1ti
(5)
n!
∀i, ∀n = 0, 1, . . . , m where Sti−1 is the number of occupied
spaces at the time ti−1 . The expected number of departing
vehicles during the ith interval is then given by:
E[Li |Sti−1 = m] =
m
X
[m.µ′ .1ti ]n
i
n=0
(n − 1)!
′
.e−m.µi .1ti
∀i
(6)
Expected number of EVs in the parking lot at the end of ith
interval is given by:
E[Sti ] = Sti−1 − E[Li |Sti−1 ] + E[Ni ] ∀i = 1, 2, . . . , 24 (7)
III. DAY-AHEAD PLANNING AND OPERATIONAL
CONTROL
In order to estimate potential market benefits, an economic
dispatch model is developed under the PJM fast regulation
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market (RegD) rules [32]. The facility owner commits the
maximum capacity in peak-priced hours while ensuring that
sufficient capacity is available to provide both regulations
up/down (discharging/charging) services. For demonstration
purposes, we use 2016 PJM day-ahead regulation market
data for capacity and performance clearing prices [33]. For
the wholesale arbitrage, the facility owner may charge EV
batteries when the electricity price is low and sell it back to
the grid when the price is high, while the EV SoC demands
are met.
A. DAY-AHEAD PLANNING MODEL
FR capacity commitment and net injected power, i.e. aggregate charge minus aggregate discharge, must be considered
in the day-ahead planning which is scheduled based on the
number of EVs, St , types of batteries reflecting EVs’ rated
power and energy capacities, Pv and E v respectively, and
initial and final desired SoCs of the batteries, denoted by
SoCvInt and SoCvFnl respectively, at any time step t and for all
EVs indexed by v in the parking lot. Moreover, market variables such as electricity price, i.e., LMP (λt ), and FR credit
(FRCR
t ) could influence the planning. These input variables
are stochastic, hence stochastic optimization is applied. The
outputs of the model are optimal discount factor assigned to
EVs (for V2G permission), aggregated planned capacity for
FR commitment (at each time step), aggregated amount of
electricity required to charge EVs, and aggregated amount of
discharged electricity during each time step. Fig. 2 depicts
the functional diagram of the day-ahead stochastic planning
model.
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FIGURE 2. Day-ahead stochastic planning model’s functional diagram.
The following equation explains the inputs and outputs of
our proposed stochastic day-ahead planning function fp (.):
{Regt ; ∀t}, {PVt 2G ; ∀t}, {PG2V
; ∀t}, ϕ = fp {St ; ∀t},
t
Int
Fnl
{λt ; ∀t}, {FRCR
t ; ∀t}, {SoCv ; ∀v}, {SoCv ; ∀v}
(8)
where {Regt ; ∀t} is the time series of the aggregated planned
; ∀t} are the time series
capacity for FR; {PVt 2G ; ∀t} and {PG2V
t
for the aggregate planned discharged and charged power for
the parking lot; and ϕ is the optimally planned discount factor
for the V2G enabled EVs. To capture the stochasticity of input
variables, a Monte-Carlo (MC) simulation is implemented to
generate sample paths according to the stochastic input distributions, one of which is vehicle arrival process characterized
by the queueing model of Section II-B. An optimal day-ahead
plan for a given path in Monte-Carlo simulation is calculated
using the revenue optimization model described next. The
plans for randomly generated MC paths are then aggregated
into statistical distribution of output variables in the planning
phase.
B. OPERATIONAL CONTROL MODEL
The objective function includes revenue and cost terms, and
constraints are driven by market, demand type and other
factors. We start with the main sources of revenue:
1) FR CREDIT
FR credit in PJM RegD market is based on the capability
offered and the performance provided, where the former is
related to the hourly integrated regulation capacity, while the
latter is related to how fast ESS responses to regulation signals [32]. The integrated committed capacity, Regt , receives
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credit FRCR
t at time t which is calculated as:
FRCR
t = Regt × ρ × (RMCCPt + βt × RMPCPt )
(9)
where RMCCPt and RMPCPt , both in $/kWh, are adopted
from PJM [33]. ρ is a score between 0 to 1 indicating a unit’s
performance in following the regulation signal. Since battery
storage response is quick, this performance score is close to 1.
Regt is also defined as:
Regt =
St
X
FRv,t
(10)
v=1
where FRv,t is the committed capacity to FR market from EV
v during time step t, and βt is PJM mileage ratio [32].
2) SELL BACK ENERGY TO THE MAIN GRID
The facility owner’s benefit as a result of selling energy to the
main grid in time step t is calculated as:
= λt × PVt 2G
SBRev
t
(11)
where PtV 2G is the aggregated discharged electricity from EVs
at time t, and λt is day-ahead locational marginal price (LMP)
adopted from PJM 2016 data [34].
3) CHARGING EVs
The facility sells electricity to the EVs for battery charging.
We assume that EV pays to the parking lot operator the
average price during the time it is parked in the facility.
Moreover, EVs which give the V2G permission to the parking
lot operator pay less. The amount of money that EV v pays to
the operator, denoted by EVvChCst , is formulated as:
EVvChCst = 1 − ϕ × ϑvV 2G × λv × Dv
(12)
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
where λv and Dv are the average price in $/kWh during the
EV v parking time, and EV v demand in kWh, respectively.
ϑvV 2G is a binary variable equal to 1 if EV v gives the V2G
permission to the facility operator, and 0 otherwise. ϕ is also
a variable between 0 and 1 and represents the discount factor
offered by the operator to the EV owners in exchange for V2G
permission. The only daily operation cost element for the
facility is the cost of buying electricity from the main grid to
charge EV batteries. Here we assume PJM hourly day-ahead
LMP as a unit price of electricity. This cost element is then
formulated as:
PEtCst = λt × PG2V
t
∀t
(13)
are cost of purchasing electricity
where PEtCst and PG2V
t
in $ at time t and the amount of electricity purchased at
time t, respectively. EV owners may make cuts in their cost
of charging EV’s battery if they give the V2G permission to
the operator. Thus, EV v’s cost-saving, denoted by EVvSve ,
is modeled as:
EVvSve = ϕ × λv × Dv
(14)
The cost element related to the EV owner is the excessive
degradation of battery due to V2G permission. We assume
that battery degradation is proportional to the extra time that
EV is parked in the lot. The time that a vehicle stays in the lot
in excess of time it needs for charging can be considered as
committed capacity to the FR market. Deploying EV battery
in FR market or arbitrage during this extra time causes the
excessive degradation, which results in an earlier replacement
of EV battery. We convert this degradation to a dollar value
by equation (15) below.
EVvDegCst = γv × TvExt ×
Pv
2E v
CapCst
×
EVv
Cyc
∀v
(15)
Nv
In (15), TvExt is the extra parking time corresponding to EV v;
Pv and E v are respectively the rated capacity in kW and the
energy capacity in kWh of battery in EV v. The expression
Pv
models the number of full cycles the battery may
TvExt × 2E
v
have during the extra time. γv is the fraction of time that
CapCst
battery in EV v is deployed by parking operator. EVv
Cyc
is the capital cost of battery in EV v and Nv is the maximum number of cycles that battery could be charged and
discharged. Equation (15) illustrates the portion of battery
capital cost that can potentially be used for V2G permission.
We assume that the EV monitoring system is smart enough to
estimate the degradation cost in (15) and the revenue in (14)
as a result of V2G permission. As such, EV owner gives V2G
DegCst
permission if EVvSve > EVv
, i.e.:
(
DegCst
1 if EVvSve > EVv
ϑvV 2G =
(16)
0 otherwise
facility has renewable generation such as Photovoltaic (PV),
the objective function is formulated as:
T
X
Rev
2G
Max
FRCR
− PEtCst + λt × PPV
t + SBt
t
t=1
+
NEV
X
EVvChCst
v=1
2G is the power flow from PV to the main grid
where PPV
t
are
during time step t. As mentioned before, PVt 2G and PG2V
t
integratedP
power flow due toPdischarging or charging, and are
NEV G2V
EV
V 2G
V 2G
given by N
v=1 Pv,t and
v=1 Pv,t , such that Pv,t and
G2V
Pv,t are the power flows from EV v to the main grid during
time step t and vice versa. Moreover, the quantity allocated to
the FR market reduces the maximum power flow for charging
and discharging as:
PVv,t2G + FRv,t ≤ ξv,t × Pv
PG2V
v,t
2V
+ PPV
v,t
The facility owner’s problem aims at maximizing the revenue
subject to V2G permissions from EV owners. In the case the
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∀v, t
(17)
+ FRv,t ≤ ξv,t × Pv
∀v, t
(18)
where ξv,t is a binary parameter equal to 1 if EV v is parked
in the lot during time step t, and 0 otherwise; PG2V
v,t is the
power flow from the main grid to EV v during time step t;
PV 2V is the power flow from the PV to EV v during
and Pv,t
time step t. In addition, the SoC of the EV battery is limited
by its capacity minus the allocated capacity to the FR market,
which is modeled as:
FRv,t ≤ SoCv,t ≤ E v − FRv,t
∀v, t
(19)
and the SoC of EV v battery at time step t is formulated as:
PV 2G
v,t
PV 2V
− d
SoCv,t = SoCv,t−1 + ηc PG2V
v,t + Pv,t
η
(20)
over ∀v, t ∈ [tvInt +1, tvFnl ]. ηc and ηd are the battery charging
and discharging efficiencies; and tvInt and tvFnl are the arrival
and departure times of EV v, respectively. The initial SoC
of an EV battery is random and depends on the arrival time.
We assume that if an EV stays long enough at the parking
lot, the owner will request for the full charge. Further, power
flow form EV to the grid and the capacity allocation to the FR
market is allowable according to the EV owner permission.
Therefore:
0 ≤ PVv,t2G ≤ ϑvV 2G × Pv
0 ≤ FRv,t ≤
0≤
0≤
0≤
0≤
C. THE FACILITY OWNER’S OPTIMIZATION PROBLEM
(P1)
ϑvV 2G
× Pv
G2V
Pv,t ≤ Pv ∀v, t
2V
PPV
≤ Pv ∀v, t
v,t
PV 2V
Pv,t
≤ PPV
∀v, t
t
PV 2G
PV
Pt
≤ Pt
∀t
∀v, t
(21)
∀v, t
(22)
(23)
(24)
(25)
(26)
where PPV
t is the PV output power generated during time step
t depending on the PV rated capacity and solar irradiance
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
Algorithm 1 Optimal Discount Factor
1: Initialize k ← 1.
2: while k ≤ 101 do
3: ϕ̂k ≜ k−1
100
4: Solve Problem (P1) such that ϕ = ϕ̂k
5: Objk ≜ Optimal objective function value in (P1) in
iteration k
6: k ← k + 1 and go to step 2.
7: end while
8: ϕ ∗ ≜ argmaxϕ̂k Objk
9: return ϕ ∗
FIGURE 4. Top) Day-ahead locational marginal prices (DA-LMP), bottom)
regulation market clearing prices (RMCP).
FIGURE 3. Top) Number of EVs parked in the lot, bottom) aggregate
capacity of batteries.
at time t [35]. Finally, the parking lot operator’s problem is
summarized as:
Solve P1
s.t. Constraints (9) − (26).
Relation (16) makes the proposed optimization problem
non-linear. To solve this mix-integer nonlinear programming
(MINLP) problem, we iteratively solve the model for different values of ϕ, where ϕ ∈ [0, 1], until the convergence is
reached at ϕ ∗ . In each iteration, the problem is converted to a
mix-integer linear programming (MILP) problem by assigning a value to ϕ and determining the V2G binary variable
according to (16) (see Algorithm 1). The equivalent MILP
problem is solved by using the YALMIP toolbox in MATLAB
platform [36]. It is worth mentioning that the algorithm can
be carried out on a daily basis as well, which yields different
hourly optimal discount factors.
IV. NUMERICAL EXPERIMENTS
We start with day-ahead planning examples. We illustrate
results for a commercial parking lot with 120 parking spaces.
EV arrivals are assumed to be Markovian. The capacity
of batteries and their initial and final SoCs are randomly
generated according to their stochastic distributions while
market information, viz. FR credit and electricity prices, are
unchanged. Fig. 3 depicts the boxplots for the number of
EVs parked in the lot and the aggregated capacity of batteries
based on 100 MC sample paths. The parking lot is almost
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FIGURE 5. Top) FR capacity, middle) Elec. power required for charging,
bottom) Elec. Power to discharge.
fully-occupied during 4-6 PM. The market data remains fixed
for all scenarios as given in Fig. 4. Then, the optimal plans are
calculated for each sample path, and results from all paths are
compiled into distributions.
Fig. 5 shows the Reg. Cap, charging and discharging power
over 24-hour. It is observed that the optimal decisions during
the planning phase is highly sensitive to the market values.
Although there is relatively more available capacity at 4 PM
compared to 3 pm, FR committed capacity is less at 4 pm.
This is due to the higher RMCP value at 3 pm compared to
4 pm. Analogous to the other example, as shown in Fig. 5
at the bottom, selling to the grid is an optimal decision
at 6 PM when the electricity price is high. The day-ahead
plan is estimated by taking the average over all scenarios.
The planned capacity for FR participation and net demand
are shown in Fig. 6.
The following sources of uncertainty exist in the planning phase. If the FR market participants are called
for regulation service but fail to provide the requested
capacity due to overestimation in planning phase, they
get penalized by the market operator. Thus, there is a
risk associated with the day-ahead plan calculated as the
probability that the actual capacity for FR participation
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
FIGURE 6. Top) Planned FR capacity, bottom) planned net injected power.
FIGURE 8. Parking facility net demand: Top) Case I: Without V2G, bottom)
Case II: With V2G.
FIGURE 7. FR planning risk during different hours of the day.
FIGURE 9. Average net demand profile.
becomes less than the planned capacity, i.e. Prα =
Pr (Actual FR Cap < α% of Planned FR Cap) where α is
the planning risk. Fig. 7 depicts the planning risks over
24-hour period. As illustrated in Fig. 7, the risk related to the
FR planning capacity is negligible during the peak time when
the parking lot is almost fully-occupied. However, FR planning based on the average scenario has a higher risk during
the off-peak hours (6-8 AM and 8-10 PM). The uncertainty
of the ESS planned capacity can also have voltage fluctuation effects on the distribution network that it is connected
to. Such an uncertainty can be dampened, and adversarial
effects can be eliminated if the distribution network includes
conventional energy storage.
V2G integration can reduce the peak demand of the parking
lot and this can be a major source of savings to the lot owner.
Consider the commercial lot with 120 parking spaces. Two
V2G scenarios are analyzed, i.e. Case I and Case II. In Case I,
the V2G system is not enabled and EVs only consume electricity to charge their batteries, while in Case II, V2G is active
which enables the lot’s owner to send electricity back to the
main grid. Fig. 8 shows the facility net demand in Cases I
and II over all EV arrival scenarios in the MC simulation.
As depicted in Fig. 8, the peak demand in Case II is much
lower compared to the Case I. The reason is the flexibility
in charging and discharging of batteries due to bi-directional
V2G technology. The facility operator can manage the power
flow in a way to reduce peak demand which results in lower
electricity cost. Also, Fig. 9 shows the average net demand
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profile of the lot node for Cases I and II. From Fig. 9, it can
be observed that using V2G system reduces the peak demand
by almost 40%.
In order to demonstrate the impacts of parking facility
peak-hours and the number of EV parking spots on the ESS
valuation, the following case studies are investigated:
• Case 1: A commercial lot with 80 EV parking spaces.
• Case 2: A commercial lot with 120 EV parking spaces.
• Case 3: A residential lot with 80 EV parking spaces.
• Case 4: A residential lot with 120 EV parking spaces.
Note that the peak hours for Cases 1 and 2 are assumed to
be around noon and for Cases 3 and 4 during night. Fig. 10
shows the average aggregated capacity of batteries parked in
the facility and the percentage of occupied parking spaces
for the commercial and residential lots. From Fig. 10, the
commercial lot is almost fully occupied during noon times,
however, the peak hour in a residential lot is during the
night time. In terms of the average parking times, for the
residential lot, vehicles usually arrive during the evening time
and stay in the lot until the next morning. Thus, as shown in
Table 2, on average, EVs stay in the residential lot for a longer
duration.
Multiple scenarios for each case are simulated, each of
which corresponds to various hourly LMP, RMCCP, and
RMPCP profiles. Fig. 11 depicts the average LMP and FR
market clearing price which are fed into the simulated scenarios. Moreover, for each scenario, the arrival and stay times
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
FIGURE 10. Top) dynamic storage aggregated capacity (kWh), bottom)
percentage of occupied EV parking spaces.
TABLE 2. Parking lot characteristics.
FIGURE 11. Top) average hourly LMP, bottom) average hourly FR credit.
TABLE 3. Optimal average discount factor and annual revenues for all
4 case studies.
of EVs are randomly generated according to the queueing
model. We also assume two battery capacities, 60 kWh and
90 kWh, with equal probabilities. All chargers are considered
to be level-2 with 15 kW power rating and 90% charging
and discharging efficiencies. Utilizing the proposed optimal
operational control model, the dollar amounts obtained from
different sources for each of illustrative cases are summarized
in Table 3. Note that for annual net benefit calculation, the
cost of electricity to charge EVs is also included.
We note that the overall income is small for these examples, but these numbers can significantly increase with the
lot capacity and market prices of ancillary services. There
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may also be credits for clean energy and reduced carbon
footprints that are not considered here. The net benefit can
be significantly increased if the parking lot is powered by its
own or a community owned solar farm.
Furthermore, the following observations are noted:
1) Capacity commitment of the commercial lot in the FR
market is more valuable than the residential lot due to
the higher FR credit during the day times (see Fig. 10;
bottom). Also, the capacity requirement for the FR
during the day is more than the night, thereby, commercial lot can make more revenue in the FR market.
2) Selling back electricity to the grid is more beneficial
for the residential lot due to the higher variation in the
hourly LMPs during night times (see Fig. 10; top). The
facility operator can charge EVs when the electricity
price is low and discharge to the grid when the price
is high. Also, EVs are parked for a longer duration
in the residential lot leading to more opportunities for
arbitrage.
3) Since ϕ ∗ in the residential lot is higher than the commercial lot, the lot owner’s revenue from charging the
EVs in the residential lot is less than the commercial
lot.
4) Commercial lot generates more revenue from the FR
market than selling electricity to the grid; by discharging to the grid, the lot operator must recharge the
batteries to the full SoC per EV owners’ requests.
This problem can go away if the lot is co-located with
a solar farm and receives its power from that farm.
Around 40% electricity peak reduction was observed
for the commercial lot with V2G-enabled charging stations. This reduces the power loss in the distribution
network and defers the needs for the T&D capacity
upgrades.
As discussed, LMP and FR credit affect the parking lot
owner’s revenue. In order to consider these pricing elements
during the peak-hours of the parking lot, here we define four
new terms via (27)-(30) in the following, namely weighted
LMP by aggregated battery capacity, λ̂ACap , weighted LMP
by percentage of the occupied spaces, λ̂OSpc , weighted
ˆ CR,ACap , and
FR credit by aggregated battery capacity, FR
weighted FR credit by percentage of the occupied spaces,
ˆ CR,OSpc , respectively. Thus we have:
FR
λ̂ACap =
λ̂OSpc =
ˆ CR,ACap =
FR
ˆ CR,OSpc =
FR
24
X
t=1
24
X
t=1
24
X
t=1
24
X
ACapt × λt
(27)
OSpct × λt
(28)
ACapt × FRCR
t
(29)
OSpct × FRCR
t
(30)
t=1
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
FIGURE 12. Correlation analysis of the daily revenue with respect to weighted LMP and FR credit.
where ACapt and OSpct denote the aggregated capacity of
batteries parked in the parking lot and the percentage of
occupied parking spaces at time t, respectively. Fig. 12 shows
the correlation between these four new factors and the daily
revenue of the parking lot. As can be observed from Fig. 12,
the parking lot owner’s daily revenue has a strong correlation
with the weighted FR credit for both weighted capacity and
occupied spaces. However, Fig. 12 does not show a strong
correlation between LMP and daily value. Table 4 presents
the correlation value between these four factors and the daily
value of the parking lot.
Analysis of the daily parking lot owner’s revenue for all
of the four cases reveals that the LMP and FR credit during
the peak-hour of the parking lot has an impact on its value.
Moreover, it has been illustrated that FR credit has the most
significant impact on the evaluation process. In other words,
high FR credit during the busy hours of the parking lot causes
high value for the parking lot operator. Furthermore, more
capacity for EVs in the parking lot results in more revenue
for the parking lot operator. As part of this analysis, it has
been observed that with the current state of the energy and
regulation markets, commercial parking lots with noon-time
peak are more beneficial from the parking lot operator’s point
of view. The reason is the high regulation market clearing
price during the day-time, which coincides with peak-hours
of the commercial parking lots. Moreover, V2G capability
can reduce the peak electricity demand by almost 40%, which
leads to power loss reduction in the distribution network
and defers the needs for the capacity upgrade. From the
EV owners’ perspective, the discount they receive from the
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TABLE 4. Correlation coefficient values.
parking lot operator compensates for the additional battery
degradation cost. Also, EV owners (same as all rate-payers
in the distribution network) could benefit from the lower
electricity tariff-rate, which is expected because of the peak
reduction in the utility grid.
V. CONCLUSION AND FUTURE WORK
This paper presented an integrated framework which optimally plans for the charge and discharge of EVs in a parking
lot to maximize the parking lot owner’s benefits. The economic benefit to EV owners through reduced parking fees or
discounted charging fees was also taken into account, which
compensated the additional degradation of the vehicle battery.
We showed that the proposed model is capable of quantifying
the impacts of such parking lot on the power distribution
network, where approximately 40% power peak reduction
was observed for the commercial parking lot with V2Genabled charging stations. This reduces the power loss in the
distribution network and defers the needs for T&D capacity
upgrades. The analysis also revealed that, with the current
state of energy arbitrage and regulation market, commercial
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K. Mahani et al.: EV Parking Lots for Flexible Energy Sourcing
parking lots are more beneficial from the parking lot operators’ point of view compared to the residential parking lots,
which are occupied during the night time. The reason is the
higher regulation market clearing price during the noon-time,
which coincides with peak-hours of the commercial parking
lots.
The extension of the above model to multiple EV parking
lots can benefit cities, especially in under-privileged communities, where brown fields can be transformed into clean
energy and income generating lots. The collective flexibility
offered by a network of EV parking lots (as modeled here)
can significantly mitigate and reduce the peak loads that are
anticipated due to high market penetration of EVs. At the
same time, these lots can help stabilize LMPs at times of
peak loads, hence, reducing for additional T&D infrastructure investments. Moreover, developing an integrated model
that accommodates different EV classes, including Level-1,
Level-2, and DC fast charging (DCFC), is in order as our very
close future work.
ACKNOWLEDGMENT
The authors would like to thank the editor and the anonymous
reviewers for their constructive comments and suggestions,
which improved the quality and clarity of this article. The
statements made herein are the sole responsibility of the
authors.
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KHASHAYAR MAHANI received the B.Sc.
degree in electrical and control engineering from
the University of Tehran, Tehran, Iran, in 2011,
and the Ph.D. degree in industrial and system
engineering from Rutgers University, NJ, USA,
in 2019. His research interests include energy storage management, building energy management,
model predictive control, and network-aware planning and control.
38782
FARHAD ANGIZEH (Graduate Student Member,
IEEE) received the B.Sc. degree in electrical engineering from the Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran, in 2010,
and the M.Sc. degree in energy systems engineering from the Sharif University of Technology,
Tehran, in 2014. He is currently pursuing the Ph.D.
degree with the Industrial and Systems Engineering Department, Rutgers University, NJ, USA. His
research interests include demand response and
energy management, the modeling and integration of distributed and renewable energy resources, and the optimization of smart electricity grids.
MOHSEN A. JAFARI (Member, IEEE) received
the Ph.D. degree from Syracuse University,
in 1985. He has directed or co-directed a total of
over 23 million U.S. dollars in funding from various government agencies, including the National
Science Foundation, the Department of Energy,
the Office of Naval Research, the Defense Logistics Agency, the NJ Department of Transportation,
FHWA, and industry in automation, system optimization, data modeling, information systems, and
cyber risk analysis. He actively collaborates with universities and research
institutes abroad. He has also been a consultant to several Fortune 500 companies and local and state government agencies. He is currently a Professor and the Chair of Industrial and Systems Engineering with Rutgers
University–New Brunswick. His research interests include manufacturing,
transportation, healthcare, and energy systems. He is a member of IIE.
He received the IEEE Excellence Award in Service and Research.
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