ELEKTROTEHNIŠKI VESTNIK 78(4): 205-210, 2011 
ENGLISH EDITION 
Profit Optimization of Energy Supply of Electric Drive Vehicles 
Damir Imširović, Matej Rejc, Miloš Pantoš 
University of Ljubljana, Faculty of Electrical Engineering, Tržaška 25, 1000 Ljubljana, Slovenia 
E-mail: damir.imsirovic@fe.uni-lj.si, matej.rejc@fe.uni-lj.si, milos.pantos@fe.uni-lj.si 
 
Abstract. An increased electric drive vehicle (EDV) use is expected in the future due to the rapid development of 
new EDV technologies, increased environmental concerns, increasing petroleum-based fuel prices and the 
possibility of EDV participation on electricity markets. In this paper, an optimization algorithm for EDV charging 
and discharging for electricity-spot market participation is presented. The use of the presented algorithm would 
bring lower EDV driving costs for its users and a competitive advantage for the EDV electricity provider that 
would use the EDV batteries as a storage system in order to purchase and sell additionally stored energy on the 
electricity market. To simplify the optimization algorithm, individual EDVs are grouped into larger EDV fleets. 
The use of EDV fleets introduces a constant number of optimization variables in the optimization process. K-
means the clustering algorithm is used to group individual EDVs into larger fleets. The optimization problem was 
approached deterministically and in future work, a probabilistic approach to the problem will be presented. 
 
Keywords: k-means clustering method, electricity-spot market, linear optimization 
 
 
 
1 INTRODUCTION 
An increased electric drive vehicle (EDV) use is 
expected in the future due to the rapid development of 
new EDV technologies, increased environmental 
concerns, increasing petroleum-based fuel prices and 
the possibility of EDV participation on electricity 
markets. 
With an ever increasing number of EDVs, electric 
power systems (EPS) will be subjected to large 
technological changes, demands for new investments, 
such as the construction of new EDV charging stations 
and power system enhancements in transfer capabilities 
and voltage support. 
Also, additionally, EDV batteries are expected to be 
used on the electricity spot markets, where the EDV 
batteries could be used as an energy storage system [1]. 
 In this paper, an optimization algorithm for EDV 
charging and discharging is presented with the goal of 
optimal electricity spot market participation. The 
presented algorithm enables the electricity providers to 
maximize the revenue from using additionally stored 
energy in EDV batteries on the electricity spot market. 
The EDV electricity providers are expected to be the 
already functioning distribution companies and 
electricity providers. This would allow lower driving 
costs for EDV users, which would attract more EDV 
users to allow their vehicles to be used in the electricity 
markets. 
 To simplify the optimization algorithm, EDVs were 
merged into larger EDV fleets with similar driving 
needs. This enables the number of optimization 
variables to remain constant, even with the number of 
individual EDV changing. The change in the number of 
EDVs only affects the optimization algorithm as a 
change in the required power-demand curve for driving 
schedules. Therefore, a k-means clustering method is 
presented in this paper to group the various EDVs into 
fleets. This enables the presented algorithm to give 
optimal charging and discharging times for individual 
fleets with electricity spot market participation in mind. 
This enables the EDV electricity provider to purchase 
the required energy for EDV at times of lower 
electricity costs and sell the additionally stored energy 
at times of higher electricity costs. 
 In the literature, various studies in the EDV charging 
impact on EPS have appeared [1-3]. The increased 
interest in EDV participation on electricity markets has 
been noted [4, 5]. 
 In this paper, the basis for further EDV participation 
on electricity markets is presented, where probabilistic 
approach can be included as well as taking into account 
other electricity markets and various other economic, 
environmental and technical impacts of EDV. 
 The paper is organized as follows. A short 
description of EDV and EDV electricity providers is 
given in Section 2. In Section 3, the developed 
optimization algorithm for EDV charging and 
discharging are presented and the k-means clustering 
method. In Section 4, results of the optimization 
algorithm for a test case are shown. Finally, in Section 
5, the main findings of this paper are summarized. 
 
 
Received September 28, 2011 
Accepted October 24, 2011 

206 IMŠIROVIĆ, REJC, PANTOŠ 
2 ELECTRIC VEHICLE AND ELECTRIC 
VEHICLE ELECTRICITY PROVIDER 
DESCRIPTION  
During the last few decades the development of new 
EDV technologies has led to a renewed interest in the 
electric transportation infrastructure. According to the 
Slovenian Green Paper for the National Energy Policy, 
EDV will amount to all the newly sold vehicles in 2030. 
The EDV advantages are their energy conversion 
efficiency from batteries (90 % efficiency as opposed to 
the 30 % efficiency of internal combustion vehicles 
from the stored fuel), locally lower emissions (CO2 
emissions are expected to lower thrice [6]), and 
decreased foreign oil dependency. The disadvantages 
are currently numerous and are most commonly linked 
to the current batteries and EDV prices. The range of 
the current EDVs is approximately 150 km per 
charging, which is approximately three times less than 
internal combustion vehicles. The charging time of the 
current EDV batteries also has its disadvantages, as 
charging can take from 4 to 8 hours [7]. Additional 
environmental issues must be taken into account, as 
large amount of EDV batteries will have to be properly 
recycled. Increased investments in the EPS will also be 
required, new smart grid technologies will be mandatory 
and new regulatory rules for EDV electricity providers 
created. 
 With the implementation of new smart grid 
technologies, EDV will be able to participate in 
electricity markets, aid in EPS frequency regulation and 
congestion management, participation in balancing 
markets, etc.. The basic idea is the use of EDV batteries 
as a storage system, and charging or discharging 
activated at optimal times during the day. This would 
enable the electricity provider to lower charging costs 
for EDV users, as the profits from participating on 
electricity markets would cover a certain amount of 
purchased electricity costs. This would bring 
competitive advantages to electricity providers 
participating in the above services. 
 
3 OPTIMAL CHARGING AND DISCHARGING 
ALGORITHM FOR ELECTRICITY SPOT-MARKET 
PARTICIPATION  
The electricity provider will require an optimization 
algorithm to determine optimal charging and 
discharging times for EDV to optimally participate on 
the electricity spot market. This will allow the provider 
to reduce the costs of energy purchases required for 
EDV driving needs and lower the electricity prices for 
EDV users. This would result in a competitive 
advantage over other electricity providers not using 
such tool. To simplify the optimization problem, the 
EDV driving schedules were grouped into larger EDV 
fleets thus limiting the amount of optimization variables 
to a smaller constant value not changing with the 
change in the number of EDVs under contract with the 
electricity provider.  
 As the driving schedules are mostly dependent on the 
EDV-user work habits, we used the k-means clustering 
method to group various EDVs into fleets with similar 
driving schedules (e.g. the EDV users driving to work at 
a specific time – early mornings, late evenings, during 
peak-traffic hours, etc.). In Subsection 3.1 we present 
various EDV driving schedules, reasons for grouping 
EDVs into fleets and the k-means clustering method. In 
Subsection 3.2, we describe on optimization algorithm 
for optimal charging and discharging times enabling 
electricity spot market participation. 
 
3.1 Clustering of EDV driving schedules into 
EDV fleets 
 EDV driving schedules of various users present a 
large uncertainty problem, as different users can drive at 
different times and require different amounts of energy 
for their driving needs. Moreover, optimizing charging 
and discharging times for individual EDVs is not 
recommended, as the large amount of EDVs in the 
optimization problem represented as optimization 
variables would cause serious problems to even the 
most capable optimization solvers. In this paper, we 
group individual EDVs into larger EDV fleets to limit 
the number of variables to a constant number, i.e. the 
number of fleets. The used k-means clustering algorithm 
creates representative clustered driving schedules for 
individual fleets to group individual EDV driving 
schedules into a fleet. As the number of EDVs changes, 
only the total battery capability in the fleet changes; the 
number of optimization variables remains unchanged. 
 In this paper, the k-means clustering method [8] is 
used to group individual EDV driving schedules into 
fleets with representative driving patterns.  
 The k-means clustering method uses an iterative 
refinement technique with the clustering algorithm 
aiming at minimizing the criterion (1) in order to group 
the individual EDV driving schedules into fleets. The 
method is a very popular clustering technique due to its 
simplicity. 
 
j
k
2
j g
g 1 g
min J
= ∈
= −
∑∑
d
d μ , (1) 
 
j
g j
g
g
1
 ,
m
∈
=
∑
d
μ d (2) 
where J is the criterion function, k is the number of 
EDV fleets, d
j
 = [d
j,1
, d
j,2
,…, d
 j,t
] is the driving schedule 
of the j-th EDV, (t = 24 hours). μ
g
 = [μ
g,1
, μ
g,2
,…, μ
g,t
] is 
the arithmetic mean of all the driving schedules in the g-
th EDV fleet, m
g
 represents the number of EDVs in the 
g-th EDV fleet. The arithmetic mean represents the 
representative clustered driving schedule of the g-th 
EDV fleet, which is the goal of the k-means clustering 
method in this paper.  

PROFIT OPTIMIZATION OF ENERGY SUPPLY OF ELECTRIC DRIVE VEHICLES 207  
 The k-mean clustering method consists of four steps. 
The aim of the method is to iteratively define the 
arithmetic mean of the driving schedules of the k EDV 
fleets in order to reach the minimum of the criterion 
function (1). 
1. In the first iteration, the number of EDV fleets is 
selected, i.e. k, where k<m and the arithmetic 
mean of the k EDV fleets is calculated μ
g
(1). 
2. In the q-th iteration, the driving schedules of 
individual EDV vehicles are assigned into the 
EDV fleets. The individual driving schedules 
are placed into the g-th EDV fleet if: 
 
j g j ng
(q) (q) ,
1, 2,...,k g ng,
− < −
∀ ∨ ≠
d μ d μ
 (3) 
where ng are all the other EDV fleets, except 
the g-th EDV fleet.. 
3. New arithmetic means of the k EDV fleets are 
calculated μ
g
(q+1). 
4. If μ
g
(q+1) = μ
g
(q) for all the k EDV fleets, the 
iterative process is completed. 
 
 To use the k-means clustering method, the user 
should experiment and observe the behavior of the 
clustering analysis in regard with the number of pre-
defined EDV fleets and starting arithmetic means. 
The results of the described clustering analysis are the 
combined representative driving schedules for each 
EDV fleet. The process is shown in Figure 1. 
Fleet 1
Fleet g
Fleet 2
t
t
t
t
μ
1
μ
2
μ
g
Individual driving 
scheduls of EDV
Fleet k
t
μ
k
d
1
d
j
d
m
t
d
j
Driving schedule 
of j-th EDV
 
Figure 1. Clustering of EDV driving patterns into fleets 
 
3.2 Optimization algorithm description 
 The proposed optimization algorithm enables optimal 
EDV charging and discharging with the goal of optimal 
participation on the electricity spot market. The goal of 
the optimization is to increase profits of the electricity 
provider by using EDV batteries as a storage system to 
participate on the electricity market [2-4]. 
 Figure 2 presents the charging/discharging 
optimization algorithm with the aim of profit 
maximization for the electricity provider. The algorithm 
requires the k-means clustering method to define the 
representative combined driving schedules for the EDV 
fleets, as presented in Subsection 3.1. This requires 
either the EDV users or the electricity provider to 
provide driving schedules for individual cars for the 
day-ahead. Using the forecasted driving schedules, the 
optimization algorithm defines optimal EDV charging 
and discharging for electricity spot market participation. 
 
 
Figure 2. EDV optimization algorithm 
 
 Equations (4) to (10) describe the optimization 
algorithm for EDV charging and discharging. The 
criterion function describing the optimal EDV fleet 
market participation of the g-th fleet is as follows: 
 
t t
g i g,i pra i g,i
i=1 i=1
pol
1
 max J c y c x η
η
= ⋅ ⋅ − ⋅ ⋅ ⇒
∑ ∑
 (4) 
where t is the number of the hours taken into account in 
the optimization algorithm, c
i
 is the spot market price at 
the i-th hour, y
g,i
 is the optimization variable 
representing the amount of energy that can be sold on 
the electricity spot market for the g-th EDV fleet at the 
i-th hour, η
pol
 is the average efficiency of EDV battery 
charging of the g-th fleet, x
g,i
 is the optimization 
variable that represents the amount of energy that must 
be purchased for EDV driving needs and for electricity 
spot-market participation for the g-th fleet at the i-th 
hour, η
pra
 is the average efficiency of EDV battery 
discharging of EDV in the g-th EDV fleet. 
 The criterion function and the optimization algorithm 
do not take into account the increased battery-life 
degradation resulting from intensified use of EDV 
batteries. Also, the cost of the decreased battery life is 
neglected. The used optimization limitations are given 
in the next paragraphs. 
 The EDV battery charging rate is defined by the 
current limitation of charging stations, where EDV of 
the g-th fleet are charged: 
 
g,i pol
pol
1
0 x P
η
≤ ⋅ ≤ , (5) 
where P
pol
 is the maximum charging power and is 
constant for all hours in the optimization process. 
 The battery discharging rate for market participation 
(i.e. the rate for discharging the stored energy into EPS) 
is also limited by the current limitation of the charging 
station where EDVs of the g-th fleet are discharged: 

208 IMŠIROVIĆ, REJC, PANTOŠ 
 
g,i pra pra
0 y P η ≤ ⋅ ≤ , (6) 
where P
pra
 is the maximum discharging power and is 
constant for all hours in the optimization process. 
 The amount of energy stored in EDVs of the g-th 
fleet cannot exceed its total capacity K
g,i
 at the i-th hour: 
 
j j j
g,i g,i pra g,i g,i
i=1 i=1 i=1 pol
1
0 ,
j=2,...,t ,
x y V K η
η
≤ ⋅ − ⋅ − ≤
∀
∑ ∑ ∑
 (7) 
where V
g,i
 is the energy needed for EDV driving needs 
of the g-th fleet. 
 
When EDVs of the g-th fleet are not connected to EPS, 
they cannot participate as a storage unit:  
 
g,i g,i
0 x y = = . (8) 
The EDV batteries must be charged so as to cover all 
driving needs and market participation up to the hour of 
the EDV use or EDV energy discharge into EPS: 
 
j j j
g,i g,i pra g,i
i=1 i=1 i=1 pol
1
0,
j=2,...,t ,
x y V η
η
⋅ − ⋅ − ≥
∀
∑ ∑ ∑
. (9) 
The optimization variables must take into account the 
following limitations: 
 
g,i g,i
0, 0,
i=1,...,t
x y ≥ ≥
∀
 (10) 
In Section 4, results of the k-means clustering and 
optimization algorithm are shown for the presented test 
case. 
 
4 RESULTS 
In order to test the proposed optimization algorithm, we 
analyzed a test case of 17162 EDV with various driving 
schedules. The EDV number represents 6 % [6] of the 
total EDV consumption at the distribution level for the 
year 2030. The driving schedules ware defined by using 
the current driving habits of various Slovenian driver 
groups (industry workers, public service workers, 
students, professional drivers, etc.) and the following 
assumptions:  
- The current traffic peak hours on the main Slovenian 
roads and random hours during the days representing 
the random impulsive drives during the day (e.g. 
short trips, shopping, etc.). 
- The EDV energy use equals to 0.1 to 0.2 kWh/km 
[1, 2]. 
- The average driving range equals to 30 km for most 
of EDV users in urban areas and 60 km EDV users 
in rural areas.  
 
The optimization algorithm was tested for one day on an 
hourly basis. The input data and assumptions used are: 
- The EDV charging and discharging rate is defined 
by the current limitation of a charging station. This 
equals to 16 A, which represents the 
charging/discharging rate of 3,7 kWh/h. 
- The EDV battery capacity is 16 kWh, which equals 
to a 80 – 160 km driving range [1, 2]. 
- The EDV battery efficiency for charging and 
discharging equals to 90 %. 
- The total EDV battery capacity is not decreased over 
time and the cost of the reduced battery-life was not 
taken into account.  
 
The EDV driving costs ware assumed to be: 
- The EDV driving cost equals to 0.175 EUR/kWh, 
which is the average price for one tariff household 
counter [9]. The electricity provider margin is 
included in the price. 
- All the revenue gained by the electricity provider by 
using EDV as a storage system for electricity spot-
market participation is used to reduce the EDV 
driving costs in order to gain a competitive 
advantage. 
- The electricity purchase and selling prices are equal. 
- There is always enough demand and supply on the 
electricity market. 
- The EDV batteries are either empty or have enough 
energy for the first hour in the day for EDV to be 
driven at the first hour. 
 
Figure 3 shows the EDV plug-in times into charging 
stations and the amount of the energy used in the 
previous drive. Each column represents the plug-in 
time and the amount of energy used for the previous 
drive. The figure shows that most EDV users drive 
between 6 a.m. and 10 a.m. hours and from 1 p.m. to 
6 p.m., as larger concentrations of columns. The 
average consumption EDV per drive equals to 1.6 
kWh/h, which is the average driving distance of 16 
km per drive with a 160 km maximum driving 
range. 
 
Figure 3. Connection of EDVs on charging stations and EDV 
energy consumption 
 
 To simplify the optimization problem, EDVs are 
clustered into different fleets. In this paper, five fleets 
were used in order to encompass all the possible driving 
needs of various EDV users. 
Using the k-means clustering method, clustered 
representative driving schedules of the EDV fleets were 
obtained and the fleet is considered as a large energy 
storage system with a combined total storage capacity of 
all EDVs in the fleet.  

PROFIT OPTIMIZATION OF ENERGY SUPPLY OF ELECTRIC DRIVE VEHICLES 209  
 Figure 4 shows the combined representative driving 
schedules of all the five fleets and the energy consumed 
by the fleets for their driving needs. 
 
Figure 4. Fleet patterns 
 
 Figures 5 and 6 show results of the our optimization 
algorithm for the second fleet representing the driving 
schedules at 6 a.m. and 2 p.m. and the third fleet 
representing the driving schedules at 7 a.m. and 3 p.m.  
 
Figure 5. Optimal market participation of the second fleet 
 
The optimization algorithm for the presented case 
almost always purchases the energy needed for EDV 
driving needs were the electricity price reaches its 
lowest value. The larger amount of EDVs in the second 
fleet drives at 6 a.m. and 2 p.m. and a lesser amount of 
EDV drives at 1 p.m. and 3 p.m. At 4 p.m. and 8 p.m. 
approximately 10 MWh of energy was sold on the 
market (this was limited by the current limitations of the 
charging stations). The purchase of energy at 5 p.m. was 
performed for market participation at 8 p.m. By 
participating on the market, a certain profit is made. It is 
used to reduce the EDV driving costs.  
 
Figure 6. Optimal market participation of third fleet 
 
 The third fleet is larger than the second fleet 
considering the total number of EDVs inside each fleet. 
It thus requires more energy for its driving schedule. 
The purchase of energy for the driving needs at 7 a.m. 
and 3 p.m. is performed at 1 a.m., 2 a.m., 4 a.m. and 6 
a.m. In like in this case in the second fleet, there is no 
additionally stored energy at 4 p.m., which could be 
sold on the electricity-spot market and so this fleet can 
only participate on the electricity-spot market at 20 
p.m., as shown in Figure 6. 
 The EDV driving costs are shown in Table 1 and the 
electricity provider profits by using EDV as a storage 
system and using the additionally stored energy on the 
electricity-spot market. Reduction in the EDV driving 
costs due to market participation is shown too. 
The first fleet has the smallest reduction in the EDV 
driving costs as EDVs in this fleet drive throughout the 
day and the batteries cannot be additionally charged to 
such a degree to effectively participate on the market. 
The second, fourth and fifth fleets have the largest EDV 
driving cost reduction for being available for market 
participation during the energy-price peak hours. As the 
third fleet uses most of its energy for driving needs, the 
resulting EDV driving costs are not reduced to the 
degree of the second, fourth and fifth fleet. The fourth 
and the fifth fleet diverge at 5 p.m., as the vehicles of 
fifth fleet are not available for additional charging in 
order to participate on the market at 8 p.m. 
 
Table I. EDV driving costs and cost reductions 
Fleet EDV 1 2 3 4 5 
Number of EDV 
1529 2889 5607 4928 2209 
Average consumed 
energy for driving 
needs per day (kWh) 
3.54 7.24 5.01 5.24 4.74 
EDV driving cost 
(EUR/day) 
0.63 1.27 0.88 0.92 0.83 
Profit of one EDV due 
to market participation 
(EUR/day) 
0.02 0.06 0.028 0.046 0.04 
One EDV driving cost 
reduction due to market 
participation (%) 
3.17 4.73 3.2 5.02 4.82 
 
By participating on the electricity-spot market, a certain 
profit can be made using the presented optimization 
algorithm thus reducing the EDV user driving costs. 
This enables the electricity provider to gain a 
competitive advantage over other electricity providers 
not participating on the electricity market. 
 
5 CONCLUSION 
An increased EDV use is expected in the future as a 
result of the rapid development of new EDV 
technologies, increased environmental concerns, 
increasing petroleum-based fuel prices and the 
possibility of EDV participation on electricity markets. 
Electricity providers will be able to use EDVs as an 
energy storage system and purchase and sell energy on 
2 4 6 8 10 12 14 16 18 20 22 24
0
10
20
30
t (h)
P (MWh/h)
 
 
Purchasing
Selling
Driving
2 4 6 8 10 12 14 16 18 20 22 24
50
60
70
80
90
Price (EUR/MWh )
t (h)
 
 
Spot Price
2 4 6 8 10 12 14 16 18 20 22 24
0
20
40
60
t (h)
P (MWh/h)
 
 
Purchasing
Selling
Driving
2 4 6 8 10 12 14 16 18 20 22 24
50
60
70
80
90
Price (EUR/MWh )
t (h)
 
 
Spot Price

210 IMŠIROVIĆ, REJC, PANTOŠ 
the electricity market in order to gain profits, which 
would in turn reduce EDV driving costs. 
In this paper, an optimization algorithm for charging 
and discharging enabling electricity-spot market 
participation is presented. To simplify the optimization 
procedure, individual EDVs are combined into EDV 
fleets representing combined driving schedules of 
individual EDVs. This in turn gives us a constant 
number of optimization variables in the optimization 
algorithm despite of changes in the number of 
individual EDVs. To group EDVs into fleets, a k-means 
clustering method was developed and is presented in 
this paper. 
 By combining the EDV driving schedules into fleets, 
the optimization algorithm determines optimal charging 
and discharging as needed to participate on the 
electricity-spot market. The result is the reduction in the 
EDV driving costs due to additional profits assured by 
using EDV batteries as a storage system for the 
electricity market purposes. The reductions in the EDV 
driving costs vary depending on the driving schedules of 
EDV users. For the given test case, the profits due to 
EDV market participations range from 0.02 EUR/day to 
0.06 EUR/day, which represents from 3 % to 5 % EDV 
driving cost reduction.  
 In this paper, a deterministic solution to the presented 
optimization problem is proposed. It can be expanded to 
include probabilities and inherent uncertainties in the 
EDV driving schedules. Other electricity markets and 
EPS services can be included as well as other technical 
and economical limitations, such as battery-life 
reduction costs and battery recycling costs, too. 
 
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Damir Imširović received his Diploma Engineer degree from 
the Faculty of Electrical Engineering of the University of 
Ljubljana, Slovenia in 2009. He is employed with the same 
faculty as a researcher. His main research field includes 
power-system operation, power market and ancillary services. 
 
Matej Rejc received his Diploma Engineer degree from the 
Faculty of Electrical Engineering of the University of 
Ljubljana, Slovenia in 2007. He is employed with the same 
faculty as teaching assistant. His main research field includes 
power-system operation, protection and control and ancillary 
services. 
 
Miloš Pantoš received his Diploma Engineer and Dr. Sc. 
degrees from the University of Ljubljana, Slovenia, in 2001 
and 2005, respectively. He is employed as an assistant 
professor with the Faculty of Electrical Engineering of the 
University of Ljubljana. He is the head of the Laboratory of 
Power Systems. His main research field includes power-
system operation, protection and control, power market and 
ancillary services.