Application Independent Flexibility Assessment and Forecasting for

Controlled EV Charging

Marcus Voß, Mathias Wilhelm and Sahin Albayrak

DAI-Labor, Technische Universtität Berlin, Ernst Reuter Platz 7, 10587, Berlin, Germany

Keywords:

EV Flexibility Modeling, EV Flexibility Forecasting.

Abstract:

Electric vehicles (EVs) have been proposed to provide ﬂexibility to the energy grid in various ways. With EV

exhibiting very diverse usage patterns on the one hand, and many demand response (DR) schemes and their

respective requirements on the other, aggregators of ﬂexibility, as well as operators of controlled charging

infrastructure, need models and methods to assess the suitability of speciﬁc EVs for speciﬁc schemes. In this

paper, we provide an application independent ﬂexibility model that allows quantifying the potential amount of

ﬂexibility based on a historical dataset. Further, we provide a process to assess the predictability of ﬂexibility

through modeling it as a short-term load forecasting problem suitable also for smaller aggregations. Our key

ﬁndings using real-world data of over 200 charging points are that up- and downwards ﬂexibility per interval

have a similar magnitude, but it is unexpectedly low for the high number of charging points. Further, we ﬁnd

that forecast errors are quite high, although we can improve upon naïve benchmarks by almost 20% in mean

absolute errors with learning models.

1 INTRODUCTION

In the transition to more intelligent decentralized en-

ergy systems with increasing shares of ﬂuctuating and

uncertain renewable energy supplies, aggregations of

electric vehicles (EV) have been proposed to provide

ﬂexibility to the energy system. In this work, we aim

at both market DR and physical DR (cf. (Palensky

and Dietrich, 2011)). In market DR schemes, EVs

are typically integrated through aggregators, and dif-

ferent energy markets have been proposed, such as

reserve markets (Goebel and Jacobsen, 2016), day-

ahead markets (Vayá and Andersson, 2015) or intra-

day/imbalance markets (Sortomme and El-Sharkawi,

2012). Here, the EVs may even be physically dis-

tributed, but typically within a virtual balancing group

or virtual power plant. Physical DR may aim at for in-

stance grid congestion control (Rivera et al., 2015),

local load management, power-balance across dis-

tricts (Yu et al., 2016), or local renewable energy

share maximization (Tushar et al., 2016; Hrabia et al.,

2015). In this case, the EVs are typically physically

close in either a local area network or a part of the dis-

tribution grid. Neupane et al. (Neupane et al., 2015)

evaluate the value of ﬂexibility, by examining energy

regulation markets. In their simulation study they

show that even small loads can be aggregated efﬁ-

ciently, and ﬁnd that if in the Nordic power markets

3.87% of total demand would be ﬂexible, regulation

costs can be reduced by 49%.

So with these schemes, on the one hand, there are

EVs that exhibit very diverse usage patterns on the

other. While some EVs used by private owners may

exhibit commuter patterns with quite regular behav-

ior, and long parked times at both work and home,

others exhibit quite irregular behavior (Goebel and

Voß, 2012). Within research projects, we encoun-

tered several different EV use cases, such as station-

ary and free ﬂoating car sharing, and different com-

pany cars in Micro Smart Grid EUREF, or parcel de-

livery and nursing service staff ﬂeets in Smart E-User

(see (Lützenberger et al., 2015) for project descrip-

tions). These and ongoing projects cover private, pub-

lic and semi-public controlled charging infrastructure,

each with a central charging control. Further, EV may

be fully electric or plug-in hybrids, which may exhibit

different charging patter (Martinez et al., 2017).

So for a speciﬁc EV use case, aggregators need

methods and tools to assess the potential ﬂexibility of

speciﬁc EVs and charging stations, to choose a suit-

able DR scheme. Or with a speciﬁc DR scheme in

mind, the aggregator could improve an EV portfolio

towards speciﬁc requirements, e.g. towards high up-

or downwards ﬂexibility at certain times. To analyze

108

Voß, M., Wilhelm, M. and Albayrak, S.

Application Independent Flexibility Assessment and Forecasting for Controlled EV Charging.

DOI: 10.5220/0006795601080119

In Proceedings of the 7th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2018), pages 108-119

ISBN: 978-989-758-292-9

this, two dimensions are important: how much ﬂex-

ibility can a ﬂeet provide within speciﬁc time inter-

vals and how well can a speciﬁc ﬂeet’s ﬂexibility be

predicted. In this work, we provide an application

independent simple ﬂexibility model that allows to

quantify the potential amount of ﬂexibility for single

intervals retrospectively, based on historical data, as

well as a method to assess the predictability through

modeling it as a short-term load forecasting problem.

The model is suitable for smaller aggregations of EV

(e.g., a few tens to hundreds of charging stations/EV),

which typically have high uncertainties. Due to the

high uncertainties for few stations, as well as typi-

cally unavailability of relevant state data (such as the

state of charge of battery), our model allows only

for control within a speciﬁc control band and makes

assumptions independent from speciﬁc smart control

systems.

First, we survey related work in the next section.

Then, we present our ﬂexibility model in section 3.1

and the method to assess the predictability in sec-

tion 3.2. We evaluate the models and methods on

a private real-world dataset of 214 charging stations.

The dataset used is introduced in section 4.1 and we

demonstrate the ﬂexibility model in section 4.2 and

evaluate an instantiation of the forecasting process

with speciﬁc machine learning and benchmark mod-

els in section 4.3. Finally, we summarize our contri-

butions and ﬁndings in section 5.

2 RELATED WORK

Work on EV ﬂexibility aims at quantifying ﬂexibility

typically as a result of scheduling optimization with a

speciﬁc goal, such as in (Goebel and Jacobsen, 2016),

where EV ﬂexibility is analyzed for utilization in pay-

as-bid reserve markets and results of a mixed-integer

linear program. They evaluate their approach on a

simulation study of 10,000 vehicles. However, cur-

rently there are no systems in place where aggrega-

tors control such large ﬂeets centrally. Hence, we fo-

cus on smaller ﬂeets and not on speciﬁc scheduling

solutions. Goebel et al. treat uncertainties through a

schedule repair mechanism, but only make assump-

tions regarding the departure time distribution (them

being normally distributed), but they don’t discuss

how to predict them. Similarly, Sortomme and El-

Sharkawi (Sortomme and El-Sharkawi, 2012) don’t

base driving behavior on real data, but simple assump-

tions of EV behavior (i.e. 10% of unexpected leaving

during the day and 20% in evening hours). Sundström

and Binding (Sundstrom and Binding, 2012) make

forecasts of EV usage a central part of their frame-

work, but assume perfect forecasts. In contrast, Bessa

et al. (Bessa et al., 2012) more speciﬁcally compare

how their aggregation framework behaves with fore-

cast errors by comparing a perfect forecast of EV load

proﬁles to a naïve forecast – the same as used in our

work as lower bound benchmark – and ﬁnd that fore-

cast errors increase costs by up to 17 %. Vayá and

Andersson (Vayá and Andersson, 2015) demonstrate

simulation results to analyze bidding strategies for EV

ﬂeets. They ﬁnd that while for larger ﬂeets (e.g. <

1,000 EV) the error due to uncertainty in driving pat-

terns is neglectable, but for smaller aggregations un-

certainty of EV usage is a large issue. Mathieu et

al. (Mathieu et al., 2013) show more speciﬁcally in

one of their two case studies (the other is for air condi-

tioners) how the uncertainty of EV load proﬁle predic-

tion decreases drastically when moving from 1,000 to

100 vehicles. However, their ﬁndings are also based

on simulated data.

There is not much existing work on real-world EV

usage forecasting. In a late broad study on data min-

ing for energy-related time series no EV applications

were presented (Martínez-Álvarez et al., 2015). Some

work on predicting EV usage was done by deriving

conclusions from combustion engine cars, such as

data from a GPS-based study with 76 vehicles over a

year in Winnipeg. It was used for instance in (Ashtari

et al., 2012) to generate charging proﬁles. Panahi et

al. (Panahi et al., 2015) forecast proﬁles based on gen-

erated data which again is based on a study where

data was collected manually through driver’s logs.

Such approaches predict typical driver proﬁles, which

could be and have been used to assess ﬂexibility for

market integration. However, they do not conduct ac-

tual short-term forecasts. Depending on the applica-

tion, day-ahead forecasts or forecasts of up to a few

hours may be of interest. Hence, for assessing the

predictability we need to evaluate how well the short-

term behavior can be predicted. For that Goebel and

Voß analyzed how well the next departure time for

residential drivers (ﬁrst daily departure time) can be

predicted (Goebel and Voß, 2012). There analyses

was based on data of the Trafﬁc Choices Study (TCS)

collected by the Puget Sound Regional Council in

2005. They found that for a subset of "well-behaved"

commuters the behavior is very predictable and of-

fered a method to ﬁrst cluster the EV based on that

property and compared for different subsets how well

the departure time can be predicted based on calendar-

based features such as the hour of day, day of week

and if the day is a workday or not. Similarly, Kirk et

al. (Kirk and Dianov, 2015) offer an approach to the

same problem, however more from a ﬂeet then from

an individual driver’s perspective, which is based on

Application Independent Flexibility Assessment and Forecasting for Controlled EV Charging

109

a Gaussian modeling approach. They evaluated their

approach on data of the NREL’s Secure Transporta-

tion Data Project, and found that the number of ve-

hicles that will depart in a 15-minute time interval

can be predicted with high conﬁdence (around 95%).

For commercial infrastructure with small amounts of

charging points (<20) it was shown through the exam-

ple of a campus that for smaller groups of charging

stations the amount of plugged-in vehicles is hard to

predict (cf. (Hrabia et al., 2015)).

In summary, current work on EV ﬂexibility fo-

cuses mainly on very large ﬂeets (a few thousand

EV), where uncertainty through usage is not such a

big issue. For smaller ﬂeets of a few tens or hun-

dreds of EV however, uncertainty is a very impor-

tant issue that needs to be considered and it has been

shown that costs can increase signiﬁcantly due to er-

rors. Hence, there is a motivation to improve forecast-

ing (e.g., compared to the presented results of a naive

forecast). However, there is not much work yet on EV

forecasting. This may be due to a lack of available

datasets on EV ﬂeet usage. All the presented stud-

ies are based on data for combustion engines, or on

simulated data, hence not suitable for actual forecast-

ing evaluation. Further, the studies focus on residen-

tial EV, but arguably commercial EV ﬂeets will much

earlier be used in aggregator applications, as they are

easier to integrate into central control schemes and

businesses are more prone to evaluating cost saving

potentials through controlled charging.

3 CONCEPTUAL BACKGROUND

3.1 Flexibility Modeling

In general ﬂexibility is the possibility to adapt an

electricity consumption proﬁle, e.g. through shift-

ing or simply changing loads. Neupane et al. (Neu-

pane et al., 2015) provide a general taxonomy of ﬂex-

ibility as time ﬂexibility and amount ﬂexibility. Time

ﬂexibility is the possibility of shifting the amount of

energy in time, while amount ﬂexibility is the range

between the minimum and maximum energy demand

at a particular point in time. We believe that for a

generic approach the notion of amount ﬂexibility mat-

ters more, as it is mostly of interest how much load

can be changed upwards or downwards for a certain

time interval and is therefore the ﬂexibility notion

we focus on in this work. Similarly to De Coninck

et al. (De Coninck and Helsen, 2013) in the build-

ing energy management domain, we want to view

ﬂexibility as the possibility to deviate from a refer-

ence scenario within a certain time interval indepen-

dently from the possible changes in other time inter-

vals. Inter-dependencies between intervals of course

exist in reality, for instance, several intervals may be

affected in an optimal schedule. Therefore, viewing

only one interval at a time can be seen as a theoretical

lower and upper bound, which will, for the purpose of

analyzing the potential of a ﬂeet, still give a useful in-

dication. For the EV charging domain, the reference

scenario is the naïve charging case, where the vehicle

charges with the highest possible power for each point

of time, as determined by the infrastructure involved.

Similar to (De Coninck and Helsen, 2013) and (Ne-

upane et al., 2015), we refer to positive ﬂexibility as

increasing load for the considered interval and refer

to negative ﬂexibility as decreasing load, compared to

the reference scenario.

Table 1: Flexibility model parameters.

Parameter Description

l The length of the equally sized inter-

vals i ∈ I. In the context of energy

metering and markets, the intervals

are typically ﬁxed at l = 15 or l = 60

minutes.

S Set of controllable charging sta-

tions for a ﬂeet with parameter p

min

which denotes the conﬁgured mini-

mum charging power.

C A historic set of charging events of

the form (t

arr

dep

, p

max

) : T ×

T ×E ×P.

An ordered set of tuples (i, p) : I ×P

which represents a metered time se-

ries of historic average power val-

ues.

We calculate the ﬂexibility with the two functions

CalculatePosFlexibility : I → P and CalculateNeg

Flexibility : I → P. Here, I denotes a set of equally

sized time intervals with length l. P models the do-

main of power values. A variable of this domain mod-

els the average power for a given interval. The re-

sult of the function is the amount ﬂexibility, that is

the maximum possible change of power within the

considered interval. Table 1 gives an overview over

parameters relevant to calculate the ﬂexibility. This

ﬂexibility is calculated for a ﬂeet, or more speciﬁ-

cally a set of controllable charging stations S of a ﬂeet.

To calculate the ﬂexibility, a historic set of charging

events C has to be provided as well as a metered time

Note, that an inverted notion is sometimes used for ﬂex-

ibility, mainly when generators are considered.

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110

series P

in a regularly sampled interval (e.g., 15 min-

utes or one hour).

pmin

pics = pmax

tarr tdep

i1 i2 i3 i4

pmin

pmax

I / T

tarr tdep

Pics = pmin

pmax

tarr tdep

fics

fics

pics

i1 i2 i3 i4 i5

pics

I / T

Figure 1: Overview of ﬂexibility concepts for example

charging event c.

Figure 1 provides an overview of the nomencla-

ture throughout a typical charging event c. A charg-

ing event is bound by the time of arrival t

arr

(which

we assume to be the plug-in time, as well as start of

charging) and the departure time t

dep

(which we as-

sume to be the plug-out time). The curve presents

an uncontrolled charging curve of the typical shape,

where the load descents towards the end as the inner

battery resistance increases. Domain T denotes points

in time and E denotes amount of energy. e

∈ E

shows how much energy is charged within a charging

event. Further, the ﬁgure demonstrates how we cal-

culate ﬂexibility from the naïve charging case (rep-

resented on the left) for a single charging event in

a speciﬁc interval. On the right it shows the posi-

tive and negative ﬂexibility f

↑

and f

↓

for interval

which is the maximum possible increase (top) or

decrease (bottom) in average load within one consid-

ered interval i (going from naïve charging power p

ics

to controlled charging power p

ics

, for each charging

station s and event c). This value is constrained by

two constants: p

max

and p

min

, where p

max

denotes

the aforementioned maximum charging power of the

naïve case and therefore is deﬁned per charging event

and for each interval, as it is determined by the spe-

ciﬁc car, station and cable used. The charging power

must therefore remain below p

max

for each interval of

the charging event. Secondly, we introduce the mini-

mum charging power p

min

as a constraint, which shall

not be undershot within each interval where the ve-

hicle is connected and the battery could still charge.

This minimum power comes on the one hand from

practical issues, which arise either from the charging

infrastructure, for instance EV may go into a stand-

by mode if electric current is below a certain thresh-

old. On the other hand side, it ensures that even if t

dep

occurs much earlier than expected that at least some

energy was charged. With range anxiety being one of

the main inhibitors of EV spreading, we therefore de-

sist from allowing the full degrees of freedoms within

the control band, which is also the most common type

of controlled charging currently in practice. From our

prior experience with different e-mobility ﬂeets and

their use cases, such as car sharing, home care, deliv-

ery or company vehicles, as well as from the current

state in the industry, we ﬁnd that further neither the

current state-of-charge (SoC) of the battery, nor the

disposition data of the vehicles should be assumed to

be known to a central optimization. The reasons range

form lack of standard protocols, lack of processes and

privacy concerns.

Positive Flexibility. We want to present more in de-

tail how we calculate positive ﬂexibility, the max-

imum possible increase in average load within one

considered interval i which can be calculated indepen-

dently per charging event c and station s:

↑

ics

= p

ics

−p

ics

, p

ics

> p

ics

(1)

The charging power p

ics

is as stated constrained

by p

max

for each considered interval. Therefore, the

following constraint must hold:

↑

ics

<= p

max

−p

ics

(2)

Further, we deﬁned that the total energy e

charged within a charging event should remain unal-

tered. This can be ensured if the amount in the rele-

vant interval i is changed by as much, as the sum of

all changes in all other intervals:

0 = f

↑

ics

−

∑

j∈I\{i}

jcs

−p

jcs

(3)

The downward change in all the other intervals is

then constrained as stated by p

min

. Therefore, with

equation 3, the change upwards within one interval is

constrained as follows:

↑

ics

∑

j∈I\{i}

jcs

−p

min

(4)

So in summary, the maximum change from p

ics

to p

ics

is constrained by either maximum charging

power (equation 2) or the amount that can be de-

creased within the other intervals (equation 4). So we

can deﬁne the maximum positive ﬂexibility for an in-

terval i within a charging event c to be the minimum

of the two:

↑

ics

= min{p

max

−p

ics

;

∑

j∈I\{i}

−p

min

} (5)

Finally, to calculate the total positive ﬂexibility of

all the charging stations:

CalculatePosFlexibility(i) =

∑

s∈S

∑

c∈C

↑

ics

(6)

Application Independent Flexibility Assessment and Forecasting for Controlled EV Charging

111

Negative Flexibility. Similarly, negative ﬂexibility

↓

describes the maximum possible decrease in aver-

age load within one considered interval i:

↓

ics

= p

ics

−p

ics

, p

ics

< p

ics

(7)

It is constrained by the minimum charging power:

↓

ics

<= p

ics

−p

min

(8)

As for positive ﬂexibility, E

should remain con-

stant, therefore:

0 = f

↓

ics

−

∑

j∈I\{i}

jcs

−p

jcs

(9)

Also, the charging power must for all other inter-

vals of the charging event remain below p

max

↓

ics

∑

j∈I\{i}

max

−p

jcs

(10)

Therefore, we can deﬁne the maximum negative

ﬂexibility for an interval i within a charging event c

to be the minimum of the constraints (equations 8 and

10):

↓

ics

= min{p

ics

−p

min

;

∑

j∈I\{i}

max

−p

} (11)

And ﬁnally, to calculate the total negative ﬂexibil-

ity:

CalculateNegFlexibility(i) =

∑

s∈S

∑

c∈C

↓

ics

(12)

3.2 Predictability Modeling

In addition to the amount of ﬂexibility, we are in-

terested in assessing in a second dimension: how

well the amount can be predicted. For most market-

targeted and other energy management use cases the

relevant horizon for forecasting EV load is from a

few hours up to day-ahead which in the load fore-

casting literature is mostly referred to as short-term.

As for electric load in general, EV load is mostly de-

pended on calendar-based independent variables (fea-

tures). Weather-based features may also play a role,

but with a lack of real-world data, this is not satisfac-

torily studied and will most likely vary for different

ﬂeets.

We calculate predictability of positive and nega-

tive ﬂexibility with the function CalculateResiduals :

(I → P) → P, where the input is the ﬂexibility as de-

scribed in section 3.1, and the result corresponds to

the residuals based on the evaluation of a forecasting

model on a test set. The calculation of predictabil-

ity has the parameters in table 2, which are described

in more detail in the following paragraphs. So more

speciﬁcally, given a time series F = {(i

, p

),(i

, p

Table 2: Predictability model parameters.

Parameter Description

A(H ) Forecasting algorithm to use with

hyper-parameters H .

h Forecast horizon to evaluate forecast

on.

Cov Covariate structure to use.

f ore

Forecast time.

f old

∈ N Number of folds for evaluation

scheme.

split ∈

[0,1]

Split of dataset into training and

evaluation parts.

.. .,(i

, p

)}, where the values of p are the values of

calculated ﬂexibility as described above (either posi-

tive or negative), we split the available data at thresh-

old split into a training set of intervals F

and an

evaluation set F

. Then the features are engineered

according to Cov. The forecasting algorithm A(H )

is trained and iteratively applied to produce fore-

casts of horizon h at forecast time t

f ore

. The fore-

cast

F = {(i

),(i

), . ..,(i

)} is then com-

pared against the actual series to calculate residuals

R = {(i

, p

−

),(i

, p

−

), . ..,(i

, p

−

)}.

Forecasting Algorithms. We treat the problem of

forecasting ﬂexibility of small EV ﬂeets similarly to a

load forecasting problem for buildings. As shown in

the aforementioned survey (Martínez-Álvarez et al.,

2015), the most popular algorithms applied are arti-

ﬁcial neural networks (ANN), support vector regres-

sion (SVR) and multiple linear regression (MLR), and

each may perform better on different datasets (e.g.,

different level of aggregation). We will hence in-

clude these as well as other non-linear regression al-

gorithms and compare all against two simple bench-

marks which should present the lower bounds. Each

of the algorithms has hyper-parameters which inﬂu-

ence the performance of the algorithms. We ﬁne-tune

the selection of these parameters using grid search

and the cross validation scheme as described below.

The algorithms A and their respective most important

hyper-parameters H to tune are the following:

• Naïve Last Day Type (Na¨ıve(τ)): A simple bench-

mark model that predicts the value based on the

value of the same time of day from the pre-

vious day of the same day type as determined

by τ. It is expected to be the lower bound of

forecasting accuracy. The parameter τ could be

workday/¬workday, weekday/weekend or day−

o f −week.

• Middle 4–of–6 Day Type (Middle4o f 6(τ)): An-

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112

other simple benchmark that predicts the value for

an hour of the day based on the mean value of

the same hour of the past 6 days of the same day

type as determined by τ, ignoring the minimum

and the maximum value. The parameter τ could

be workday/ ¬workday, weekday/weekend or

day −o f −week.

• Ridge Regression (MLR(r)): Multiple linear re-

gression with l2 regularization and ridge parame-

ter r.

• K-nearest neighbors (kNN(k)): A regression

scheme that predicts based on the nearest k neigh-

bors. If k > 1 the mean of the cluster is used.

• Gaussian Processes (GP(l, K)): A probabilistic

regression scheme based on ﬁtting multivariate

Gaussian distributions. With a noise level l and a

Kernel K with hyper-parameters. Here, the radial

basis function (RBF) kernel with parameter γ and

the polynomial kernel with maximum exponent e

are applied.

• Artiﬁcial Neural Network (ANN(α,m,n,(h

)

i=1

)):

A regression scheme that uses backpropagation to

train the weights of a network of nodes that are

activated by a sigmoid activation function. The

backpropagation algorithm is parameterized with

a learning rate α and a momentum m. Further, the

amounts of hidden nodes n have to be speciﬁed

being the number of hidden neuron on hidden

layer i).

• Support Vector Regression (SV R(c,K)): Support

Vector Machine for regression with complexity

constant c and a kernel K analogous to the Gaus-

sian Process.

As most of the algorithms are only capable of

learning one dependent variable (the class value)

at a time, we use an iterated (also recurrent or

closed-loop) prediction scheme to produce multiple-

step ahead forecasts. That means in order to fore-

cast steps beyond one-step ahead up to horizon h,

t+2

, p

t+3

,. .., p

t+h

, the previous forecasted values

t+1

, p

t+2

,. .., p

t+h−1

are used as input.

Feature Modeling. As stated above, assuming no

other external available data such as booking times,

we can base our prediction mainly on the histori-

cal consumption and the dependency on its historic

values (autocorrelation) and calendar-based features,

as well as weather information. Table 3 gives an

overview of the proposed features. These should be

chosen according to the speciﬁc requirements of the

application and the speciﬁc ﬂeet data as shown in sec-

tion 4.3 applying cross-validation as described in the

Table 3: Proposed input features.

Feature Deﬁnition

Short-term lags p

t−1

, p

t−2

,. .., p

t−(60/l)·lag

short

Medium-term

lags

t−(60/l)·24

, p

t−(60/l)·48

.. ., p

t−(60/l)·lag

med

Hour of day hr ∈{0, 1,. ..,23}

Day of week d ∈ {1, 2,...7}

Month of year m ∈ {1, 2,...12}

Weekday or not w ∈ {weekday,¬weekday}

Temperature Temp

i−1

following paragraph. Therefore, we add lagged val-

ues of consumption to Cov. For very short-term fore-

casting the lagged consumption of the recent time in-

tervals up to lag

short

are most important. Electric load

forecasting data exhibit typically daily and weekly

seasonality, so that any lagged values lag

med

of the

same time of the day within a sliding window of one

week may be relevant features. Additionally, some

calendar-based variables are included as categorical

labels. At minimum the hour of the day hr and the

day of the week d should be included. If the data

spans several months the month of the year m should

be included. If holiday data is available a variable

may be used to model workdays and non-workdays

w. If available, we propose to add the lagged tem-

perature Temp

i−1

, if the ﬂeet under consideration is

in the same region and data is available. For the ma-

chine learning algorithms these categorical variables

are one-hot encoded (dummy encoded) and all nu-

meric features are normalized (scaled to the interval

of [0,1]). Depending on the residual characteristics,

transformations of the load data may be considered.

Evaluation Scheme. A classic approach to time se-

ries forecast evaluation is out of sample (OSS) ap-

proach, where a model is ﬁtted (trained) on a ﬁrst part

of the data and then iterativly evaluated on a second

part. Per iteration a forecast is produced and error

metrics are calculated. When using highly non-linear

predictive models n-fold cross-validation (CV) is a

common good practice to evaluate the generalization

of the model to an independent dataset. However, the

general scheme of splitting up the dataset randomly

into training and evaluation parts has been shown to

be problematic for time series data, as the folds may

no longer be i.d.d. (cf. (Bergmeir and Benítez, 2012)).

However, a "blocked" CV scheme, where large parts

of the data remain together, may still improve upon

the OOS scheme and could be used. We propose to

utilize a time series speciﬁc blocked cross-validation

scheme (TSCV), where at any moment only blocks of

Application Independent Flexibility Assessment and Forecasting for Controlled EV Charging

113

the past are used to train the model, which basically

simulates forecasting operation, were future blocks

would not be available. The size of each block could

be any length, but should best be chosen according

to typical calendar intervals, such as days, weeks or

months, depending on the size of the dataset, the fore-

cast horizon h and the highest lagged value lag

med

More speciﬁcally each block should be considerably

larger than the sum of the highest lag and the horizon.

Evaluation Metrics. To assess the predictability vi-

sually, mostly the actual residuals are used, as this ab-

solute measure allows for better comparison with the

ﬂexibility results, and is most intuitively interpretable

from the application side. Therefore, we propose to

report the mean absolute error (MAE) if scores are

needed. However, to compare performance of the

algorithms on one speciﬁc dataset we propose as is

common, to use root mean square error (RMSE). To

compare the performance across datasets scale inde-

pendent measures should be reported. Due to the in-

termittency of the ﬂexibility time series and the many

actual values of zero, the relative measure mean ab-

solute percentage error (MAPE) is not deﬁned. For

the symmetric MAPE (sMAPE), also the denomina-

tor tends to be too close to zero, making the calcula-

tion unstable (cf. (Hyndman, 2006) for a discussion

of forecasting error metrics). We propose to use the

scale independent metric coefﬁcient of variation of

the RMSE, the CV(RMSE), which is deﬁned as fol-

lows, with

F the mean of the ﬂexibility values:

CV (RMSE) =

RMSE

(13)

4 EXAMPLE CASE STUDY

4.1 Dataset

We want to give an example assessment of ﬂexibil-

ity and its predictability using the introduced models

within a case study. We have no complete suitable

real-world dataset at hand, but we merged two pri-

vate real-world datasets Charging Events and Charg-

ing Metering and add some additional static informa-

tion based on suitable assumptions (Charging Station

Information). The ﬁrst contains data of 214 differ-

ent charging points operated by a German distribu-

tion grid operator over the course of a year (2013) in

two different German cities. It contains event-based

information for in total 25,462 charging events (cor-

responding to C), most interestingly for us plug-in

and plug-out times, as well as the amount of energy

charged per charging event (t

arr

dep

). The sec-

ond dataset consists of 497 metered charging curves

which we collected within different research projects

of the International Showcase of Electric Mobility

(Berlin-Brandenburg), and are hence of a variety of

different types of mostly unknown vehicles. These

charging curves represent P

and are associated to

the charging events so that it best ﬁts to the charged

amount e

of the charging event. In absence of any

recorded information regarding p

max

(which could be

communicated via charging protocols), here the max-

imum metered value of an event is assumed to be the

maximum. Third we needed to add some static in-

formation to the charging stations, most importantly

the minimum charging power allowed p

min

. Here

we used different thresholds p

min

= 1.2kW, p

min

2.4kW and p

min

= 4.2kW. 1.2 kW and 4.2 kW cor-

respond to about 6 Ampere in 230 V/1-phase and

400 V/3-phase systems. These are to typical techni-

cal threshold in mode 2 systems. We also compiled a

mixed set with 1.2 kW and 2.4 kW, where the thresh-

olds where assigned randomly as it best ﬁts the data.

This mixed set is used below, when no other informa-

tion is given.

4.2 Flexibility Case Study

Figures 2a and 2b demonstrate how positive and neg-

ative ﬂexibility compare to the whole available load.

They are the mean positive and negative ﬂexibility for

all Mondays (ﬁg. 2a) and all Sundays (ﬁg. 2b) in

the dataset, so over a year and the mixed variation for

min

. It becomes obvious that for our dataset most

ﬂexibility is available from around noon, where also

average loads reach a maximum of around 50kW, and

into the evening where loads are decreasing. Here it

seems that the data does not come from private house-

holds, where one would expect larger peaks around

6-8 p.m. On Sundays the load is a lot lower peaking a

little later than on Mondays at 20kW. Loads and ﬂex-

ibility are quite low in the middle of the night, around

3-6 a.m., which is the time when the connected vehi-

cles are all charged to their maximum capacity. Fig-

ure 2 shows the distribution of positive and negative

ﬂexibility per interval for all Mondays (ﬁgure 2c) and

all Sundays (ﬁgure 2d) in the dataset, so over a year

and the mixed variation for p

min

. It becomes obvious

that for our dataset most ﬂexibility is available from

around noon, where also average total loads reach a

maximum of around 50 kW (not shown here due to

space issues), and into the evening where loads are

decreasing. Here it seems that the data does not come

from private household charging stations, where one

would expect larger peaks around 6-8 p.m. On Sun-

SMARTGREENS 2018 - 7th International Conference on Smart Cities and Green ICT Systems

114

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

Power (kW)

↑

↓

(a) Mean pos. and neg. ﬂexibility in comparison to total load

for all Mondays.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

Power (kW)

↑

↓

(b) Mean pos. and neg. ﬂexibility in comparison to total load

for all Sundays.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

Power (kW)

↑

↓

Mondays (l = 60min).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

Power (kW)

↑

↓

(d) Distribution of pos. and neg. ﬂexibility per interval for

Sundays (l = 60min).

Figure 2: Flexibility case study results.

days the load is a lot lower peaking a little later than

on Mondays at 20 kW (also not shown). Loads and

ﬂexibility are quite low in the middle of the night,

around 3-6 a.m., which is the time when the con-

nected vehicles are all charged to their maximum ca-

pacity. The highest ﬂexibility is also around the early

afternoon and it lags the highest value of power by

few hours. Also, positive ﬂexibility is just slightly

higher than negative ﬂexibility, at around 7-8 kW pos-

sible increase or decrease and is lowest in the hours

between 3-5 a.m. with mean ﬂexibility close to 0 kW.

It is further interesting to see: while the mean is quite

similar for Mondays between 1 p.m. and 5 p.m., the

variance is increasing in these intervals. When com-

pared with the loads, it becomes obvious that for our

data the mean ﬂexibility for this ﬂeet is only slightly

higher on Mondays as compared to Sundays, while

the difference in total load is much more signiﬁcant.

4.3 Predictability Case Study

As for ﬂexibility, we will evaluate the predictability

modeling on the real world dataset as described above

in section 4.1. We want to compare all the different

forecasting algorithms A(H ). If not otherwise stated,

the analyses are done on the full set of 214 charging

stations with the mixed p

min

and l = 60min. The fore-

casting is implemented in JAVA and is based on the

WEKA

machine learning library to implement the

machine learning models, as well as the benchmark

models described in section 3.2.

Figure 3 shows the yearly proﬁle of hourly val-

ues of positive and negative ﬂexibility, as well as the

weekly proﬁle of a random week. It can be seen

that there are as expected clear daily and weekly pat-

terns. Most days have peaks around the early af-

ternoon and in the evening. There is no obvious

strong yearly pattern for our data. We analyzed auto-

correlation and found that there is signiﬁcant cor-

relation in the lags preceding the current time, as

well as in all lags that are multiples of 24 hours for

both positive and negative ﬂexibility. We therefore

include the lagged consumption of the last 3 hours

which is most valuable for short-term forecasts and

then the multiples of 24 hours within a window of a

week. Unfortunately we cannot easily associate the

dataset with weather information, as the charging sta-

tion locations are within at least two different Ger-

http://www.cs.waikato.ac.nz/˜ml/weka/

Application Independent Flexibility Assessment and Forecasting for Controlled EV Charging

115

Jan-14 Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14

local

ime

Power (kW)

↑

↓

Mon, 12:00 Tue, 12:00 Wed, 12:00 Thu, 12:00 Fri, 12:00 Sat, 12:00 Sun, 12:00

Power (kW)

Figure 3: Yearly (top) and weekly (bottom) proﬁle of positive and negative ﬂexibility.

Mon, 12:00 Tue, 12:00 Wed, 12:00

Power (kW)

Actual

kN N

Middle4of6

Na¨ıve

Figure 4: Comparison of forecasts.

man cities. For similar reasons we could not asso-

ciate the data with local holiday information, which

could also be done in future improvements. Further

we add the hour of the day, the day of the week

and the month of the year as additional covariates,

so Cov = {p

t−1

, p

t−2

, p

t−3

, p

t−24

, p

t−48

, p

t−72

, p

t−96

t−120

, p

t−144

, p

t−168

,hr,d,m}.

In a ﬁrst run we compared the performance of the

algorithms on the raw dataset, for day-ahead forecast-

ing with h = 24, t

f ore

= 00:00. When analyzing the

residuals, we found they exhibit a very skewed dis-

tribution with high heteroscedasticity and non-zero

mean. Changing the complexity parameters of the

learning models could weaken the high bias slightly,

but usually at the cost of higher RMSE. Therefore, we

decided to apply the models on transformed data. We

explored therefore log transformations, the inverse

hyperbolic sine transformation, as well as the Box-

Cox (box) transformation, which we found improved

residuals the most, while not considerably worsen

forecast results. The Box-Cox transformation is de-

ﬁned as follows:

(

(p+C)

−1

,ifλ 6= 0,

ln(p +C),ifλ = 0

(14)

Here, C = 1 is a shift parameter to avoid logarithm of

zero, λ is a form parameter which is ﬁtted to the data

based on a likelihood function. We ﬁtted it in one

variation to the whole data and in another to the data

excluding zero values, which resulted in λ = 0.21 for

the ﬁrst and λ = 0.3 for the second. The latter vari-

ation improved residual properties the most, so that

the distribution of the residuals only exhibited a slight

skew and slightly fat tails, but was other than that

close to normal using histograms and QQ-plots (not

shown for spatial reasons), which would make most

importantly ﬁtting prediction intervals in this trans-

formed domain a lot easier. However, for both the

Kolmogorov-Smirnov and Shapiro-Wilk test, the hy-

pothesis of a normal distribution has to be rejected at

p-value 0.05. In the following, all analyses are done

on box-transformed data with λ = 0.3.

Table 4 reports results for the comparison of all

the algorithms on the transformed data for day-ahead

forecasting, with n

f old

= 3, split = 0.75 and as be-

fore h = 24, and t

f ore

= 00:00. Here, the learning ap-

proaches can as expected considerably improve upon

the Na¨ıve benchmark model, with the best model im-

proving the MAE by 19.7% and RMSE by 19.3%.

kNN and MLR were performing most robust and with

best-achieved error values and were quite fast with

a second or less for training and just milliseconds

for forecasting on a laptop with 2.69GHz and 12GB

RAM. GP, SV R and ANN which are more complex

algorithms were very prone to overﬁtting and are

hence often performing worse on the evaluation sets.

This becomes for instance obvious when looking at

the best performing kernel, the poly-kernel with low

exponents of 2 and 3.

Figure 4 shows example traces of the actual val-

ues and the predictions on random three days. Here,

kNN shows exemplarily how the learning approaches

SMARTGREENS 2018 - 7th International Conference on Smart Cities and Green ICT Systems

116

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

−10

−5

Power (kW)

↑

↓

(a) Distribution of pos. and neg. errors per interval for Mon-

days (l = 60min).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

−10

−5

Power (kW)

↑

↓

(b) Distribution of pos. and neg. errors per interval for Sun-

days (l = 60min).

Figure 5: Predictability case study results.

Table 4: Comparison of forecasting algorithms on box transformed data.

A kNN MLR GP SV R Middle4o f 6 ANN Na¨ıve

H k = 40 r = 10.0 K =

Poly(e = 3),

l = 5.0

K =

Poly(e = 2),

c = 1.0

weekday/

¬weekday

α = 0.05,

m = 0.2,

n = 1,

= 32

last same

day

↑

MAE 3501.1 3505.7 3544.7 3635.6 3690.1 3736.7 4362.1

RMSE 5249.7 5460.5 5647.3 5339.2 5369.8 5965.1 6499.3

train

0.18 1.25 430.50 70.68 0.02 43.29 0.01

pred

0.038 0.024 0.06405 0.04019 0.003 0.016 0.001

↓

MAE 3486.5 3511.9 3556.7 3635.6 3833.7 3556.6 4323.9

RMSE 5523.1 5529.6 5646.6 5339.2 5687.9 5663.0 6368.0

train

0.20 1.10 487.48 95.56 0.01 64.49 0.01

pred

0.042 0.021 0.06037 0.05617 0.003 0.017 0.001

25 50 100 200

|S|

CV(RMSE)

0.0

0.5

1.0

1.5

2.0

Mean Flexibility

F (kW)

Figure 6: Comparison of different sizes of charging stations.

1 2 3 4 5 6 7 8 9 10 11 12

−0.2

0.0

0.2

0.4

0.6

0.8

1.0

MAE (kW)

00:00

06:00

12:00

18:00

Figure 7: Comparison of errors for different horizons, pre-

sented as difference from the day-ahead errors.

tend to underestimate the values more often when

compared to the benchmarks, but so avoiding higher

penalties due predicting peaks at times, where there

are none. One such example is presented on Monday,

where the Na¨ıve forecaster predicts very high peaks

based on the same day one week ago. It also shows

that the Middle4o f 6 does not forecast the peak, as

it averaged out this high peak. It generally predicts

higher values than the learning approaches. Figure

5 allows a visual predictability assessment, by show-

ing the errors per hour and for the whole dataset and

determined by the kNN algorithm for Mondays and

Sundays. Here, variability is slightly less for week-

ends and is typically higher for negative ﬂexibility.

Errors are also highest for the time were ﬂexibility

is typically highest, around noon and in the evening.

The forecasts are less biased on the weekend when

compared to the weekdays. Figure 6 shows how the

forecast accuracy changes for different sizes of the

dataset. Here, four different sizes of datasets were

randomly generated (25, 50, 100 and 200). While

mean ﬂexibility scales as expected linearly with size,

the forecasting accuracy, expressed by CV(RMSE),

Application Independent Flexibility Assessment and Forecasting for Controlled EV Charging

117

decreases exponentially, with relatively higher errors

for smaller sets. Figure 7 shows how errors behave

over different horizons for different times of the day

when compared to a day-ahead forecast without any

short-term lags. During the day, the forecast can be

improved by as much as an average 1kW compared

to the day-ahead forecast for the same time, conﬁrm-

ing the importance of the short-term lags. This effect

is signiﬁcant for horizons of around 3-4 hours.

5 CONCLUSION

With the goal to implement a generic ﬂexibility as-

sessment framework for EV aggregators to analyze

EV ﬂeets and charging stations regarding their ﬂex-

ibility, we developed a ﬂexibility model incorporat-

ing our project experience and reﬂecting current con-

trolled charging strategies in the industry. It does not

allow for complete rescheduling of charging events,

but only for controlling load within a control band.

We note that the model can only be used retrospec-

tively, as e.g. for planning ahead, uncertain data such

as arrival times would have to be forecasted (which

is current work in project Mobility2Grid), or have

to be provided by charging protocolls such as ISO

15118. But as the speciﬁc operation would differ any-

how for each use-case, we focused on an application-

independent model that would still give a useful in-

dication to a ﬂeet operator about ﬂexibility charac-

teristics of its ﬂeet. For instance, in the case study

on real-world data, we found that up- and downwards

ﬂexibility per interval have a similar magnitude and

lag the peaks in load by few hours. As expected the

available amount differs for weekdays and weekends

and is highest in the afternoon. We further ﬁnd that

it is unexpectedly low for the high number of charg-

ing points. This can be explained by the data being

recorded in a year with not yet much electric trafﬁc in

the considered cities, and therefore a lot of charging

stations with few charging events. Regarding uncer-

tainty, we conﬁrmed that for smaller amounts of EV,

uncertainty is quite high. We further found that learn-

ing approaches can improve upon the simple bench-

mark by almost 20% (considering mean absolute er-

rors), and that less complex models such as ridge

regression and kNN regression perform more robust

than more complex models such as ANN, SVR and

Gaussian Processes for hourly data without tempera-

ture inﬂuences. Currently, there are unfortunately no

publicly available datasets on EV ﬂeet and charging

station usage. Some work on predicting EV usage

was done by deriving conclusions from combustion

engine cars. More real-world data is needed to im-

prove research in this area and also to evaluate our

approach more thoroughly and for other ﬂeets. To

further improve forecasts it could help to train differ-

ent models for different parts of the day (e.g. each

hour, or day and night), the week (e.g., per day, per

weekend) or even for different parts of the ﬂeet, as

forecasts tend to be very biased in certain situations.

This could also be done automatically, by ﬁrst clus-

tering the data, similar to the approach by Wijaya

et al. (Wijaya et al., 2015) for households, or mix-

ture models could be utilized. More features such

as other weather variables, or EVSE backend infor-

mation (e.g. ID of vehicles) could be used. Here,

privacy-preserving data-management strategies are an

interesting research direction. The ﬂexibility model

could be extended for instance to allow calculation for

multiple intervals and also to model vehicle-to-grid

schemes. The concepts have been implemented as a

web-based tool prototype within the research project

EVA service company (Electric Vehicle Aggregator)

to demonstrate how they could be applied by aggre-

gators to optimize their portfolio or choose the right

market scheme.

ACKNOWLEDGMENT

The work in this paper has been partially funded

from research projects EVA service company (Electric

Vehicle Aggregator) funded by EIT Digital, as well

as project EUREF Forschungscampus Mobility2Grid

(FKZ: 03SF0520A).

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