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Genetic Algorithm for Optimal Charge Scheduling of Electric Vehicle
Fleet
MABROUK ELMEHDI
Mohammadia school of Engineers
Mohammed V University
Rabat, Morocco
+212 617397822
mabrouk.elmehdi@gmail.com
MAACH ABDELILAH
Mohammadia school of Engineers
Mohammed V University
Rabat, Morocco
+212 600032049
amaach@gmail.com
ABSTRACT
Electric Vehicles (EV) are gradually conquering more roads and
replacing pollutant conventional vehicles. They seem to be used
to store energy in clean and smart grids to mitigate greenhouse
gas emissions and eliminate harmful peak loads. This paper
establishes a stochastic procedure for modeling and analyzing an
electric vehicle (EV) fleet to generate an accurate charging and
discharging profiles. For the purpose of managing the EV fleet
we use a single-objective optimization, namely, the Genetic
Algorithm (GA) to determine the optimal charging/discharging
schedule for each EV in the fleet. The proposed optimization
allows to make the optimal trade-off between V2G and G2V
operations cost to highly increase benefits from EV batteries by
scheduling the charging mode in the low power price periods and
discharging mode in the high-power price periods. Moreover, we
compare our approach that considers the stochastic nature in the
initial state-of-charge (SOC), arriving and departing times to the
grid and the characteristic of EV battery packs for each connected
EV in workplace and home parking lots, with a naive charging
strategy.
CCS Concepts
• Computing methodologies➝Symbolic and algebraic
algorithms➝Optimization algorithms • Computing
methodologies➝Artificial intelligence➝Planning and
scheduling➝Planning under uncertainty.
Keywords
Electric vehicles; V2G; charging/discharging; smart grid;
Genetic Algorithm.
1. INTRODUCTION
The global electric car fleet has exceeded 2 million vehicles in
2016 after crossing the 1 million threshold in 2015, with a
promising vision that indicates that it will reach 9 million-20
million electric car on the road by 2020 and between 40 million
and 70 million by 2025[3-4]. This symbolic outlook highlights the
need for developing the deployment of electric vehicles in smart
grid to reduce both the greenhouse gas emissions and the
transportation energy consumption [5]. In the other words, the full
exploitation of this vehicles includes the making use of their
batteries as an important means of energy storage to facilitate the
development of renewable energy and to give more flexibility to
smart grids [6]. However, this high adoption of EV may
simultaneously increase the consumption of electricity and peak
power load. This paper tries to establish a stochastic modeling and
analyzing an EV fleet to deepen the cooperation between EV and
smart grids by also managing the charging and discharging of
each connected EV and avoiding any imminent and substantial
increase of power load which may lead to an apparent conflict of
interest. The purpose of this study is to make an important
contribution which can be established on: First, we propose a
model that considers the stochastic nature of the EV users’
behavior, initial state-of-charge (SOC), arriving and departing
times to the grid. Second, we introduce an efficient and effective
algorithm, namely, the Genetic Algorithm (GA) to determine the
optimal charging/discharging profiles for each EV in the fleet.
The remainder of the paper is organized as follows: Section 2
introduces a formulation of the charging/discharching scheduling
problem considering both the intermittent prices at a given
scheduling interval and the stochastic nature of the EV users’
behavior. Our approach is evaluated and compared to a naive
charging strategy in the four case studies with simulation results
in Section 3. Finally, Section 4 concludes the paper with a brief a
summary of the interesting results and findings.
•
Related works
An extensive research for the energy scheduling EV charging-
power demand has been carried out to investigate the impact on
power distribution systems using both deterministic and stochastic
methods [7–21]. In [21], another proposed EV charging demand
forecasting model based on the processing of the historical real-
world traffic distribution and weather condition data in South
Korea by big data technologies. In [22], a stochastic model of an
EV load considering the stochastic nature in the beginning battery
charging time and the initial state-of-charge (SOC) of the battery
to optimize the start time and the number of batteries starting
charging and analyze their impacts on both the system and EV
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NISS19, March 27–29, 2019, Rabat, Morocco © 2019 Copyright is held
by the owner/author(s). Publication rights licensed to ACM. ACM ISBN
978-1-4503-6645-8/19/03…$15.00
DOI: https://doi.org/10.1145/3320326.3320329
owners. A recent study [23] also presented a new approach to
determine both number and position of EVs charging stations in a
road network considering the EV flow, the features of the vehicles
and the charging station parameters. On the subject of the EV
charging scheduling, an important many research works carried
out in order to achieve the best trade-off between a fair charging
strategy and load curtailment. The most dominant strategy is naive
charging strategy (uncontrolled) [24], in which the EV’s owners
charge their batteries whenever they want or immediately plugged
into the system, for the reason that they not receive the hourly
information(off-peak electricity, tariffs …) in time to schedule the
charging of their batteries. This kind of strategies may cause
several problems for the electric system ( expensive charging,
increasing load demand, excessive overloading problem …). The
same paper [24], propose a mathematical model to provide
optimal charging profile of the plug-in hybrid electric vehicles
with quadratic programming to minimize the power losses which
does not consider V2G ability. In the bidirectional technology[25-
27], where two-way power transfer and which every EV can give
or receive energy from power grid but without considering the
remaining amount of energy in EV’s batteries, departing and
arriving times. Although various approaches have been explored
for solving EV charging scheduling problems, but they never
come closer as our study which considers the behavior and
characteristics of EV’s owners which affect the initial state-of-
charge (SOC) of their batteries, arriving and departing times to the
grid.
2. THE CHARGING STRATEGY
2.1 Deterministic Uncertainties
Probabilistic uncertainties refer to the parameters which related to
EVs and the behavior of their owners. Three uncertainties that
may effect on the EV charging/discharging profiles are presented
in this section:
2.1.1 Types
In this paper we assume that there are only two types of EV
battery:
• Battery Electric Vehicles (BEVs) are those vehicles that
can be supplied by an electrical source to feed their
energy storage unit.
• Plug-in Hybrid Electric Vehicles (PHEVs) with the
ability of switching between two engines: an internal
combustion engine (ICE) and a pure electric engine.
Where , and are representing, respectively, the total
number of EVs combined both BEV and PHEV numbers.
= +
2.1.2 EV battery capacity
Both types of EVs have different battery capacity which varies
notably with reference to its daily need. Most BEVs are utilizing a
mid-sized battery pack compared to the less sized battery packs
that are in PHEVs. Assuming that the battery pack for a BEV has
a 20-30 kWh pack and for a PHEV, 5-15 kWh [28].
2.1.3 Time duration availability and scheduling time
This paper hypothesized that 50% of electric vehicles of the fleet
are plugged-in to be charged at the workplace in the parking lots
and the other electric vehicles are connected to the grid to be
charged at home in the evening. Both, John Bates and David
Leibling investigated in their report that has been realized for the
Royal Automobile Club Foundation [29], They give a detailed
insight on the fluctuations of parking acts throughout the year
with seasonality and design hours, they describe the profile of the
start times of parking acts that concentrates on the most frequently
occurring period of the day at 7 a.m. to 7 p.m. Furthermore, it is
noted in the report that the overall average duration of parking
acts at workplaces is about 7.6 hours. In this study, we have taken
into account the starting time of each parking event on the above-
mentioned report and we have considered these long parking
periods that can be considered as recharging opportunities, as an
inspiring pattern to assume that every Plugged Electric Vehicle
(PEV) could start its recharge cycles every day around a bounded
period 7:00 a.m. to 7:00 p.m. Looking at the working day parking
acts information, it can be observed that the entire average
duration of parking acts at workplaces is about 7 hours, this period
is considered in this paper as the scheduling time at workplaces.
Same thing for the evening period, we have assumed that the night
charging period at home is between 9:00 pm and 6:00 a.m. and the
scheduling period would be 9 hours, for the reason that vehicles
are not actively-driven during the night period. Besides, the
parking lots at home or at work must be suitably equipped and
appropriately switched over to smart parking lots able to charge
and discharge EVs.
2.2 Probabilistic Uncertainties
Probabilistic uncertainties refer to the parameters which related to
EVs and the behavior of their owners. Three uncertainties that
may effect on the EV charging/discharging profiles are presented
in this section:
2.2.1 Initial State-of-Charge:
The behavior of EV owners is one of the crucial factors which can
indicate the amount of stored power in EVs batteries and their
availability in grid. Moreover, such detailed analysis and behavior
observations have already brought other important data such as
the starting time of charging/discharging as well as the daily
distance driven by a vehicle. Besides, this distance has a direct
impact on the batteries consumption that will in its turn indirectly
effect on the initial battery SOC value of each EV of the fleet.
Based on the general information extracted from private and
company vehicle travel [30] [31], both the travelling and daily
distance driven by a vehicle satisfies probability distribution
functions. Here is the probability density function for vehicle
travel can be modeled as :
, d >0
(1)
where g is the probability density function and d , µ, σ are the
daily mileage, mean and standard deviation value, respectively.
According to the data of private vehicles mentioned in [32], the
mean distance of the distribution is 22.3 miles and the
standard deviation is 12.2 miles. Otherwise the mean daily
mileage and standard deviation, for the company vehicles, are
respectively 54.1 and 15.2 miles. For the purpose of determining
the SOC at the beginning of a recharge cycle, a statistical data of
the state-of-charge of vehicles is typically needed. Thus, the SOC
at the beginning of a recharge cycle can be approximated by its
characteristic linear drop with the distance of travel:
(2)
Where denote the initial SOC of the i-th EV battery, and
denote the average of the daily travel distance. Hence, the PDF of
the initial SOC after two days of use is
, 0 <
<1
(3)
Where is the standard deviation, and is the mean of the initial
SOC of the battery.
2.2.2 EV power capacity
Since not every EV has the ability to be discharged daily, these
EVs typically charge when their batteries are low, and they only
need to be charged and not participate in discharging. Such EVs
are regarded as charging-only EVs (i.e., some EVs’ owners might
refuse to participate to the V2G program to preserve all the time
their EVs batteries in a high level of energy for future usage).. The
other EV owners, that may charge and/or discharge daily, these
are considered as flexible EVs. It is noted that Np + Na = N,
where Np and Na are, respectively, the charging-only EVs and
flexible EVs.
2.2.3 Chargers
In the V2G technology, the most important factor is considering
the time consumed for bidirectional power flow between the grid
and the battery in the charging or discharging processes. This is
conditional on both the power rate of the charger and total energy
amount stored in the battery. Here in Table1 presents a different
proportion of the proposed topologies for bidirectional charging
technology for the electric vehicles.
• (3kW, 16A) Slow charging A.
• (7kW, 32A) Slow charging B.
• (22kW, 32A) Intermediate charging.
• (43kW, 64A) Fast charging.
Table 1. presents the charging level distribution.
Charging level
Proportion of EVs chargers
Slow charging A
40%
Slow charging B
33%
Intermediate charging
24%
Fast charging
3%
2.3 Formulation of PEV Scheduling Problem
The EV scheduling optimization problem can be formulated as a
single-objective function in keeping with feasibility constraints:
min
(4)
s.t.
The aim of the EV charging/discharging scheduling is to
minimize the overall cost of the power in the G2V operations of
fleet vehicles. Therefore, the optimization problem is
modeled in the following expression:
Where are the charging/discharging efficiency,
is the hourly price of electricity and is the power
received or delivered from vehicle n.
determines the EV mode from the given three states:
•
: indicate that the EV is in the charging state
•
: indicate that the EV is in the discharging state
•
: indicate that the EV battery is in idle mode
(not charging or discharging state)
The two components are constituting the aforementioned
objective function: the first component describes the cost of the
power delivered to the EV battery; the second on describes the
cost of the power supplied from the EV battery to the grid.
(6)
(7)
(9)
(10)
Constraint (8), guarantee that the system meets each single PEV’s
energy need at the unplugging time (
) at any recharging
cycle. Constraints (9) and (10) ensure that the SOC is scheduled
within a predefined range between
and
(generally the customer pre-set this range for the battery Depth-
of-Discharge (DOD)). Where the
is assumed to be 20% as
well as the
is considered as 90%.
2.4 Solution Method
Genetic algorithms are designed to mimic exactly the metaphor of
natural evolution (biological selection). GAs are considered as the
elegant tool for finding optimal solutions using special techniques
to a particular computational problem that needs to maximize or
minimize its objective function. These algorithms represent only
one component that forms the field of so-called evolutionary
computation [33], in that they use improved techniques such as
crossover, selection and mutation, which are the bio-inspired
mechanisms that tend to imitate the process of reproduction and
natural selection. Through the wide range of exhaustive search
algorithms, GA are far more efficient and very flexible that can be
adapted to a huge range of different problems which requires no
extra information about them. Since genetic algorithms are
inspired by biological process, much of the applicated
terminology is borrowed from its biological counterpart. In GA
terminology, the term of chromosome indicates a set of
parameters (values, known as Genes) that represent a candidate
individual or candidate solution to the problem that the genetic
algorithm is trying to solve. A group of individuals or solutions
form a population, the following child populations of the new
generations are created from a recombination that combines parts
of two or more individuals that belong to the precedent generation
(parental solutions).
The creation of the first generation is randomly done. The
crossover operator is the process of combining the
genes(parameters) of one chromosome with those of another (the
parents) to discover with their differentiated offspring promising
new areas in the solution space (exploration). To prevent falling
all individuals of the newt generations into a local optimum of a
given solved problem, a promising mutation operator that would
change randomly the genes of the chromosomes which could also
change their characteristics.
Figure 1 : A Flowchart represents the setup of the approach employed in this paper
The allocation of the survival individuals for the next generation
ensures holding the fittest solutions with higher fitness values till
the final generation. The main process of selection is to prioritize
better individuals to worse ones, and many selection methods
have been proposed in the literature, including stochastic
universal selection [34], roulette-wheel selection [35], tournament
selection[36]. and ranking selection [37]. The fitness of an
individual indicates how high an individual is fitted to the
optimization problem and determines its probability to be a
survival individual for the following generation. The fitness value
is determined by evaluating the objective function. During the
single-objective genetic algorithm, the highest fitness value
solutions are chosen to form the next generation. By getting rid of
candidate individuals with poor fitness in the creation process of
the next populations, which they are prevented to be reigned by a
single individual. There are many different genetic algorithms that
use various efficient techniques which their performances were
investigated in several comparative studies. The progress of GA is
they are very flexible since they are carrying out a huge range of
different techniques and operators. However, to obtain the finest
performance possible a well-thought-out choice of the algorithm
and its operators is indispensable. The optimal balance between
exploration and exploitation through crossover or mutation
probabilities can guarantee a best offspring production quality and
fast convergence speed of the optimization algorithms.
Accordingly, a non-thoughtful production probability may lead to
an undesirable local optimum convergence.
3. SIMULATION RESULTS
3.1 Simulation Study
The simulation results and discussion are included in this section
to assess the performance of the proposed charging/discharging
algorithm. We have used MATLAB to perform the simulations.
This section presents four case studies that illustrate the use of the
developed demand and excessive charging of EVs fleet over the
day. Let us consider a fleet of 200,000 EVs are assumed to be
plugged-in into a smart grid via an adequate equipment that
ensure the charge and discharge these vehicles in the period of 24
hours. As our main goal is to study the use of smart scheduling in
the context of intensive use of EVs, we have included both the
initial SoC and the starting time for each vehicle in this study, to
determine load evolution over time. These uncertain parameters
are generated randomly using the probability density functions of
the normal distribution, where the means and standard deviations
are presented in the following table.
Figures 2-7: These plots represent resulted Optimal SOC profiles of 6 plugged in EVs. The profiles of EV number 11, 43, 69, 737,
983, 3493 are selected randomly
Table 2: Symbols and Values
Symbols
Values
µ
3.20
σ
0.6528
µ1/ µ2 arrival
8a , 23b
σ1/ σ2 arrival
2a,2b
0.975
1.025
Time Slot
15 min
Number of time slots
24*6=144
Scheduling Time
7a,9b
Nt
200 000
Char/Disch Frequency
1 per day
3.2 Discussion
From a simulation of 200,000 EVs, we select arbitrarily 6
graphs that illustrate the optimal schedule of EVs batteries
seeking themost beneficial charging and discharging planification
over a 24 hours period. The figures include two different curves;
the curve shown in red represents the naïve charging case of each
EV the curve in green illustrates the optimal variation of the SoC
obtained by running the Genetic Algorithm (flexible charging).
So, the graphs 2-7 indicate the excellent performance of the
used optimization algorithm by satisfying the EVs owners need
and get their EVs batteries ready for future trips or making it
fully-charged. In the contrary of the naïve charging strategy, the
flexible charging strategy permits to the PEVs to act as load
sources that would supply the grid in the electricity pricey periods
or act as an energy storage unit in the economically low periods.
As example, figure 5, the proposed approach is facing one of the
most common cases where the PEV’s battery contains a small
amount of energy left over. In the final stages of our charging
strategy, the PEV’s battery reaches its required charging level
with exchanging its power with network at the optimal time slots.
While conversely, in the figure 3, PEV exchanges a considerable
amount of power with network, meanwhile, it’s charged with a
variant rate swinging within the quick price changes in every time
slots in order to take maximum profits or avoid losses.
Figure8 includes the different bi-directional power flows
received from EVs or delivered to smart grid systems of all
scenarios A,B,C,D. It is shown from the blue curve of the 100%
PEV’s only charging scenario in each hour, and the red curve
highlights the mix of flexible charging/discharging (25%) and the
only charging (75%) in scenario B, and the yellow and purple
curves represents scenario C (50% of flexibles) and D (75% of
flexibles) respectively.
In Scenario A, huge and undesirable charging loads are
occurred similarly during the peak and sub-peak periods, even in
the high energy price periods, including 4:00–6:00, 7:00–9:00 and
12:00–14:00. The charging loads will nearly reach 52.58 MW
because of the high amount of energy that must be stored in the
vehicles’ batteries. Among this result, the naïve charging strategy
takes care of only quick fulfilling EV’s batteries without taking
into consideration the risk of damage that will be occurred in the
increasing peak demands where the existing smart grid may not
able to respond to these demands.
In the contrary of Scenario A, the Scenario B contains small
proportion of flexible vehicles that will bring to the grid a certain
suppleness. This proportion contributes significantly to smooth
the charging loads curve by discharging the energy stored in their
batteries or switched to the idle mode during the peak and sub-
peak periods such as 4:00–6:00 and 12:00–14:00.
In the scenarios C and D, by comparing with the results of the
scenario B and with higher proportion of flexible EVs that will
gradually plugged-in to the grid, the curve significantly continues
the making headway toward an optimal distribution over the day
by avoiding high energy price periods and letting EVs render an
extra power to the smart grid by setting them in discharging mode
during high price hours. When the electricity price is in its highest
values, EVs tent to deliver the electricity stored in EVs to gird.
So, the EVs charging loads are quite lightly increased in the sub-
peaks between 4:00–6:00 and 11:00–18:00, while the existing
amount of energy in the EVs batteries decrease significantly. On
the other hand, for the other time slots when the electricity prices
are low, the mode of the most connected EVs is changed to
discharging mode; therefore, a peak which appears the
discharging power in the period between 19:00–1:00. As a result,
using our flexible approach for EV charging can effectively
smoothing load demands and avoiding excessive grid stresses and
losses caused by extreme loads, which is clearly appeared in
figure 8, but more than that it can be considered as an appropriate
strategy for EV’s owners to charge their batteries within time slots
when the electricity prices are low.
Figure 8: This plot represents bi-directional power flows received from EVs or delivered to the smart grid
4. CONCLUSION
This paper established a stochastic procedure for managing the
EV fleet to determine an optimal charging and discharging
profiles through the application of a powerful genetic algorithm-
based optimization technique. The deployed optimization
algorithm, for generating intelligent charging and discharging
schedules of EV fleet, shows an excellent performance by
fulfilling the demand of every EV owner and making their EV
batteries fully-charged and ready for future trips. The developed
methodology depends on stochastic parameters in order to better
replicate EV owner behavior and by use generalized assumptions
and conditional probabilities of the arrival and departure times,
initial SOC, parking time and place, trip number …This paper
would also useful to researchers and stakeholders for integrating
electric vehicles on smart grid and deciding what EV charging
equipment, infrastructures and operation plans to invest on. To
achieve more realistic and practical prediction result, some real-
world EV battery data could be supplied and used to predict EV
fleet charging-power demand, they could help our approach to
manage uncertainty issues (irregular EVs departures and
arrivals…). As the future work, we plan to extend this research by
incorporating the power system generation and the excessive
charging of EVs fleet which could engender an intermittent and
high fluctuations of extra power demand on the grid over the day.
Another issue worth to be investigated is the evaluation of the
ability of feeding back the energy stored in EV batteries pack to
electrical grid, and its impacts on the economic and
environmental aspects of the generation system and the interests
of EV owners.
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