Sustainable supply chain management of electric grid power

consumption load for smart cities based on second-order exponential

smoothing algorithm

THEODOROS ANAGNOSTOPOULOS1,*, FAIDON KOMISOPOULOS1, ANDREAS VLACHOS2,

ALKINOOS PSARRAS1, IOANNIS SALMON1, KLIMIS NTALIANIS1

1Department of Business Administration

University of West Attica

Ancient Olive Grove Campus

250 Thivon & P. Ralli Str, Egaleo

Postal Code 12241, Athens

GREECE

2School of Social Sciences

Hellenic Open University

Aristotelous 18, Patra 263 35

GREECE

Abstract: - Electric grid power consumption load is one of the fundamental areas that need to be faced to

provide a sustainable and green ecosystem in smart cities. Consumption load as well as supply and availability

of electricity to suppliers and customers is a major issue to be faced to have a balanced smart city power grid

infrastructure. Balancing in this case is assumed as a well-designed supply chain management system to be

applied in the Smart City (SC) of Athens, Greece. Core of such a system is the knowledge of electric power

consumption load per weekly basis of a year, that is the granularity of the proposed system is one week of the

system’s operation. In this paper, focus is given on the electric load forecast component of an Energy

Management System (EMS) such as the Independent Power Transmission Operator (ITPO) of Greece.

Concretely, stochastic data of electric energy consumption load are used to predict the demand or offering of

electric power in the future. This is achieved by incorporating a machine learning second-order exponential

smoothing algorithm. Such an algorithm is able to speculate near or far in the future power consumption load

thus providing a promising parameter to predict smart city needs for electric power in the future. Adopted

system is evaluated by the evaluation metric of Normalized Root Mean Square Error (NRMSE), which assures

that the system can be used for future predictions of electric power consumption load in smart cities.

Key-Words: sustainable management, supply chain, electric grid, exponential smoothing, smart cities

Received: August 25, 2021. Revised: October 20, 2022. Accepted: November 17, 2022. Published: December 9, 2022.

1 Introduction

Sustainable and green energy is an area of great

importance in smart cities in modern societies

around the globe, [1]. Electric energy is one area of

such high importance that needs to be treated

rationally to become environmentally friendly, [2].

Electric grid is used to transfer electric energy in

every place of a smart city to provide advanced

wellbeing to citizens of the city, [3]. However,

electric power has a disadvantage, that it cannot be

stored in huge quantities, [4]. For this purpose, it is

fundamental that the city, such as the Smart City

(SC) of Athens in Greece, should produce that

amount of electric energy that covers its needs

without great variance in the produced energy, [5].

Specifically, production should be confronted

between two thresholds, that is production of less

electric power and production of more electric

power than that the population of the city can

consume, [6]. Less production leads to buying

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Theodoros Anagnostopoulos, Faidon Komisopoulos,

Andreas Vlachos, Alkinoos Psarras,

Ioannis Salmon, Klimis Ntalianis

E-ISSN: 2224-2678

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electric power quantity required from electric

energy suppliers, while high production of electric

energy leads to selling surplus to potential electric

power customers, [7]. Although it is important to

have exactly the amount of electric power needed it

is rare this balance holds, [8]. Concretely, it is about

a supply chain management system, which should

be at any time ready to balance surplus or deficit of

electric power incorporated by the smart city

electric demand infrastructure, [9]. Intuitively, an

Energy Management System (EMS) is a system

with certain computer applications, automation and

control for monitoring. Controlling, scheduling and

analysis of the energy power system operation at all

levels (production, grid, demand), [10]. Concretely,

an EMS comprises a variety of applications and

automation technologies, falling in the following

basic categories: (1) power system simulator, (2)

operation training, (3) state estimation and system

monitoring, (4) risk and contingency analysis, (5)

load forecast, (6) real time voltage control and grid

operation, (7) load shedding, (8) economic dispatch

and automatic generation control, and (9) Data

analysis.

In this paper we focus on the green and

sustainable supply chain management technology of

electric energy produced and consumed by the smart

city of Athens, Greece. Proposed research effort

would not be feasible to operate without the

proliferation of Internet of Things (IoT) and

artificial intelligence technologies, which provide a

safe and sound framework where upcoming

technologies can be invented, analyzed and applied

in the wider area of a SC. Specifically, we are

interested in the electric load forecast component of

an EMS such as in the Independent Power

Transmission Operator (ITPO) of Greece, [11].

Concretely, special focus is given on the ability to

predict the electric energy produced by the city in a

granularity of a weekly basis during one year. Such

a knowledge would provide us the advantage of

when to proactively trigger suppliers or customers

of electric power to balance the smart city electric

energy. Specifically, we use stochastic historic data

from the previous year and apply second-order

exponential smoothing machine learning algorithms

to speculate future values of electric power required

by the city, [12]. To achieve these certain

parameters are required, such as the number of the

past weekly used values, the prediction time sliding

window as well as the time distance in the future we

would like to make a prediction. Actually, the

adopted machine learning model provides us the

opportunity to choose several future values to make

a desired prediction. Our model is evaluated with

the Normalized Root Mean Square Error (NRMSE)

evaluation metric, where results indicate that the

adopted approach could be incorporated in actual

cases of electric power consuming prediction in the

next few years.

Proposed approach focuses on the significance of

the current research effort, which can be described

in the following list:

 Electric load forecast component applied in the

SC of Athens, Greece.

 Online and in real time prediction of electric

energy consumed by the city.

 Granularity of the system is defined to be one

week, which results in a more robust

environment compared with granularities of less

time quantities.

 Proposed algorithm is lightweight thus less

complex compared with Neural Networks

approaches incorporated by other studies in the

literature.

 Data used in the proposed research are real and

provided by the ITPO of Greece.

The rest of the paper is structured as follows. In

Section 2 related work is provided. Section 3

describes the proposed machine learning prediction

system algorithm. Section 4 presents the evaluation

metric used to assess the efficiency of the proposed

machine learning second-order exponential

smoothing algorithm. Section 5 analyzes adopted

system parameters. In Section 6 certain experiments

are based on real data. In addition, results are

presented based on the adopted system parameters

and the proposed machine learning algorithm.

Section 7 performs detailed discussion of the results

observed to understand the behavior of the proposed

algorithm and its application in the smart city of

Athens, Greece. Finally, Section 8 concludes the

paper presenting the main aspects of the proposed

machine learning algorithm as well as proposes

specific research parameters eligible to be

performed by certain future work.

2 Related Work

Contemporary research in the area of electric power

grid consumption load focuses on efficient

prediction schemas, which are able to predict

electric energy load in smart cities. Research

approaches are sorted based on the parameters of the

energy management functions they provide.

Concretely, certain groups of research efforts

emerged based on prediction spatial scope,

granularity and time horizon values incorporated.

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Ioannis Salmon, Klimis Ntalianis

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2.1 Spatial Scope

According to spatial scope (i.e., the grid area

covered) systems are divided in efforts, which cover

the whole area of a SC and systems which cover a

limited area of the city.

2.1.1 Whole Area of a Smart City

Specifically, a scheduling framework using dynamic

optimal electric power flow of electric energy

consumption load for battery energy storage systems

is proposed, which focuses on mitigating the

predicted limits of renewable electric power

generation for the smart city infrastructure, [13]. An

energy management system, which is designed

incorporating fuzzy logic control for relaxing the

electric grid power profile of a residential electro-

thermal microgrid is proposed for predicting electric

consumption load in smart cities, [14]. Such a

system aims to design an energy management model

to reduce the impact of grid power in cases of

overloading.

2.1.2 Limited Area of a Smart City

A hybrid robust system, which considers outliers on

real time for electric consumption load series

prediction is introduced in, [15]. Specifically,

electric consumption load prediction is treated as an

important operation of electric power grids, where

cost reduction in the production of power is of

increased managerial significance. A multi-model

fusion short-term electric energy consumption load

forecasting system, which is based on random forest

feature selection to input a hybrid neural network

exploiting sliding window technique, proposed in

the literature, [16]. Such a system is able to

distinguish the non-linear relationship between

various input features.

2.2 Granularity

Research efforts in this category are divided

according to the granularity of the designed system

(i.e., the single time unit), which might be a single

hour, a week or a month ahead of electric load

forecast component operation.

2.2.1 Single Hour Ahead Operation

An electric consumption load prediction based on

artificial intelligence deep learning model is used to

optimize power grid behavior in smart cities, [17].

Proposed system is enhanced by the execution of a

heuristic algorithm able to balance electric load in

an occupied smart grid. Specifically, the system

supports decision making of a smart electric power

grid incorporating a feature selection algorithm to

mitigate the curse of dimensionality of the input

parameters. Adopted system was tested on hourly

load data and proved to have an effective accuracy.

An improved Long Short-Term Memory (LSTM)

spatial-temporal forecasting method is proposed in

the literature, which covers electric power grid

consumption load needs based on effective Internet

of Things (IoT) analysis, [18]. Such a system is

implemented based on an efficient machine learning

model and compared with other intelligent

algorithms in different electric power energy

datasets with regards to prediction accuracy

evaluation metric. Proposed system achieved higher

prediction accuracy than the other machine learning

algorithms. Electric consumption load prediction

scheme under false data injection attacks is able to

be faced using an artificial intelligence deep

learning model, [19]. Such a system is able to

forecast electric load at different time horizons

balancing the needs of producers and customers of a

smart city. A cyber-secure deep learning model is

constructed, which is able to predict effectively

electric consumption load in power grids for a

sliding time spanning from an hour up to a week of

continuous operation.

2.2.2 A Week Ahead Operation

A demand response visualization system, which is

applied for electric power consumption load systems

is proposed, [20]. Such a system is refers to

activities designed to manage and control electric

loads in a smart city. Proposed system also provides

visualization capabilities to utilize electric power

distribution networks to enable efficient network

operation. Short-term electric power consumption

load forecasting, which is based on gate recurrent

unit networks exploiting cloud computing platform

flexibility is proposed, [21]. Such a system has an

important role in the entire smart grid infrastructure

due to its impact on the scheduling and production

of electric power units located in smart cities’

infrastructures.

2.2.3 A Month Ahead Operation

Electric power system load prediction analysis

incorporating computer neural network technology

is proposed, which focuses on economic

development of electric power stations in smart

cities, [22]. Such a system is related to sustainable

industrial economic development to balance electric

power consumption needs in smart cities. An

electric power load prediction model applied to an

electric power substation, which incorporates an

efficient artificial neural network is analyzed in,

[23]. Such a model is able to estimate, with effective

prediction accuracy, the electric power of

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Theodoros Anagnostopoulos, Faidon Komisopoulos,

Andreas Vlachos, Alkinoos Psarras,

Ioannis Salmon, Klimis Ntalianis

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consumption load produced by a power grid

substation. Adopted model incorporates a system

operator to assure a reliable and optimal behavior.

2.3 Time Horizon

Time horizon parameter is divided with regards to

size of available history as well as size of future

prediction. According to this definition there are

systems, which use massive information of available

history and limited future to be prediction sizes as

well as systems that use limited information of

available history and also limited future prediction

sizes.

2.3.1 Massive Information of Available History

A detailed analysis on Cyber-Physical Power

System (CPPS) environments for enabling safe as

well as sustainable electric power grids for active

consumption load is proposed in the literature, [24].

Examined research effort focuses on the stochastic

analysis of cyberattacks in the energy sector of a

smart city. Such analyses incorporate the

heterogeneous nature of the CPPS to evaluate

possible emerging vulnerabilities and threats in the

smart city energy infrastructure. A multi-step ahead

prediction for electric power consumption load

incorporating an ensemble machine learning model

is proposed in, [25]. Specifically, the model is based

on a two-layer robust structure, which enables

experiments to be conducted with different

prediction horizons in the future to assess its

performance.

2.3.2 Limited Information of Available History

Pricing information in smart electric energy grids

focusing on a quality-based data valuation paradigm

is proposed, which exploits important assets for the

optimal operation and planning of electric power

consumption load systems, [26]. A smart electric

power grid for forecasting electric consumption load

in a smart city network is analyzed, [27]. Such a

system aims to frame the deployment of a smart grid

based on smart technologies assessment towards an

efficient electric energy source for smart grid

integration. A mean shift densification of certain

data sources feeding short-term electric power load

prediction for special days within a year is studied,

[28]. Such short-term forecasting has a significant

role regarding the operation of electric systems and

planning maintenance decision support operation

processes within a smart city infrastructure.

Current research efforts focus on accurate supply

chain prediction of electric consumption load

required by smart cities’ power grid infrastructure.

There are effective artificial intelligence and

machine learning models, which are able to support

suppliers and customer balance for electric power

during a period stemming from one hour up to one

week of operation. However, such proposed

solutions are computational inefficient, since they

use complex forecasting algorithms, thus burdening

the whole smart city electric energy infrastructure.

In this paper there is an intention to design a

computationally lightweight machine learning

algorithm to provide a less complex prediction

schema for smart cities’ operation. Specifically, we

propose to use a supply chain second-order

exponential smoothing algorithm, which is able to

predict electric consumption load required by smart

city power grid operation. Such an algorithm is

simple to be designed and applied in the existing

infrastructure as well as is also able to predict with

efficient prediction accuracy the consumption of

electric load required on a weekly basis for a smart

city’s electric energy operational behavior.

Intuitively, proposed research focuses on a

prediction spatial scope (i.e., the grid area covered)

of the whole area of the SC of Athens, Greece. In

addition, granularity of the designed system (i.e., the

single time unit) is defined to be one week of

operation. Concretely, time horizon follows the

limited information size of available history (e.g.,

five prior weeks), while size of future to be

predicted is experimentally defined to be one week

ahead.

Prediction spatial scope is defined to be the

whole area of the SC of Athens since real data

provided by the Independent Power Transmission

Operator (ITPO) of Greece, [11], cover the actual

needs of electric load consumption for the city of

Athens. Concretely, the proposed system algorithm

is based on the provided data to exploit electric load

consumption of large-scale performance such as the

case of the capital city of Athens, Greece.

Intuitively, granularity of input data to the proposed

system is defined to be a week since less time period

would not have practical interest. Actually, provided

data are describing hourly electric load consumption

for the city of Athens. However, such detailed

information would cause latencies and delays in the

proposed system algorithm execution, thus it is

performed aggregation of the provided data into

weekly basis. Subsequently, the time horizon size of

available history is defined to be five weeks so as to

be one whole month of the system’s operation plus

the consecutive week of the provided data. This

experimental setup provides the algorithm with

more robust historic data thus leading to an efficient

system behavior. Concretely, the size of the future is

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DOI: 10.37394/23202.2022.21.27

Theodoros Anagnostopoulos, Faidon Komisopoulos,

Andreas Vlachos, Alkinoos Psarras,

Ioannis Salmon, Klimis Ntalianis

E-ISSN: 2224-2678

250

Volume 21, 2022

defined to be one week because prediction in a more

extended time horizon would lead to loss of precise

results, which might result in failure of the system

algorithm to provide effective predictions.

Fig. 1. Visualization of the proposed second-order

exponential smoothing algorithm.

3 System Algorithm

Proposed system algorithm is based on the second-

order exponential smoothing for the current research

effort, which exploits stochastic historical electric

data values to predict the next electric consumption

load value in the future horizon of a weekly smart

city operation, [12]. Such a system is based on the

input of continuous weekly electric consumption

load measurements the model from    up to .

Specifically,    is a period of electric values in

the past from where the algorithm takes input, while

electric measurement value of  is the current

electric consumption measurement. Concretely, a

sliding window, which contains the last  values is

used to input such values to the algorithm. Since the

considered values are constrained by the length of 

the algorithm is characterized as local, thus in a

certain instant it is only processing the  input

values. Subsequently, the local second-order

exponential smoothing algorithm function, ,

performs at time instant  a prediction of the next

electric consumption value. However, prediction at

time instant  is possible to be done in a time

horizon of  weekly measurement steps in the

future, thus prediction can be performed in a weekly

horizon of    electric values. Intuitively, the

proposed algorithm should be evaluated with

regards to the quality of its prediction based on a

threshold , which is a threshold used to assess the

value of the Normalized Root Mean Square Error

(NRMSE), , observed by the algorithm. A

predicted electric consumption value is considered

as successful if it is less or equal to, in the

opposite case the value is considered as a failure of

the adopted algorithm. A visualization of the

proposed second-order exponential smoothing

algorithm is presented in Fig. 1.

Technically second-order exponential smoothing

algorithm, as customized for current research effort,

is input by continuous weekly electric values, where

the examined actual value is denoted with , which

beginning at time instant    [12]. Concretely, it

is used in the notation  to represent the smoothed

weekly electric consumption value for time .

Subsequently, notation  is used to characterize the

optimal estimate of the algorithm’s trend at time .

Intuitively, at this stage it is presented as the output

of the second-order exponential smoothing

algorithm, which is denoted as , which is an

estimate of the value  at time instance   

according to the historical weekly electric values

from the sliding window formed between the past

time instances from  up to time . is defined

by the following equation:

     

(1)

Concretely, given certain input to the machine

learning system algorithm specific output is

expected to observe a computed electric power

weekly consumption load prediction. Second-order

exponential smoothing algorithm is presented in

Table 1.

4 Evaluation Metric

Assessing the efficiency of an algorithm implies the

existence of an evaluation metric. In case of the

proposed second-order exponential smoothing

algorithm it is adopted the Normalized Root Mean

Square Error (NRMSE), , which takes values

within the interval,   󰇟 󰇠. Concretely,  is

defined in the following equation:

    





(2)

Where, , are the dependent predicted

electric consumption load values, , are the actual

values, and , is the average of the actual values of

the dependent variable. A low value of  means an

efficient exponential smoothing algorithm, while a

high value of  means a weak system algorithm. A

threshold of    indicates that the adopted

algorithm has an acceptable prediction behavior,

while a value of    indicates that the mean of

the dependent variable distribution cannot be

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Theodoros Anagnostopoulos, Faidon Komisopoulos,

Andreas Vlachos, Alkinoos Psarras,

Ioannis Salmon, Klimis Ntalianis

E-ISSN: 2224-2678

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Volume 21, 2022

predicted, which means that the algorithm is very

weak [29].

Table 1. Second-order exponential smoothing

algorithm.

Second-order exponential smoothing algorithm

Input: 

Output: 

Begin

 

  

For 󰇛  󰇜 Do

󰇛  󰇜󰇛  󰇜 // Where 󰇛    󰇜,

// data smoothing factor

 󰇛 󰇜  󰇛  󰇜 // Where 󰇛    󰇜,

//trend smoothing factor

End For

      // To predict beyond 

Return ()

End

Table 2. Adopted system parameters.

Parameter

Value

 Electric load value (Megawatt hour)

[24.29, 78.89]

 Sliding window size (Week)

[1, 52]

 Future prediction horizon (Week)

[1, 5]



NRMSE evaluation metric (Net number)

[0, 1]

 NRMSE threshold value (Net number)

0.5

5 System Parameters

Proposed system was tested on real data, which

were provided by the Independent Power

Transmission Operator (ITPO) of Greece, [11].

Specifically, input data feed the proposed algorithm

are numerical values measured in Megawatt hour.

Such electric load is used by the smart city of

Athens, Greece supply chain infrastructure to

provide the adequate electric consumption energy to

balance demand and supply between its citizens’

needs as well as the interested suppliers and

customers. Electric values are aggregated to weekly

consumption by ITPO to provide a stable electric

flow in the power grid of the city. Megawatt hour in

the city for a weekly basis is within the following

numeric interval   󰇟󰇠. Sliding

window size required by the proposed algorithm to

operate is within the following interval,   󰇟 󰇠,

since working weeks of a year are approximately 52

weeks. Future prediction horizon of a forecasted

electric consumption load value is defined to be

within the interval,   󰇟 󰇠. Normalized Root

Mean Square Error (NRMSE), , is defined to have

the following threshold value  , which is net

number. Adopted system parameters are presented

in Table 2.

Table 3. Experimental benchmark dataset values in

Megawatt hour per week granularity.

Week

Value

Week

Value

Week

Value

Week

Value

24.29

63.75

73.56

61.69

67.28

71.31

71.89

58.83

74.94

76.67

75.08

55.38

77.82

77.36

72.05

51.27

65.64

77.85

73.09

48.59

58.09

65.04

74.44

25.49

57.86

70.62

76.78

27.37

65.68

62.58

78.12

66.88

56.18

66.61

72.21

61.91

58.97

64.24

75.56

52.98

67.32

70.06

67.52

49.91

69.52

78.89

68.86

34.16

72.13

75.22

65.37

25.59

6 Experiments and Results

We experimented with the proposed second-order

exponential smoothing algorithm based on the

adopted evaluation metric NRMSE, , and defined

system parameters. Experimental smart city is the

capital city of Greece, which is Athens. Data used

for the experiments are denoting electric energy

load consumption per week of electric power grid

operation by the smart city of Athens as provided by

the system parameter, . Experiments are performed

to evaluate the effectiveness of the proposed

algorithm with further scope to adopt such a system

in real life scenarios, which may emerge and need

treatment by the load forecast component of the

ITPO. Such a benchmark dataset is consisting of

real data for the year 2021, which are available

online by the ITPO [11]. Concretely, experimental

data are processed in a granularity of a week

operation, which input the load forecast component

of the SC of Athens, Greece ITPO. Detailed values

of the available real data per week for a total period

of 52 weeks, which cover the period of a working

year are presented in Table 3.

Proposed machine learning algorithm is

implemented in Python release version 3.9.10, while

experiments were performed on a HP ProBook

455R G6 computer with 8.00 GB memory. We

performed 1000 experimental iterations invoking

adopted second-order exponential smoothing, where

the observed results were visualized. Specifically,

experiments focused on defining the optimal value

of defined evaluation metric NRMSE, , for sliding

window size, , while simultaneously fine tuning

the optimum value for future prediction horizon, ,

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according to certain error threshold, . Experimental

results are presented in Fig. 2.

Fig. 2. Visualization of the NRMSE, , values for

certain sliding window size, , values and adopted

future prediction horizon, , values.

Fig. 3. Visualization of actual and predicted values

for certain sliding window size,   , value and

adopted future prediction horizon,   , value.

It can be noted that optimal predicted values are

observed for sliding window size value,   , and

future prediction horizon,   . Concretely,

NRMSE observed values are within range  

󰇟 󰇠. Predicted observations along with

actual data values, for such parameter settings, are

presented in Fig. 3.

7 Discussion

Proposed second-order exponential smoothing

algorithm is a lightweight solution to the electric

load prediction problem since it can provide

relatively accurate predictions online and in real

time. Concretely, the adopted algorithm is able to

quantify in its analytical formulae the quantities of

input data and their trend towards an output

prediction. However, an extension of this algorithm

would take into consideration the quantity of

seasonal change smoothing factor, which might

affect positively and improve the effectiveness of

the algorithm. This is an open issue the authors have

scheduled to study in the future work.

Intuitively, the proposed algorithm incorporates

several parameters, which should be explained in

more depth to understand how the algorithm infers a

prediction in the future. Input values are the

sequential values of the electric load data stream,

which actually has a vital impact on the overall

performance of the adopted algorithm. Concretely,

an electric energy value data stream may be

accessed as a data signal and as that a safe and

sound input flow is more possible to lead to valid

output predictions than that in case of a random like

data stream. Subsequently, data smoothing factor, ,

is better understood as a factor which unlocks the

potentiality of arithmetic electric load data values,

which can then be exploited better by the algorithm.

Intuitively, trend smoothing factor,, can contribute

in making the algorithm to understand the current

positive or negative arithmetic trend the

manipulated data have while time is passing and

prediction is required as soon as possible. However,

there is no golden ratio or default known values for

the computed  and  values since they both depend

on the quality and inherent noise of the input

electric load data stream values. Actually, this is the

existing issue in machine learning since there is

nothing to be taken for granted. Instead, every single

parameter of the selected algorithm should undergo

a certain number of iterations to converge in an

acceptable efficiency level where the parameters are

considered stable and able to provide valid

predictions.

A challenging issue the proposed model has to

deal with in real-life environments is the balance of

the SC’s electricity grid. Such a problem is crucial

to maintain an operational electricity grid in SCs.

Specifically, the amount of electricity load input to

the electricity grid should in any case be equal to the

amount of electric load consumed. If this is not

feasible there is a high possibility of a black-out in

the city’s infrastructure. Subsequently, the

contemporary increase of renewable electric

production that can significantly vary depending on

the weather conditions has a more complicated

impact to the existing electric balance issue. In

addition, existing power plants should be able to

compensate for these constant fluctuations, since

there is not the feasibility to store electricity in vast

quantities over a long period of time [30]. Since the

proposed algorithm is part of the load forecast

component of the adopted EMS for the SC of

Athens, Greece it is able to predict the future

electric consumption values required by the SC.

Such knowledge enhances the EMS to achieve

electricity balance proactively, that is before this

situation will actually happen. Intuitively, this

possible proactiveness is a strategic managerial tool,

which is feasible due to the adopted algorithm.

Concretely, results of the proposed machine

algorithm are promising to provide efficient supply

chain sustainable management services by the smart

city of Athens, Greece. Specifically, experiments

WSEAS TRANSACTIONS on SYSTEMS

DOI: 10.37394/23202.2022.21.27

Theodoros Anagnostopoulos, Faidon Komisopoulos,

Andreas Vlachos, Alkinoos Psarras,

Ioannis Salmon, Klimis Ntalianis

E-ISSN: 2224-2678

253

Volume 21, 2022

performed for a period of a year containing electric

energy consumption load for 52 weeks of system

operation provide a robust power grid infrastructure.

As it can be observed by the obtained NRMSE, ,

values, proposed system algorithm is able to predict

future electric power consumption load for the smart

city for certain values of sliding window size, , per

certain values of future prediction horizon, .

NRMSE, , efficiency increases, thus values of

NRMSE, , are decreased since these are error

values and the smaller they are the better the

adopted second-order exponential smoothing

algorithm performance is achieved.

We can observe that NRMSE, , decreases as

sliding window size , increases from one week of

operation up to five weeks of power grid operation

for all values of future prediction horizon .

However, we can observe there is a global minimum

at the sliding window size, , for value of   ,

while increased values of  lead to higher values of

, thus performance of the system is decreasing.

This is explained since the system learns from

incremental experience for   󰇟 󰇠. When   

algorithm has learned the behavior of electric

energy consumption load in the smart city for a

month and a new week, i.e., the 5th week of

operation. Since with    the system is more

robust due to the completion of a whole circle of

temporal training plus a new unseen instance, which

is the first week of the next month, is now ready to

perform its first extrapolation attempt with values of

  󰇟 󰇠.

It can be observed that the    proposed

algorithm can predict well with almost all future

prediction horizons , values. However, if we need

more insight into future need for electric power

consumption by the smart city we would feed the

algorithm with more increasing values of sliding

window size, thus   󰇟 󰇠. It is obvious that as 

increases external noise is entered to the algorithm,

which has a negative impact to its . So, the more

the input  values the worse  values observed.

Concretely, the future horizon of prediction is going

worse for all values of . However, it is interesting

to observe that in this condition lower values of 

achieve lower values of , thus overall performance

for    is marginally better for other values, i.e.,

  󰇟 󰇠. By this point of view future work in this

research area should focus on computationally

lightweight machine learning algorithms, as the

proposed second-order exponential smoothing

algorithm, which should exploit the dynamics of

such prediction property, (i.e., better future

prediction outcomes for   ), of the examined

electric power weekly grid supply.

Intuitively, in Fig. 3 it can be observed the actual

input values to the model and the output predicted

values, which are provided to the load forecast

component of the examined system. Specifically, in

Fig. 3 it is presented the actual and predicted electric

consumption load values for a period of the year

2021 aggregated per working week, thus a total of

52 weeks of a year. Note that the output predicted

values’ plotted line marginally well aligned with the

actual input values’ plotted line, respectively.

Subsequently, it can be inferred that the NRMSE

error range is within,   󰇟󰇠, which

indicates that the proposed algorithm is efficiently

accurate and can be proposed for adoption to the SC

of Athens, Greece ITPO. Such a concrete

framework can face daily emerging situations,

which may occur in the electric energy grid of the

city in the next years of online and in real time

operation.

8 Conclusions and Future Work

A sustainable supply chain technology is analyzed

in this paper, which incorporates a second-order

exponential smoothing machine learning algorithm

to balance electric power dynamics between

suppliers and customers of the smart city of Athens,

Greece. Such an algorithm is part of the load

forecast component of the SC’s EMS, which is

responsible to maintain electricity balance in the

city. This is highly important since an unbalanced

electric grid is prone to an unexpected black-out.

Electric power consumption load is treated as a

machine learning data source, which inputs the

proposed algorithm to provide a green ecosystem

based on existing electric power grid infrastructure.

Balancing the needs or surplus of electric energy is

feasible due to continuous operation of the adopted

machine learning algorithm. Core of the system

algorithm is the knowledge of electric power

consumption load per weekly basis of a year.

Concretely, stochastic data of electric energy

consumption load are used to predict the demand or

offering of electric power in the future. Such a

prediction is feasible by using the proposed second-

order exponential smoothing algorithm, aiming to

speculate near or far in the future power

consumption load thus providing a promising

parameter to predict smart city needs for electric

power consumption load in the future. Main

parameters of the algorithm are data, , and trend,

, smoothing factors, which exploit the nature of the

input data as well as their positive or negative trend.

Adopted system is evaluated by the evaluation

metric of Normalized Root Mean Square Error

(NRMSE), which assures that the system can be

used for future predictions of electric power

consumption load in smart cities. Subsequently,

predicted electric consumption load values observed

WSEAS TRANSACTIONS on SYSTEMS

DOI: 10.37394/23202.2022.21.27

Theodoros Anagnostopoulos, Faidon Komisopoulos,

Andreas Vlachos, Alkinoos Psarras,

Ioannis Salmon, Klimis Ntalianis

E-ISSN: 2224-2678

254

Volume 21, 2022

are marginally well aligned to the input actual

values, which is an indicator of the proposed

system’s efficiency. Future work should focus on

exploiting the quantity of the seasonal change

smoothing factor, which might affect the

effectiveness of the proposed model. However, there

is no golden ratio or default known values for the

computed  and  values since they both depend on

the quality and inherent noise of the input electric

load data stream values. Actually, this is the existing

issue in machine learning since there is nothing to

be taken for granted. Instead, every single parameter

of the selected algorithm should undergo a certain

number of iterations to converge in an acceptable

efficiency level where the parameters are considered

stable and able to provide valid predictions.

Intuitively, since the proposed system is lightweight

it should be compared with other approaches in the

literature to compare its effectiveness with more

complex algorithms in consecutive future work.

Subsequently, such comparison should be done with

regards to certain experimental parameters that are

the variety of prediction spatial scope, granularity

and time horizon values as defined in the current

research effort. Focus will be on the principle of

equal treatment for all of the compared electric grid

consumption load solutions applied in a green and

sustainable SC infrastructure.

References:

[1] Maris, G.; Flouros, F. The Green Deal,

National Energy and Climate Plans in Europe:

Member States’ Compliance and Strategies.

MDPI Administrative Sciences 2021, Volume

11(3), pp. 75 – 92.

[2] Elia, G.; Margerita, A.; Ciavolino, E.;

Moustaghfir, K. Digital Society Incubator:

Combining Exponential Technology and

Human Potential to Build Resilient

Entrepreneurial Ecosystems. MDPI

Administrative Sciences 2021, Volume 11(3),

pp. 96 – 112.

[3] Gorelova, I.; Dmitrieva, D.; Dedova, M.;

Savastano, M. Antecedents and Consequences

of Digital Entrepreneurial Ecosystems in the

Interaction Process with Smart City

Development. MDPI Administrative Sciences

2021, Volume 11(3), pp. 94 – 108.

[4] Zhang, X.; Chen, Y.; Wang, Y.; Ding, R.;

Zheng, Y.; Zha, X.; Cheng, X. Reactivate

Voltage Partitioning Method for the Power

Grid With Comprehensive Consideration of

Wind Power Fluctuation and Uncertainty. IEEE

Access 2020, Volume 8, pp. 124514 – 124525.

[5] Abomazid, M.A.; El-Taweel, N.A.; Farag,

H.E.Z. Optimal Energy Management of

Hydrogen Energy Facility Using Integrated

Battery Energy Storage and Solar Photovoltaic

Systems. IEEE Transactions on Sustainable

Energy 2022, Volume 3(3), pp. 1457 – 1468.

[6] Jiang, H.; Qi, B.; Du, E.; Zhang, N.; Yang, X.;

Yang, F.; Wu Z. Modeling Hydrogen Supply

Chain in Renewable Electric Energy System

Planning. IEEE Transactions on Industry

Applications 2022, Volume 58(2), pp. 2780 –

2791.

[7] Agarwal, U.; Rishiwal, V.; Tanwar, S.;

Chaudhary, R.; Sharma, G.; Boroko, P.N.;

Sharma R. Blockchain Technology for Secure

Supply Chain Management: A Comprehensive

Review. IEEE Access 2022, Volume 10, pp.

85493 – 85517.

[8] Chen, M.; Jie, Y.; Wang, C.; Li, G.; Qiu, L.;

Zhong, W. Optimized Reactive Power Control

of Module Power Imbalance of Cascaded

Converter. IEEE Open Journal of Power

Electronics 2022, Volume 3, pp. 2 – 12.

[9] Home, R.; Weiner, M.; Schader, C. Smart

Mixes in international Supply Chains: A

Definition and Analytical Tool, Illustrated with

the Example of Organic Imports into

Switzerland. MDPI Administrative Sciences

2021, Volume 11(3), pp. 99 – 118.

[10] Turner, W.C. Energy Management Handbook,

1st ed.: Fairmont Press: Lilburn, USA, 2001;

pp. 21 – 34.

[11] Independent Power Transmission Operator

(ITPO). Available online:

https://www.admie.gr/en (accessed on 2

November 2022).

[12] Nahmias, S.; Olsen, T.L. Production and

Operations Analysis, 7th ed.; Waveland Press:

Illinois, USA, 2015; pp. 107 – 142.

[13] Fan, F.; Kockar, I.; Xu, H.; Li, J. Scheduling

framework using dynamic optimal power flow

for battery energy storage systems. CSEE

Journal of Power and Energy Systems 2022,

Volume 8(1), pp. 271 – 280.

[14] Arcos-Aviles, D.; Pascual, J.; Guinjoan, F.;

Marroyo, L.; Garcia-Gutierrez, G.; Gordillo-

Orquera, R.; Llanos-Proano, J.; Sanchis, P.;

Motoasca, T.E. An Energy Management

System Design Using Fuzzy Logic Control:

Smoothing the Grid Power Profile of a

Resiential Electro-Theraml Microgrid. IEEE

Access 2021, Volume 9, pp. 25172 – 25188.

[15] Yang, Y.; Tao, Z.; Qian, C.; Gao, Y.; Zhou, H.;

Ding, Z.; Wu, J. A hybrid robust system

considering outliers for electric load series

forecasting. Applied Intelligence 2021, Volume

52, pp. 1630 – 1652.

[16] Xuan, Y.; Si, W.; Zhu, J.; Sun, Z.; Zhao, J.; Xu,

M.; Xu, S. Multi-Model Fusion Short-Term

Load Forecasting Based on Random Forest

Feature Selection and Hybrid Neural Network.

IEEE Access 2021, Volume 9, pp. 69002 –

69009.

WSEAS TRANSACTIONS on SYSTEMS

DOI: 10.37394/23202.2022.21.27

Theodoros Anagnostopoulos, Faidon Komisopoulos,

Andreas Vlachos, Alkinoos Psarras,

Ioannis Salmon, Klimis Ntalianis

E-ISSN: 2224-2678

255

Volume 21, 2022

[17] Hafeez, G.; Alimgeer, K.S.; Khan, I. Electric

load forecasting based on deep learning and

optimized by heuristic algorithm in smart grid.

Applied Energy 2020, Volume 269, pp. 114915

– 114933.

[18] Li, M.; Han, X.; Huang, H.; Ni, J.; Cui, B.;

Cheng, H.; Liu, M.; Wang, X. Improved LSTM

Spatial-temporal Prediction Method for Power

Grid IoT Analysis. In Proceedings of the 20th

IEEE/WIC/ACM International Conference on

Web Intelligence and Intelligent Agent

Technology (WI-IAT), Melbourne, Australia,

14 December 2021.

[19] Moradzadeh, A.; Mohammadpourfard, M.;

Konstantinou, C.; Genc, I.; Kim, T.;

Mohammadi-Ivatloo, B. Electric load fore

casting under False Data Injection Attacks

using deep learning. Energy Reports 2022,

Volume 8, pp. 9933 – 9945.

[20] Negnevitsky, M.; Wong, K. Demand response

visualization tool for electric power systems.

Visualization in Engineering 2015, Volume 3,

pp. 7 – 21.

[21] Li, X.; Zhuang, W.; Zhang, H. Short-term

Power Load Forecasting Based on Gate

Recurrent Unit Network and Cloud Computing

Platform. In Proceedings of the 4th

International Conference on Computer and

Application Engineering (CSAE), Sanya,

China, 20 October 2020.

[22] Wang, Q.; Li, H. Power System Load Forecast

Analysis Based on Computer Neural Network

Technology. In Proceedings of the 3rd

International Conference on Artificial

Intelligence and Advanced Manufacture

(AIAM), Manchester, United Kingdom, 23

October 2021.

[23] Veeramsetty, V.; Deshmukh, R. Electric power

load forecasting on a 33/11 kV substation using

artificial neural networks. SN Applied Sciences

2020, Volume 2, pp. 855 – 865.

[24] Yohanandhan, R.V.; Elavarasan, R.M.;

Pugazhendhi, R.; Premkumar, M.; Mihet-Popa,

L.; Terzija, V. A holistic review on Cyber-

Physical Power System (CPPS) testbeds for

secure and sustainable electric power grid –

Part – I: Background on CPPS and necessity of

CPPS testbeds. International Journal of

Electrical Power and Energy Systems 2022,

Volume 136, pp. 107718 – 107746.

[25] Zhao, Y.; Guo, N.; Chen, W.; Zhang, H.; Guo,

B.; Shen, J.; Tian, Z. Multi-step ahead

forecasting for electric power load using an

ensemble model. Expert Systems with

Applications 2022, Volume 211, pp. 118649 –

118662.

[26] Yu, M.; Wang, J.; Yan, J.; Chen, L.; Yu, Y.; Li,

G.; Zhou, M. Pricing Information in Smart

Grids: A Quality-Based Data Valuation

Paradigm. IEEE Transactions on Smart Grid

2022, Volume 13(5), pp. 3735 – 3747.

[27] Raza, M.A.; Aman, M.M.; Abro, A.G.; Tunio,

M.A.; Khatri, K.L.; Shahid, M. Challenges and

potentials of implementing a smart grid for

Pakistan’s electric network. Energy Strategy

Reviews 2022, Volume 43, pp. 100941 –

100956.

[28] Rego, L.; Sumaili, J.; Miranda, V.; Frances, C.;

Silva, M.; Santana, A. Mean shift densification

of scarce data sets in short-term electric power

load forecasting for special days. Electrical

Engineering 2017, Volume 99, pp. 881 – 898.

[29] Frank, E.; Hall, M.A.; Witten, I.H. The Weka

Workbench. Online Appendix for Data Mining:

Practical Machine Learning Tools and

Techniques, 4th ed.; Morgan Kaufmann:

Burlington, USA, 2016; pp. 69 – 75.

[30] Energuide.be – Why does the electricity grid

have to stay in balance? Available online:

https://www.energuide.be/en/questions-

answers/why-does-the-electricity-grid-have-to-

stay-in-balance/2136/ (accessed on 6 November

2022).

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

Theodoros Anagnostopoulos has contributed in

conceptualization, methodology, software, and

writing original draft.

Faidon Komisopoulos has contributed in validation

and resources.

Andreas Vlachos has contributed in investigation

and visualization.

Alkinoos Psarras has contributed in formal analysis,

writing review and editing.

Ioannis Salmon has contributed in data curation and

funding acquisition.

Klimis Ntalianis has contributed in supervision and

project administration.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

This research was funded by the course of

Advanced Quantitative Statistics of the Master of

Business Administration, at the Department of

Business Administration, at the University of West

Attica, Greece.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

WSEAS TRANSACTIONS on SYSTEMS

DOI: 10.37394/23202.2022.21.27

Theodoros Anagnostopoulos, Faidon Komisopoulos,

Andreas Vlachos, Alkinoos Psarras,

Ioannis Salmon, Klimis Ntalianis

E-ISSN: 2224-2678

256

Volume 21, 2022