Effects of number of electric vehicles charging/discharging on total electricity costs in commercial buildings with time-of-use energy and demand charges

Abstract

Electric vehicle (EV) penetration has been increasing in the modern electricity grid and has been complemented by the growth of EV charging infrastructure. This paper addresses the gap in the literature on the EV effects of total electricity costs in commercial buildings by incorporating V0G, V1G, and V2B charging. The electricity costs are minimized in 14 commercial buildings with real load profiles, demand and energy charges. The scientific contributions of this study are the incorporation of demand charges, quantification of EV and smart charging electricity costs and benefits using several representative long-term datasets, and the derivation of approximate equations that simplify the estimation of EV economic impacts. Our analysis is primarily based on an idealized uniform EV commuter fleet case study. The V1G and V2B charging electricity costs as a function of the number of EVs initially diverge with increasing charging demand and then become parallel to one another with the V2B electricity costs being lower than V1G costs. A longer EV layover time leads to higher numbers of V2B charging stations that can be installed such that original (pre-EV) electricity costs are not exceeded, as compared to a shorter layover time. Sensitivity analyses based on changing the final SOC of EVs between 90% to 80% and initial SOC between 50 to 40% (thereby keeping charging energy demand constant) show that the total electricity costs are the same for V0G and V1G charging, while for V2B charging the total electricity costs decrease as final SOC decreases.

Full text

1
Effects of number of electric vehicles charging/discharging on total electricity
1
costs in commercial buildings with time-of-use energy and demand charges
2
3
Avik Ghosh*, Mónica Zamora Zapata, Sushil Silwal, Adil Khurram, Jan Kleissl
4
5
Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA
6
92093-0411, United States
7
8
*Corresponding author
9
Email address: avghosh@eng.ucsd.edu
10
11
Abstract
12
Electric vehicle (EV) penetration has been increasing in the modern electricity grid and has been
13
complemented by the growth of EV charging infrastructure. This paper addresses the gap in the
14
literature on the EV effects of total electricity costs in commercial buildings by incorporating V0G,
15
V1G, and V2B charging. The electricity costs are minimized in 14 commercial buildings with real
16
load profiles, demand and energy charges. The scientific contributions of this study are the
17
incorporation of demand charges, quantification of EV and smart charging electricity costs and
18
benefits using several representative long-term datasets, and the derivation of approximate
19
equations that simplify the estimation of EV economic impacts. Our analysis is primarily based on
20
an idealized uniform EV commuter fleet case study. The V1G and V2B charging electricity costs
21
as a function of the number of EVs initially diverge with increasing charging demand and then
22
become parallel to one another with the V2B electricity costs being lower than V1G costs. A longer
23
EV layover time leads to higher numbers of V2B charging stations that can be installed such that
24
original (pre-EV) electricity costs are not exceeded, as compared to a shorter layover time.
25
Sensitivity analyses based on changing the final SOC of EVs between 90% to 80% and initial SOC
26
between 50 to 40% (thereby keeping charging energy demand constant) show that the total
27
electricity costs are the same for V0G and V1G charging, while for V2B charging the total
28
electricity costs decrease as final SOC decreases.
29
30
Keywords: Demand charge; Smart charging; Electric vehicles; Buildings; Electricity cost
31
minimization; Optimization
32
33
Nomenclature
BC
EV battery capacity (kWh)
𝑅
rate of energy charges ($/kWh) / rate of
demand charges ($/kW)
BE
EV battery energy (kWh)
RT
regularization term
CD
EV charging demand (kWh)
SOC
EV state of charge
𝑑
date index of month
𝑡
time (hours)
EC
energy charges ($)
∆𝑡
time resolution (hours)

2
ED
energy demand (kWh)
𝑤
weight
EV
electric vehicle / electric vehicle charging
rate (kW)
𝑤𝑓
weighing factor for regularization term
𝑗
EV index
Subscripts
𝐿
original (pre-EV) building load (kW)
𝑐𝑜𝑟
corrected
𝑚
number of days in a month
day
daily
𝑛
total number of EVs
end
end of simulation time
NC
non-coincident
𝑓
final
NCDC
non-coincident demand charge ($)
𝑖
initial
NCDP
non-coincident demand peak (kW)
𝑜𝑓𝑓
off-peak layover period
NL
optimized net load of buildings (kW)
𝑜𝑛
on-peak layover period
OC
other charges ($)
𝑜𝑝𝑡
optimum
OPDC
on-peak period demand charge ($)
𝑜𝑟𝑔
original
OPDP
on-peak period demand peak (kW)
𝑡ℎ𝑟
threshold
PP
on-peak period
34
1. Introduction
35
36
1.1 Motivation
37
38
The use of electric vehicles (EVs) has significantly increased in the past decade and is
39
projected to increase even more in the coming decade. The push towards the increasing market
40
penetration of EVs has also been complemented by the strong growth of EV charging
41
infrastructure along interstate highways, at workplaces, and at public parking lots 1. There are three
42
popular types of EV charging: V0G (“dumb” charging at constant full power from when the
43
vehicles are plugged in until they are unplugged or full, whichever occurs earlier), V1G
44
(unidirectional, grid-to-vehicle variable smart charging) and V2G (bidirectional, grid-to-vehicle
45
and vehicle-to-grid variable smart charging). V2B (bidirectional, grid-to-vehicle and vehicle-to-
46

3
building variable smart charging) is a variant of V2G, where the EVs, instead of feeding back
47
energy directly to the grid, reduce the building’s net load peak (grid import). Smart charging
48
optimally charges and discharges (in case of V2G/V2B) the EVs to provide economic benefit to
49
EV owners, microgrid/EV charging station operators, and/or grid operators 2.
50
1.2 Literature Review
51
52
V2G chargers are gaining importance and making a stronger business case because of value
53
streams associated with operational flexibility as compared to V1G chargers 3. While the EV
54
charging literature is vast, the following literature in this paragraph only discusses studies that
55
incorporate V2G charging. Alusio et al. 2 described an optimal day ahead operating strategy for
56
microgrids with V2G EVs to minimize operating costs based on forecasted load demand and
57
renewable generation. The authors used time-of-use energy rates for the analysis and demonstrated
58
the optimization algorithm on a test microgrid. In Ref. 4, the authors carried out a techno-economic
59
analysis of V2G in the Indonesian power grid considering 3 different tariffs: i) a fixed tariff which
60
provided flat charging and discharging energy rates to EV owners, ii) a “natural” tariff which
61
provided energy rates based on the electric generating resources, for example, geothermal, hydro,
62
coal etc., iii) a demand response tariff which provided energy rates and incentives depending upon
63
the amount of electricity supply and demand, i.e. the demand response tariff will increase when
64
demand is high. The authors reported the environmental and economic advantages of incorporating
65
V2G charging for both EV owners and utility companies. The authors in Ref. 5 presented an
66
adjustable robust optimization scheduling model for a microgrid with renewable energy
67
generation, V2G EVs, and time-of-use energy rates. Results showed improvements in the
68
operational stability and economic performance of the microgrid, such as increasing the wind
69
energy utilization, reducing peak-loads, and increasing minimum loads. Kiaee et al. 6 developed a
70

4
V2G simulator to undertake power flow analyses to compare the total charging cost of EVs with
71
and without V2G technology within a power system consisting of 5,000 EVs using time-of-use
72
energy rates. The control algorithm took advantage of arbitrage, while considering the EV
73
capacity, the SOC, vehicle movement within the system and the requirements of drivers and power
74
system operators. V2G charging achieved a 13.6% reduction in charging cost. A review paper 7
75
sheds light on various optimization algorithms used for EV scheduling for grid integration.
76
Schuller et al. 8 compared the weekly charging cost of EVs owned by different socio-
77
economic groups by implementing V0G, V1G, and V2G charging strategies for residential
78
charging with a time-of-use energy rate. Employees and retirees are the two socio-economic
79
groups with the greatest contrast in driving behavior, driving 228 km and 119 km on average per
80
week, respectively. For employees, weekly average costs are 32% and 45% less for V1G and V2G
81
charging respectively as compared to V0G. For retirees, V1G and V2G charging saved about 51%
82
and 62% respectively as compared to V0G. Datta et al. 9 proposed a charging/discharging strategy
83
according to the price of electricity during off and on peak hours (i.e., time-of-use energy rates),
84
and illustrated that the monthly cost savings associated with V2B is 11.6% as compared to V1G.
85
Zhou et al. 10 optimized the provision of ancillary services to bring economic benefits to V2G EV
86
owners in China under time-of-use energy rates. Refs. 11,12 further shed light on the capability of
87
V2G EVs to shift charging from peak to off peak periods depending on time of use energy rates
88
and demand response programs.
89
None of the studies discussed in the above literature review considered the effect of
90
demand charges while optimizing V2G/V2B EV charge scheduling, even though demand charges
91
are a significant portion (30 - 70%) of the electricity bill for commercial and industrial customers
92
13. Very few studies directly deal with demand charges for EV charging 14. Zhang et al. 14 proposed
93

5
a V1G charging scheme for demand charge reductions, with the EV charging stations installed at
94
four locations: large and small retail, recreation area, and workplace. The authors used real world
95
Level 2 EV charging data for the analyses, where for the large retail (which is least flexible due to
96
shorter charging events and higher EV mobility), 80% of the charging events were shorter than 3
97
hours. The proposed V1G smart charging scheme reduced monthly demand charges for large retail
98
by 20-35% as compared to no-control charging for 30% EV demand penetration level, which is
99
the percentage of EV energy demand with respect to the original (pre-EV) energy demand of the
100
building. Refs. 15 and 16 considered demand charges for electric bus V1G fast charging stations but
101
charging schedules of public buses differ from passenger EVs 15 with bus driving schedules being
102
longer and rigid and energy requirements larger 15, and thus public bus charging is a unique
103
problem 16. Additionally, to the best of the authors’ knowledge, only one previous work 8 presented
104
a direct economic performance comparison of both V2G and V1G charging. Also, no previous
105
work incorporated demand charges for commuter V2G/V2B EVs which the present work
106
considers.
107
Although V2G/V2B scheduling strategies for economic cost optimization for time-of-use
108
energy rates have been investigated previously, there are very few works on the long-term
109
economic impact of smart charging. Most of the literature present case studies over a single day,
110
week, or month to prove the efficacy of the schemes conceptually, as summarized in Table 1.
111
However, at least year-long studies are needed to capture seasonal variations in building loads, EV
112
demand, and tariffs.
113
Table 1. Simulation duration of other studies in literature
114
Work
Duration
Alusio et al. 2
1 day
Shi et al. 5
1 day

6
Zhou et al. 10
1 day
Onishi et al. 11
1 day
Zhang et al. 14
1 day
Kiaee et al. 6
5 weekdays
Schuller et al. 8
7 days/1 week
Datta et al. 9
30 days/1 month
Huda et al. 4
1 year
Present Work
1 year
Li et al. 12
10 years
115
1.3 Present work and its objective
116
117
In the present work, we analyze workplace V2B, V1G, and V0G charging with real load
118
profiles from 14 commercial buildings, with 100% EV charging/discharging efficiency. The
119
objective function minimizes the building electricity bill consisting of time-of-use energy and
120
demand charges. One objective of this study is to report the optimal number of V2B charging
121
stations to be installed at a particular building such that the original (pre-EV) operating electricity
122
bill is not exceeded. The study also compares the electricity costs for 14 buildings under V0G,
123
V1G and V2B charging strategies. Sensitivity analyses elucidate the effects of varying arrival and
124
final state of charges (SOCs) on the total electricity bill. EV charging stations at commercial
125
buildings are generally added “behind the meter” such that the energy consumed is lumped with
126
the building energy consumption and adds to the commercial building owners’ electricity costs.
127
Commercial building owners typically either provide free charging to their employees or they
128
contract with a third-party operator who collects charging fees from the EV owners. Charging fees
129
can be structured such that charging (and discharging) flexibility is rewarded. Therefore, while the
130

7
total electricity costs analyzed in this paper only directly apply to commercial building owners,
131
some of the savings can be passed on to EV owners.
132
1.4 Novelty of the present work
133
134
The novelties of the present work are as follows:
135
• Realistic demand charges, which vary according to the time of the day and
136
summer/winter season have been considered in the electricity bill. Ref. 14 considers
137
demand charges whose rate varies according to the tier of demand (first 35 kW costs
138
$0/kW, next 115 kW costs $5.72/kW and the remaining costs $10.97/kW), but not
139
according to time-of-day or season-wise. Ref. 14 also only considers V1G smart
140
charging (no V2G/V2B analysis), and only for one EV demand penetration level (refer
141
to Section 1.2).
142
• Two case studies are presented to quantify the electricity bill savings obtained by using
143
V2G/V2B over V1G/V0G charging at commercial buildings: (A) A year-long case
144
study, with variable number of EVs, using two daily EV layover intervals that are
145
realistic, but uniform across the fleet; (B) A 5 day case study which is representative
146
of a monthly analysis, based on historical EV charging data. Only Refs. 4 and 12
147
present studies with similar (or longer) time duration. Ref. 4 presents a year-long
148
analysis of only V2G EV charging to show its effect on electricity cost reduction, but
149
for a predefined fixed number (1 million) of V2G EVs. Ref. 12 presents a ten year
150
analysis but also only considering V2G EVs. The motivation of Ref. 12 is also different,
151
where V2G user and power grid company economic benefits (cost savings) are
152
analyzed solely as a function of discharging power of the V2G EVs at the peaks (peak
153
shaving load). Our study evaluates the electricity bill savings for commercial buildings
154

8
incorporating V2B charging as a function of number of EV charging stations, and
155
additionally compares the V2B electricity costs to V1G and V0G charging electricity
156
costs.
157
• The year-long analysis predicts the optimum number of V2B charging stations to be
158
installed at a building, so as not to exceed the original (pre-EV) electricity bill.
159
• We derived and validated approximate analytical expressions for the total electricity
160
costs as a function of EV charging demand. This is the first time that such equations
161
have been derived. The equations allow for quick estimation of EV benefits worldwide.
162
The rest of the paper is organized as follows: Section 2 presents the problem formulation
163
and discusses the optimization algorithm. Section 3 presents the results and discussion, and Section
164
4 presents the conclusions. Supplementary material is included at the end to present relevant
165
discussion and results that expand upon the results presented in Section 3 of the main text. Any
166
Section, Figure or Table referred to in this paper indicates to those in the main text unless
167
specifically mentioned. References to the Supplementary material are explicitly mentioned
168
wherever necessary.
169
2. Problem formulation and optimization algorithm
170
2.1 Overview of the fleet and charging scenarios
171
We aim to minimize the building electricity costs following the installation of a variable
172
number of EV charging stations. To obtain representative savings, the analysis covers EV charging
173
on all weekdays in 2019, while the weekend EV load is assumed to be zero. Weekends are
174
excluded from EV charging as smaller building loads and less workplace charging preclude
175
demand charge events, and time-of-use energy rate differences are smaller. Therefore, weekend
176
EV charging does not materially impact the annual utility bill savings. Two case studies (A) and
177

9
(B) are considered. Case study (A), presented in part in the main text, and in part in Sections 1.1
178
through 1.2 of the Supplementary material, consists of an idealized uniform commuter fleet, where
179
all EVs have the same battery, and arrive and depart daily at the same time, with the same initial
180
and final SOC, respectively. The assumption of EVs arriving and departing at the same time daily
181
is valid for certain type of buildings, such as hospitals and corporate buildings. Case study (A) is
182
carried out for 14 commercial buildings located on the University of California (UC) San Diego
183
campus, whose original load data can be found in Ref. 17. The buildings’ primary functions are
184
diverse and include classrooms, libraries, office spaces, and research laboratories. The load
185
characteristics of the buildings for the analysis period (year 2019), along with their floor areas and
186
year of construction are given in Table 2. Case study (B), presented completely in Section 3.5,
187
considers a realistic case using historical EV charging data for a parking structure with 16 EV
188
charging stations for 5 weekdays in February 2020, with the EV load being mapped to a building
189
having 0 original load (the EV load thus becomes the net load of the building). The historical EV
190
charging dataset contains the time of EV connection, disconnection and end of charging time, the
191
amount of energy charged, the port type (Level 2 or Direct Current Fast Charger), and the initial
192
and final SOC.
193
For V0G charging, the EVs charge at their maximum battery power, starting from the time
194
the EVs are plugged in until meeting the charging energy demand, without any regard for the
195
original building load. However, V1G and V2B EVs charge smartly to optimize the electricity
196
costs, with V2B EVs having the additional capability to discharge back to the grid. Case studies
197
(A) and (B) cover the application of the model for uniform EV fleet, and non-uniform realistic
198
scenario based on historical EV charging data respectively, showing the efficacy of the
199
optimization model in minimizing electricity costs for various scenarios.
200

10
Table 2. Mean original real load for all weekdays, mean of original monthly non-coincident
201
demand peak and on-peak period demand peak (see definitions in Section 2.2), floor areas,
202
number of floors, and year constructed of the buildings analyzed for the year 2019.
203
Building name
(Building number)
Mean original
real load (kW)
Mean original non-
coincident demand
peak (kW)
Mean original on-
peak period
demand peak (kW)
Building floor area
(ft2)
# of
floors
Year
Constructed
Mandeville Center
(I)
32.2
60.1
56.9
131,365
4
1974
Police Department
(II)
38.1
59.9
54.3
14,567
1
1991
Hopkins Parking
Structure (III)
57.6
99.4
78.6
446,095
7
2006
Rady (Wells Fargo)
Hall (IV)
60.3
103.1
98.8
93,440
4
2012
Pepper Canyon Hall
(V)
62.0
102.4
91.5
85,985
4
2004
Otterson Hall (VI)
90.9
133.6
131.6
104,363
4
2007
Music Center (VII)
91.9
137.5
132.1
91,957
4
2008
Robinson Hall - 3
buildings (VIII)
95.0
134.7
129.9
32,932 + 5,142 +
29,618 = 67,724
4, 1, 2
1990
East Campus Office
(IX)
118.3
156.4
146.4
77,164
3
2011
Center Hall (X)
122.8
194.4
186.2
83,288
4
1995
Student Services
Center (XI)
140.5
242.9
202.1
135,085
4
2007
Social Sciences
Building (XII)
146.5
200.0
184.5
84,386
5
1995
Galbraith Hall
(XIII)
196.0
307.4
301.7
127,979
4
1965

11
Geisel Library
(XIV)
532.0
649.2
644.0
416,509
10
1970
204
2.2 Objective function
205
The objective function to be minimized is the total electricity charges of the building plus
206
a regularization term. The objective function is
207
!"#$%!"#"
&
'
(
)*+,-.%$%#"
&
'
(
)/-,-.
01 1
&%&"
&
'
(
)*2'()
&
34'
(
)*+,-./0)
)*1 )
2*3
2*4
208
5'(6./+7
&
34'
(
.897
&
34'
(:, (1)
209
where
%!"#"
is the non-coincident demand charge rate,
*+,-
is the non-coincident demand peak
210
which is the maximum load demand from the grid at any 15 min interval of the month,
%$%#"
is
211
the on-peak demand charge rate,
/-,-
is the on-peak period demand peak which is the maximum
212
load demand from the grid at any 15 min interval between 16:00 and 21:00 hours of all days of the
213
month,
%&"
&
'
(
7
is the time-of-use energy charge rate,
*2'()
is the building optimized net load
214
demand from the grid,
3
is the index of the day of the month,
;
is the number of days of the
215
month,
'
is the time of the day in hours,
5'
is the time resolution which is chosen as 15 minutes
216
(0.25 hours), consistent with the real load input data from the buildings,
/+
is other charges
1
,
217
and
789
is a regularization term which guarantees a unique solution of Eq. (1). The first term in Eq.
218
(1) is the non-coincident demand charge, the second term is the on-peak period demand charge,
219
and the third term covers the off-peak and on-peak period energy costs over the entire month. The
220
third term in Eq. (1) shows that for each day, the energy costs are covered from
'< =
to
'<221
1
Other costs are the DWR Bond Charge ($0.00580
×
Total energy usage in a month), the City of San Diego Franchisee
fee ($0.0578
×
[
R!"#"
(
𝑡
)
×NCDP + R$%#"
(
𝑡
)
×OPDP + {
∑ ∑
(𝑅&"(𝑡) × NL'()
(
𝑑, 𝑡
)
)*+,-./0)
)*1 × ∆𝑡)}
2*3
2*4
]), the
DWR Bond franchisee fee (($0.0688
×
DWR Bond Charge), the CA State Surcharge (($0.00030
×
Total energy usage
in a month), and the CA State Regulatory charge ($0.00058
×
Total energy usage in a month).

12
>?7@A5'
.
'< =
corresponds to the time period from 00:00 to 00:15 hours, while
'< >?7@A5'
222
corresponds to the time period from 23:45 to 24:00 hours, thus covering the entire day. RT aims
223
to minimize the deviation of the optimized net load from the original load (which indirectly avoids
224
unnecessary charging/discharging cycles of the EV) as
897
&
34'
(
<BC)225
1 1 DE
*2'()
&
34'
(
AF'56
&
34'
(ED
)*+,-./0)
)*1
2*3
2*4
, where G
H
G is the 2-norm,
BC
is a weighting factor
226
which is set as 0.01, and
F'56
is the original baseline building load.
227
2.3 Constraints
228
In this Section, for simplicity,
3
is dropped from the variable argument, with only
'
being
229
retained, as the constraints are presented for one day. E.g.,
*2'()
&
34'
(is written as
*2'()
&
'
(. The
230
daily power balance for each building is formulated as
231
*2'()
&
'
(
<F'56
&
'
(
.7
1
IJ7
&
'
(
7*8
7*4
, (2)
232
where
K
is the number of EVs,
IJ7
is the jth electric vehicle charging rate where
L
is the EV index.
233
Power flow from the grid to the EV (charging) is considered positive.
234
The EV charging rate is constrained as
235
!"#IJ7MIJ7
&
'
(
M!NOIJ7
, (3)
236
where the maximum and minimum EV charging rate depends upon the charging technology used
237
(V0G/V1G/V2G/V2B). For V0G and V1G,
!"#IJ7<=
, whereas for V2G/V2B,
!"#IJ7<238
7A!NOIJ7H
239
The EV battery energy constraints are formulated as
240
!"#PI7MPI77
&
'
(
M!NOPI7
, (4)
241
where
7PI7
is the Battery Energy of the jth EV.
242
The minimum and maximum SOC of the battery are inputs, which in turn predefine the
243
minimum and maximum battery energy limits.
244

13
The initial battery energy of the EV at the time of connection is formulated as
245
PI77
Q
'< '9
7
R
<S/+9
77)P+7
, (5)
246
where
S/+9
7
is the initial state of charge of the jth EV,
7
'9
7
is the time the jth EV is connected to the
247
charging station,
TUV
stands for “initial”, and
P+7
is the battery capacity of the jth EV.
248
The battery energy variation with time is
249
PI77
&
'.5'
(
<PI77
&
'
(
.IJ7
&
'
(
7)5'
. (6)
250
The total energy demand of the jth EV (
I,7
) is known beforehand as we use perfect
251
forecasts. The final EV battery energy is constrained as
252
PI77
Q
'< ':
7
R
<PI77
Q
'< '9
7
R
.I,74
(7)
253
where
':
7
is the disconnection time of the jth EV, and
TCV
stands for “final”. Furthermore, the total
254
energy demand of the EV is formulated as
255
I,7<
Q
S/+:
7A7S/+9
7
R
)7P+7H
(8)
256
In case study (B), if Eq. (8), gives an infeasible energy demand (
I,7
greater than the
257
charging ability of the battery given the layover time), then the energy demand is corrected (
I,;'5
7(
258
as
259
I,;'5
7<!"#
WQ
':
7A'9
7
R
)!NOIJ74I,7
:, (9)
260
where Q
':
7A'9
7
R
7
is the layover time.
261
Charging/discharging takes place within the layover period only and is constrained as
262
IJ7
&
'
(
<=777777777777777777777777777777777777= M' X'9
7
, (10)
263
IJ7
&
'
(
<=777777777777777777777777777777777777':
7X' M'<=>
7
, (11)
264
where
'< =
and
'< '<=>
7
correspond to the times at the start and end of the simulation.
265

14
2.4 Optimization software
266
The optimization is carried out in CVX, a package for specifying and solving convex
267
programs 18,19 in the MATLAB environment. A flowchart for the optimization algorithm is shown
268
in Fig. 1.
269
270
Figure 1. Flow chart of the optimization algorithm
271
2.5 Input Data for Case study (A) and (B)
272

15
Case study (A) is carried out for 14 metered UC San Diego buildings without EVs. The
273
Case study (A) is further subdivided into two layover periods, a) 07:45 hours to 16:45 hours, which
274
is representative of a typical office employee layover consisting of 8 hours of work-time, a 30 min
275
lunch break and 30 mins for travel from the parking lot to the office and vice versa; and b) 06:30
276
hours to 19:30 hours, which is representative of a typical medical worker shift, consisting of 12
277
hours of work-time, a 30 min lunch break and 30 mins for travel from the parking lot to the medical
278
center and vice versa. For Case study (A), the input variables that stay constant throughout the
279
analysis are as follows. The battery capacity of all EVs (for j =1 through n) is chosen as
P+7<7
60
280
kWh which is representative of a typical EV 20. The minimum and maximum SOC of the EVs are
281
fixed at 20 and 90% respectively, to limit battery degradation during extreme charging states. The
282
maximum charging rate of the EVs are
!NOIJ7<
6.6 kW, which is a typical value for a Level 2
283
charger, which is the most prevalent type of EV charger in the United States 21. For Case study
284
(B), the minimum and maximum SOC of the EVs are fixed at 0 and 100% respectively, with
285
variable EV battery capacity and initial & final SOCs per the real charging dataset. Furthermore,
286
in case study (B), the maximum charging and discharging rate of the EVs depends on the type of
287
EV charging port they are plugged into (Table 7). Case Study (B) uses real data from ChargePoint
288
at UC San Diego, where the initial and final SOC is given for a subset of charging events. For
289
these subsets of EV charging events, initial and final SOC varied between 0-100%. Thus, to impute
290
the missing data consistent with the original data, the SOC range for Case study (B) is fixed
291
between 0-100%.
292
The break-down of the electricity bill components levied by San Diego Gas & Electric are
293
shown in Table 3. The non-coincident demand charge rates are constant throughout the year and
294
are higher than the on-peak period demand charge rates in winter, but lower than the on-peak
295

16
period demand charge rates in summer. The on-peak period energy charge rates are higher than
296
the off-peak period energy charge rates throughout the year.
297
Table 3. Breakdown of electricity bill components - SDG&E AL-TOU tariff. The on-peak
298
period is 16:00-21:00 hours, with the remaining hours being off-peak period hours. June 1
299
to October 31 are summer months with the rest of the year being winter.
300
Cost Component
Symbol
Value
Non-coincident demand charge rate (both summer and
winter)
𝑅!"#"
(
𝑡
)
$24.48/kW
On-peak period demand charge rate (summer)
𝑅$%#"(𝑡)
$28.92/kW
On-peak period demand charge rate (winter)
$19.23/kW
Off-peak period energy charge rate (summer)
𝑅&"
(
𝑡
)
$0.10679/kWh
Off-peak period energy charge rate (winter)
$0.09506/kWh
On-peak period energy charge rate (summer)
$0.12628/kWh
On-peak period energy charge rate (winter)
$0.10626/kWh
301
2.6 Input data for sensitivity analysis
302
A sensitivity analysis based on case study (A) is carried out to study the effect of varying
303
the initial and final SOC of the EVs in Section 3.4. Initial and final SOC combinations of 40-80%,
304
45-85% and 50-90% are analyzed to study the effect of changing the initial and final SOCs while
305
keeping the energy demand of the EVs constant. Energy demand sensitivity analyses are also
306
carried out for initial and final SOC combinations of 50-85% and 50-80% to elucidate the effects
307
of changing the final SOC while keeping the initial SOC constant.
308
3. Results and discussion
309
3.1 Idealized uniform commuter EV fleet case study
310
The results for building V (randomly selected) for initial and final EV SOC of 50% and
311
90% respectively for Jan (January) 2019 and the entire year 2019 are presented in Section 3.2 of
312

17
the main text and Section 1.2 of the Supplementary material with graphics and summarized in
313
Table 4. The
P+7<7
60 kWh, and the initial and final SOC of 50 and 90% respectively correspond
314
to a daily charging demand of 24 kWh per EV. Thus, the charging demand is increased in multiples
315
of 24 kWh with each additional charging station / EV (see legend of figures in Section 3.2). The
316
analyses are carried out up to 432 kWh charging demand (18 EV charging stations) as the changes
317
in electricity costs per EV thereafter become independent of charging demand. The layover periods
318
shown in the graphical analysis are 06:30 hours to 19:30 hours (Section 3.2) and 07:45 hours to
319
16:45 hours (Section 1.2 of the Supplementary material).
320
Figure 2 shows the original (pre-EV) load for building V for Jan 2019. The electricity load
321
is low on holidays (Jan 1) and weekends (Jan 5, 6, 12, 13, 19, 20, 26, 27) when the building
322
occupancy is low. The original non-coincident (NC) and on-peak period (PP) peak occur on Jan
323
31 at 14:00 hours at 109.0 kW and Jan 16 at 16:00 hours at 96.5 kW, respectively.
324

18
325
Figure 2. Original building V Load for Jan 2019
326
Table 4 shows the NC and PP demand peaks for Jan 2019 for building V for selected EV
327
charging demand scenarios for both layover periods.
328
Table 4. Summary of the NC and PP demand peaks for all charging strategies for Jan 2019
329
for building V. The original NC and PP demand peaks are 109.0 and 96.5 kW respectively.
330
The peak values (with EV charging) which are larger / smaller than the original are marked
331
in red / green font.
332
Daily EV
charging
demand
Layover 06:30-19:30 hours
Layover 07:45-16:45 hours
NC demand peak
(kW)
PP demand peak
(kW)
NC demand peak
(kW)
PP demand peak
(kW)

19
(kWh) (#
of EVs/
charging
stations)
V0G
V1G
V2B
V0G
V1G
V2B
V0G
V1G
V2B
V0G
V1G
V2B
24 (1)
110.6
109.0
102.4
96.5
96.5
89.9
111.0
109.0
102.4
96.5
96.5
91.0
48 (2)
117.2
109.0
99.5
96.5
96.5
83.5
117.6
109.0
102.6
96.5
96.5
91.0
72 (3)
123.8
109.0
101.5
96.5
96.5
82.4
124.2
109.0
105.0
96.5
96.5
91.0
96 (4)
130.4
109.0
103.1
96.5
96.5
82.4
130.8
109.0
107.6
96.5
96.5
91.0
120 (5)
137.0
109.0
105.0
96.5
96.5
82.4
137.4
109.8
110.3
96.5
96.5
91.0
144 (6)
143.6
109.0
107.1
96.5
96.5
82.4
144.0
112.7
113.2
96.5
96.5
91.0
168 (7)
150.2
109.0
109.6
96.5
96.5
82.4
150.6
115.6
116.1
96.5
96.5
91.0
192 (8)
156.8
109.0
112.1
96.5
96.5
82.4
157.2
118.5
119.0
96.5
96.5
91.0
216 (9)
163.4
109.5
114.7
96.5
96.5
82.4
163.8
121.4
121.9
96.5
96.5
91.0
240 (10)
170.0
112.0
117.2
96.5
96.5
82.4
170.4
124.3
124.8
96.5
96.5
91.0
432 (18)
222.8
132.2
137.4
96.5
96.5
82.4
223.2
147.6
148.1
96.5
96.5
91.0
333
3.2 Layover 06:30 hours to 19:30 hours- medical worker shift
334
3.2.1 V0G charging
335
The V0G EVs start charging the moment they are plugged in (06:30 hours) at the highest
336
possible EV battery power rate (6.6 kW), resulting in charging terminating by 10:15 hours. The
337
highest original load in the 06:30-10:15 hours period occurs on Jan 22 at 09:30 hours and is 104.0
338
kW. Therefore, on Jan 22 the net load (with V0G EVs) at 09:30 hours for 24 kWh (1 EV) of
339
charging demand, which contributes 6.6 kW of charging load, becomes the V0G NC monthly
340

20
demand peak at 110.6 kW (see Table 4). The V0G monthly demand peak increases with further
341
increasing charging demand by 6.6 kW per EV. As all charging occurs before the on-peak period,
342
the PP demand peak remains the same as the original at 96.5 kW. Refer to Figure 1 of the
343
Supplementary material for a graphical representation.
344
3.2.2 V1G charging
345
V1G chargers cannot discharge back into the grid, and hence the optimized net load (with
346
EV charging) cannot be smaller than the original load. Figure 3(a) shows that on Jan 31, with up
347
to 192 kWh of charging demand, the NC demand peak remains the same as the original at 109.0
348
kW. Increasing the charging demand to 216 kWh increases the NC demand peak to 109.5 kW,
349
which exceeds the original NC demand peak. With the addition of more V1G EV charging demand
350
(above 216 kWh charging demand), the optimal NC peak demand increases by 2.5 kW per EV
351
because the increasing charging demand (of 24 kWh per EV) is uniformly spread out over the 9.5
352
hour off-peak layover period from 06:30-16:00 hours (see Section 3.2.4 for a detailed explanation).
353
Figure 3(b) shows that the PP demand peak remains the same as the original at 96.5 kW
354
for all charging demands. Because of the higher energy and demand charges applicable in the on-
355
peak period as compared to the off-peak period, all charging will take place in the off-peak layover
356
period before 16:00 hours if feasible. A complete charging before 16:00 hours occur on some days
357
(e.g. Figure 3(b) for 1 or 2 EVs) when accommodating all the charging demand within the off-
358
peak layover period does not lead to an increase of the NC demand peak beyond the original.
359
However, complete charging before 16:00 hours is not optimal on days when the original off-peak
360
load curve during the layover period cannot accommodate the charging demand without increasing
361
the NC demand peak. Therefore, charging during the off-peak layover period (from 06:30-16:00
362
hours) takes place until the optimized load becomes constant at the original NC demand peak. A
363

21
further increase in the charging demand results in EVs being charged during the on-peak layover
364
period (16:00-19:30 hours) until the optimized on-peak layover period load becomes constant at
365
the original PP demand peak. With further increasing the charging demand, charging occurs again
366
exclusively in the off-peak layover period (06:30-16:00 hours), leading to increasing NC demand
367
peak beyond the original demand peak (see Fig. 3(c)). Specifically, the additional charging demand
368
is spread out uniformly over the off-peak layover period. The reasoning for the optimized charging
369
strategy is given in Section 3.2.4.
2
370
Figure 3(c) shows the V1G timeseries analysis on Jan 22 to elucidate the optimized
371
charging strategy. For a charging demand of 24 kWh, the entire charging takes place in the off-
372
peak layover period. With further increasing charging demand (192 kWh), charging continues to
373
occur in the off-peak layover period until the off-peak layover period load becomes constant at the
374
original NC demand peak (109.0 kW), with the rest of the charging occurring in the on-peak period
375
without increasing the PP demand peak (96.5 kW). For a charging demand of 216 kWh, additional
376
charging occurs initially in the on-peak period until the on-peak layover period load becomes
377
constant at the PP demand peak, with the rest of the additional charging demand being uniformly
378
accommodated in the off-peak layover period increasing the NC demand peak to 109.5 kW. With
379
further increasing charging demand (above 216 kWh), additional charging occurs exclusively in
380
the off-peak layover period, with the additional charging demand spread out uniformly, leading to
381
an increase in the NC demand peak by 2.5 kW per EV (see Table 4). Comparing Figs. 3(a) and
382
3(c) show that for some charging demands, the optimized NC and PP demand peaks are reached
383
on multiple days.
384
2
Note that in rare cases the maximum EV charging rate can restrict the maximum charging such that charging deviates
slightly from the strategy described above. But most of the results relevant to this paper can be explained by the
optimized charging strategy discussed above.

22
385
(a)
386
387
(b)
388

23
389
(c)
390
Figure 3. V1G charging for the 06:30-19:30 hours layover: (a) NC demand peak for Jan 31
391
2019, when the original NC demand peak also occurs, (b) PP demand peak for Jan 16 2019,
392
when the original PP demand peak also occurs, and (c) NC and PP demand peak for Jan 22
393
2019, which provides the greatest limitation for accommodating PP EV charging. The
394
legend shows total daily EV charging demand and the number in brackets in the legend
395
correspond to the number of EVs/charging stations. The yellow shading denotes the off-
396
peak layover period, the red shading denotes the on-peak layover period, while the un-
397
shaded area denotes the non-layover period. The original NC and PP demand peaks are
398
109.0 and 96.5 kW, respectively.
399
400
3.2.3 V2B charging
401
Figure 4(a) shows that the V2B chargers can discharge and decrease the optimized net load
402
below the original load. For example, the NC demand peak decreases from 109.0 kW to 102.4 kW
403
and then to 99.5 kW as the charging demand increases from 0 kWh to 24 kWh and then to 48 kWh
404
respectively. This occurs because as the number of EVs increases, the total discharge power also
405
increases. However, from a charging demand of 72 kWh, we see a monotonous increase in the NC
406
demand peak, and starting at 168 kWh the optimized NC demand peak exceeds the original NC
407
demand peak. Above a charging demand of 168 kWh, the NC demand peak increases by 2.5 kW
408

24
per EV (see Table 4), as the additional charging demand (over 168 kWh) is spread out uniformly
409
over the entire off-peak layover period. The reasoning for this optimized V2B charging strategy is
410
elucidated in Section 3.2.4. The variation in the optimized net load around 07:00 hours for all
411
energy demands in Fig. 4(a) occurs due to the regularization term in the objective function that
412
penalizes the deviation from the original load curve. The optimized load is equal to the NC demand
413
peak after about 10:00 hours since no extra cost is incurred when the optimized load is equal to
414
the NC demand peak threshold. A detailed discussion is provided in Section 1.1.2 of the
415
Supplementary material.
416
Figure 4(b) shows the on-peak period on Jan 16 which is the day with the original PP peak.
417
With increasing charging demand from 24 kWh to 72 kWh, the PP demand peak decreases. The
418
increased discharging capacity with the addition of more EVs is responsible for the reduction of
419
the PP demand peak. With further increasing charging demand, the PP demand peak remains
420
constant at 82.4 kW. The NC and PP demand thresholds for Jan are decided by different days
421
depending on charging demand. Jan 16 decides the demand thresholds for 1 EV (for 24 kWh daily
422
charging demand). Then, Jan 22 (shown graphically in Fig. 2 of Supplementary material) decides
423
the demand thresholds for 2 or more EVs as shown by flat lines at 83.5 kW (2 EVs, 48 kWh) and
424
82.4 kW (3 or more EVs, 72 kWh or more).
425

25
426
(a)
427
428
(b)
429
Figure 4. V2B charging for the 06:30-19:30 hours layover: (a) NC demand peak for Jan 31,
430
2019, when the original NC demand peak also occurs, and (b) PP demand peak for Jan 16,
431
2019 when the original PP demand peak also occurs. The original NC and PP demand
432
peaks are 109.0 and 96.5 kW, respectively.
433
434
3.2.4 Effect of charging type, load shape and layover period on electricity costs
435
3.2.4.1 Cumulative results: 06:30-19:30 hours layover
436

26
Section 3.2.1 through 3.2.3 elucidate the effect of the charging demand (or number of
437
charging stations) on the NC and PP demand peaks for Jan 2019 for the layover period 06:30-
438
19:30 hours. In Section 3.2.4, we compare the performance between V0G, V1G and V2B charging
439
strategies in terms of total electricity costs for Jan and the entire year 2019 for the layover period
440
06:30-19:30 hours. We also derive general mathematical expressions for the slopes (once they
441
become constant) of the V0G, V1G and V2B total electricity charges versus daily energy demand
442
curves month-wise, daily charging demand when the V1G and V2B curves transition to constant
443
slope, and final offset between V1G and V2B total electricity charges. Although, we mostly
444
present results from building V in this paper, the mathematical expressions are applicable to all
445
the other buildings and for other layover periods.
446
Figures 5 shows that for both Jan (Fig. 5a) and the entire year 2019 (Fig. 5b), the total
447
electricity costs with V2B are lower than the original building costs for charging capacities up to
448
120 kWh (or 5 V2B charging stations), making 5 the optimal number of V2B charging station
449
installations for building V for the layover period 06:30-19:30 hours.
450
451
(a)
452

27
453
(b)
454
455
Figure 5. Total electricity charges versus total daily EV energy demand for (a) Jan 2019
456
and (b) the entire year 2019 for the layover period 06:30-19:30 hours at building V.
457
458
Figures 5 also shows that V0G charging incurs the highest electricity costs, followed by
459
V1G and V2B respectively. This is expected as V0G cannot time-shift load demand from the grid
460
and charges at the maximum charger power of 6.6 kW, while for V1G and V2B, charging is spread
461
out smartly to optimize electricity costs. V2B reduces the electricity costs compared to V1G
462
because the V2B discharging capability reduces the demand peak costs. The net summation of NC
463
and PP demand peak charges are less for V2B than V1G which results from a greater reduction in
464
PP demand peak charges compared to the increase in NC demand charges (Table 4). The net cost
465
savings as a result of shifting demand from the on-peak to off-peak layover period of V2G/V2B
466
EVs are demonstrated for a hypothetical case study in Section 1.3 of the Supplementary material.
467
Initially the V2B and V1G electricity costs diverge because with an increasing number of
468
EVs, the V2B EVs can discharge during the non-coincident and on-peak period peaks, while
469

28
charging at other times, which leads to reduced costs. However, after a certain energy demand,
470
Figs. 5(a) and 5(b) show that the V1G and V2B cost curves become parallel to each other.
471
For V1G, as described in Section 3.2.2, after both the off-peak and on-peak layover period
472
loads become constant (at their respective original peaks), additional charging demand is
473
accommodated in the off-peak layover period only. Accommodating the additional charging
474
demand exclusively in the off-peak layover period leads to an increase of the non-coincident
475
demand peak as,
5*+,-<0"#567
4?-.-@-)8
97
, where
5*+,-7
is the increase of the NC demand peak,
476
5+,>AB
is the daily increase in the charging demand and (
YZ7@7[7'9
7(
is the off-peak layover which
477
is 9.5 hours (06:30-16:00 hours) for the 06:30-19:30 hours layover. Accommodating the daily
478
increase in charging demand exclusively in the on-peak layover period would increase the on-peak
479
period demand peak as,
5/-,-<0"#567
):
9/4?-.7
, where
5/-,-7
is the increase of the PP demand peak
480
and
&':
7AYZ7@(7
is the on-peak layover which is 3.5 hours (16:00-19:30 hours) for the 06:30-19:30
481
hours layover. Therefore, after the net loads are flat, V1G charging only occurs in the off-peak
482
layover period if
5*+,-)%!"#"
&
'
(
7A5/-,-)%$%#"
&
'
(
7X=
, which is the case as
C;<=<
D
E
F
-
C>?=<
D
E
F
X483
4?-.-@-E@
A
EB
AG4?-.
for both summer and winter. Table 3 shows that the ratio of
%!"#"
&
'
( to
%$%#"
&
'
( is 1.27
484
for winter and 0.85 for summer. For the 06:30-19:30 hours layover, the ratio of off-peak (9.5 hours)
485
to on-peak (3.5 hours) layover duration is 2.7. Table 3 also shows that the PP energy charges are
486
higher than the off-peak period energy charges for both summer and winter. Thus, after the net
487
loads are flat, accommodating the additional charging demand uniformly in the off-peak layover
488
period is most economical from both the energy and demand charges point of view.
489

29
For V2B, with a small charging demand it is economical to discharge during the off and
490
on-peak period peaks, and charge at other times such that the off and on-peak layover period loads
491
become constant, since a constant net load by definition has the smallest peak. The divergence of
492
V2B and V1G electricity costs for a small number of EVs occurs as the V2B EVs – unlike V1G -
493
can discharge during the original off-peak and on-peak period peaks, reducing the NC and PP
494
demand peaks. With further increasing charging demand, once the off peak and on peak period
495
loads are constant, it is most economical to spread out the additional charging demand exclusively
496
over the off-peak layover period, keeping the PP load constant (as shown in Fig. 2 in
497
supplementary material above 168 kWh charging demand) for the same reason discussed above
498
for V1G charging. When additional charging demand is accommodated by charging in the off-
499
peak layover period only, V2B offers no further economic advantages over V1G. If the V2B EVs
500
were to discharge at a given time, the same amount of energy would have to be charged at another
501
time and therefore introduce a new peak. Thus, the V1G and V2B electricity costs become parallel
502
after a certain energy demand as the additional energy and demand cost per added vehicle is
503
identical. The trends of the total electricity charges versus the total daily EV energy demand curve
504
for electricity tariff structures other than those in this paper are similar to Fig. 5 as discussed in
505
Section 1.4 of the Supplementary material.
506
3.2.4.2 Final slope of total electricity charges versus daily EV charging demand curve
507
For V0G charging in Jan 2019 and daily charging/energy demand over 24 kWh (see Table
508
4), when the slope of the V0G total electricity charges versus charging demand curve becomes
509
constant (see Fig, 5(a)), with every 24 kWh of daily additional EV charging demand (
5+,>AB
), the
510
5*+,-
is 6.6 kW while the
5/-,-
is 0, which leads to an increase in the NCDC as
5*+,+<511
5*+,-)%!"#"
&
'
(, where
%!"#"
&
'
( is $24.48/kW. The total charging demand increase in the
512

30
month is
5+,HI=E. <5+,>AB )\]]^_N`a
, where
\]]^_N`a<>b
for Jan 2019. The entire
513
charging demand is added in the off-peak layover period which leads to increasing monthly energy
514
charges as
5I+HI=E. <75+,HI=E. )%&"
&
'
(, where
%&"
&
'
( is $0.09506/kWh. Due to the increase
515
in
*+,+
and energy charges, there is a corresponding increase in other charges as
5/+<516
$
=H==cd=.=H===b=.=H===cd.
&
=H=Zdd)=H==cd=
(e
)75+,HI=E. .=H=cfd)
&
5*+,+.517
5I+HI=E.
(.
518
For the V1G and V2B charging, when the final slopes of their total electricity charges
519
versus daily energy demand curves become constant for a month, further increasing daily charging
520
demand (
5+,>AB
) is accommodated and spread out uniformly over the off-peak layover period.
521
This leads to
5*+,-<0"#567
4?-.-@-)8
9
, while the equations governing
5*+,+
,
5+,HI=E.
,
5I+HI=E.
and
522
5/+
remain the same as those of V0G. The final slope of the V0G, V1G and V2B total electricity
523
charges versus energy daily demand curves, once they become constant for the month, is governed
524
by
525
Sghi]CDE
CFE
CGH <0!"#"J0&"IJKLMJ0$"
0"#567
, (12)
526
where the difference between the slopes of V0G and V1G/V2B, once they become constant, is
527
determined by
5*+,-
(and hence
5*+,+
), which are different for V0G and V1G/V2B charging.
528
3.2.4.3 Daily EV charging demand when the V1G and V2B total electricity charges versus daily
529
EV charging demand curve transitions to constant slope
530
The daily V1G charging demand above which the final slope of the total electricity charges
531
versus daily energy demand becomes constant for a month is approximated by calculating the V1G
532
threshold daily charging demand (
+,>ABKE.LKM4N(7
above which charging takes place in the off-peak
533
layover period only.
534

31
For any weekday of the month, for daily charging demands (
+,>AB(
for (and above) which
535
V1G charging takes place in the off-peak layover period only satisfies
536
I,'56
&
3
(
.+,>AB j7*+,-'56 )&YZ@A'9
7(./-,-'56 )
Q
':
7AYZ@
R, (13a)
537
where
*+,-'56
and
/-,-'56
are the original NCDP and OPDP, respectively. Furthermore,
538
I,'56
&
3
( is the original energy demand during the EV layover period on “
3
” day of the month,
539
formulated as
I,'56
&
3
(
<
1
&F'56
&
34'
(
)5'(
):
9
)8
9
.
540
The V1G threshold daily charging demand is calculated by using an equality operator in
541
Eq. (13a), for the day of the month when the original energy demand for the day during the layover
542
period is maximum, and is formulated as
543
+,>ABKE.LKM4N <*+,-'56 )
Q
YZ@A'9
7
R
./-,-'56 )
Q
':
7AYZk
R
A!NO7I,'56
, (13b)
544
where
!NO7I,'56
is the maximum of
I,'56
&
3
( of all weekdays of the month.
545
If there are no limitations on the optimized charging due to maximum power constraints
546
(as is the case for the 06:30-19:30 hours EV layover at building V, discussed in Section 3.2.2), Eq.
547
(13b) accurately predicts the daily V1G charging demand above which the final slope of the total
548
electricity charges versus daily energy demand becomes constant. Otherwise, Eq. (13b) yields a
549
lower bound.
550
Ideally, the V2B EVs would discharge at their maximum power back to the grid at the
551
original NC and PP demand peak times resulting in the off-peak and on-peak period loads
552
becoming constant at the reduced off-peak and on-peak demand peaks. After that, charging should
553
take place in the off-peak layover period only. The V2B threshold daily charging demand
554
(
+,>ABKE.LKM+O(
above which charging takes place in the off-peak layover period only is
555
approximated as
556

32
+,>ABKE.LKM+O <$*+,-'56 A!NOIJ7)le)
Q
YZ@A'9
7
R
.$/-,-'56 A!NOIJ7)le)
Q
':
7A557
YZ@
R
A7!NO7I,'56
, (14a)
558
where
l
is the number of EVs corresponding to
+,>ABKE.LKM+O
.
559
l< "#567NLMONCGH
"#PC
, (14b)
560
where
+,&M
is the daily charging demand of one EV.
561
Combining Eqs. (14a) and (14b), we get
562
+,>ABKE.LKM+O <!"#%QRSP
Q
4?./)8
9
R
J$%#%QRSP
Q
):
9/4?S
R
/HAT-&#QRS
4JI6TPC9U
V
FWMXY8
9
Z
<=PC -J-I6TPC9U
V
Y:
9XFWM
Z
<=PC
7H7
(14c)
563
+,>ABKE.LKM+O
is a lower bound for the daily V2B charging demand above which the final
564
slope of the total electricity charges versus daily energy demand becomes constant. This is because
565
V2B EVs do not discharge at the maximum power at the original NC and PP demand peak times
566
as Eq. (14c) does not take into account if the EV charging demand is met or not at the time of the
567
EV departure.
568
+,>ABKE.LKM+O M+,>ABKE.LKM4N
because of V2B EV’s ability to discharge (V1G is the
569
limiting worst case of V2B). Thus, the threshold daily charging demand above which charging
570
takes place in the off-peak layover period only for both V1G and V2B is decided by
571
+,>ABKE.LKM4N7
calculated from Eq. (13b).
572
3.2.4.4 Final monthly offset between the V1G and V2B total electricity charges
573
The final monthly offset between V1G and V2B (the difference between the V1G and V2B
574
total electricity charges) once the final slopes of both V1G and V2B total electricity charges versus
575
daily energy demand curves become constant can be approximated for any
+,>AB j+,>ABKE.LKM4N
.
576

33
Choosing a
+,>AB
corresponding to
l
number of EVs where
+,>AB j+,>ABKE.LKM4N
, the final
577
monthly offset between V1G and V2B is
578
/mma]n<%!"#"
&
'
(
)&*+,-M4N A*+,-M+O(.%$%#"
&
'
(
)&/-,-M4N A/-,-M+O(.579
o
1
&
U<<V>ABW I+>ABKM4N AI+>ABKM+O(6.&/+M4N A/+M+O(
, (15)
580
where the energy charges (
I+
) and the
/+
are calculated for the EV layover period times on
581
weekdays only. Outside the EV layover times, the electricity charges for V1G and V2B are
582
identical and equal to the original electricity charges.
583
For V1G charging, for the
+,>AB
above which charging takes place in the off-peak layover
584
period only,
/-,-M4N
is
585
/-,-M4N </-,-ILX
. (16a)
586
*+,-M4N
is calculated based on the day of the month when the original energy demand
587
during the layover period is maximum, and is formulated as
588
*+,-M4N <
Y
HAT-&#QRSJ"#567/$%#%CFEP
Q
):
9/4?.
RZ
Q
4?-.-@-)8
9
R (16b)
589
I+>ABKM4N <I+>ABKM4N[I\\ .I+>ABKM4NKI=
, (16c)
590
where
I+>ABKM4N
,
I+>ABKI\\KM4N
, and
I+>ABKI=KM4N
are the daily V1G total, off-peak, and on-peak
591
layover energy charges, respectively. For one weekday,
I+>ABKI\\KM4N
and
I+>ABKI=KM4N
is
592
approximated as
593
I+>ABKI\\KM4N <
1
!"#7$&F'56
&
'
(
.!NOIJ7)l(4*+,-M4Ne)%&"
&
'
(
)5'
4?-.
)8
9
. (16d)
594
I+>ABKI=KM4N <o&
1
F'56
&
'
(
(
):
9
)8
97."#567
0) A
1
!"#7$&F'56
&
'
(
.!NOIJ7)l(4*+,-M4Ne6
4?-.
)8
9)595
%&"
&
'
(
)5'H
(16e)
596

34
For V2B charging, on the day which determines the
/-,-M+O
, the EVs charge to their
597
maximum SOC during the off-peak layover to have maximum discharging capability during the
598
on-peak layover. The on-peak layover energy demand (
I,'8(
on the day which determines the
599
/-,-M+O
is formulated as
600
I,'8 <oPI77
Q
'< ':
7
R
A!NOPI76)l7H
(17a)
601
The
/-,-M+O
is calculated based on the day of the month when the original energy demand
602
during the on-peak layover period is maximum. Let
I,'56K'8
&
3
(
<
1
&F'56
&
34'
(
)5'(
):
9
4?-.
be the
603
original energy demand during the on-peak EV layover period on “
3
” day of the month and
604
!NO7I,'56K'8
be the maximum
I,'56K'8
&
3
( of all weekdays of the month, then the
/-,-M+O
is
605
formulated as
606
/-,-M+O <7
]
HAT-&#QRSNQ[J-&#Q[
^
D):
9/4?-.F
. (17b)
607
*+,-M+O
is calculated based on the day of the month when the original energy demand
608
during the layover period is maximum, and is formulated as
609
*+,-M+O <
Y
HAT-&#QRSJ"#567/$%#%CGHP
Q
):
9/4?.
RZ
Q
4?-.-@-)8
9
R. (17c)
610
The energy charges for V2B are formulated similarly to Eq. (16c), (16d) and (16e), with
611
“V1G” subscripts being replaced by “V2B”.
612
3.2.4.5 Implementation of the mathematical approximations for Jan 2019
613
Table 5. Comparison between optimization and analytical results for Jan 2019 for the 06:30-
614
19:30 and 07:45-16:45 hours layover periods.
615
Metric
Symbol
Layover 06:30-19:30 hours
Layover 07:45-16:45 hours
Optimization
Analytical
Optimization
Analytical
Final V0G slope ($/kWh/day)
Slope!"#
9.6
9.6
9.6
9.6

35
Final V1G slope ($/kWh/day)
Slope!$#
5.2
5.2
5.6
5.6
Final V2B slope ($/kWh/day)
Slope!%&
5.2
5.2
5.6
5.6
V1G threshold daily charging
demand (kWh)
CD'()*+,-*!$#
216
211
144
114
V2B threshold daily charging
demand (kWh)
CD'()*+,-*!%&
168
46
144
33
Final monthly offset ($) between
V1G and V2B
156.4
164.6
97.9
99.0
Table 5 shows a comparison between the optimization and analytically derived (Eqs. 12
616
through 17) V0G, V1G and V2B metrics for the 06:30-19:30 hours layover in Jan 2019. The final
617
V0G, V1G and V2B slopes are predicted without error by the analytical method (Eq. (12)), because
618
charging takes place exactly according to the strategy described in Section 3.2.4.1. The7
619
+,>ABKE.LKM4N
7is predicted accurately analytically, and the difference between the optimization and
620
analytical values occurs primarily because we increase the daily charging demand in multiples of
621
24 kWh for the optimization (see discussion of Fig. 3(c), where increasing the
+,>AB
from 192 to
622
216 kWh changes the off-peak layover period load from 109.0 to 109.5 kW and makes the on-
623
peak period layover load constant at 96.5 kW. If the
+,>AB
were 211 kWh, both the off-peak and
624
on-peak period layover loads would have been constant at 109.0 and 96.5 kW respectively, after
625
which the excess charging demand is accommodated uniformly in the off-peak layover period).
626
+,>ABKE.LKM+O
7is underpredicted by the analytical method and gives only a lower bound of the actual
627
daily threshold charging demand.
+,>ABKE.LKM+O
is underpredicted because according to Eq. (14a)
628
through (14c) the V2B EVs are assumed to discharge at their maximum capacity during the
629
original NC and PP demand peaks, resulting in the off-peak and on-peak loads becoming constant
630
at their reduced peaks, without regard for the EV final SOC constraints. The
/mma]n
is calculated
631

36
analytically with high accuracy with the maximum error being less than 6% with respect to the
632
optimization value. The error is caused due to the approximate energy (in Eq. (16d) and (16e) of
633
main text) and other charges, as the NC and PP demand charges are calculated accurately (not
634
shown in Table 5).
635
For the layover period of 07:45-16:45 hours, Table 5 shows that for Jan 2019, the final
636
V0G, V1G and V2B slopes are predicted exactly by the analytical method. 7
637
9@]7
+,>ABKE.LKM4N
7is underpredicted analytically, and the difference between the optimization and
638
analytical values occurs primarily because above 114 kWh of daily charging demand, additional
639
charging takes place exclusively in the off-peak period, but the charging is non-uniform; only at
640
approximately 144 kWh of daily charging demand, the additional charging demand is spread out
641
uniformly over the off-peak period leading to a constant slope. Like the 06:30-19:30 hours layover,
642
the
/mma]n
is calculated analytically with high accuracy with maximum error being about 1.2%.
643
3.2.4.6 Interpretation of the total electricity charges versus daily EV charging demand curve
644
Figure 5(a) shows that for Jan 2019 V0G charging for the 06:30-19:30 hours layover, the
645
slope becomes constant at $9.6/kWh/day with increasing daily charging demand above 24 kWh.
646
These costs should not be confused with electricity (energy) costs per kWh charged. Since there
647
are 23 weekdays in the month when EV charging occurs, $9.6/kWh/day = $0.42/kWh/month; in
648
other words, the average electricity cost per kWh charged is 42 cents. Since all graphs are presented
649
in kWh of daily EV charging (energy) demand, we chose to continue to report results using the
650
$/kWh/day metric.
651
For V1G charging, the slope is initially constant at $2.5/kWh/day until 144 kWh of daily
652
charging demand, because charging takes place in the off-peak layover period only, without
653
increasing the NC demand peak over the original. The slope until 144 kWh of daily charging
654

37
demand can be found from Eq. (12), with
5*+,+<=
. Finally, the V1G slope becomes constant
655
at $5.2/kWh/day with additional daily charging demand above 216 kWh. For V2B charging, the
656
slope is negative initially, then becomes positive and increases to $5.1/kWh/day with increasing
657
daily charging demand up to 168 kWh. With additional charging daily demand above 168 kWh,
658
the slope becomes constant at $5.2/kWh/day, resulting in parallel V2B and V1G curves above 216
659
kWh of daily charging demand. The slope of the V2B electricity charges curve increases faster
660
than V1G from 48 to 216 kWh of daily charging demand because the addition of daily charging
661
demand (from 48 kWh to 216 kWh) results in a greater increase of the NC demand peak for V2B
662
as compared to V1G (see Table 4 V1G and V2B NC and PP demand peaks for the 06:30-19:30
663
hours layover). For example, for 72 to 216 kWh of daily charging demand, the PP demand peak
664
remains constant for V1G at 96.5 kW and at 82.4 kW for V2B and does not affect the slope of
665
electricity costs versus daily energy demand curve. On the other hand, the NC demand peak costs
666
increase faster for V2B resulting in a faster increasing slope of electricity costs versus daily energy
667
demand for V2B compared to V1G.
668
Figure 5(b) shows that for the entire year 2019, the slope of V0G charging for the 06:30-
669
19:30 hours layover, becomes constant at $114.9/kWh/day above 48 kWh of daily charging
670
demand. For V1G charging, the slope is $29.4/kWh/day until 120 kWh of daily charging demand,
671
then increases, and becomes constant at $62.2/kWh/day with daily charging demands above 240
672
kWh. For V2B charging, the slope is negative up to a daily charging demand of 48 kWh, then
673
becomes positive and increases, and finally becomes constant at $62.2/kWh/day above 216 kWh
674
of daily charging demand, resulting in parallel V2B and V1G curves above 240 kWh of daily
675
charging demand.
676
3.3 Overall results for all buildings
677

38
To explain the building-to-building differences in the electricity charges associated with
678
EV charging, in this Section we discuss the results for all buildings for one sample initial and final
679
SOC combination (50 & 90% respectively) and one layover period (06:30-19:30 hours). The initial
680
and final SOC combination is chosen as 50 & 90% respectively to be consistent with the rest of
681
the paper.
682
Figure 6 shows that for all buildings, V0G incurs the highest EV charging costs (the
683
difference between post and pre-EV charging building electricity costs), followed by V1G and
684
V2B. For V0G charging, all charging takes place between 06:30-10:15 hours (see Section 3.2.1).
685
The difference between the V0G EV charging costs from building-to-building is driven by
686
differences in the NCDC. The monthly increase in the NCDC for a building depends on two
687
factors: (a) The intersection of the original NC demand peak time with the time of V0G charging.
688
If the original NC demand peak falls within the V0G charging time, the post-EV charging new NC
689
demand peak increases at the charging power of the EV; (b) If there is no intersection in (a), the
690
difference between the original NC demand peak and the maximum original load in the month
691
during the V0G charging time. If the original NC demand peak time falls outside the V0G charging
692
time, and the lower the difference between the original NCDP and the maximum original load in
693
the month in the V0G charging time, the higher the chance that a particular number of EV will
694
increase the NCDP. For V0G, most buildings show EV charging cost increases consistent with 6.6
695
kW per EV of increased NCDP for daily EV energy demand over 100 kWh, but building XIII
696
shows smaller cost increases as the original NC demand peak is much larger than the maximum
697
load during the EV charging time.
698
Building XIII is also the main outlier for V1G and V2B as the charging can be spread over
699
the layover period such that the building load stays below the original peak demand even for 432
700

39
kWh of daily EV charging demand. Therefore, electricity cost increases for building XIII reflect
701
only the additional energy charges and there is no demand charge contribution. For V1G and V2B
702
charging at the other buildings, the variation between the EV charging costs from building-to-
703
building is driven by NCDC, OPDC (only for V2B), and off and on-peak energy costs. For V1G,
704
the electricity costs initially increase with a slope that is consistent with only energy charges from
705
off-peak charging, but eventually transition to a slope consistent with energy and demand charges
706
from constant charging during the off-peak period. The transition occurs mostly between 100 to
707
400 kWh of charging demand, depending on the building. The smaller the difference between the
708
original demand peaks and the off and on-peak layover period mean loads, the higher the chance
709
that a particular number of EVs will increase the peak demand charges.
710
For V2B, the final slopes are consistent with the V1G slopes and the ordering of the EV
711
charging costs for high daily EV energy demand is also consistent with V1G. The lower envelope
712
of the initial decrease in V2B electricity costs is consistent with a decrease of 6.6 kW in both NC
713
and PP demand charges, i.e. EVs discharging at full power. Depending on the building, the slope
714
is maintained for up to 3 EVs (72 kWh of charging demand), is followed by a slower decrease
715
(less than 6.6 kW decreases in NC and PP demand charges), and eventually becomes positive as
716
demand charge reductions become infeasible and the energy costs increase, and eventually the
717
demand charge increases dominate. The intersection of the original demand peak times along with
718
the layover period plays a large role for V2B. Specifically, if the original demand peak times do
719
not fall within EV layover time, V2B charging cannot reduce costs.
720

40
721
Figure 6. EV charging cost versus total daily EV energy demand for all buildings for the
722
06:30-19:30 hours layover for the entire year 2019 for initial and final SOC of 50 & 90%
723
respectively for (a) V0G charging, (b) V1G charging, and (c) V2B charging. The legend
724
represents the building number.
725
726
The results for the total electricity charges (not shown graphically) elucidate that for all
727
three charging strategies, generally, as the mean original real load (proxy for the original load of
728
the buildings) of the buildings increase (Table 2), the total electricity charges also increase, as the
729
demand and energy charges are higher for a building with higher original load.
730
Table 6 shows the optimal number of V2B EV charging stations to be installed at a building
731
such that the original (pre-EV) electricity costs are not exceeded. Generally, for a given month,
732

41
the larger the difference between the original NCDP & the mean load in the off-peak period, and
733
the original OPDP & the mean load in the on-peak period (as quantified in Eq. (18), the more V2B
734
EV charging reduces the NCDC and PPDC. It then follows that the greater the NCDC and PPDC
735
savings, the higher the number of optimal V2B charging stations for a building. Hence, in Table
736
6, we present the optimal number of V2B charging stations as a function of a metric
B
, which
737
weights the difference in original peak and mean loads by the off and on-peak layover times
738
averaged over the 12 months in 2019.
B
is formulated as
739
B< !]N#7
p1qQ
*+,-'56 A!]N#
0Q1 1
F'56
&
34'
(
)*4?-./0)
)*1
2*3
2*4
R
.
HI=E.*4+
HI=E.*4
740
Q1 1
F'56
&
34'
(
)*+,-./0)
)*+4-.
2*3
2*4
RrR
)D4?-./)8
9F
D):
9/)8
9F.
Q
/-,-'56 A!]N#
01 1
F'56
&
34'
(
)*+4-.
)*4?--.
2*3
2*4
rR
)741
D):
9/4?-.F
D):
9/)8
9F
st, (18)
742
where
3
takes the value of the date index of the month for only weekdays (when EV charging
743
occurs). The
!h#n@
argument is dropped from
*+,-
,
/-,-
and
F'56
for simplicity of
744
presentation of Eq. (18).
745
Table 6. Optimal number of V2B EV charging stations by building
746
Buildings arranged in increasing
order of 𝒘 (Eq. 18)
𝒘
Optimal # of V2B charging
stations
II
20.8
3
I
29.2
4
III
38.2
6
VII
40.6
6
IX
42.4
5
V
44.0
5

42
IV
44.7
5
VII
44.9
6
VI
48.0
5
XII
53.6
7
X
81.6
9
XI
104.0
13
XIII
114.4
1
XIV
134.2
12
Table 6 shows that generally as
B
increases, the optimal number of V2B charging stations
747
also increases. The optimal number of V2B charging stations for building XIII is an outlier
748
because, for the EV layover period (06:30-19:30 hours) considered, for most of the months (9 out
749
of 12) its
*+,-'56
occurred outside the layover period and for the remaining 3 months it occurred
750
in the PP period, giving the V2B EVs little chance to reduce the NCDP. For some of the months,
751
the
/-,-'56
of building XIII also occurred out of the layover period, further preventing load
752
shifting and electricity cost reduction by V2B.
753
3.4 Sensitivity analyses
754
Section 3.2 presented a case study for the idealized uniform commuter EV fleet for initial
755
and final SOC of 50 and 90% respectively for the 06:30-19:30 hours layover for building V for
756
the year 2019. In this Section, we carry out sensitivity analyses based on the initial and final SOCs
757
of 45 & 85%, 40 & 80%, 50 & 85%, and 50 & 80%, to present the effect of varying the initial and
758
final SOCs on the NC and PP demand costs, energy costs, and total electricity costs for both
759
layover periods for the year 2019. The effect of varying initial and final SOCs on total electricity
760
costs is presented graphically for building V for 2019 in this Section (consistent with the rest of
761
the paper), while the variation of all metrics (NC and PP demand costs, energy costs and total
762

43
electricity costs) for the SOC combinations with the same daily charging energy demand, for all
763
buildings for both the layover periods is presented in Tables S1, S2 and S3 of the Supplementary
764
material.
765
If the final SOC is reduced below 90% (note that for our analyses the maximum and
766
minimum SOC of the EV battery is 20 and 90% respectively), it is possible for the V2B EVs to
767
discharge immediately before disconnecting and therefore further discharge during the on-peak
768
period. In Section 3.2.3, typically the net V2B charging demand during the on-peak period was
769
zero or positive (if charging up to 90% during the off-peak period was not optimal, resulting in net
770
charging during the on-peak period), while in this Section (for final SOCs below 90%) the net V2B
771
charging demand during the on-peak period is expected to be negative (net discharging).
772
Figures 7(a) and 7(c) show results for EVs having different initial and final SOCs but the
773
same daily charging energy demand for the 06:30-19:30 hours and 07:45-16:45 hours layover,
774
respectively. For a particular layover period, the V0G and V1G total electricity charges are the
775
same if the daily charging energy demand of the EVs is the same, as the V0G and V1G EV
776
charging costs do not depend on the final SOC because they do not have the ability to discharge.
777
V2B EVs make use of the lower final SOC, to shift demand from the on-peak period to the off-
778
peak period resulting in cost savings, as the on-peak period has higher energy charge rates and
779
additional demand charges over the off-peak period. The V2B total electricity costs decrease for
780
both layover periods as the final SOC decreases from 90 to 80% (with initial SOC decreasing from
781
50 to 40%) because the smaller the final SOC the more flexibility for discharging during the on-
782
peak period. The strategy of V2B EVs to discharge more during the on-peak period as final SOC
783
decreases from 90 to 80% is accompanied by more charging during the off-peak period, which
784

44
ultimately leads to net total electricity cost savings, i.e., the decrease in the on-peak periods costs
785
is greater than the increase in the off-peak period costs.
786
Figures 7(b) and 7(d) correspond to EVs having different final SOCs (with initial SOC
787
fixed at 50%) and thus different daily charging energy demand for the 06:30-19:30 hours and
788
07:45-16:45 hours layovers, respectively. The total electricity charges for both layover periods for
789
all charging strategies are smallest for a final SOC of 80% and increase as the final SOC increases
790
to 85 to 90%. The smaller cost for V0G and V1G, for lower final SOCs is due to the smaller total
791
charging energy demand (as initial SOC is fixed at 50%). The V1G costs decrease more than V0G
792
because, as the final SOC (and thus charging demand) decreases, the V1G average load (and
793
therefore incremental NCDC) is proportional to the charging demand per Eq. (16b), as opposed to
794
V0G which charges without regard for the original load curve and costs. For V2B, in addition to
795
the former point, there is an added benefit of more discharging potential during the on-peak period
796
when the final SOC is lower than 90%. The sensitivity analyses (comparison between Figs. 7(a)
797
& 7(c), and 7(b) & 7(d)) also show that the shorter layover period of 07:45-16:45 hours leads to
798
higher total electricity charges compared to the longer layover period of 06:30-19:30 for all
799
charging strategies for any particular initial and final SOC combination.
800
Tables S1, S2 and S3 of the Supplementary material present the results with initial and
801
final SOC of 50 & 90%, 45 & 85%, and 40 & 80%, respectively.
802

45
803
804

46
Figure 7. Total electricity charges versus daily number of EVs for the for the entire year
805
2019 for the layover period (a, b) 06:30-19:30 hours, and (c, d) 07:45-16:45 hours, at
806
building V for (a, c) same daily charging demand with initial and final SOCs being 40 &
807
80%, 45 & 85%, and 50 & 90%, respectively, and (b, d) different daily charging demand
808
with initial and final SOCs being 50 & 80%, 50 & 85%, and 50 & 90%, respectively. The
809
legends in the figure correspond to the charging strategies along with their initial and final
810
SOCs. For example, V0G__SOC__50-80 indicates V0G charging with initial and final SOC
811
of 50 and 80% respectively.
812
3.5 A realistic case using historical data
813
A realistic case study is carried out using historical EV data of charging records available
814
from ChargePoint at UC San Diego. The relevant historical data used in this analysis are the time
815
of EV connection and disconnection, end of charging, charging demand, initial and final SOC (for
816
a subset of events only), EVSE IDs, and port type (Level 2 (L2) and Direct Current Fast Chargers
817
(DCFC)). For a data sample, see Ref. 17. Originally the EVs were charged with the V0G charging
818
strategy, which did not make use of the flexibility afforded by the complete layover time, i.e.,
819
originally the EVs charged too quickly when more suitable later times were available for charging.
820
The EV battery capacity is required to understand the EV discharging or delayed charging
821
opportunities. The ChargePoint data does not (directly) contain the EV (rated) battery capacity
822
data, but the initial and final SOCs are given for 5,754 out of the total of 168,122 charging events
823
that occurred between March 15, 2016 and August 4, 2020. For the 5,754 events, EV battery
824
capacity is calculated as
P+7<&#9
Q
_$":
9/-_$"8
9
R. We observe an anomaly for five charging events, for
825
which the calculated battery capacity is above 200 kWh. We remove these five datapoints from
826
our analysis as most EVs have a battery capacity below 200 kWh 22. To impute the missing EV
827
battery capacity for the remaining 162,368 charging events, we randomly draw data from the
828
calculated battery capacity (5,749 events).
829
Following these calculations, we set the following charging constraints: (i) The missing
830
final SOC is initially imputed by randomly drawing from the given “valid” final SOCs. (ii) The
831

47
missing initial SOC is calculated from the final SOC, energy demand, and the EV battery capacity
832
data as
S/+9
7<S/+:
7A&#9
O"9
. (iii) If the
S/+9
7
is calculated as less than 0% by (ii), it is corrected
833
and fixed at 0% as the SOC range for the analyses is 0-100%. Correspondingly the battery capacity
834
is again updated for that EV as
P+7<&#9
Q
_$":
9/-_$"8
9
R , for which
S/+9
7
= 0. (iv) The maximum
835
charging and discharging rate of EVs is 7.2 kW for L2 and 50 kW for DCFC. The input variables
836
for the realistic analysis are shown in Table 7.
837
Table 7. Inputs for the realistic case study
838
Metric
Symbol
Value
Maximum charging rate of L2 chargers
max EV\+
]
7.2 kW
Maximum charging rate of DCFC chargers
max EV#"^"
]
50 kW
Data sampling interval
∆𝑡
1 hour
Table 7 shows that the data sampling interval is chosen as 1 hour instead of 15 minutes as
839
for the uniform fleet Case study (A), because of unreasonably long run-times for 15-minute
840
timesteps in the realistic case study. The actual time of EV connection and disconnection is mapped
841
onto the hourly scale, depending on the minute of the hour of the connection or disconnection from
842
the charging station. Initially the EV connection and disconnection time is rounded up to the
843
nearest hour. For example, if an EV originally connects at 00:29 hours and disconnects at 1:35
844
hours on the same day, it is assumed in our algorithm that the EV connects at 00:00 hours and
845
disconnects at 02:00 hours on that day. After the initial rounding to the nearest hour, a correction
846
is implemented for the EVs that have the same connection and disconnection time. In these cases,
847
the connection time is assumed to be the beginning of the hour and the disconnection time is
848
assumed to be the end of the hour. For example, if an EV originally connects at 16:45 hours and
849
disconnects at 16:59 on the same day, rounding to the nearest hours would cause both the
850

48
connection and disconnection time to be 17:00 hours on that day. The correction assumes that the
851
EV connects at 16:00 hours and disconnects at 17:00 hours.
852
Our analysis is carried out for 5 weekdays of February 2020. The EV charging stations are
853
located in the Osler Parking Structure. The Osler Parking Structure is chosen for the analysis as it
854
consists of 16 L2 (with 14 being in use for this analysis) and 2 DCFC fast chargers which is
855
representative of an EV charging station installation infrastructure at a single location 23. The total
856
load of the Osler Parking Structure EV charging stations is mapped to a single building having 0
857
original load, i.e. the optimized EV load is assumed to equal the final building net load. As per the
858
original V0G charging schedule the NC demand peak occurs on Feb 14, 2020, we choose the
859
weekdays Feb 10 to Feb 14, 2020 for the analyses, so that the NC demand peak is representative
860
for the entire month of February 2020. 338 charging events occur from Feb 10 through 14, 2020,
861
with average layover, charging time, and energy demand of 3 hour 29 minutes, 1 hour 38 minutes,
862
and 9.8 kWh respectively, with 256 events occurring at L2 chargers and 82 events occurring at
863
DCFC chargers. 251 charging events at L2 chargers have charging flexibility, whereas all the
864
events at DCFC chargers have charging flexibility (i.e.
&':
7A'9
7()!NO7IJ7uI,7
). Since there
865
are some inconsistencies in the dataset, the final EV energy demand is corrected for 5 L2 charging
866
events by charging at maximum power during the entire layover period (refer to Eq. (9)). The
867
objective function minimized is Eq. (1), with the cost components (NC and PP demand charges,
868
energy charges, and other charges) being adjusted for 5 days instead of the entire month.
869
Figure 8(a) shows the timeseries for February 10 through February 14, 2020 for all 3
870
charging strategies. Figure 8(b) shows the NC and PP demand charges along with the total
871
electricity costs for our analysis. The total electricity costs incurred by the EVs based on the
872
original V0G charging, and the optimized V1G and V2G charging are $5,694, $3,402, and $2,598
873

49
respectively. The results show that the V2G and V1G charging strategies results in 54.4 and 40.3%
874
total electricity cost savings, respectively over the original V0G charging schedule.
875
876
(a)
877
878
(b)
879
Figure 8. (a) Original (V0G) and optimized net load (= EV charging) timeseries analysis,
880
and (b) Electricity cost components for the 3 charging strategies, for the realistic case study
881

50
from February 10 through 14, 2020. The total electricity charges in (b) differ from the sum
882
of the NC and PP demand charges because they also include energy charges.
883
4. Conclusions
884
We carry out a techno-economic analysis of three different types of workplace EV charging
885
strategies (V0G, V1G and V2B) in 14 commercial buildings with real load profiles. We primarily
886
base our analysis on an idealized uniform EV commuter fleet case study with a layover period of
887
06:30-19:30 hours for the year 2019.
888
V0G incurs the highest year-around electricity costs followed by V1G and V2B. For V0G,
889
the building-to-building difference in EV charging costs depends on the intersection of the original
890
NC demand peak time with the EV charging time, and the difference between the original NC
891
demand peak and the maximum original load during the EV charging time. For V2B, the building-
892
to-building difference in EV charging costs depends on the intersection of the original NC and PP
893
demand peak times with the EV layover time. For V1G and V2B the building-to-building
894
difference depends on the difference between the original demand peaks and the mean original
895
load during the on and off-peak layover periods.
896
The V1G and V2B total electricity costs initially diverge with increasing daily charging
897
demand (or number of EV charging stations) and then become parallel to each other. As the daily
898
charging demand increases, the cost savings of V2B charging over V1G reduce and the V2B
899
charging costs exceed the original (pre-EV) costs. A longer layover period generally leads to more
900
cost savings over a shorter layover period for V1G and V2B, as the charging is spread out over a
901
longer duration for V1G, while for V2G there is an additional flexibility of shifting on-peak loads
902
to off-peak periods. Correspondingly, a longer layover period also leads to a higher number of
903
optimal V2B charging stations (the number of V2B charging stations to be installed at a building
904
such that its operating electricity costs do not exceed the pre-EV original electricity costs), as
905

51
compared to a shorter layover period. Generally, with increasing difference between the original
906
NCDP & mean off-peak period load and the original OPDP & mean on-peak period load, weighed
907
over the off-peak and on-peak layover times respectively, the optimal number of V2B charging
908
stations increases.
909
Sensitivity analyses based on changing both initial and final SOC of EVs while keeping
910
the energy demand constant for all the buildings for both layover periods show that, as the final
911
SOC decreases from 90 to 80% (with the initial SOC decreasing from 50 to 40%), the total
912
electricity costs remain the same for V0G and V1G, while for V2B the total electricity costs
913
decrease because of the additional flexibility of discharging during the on-peak period.
914
A realistic case study based on historical data for 5 high charging demand weekdays in
915
February 2020 for 14 EV charging stations shows that the V2G and V1G charging strategy results
916
in 54.4% and 40.3% total electricity cost savings respectively over the original V0G charging
917
schedule.
918
While the results discussed so far were all based on convex optimization, we also provided
919
general equations that allow estimating V1G and V2B benefits based on a pre-EV building load
920
profile and EV and tariff data. Although the number of V2B charging stations such that the original
921
(pre-EV) operating electricity bill is not exceeded cannot be predicted exactly without carrying out
922
the convex optimization, we provided a framework (using Eq. (18), in conjunction with Table 2
923
and Table 6) to approximate the optimal number of V2B charging stations without carrying out
924
the convex optimization, which may be of interest to building owners.
925
One of the limitations of this study is the assumption of 100% charging/discharging
926
efficiency for the EVs. In reality, each time an EV charges/discharges there are costs due to energy
927
losses and battery degradation. Therefore, if the losses were considered, the V2G/V2B charging
928

52
economic benefits, which depend on more charging/discharging cycles, would reduce. Another
929
limitation of the study is that uncertainties in layover periods and battery capacity (which may
930
occur due to ageing) are not considered. Future work will focus on tackling these limitations to
931
make the study more robust and accurate and increase its applicability to more realistic scenarios.
932
Supplementary material
933
See the Supplementary material attached alongside the manuscript, for some Results and
934
discussions which could not be discussed in the main text due to space limitations. Section 1.1 of
935
the Supplementary material expands upon the uniform fleet V0G and V2B analysis already
936
presented in Section 3.2.1 and 3.2.3 of the main text respectively for building V for the 06:30-
937
19:30 hours layover. Section 1.2 of the Supplementary material presents the V0G, V1G, and V2B
938
analyses for building V for the 07:45-16:45 hours layover. Section 1.3 of the Supplementary
939
material presents a hypothetical case study demonstrating the ability of V2G/V2B EVs to save
940
electricity costs by shifting load from the on to the off-peak layover period. Section 1.4 of the
941
Supplementary material elucidates on the general applicability of the optimization model and the
942
trend of total electricity charges versus total daily EV energy demand curve for electricity tariff
943
structures other than those used in our paper. Tables S1, S2 and S3 of the Supplementary material
944
present the effect of varying both the initial and final SOCs of the EVs on the NC and PP demand
945
costs, energy costs and total electricity costs, while keeping the charging energy demand constant
946
for the year 2019 for all buildings for both layover periods.
947
Data availability statement
948
The data that supports the findings of this study are available within the article and its
949
supplementary material.
950
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951

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984
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