# Carbon-Aware EV Charging

Kai-Wen Cheng14,Yuexin Bian14, Yuanyuan Shi1, Yize Chen2

<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>1115
Authors contributed equally 1 Department of Electrical and Computer
Engineering, University of California San Diego, San Diego, CA 92161
2Lawrence Berkeley National Laboratory, Berkeley, CA 94720

###### Abstract

This paper examines the problem of optimizing the charging pattern of electric
vehicles (EV) by taking real-time electricity grid carbon intensity into
consideration. The objective of the proposed charging scheme is to minimize
the carbon emissions contributed by EV charging events, while simultaneously
satisfying constraints posed by EV user’s charging schedules, charging station
transformer limits, and battery physical constraints. Using real-world EV
charging data and California electricity generation records, this paper shows
that our carbon-aware real-time charging scheme saves an average of $3.81\%$
of carbon emission while delivering satisfactory amount of energy.
Furthermore, by using an adaptive balanced factor, we can reduce $26.00\%$ of
carbon emission on average while compromising $12.61\%$ of total energy
delivered.

††publicationid: pubid: 978-1-6654-3254-2/22/$31.00 ©2022 IEEE
§§footnotetext: Equal contribution

##  I Introduction

The adoption of electric vehicles (EV) is significant to the carbon neutrality
goal since it helps reducing carbon emission of the transportation sector.
Despite the numerous benefits of EV on the emission front, the rapid increase
in EV charging events has become an emerging operational concern on the power
grid level. With more than a quarter million of EVs sold in the United States
in 2021 and more projected in the future, the grid-level power consumption
will face an expedited increase. Moreover, since the transportation sector and
the electric power accounts for $30\%$ and $25\%$ of carbon emissions [1]
respectively, there are growing interests on how we can efficiently reduce
grid-level carbon emissions in accompany with transportation electrification.
While driving EVs decreases the direct carbon emission in transportation,
charging EVs could possibly increase carbon emission in electricity generation
due to mismatch in low carbon emission interval and peak charging interval. A
German study indicated that if EV adoption rate exceeds $25\%$, we could see
an increase in peak power demand of $30\%$ in some location [2]. As the
electricity generation energy mix becomes time-varying due to wind and
photovoltaic (PV) energy source, increase in EV charging demand may lead to
increasing use of fossil fuel generations during peak hours, which contradicts
the carbon reduction goals.

In this paper, we examine the possibility of designing carbon-intensity-
adaptive charging policies to optimize the carbon trajectories of EV charging
sessions. Take California as an example, the fast adoption of solar PV in
California has made phenomenal impact on the state’s grid energy mix, leading
to the “duck curve” - the imbalance between electricity demand and renewable
generation [3]. With respect to carbon emission, the “duck curve” also
applies. In day time, the large amount of clean energy supply help lower the
average carbon intensity. Depending on the season, we can also see a
difference of 0.12 to 0.15 kgCO2/kWh between the day-time and night-time
carbon intensity. This implies the potential of shifting EV charging demand to
the hours with higher penetration of renewables (low carbon intensity),
therefore, absorbing the excess supply of electricity and reducing the overall
carbon emission.

Figure 1: Schematic of proposed carbon-aware EV charging scheme. By
investigating the flexibiliy coming from both grid carbon intensity and EV
arrival/charging patterns, we are able to design adaptive charging algorithm
to minimize charging station’s carbon emissions. The top left figure
represents the time-series of the mix of different energy sources, which is
detailed in Section III.A.

While the flexibility in EV charging schedule can reduce the environmental
impact, it is important to take individual charging session’s time and energy
constraint into consideration in real life. In this paper, we take the
perspective of an EV charging station operator that aim to reduce overall EV
charging emission while satisfying individual user’s charging needs. The goal
is achieved by exploring the interactions among time-varying grid carbon
intensity, EV charging patterns, and charging infrastructure’s physical
constraints. Specifically, we would like to answer the following research
question: _what is the potential for reducing carbon emission of charging
events by leveraging the flexibility of EV charging sessions?_

The contributions of this work are as follows. First of all, this paper
introduces the carbon optimization problem in contrast to cost optimization
for EV charging stations. With ongoing demand for low-carbon initiatives and
action terms, this paper also brings carbon-awareness to the attention. On top
of that, this paper shows the effectiveness of such optimization algorithm by
solving the optimization with real-world data collected in the Berkeley Lab
campus. Last, the introduction of carbon intensity forecasting enables online
EV scheduling, which makes EV carbon minimization applicable in real-life
using the the algorithm introduced222In this work, we consider the carbon
emissions from charging sessions, excluding from, e.g., vehicle manufacturing,
power unit construction or end-of-life..

Numerical studies on real-world charging data from Berkeley campus and CAISO
generation fuel mix data validate the effectiveness of the proposed method on
optimizing EV charging events’ carbon footprints in a real-time fashion. Our
results show that the proposed charging scheme can save an average of 3.81$\%$
of carbon emission without sacrificing total delivered energy. From our data
and simulation, the charging station emits on average around 57 kgCO2 each day
while delivering 288 kWh of energy. A 3.81$\%$ carbon reduction is equivalent
to 792.7 kgCO2 per year. Moreover, with a 12.61$\%$ sacrifice on the energy
delivery, we can further reduce the carbon emission by 26.00$\%$, which is
around 5,143 kgCO2 per year. According to the latest social cost of carbon
(SCC) estimate by the US government, the current SCC is priced at $\$$50 per
ton [4]. This indicates that our algorithm can reduce social cost by $\$257$
with a slight comprise of energy delivery. Assuming one charging session per
day per EV in California, this means given current renewables penetration, we
can reduce SCC by 5.47 million dollars per year. The cost reduction amount
will continue to increase as more EVs are adopted in California.

###  I-A Related Work

Researchers have been discussing the potential of designing EV charging
scheduling algorithms to alleviate grid congestion [5], to better integrate
increasing renewables [6], and to accommodate economical objectives as well as
operating constraints [7]. Real-time algorithm considering arrival and
departure statistics are discussed in [8]. Bi-directional charging strategies
and vehicle-to-grid (V2G) technologies have been also discussed in [9].

There are some existing work on approaching load shifting problem via solving
optimization problem explicitly [10, 11, 12] or via time-of-use pricing. Even
though electricity prices follow some characteristic of the the load curve
(lower cost during the noon and higher cost during the evening), cost
optimization using TOU pricing is an indirect approach for optimizing carbon
emissions. Based on a recent EV industry report [13], there is unutilized
potential of carbon reduction via enabling flexible charging windows.

Carbon-aware EV charging scheduling is still novel in the way that it combines
grid carbon intensity data, EV statistics and optimization framework. [14]
conducted a survey on EV owners’ preferences regarding carbon-neutral charging
services. In [15], empirical studies validate that different geographical
regions and charging schedules can lead to different carbon emissions. [16]
proposed a heuristic method to match EV charging with renewable energy
resources on a macro scale without considering individual characteristics of
charging sessions and charging station’s physical constraint. In [17], a
demand response scheme with simplified charging models is proposed for the
overall US market.

Our technique bears the closest resemblance to the industrial advances
mentioned in [18, 19], and is partly inspired by the carbon-aware cloud
computing considering flexible data center loads [20]. The key distinction
lies in how we formulate and solve the optimization problem by taking both
carbon intensity forecasts and engineering constraints into account. We also
develop carbon intensity forecasting method to accommodate real-time
scheduling.

##  II Carbon-Aware Charging Framework

In this paper, we consider the daily operation of an EV charging station. The
charging station is connected to the electricity grid via a power distribution
feeder. The charging current signal is communicated from the charging station
to the vehicle’s on-board charger. Upon arrival of each EV, the charging
station is notified of their arrival battery energy level, requested energy
and departure time according to inputs set by the user.

We are interested in designing a charging scheduling algorithm to achieve
station-level load shaping. In particular, since both the EV charging demand
and grid-level carbon intensity are time-varying, there is potential to reduce
station-level carbon emission by shifting charging load from periods with high
carbon intensity to low carbon intensity periods, as long as the charging
demand is satisfied before departure time.

The implemented algorithm is composed of several major components as are shown
in Fig. 1: (i) extract and process grid-level energy mix data; (ii) predict
the day-ahead carbon intensity (iii) receive and communicate session-specific
charging statistics (arrival time, departure time, battery limits, and
requested energy); and (iv) optimize carbon emissions with resource and
charging schedule limits.

##  III Method

In this section, we firstly introduce carbon intensity calculation, and then
illustrate how carbon reduction goal is integrated into charging station
operation considering the stochasticity of EV charging requests and grid
carbon intensity.

###  III-A Carbon Intensity

We denote the time-varying carbon emission (carbon intensity) as $C(t)$ with a
unit of kgCO2/kWh or mTCO2(Metric ton CO2)/MWh. Carbon intensity data is a
time-series data that reflects the grid-level carbon emission per energy unit.
Carbon intensity depends on the power grid’s operational plan and carbon
intensity of each energy resource. In this paper, we specifically examined the
carbon intensity for the California grid with data provided by CAISO
(California Independent System
Operator)333http://www.caiso.com/todaysoutlook/pages/emissions.html. To
calculate the carbon intensity, we consulted the carbon emission of the grid
resources as well as the supply trend of the grid. Figure 2 describes the
feature of the two data sets. In Fig 2 (left) there are two main contributors
to the state’s grid emission: imports and natural gas.

$C(t)=\sum_{i=1}^{N}C_{i}(t)\cdot\frac{P_{i}(t)}{P_{total}(t)},\;\forall
i\in\mbox{grid mix};$ (1)

where $C_{i}(t)$ is a time-series data of the carbon intensity of each energy
source, $P_{i}(t)$ is the power supplied by the energy source and
$P_{total}(t)$ is the total power generated on the specific day at time $t$.
From the formula and the data, we can expect the carbon intensity to be high
during the night and the early morning when solar energy is less available. On
the other hand, the carbon intensity of the grid tends to be low during the
day as solar energy and other renewables become a major contributor to the
state’s power supply.

Figure 2: (Left) The carbon intensity of each resources. We exclude biogas,
biomass, geothermal, and coal since it has relatively low carbon contribution
in California. (Right) Daily average power supply per resource. We exclude
coal and hydro since it is less significant.  Figure 3: Average carbon
intensity during different seasons.

Carbon intensity is not only grid-mix dependent and time sensitive, but is
also seasonally sensitive. Fig 3 shows an example of carbon intensity
calculated using the above formula throughout the year. We notice that carbon
intensity is lower especially during the spring. On top of that, we also
notice a shift in time for the carbon intensity curve in autumn as well as
winter. We can attribute this to the daylight saving hours policy in
California.

###  III-B Charging Station Operation Model

As mentioned in Section II, our charging framework takes into account of the
user constraints as well as the infrastructure constraints. These constraints
are discussed below. We use the discrete time model, where the time step is
indexed in $\mathcal{T}:=\\{1,2,3,\ldots,T\\}$. $\mathcal{V}$ is the set of
all EVs. For each vehicle $i\in\mathcal{V}$, we denote the charging demand
information is $(x_{i,arrival},x_{i,depart},t_{i,arrival},t_{i,depart})$,
where $x_{i,arrival}$ is the state-of-charge SoC of EV $i$ upon its arrival of
the charging station, $x_{i,depart}$ is the desired state-of-charge SOC of EV
$i$ upon its departure. and $t_{i,arrival},t_{i,depart}$ is the time index
when the vehicle $i$ arrive in / depart from the charging station,
$t_{i,arrival},t_{i,depart}\in\mathcal{T}$.The above four factors are all
externally determined by the user. Arrival time $t_{i,arrival}$ and initial
energy level $x_{i,arrival}$ are determined when user plugged in the EV.
Departure time $t_{i,depart}$ and charge $x_{i,depart}$ are input by the user
when they initiate the charging session.

The model aims at deciding the charging power $u_{i}(t)$ for vehicle $i$ at
time $t$, and the state-of-charge (SoC) $x_{i}(t)$ for EV $i$ at time $t$
given the specific objective. We are interested in solving the following
optimization problem:

$\displaystyle\min_{\mathbf{u}}\quad$
$\displaystyle\sum_{t\in\mathcal{T}}\sum_{i\in\mathcal{V}}C(t)u_{i}(t)\Delta
T+\lambda\sum_{i\in\mathcal{V}}|x_{i}(T)-x_{i,depart}|$ (2a) $\displaystyle
s.t.\quad$ $\displaystyle x_{i}(0)=x_{i,arrival},$ (2b) $\displaystyle
x_{i}(t)=x_{i}(t-1)+\frac{\delta u_{i}(t)}{E_{i}},\;t\geq 1;$ (2c)
$\displaystyle 0\leq x_{i}(t)\leq\bar{x}_{i},\;i\in\mathcal{V};$ (2d)
$\displaystyle 0\leq u_{i}(t)\leq\bar{u}_{i},\;i\in\mathcal{V};$ (2e)
$\displaystyle\sum_{i\in\mathcal{V}}u_{i}(t)\leq\bar{P},\quad
t\in\mathcal{T};$ (2f) $\displaystyle u_{i}(t)=0,\quad
t\notin[t_{i,arrival},t_{i,depart}),\;i\in\mathcal{V}.$ (2g)

The above optimal charging scheduling problem minimizes the total carbon
emissions while satisfying charging sessions’ time and energy constraints,
defined by the objective function (2a). We firstly consider the case when
$C(t)$ and EV charging demand information for next $T$ steps are available and
communicated to the charging station operator. We denote $\Delta T$ to be the
discretization interval, and in our case, $\Delta T$ is 5 minutes aligned with
the carbon intensity measurement interval published by CAISO. $\lambda$ is a
balanced factor to trade off between carbon reduction and energy delivery. The
operational constraints considered in this framework are described as follows:
EV charging constraints: Constraint (2b) defines the SoC level of EV upon
arrival; and (2c) depicts the dynamics between charging power and battery SoC,
where $E_{i}$ is the battery energy capacity (kWh). $\delta$ is an EV-specific
charging parameter, which is known before the operation and is computed based
on the charging efficiency and discretization, e.g., if charging efficiency is
$90\%$, and discretization interval is 15 minutes, $\delta=0.9\times
15/60=0.225$. (2d) and (2e) constrain the admissible charging power for single
EV, where the battery maximum SoC is $\bar{x}_{i}$ and maximum charging power
is $\bar{u}_{i}$.
Charging station constraints: (2f) limits the total available charging power
$\bar{P}$ at the charging station. We note that in this paper, we assume there
is a known $\bar{P}$ decided by the charging station’s transformer.
Temporal logic of charging sessions: (2g) describes the temporal logic that
the charging session has to satisfy, as no charging power shall be delivered
whenever EV $i$ has not arrived ($t<t_{i,arrival}$) or has departed $(t\geq
t_{i,depart}).$
Other Factors to generalize: The optimization problem that we introduced in
(2a) is a general model that can be further generalized. For example, battery
health is another important factor to be considered in EV charging. A more
complex version of this optimization problem could potentially include penalty
terms in the objective to discourage sudden change in charging power, which
prevents battery health from deteriorating.

##  IV Real-Time Scheduling

In this section, we propose a forecasting module to inform charging station
operators day-ahead carbon intensity, and extend the framework described in
Sec III to real-time settings.

Offline algorithm assumes we have access to all the information including
future arrival statistics. While in the real-time algorithm, we assume we can
only decide charging rate based on the predicted carbon intensity and
information of arrived electric vehicles. An online algorithm is crucial for
the real life applicability of our charging strategy because there are two
main factors that changes daily in our optimization problem: daily average
carbon intensity and daily EV arrival pattern. From figure 5 and 6, we can see
that daily EV arrival varies from 5 vehicles to more than 40 vehicles per day.
An online scheduling algorithm will be able to adjust scheduling the given
arrival of EV’s. On top of that, our discussion of carbon intensity also
demonstrated seasonal volatility. With EV arrival uncertainty combined with
carbon intensity uncertainty, and online algorithm allows the charging station
to adjust it’s charging strategy given different scenario.

###  IV-A Carbon Intensity Day-Ahead Forecasting

We use the 2021 CAISO data (shown in Fig 2) and CAISO day-ahead load forecast
data $Load(t)$ to fit and evaluate the carbon predictor model. The grid’s day-
ahead carbon intensity $\hat{C}(t)$ is closely related to the future
electricity demand, calendar features, and past carbon intensity patterns. We
randomly choose $80\%$ data to fit the linear regression model and rest data
for testing the model performance. The resulting forecasting model is as
follows:

$\begin{split}\hat{C}(t)&=\beta_{0}+\beta_{1}\times Minute+\beta_{2}\times
Hour+\beta_{3}\times Day\\\ &+\beta_{4}\times Month+\beta_{5}\times
Load(t)+\beta_{6}\times MA(C(t))_{24}\\\ &+\beta_{7}\times
MA(C(t))_{12}+\beta_{8}\times MA(C(t))_{1};\end{split}$ (3)

where $MA(\cdot)_{a}$ denotes the moving average of past $a$ hours. Fig 4
illustrates the ground truth carbon intensity and forecasted carbon intensity
using the fitted model (3). We note that other statistical and machine
learning models can also be used for carbon intensity prediction. We use the
linear regression model since it is simple and provides accurate prediction
result. For the CAISO case study, the overall testing mean squared absolute
error is $0.0085$. We also demonstrate such forecasts can be readily
integrated into the proposed charging scheduler without affecting the
algorithm performance. Power grid CO2 emission intensity forecast is also
investigated in [21] by considering additional features and an autoregressive
model.

Figure 4: The ground truth (blue) and predicted carbon intensity (red) for
two-day sample in January and July respectively.

We calculate and forecast the average carbon intensity rather than marginal
carbon intensity, as in this study, we focus on the operating strategies for
single EV charging station. Such single-station operation scheme shall pose
minimal effects to transmission grid carbon profiles. We refer to [22] for a
more complete review and open-source data on electricity grid carbon
intensities.

###  IV-B Online Algorithm

With the predicted carbon intensity $\hat{C}(t)$, we are ready to implement
proposed carbon-aware charging scheduler in an online fashion. Denote the
optimization problem (2) as SCH with input information coming from the
charging infrastructure and EVs’ peak power constraints $\bar{P}$ and
$\bar{u}$, predicted carbon intensity, the active charging vehicles
$\mathcal{V}_{k}$ along with their states $x_{\mathcal{V}_{k}}$ where
$k\in\mathcal{K},\mathcal{K}:=\\{1,2,3,\ldots,K\\}$, the algorithm is
summarized in Algorithm 1.

Algorithm 1 Online Carbon Aware EV Charging

Charging infrastructure and each EV’s peak charging power limit $\bar{P}$ and
$\bar{u}$, operation time length $K$.

Charging power $(u_{i}(1),u_{i}(2),\ldots,u_{i}(K),i\in\mathcal{V})$.

for $k=1,\ldots,K$ do

$\mathcal{C}_{k}:=\\{\hat{C}(k),\ldots,\hat{C}(k+T-1)\\}$

$\mathcal{V}_{k}:=\\{i\in\mathcal{V}|x_{i,arrival}\leq k\textbf{ AND
}x_{i,depart}>k\\}$

$x_{\mathcal{V}_{k}}:=\\{x_{i}(k)|i\in\mathcal{V}_{k}\\}$

compute

$(u^{*}_{i}(1),\ldots,u^{*}_{i}(T),i\in\mathcal{V}_{k})=\textbf{SCH}(\mathcal{C}_{k},\mathcal{V}_{k},x_{\mathcal{V}_{k}})$

update $u_{i}(k)=u^{*}_{i}(1)\,,\forall i\in\mathcal{V}_{k}$ and
$u_{i}(k)=0,i\not\in\mathcal{V}_{k}$.

update $x_{i}(k+1)=x_{i}(k)+\frac{\delta u_{i}(k)}{E_{i}},\forall
i\in\mathcal{V}$.

end for

At each time step $k=1,2,\ldots,K$, we take the forecasted carbon intensity
for the next $T$ steps,
$\mathcal{C}_{k}:=\\{\hat{C}(k),\ldots,\hat{C}(k+T-1)\\}$, the current
available EVs $\mathcal{V}_{k}$ and their SoC levels $x_{\mathcal{V}_{k}}$,
and solves the optimization (2). With the optimized charging schedule
$(u^{*}_{i}(1),\ldots,u^{*}_{i}(T),i\in V_{k})$, we assign $u^{*}_{i}(1)$ to
the charging power of EV $i$ at time step $k$ to $u_{i}(k)=u^{*}_{i}(1)$ for
the active vehicles and update state of charge accordingly for every vehicle
$x_{i}(k+1)=x_{i}(k)+\frac{\delta u_{i}(k)}{E_{i}},\forall i\in\mathcal{V}$.

##  V Simulation Results

We use real-world, campus-wide EV charging station data from the Lawrence
Berkeley National Laboratory campus for the experiment, which contains all
charging sessions from the year of 2021 including EV arrival time, energy
consumption and depart time. We assume the battery capacity is 50 kWh for all
the vehicles, the available charging power from the charging station is 180
kW, and maximum charging rate is 7.5 kW444We aggregate all on-campus EV
chargers together as a single charging station and evaluate the algorithm..
Without loss of generality, we choose the simulation interval $\Delta T$ as 5
minutes, and there are 288 time steps per day. Source code and data for our
experiments are available at
https://github.com/kaicheng0824/carbon_aware_ev_charging.

Figure 5: The distribution of arrival time (left) and duration (right) of EV
charging sessions in 2021.

We include a brief introduction of the benchmarking EV charging scheduling
methods:

  * •

The equal sharing (ES) algorithm allocates available charging power supply
$\bar{P}$ _equally_ to all active EV charging sessions at each time step,
while satisfying each EV’s maximum charging rate and energy constraint.

  * •

The earliest deadline first (EDF) algorithm assigns the maximum allowable
charging power $\bar{u}_{i}(t)$ to EVs with earliest departure time while
keeping the sum of charging power less or equal to the infrastructure power
limit $\bar{P}$.

  * •

The time of use price aware (TOU) algorithm solves the optimization problem
that minimizes the charging cost and required energy deviation.

We report energy delivery quality EDQ (%) for the overall charging station
(EDQ-Station) and the average energy delivery quality (%) per session (EDQ-
Session) for performance evaluation according to (4):

$\displaystyle\text{EDQ-
Station}=\frac{\sum_{i\in\mathcal{V}}|x_{i,T}-x_{i,arrival}|}{\sum_{i\in\mathcal{V}}|x_{i,depart}-x_{i,arrival}|},$
(4) $\displaystyle\text{EDQ-
Session}=\frac{1}{|\mathcal{V}|}\sum_{i\in\mathcal{V}}\frac{|x_{i,T}-x_{i,arrival}|}{|x_{i,depart}-x_{i,arrival}|}.$

Fig 5 shows the distribution of vehicle arrival time and yearly staying time.
We can see that most vehicles arrive before noon when the carbon intensity is
lower, which leave room for charging flexibility. Most arrived vehicles stay
for less than four hours in the charging station.

Figure 6: The carbon emission shift compared with the baseline (EDF) in four
seasons. Carbon intensity exhibits the feature of duck curve among four
seasons, and our method takes advantage of the low carbon intensity pattern
and tends to postpone the charging to the time when carbon intensity becomes
lower.

####  V-1 Seasonal Shift

We first present the seasonal carbon emission shift using our method and the
baseline EDF method. We select days from March 1 to May 31 as spring, June 1
to August 31 as summer, September 1 to November 30 as autumn and December 1 to
February 28 as winter. Fig 6 shows the comparison of carbon emission and
energy delivery (%) among four seasons with the balanced factor
$\lambda=0.35$. From the figure, we can see that carbon intensity is lower at
noon than other time. Our method takes advantage of the low carbon intensity
pattern and shifts the flexible charging demand to the time when carbon
intensity is low, such that the carbon emission is reduced efficiently.

####  V-2 The impact of the balanced factor

We use the first 20 days in the dataset to show how balanced factor $\lambda$
in (2a) influences the carbon emission and energy delivery quality. Fig 7
shows the change of total carbon emission (red curve) and energy loss (blue
curve) using different balanced factors. We can see that with the balanced
factor decreasing, the carbon emission will decrease while the energy loss
will increase. We also compare the performance with the baseline EDF method.
Using a balanced factor $\lambda\geq 0.4$, we can achieve the same energy
delivery while reducing 5.6% CO2 for 20 days.

Figure 7: The tradeoff between the total carbon emission and percentages of
energy loss among different balanced factor using our method and baseline
(EDF). We use the first 20 days to simulate the result.

####  V-3 Comparison with baselines

Here we use the entire dataset in 2021. We compare our method with three
baseline methods: ES, EDF and TOU. We test our method with a fix balanced
factor $\lambda=0.3$ (denoted as Offline(0.3)) and $\lambda=0.4$ (denoted as
Offline(0.4)), respectively. We also test the carbon-aware charging algorithm
with a flexible factor scheme (denoted as Offline(+)), where we choose
$\lambda=0.3$ for days with vehicle size $n\leq 20$, $\lambda=0.25$ for days
with $n\in[21,30]$ and $\lambda=0.35$ for other cases. Secion V-2 shows that
larger balanced factor is more likely to deliver the required energy while
leading to less carbon reduction. Since group one (less than 20 charging
sessions per day) has relatively low carbon emission, and group three (more
than 30 sessions charging sessions per day) has less flexibility in shifting
charging demand, we choose larger balanced factor for group one and three to
prioritize the energy delivery. The results are shown in Figure 8. With
$\lambda=0.4$, the offline optimization can reduce $3.97\%$ carbon emission
while slightly improves the energy delivery quality by $0.03\%$ compared to
EDF and ES, and it can reduce $1.50\%$ carbon emission and maintain the same
energy delivery quality compared to TOU. This is because EDF and ES will
schedule charging instantly once EVs arrive, while TOU and our approach adjust
the charging power by solving the current optimization instance. TOU rate and
carbon intensity is higher after 4pm. To minimize the energy cost, ToU-aware
policy is likely to encourage chargers to finish charging before 4pm, and in
this way it can also partially help reduce the carbon emission. With
$\lambda=0.3$, the carbon aware optimization method Offline(0.3) can save
$24.7\%$ and $22.71\%$ carbon emission compared to EDF/ES and TOU
respectively, while also lead to $18.20\%$ in reduction in energy delivery
quality. With flexible balanced factors, Offline(+) saves $3.17\%$ carbon and
improves $5.55\%$ in delivery quality compared to Offline(0.3). An interesting
future direction is to develop a more principled method of adaptively choosing
the balanced factor according to daily charging patterns, that can both
maintain the high energy delivery quality and effectively reduce carbon
emission.

Strategy | Carbon emission (kg)
---|---
Equal Sharing | 2.913
Earliest Deadline First | 2.913
ToU price aware | 2.840
Offline (0.4) | 2.798
Offline (+) | 2.127
Offline (0.3) | 2.195
TABLE I: Average carbon emission for each charging session using different
approaches.

Table I shows the average carbon emission for each charging session. Compared
to EDF, offline with $\lambda=0.4$ reduces 0.115 kg CO2, which is equivalent
to travelling 1.15 miles555Tesla’s 2021 Impact Report; offline with adapted
balanced factors saves 0.786 kg CO2, corresponding to the travelling distance
of 7.86 miles.

Figure 8: The comparison of average energy deliver quality per session (EDQ-
Session) and carbon emissions: offline (0.3), offline (+) (smarter balanced
factor strategy), offline (0.4), ToU aware (TOU), earliest deadline first
(EDF), equal sharing (ES).

###  V-A Online EV Charging Scheduling Results

We next demonstrate the performance of the online scheduling algorithm. We use
the carbon intensity prediction and online EV information to generate the
charging schedule, that is, at each time step $t$, the model only knows the
information of arrived vehicles, and use predicted carbon intensity data for
the optimization.

Fig 9 shows that our online algorithm does not hurt the performance much
compared to the offline optima. With $\lambda=0.3$, the online algorithm
delivers $0.21\%$ less energy and generates $0.08\%$ less carbon emission
compared to the offline algorithm. With $\lambda=0.4$, the online algorithm
delivers $0.002\%$ less energy and generates $0.15\%$ more carbon emission
compared to the offline algorithm. Compared to EDF and ES, the real-time
scheduling saves $3.81\%$ of carbon emission and can keep delivering the same
energy; compared to TOU, it saves $1.50\%$ carbon and maintain the same energy
delivery quality. With balanced factor $\lambda=0.3$, the online algorithm can
further reduce $27.01\%$ of carbon emission at the cost of delivering
$14.21\%$ less energy than EDF and ES; and reduces $25.13\%$ carbon at the
cost of delivering $12.61\%$ less energy compared to TOU. All results indicate
the online algorithm is highly efficient compared to the offline solutions.

Figure 9: The comparison of energy delivery quality for station (EDQ-Station)
and carbon emission: offline (carbon aware offline), online (real time carbon
aware), ToU aware (TOU), EDF, and ES. Proposed online algorithm achieves
similar performances compared to offline benchmarks.

##  VI Conclusion and Future Work

In this paper, we explore how EV charging scheduling will positively affect
the carbon emissions of EV charging. More interestingly, in this paper, we use
the grid-level average carbon intensity as an indicator for optimizing
charging facilities’ emission profiles. In the future work, we will
investigate the choices of carbon and economical objectives, and explore the
planning and operation mechanisms considering multiple EV charging stations.
We will also explore how pricing mechanisms can affect the session-specific
carbon emissions.

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