Received: 17 April 2021 - Revised: 16 May 2021 - Accepted: 18 May 2021 - IET Electrical Systems in TransportationDOI: 10.1049/els2.12028
CA S E S TUDY
Short‐term load forecasting at electric vehicle charging sites
using a multivariate multi‐step long short‐term memory: A case
study from Finland
Tim Unterluggauer1,2,3 | Kalle Rauma2 | Pertti Järventausta1 | Christian Rehtanz2
1Unit of Electrical Engineering, Tampere University, Abstract
Tampere, Finland This study assesses the performance of a multivariate multi‐step charging load prediction
2Institute of Energy Systems, Energy Efficiency and approach based on the long short‐term memory (LSTM) and commercial charging data.
Energy Economics, TU Dortmund University,
Dortmund, Germany The major contribution of this study is to provide a comparison of load prediction be-
3 tween various types of charging sites. Real charging data from shopping centres, resi-Department of Electrical Engineering, Technical
University of Denmark, Denmark dential, public, and workplace charging sites are gathered. Altogether, the data consists of
50,504 charging events measured at 37 different charging sites in Finland between January
Correspondence 2019 and January 2020. A forecast of the aggregated charging load is performed in 15‐
Kalle Rauma, Institute of Energy Systems, Energy min resolution for each type of charging site. The second contribution of the work is
Efficiency and Energy Economics, TU Dortmund the extended short‐term forecast horizon. A multi‐step prediction of either four (i.e., one
University, Emil‐Figge‐Str. 76, 44227 Dortmund,
Germany. hour) or 96 (i.e., 24 h) time steps is carried out, enabling a comparison of both horizons.
Email: kalle.rauma@tu-dortmund.de The findings reveal that all charging sites exhibit distinct charging characteristics, which
affects the forecasting accuracy and suggests a differentiated analysis of the different
Funding information charging categories. Furthermore, the results indicate that the forecasting accuracy
The German Federal Ministry of Transportation and strongly correlates with the forecast horizon. The 4‐time step prediction yields consid-
Digital Infrastructure
erably superior results compared with the 96‐time step forecast.
Open access funding enabled and organized by
Projekt DEAL.
1 | INTRODUCTION could facilitate the seamless integration of intermittent
renewable energy sources into the power grid [5–7]. A large
In 2017, the transport sector was responsible for 27% of all number of EVs could also benefit transmission system
greenhouse gas emissions in the European Union, with pas- operators by providing their flexibility in the form of a control
senger cars accounting for 44% of the transport emissions [1]. reserve to the energy market [8, 9], or assist distribution system
Electric vehicles (EVs) are one of the solutions to cut carbon operators in terms of voltage regulation, congestion manage-
emissions in the transport sector and achieve the climate ment, peak shaving, and valley filling measures [10–12].
protection goals. Other related concerns, such as urban air For both cases, an accurate short‐term EV charging load
pollution and its impact on health, have also encouraged pol- forecast is of utmost importance. For grid operators, the
iticians to promote the adoption of EVs [2]. aggregated charging load forecast is relevant to detect bottle-
The resulting anticipated large‐scale EV rollout represents necks in the distribution grid at an early stage and initiate
both a considerable challenge and an opportunity for the po- appropriate measures [13]. Aggregators, who aggregate a large
wer system. On the one hand, the simultaneous charging of a number of EVs, also rely on accurate capacity predictions to be
large number of EVs could lead to severe bottlenecks in the able to market EV flexibilities in the energy market for ancil-
distribution network, requiring costly grid upgrades [2–4]. On lary services [4, 14].
the other hand, EVs could also benefit the power system by With this motivation in mind, this work introduces a novel
providing ancillary services. Due to their fast‐response ability, charging load prediction application based on the long short‐
high degree of flexibility, and energy storage capacity, EVs term memory. A multivariate multi‐step forecasting approach
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is
properly cited.
© 2021 The Authors. IET Electrical Systems in Transportation published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.
IET Electr. Syst. Transp. 2021;1–15. wileyonlinelibrary.com/journal/els2 - 1
2 - UNTERLUGGAUER ET AL.
is presented, which considers important determinants of the predictions. Compared to their linear counterparts, non‐linear
load curve as multivariate inputs and allows the forecast of the approaches rely on non‐linear functions to capture more
whole prediction horizon in a single computation. complex time series behavior. Study [20] applies four different
The subsequent parts of this paper are organised as fol- algorithms, namely the RF, support vector regression (SVR),
lows. Section 2 presents the state of the art in recent studies. time weighted dot product based nearest neighbor
Section 3 deals with the basics of LSTMs and the origin of the (TWDPNN), and MPSF for 24‐h charging load forecasting.
data used in this work. Section 4 introduces the methodology The evaluation is based on two different datasets – charging and
of the charging load forecast. Section 5 presents the results, station measurements. The most accurate predictions based on
which are further discussed in Section 6. Conclusions and di- the charging measurement are achieved by using the TWDPNN
rections for future research are provided in Section 7. approach, whereas the MPSF provides the most precise results
for the station measurement dataset. An approved RF algo-
| rithm is applied to predict the EV charging load of single and2 RELATED RESEARCH grouped EV charging stations in [21]. The analysis reveals that
in contrast to an aggregated prediction, more precise results are
In this section, a literature review of the state of the art in the obtained while performing individual forecasts.
field of EV short‐term charging load forecasting is conducted Moreover, considerable attention has been paid to artificial
to identify the shortcomings in previous research and highlight neural networks (ANNs) lately. The predictive performance of
the contributions of this work. different neural networks (NN) is frequently addressed in the
literature [22–25]. Article [22] performs a 24‐h charging load
2.1 | Linear methods forecast based on historical driving patterns. Three different
ANNs – a simple ANN, a rough artificial neural network
Linear forecasting approaches use linear functions to model (R‐ANN), and a recurrent rough artificial neural network
time series behaviour. Popular methods include autoregressive, (RR‐ANN) – are deployed and compared to a Monte Carlo
moving average, autoregressive moving average, and autore- simulation (MCS). RR‐ANNs generate the most accurate pre-
gressive integrated moving average (ARIMA) processes. Con- dictions. In [23], a novel reinforcement learning technique is
cerning the prediction of the EV charging load, ARIMA introduced to forecast the EV charging load under three sce-
models in different versions are particularly popular among all narios – uncoordinated, coordinated, and smart charging. The
linear approaches. A plain ARIMA model is introduced in [15] proposed Q‐learning technique increases the prediction accu-
to forecast the day‐ahead EV charging demand in 15‐min racy compared to a simple ANN and a recurrent neural network
(min) resolution. The prediction error is lowered with larger (RNN). The work carried out in [24] studies the short‐term
aggregation. Another work [16] examines the applicability of charging load predictability of four different types of ANNs
an ARIMA model to predict the EV charging demand of the – a deep neural network (DNN), an RNN, an LSTM, and a
next 24 h (h). The proposed decoupled forecaster, which gated recurrent unit (GRU). GRUs with one hidden layer
independently predicts the charging demand and the conven- achieve the most accurate prediction results. Study [25] pro-
tional electrical load, significantly reduces the prediction error vides a further evaluation of different ANN approaches for
compared to an integrated forecaster. super short‐term charging load forecasting. The predictive
The works in [17–19] present a more sophisticated version performance of a simple ANN, an RNN, an LSTM, a bidi-
of the ARIMA model. While paper [17] introduces a fractional rectional LSTM, a GRU, and a stacked auto‐encoder (SAE) are
autoregressive integrated moving average (FARIMA) model, analyzed. The LSTM yields the best performance in both case
article [18] proposes several seasonal autoregressive integrated studies – the charging in public and at commercial buildings.
moving average (SARIMA) approaches for EV charging load Similar to the results in [25], articles [26–28] demonstrate the
forecasting. The FARIMA model outperforms various ARIMA superior performance of the LSTMs for EV load forecasting.
models for all forecast horizons up to 120 min. The SARIMA The study in [26] develops an LSTM for single‐step predictions.
models achieve superior results compared to a persistence The analysis demonstrates that the LSTM outperforms a simple
forecast and a modified pattern sequence‐based forecast ANN, both for a forecast horizon of 15 and 30 min and that the
(MPSF). Similar to the work in [18], study [19] introduces two prediction error diminishes with decreasing forecast horizon.
seasonal autoregressive integrated moving average models with Another LSTM forecasting approach is presented in [27]. The
exogenous variables (SARIMAX). Compared to a random work considers four types of EVs – private and commercial EVs,
forest (RF) and gradient boosted regression tree (GBRT) electric busses, and electric taxis. Based on the MCS, the LSTM
model, the SARIMAX models outperform both machine outperforms a backpropagation (BP) network and SVR. Paper
learning algorithms for different forecast horizons. [28] proposes an LSTM‐based approach with hybrid classifica-
tion to forecast EV travel behaviour and their electrical demand.
Compared to copula, quasi‐MCS, and MCS, the novel approach
2.2 | Non‐linear methods improves the forecast accuracy, thus, resulting in lower EV
aggregator costs. The research in [29] presents a hybrid model of
Contrary to the results in [19], several studies indicate a superior extreme gradient boosting and LSTM for domestic charging
performance of non‐linear methods for EV charging load station load forecasting. Multivariate inputs are used to predict
UNTERLUGGAUER ET AL. - 3
the EV consumption in the next period. Study [30] proposes a � Comparing and assessing the forecasting accuracy at
hybrid approach of a deep belief network (DBN) and the LSTM different categories of charging sites which exhibit different
network for short‐term EV load prediction. The LSTM‐DBN charging characteristics, and
achieves superior forecasting results compared to a single � Using a large amount of high‐quality charging data from
DBN and single LSTM. various commercial charging sites.
2.3 | Hybrid methods 3 | DESCRIPTION OF THE DATASET
AND LSTM
Similar to studies [29, 30], other hybrid approaches as com-
pounds of different models have gained great popularity in This section deals with both the characteristics of the real
recent studies. Paper [33] combines a deterministic bottom‐up charging data used in this work and the LSTM fundamentals.
approach with a probabilistic RF model for the short‐term
forecast of the aggregated load of 46 privately owned EVs in
Austin, Texas. The proposed model shows superior perfor- 3.1 | Introduction of the dataset
mance compared to a persistence forecast, but similar to a
GBRT model. The study in [31] combines a least squares This study is based on real charging data of 50,504 slow
support vector machine (LSSVM), fuzzy clustering (FC), and a charging events with a maximum capacity of 22 kW, measured
wolf pack algorithm (WPA) to predict the load of electric bus at 37 different charging sites in Finland between January 2019
charging stations. The FC‐WPA‐LSSVM model outperforms a and January 2020. While the smallest charging site contains less
WPA‐LSSVM, a regular LSSVM and a BP‐NN. Article [32] than 10, the largest one features nearly 300 charging stations.
proposes another hybrid approach, combining a lion algorithm An overview of the characteristics of the charging data is
with the niche immune (NILA) and a convolutional neural illustrated in Table 2.
network (CNN), for short‐term EV charging load forecasting. The charging events are clustered according to the four
Taking into account the multivariate inputs, the NILA‐CNN categories of charging sites selected for this work. The data for
shows superior performance to a single CNN, a lion algo- the first category, the charging at shopping centres (SCc), stems
rithm, CNN, and an SVM. The work in [34] introduces a from one charging site. The charging events of 21 sites are
hybrid model, based on wavelet decomposition (WT), con- assigned to the second category named residential charging
volutional neural networks, and probabilistic queuing, for day‐ (REc), representing the charging at home. The third category,
ahead charging load predictions. The WT‐CNN outperforms a public charging (PUc), covers the charging at car parks that can
BP‐NN, an SAE, an RNN, an SVR, a time‐delayed neural be used by all EV drivers. The last category, workplace
network (TDNN), and a growing DBN. charging (WOc), refers to EV charging at company premises
that can only be used by the staff working in the vicinity. Eight
| and seven sites are assigned to PUc and WOc, respectively.2.4 Research gaps and contributions of
this work
|
Table 1 outlines the main findings of the literature review. All in 3.2 Long short‐term memory
all, three major limitations can be summarised. The studies
either lack real charging data [16, 17, 22, 23, 27] or the data The charging load of EVs is typically subject to strong time
employed is outdated, making it difficult to transfer the results dependencies as the load corresponds to cyclical and seasonal
to today's strongly changed situation in terms of a larger patterns. The LSTM is able to overcome the vanishing or
number of EVs, different charging powers, and the altered exploding gradient problem of RNNs, and to learn both
utilization of EVs [15, 18–20, 33, 34]. Moreover, most of the long‐term and short‐term dependencies, thus making it an
works only perform single‐step predictions [16, 20, 21, 23–27, ideal choice for this work [35]. The ability to learn temporal
29, 31, 32] which limits the scope of practical applications due correlations stems from the unique structure of an LSTM
to the short forecast horizon. Lastly, although in Ref. [25] it has cell, illustrated in Figure 1. The LSTM at a single ts t consists
been indicated that the achievable prediction accuracy may be of three gate units, namely the forget f t, input i t, and output
dependent on the type of charging, no attention has been paid gate ot.
to the analysis and comparison of different charging sites. The functionality of the LSTM cell can be expressed
This work contributes to the identified research gaps in the mathematically by the following formulas [36]
following ways:
 �
� Introducing a novel multivariate, multi‐step LSTM applica- f t ¼ σ W f ;xxt þW f ;hht−1 þ bf ð1Þ
tion, which significantly extends the existing short‐term
forecast horizon by providing a 4‐time step (ts) or 96‐ts  �
prediction at once, i t ¼ σ W i;xxt þW i;hht−1 þ bi ð2Þ
4 - UNTERLUGGAUER ET AL.
TABLE 1 Literature review on studies addressing the issue of short‐term EV charging load forecasting
Baseline Superior Reso‐ Data Data origin
Year ref. Proposed model(s) model(s) model Forecast approach Lution characteristics [year]
2016 [16] ARIMA – Decoupled 24‐h (single‐step) 1‐h Travel behaviour USA
forecast
2016 [20] MPSF, SVR,RF, – MPSF, 24‐h (single‐step) 1‐h Charging &Station UCLA (USA)
TWDPNN TWDPNN records [Dec 2011 ‐
Feb 2014]
2016 [17] FARIMA ARIMA FARIMA 2‐h 1.2‐min Travel behaviour Seattle (USA)
2017 [18] SARIMA MPSF,Persistence SARIMA 1‐, 2‐, & 24‐h 1‐h Charging data California (USA)
(aggregated) [Jan 2011 ‐
Jan 2013]
2018 [31] FC‐WPA‐LSSVM BP‐NN, LSSVM, FC‐WPA‐ 24‐h (multivariate & 1‐h Electric bus Baoding (China)
WPA‐LSSVM LSSVM single‐step) charging data [2017]
2018 [32] NILA‐CNN CNN, SVM,Lion NILA‐CNN 24‐h (multivariate & 30‐min Public charging Beijing (China)
CNN single‐step) (aggregated) [Jun 2017 ‐
Nov 2017]
2018 [21] RF – – multivariate & single‐ 15‐min Public charging Shenzhen (China)
step (single & aggr.) [2016 ‐ 2018]
2019 [15] ARIMA – – 24‐h 15‐min Non‐residential California (USA)
charging (aggr.) [2013]
2019 [22] ANN, R‐ANN,RR‐ MCS RR‐ANN 24‐h 1‐h Travel behaviour USA [2017]
ANN
2019 [26] LSTM ANN LSTM 24‐h (Single‐step) 15‐ &30‐ Public charging Shenzhen (China)
min (aggregated) [Jul 2017 ‐ Jul
2018]
2019 [25] ANN, GRU, LSTM, – LSTM 1‐, 5‐, & 15‐min 1‐min Public & Shenzhen (China)
RNN, SAE, DNN, (single‐step) commercial [ Jun 2017 ‐
charging (aggr.) Jul 2018]
2019 [24] GRU, bidirectional – GRU 24‐h (multivariate & 1‐h Public charging Shenzhen (China)
LSTMLSTM, single‐step) (aggregated) [Apr 2017 ‐
RNN Jun 2018]
2019 [33] Bottom‐up RF GBRT,Persistence Bottom‐up RF 24‐h (multivariate) – Residential Austin (USA)
charging (aggr.) [2015]
2019 [19] GBRT, RF,SARIMAX Persistence SARIMAX 7‐, 14‐, & 28‐days 24‐h Charging data Netherlands
(aggregated) [ Jan 2012 ‐
Mar 2016]
2019 [27] LSTM BP, SVR LSTM Univariate & single‐ 1‐h Simulated charging –
step data
2020 [23] Q‐learning technique ANN, RNN Q‐learning 24‐h (single‐step) 1‐h Simulated charging –
data
2020 [34] WT‐CNN & BP‐NN, SVR, WT‐CNN 24‐h (multi‐step) 1‐h Traffic flow data England, U.K
probabilistic SAE, TDNN, [ Jan 2014 ‐
queuing model RNN, DBN Dec 2014]
2020 [30] LSTM‐DBN DBN, LSTM LSTM‐DBN Multivariate 15‐min Charging data Liaoning, China
(aggregated) [Jan 2018 ‐
Mar 2018]
2020 [28] LSTM Copula, MCS, LSTM Day‐ahead 1‐h Travel behaviour USA [2017]
quasi MCS
2021 [29] Extreme gradient – – Multivariate & single‐ 1‐h Charging data Jiangsu, China
boosting LSTM step (aggregated) [ Jan 2017 ‐
Dec 2018]
UNTERLUGGAUER ET AL. - 5
TA B LE 1 (Continued)
Baseline Superior Reso‐ Data Data origin
Year ref. Proposed model(s) model(s) model Forecast approach Lution characteristics [year]
2021 This Novel LSTM Comparison of different 1‐h & 24‐h 15‐min Charging data Finland [ Jan
paper implementation charging sites & forecast (multivariate & (aggregated) 2019 – Jan
with multivariate horizons multi‐step) 2020]
inputs and multi‐
step forecast
horizon
Abbreviations: ANN, Artificial neural network; ARIMA, autoregressive integrated moving average; CNN, Convolutional neural network; DBN, Deep belief network; DNN Deep neural
network EV, electric vehicle; FARIMA, Fractional autoregressive integrated moving average; FC, Fuzzy clustering; GRU, gated recurrent unit; LSTM, long short‐term memory; MCS,
Monte carlo simulation; MPSF, modified pattern sequence‐based forecast; NILA, Lion algorithm by niche immune; R‐ANN, rough artificial neural network; RR‐ANN, recurrent rough
artificial neural network; RF, Random forest; SAE, stacked auto‐encoder; SARIMAX, Seasonal autoregressive integrated moving average (with exogenous variables; TWDPNN, time
weighted dot product based nearest neighbour; SARIMA, Seasonal autoregressive integrated moving average; WPA, Wolf pack algorithm.
TABLE 2 Characteristics of the EV charging data
W f ;x, W f ;h, W i;x, W i;h, W o;x, W o;h, W ~c x, and W; ~c;h label
# Charging # Charging weight matrices, bf , bi, bo, and b are bias vectors. Operations
Type of charging sites events Measured period ~cþ and ⊙ denote the element‐wise addition and multiplication,
Shopping centre 1 9283 01.01.19 –31.12.19 and ϕ depicts the tanh activation function. The forget gate de-
Residential 21 10,920 21.01.19–20.01.20 termines which information from the previous cell state, c t−1, is
preserved. The cell state represents the long‐term memory of
Public 8 18,785 31.01.19–30.01.20 the LSTM. The input gate decides which information from the
Workplace 7 11,516 31.01.19–30.01.20 candidate cell state, c~t, is to be used to update the previous cell
state. The output gate controls which part of the new cell state,
Abbreviations: EV, electric vehicle.
c t, to output and pass as the hidden state, ht, the short‐term
memory, to the next LSTM cell. The current input, x t , and
the previous hidden state, ht−1, are multiplied with their
respective weights along the bias vectors form the inputs for all
three gates. The sigmoid function, σ, introduces non‐linear
characteristics to the gates and decides which signals pass the
gates. While a value of zero causes signals to disappear, a value of
one ensures that the signals pass the gate.
4 | METHODOLOGY
The methodology of the proposed multivariate multi‐step
LSTM is shown in Figure 2 and consists of three main
stages – data preprocessing, LSTM implementation and
F I GURE 1 Architecture of an long short‐term memory cell at a single training, and LSTM forecasting. EV, electric vehicle; LSTM,
time step t. long short‐term memory
4.1 | Data preprocessing
 �
c~t ¼ ϕ W c xx t þW c hht−1 þ bc ð3Þ~; ~; ~ The following paragraph details the data preprocessing.
c t ¼ f t ⊙ c t−1 þ i t ⊙ c~t ð4Þ 4.1.1 | Aggregated charging load time series
 � generation
ot ¼ σ W o;xx t þW o;hht−1 þ bo ð5Þ
In the first step, the event‐based charging data is converted
into a time series of aggregated charging load values in 15‐min
ht ¼ ot ⊙ ϕðc tÞ ð6Þ resolution under the assumption of a constant charging power.
6 - UNTERLUGGAUER ET AL.
F I GURE 2 Methodology of the LSTM EV
charging load forecast
The data contains both the plug‐in‐ and power‐to‐zero‐ energy
timestamps and the original amount of energy, energyor , load ¼
or
new ð8Þ
charged for each charging event. Consequently, initially, the tnew
original charging time, tor , in min is derived by measuring the
deviation between both timestamps. In case the power‐to‐
zero‐timestamp is missing due to measurement errors, a 4.1.2 | Multivariate input selection
nominal charging power of 1.8 kW is assumed as most of the
charging events indicate charging at low powers. The original To determine the important features to be fed to the LSTMas
charging time is calculated by dividing the original amount of multivariate inputs to support the detection of interrelation-
energy charged by the assumed charging power. Subsequently, ships, an analysis of the characteristics of the charging load is
since the charging times might change due to the analysis in- carried out. Figure 3 illustrates the development of the
terval of 15 min, the original charging time is adjusted subse- aggregated charging load over the course of a year at all four
quently. If the original charging time lasts less than 15 min, it is categories of charging sites and reveals two particularities. First,
rounded up to a full 15‐min interval. Otherwise, a modulo an increase of the aggregated load over the course of the year
operation, mod, is performed and the modified charging time, can be observed for all charging sites. The strong impact of
tnew, is calculated according to (7). holiday periods on REc, PUc, and WOc marks the second
conspicuity. The Finnish summer holidays in July and the
8 9 winter holidays in December noticeably reduce the load. Both
< 15 tor < 15min = findings support the selection of a month indicator as a feature.
tnew ¼ tor −modðtorÞ modðtorÞ < 7:5min ð7Þ
: ; However, since the data only covers one year, a feature monthtor −modðtorÞ þ 15 else would lead to unknown indicators during the data split and is,
thus, omitted.
Furthermore, the modified charging load, loadnew , of each Figure 4 provides a detailed analysis of the charging sites by
charging process is calculated according to (8) under the visualising the charging load for three different weeks of the
premise of a constant amount of energy charged. Lastly, by year. When comparing the load curve of the first week of
aggregating the calculated load of each charging event, the February (green) with that of the end of November (grey), the
charging load time series is generated, spanning one year with increase in charging load over the course of a year is evident.
96 load values for each day. Moreover, a clear impact of the type of day and time of the day
UNTERLUGGAUER ET AL. - 7
F I GURE 3 Aggregated electric vehicle charging load over the course of one year illustrated for each category of charging site
F I GURE 4 Aggregated charging at each
category of charging site exemplified for three
different weeks
can be seen for REc, PUc, and WOc. The charging load varies 4.1.3 | Scaling and encoding of data
significantly between weekdays and weekends, and the time of
the peak load follows a clear pattern. SCc is the only charging To avoid data leakage, the time series is split into training and
site that exhibits a highly random load pattern. When looking test sets with a 90% to 10% ratio prior to the scaling and
at the purple plot, the influence of public holidays on the load encoding. Furthermore, 20% of the training data is used to
is evident as well. For all charging sites, the load is considerably validate the model performance during training, resulting in a
reduced during the three Christmas holidays. Consequently, to 72% training, 18% validation, and 10% test split.
help the LSTM to detect interrelationships, each load value is To accelerate network convergence and allow the LSTM to
linked to a quarter hour indicator, type of day indicator, and process categorical features, the load is normalised, and the
public holiday indicator, collectively representing the multi- indicators are encoded. The commonly used min‐max scaling
variate inputs to the LSTM. method is used to normalise the load values [37]. The popular
8 - UNTERLUGGAUER ET AL.
one hot encoding technique is used to encode the binary In stateless mode 4, 8, 16, and 32 ts are tested as inputs for the
character of the public holiday indicator [38]. For the quarter 4‐ts forecast, 96, and 192 ts for the 96‐ts prediction. The equal
hour and type of day indicators, sine/cosine encoding is tested amount of input and output ts are applied in the stateful mode.
as well to allow a better representation of the cyclic nature of Subsequently, based on the minimal validation loss, the most
both indicators [39, 40]. suitable approach undergoes tuning.
4.1.4 | Supervised learning framing and reshaping 4.2.1 | Training and hyperparameter tuning
of data implementation
Finally, the data is converted into a supervised learning prob- The LSTM is implemented as illustrated in Figure 5, using the
lem and formatted such that the shape meets the specific Sequential Model in Keras. While indices n denote the number
LSTM requirements. In the first step, the normalised and of input features, indices tin depict the amount of input ts for
scaled data is concatenated into a single array for every 15‐min each sample. Indices tout define the number of predicted load
ts. Using one hot encoding, each ts possesses 106 dimensions values subsequent to the input sequence.
of feature space, this number is reduced to seven while using Table 3 provides an overview of the hp selected for initial
the sine/cosine encoding. training and hp tuning. The tuning, based on a random search,
Subsequently, the data is framed in a supervised learning is performed in hyperopt, a popular library for conducting hp
manner by separating the data into input and output sequences. optimisation in Python. A detailed description of the hyperopt
In this study, two approaches are examined – the stateless and is given in [40]. The number of evaluations is set to 50 and the
stateful mode. The sliding window approach is applied for the seeding is set to one to ensure the comparability between the
stateless mode. In the stateful mode, the data is prepared in different charging sites and reproducibility of the results.
such a way that the fixed input sequences adjoin each other
without overlapping. For both cases, the input data contains
the load value and all indicators for each ts, the output only 4.2.2 | LSTM training process
contains the load to be compared with the predicted load.
In the last step, the data is reshaped in the required 3‐ The training proceeds as follows. The training and validation
dimensional shape, defining the number of samples, the data is shown to the LSTM in the input layer. Both data sets
number of input ts, and the number of features for each ts. consist of multiple samples which are successively processed
by the hidden layer(s), each comprising the input and output
sequences. For each sample, the concatenated features of each
4.2 | Long short‐term memory ts form the current input for the LSTM cell. In the stateless
implementation and training mode, the final state of each processed batch is removed. In
the stateful mode, however, the final state is provided as the
The most suitable LSTM configuration is selected in two steps. initial state for each sample in the next batch. The state is
First, the LSTM is trained with initially selected hyper- manually reset after each epoch as each epoch contains the
parameters (hp) on different approaches: the two encoding same time series data. After the input data has been processed
techniques, the two modes, and a varying number of input ts. by either one or two hidden layers, the final state of the last cell
F I GURE 5 Architecture and training process
of the long short‐term memory. MSE, mean
squared error
UNTERLUGGAUER ET AL. - 9
TABLE 3 Initial hyperparameters and
Type of hp Initial Training Hp Tuning
search space
Optimiser Adam No tuning
Loss function MSE No tuning
Activation function Tanh & hard sigmoid (cell), ReLU (dense layer) No tuning
# Epochs 500 1000 (no tuning)
# Hiddenlayers 1 1, 2
# Units 2, 8, 32, 128 2, 4, 8, 16, 32, 64, 128
Learning rate 0.001 0.01, 0.001, 0.0001
Batch size 1 (stateful), 32 (stateless) 16, 32, 64, 96
Dropout [%] 0 0, 20, 50
Abbreviations: MSE, mean squared error; ReLU, Rectified Linear Unit activation function.
in the last hidden layer is passed to a dense layer which outputs scale‐dependent, which implies the need for additional error
the number of ts to be predicted for each input sequence. metrics to allow a better comparison of the different charging
Once a certain number of samples, defined by the batch size, is sites. Given its scale‐independence, the popular mean absolute
processed, the predicted values are compared with the desired percentage error (MAPE) would provide an easily interpreta-
real load values to calculate the training and validation loss. tive error metric. However, the charging load time series
Based on the mean squared error (MSE) during training, the exhibit a charging load of zero at numerous points in time. For
weights are then modified after each batch size by the Adam this reason, MAPE cannot be used for overall comparison, as
optimiser using backpropagation through time. This process is the calculation is based on the division of the error by the true
repeated until the maximum number of epochs is met or the load value at each ts. To overcome these difficulties, two var-
training is terminated prematurely by the implemented early iants of the normalised mean absolute error (NMAE) are used
stopping callback. as shown in Equations (10) and (11). The MAE is normalised
by the mean charging load and the difference between the
maximum loadmax and minimum load loadmin, respectively.
4.3 | LSTM forecasting
1 XN
After the completion of the random search, the LSTM with the MAE ¼ jloadt − loâdtj ð9ÞN
optimal hp configuration performs the load forecast. t¼1
, 1 XN
| NMAE1¼MAE loadt ð10Þ4.3.1 Implementation of the forecast N t¼1
The forecast is carried out with a batch size of one, to avoid
errors in the prediction process caused by the varying batch MAENMAE2¼ ð11Þ
sizes during training. For every input sequence of the test data, loadmax − loadmin
the model predicts the subsequent four or 96 ts. Afterwards,
both the normalised real and predicted load are converted to For the 96‐ts forecast, three additional metrics are used to
load values in kW. The inverse normalisation is performed with better assess how well the daily peak load can be predicted,
the initial parameters of the min‐max scaler that have been both in terms of temporal occurrence and magnitude of the
saved during the preprocessing stage for this purpose. peak load. The timing and magnitude of the peak load are
especially important for assessing possible congestions in the
distribution network. The average peak deviation, pdev, in
4.3.2 | Metrics kW between the actual daily peak load, loaddm, and predicted
daily peak load, loâddm, is calculated according to Equa-
Six different error metrics are employed to evaluate the model tion (12). While D specifies the number of predicted days, dm
performance. The mean absolute error (MAE) in kW, calcu- denotes the daily peak. Likewise, the MAPE in % is calcu-
lated according to (9), measures the precision of the forecast by lated according to Equation (13). Finally, Equation (14)
averaging the error between the predicted and real load, and is specifies the average time deviation, tdev, in min separating
selected due to its simple comprehensibility. While N depicts the real and predicted peak load. Variable slot corresponds to
the number of forecasts, loadt indicates the real charging load the respective 15‐min interval of the real and the predicted
at time t, and loâdt the predicted one. However, the MAE is peak load.
10 - UNTERLUGGAUER ET AL.
TABLE 4 Summary of the best approach after initial training
1 XD
pdev¼ jload − loâd j ð12Þ SCc REc PUc WOc
D dm dm Site
d¼1 horizon 4‐ts 96‐ts 4‐ts 96‐ts 4‐ts 96‐ts 4‐ts 96‐ts
Min. Val. lossa 5.29 8.94 2.83 8.35 2.02 9.79 1.85 6.95
1 XD ,
MAPE ¼ ðloaddm − loâddmÞ loaddm � 100 ð13Þ # Epochs 17 7 49 31 14 147 221 130D
d¼1 # Input ts 16 96 16 96 4 96 16 96
Modeb SL SL SL SL SL SL SL SL
1 XD Encodingc S/C OH S/C S/C S/C S/C S/C OH
tdev¼ jslotðloaddmÞ − slotðloâddmÞj � 15 ð14ÞD
d¼1 Abbreviations: PUc, public charging; REc, residential charging; SCc, shopping center
charging; WOc, workplace charging.
aAll MSE values (validation loss) are given in units of 10−3.
bSL = Stateless mode.
5 | RESULTS cS/C = Sine/Cosine encoding, OH = One hot encoding.
Having covered the methodology of this work, this chapter training, except for the 96‐ts REc forecast. Lastly, in most of
addresses the training, tuning, and prediction results. the cases, the learning rate of 0.001 yields the lowest loss.
5.1 | Initial training results 5.3 | Forecasting results
Table 4 illustrates the selected approach for each charging site In the following sections, the forecasting results are analysed
and forecast horizon based on the minimum validation loss both graphically and numerically.
obtained during initial training. In all cases the minimum loss is
recorded while training the LSTM with 128 units.
The small epoch number for most of the charging sites 5.3.1 | Graphical results
indicates that the LSTM suffers from early overfitting. More-
over, the different modes, encoding techniques, and input ts Figure 6 illustrates the forecasting results for the 36 days of
only yield small differences in the validation loss. However, in test data for each category of charging site for both the 4‐ts
all the cases the lowest MSE is obtained while using the (green) and 96‐ts (purple) prediction. While comparing the
stateless mode. The sine/cosine encoding shows a slightly outcomes with the real charging load (grey), it becomes
superior performance in most cases. Finally, using the same apparent that the 4‐ts prediction achieves superior results
amount of input ts yields the lowest MSE for the 96‐ts fore- compared to the 96‐ts forecast. The 4‐ts forecast yields a
cast. For the 4‐ts prediction, 16 input ts results in the lowest relatively precise picture of the real load curve in grey, with
validation loss for SCc, Rec, and WOc, whereas four input ts no major outliers to be seen.
achieve the best fit for PUc. Considering the 96‐ts prediction results, three short-
comings can be identified. First, the LSTM is not capable
of predicting the charging load on public holidays. The
5.2 | Hyperparameter tuning results projected load almost exclusively exceeds the real load by a
substantial margin and exhibits a course similar to that of
The maximum and minimum validation loss obtained during non‐holidays. Second, the LSTM is not able to accurately
tuning, and the chosen superior hp combination is given in predict the level of real peak load for most days, frequently
Table 5. The maximum and minimum validation loss differ exceeding the predicted peak load substantially. Finally, the
considerably. The highest MSE values are obtained for the 4‐ts LSTM struggles to anticipate the impact of holiday periods.
prediction while using a high dropout or learning rate. For the This is particularly evident for REc, where the forecast
96‐ts forecast, a small number of units lead to the highest significantly exceeds the reduced real charging load during
validation losses. While comparing the minimum loss between the winter holiday period.
random search and initial training, it is evident that the hp
tuning only yields improvements for half of the forecasts. The
lowest losses are obtained with a high number of units (64 or 5.3.2 | Numerical results
128). In most cases, an LSTM with only one hidden layer
seems sufficient. Only for the REc 96‐ts forecast and WOc 4‐ Table 6 summarises the numerical results. As previously evi-
ts prediction the minimum loss is recorded while using two denced during the graphical analysis, reducing the forecast
hidden layers. All batch sizes are applied for the different horizon from 96 ts to 4 ts considerably reduces the prediction
forecasts. Dropout generally does not have a positive effect on error. The MAE for REc, PUc, and WOc can be more than
UNTERLUGGAUER ET AL. - 11
TABLE 5 Summary of tuning results
and selected hyperparameters Site
SCc REc PUc WOc
horizon 4‐ts 96‐ts 4‐ts 96‐ts 4‐ts 96‐ts 4‐ts 96‐ts
Min. lossa 33.68 13.51 10.17 21.04 12.08 32.34 47.24 14.55
Max. lossa 5.33 8.78 2.83 8.00 2.03 9.05 1.59 7.25
Improvement No Yes No Yes No Yes Yes No
# Hidden layer 1 1 1 2 1 1 2 1
# Units 128 128 128 128 128 64 64 128
Batch size 32 64 32 16 32 96 96 32
Dropout [%] 0 0 0 20 0 0 0 0
Learning rate 0.001 0.01 0.001 0.001 0.001 0.0001 0.0001 0.001
Abbreviations: PUc, public charging; REc, residential charging; SCc, shopping center charging; WOc, workplace charging.
aAll MSE values are given in units of 10−3.
F I GURE 6 Forecasting results for the 36 days of test data illustrated for all categories of charging sites
halved in most of the cases. For SCc, the MAE is reduced in all Conversely, while using the NMAE2 as the evaluation crite-
cases by more than 2 kW. The lowest overall MAE for both the rion, varying results are visible depending on the type of day.
forecast horizons is recorded for REc. WOc generates the For weekdays the most accurate predictions are seen for WOc
second lowest MAE values, followed by PUc. The highest followed by PUc, Rec, and SCc. While REc yields the most
MAE values are seen for SCc. exact forecast for weekends, WOc, PUc, and SCc take the
A different picture emerges while looking at the NMAE1 second, third, and fourth place. For public holidays, REc ranks
and NMAE2 results. For the 4‐ts prediction, the lowest first again, followed by SCc, PUc, and WOc. Similar findings to
NMAE1 is obtained for PUc, followed by REc, WOc, and SCc. the NMAE1 results of the 4‐ts forecast can be seen for the
Conversely, using the NMAE2, the most precise results are NMAE1 results of the 96‐ts forecast. REc and PUc achieve the
seen for WOc, followed by PUc, Rec, and SCc. For the 96‐ts most precise scores in most of the cases. However, for public
forecast the lowest NMAE1 again is obtained for PUc and holidays, SCc outperforms PUc and comes in the second place,
REc, however, the least accurate prognosis is given for WOc behind REc. Looking at the NMAE2 results, the poorest
this time. In contrast, the lowest NMAE2 is seen for WOc, performance for weekdays can be observed for Rec, whereas
followed by SCc and PUc. REc ranks last. SCc yields the most accurate results. On weekends SCc ranks
While comparing the clustered NMAE1 results, it can be first again, and WOc ranks the last. For public holidays, WOc
seen that the 4‐ts forecast yields the most accurate forecast for performs particularly poor again. REc obtains the most
PUc and REc. SCc and WOc score the poorest results. favourable score.
12 - UNTERLUGGAUER ET AL.
Table 7 quantifies the LSTM’s difficulties in predicting absolute errors are seen for public holidays, although the time
peak loads with a forecast horizon of 96 ts in numerical terms. deviation is minimised. For PUc and WOc, according to the
The pdev, the MAPE, and the tdev are given for each charging MAPE, the most precise results are achieved during the week.
site. For all forecasts, the average deviation between true and For WOc predictions on weekends, the absolute error amounts
predicted peak load amounts to 29.16 kW for SCc, 6.37 kW for to 4.73 kW and the MAPE to 100% due to a constant pre-
REc, 14.17 kW for PUc, and 17.85 kW for WOc. The MAPE diction of 0 kW. Therefore, no deviation between the time of
amounts to 53.19% for SCc, 34.38% for REc, 37.16% for PUc, the true and predicted peak load can be calculated. The highest
and 128.97% for WOc. The average deviation between real and error scores between the real and predicted peak load are
predicted time of the peak load in minutes are 153, 88, 104, recorded on public holidays for both charging sites and the
and 285 for SCc, REc, PUc, and WOc, respectively. time deviation between true and predicted peak load amounts
Examining the scores grouped by weekdays, weekends, and to a multiple of the deviation during the week.
public holidays, several discrepancies between the charging
sites can be highlighted. For SCc, on weekends and public
holidays, the absolute and relative errors can be reduced rela- 6 | DISCUSSION
tive to weekdays. In addition, the time deviation between true
and predicted occurrence of the peak load is significantly In this section, the initial training, hp tuning, and forecasting
lowered as well. For REc, in contrast, the highest relative and results are discussed in more detail.
TABLE 6 Evaluation of forecasting results 6.1 | Initial training results
Charging site SCc REc PUc WOc Four key findings can be summarised. To begin with, the in-
horizon 4‐ts 96‐ts 4‐ts 96‐ts 4‐ts 96‐ts 4‐ts 96‐ts clusion of multivariate inputs shows a positive influence on the
training results in terms of validation loss. However, a detailed
MAEa (all) 4.35 6.78 1.53 3.37 2.7 5.84 1.85 5.35 analysis of the impact on the training results and forecasting
results was not part of the analysis. Since the training data used
NMAE1 (all) 0.352 0.549 0.178 0.391 0.166 0.359 0.204 0.59 in this work spans less than one year for each category of
NMAE2 (all) 0.041 0.065 0.038 0.083 0.032 0.068 0.021 0.06 charging site, the inclusion of multivariate inputs is selected to
MAEa (wd) 4.41 6.75 1.52 3.33 3.1 6.37 2.56 6.56 help the LSTM identify patterns in the data. With multiyear
data available, the importance of including multivariate inputs
NMAE1 (wd) 0.369 0.564 0.175 0.381 0.152 0.312 0.191 0.489 may decrease or become obsolete.
NMAE2 (wd) 0.042 0.064 0.038 0.082 0.036 0.075 0.029 0.073 Next, the early overfitting indicates that the complexity of
MAEa (we) 4.39 7.15 1.6 3.62 1.83 3.2 0.49 1.31 the model, relative to the size of the available data, is too high,
and due to changing load characteristics throughout the year,
NMAE1 (we) 0.329 0.536 0.189 0.428 0.208 0.363 0.377 1.00 the validation data is not fully representative for the entire
NMAE2 (we) 0.06 0.097 0.047 0.106 0.056 0.098 0.054 0.142 dataset. The access to charging data measured over a longer
MAEa (ph) 3.71 5.74 1.36 2.89 2.48 10.64 0.88 9.51 period is, thus, of great interest to enhance the performance of
the model in future.
NMAE1 (ph) 0.312 0.484 0.162 0.345 0.262 1.124 0.595 6.454 Furthermore, the different encoding techniques and input ts
NMAE2 (ph) 0.073 0.113 0.047 0.099 0.092 0.393 0.16 1.739 variants only cause negligible differences in the validation loss.
Thus, the extra time needed to implement and train the LSTM
Abbreviations: MAE, mean absolute error; NMAE, normalised mean absolute error;
ph = public holiday; PUc, public charging; REc, residential charging; SCc, shopping with various variants cannot be justified. Hence, the selection of
center charging; WOc, workplace charging; wd = weekday, we = weekend. the same number of input ts and encoding choice for all sites
aAll MAE values are given in kW
TABLE 7 Summary of the peak deviation, MAPE and time deviation results of the 96‐ts prediction
Charging site SCc REc PUc WOc
Pdev MAPE Tdev Pdev Tdev Pdev Tdev Pdev Tdev
metric (kW) (%) (min) (kW) MAPE (%) (min) (kW) MAPE (%) (min) (kW) MAPE (%) (min)
All days 29.16 53.19 153 6.37 34.38 88 14.17 37.16 104 17.85 128.97 285
Weekdays 30.96 53.65 187 6.24 34.71 86 13.75 23.50 52 20.54 35.50 35
Weekends 26.37 53.11 95 6.29 32.00 99 11.39 43.28 116 4.73 100.00 ‐
Public holidays 24.65 49.90 85 7.64 39.80 65 26.62 121.46 615 41.01 942.13 435
Abbreviations: MAPE, mean absolute percentage error; Pdev, average deviation between real and predicted peak load; PUc, public charging; REc, residential charging; SCc, shopping
center charging; Tdev, average time deviation of predicted peak load.
UNTERLUGGAUER ET AL. - 13
seems to be more rational. Whereas the sine/cosine encoding noticeably, but the entire load series shows strongly fluctu-
offers a viable encoding variant, 16 input ts for the 4‐ts and 96 ating load characteristics. Thus, the impact of public holidays
input ts for the 96‐ts prediction seem to be appropriate. remains small.
Lastly, the stateful mode does not provide benefits Similar findings can be seen while looking at the peak
compared to the stateless mode under the given conditions. deviation and MAPE results. While for SCc and Rec, the
However, when multi‐year data becomes available in the MAPE difference between weekdays and public holidays
future, the stateful mode may reveal its strengths, as seasonal amounts to only 3.75 and 5.09 percentage points, respec-
relationships can be identified by the LSTM. Consequently, tively, the figure for public and workplace charging increases
with the availability of data over several years, a further com- by 97.96 and 906.63 percentage points, respectively. Once
parison of the different modes is advisable. again, the discrepancies can be explained by the impact of
public holidays on the load pattern. Analysing the weekday
results, the significant discrepancies in the MAPE and time
6.2 | Hyperparameter tuning results deviation, likewise, indicate that the characteristics of the
load profile decisively impact the accuracy of the forecast.
Three relevant conclusions can be drawn. First, the significant The highly irregular load profile for SCc results in the
variation between the minimum and maximum loss during poorest accuracy for both, the predicted peak load level and
tuning reveals that the different hp combinations exert a major the time of the peak load. WOc, on the other hand, exhibits
impact on the generalisability of the LSTM and, ultimately, on the steadiest pattern concerning the time of the peak load,
its predictive power. Thus, the importance of hp tuning for which is why the average time deviation is the lowest at
selecting the most suitable LSTM model is outlined. 35 min.
Moreover, the varying combinations of hp exert a funda-
mentally different impact on the validation loss for each
charging site category and forecast horizon. Thus, it is essential 6.3.2 | Overall findings
to perform the hp tuning separately for each use case.
Finally, random search shows only minor or no enhance- The superior performance of the 4‐ts prediction compared to
ments compared with the initial training. This might be due to the 96‐ts forecast is attributable to two factors. Due to the
the limited amount of evaluations and search space. A higher shorter forecast horizon, the preceding load values are shown
number of executions, the inclusion of other hp in the search to the LSTM more frequently and assist the LSTM in mapping
space, or the use of a more subtle method, like the bayesian hp the height and course of the load more precisely. Moreover, the
tuning, could lead to further improvements. poor prediction results for the 96‐ts forecast might be traced
back to the strongly altered load profile of the test data, caused
by the increase of charging load throughout the year and the
6.3 | Forecasting results winter holiday period. Therefore, the training and validation
data might have not been fully representative of the test data,
The results of the forecast are discussed below, followed by limiting the LSTM’s predictive power.
implications for the practical application of the forecast.
6.3.3 | Implications for aggregators and network
6.3.1 | Differences between the different operators
categories of charging sites
There are two courses of action on how aggregators and
The comparison of the forecasting results of the different network operators can implement the LSTM to achieve opti-
charging sites revealed that the evaluation is highly dependent mised forecasts for their respective use case. First, it is bene-
on the metric. However, SCc almost solely yields the poorest ficial to limit the load forecast to weekdays. Weekends and
results for the 4‐ts prediction, indicating that the fluctuating public holidays are accompanied by changes in the user
load hinders the predictive power of the LSTM. behaviour that are difficult to predict and exhibit a much lower
Further, evident discrepancies involve the varying results aggregation potential and risk of bottlenecks due to the
for weekdays, weekends, and public holidays. While the reduced charging load. By focussing the forecast on weekdays,
lowest NMAE1 is obtained for SCc and REc on public a higher prediction accuracy can be obtained.
holidays, the public holiday load predictions for PUc and Second, the forecast should only be carried out for the
WOc are significantly less accurate than the predictions on periods of a day with the highest charging load, where the
weekdays and weekends. This finding is attributable to the aggregation potential is the highest, and bottlenecks in the
distinct load profile characteristics rather than to the different distribution network are most likely. By shortening the forecast
forecasting ability of the LSTM. While the load for PUc and period, the accuracy is improved as shown in this work. The
WOc shifts radically on public holidays, the change for REc forecast will be further enhanced by focussing the LSTM on a
is less pronounced. With SCc, the load profile also varies specific period of the day.
14 - UNTERLUGGAUER ET AL.
7 | CONCLUSIONS AND FUTURE Open access funding enabled and organized by Projekt
WORK DEAL.
This study proposes a novel multivariate long short‐term ORCID
memory approach for multi‐step EV charging load fore- Tim Unterluggauer https://orcid.org/0000-0002-6461-
casting with two different prediction horizons. The perfor- 7291
mance of the forecasting approach is evaluated and compared Kalle Rauma https://orcid.org/0000-0002-5553-8751
between four different categories of charging sites. The results
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