# A Deployable Online Optimization Framework for EV Smart Charging with Real-
World Test Cases

Nathaniel Tucker2 and Mahnoosh Alizadeh2  2Department of Electrical and
Computer Engineering, University of California, Santa Barbara, California,
93106, USA

###### Abstract

We present a customizable online optimization framework for real-time EV smart
charging to be readily implemented at real large-scale charging facilities.
Notably, due to real-world constraints, we designed our framework around 3
main requirements. First, the smart charging strategy is readily deployable
and customizable for a wide-array of facilities, infrastructure, objectives,
and constraints. Second, the online optimization framework can be easily
modified to operate with or without user input for energy request amounts
and/or departure time estimates which allows our framework to be implemented
on standard chargers with 1-way communication or newer chargers with 2-way
communication. Third, our online optimization framework outperforms other
real-time strategies (including first-come-first-serve, least-laxity-first,
earliest-deadline-first, etc.) in multiple real-world test cases with various
objectives. We showcase our framework with two real-world test cases with
charging session data sourced from SLAC and Google campuses in the Bay Area.

##  I Introduction

In the U.S., if federal zero-emission vehicle sales targets are met, there
could be more than 48 million electric vehicles (EVs) on the road in 2030 [1].
In order to provide charge to this growing EV population, it is estimated that
over 1.2 million public EV chargers need to be installed at on-the-go
locations and at destinations where EVs are parked for long periods [1].
Furthermore, the estimated cost for hardware, planning, and installation of
this future public charging infrastructure exceeds $35 billion (U.S.D.) [1].

Due to the increasing numbers of EVs, large investment cost of EV charging
infrastructure, and the need to charge EVs through cheaper and cleaner energy
resources, it is evident that smart charging strategies are required to
schedule the power delivery to EVs to maximize the benefits of both the EVs
and the public charging infrastructure [2, 3, 4]. In response, there has been
much academic work in the area of EV smart charging at public facilities in
recent years [5, 6, 7]; however, most of the effective and implementable
solutions require user input, are often facility/infrastructure specific, or
ignore critical infrastructure details for modeling purposes. Additionally,
the fact that some smart charging frameworks require user input, specifically
energy request amounts and departure time estimates, severely constrains their
deployment potential. First, most charging infrastructure installed today does
not have 2-way communication and would require a third-party user interface
(e.g., a touchscreen or smartphone application) to enable user input. Second,
the accuracy of user input information is often quite poor. The authors of [8,
9] showed that user input data in their real-world smart charging system has
18.6% and 26.9% mean absolute error percentages for departure time and energy
request estimates, respectively.

Furthermore, while the research area of smart charging has been thoroughly
explored in theory, there are only a few frameworks that are actually
deployable in the real-world. This is often due to simplifications of the
charging infrastructure, assumptions on data availability from the users
(i.e., assuming energy request and/or departure times are known a priori), or
the lack of real-world data to test and validate the performance of new smart
charging strategies. As such, detailed and repeatable case studies for
effective and deployable smart charging algorithms could be valuable to the
community.

Specific Challenges: There are several key challenges to designing a
deployable framework to schedule the charging profiles of numerous EVs. First
and foremost, the algorithm must run in real-time without knowledge of the
future EV arrivals. The algorithm must adapt its planned power schedules as
more information is revealed (i.e., as more EVs arrive to the parking lot).
Second, contrary to most smart charging algorithms presented in the
literature, if the system is to run on the most common standard chargers under
the J1772 standard, the algorithm must be able to function with limited
information from each EV [10], [11]. Specifically, when an EV plugs in, the
algorithm does not get access to the EV’s State of Charge (SoC) nor does it
know the EV’s future departure time (most level 2 chargers do not sense EV SoC
nor do they request user input for future departure times). As such, our smart
charging algorithm must predict how much energy an EV may consume as well as
the EV’s future departure time. Such challenges have been acknowledged in past
papers including [12, 13, 14, 15]. Third, all of the EV charging schedules
within a parking lot are coupled due to the local transformer capacity
constraint [16]. As such, the algorithm cannot over-allocate power at any
given time; therefore, the algorithm should make use of a model of the future
EV arrivals to avoid over allocating power due to unexpected arrivals.

Contribution: In this paper, we present a deployable and customizable
framework for real-time smart charging to be implemented at real large-scale
charging facilities. Three of the main contributions of our framework are as
follows:

  1. 1.

The smart charging strategy is readily deployable and customizable for a wide-
array of facilities, infrastructure, objectives, and constraints.

  2. 2.

The online optimization framework can be easily modified to operate with or
without user input for energy request amounts and/or departure time estimates
which allows our framework to be implemented on standard chargers with 1-way
communication or new chargers with 2-way communication.

  3. 3.

The online optimization framework outperforms other real-time strategies
(including first-come-first-serve, least-laxity-first, earliest-deadline-
first, etc.) in multiple real-world test cases. We showcase our framework with
charging session data obtained from collaboration with SLAC and Google
campuses [17, 18] in the Bay Area even with poor accuracy on users’ departure
time predictions.

##  II Problem Description

In the following, we consider an EV charging facility running a real-time
smart charging strategy. Specifically, we are examining a time horizon
$t=1,\dots,T$ where the facility manager wants to schedule the energy delivery
to the EVs that utilize the chargers within the facility. We denote the
variable $e_{i}(t)$ as a $T$x1 vector for the amount of energy (in kWh) that
is delivered at each time $t$ to EV $i$. It is through this variable that the
smart-charging algorithm can determine when to deliver energy and how much to
deliver. Furthermore, throughout the time horizon, we index the EV arrivals as
$i=1,\dots,I$ with each EV having an arrival time $t_{i}^{a}$, departure time
$t_{i}^{d}$, and energy demand/request amount $d_{i}$. We note that the
departure time and energy request for each arrival $i$ is unknown unless the
facility has communication infrastructure in place to solicit this information
from the users. Additionally, we note that any real-time smart charging
algorithm must be able to function without knowledge of the arrival sequence a
priori. That is, a real-time smart charging algorithm must operate as
information is revealed through arrivals and departures within the system. The
online optimization framework we present is able to function in real-time with
or without the user information for departure times and energy requests, an
aspect that is critical for deploying a smart-charging framework to existing
charging infrastructure.

###  II-A Objectives

Due to the fact that we are designing a framework that functions with or
without user input (i.e., a framework agnostic to users’ energy requests and
departure times), we must design an appropriate objective function that is
fair to all users, does well in controlling the costs incurred by the
facility, and outputs desirable load profiles for the facility.

Accordingly, in this section, we discuss several objectives that the manager
of a workplace charging facility might want to optimize. These include
maximizing the utility of the EV owners, minimizing Time-Of-Use (TOU)
electricity cost, minimizing demand charges, promoting load flattening and
equal energy sharing, or utilizing behind-the-meter renewable generation.
Likely, a facility manager would want to consider multiple objectives
simultaneously with varying importance for each objective. As such, the main
objective function of our optimization framework is a summation of various
utility functions multiplied by weights to signify their importance:

$\displaystyle\max_{\begin{subarray}{c}e\end{subarray}}U(e)=\max_{\begin{subarray}{c}e\end{subarray}}\sum_{f=1}^{F}w_{f}u_{f}(e).$
(1)

Note that $f=1,\dots,F$ are the various utility functions included in the
global objective. Additionally, $w_{1},\dots,w_{F}$ are the weights used to
tune the global objective and determine the relative importance of each
utility function. Now we will discuss several utility functions that could be
included by a charging facility operator (some of the following utility
functions were adopted from [19, 20] which present a similar real-time smart
charging algorithm and case studies; however, they make the assumption that
user input for energy request amounts and departure times is always
available).

EV Owner Utility: The main purpose of many workplace charging facilities is to
provide utility to the users of the system (e.g., employees or visitors that
drive EVs). As such, one objective that is common to many smart charging
systems is to maximize user utility based on how much energy their EV receives
during their stay (this objective can be used if energy requests are unknown):

$\displaystyle u_{OU}(e)=\sum_{i}\log(\sum_{t}e_{i}(t)+1).$ (2)

In (2), we represent the utility of user $i$ as a logarithmic function
dependant on how much energy is delivered to user $i$’s EV. The logarithmic
utility term was chosen to model the diminishing returns effect in user
utility for EVs receiving excessive amounts of energy (e.g., the first 20kWh
charged is more valuable to the EV owner than the second 20kWh). We note that
this objective does not depend on when the energy is delivered; therefore, if
the facility operator wants to emphasize quickly charging the EVs, the
following objective can be used.

Quick Charging: Here, the facility manager’s goal is to deliver as much energy
as possible to the EVs (and does not require departure time or energy request
information):

$\displaystyle u_{QC}(e)=\sum_{t}\frac{T-t+1}{T}\sum_{i}e_{i}(t).$ (3)

In (3), the utility for energy delivered at time $t$ is scaled by a term that
decreases as time progresses. That is, energy delivered to EVs in the near
future is more valuable than energy delivered later on, thus prioritizing
quick charging.

Maximizing Profit (or Minimizing Cost): In addition to maximizing user
utility, many charging facilities aim to maximize profit or minimize their
operational costs. In the following, let $q(t)$ be the price that a user has
to pay the facility for 1 kWh of energy at time $t$ and $p(t)$ be the price of
electricity from the time-of-use (TOU) rates from the local utility.
Furthermore, let us denote $z(t)$ as the energy used by other loads that are
not the EVs from behind the same meter (e.g., other buildings, lights, etc).
As such, we can write the profit maximization function as follows:

$\displaystyle
u_{PM}(e)=\sum_{t}q(t)\sum_{i}e_{i}(t)-\sum_{t}p(t)\Big{(}\sum_{i}e_{i}(t)+z(t)\Big{)}.$
(4)

If $z(t)$ is unknown or unmeasured, it can be set to zero and only the revenue
and cost of the EVs will be considered. Furthermore, setting $q(t)=0,\forall
t$ allows for the manager to only consider cost minimization.

Minimizing Demand Charges: Alongside TOU energy costs, the facility manager
needs to be conscious of the maximum demand each month. We denote the monthly
demand charge as $\hat{p}$ $/KW that gets charged based on the peak load each
month:

$\displaystyle
u_{DC}(e)=-\hat{p}\cdot\max_{\begin{subarray}{c}t\end{subarray}}\big{(}\sum_{i}e_{i}(t)+z(t)\big{)}.$
(5)

This can be a difficult objective to minimize in real-time; therefore, we use
an estimate of the peak demand from the previous month, denoted as
$\hat{e}_{old}$ and charge the facility operator for any increase
$\hat{e}_{inc}$ to the peak load estimate. As such, we adopt the following
strategy to include demand charges in our real-time optimization formulation:

$\displaystyle u_{DC}(e)=-\hat{p}\cdot\hat{e}_{inc}$ (6) where
$\displaystyle\hat{e}_{inc}=\max_{\begin{subarray}{c}t\end{subarray}}\bigg{\\{}\sum_{i}\big{(}e_{i}(t)+z(t)\big{)}-\hat{e}_{old},0\bigg{\\}}.$
(7)

Load Flattening: Another desirable outcome for a facility manager implementing
a smart charging algorithm is load flattening. This minimizes the variations
in the load from the facility which can help the local utility and reduce the
need for extra generation to account for sudden changes:

$\displaystyle u_{LF}(e)=-\sum_{t}\big{(}\sum_{i}e_{i}(t)+z(t)\big{)}^{2}.$
(8)

Equal Sharing: Another useful objective is to promote equal sharing of the
facility’s resources among the plugged-in EVs. We write this utility function
as follows:

$\displaystyle u_{ES}(e)=-\sum_{t,i}e_{i}(t)^{2}.$ (9)

Additionally, the inclusion of this term in the global objective function
ensures a unique optimal solution; specifically, if there are multiple energy
delivery schedules that yield the same total utility, then the addition of the
equal sharing objective will force the optimal solution to be the one that
most evenly distributes energy among the plugged-in EVs.

Energy Demand:  Lastly, in the offline optimal and online solutions, if users’
energy demands are known either from historical data or user input, then the
facility tries to deliver a certain amount of energy to each EV denoted as the
energy demand $d_{i}$ of EV $i$. In the offline case, the energy demand can be
ensured with a constraint; however, in the online case, to ensure feasibility,
sometimes it can be beneficial to include a penalty function for not
fulfilling the energy demand. We can denote such a penalty term as follows:

$\displaystyle u_{ED}(e)=-\sum_{i}\bigg{(}|\sum_{t}e_{i}(t)-d_{i}|\bigg{)}.$
(10)

When the demand for all the EVs is met, then $\sum_{t}e_{i}(t)=d_{i},\forall
i$ and the penalty is 0.

###  II-B Constraints

There are numerous constraints that limit how the smart charging algorithm can
distribute energy to the users’ EVs:

$\displaystyle 0\leq e_{i}(t)\leq e_{max},\quad$ $\displaystyle\forall t,i$
(11a) $\displaystyle e_{i}(t)=0,\quad$ $\displaystyle\forall
t\notin[t_{i}^{a},t_{i}^{d}]$ (11b) $\displaystyle\sum_{t}e_{i}(t)\leq
d_{i},\quad$ $\displaystyle\forall i$ (11c) $\displaystyle\sum_{i}e_{i}(t)\leq
e_{trans},\quad$ $\displaystyle\forall t$ (11d)
$\displaystyle\hat{e}_{inc}\geq\sum_{i}e_{i}(t)-\hat{e}_{old},\hskip 4.0pt$
$\displaystyle\forall t$ (11e) $\displaystyle\hat{e}_{inc}\geq 0.$ (11f)

The constraints are described as follows: (11a) constrains the minimum and
maximum amount of energy that a charger can deliver to an EV in one time slot.
Constraint (11b) ensures that an EV has to be plugged-in for it to receive
energy. Constraint (11c) ensures that the optimization does not exceed the
energy demand of each EV if the energy request amounts for the EVs are known.
Constraint (11d) is a coupling constraint across all EVs that limits the total
energy delivered at any time slot due to the infrastructure limits or the
local transformer. Constraints (11e) and (11f) describe the calculation of the
incremental increase to the maximum energy demand for demand charge
calculation.

###  II-C Offline Optimization

If the entire sequence of EV arrivals was known for a given time span (i.e.,
their arrival times, departure times, and energy demands), then one can
formulate an offline optimization using the utility functions in (2)-(10) and
constraints (11a)-(11f) to solve for the optimal smart charging strategy for a
given time period:

$\displaystyle\max_{\begin{subarray}{c}e\end{subarray}}U(e)$ subject to:
$\displaystyle\eqref{c: energy min max}-\eqref{c: demand increase 0}$

However, this is not the case in real-world charging facilities. Instead,
information is revealed to the facility manager in an online fashion, and
charging decisions must be made without perfect knowledge of the future. As
such, in the following section we discuss an online solution akin to model-
predictive-control (MPC) that solves the smart charging scheduling problem in
real-time. Additionally, it readily handles challenges that come from
inaccurate departure time information.

###  II-D Real-Time Smart Charging Algorithm (RTSC-A)

In this section, we discuss the online optimization framework to solve the
smart charging problem in real-time without knowledge of the future arrivals.
The approach is akin to model predictive control (MPC) and solves a convex
optimization problem at each time step. Specifically, for each time step
$t=1,\dots,T$ the optimization solves for the energy output of each EVSE for
the next $T-t$ periods. Then, the facility enacts the control strategy for the
next time slot, and recomputes the next set of actions at $t=t+1$ (i.e.,
rolling horizon).

Departure time scenario generation: As discussed in the introduction, users’
departure time estimates tend to be quite inaccurate or they are unavailable.
As such, we generate $n$ potential departure times that the user might leave
at (either from historical data or user input, if available), thus allowing
the Real-Time Smart Charging Algorithm (RTSC-A) to plan for multiple
scenarios. Using these $N$ candidate departure times, we create a scenario in
our optimization problem for each potential departure time and solve the
optimization across all scenarios. As time progresses, if a potential
departure time is no longer feasible (i.e., the potential departure time is
the current time step and the EV has not yet departed), then that scenario is
removed from the optimization via dynamic scenario weights (let $C_{n}$ be a
weight coefficient for each scenario that is set to 0 if the scenario is no
longer feasible). Furthermore let $x_{i,n}$ be the Tx1 binary vector that
indicates when EV $i$ is available to charge in scenario $n$.

Certainty equivalent control for future EV arrivals: We make use of our
dataset to generate a model for an average day that consists of estimated
arrival times, departure times, and energy requests for each day of the week.
We then use these daily models in the real-time optimization to account for
the unknown future EV arrivals. Specifically, at time $t$, let us assume that
there are $J$ EVs in the certainty equivalent daily model that are expected to
arrive in the future. Let $x_{j}$ be the Tx1 binary vector indicating when EV
$j$ is available to charge. The decision variables that determine how much
energy is delivered at a given time $t$ are Tx1 vectors labeled as
$e_{1},\dots,e_{I}$ for the actual EVs plugged in and $e_{I+1},\dots,e_{I+J}$
for the future EV arrivals from the model:

$\displaystyle\max_{\begin{subarray}{c}e\end{subarray}}\sum_{i=1}^{I}\sum_{n=1}^{N}\frac{1}{C_{n}}\Big{[}U(e_{i},x_{i,n})\Big{]}+\sum_{j=I+1}^{I+J}\Big{[}U(e_{j},x_{j})\Big{]}$
(13a) subject to: $\displaystyle 0\leq e_{k}\leq e_{max},\hskip 40.5pt\forall
k=1,\dots,I+J$ (13b) $\displaystyle e_{i}^{\;T}x_{i,n}\leq d_{i},\;\;\hskip
46.0pt\forall i=1,\dots,I,$ (13c) $\displaystyle\hskip 92.22464pt\forall
n=1,\dots,N,$ $\displaystyle e_{j}^{\;T}x_{j}\geq d_{j}^{min},\hskip
46.0pt\forall j=I+1,\dots,I+J,$ (13d)
$\displaystyle\sum_{k=1}^{I+J}e_{k}(t)\leq e_{trans},\;\;\hskip 20.0pt\forall
t=1,\dots,T,$ (13e)
$\displaystyle\hat{e}_{inc}\geq\sum_{k=1}^{I+J}e_{k}(t)-\hat{e}_{old},\hskip
7.0pt\forall t=1,\dots,T.$ (13f)

The first term of the objective function (13a) accounts for all $I$ EVs
currently plugged in and their $N$ potential departure times each while the
second term of the objective function accounts for all $J$ EVs in the future
model. Constraint (13b) ensures that the energy delivered is nonnegative and
less than the EVSE max $e_{max}$. Constraint (13c) ensures that the energy
demand of EV $i$ is not exceeded (if energy demand is known), constraint (13d)
ensures a minimum amount of energy is delivered to each EV in the future
model, and constraint (13e) ensures that the sum of all energy delivered by
the EVSEs at each time $t$ does not exceed the transformer constraint
$e_{trans}$. Constraint (13f) keeps track of any increase to the current
month’s peak load for the demand charge. We note that $\hat{e}_{old}$
corresponds to the previous peak energy demand that has been observed during
the month. The pseudocode for the daily algorithm can be viewed in Algorithm
1.

Algorithm 1 Real-Time Smart Charging

1: for each day do

2: Update current parking lot state

3: for each time interval $t$ do

4: if new departure from parking lot then

5: Update parking lot state

6: end if

7: if new arrival to parking lot then

8: Generate $N$ potential departure times for new arrival

9: Update Parking lot state

10: end if

11: Formulate optimization for time $t$:

12: for each EV $i$ plugged in at time $t$ do

13: Add EV $i$ to total objective function (13a)

14: Add EV $i$ to active constraints (13b)-(13f)

15: end for

16: for each future EV $j$ in daily model $t_{model}>t$ do

17: Add EV $j$ to total objective function (13a)

18: Add EV $j$ to active constraints (13b)-(13f)

19: end for

20: Solve optimization (13a)-(13f) for time $t$

21: Store planned energy schedule for each EV $i$

22: Set each EVSE’s output power for the current time interval

23: Update peak load $\hat{e}_{old}$ for demand charge calculation (if a new
peak load is observed)

24: end for

25: end for

##  III Test Cases

In the following section we compare the performance of our Real-Time Smart
Charging Algorithm with various other scheduling strategies. These include the
offline optimal (i.e., the optimal schedule solved offline with perfect
knowledge of arrival times, departure times, and energy requests),
uncontrolled (e.g., First-Come-First-Serve), Least-Laxity-First, and Earliest-
Deadline-First. Furthermore, we vary the accuracy of the departure time
information that is input to our Real-Time Smart Charging algorithm to
showcase its ability to handle inaccurate departure time estimates and still
yield good performance. Additionally, we vary the coupling constraint
(infrastructure/transformer size) to showcase the performance of our algorithm
in a constrained setting. The first test case considers a facility manager
that wants to maximize user utility and only slightly cares about TOU
electricity costs (i.e., this would be the case of a large company campus who
wants to provide free and effective charging for employees). The second test
case considers a facility manager that wants to maximize profit while
delivering adequate energy to each customer (i.e., this would be the case of a
for-profit third-party parking structure equipped with chargers and wants to
minimize TOU electricity costs and demand charges).

###  III-A Test Case Specifics

We examine a two week period from June 17 - June 29 in 2019 at a Bay Area
workplace from our Google EV dataset. The location has 57 level 2 EVSEs with
50-100 EVs arriving each weekday and is under PG&E’s E-19 rate structure.

First, the EV charging session data was filtered by weekday and then filtered
again by arrival time. Namely, each charging session was put into one of 12
possible groups corresponding to 2-hour windows for the arrival times (e.g.,
an EV charging session that started at 9:48am would be stored in the
8:00am-10:00am group). Once this was done, daily arrival time histograms were
generated and the average stay duration and average energy consumption were
calculated for each of the 12 groups. The average arrivals per weekday, the
average arrivals per 2 hour window, the groups’ average stay durations, and
the groups’ average energy consumption were then used to create the
algorithm’s future model each day and to generate potential departure times
for each EV arrival. Last, we note that all of these simulations were done in
Python with CVX and Mosek on a Laptop with an i7 processor and 16gb of RAM.
Moreover, the optimization problem’s complexity is not affected by the number
of arriving EVs each day; rather, the problem size grows only as the number of
chargers increases. Additionally, for implementation, (13a)-(13f) has to be
solved every 15 minutes and for the 57 chargers in our case study, (13a)-(13f)
was solved in less than a second. Thus, the algorithm is scalable and there is
significant extra time for computation for a larger dataset (i.e., more
chargers at the parking lot).

###  III-B Test Case 1: User Utility Maximization with TOU Rates

Figure 1: Total energy delivered for the various cases including Least-Laxity-
First and Earliest-Deadline-First (both with perfect departure time knowledge)
with varying transformer capacities. Figure 2: Cost per KWh from TOU rates for
the uncontrolled, offline optimal, and 4 MPC test cases

In this section, we consider the case of a facility manager that wants to
maximize user utility and only slightly cares about TOU electricity costs
(i.e., this would be the case of a large company campus who wants to provide
free and effective charging for employees). The following objective function
was used in the Real-Time Smart Charging Algorithm and the offline
optimization:

$\displaystyle
U_{1}(e)=15u_{OU}(e)+u_{PM}(e)+10^{-9}\Big{(}u_{LF}(e)+u_{ES}(e)\Big{)}$ (14)

In this objective function, the smart charging strategy heavily favors the EV
owner’s utility with a small emphasis on TOU electricity cost. Load flattening
and energy sharing are also included to promote a desirable energy
distribution amongst EVs and a flat demand for the utility.

In this test case, we vary the coupling constraint from the local transformer
capacity from 160KW to 100KW. We note that in the uncontrolled dataset, the
peak load during the two week period was 160.5KW.

Additionally, we vary the accuracy of the departure time estimates that are
input to our RTSC-A. This is due to the fact that users often cannot predict
their departure times with perfect accuracy (if the system solicits user
information) or due to the fact that historical data does not accurately
forecast departure times. As such, for our RTSC-A, for each EV charging
session, we consider 10 scenarios. Each of the 10 scenarios makes use of a
departure time sampled from a normal distribution centered on the real
departure time. We vary the standard deviation of the normal distribution to
model EV owners’ inaccurate departure time estimates. In the following plots,
we denote MPC0 as our RTSC-A with perfect departure time estimates (standard
deviation equal to 0) and we denote MPC5 as our RTSC-A with departure time
estimates sampled from a normal distribution with standard deviation equal to
5 time steps (1hr 15min). MPC0, MPC5, MPC10, MPC20 make use of normal
distributions with standard deviation equal to 0, 5, 10, and 20 time steps,
respectively. Furthermore, we note that in the case of MPC20, the standard
deviation in the departure time estimate is 20x15min = 5 hours, which is a
very inaccurate estimate.

Figure 1 presents the total energy delivered to EVs for the various cases
including Least-Laxity-First and Earliest-Deadline-First (both with perfect
departure time knowledge). Figure 2 presents the cost per KWh from TOU rates
for the uncontrolled, offline optimal, and 4 MPC test cases.
Test Case 1 Key Results:

  1. 1.

As shown in Figure 1, all of the charging strategies were able to deliver
900KWh of energy per day with a 160KW coupling constraint. However, as the
coupling constraint becomes more restrictive (i.e., 140KW, 120KW, or 100KW),
many of the charging strategies begin delivering less energy than the offline
optimal.

  2. 2.

Our RTSC Algorithm with inaccurate departure times consistently beats out EDF
and LLF (which are given the exact departure times). This is likely due to the
fact that the RTSC algorithm makes use of a future model for arrivals that
have not yet shown up, while EDF and LLF are myopic strategies.

  3. 3.

As shown in Figure 2, the RTSC algorithm purchases cheaper energy from TOU
rates than the uncontrolled case. The uncontrolled case consistently purchases
energy at over $0.21 per KWh for all transformer capacities while the RTSC
algorithm remains closer to the offline optimal cost per KWh, below $0.195 per
KWh.

###  III-C Test Case 2: Profit Maximization with TOU Rates and Demand Charges

Figure 3: Total revenue, total electricity cost (from both TOU rates and
demand charges), electricity cost per KWh, demand charges, and total profit
for the uncontrolled, offline optimal, RTSCA with varying departure time
accuracies, least-laxity-first, and earliest-deadline-first strategies. Figure
4: Daily loads of the charging facility for various charging strategies.

In this section, we consider a facility manager that wants to maximize profit
while delivering adequate energy to each customer (i.e., this would be the
case of a for-profit third-party parking structure equipped with chargers and
wants to minimize TOU electricity costs and demand charges). The following
objective function was used in the Real-Time Smart Charging Algorithm:

$\displaystyle U_{2}(e)=$ (15) $\displaystyle
10\Big{(}u_{PM}(e)+u_{DC}(e)\Big{)}+u_{OU}(e)+10^{-9}\Big{(}u_{LF}(e)+u_{ES}(e)\Big{)}$

In this objective function, the smart charging strategy prioritizes profit
maximization and cost minimization from both TOU rates and demand charges.
Load flattening and energy sharing are also included to promote a desirable
energy distribution amongst EVs and a flat demand for the utility.

As in the previous test case, we vary the accuracy of the departure time
estimates that are input to our RTSC-A. We vary the standard deviation of the
normal distribution to model EV owners’ inaccurate departure time estimates.
Furthermore, in this test case, we do not vary the transformer constraint, it
is set to 160KW for all tests. Additionally, we assume energy is sold to the
EV users at $0.30 per kWh.

Figure 3 presents results for total revenue, total electricity cost (from both
TOU rates and demand charges), electricity cost per KWh, demand charges, and
total profit for the uncontrolled, offline optimal, RTSC-A with varying
departure time accuracies, least-laxity-first, and earliest-deadline-first
strategies. Figure 4 presents the daily load profile of the charging facility
for various charging strategies. The top plot includes a comparison of LLF and
EDF with the uncontrolled and optimal load. The bottom plot shows the real-
time smart charging algorithm’s daily load compared to the offline optimal and
uncontrolled.

Test Case 2 Key Results:

  1. 1.

As shown in Figure 3, total revenue, total electricity cost (from TOU rates
and demand charges), and electricity cost per KWh, are similar across all the
charging strategies, with the offline optimal performing the best and the
RTSC-A with perfect departure time information performing the second best.

  2. 2.

However, in plot 4 of Figure 3, we see that the demand charges from the
uncontrolled case, EDF, and LLF are significantly more than the offline
optimal and RTSC-A.

  3. 3.

Due to the offline solution’s and RTSC-A’s ability to optimize for demand
charges, the daily net profit (plot 5 in Fig. 3) for these strategies
significantly outperforms the uncontrolled case as well as EDF and LLF. Even
the profit of RTSC-A with bad departure time estimates (RTSC-A with stddev=20)
outperforms LLF and EDF with perfect departure time estimates.

  4. 4.

RTSC-A’s average daily profit is $\sim$$40, LLF’s average daily profit is
$\sim$$23, EDF’s average daily profit is $\sim$$19, the offline optimal
average daily profit is $\sim$$52, and the uncontrolled average daily profit
is $\sim$$3.

  5. 5.

As shown in the top plot of Figure 4, EDF and LLF load profiles look similar
to the uncontrolled profile and reach the coupling constraint of 160KW in the
mid-morning. However, in the bottom plot of Figure 4, the RTSC algorithm is
able to flatten the daily profile to mimic the offline optimal, which is a
perfectly flat profile, thus significantly reducing demand charges.

##  IV Conclusion

In this paper we presented a customizable online optimization framework for
real-time EV smart charging to be readily implemented at real large-scale
charging facilities. The smart charging strategy is readily deployable and
customizable for a wide-array of facilities, infrastructure, objectives, and
constraints. The online optimization framework can be easily modified to
operate with or without user input for energy requests and/or departure time
estimates. Our online optimization framework outperforms other real-time
strategies (including first-come-first-serve, least-laxity-first, earliest-
deadline-first, etc.) in multiple real-world test cases using real charging
session data from SLAC and Google campuses in the Bay Area even with poor
accuracy on users’ departure time predictions.

Acknowledgment: This work was funded by the California Energy Commission under
grant EPC-17-020. SLAC National Accelerator Laboratory is operated for the US
Department of Energy by Stanford University under Contract DE-AC02-76SF00515.
Thank you to Rolf Schreiber from Google for providing data.

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