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Citation: Mimi, S.; Ben Maissa, Y.;
Tamtaoui, A. Optimization
Approaches for Demand-Side
Management in the Smart Grid:
A Systematic Mapping Study. Smart
Cities 2023,1, 1–33. https://doi.org/
Academic Editor: Isam Shahrour
Received: 11 May 2023
Revised: 21 June 2023
Accepted: 26 June 2023
Published: 30 June 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
smart cities
Review
Optimization Approaches for Demand-Side Management in the
Smart Grid: A Systematic Mapping Study
Safaa Mimi * , Yann Ben Maissa and Ahmed Tamtaoui
Telecommunication Systems, Networks and Services Laboratory, National Institute of Posts
and Telecommunications (INPT), Rabat 10112, Morocco; benmaissa@inpt.ac.ma (Y.B.M.);
tamtaoui@inpt.ac.ma (A.T.)
*Correspondence: safaamimia1@gmail.com
Abstract:
Demand-side management in the smart grid often consists of optimizing energy-related
objective functions, with respect to variables, in the presence of constraints expressing electrical
consumption habits. These functions are often related to the user’s electricity invoice (cost) or to
the peak energy consumption (peak-to-average energy ratio), which can cause electrical network
failure on a large scale. However, the growth in energy demand, especially in emerging countries, is
causing a serious energy crisis. This is why several studies focus on these optimization approaches.
To our knowledge, no article aims to collect and analyze the results of research on peak-to-average
energy consumption ratio and cost optimization using a systematic reproducible method. Our goal is
to fill this gap by presenting a systematic mapping study on the subject, spanning the last decade
(
2013–2022
). The methodology used first consisted of searching digital libraries according to a specific
search string (104 relevant studies out of 684). The next step relied on an analysis of the works
(classified using 13 criteria) according to 5 research questions linked to algorithmic trends, energy
source, building type, optimization objectives and pricing schemes. Some main results are the
predominance of the genetic algorithms heuristics, an insufficient focus on renewable energy and
storage systems, a bias in favor of residential buildings and a preference for real-time pricing schemes.
The main conclusions are related to the promising hybridization between the genetic algorithms
and swarm optimization approaches, as well as a greater integration of user preferences in the
optimization. Moreover, there is a need for accurate renewable and storage models, as well as for
broadening the optimization scope to other objectives such as CO
2
emissions or communications load.
Keywords:
energy efficiency management; peak-to-average-energy-consumption ratio; energy cost;
control; optimization algorithms
1. Introduction
Conventional electrical grids are built with the intent to widely distribute energy
from a limited set of producers to all the subscribed consumers. Although they meet the
challenges of the past, the integration of renewable energies, decentralized production
and demand management have more than ever highlighted the limits of conventional
electrical networks. Recently, the current Russian–Ukrainian conflict has illustrated the
need for an adaptive smart electrical grid even more [
1
]. Indeed, part of the drone and
missile attacks have targeted Ukrainian energy infrastructures, which could have been more
resilient if they were smarter and especially re-configurable. The rest of the world is also
affected by the current post-pandemic and war context: some countries in the European
Union, such as France, are expecting to perform rotating load sheddings [
2
]. This is an
exceptional situation.
The problem often lies in (1) the overload caused by spikes in the energy use pat-
tern of a conventional grid (CG), and (2) the energy cost for the consumer. We observe
during peak hours that energy consumption reaches threshold limits. This prevents the
Smart Cities 2023,1, 1–33. https://doi.org/10.3390/smartcities1010000 https://www.mdpi.com/journal/smartcities
Smart Cities 2023,12
CG from serving all its consumers, which could cause high risks of outages and physical
damage to the grid due to overheating [
3
]. The smart grid (SG) positions itself as the
modern solution for energy distribution in a bi-directional and agile manner [
4
]. Thanks to
advanced communication technologies, one of the main advantages of the SG is flexible
bi-directional demand management, where a ’win-win’ situation between consumers and
utility companies is expected [
5
], benefiting from an exchange of information between sup-
ply and demand. Demand-side management in the smart grid often consists of optimizing
energy-related objective functions, with respect to variables, in the presence of constraints
expressing electrical consumption habits. This can enable consumers to efficiently manage
their consumption loads by shifting usage from on-peak hours to off-peak hours in order to
’flatten’ the electricity consumption, increase the reliability of the network and avail various
economic incentives [
6
]. For example, utility companies and grid operators encourage con-
sumers to respond to their dynamic pricing models by declaring cheap prices of electricity
at a certain time of day [
7
]. Recently, several studies have been conducted on detailed
DSM approaches in residential, commercial and industrial networks, where researchers
propose algorithms to optimize the energy cost and peak-to-average ratio (PAR). Other
optimization objectives such as CO
2
emissions, waiting time and user preferences have
also been proposed (despite systematically requiring a heuristic because of the problem’s
NP-hardness [
8
]). In this paper, we present the first (to our knowledge) systematic map-
ping study on PAR and cost optimizationapproaches for demand-side management in
the smart grid. These techniques often use an exact algorithm or a metaheuristic to shift
the loads consumption, or plan renewable energy use at the right moment according to
pricing schemes and incentives provided by the supplier. This survey is the result of a deep
analysis of hundreds of studies that deal with the subject. The purpose of this work is to
give a structured review of the field during the last decade (2013–2022) in order to provide
researchers with a clear image of the methods used and some open research issues.The
remainder of the paper is structured as follows: in Section 2, we present as formally as
possible the background: fundamental elements related to the smart grid, demand-side
management, PAR, cost optimization and price models. Section 3details the systematic
mapping study research method: the initial paper selection process, mapping questions
definition and results of the data extraction and classification (104 studies) according to the
13 criteria. Section 4analyzes the state of the art comparatively and answers the mapping
questions. In Section 5, we discuss open research issues and recommendations for PAR and
cost optimization approaches. Section 6concludes the paper.
2. Background
In this section, we present fundamental domain concepts: some necessary elements
for understanding the peak-to-average ratio, and cost optimization for demand-side man-
agement in the smart grid.
We considered a basic intelligent grid model, which is close to several works studied
in this paper, with the addition or elimination of some constraints. The energy of this
proposed electrical network is shared by several users via the electrical line (solid line), as
shown in Figure 1. The information of the network is shared via the communication line
(dashed line). In a smart grid, the energy and information exchange is usually bi-directional.
Each user is equipped with batteries and a smart meter capable of reporting the information
centrally in order to globally optimize the energy consumption, and program electrical
devices based on the information collected. Sometimes, other energy-producing equipment
(e.g., solar panels or wind turbines) might be included in the network.
Due to the irregular consumer behavior, devices can be divided into three cate-
gories [9]:
1.
Essential devices. They are interactive with minimal scheduling freedom, fixed power
and operational periods. These devices require a steady power supply (e.g., lamps).
2.
Shiftable devices. They have specific energy consumption profiles and elastic delays.
Their operation period can be shifted (e.g., washing machines).
Smart Cities 2023,13
3.
Throttleable devices. They have a fixed operating period but can accept adjustments
in their power consumption, within a certain range (e.g., electrical vehicles).
Figure 1. Intelligent grid model.
2.1. Load Demand Description
With no loss of generality, we considered
N
loads consumed by users, where N
,|N|
is
the number of users. For each user n
∈ N
, let
Mn={In∪Sn∪Rn}
designate all household
devices, where
In
,
Sn
and
Rn
designate essential, shiftable and throttleable devices. For these
three types of devices, we define the scheduling vector for energy consumption as:
en,i ,he1
n,i, . . ., et
n,i, . . ., eT
n,ii, (1)
en,s ,he1
n,s, . . ., et
n,s, . . ., eT
n,si, (2)
en,r ,he1
n,r, . . ., et
n,r, . . ., eT
n,ri, (3)
Let x
n,t
denote the total energy consumed by user
n
during the time interval
t∈ T ={1,. . ., T}.
This means that:
xn,t =∑
i,s,r∈Mn
et
n,i +et
n,s +et
n,r t∈ T . (4)
Therefore, the total daily energy demand of user n is:
∑
t∈On
xn,t =En. (5)
For the battery profile vector of user n, it can be given as:
an=[an,1, . . ., an,t, . . ., an,T], (6)
where an,t must satisfy the maximum rate of charge and discharge,
−1≤an,t ≤1 (7)
a
n,t >
0 means that the battery of user
n
is being charged, a
n,t <
0 means that the
battery of user nis being discharged and an,t =0 is for when the battery is being idle.
After every charging and discharging, the level of each battery must be less than its
maximum capacity and greater than zero. The mathematical formulation of the constraint is:
0≤bn,0 +
t
∑
j=1
an,jrn≤Bn,∀t∈ T . (8)
We assume that, at the end of a cycle T, there is no excess or shortage of energy. Thus, the
charge level of the battery b
n,0
is always the same. This assumption can be expressed as below:
Smart Cities 2023,14
T
∑
t=1
an,t =0 (9)
During each time interval t, the energy supplied by the user’s battery is less than the
energy consumed by the user. The constraint is given as follows:
xn,t +an,trn≥0 (10)
Depending on the battery charge and discharge strategy, during each time interval,
the load demand that user nhas to purchase from the utility will be:
Ln,t =xn,t +an,trn(11)
Based on these definitions, the total consumed load by all users during time interval
t∈ T can be computed as:
Lt,∑
n∈N
Ln,t . (12)
2.2. Peak-to-Average Ratio
The peak-to-average ratio (PAR) is an important metric that can be monitored as an
indicator of the disparity level between peak consumption and the average usage. Small
PAR values indicate a stable and reliable system while, on the other hand, high values of
PAR indicate an unbalanced electricity production with cost implications [
9
]. It can be
formulated as follows [10]:
PAR =Peak energy consumption
Average energy consumption (13)
In a smart grid network, let L
p
and L
a
designate the peak load and average load.
Mathematically, they are given by:
Lp=max
t∈TLt(14)
and
La=1
T∑
t∈T
Lt. (15)
The PAR of the load is represented by ΓPAR and can be formulated as:
ΓPAR =Lp
La=Tmaxt∈TLt
∑t∈TLt(16)
One of the two optimization objectives of surveyed studies can be formulated as follows:
min ΓPAR (17)
2.3. Electricity Pricing System
Time-based demand response programs offer consumers prices that vary over time
and are defined based on the electricity cost over different time periods [
11
]. Customers
obtain the notifications and have a tendency to consume less electrical energy in high-priced
periods. Different pricing schemes were found in the works surveyed. They are as follows.
Time-of-use pricing (ToU) is the utilization of fixed prices at different time intervals,
which can be different hours in the day or different days in the week [
11
]. In the off-
peak period, the effectiveness of these systems for reducing total energy consumption
is limited, as consumers receive no practical incentive to decrease their demands. The
consumers’ response is triggered by the fact that the prices are lower during off-peak hours
and relatively higher during peak hours [12,13].
Critical peak pricing (CPP) has a kind of similitude to ToU pricing with regard to
fixed tariffs over different time periods. However, due to occasional systemic stress, the
price of at least one period may change, regularly in most cases [
14
]. Usually, participating
customers receive information of the new energy price one day in advance. As in the case
of ToU, the CPP is not economically efficient for customers, owing to the predefined prices.
In addition, the ratio between the peak and off-peak price is lower on a ToU program
Smart Cities 2023,15
than in CPP event days [
15
]. In the variable period CPP, the utility controls the start time
of the event and its duration, which imposes a limited number of hours for the event.
For example, the utility can trigger an event (CPP) 20 times in a year for a maximum of 4 h
for each event and a maximum of 60 h each year [13,16].
Real-time pricing (RTP) requires maximum customer cooperation. As part of an
RTP program, the energy supplier advertises the electricity tariff on a continuous basis;
rates are determined and announced before the beginning of each period (for example,
30 min in advance [
17
]). Therefore, two-way communication capabilities are important
for successful implementation. In an RTP-based system, the installation of an energy
management controller (EMC) is required at customer premises in order to increase the
speed of decision making. This will guarantee a significant reduction in the electricity
bill [
18
]. However, an RTP implementation requires continuous real-time exchange between
the energy supplier and the consumers, which is unattractive from the customer’s point
of view [
19
]. In addition, the great flow of information exchanged between the energy
supplier and EMCs and the lack of efficient smart meters besides scheme complexity can
be real barriers for that type of systems. Day-ahead RTP (DAP) is an alternative solution
based on RTP in which the planned real-time prices for the next day are announced in
advance to customers according to the price of that day [13].
2.4. Energy Cost Model
Utilities use cost functions to set prices for customers. A utility is supposed to sell
consumers energy from cheaper sources, such as solar, wind or hydro generators, before
switching during peak hours to more expensive fuel generators. These cost functions are
designed to encourage consumers to adapt specific consumption behaviors.
A smart cost function is required to reduce the impact of selfishness on consumer
behavior. Let us denote
Ct(
L
t)
as the cost that consumers must pay to providers for an
amount of energy L
t
during time
t∈ T
. A good cost function selection must meet various
requirements that influence the operation of demand management.
First, the utility provider is under charge for meeting all consumer needs, so the cost
function depends on the total consumption of all consumers L
t
during some time
t∈ T
.
Moreover, the cost function varies according to the time period: the cost increases during
peak periods due to the high prices declared by the utility provider. Other cost function
assumptions are:
• The cost function is an increasing demand function [20].
Ct(La
t)≥CtLb
t∀La
t≥Lb
t(18)
• The cost function is convex or strictly convex [20].
CtθLa
t+ (1−θ)Lb
t<θCt(La
t)+(1−θ)CtLb
t∀t∈ T , 0 <θ<1 (19)
When the user can produce and sell energy back, it means L
t<
0. This signifies
that the user can pay a negative amount for this energy. In other words, the user cost
function is
Ct(Lt)<0
. In this case, the quadratic cost function, C
t(Lt)=
L
2
t
, is obviously
not satisfying this condition. Alternatively, we can try C
t(Lt)=
L
2
tsin(Lt)
, which is not
convex and not satisfying the negativity condition. We set an increasing linear cost function
C
t(Lt)=
k
×
L
t
that is convex but not strictly convex. We note that
k
is a parameter
suggested to give cost values close to those of the quadratic cost functions.
In addition to the conditions of the cost function, the utility makes profits at any given
time t, where the sale price is always higher than the purchase price:
Ct(Lt)>|Ct(−Lt)|=−Ct(−Lt)∀t∈ T (20)
This condition restricts users from making excessive purchasing and selling.
Smart Cities 2023,16
3. Systematic Mapping Study
The aim of this part is to express the intention of the mapping study, outline the specific
steps to achieve the goal and formulate research problems to be investigated. Taking some
inspiration from the guidelines in [
21
], a protocol in five successive processes was adopted,
leading to the final systematic map, shown in Figure 2, as described below.
1.
Research directives define the study protocol and identify the dimensions to be analyzed,
as well as the research questions that need to be answered.
2.
Data collection identifies primary studies by using search strings on several selected
scientific databases.
3.
Screening of the papers brings together the articles related to the inclusion and exclusion
criteria defined in the protocol.
4.
Key-wording using the abstract identifies and combines keywords to seek high-level
understanding about the nature and contribution of the research, thereby generating
an organized classification.
5.
Data extraction mapping maps the existing literature according to the defined criteria
and answers the research questions.
Figure 2. Systematic mapping study protocol.
3.1. Research Directives
This section presents the adopted research protocol and the research questions de-
scription. The protocol includes the object of study (cost and PAR reduction approaches),
its purpose (mentioned previously), preliminary research questions, the search strategy,
the criteria of selection and the extraction form of data. Lastly, the protocol presents an
overview of the articles selected in terms of countries and year of publication. The five
research questions (RQs) for this systematic mapping review are as follows:
RQ1.
What are the most used algorithms and techniques for peak and cost reduction?
RQ2.
What type of energy source has been chosen (e.g., utility grid, renewable or storage)?
RQ3.
What type of building has been treated (e.g., residential, commercial, industrial)?
RQ4.
What are the optimization objectives of the algorithms cited?
RQ5.
What type of energy pricing has been chosen ?
3.2. Data Collection
In order to include relevant articles and exclude irrelevant articles, the research strategy
for this study included querying reference databases with custom search strings, followed
by a manual filtering of results using the predefined inclusion and exclusion criteria.
To minimize the risk of missing relevant articles, four reference databases were queried:
• MDPI data bases (https://www.mdpi.com/, accessed on 31 December 2022);
• Elsevier ScienceDirect (www.sciencedirect.com, accessed on 31 December 2022);
• SpringerLink (https://link.springer.com, accessed on 31 December 2022);
• IEEExplore (http://ieeexplore.ieee.org, accessed on 31 December 2022).
The main areas of focus include control systems, intelligent computation methods and al-
gorithms, simulation tools, user preferences, comfort, building types and the source of supply.
Smart Cities 2023,17
3.3. Screening of Papers for Inclusion and Exclusion
The selection filter for the published studies included the following inclusion and
exclusion criteria:
3.3.1. Inclusion Criteria
The inclusion criteria are:
1. Articles focusing on DSM in SGs.
2.
Articles proposing algorithms and control systems for optimizing PAR and reducing cost.
3. Articles published between 1 January 2013 and 31 December 2022.
4. Articles dealing with cost optimization and PAR reduction.
3.3.2. Exclusion Criteria
The exclusion criteria are:
1. Reviews and surveys. Only first-hand research work is considered.
2. Articles not related to the research.
3. Non-peer-reviewed articles.
3.4. Keywording and Selection Strategy
A multi-stage selection process was designed to provide an overview on algorithms
and methods used in SGs for PAR/cost optimization and to map their frequencies of
publication over time.
In order to perform the search and establish the search string, we derived the main
terms of the mapping questions and checked their synonyms, as well as alternative spellings.
The search string is formulated as follows:
1Dem a n d S i de M an age m e nt A N D o pti m i zat i o n
2AND sma r t g r i d A ND P A R A N D C o s t A N D al g ori t h m
Some synonyms of the previous keywords and similar expressions (e.g., “Energy
Efficiency Management” and “Energy Resource Management”, instead of “Demand Side
Management”) have also been used at later stages to make sure that the search was as
extensive as possible.
The research process (Figure 3) was applied on each of the four databases, and the
results were filtered according to inclusion and exclusion criteria, as recommended in the
systematic mapping study guidelines [
21
]. Then, on 684 potentially relevant papers, further
selection (typical of an SMS) was performed iteratively on the title, then abstract and then
full text to obtain in the end only 104 primary studies.
Figure 3. Primary selection study protocol.
Smart Cities 2023,18
3.5. Data Extraction and Classification
This subsection presents the final result of the selection process as a synthetic
Tables 1–8
gathering the 104 primary studies. The 13 classification criteria are:
1. Ref: the paper reference;
2. Year: the year of publication;
3. Country: the country of the study;
4. Journal/Conference: the publication venue;
5. Building sector: residential, commercial or industrial;
6. Energy source: utility, renewable, or energy storage;
7.
Control Schemes: the general type of control scheme (e.g., heuristic, exact method, hybrid);
8. Algorithm/method: the algorithm/method name used by authors;
9.
Pricing scheme: the pricing scheme hypothesis (e.g., time of use, real time, day-
ahead pricing);
10.
The optimization objectives: (e.g., PAR, cost, communications, appliances waiting time);
11.
User comfort: is user comfort taken into account in the optimization?
12.
User preferences: are user preferences taken into account in the optimization?
13.
Simulation tool: is there a simulation tool involved in the optimization?
Smart Cities 2023,19
Table 1. Comparative table of PAR and cost optimization approaches.
Ref. Year Country Journal/Conference Building Sector Energy Source Control Schemes Algorithm/Method Pricing Scheme
Optimization Objective(s)
User Comfort User Preferences Simulation Tool
PAR Cost CO2
Emission Communication Average
Waiting Time
[22] 2022 Saudi
Arabia Processes Residential Utility ESS
RES Meta-heuristic technique Ant colony optimization (ACO) Fixedprice √ √ √ – – – – MATLAB
2018b
[23] 2022 Pakistan IEEE Access Residential Utility RES Meta-heuristic technique Artificial bee colony RTP ToU DAP
CPP √ √ √ –√ √ – MATLAB
[24] 2022 Romania Computers and Industrial
Engineering Residential Utility Meta-heuristictechnique Signaling game model for
optimization RTP ToU √ √ – – √– – –
[25] 2022 France Applied Energy Residential Utility ESS
RES Hybrid technique Particle swarm optimization and
binary particle swarm optimization ToU √ √ – – √ √ – –
[26] 2022 India
Journal of The Institution of
Engineers (India): Series B
volume
Residential Utility Meta-heuristictechnique Particle swarm optimization RTP √ √ – – – – – MATLAB
[27] 2022 Pakistan Energy Systems Industrial Utility RES Meta-heuristic technique Genetic algorithm ToU √ √ – – – – – –
[28] 2022 UAE Cluster Computing Residential Utility Meta-heuristictechnique Grey wolf optimizer RTP √ √ – – √ √ – –
[29] 2022 Portugal Energy Residential UtilityRES Meta-heuristic technique Genetic algorithm RTP √ √ – – – √ √ Python
[30] 2022 China Computers and Electrical
Engineering Residential Utility RES
ESS Meta-heuristic technique Greywolf optimization RTP √ √ – – – – – –
[31] 2022 India Measurement: Sensors Residential Utility Meta-heuristictechnique Eagle hard optimization ToU √ √ – – – – – –
[32] 2022 Pakistan
Sustainable Energy
Technologies and
Assessments
Industrial Utility RES
ESS Meta-heuristic technique Lion’s algorithm DAP √ √ – – √ √ – MATLAB
[33] 2022 Iran Knowledge-Based Systems Residential Utility RES
ESS Meta-heuristic technique Multi-objective arithmetic
optimization algorithm CPP RTP √ √ – – √ √ – –
[34] 2022 Iran Journal of Building
Engineering
Residential
Commercial
Industrial
Utility Hybrid technique Simplex and improved grey wolf
optimization ToU √ √ – – – – – MATLAB and
CPLEX
[35] 2022 Pakistan Energies Residential Utility Hybrid technique Earth worm algorithm and harmony
search algorithms RTP √ √ – – √ √ – MATLAB
Smart Cities 2023,110
Table 2. Comparative table of PAR and cost optimization approaches.
Ref. Year Country Journal/Conference Building Sector Energy Source Control Schemes Algorithm/Method Pricing Scheme
Optimization Objective(s)
User Comfort User Preferences Simulation Tool
PAR Cost CO2
Emission Communication Average
Waiting Time
[36]2022 Saudi Arabia
and Pakistan IEEE Access Residential Utility RES
ESS Hybrid technique Ant colony optimization and
teaching–learning-based optimization RTP √ √ √ –√√√MATLAB
[37]2022 SaudiArabia Sustainability Residential Utility RES
ESS Hybrid technique Enhanced differential evolution and
genetic algorithm RTP √ √ √ –√ √ –MATLAB
R2018b
[38]2022 Iraq Inventions Residential Utility ESS
RES
Meta-heuristic
technique
Bald eagle search optimization
algorithm RTP √ √ – – – – – MATLAB and
ThingSpeak
[39]2022 India Energies Residential Utility Meta-heuristic
technique
Remodeled sperm swarm
optimization RTP √ √ – – – – – PythonGUROBI
[40]2022 Pakistan Sustainability Residential Utility ESS
RES
Meta-heuristic
technique
Cuckoo search algorithm and
mixed-integer linear programming RTP √ √ – – – – – –
[41]2022 Taiwan Sustainability Residential Utility Meta-heuristic
technique
Non-dominated sorting genetic
algorithm RTP √ √ – – √√√ –
[42]2022 india
2022 International Virtual
Conference on Power
Engineering Computing
and Control
Residential Utility Meta-heuristic
technique Sine–cosine algorithm RTP √ √ – – √ √ – MATLAB
[43]2022 India
International Conference on
Power Electronics and
Renewable Energy Systems
Residential Utility Hybrid technique Antlion optimization RTP √ √ – – – – – –
[36]2022 Saudi Arabia
and Pakistan IEEE Access Residential Utility RES
ESS Hybrid technique Ant colony optimization and
teaching–learning-based optimization RTP √ √ √ –√√√MATLAB
[37]2022 SaudiArabia Sustainability Residential Utility RES
ESS Hybrid technique Enhanced differential evolution and
genetic algorithm RTP √ √ √ –√ √ –MATLAB
R2018b
[44]2021 Brazil Journalof Cleaner
Production Residential Utility ESS
RES
Meta-heuristic
technique
Nonlinear programming, genetic
algorithms, ant colony systems and
particle swarm optimization
RTP √ √ – – – – √
[45]2021 India Journal of Building
Engineering Residential Utility RES Meta-heuristic
technique Least slack time-based scheduling RTP ToU CPP √ √ – – – √– –
[46] 2021 Saudi Arabia
2021 IEEE 4th International
Conference on Renewable
Energy and Power
Engineering
Residential Utility Meta-heuristic
technique Genetic algorithm RTP √ √ –√– – – –
Smart Cities 2023,111
Table 3. Comparative table of PAR and cost optimization approaches.
Ref. Year Country Journal/Conference Building Sector Energy Source Control Schemes Algorithm/Method Pricing Scheme
Optimization Objective(s)
User Comfort User Preferences Simulation Tool
PAR Cost CO2
Emission Communication Average
Waiting Time
[47] 2021 Pakistan IEEE Access Residential
Commercial
Utility ESS
RES Hybrid technique
Genetic algorithm, wind-driven
optimization and particle swarm
optimization
DAP √ √ √ –√ √ – MATLAB
[48] 2021 Pakistan Energies Residential Utility ESS
RES Hybrid technique Genetic algorithm and ant colony
optimization RTP √ √ √ –√ √ –MATLAB
R2013b
[49] 2021 Saudi Arabia Mathematics
Residential
Commercial
Industrial
Utility ESS
RES
Meta-heuristic
technique
Particle swarm optimization and the
strawberry optimization RTP ToU √ √ – – √– – –
[50] 2021 Pakistan Energies Residential Utility ESS
RES Hybrid technique Firefly algorithm and lion algorithm DAP √ √ – – √ √ – MATLAB
[51] 2021 Jordan Multimedia Tools and
Applications(s) Residential Utility Hybrid technique Grasshopper optimization algorithm
and differential evolution ToU and CPP √ √ – – √ √ – MATLAB
[52] 2021 India Sadhana Residential Utility RES Hybrid technique Genetic algorithm and particle swarm
optimization DAP √ √ – – – – – NI
LabVIEW.2015
[53] 2021 Romania Journal of Optimization
Theory and Applications Residential Utility Hybrid technique Stackelberg game ToU √ √ – – – – – –
[54] 2021 Egypt EnergyReports Residential
commercial Utility RES Meta-heuristic Cuckoo optimization algorithm ToU √ √ – – – – – MATLAB
[55] 2021 Pakistan IEEE Access Residential Utility ESS
RES Hybrid technique Hybrid genetic ant colony RTP √ √ √ –√ √ –MATLAB
R2018a
[56] 2021 Pakistan International Journal of
Energy Research Residential Utility ESS
RES Hybrid technique Hybrid genetic ant colony
optimization RTP √ √ √ –√ √ –MATLAB
R2013b
[57] 2021 Pakistan International Conference on
Emerging Technologies Residential Utility Meta-heuristic
technique Jaya algorithm ToUand CPP √ √ – – √ √ –MATLAB
2014a
[58] 2020 China and
Pakistan IEEE Access
Residential
Commercial
Industrial
Utility Hybrid technique Hybrid bacterial foraging and particle
swarm optimization DAP CPP ToU √ √ √ –√ √ – –
[20] 2020 Pakistan Multidisciplinary IEEE
Access Residential Utility Hybrid technique Grey-wolf-modified enhanced
differential evolution algorithm DAP √ √ – – √ √ – –
Smart Cities 2023,112
Table 4. Comparative table of PAR and cost optimization approaches.
Ref. Year Country Journal/Conference Building Sector Energy Source Control Schemes Algorithm/Method Pricing Scheme
Optimization Objective(s)
User Comfort User Preferences Simulation Tool
PAR Cost CO2
Emission Communication Average
Waiting Time
[59] 2020 South
Korea
IEEE Transaction on Smart
Grid Residential Utility ESS Heuristic technique Game theory RTP √ √ – – – – – –
[60] 2020 Pakistan IEEE Access Residential Utility ESS
RES Hybrid technique Hybrid genetic particle swarm
optimization RTP √ √ √ –√ √ – MATLAB
[61] 2020 Spain EEEICand ICPS Europe Industrial Utility Heuristic technique Linear programming DAP √ √ – – – – – –
[62] 2020 South
Korea IEEE Access Residential Utility ESS
RES Hybrid technique
Particle swarm optimization (PSO)
and binary particle swarm
optimization
DAP √ √ – – – – – Cplex/ Dicopt
[63] 2020 India Peer-to-Peer Networking
and Applications Residential Utility ESS
RES Hybrid technique Adaptive neuro-fuzzy inference
system RTP √ √ – – √– – MATLAB
[64] 2020 Singapore Applied Energy Residential Utility ESS
RES Meta-heuristic technique Game theory and genetic algorithm RTP √ √ – – – – – –
[65] 2020 Pakistan Applied Science Residential Utility Meta-heuristic technique Multi-verse optimization sine–cosine
algorithm DAP √ √ – – √– – –
[66] 2020 Poland IET Smart Grid Residential UtilityESS
RES Heuristic technique Fuzzy logic RTP √ √ – – – – – C++ with OOP
[67] 2020 Algeria Optimization and
Engineering Residential Utility Meta-heuristic technique Harris hawks optimization RTPandCPP √ √ – – – – – MATLAB
[68] 2020 Pakistan Electronics
Residential
Commercial
Industrial
Utility Meta-heuristic technique Dragonfly algorithm DAP √ √ – – √– – –
[69] 2020 Pakistan Electronics Industrial Utility Meta-heuristic technique
Grasshopper optimization algorithm
and cuckoo search optimization
algorithm
DAP √ √ – – √ √ – MATLAB
[70] 2020 Pakistan Electronics
Residential
Commercial
Industrial
Utility Meta-heuristic technique Dragonfly algorithm DAP √ √ – – √– – –
[71] 2020 Pakistan
Advanced Information
Networking and
Applications
Residential Utility Meta-heuristic technique Flower pollination algorithm and
Jaya optimization algorithm CPP √ √ – – √ √ –MATLAB
2017a
Smart Cities 2023,113
Table 5. Comparative table of PAR and cost optimization approaches.
Ref. Year Country Journal/Conference Building Sector Energy Source Control Schemes Algorithm/Method Pricing Scheme
Optimization Objective(s)
User Comfort User Preferences Simulation Tool
PAR Cost CO2
Emission Communication Average
Waiting Time
[72] 2019 Pakistan Sustainability Residential Utility ESS
RES Trajectory searchfamily Dijkstra algorithm DAP √ √ – – √ √ – MATLAB2014a
[73] 2019 South
Africa Energy Residential Utility ESS
RES Evolutionary algorithms Improved differential evolution
algorithm DAP √ √ – – √ √ – –
[74] 2019 Pakistan Web, Artificial Intelligence
and Network Applications Residential Utility Meta-heuristic technique Runner updation optimization
algorithm CPPRTP √ √ – – – – – MATLAB
[75] 2019 Ethiopia IEEE CSEE Residential Utility RES Meta-heuristic technique Grey wolf optimizer ToU √ √ – – – – – –
[76] 2019 Korea Future Generation
Computer System Residential Utility Meta-heuristic technique Mutation ant colony optimization ToU √ √ – – √– –
MATLAB VisualC#
on Visual Studio 2010
compatible with.
NET framework 4.0
[77] 2019 Pakistan Process MDPI Residential
Commercial Utility Meta-heuristic technique Grasshopper optimization algorithm
and bacterial foraging optimization DAP √ √ – – – – – MATLAB
[78] 2019 Pakistan Artificial Intelligence and
Network Applications Residential Utility Meta-heuristic technique Strawberry algorithm and earthworm
optimization algorithm RTP CPP √ √ – – √– – –
[79] 2019 Taiwan
IEEE International
Conference on Systems,
Man and Cybernetics
Residential Utility Meta-heuristic technique Search economics for home
appliances scheduling DAP √ √ – – – – – C++Clang++
[80] 2019 India Microprocessors and
Microsystems Residential Utility ESS
RES Hybrid technique Glow-worm swarm optimization and
support vector machine DAP √ √ – – – – – MATLAB2018 a
[5] 2019 China Energies Residential Utility ESS
RES Heuristic technique Game theory DAP √ √ –√– – √MATLAB 2013a
-YALMIP -ILOG’s
CPLEX v.12CPLEX
[81] 2019 UAE Ambient Intell Human
Comput Springer Residential Utility Hybrid technique Harmony search algorithm and
enhanced differential evolution RTP √ √ – – √ √ – MATLAB
[82] 2018 Pakistan Energies Residential Utility Heuristic technique Genetic harmony search algorithm RTP andCPP √ √ – – √ √ – MATLAB 2014b
[83] 2018 Kenya Power and Energy
Engineering Residential ESS RES Hybrid technique Bayesian game theory RTP √ √ – – – – – –
[84] 2018 USA IEEE Trans. Smart Grid Residential Utility Stochastic technique Game theory RTP √ √ –√– – – IBM ILOG CPLEX
Smart Cities 2023,114
Table 6. Comparative table of PAR and cost optimization approaches.
Ref. Year Country Journal/Conference Building Sector Energy Source Control Schemes Algorithm/Method Pricing Scheme
Optimization Objective(s)
User Comfort User Preferences Simulation Tool
PAR Cost CO2
Emission Communication Average
Waiting Time
[85] 2018 2]1.3cmUSA IEEE Green Technologies
Conference
Residential
Commercial UtilityESS Heuristic technique PSO ToU √ √ – – – – – –
[86] 2018 Thailand IEEE Transaction on Smart
Grid Residential UtilityESS RES Heuristic technique Fuzzy low-cost operation ToU *√ √ – – – – – –
[87] 2018 Iran IEEE Smart Grid
Conference Residential
Utility ESS
Conventional-
Units
Hybrid technique Unnamed scheduling and fuzzy logic DAPand ToU √ √ √ *–*–– – GAMS -MILP
and CPLEX
[88] 2018 Pakistan
IEEE International
Conference on Advanced
Information Networking
and Applications
Residential Utility Hybrid technique Enhanced differential harmony
binary particle swarm optimization RTP √ √ *–2*–*–√– MATLAB
[89] 2018 Romania Computers and Industrial
Engineering Elsevier Residential Utility
Evolutionary
optimization
technique
Shifting optimization algorithm ToU √ √ *–*–*–– – MATLAB
2016a
[3] 2018 Pakistan
IEEE International
Conference on Advanced
Information Networking
and Applications
Residential Utility Hybrid technique Enhanced differential harmony
binary particle swarm optimization RTP √ √ – – – √– MATLAB
[90] 2018 Pakistan
IEEE International
Conference on Advanced
Information Networking
and Applications
Residential Utility Hybrid technique Bacterial foraging tabu search RTP √ √ – – √ √ – MATLAB
[4] 2018 China Neural Comput and Applic Residential
Industrial
Utility ESS
RES Heuristic technique Game theory # Equilibrium
market √ √ – – * – – Cplex DECIS
OSL-SE
[91] 2018 Brazil Springer International
Conference, PAAMS Residential Utility Meta-heuristic
technique Gravitational search algorithm RTP √ √ – – – – – LPG
[92] 2017 Pakistan
Advances in
Network-Based
Information Systems
Residential Utility Meta-heuristic
technique
Bacterial foraging optimization and
strawberry algorithm *RTP √ √ – – √ √ – MATLAB
[93] 2017 India
IEEE International
Conference on Electrical,
Instrumentation and
Communication
Engineering
Residential Utility
Evolutionary
optimization
technique
Unnamed scheduling DAP √ √ – – – – – MATLAB
[94] 2017 India
IEEE International
Conference on Power
Systems
Residential
Commercial
Industrial
Utility Meta-heuristic
technique
Multi-objective particle swarm
optimization DAP √ √ – – – – – MATLAB
[95] 2017 UK IEEE Trans. Ind. Inf Residential RES * Artificial immune algorithm DAP √ √ – – – – – –
[96] 2017 Pakistan
Advances in
Network-Based
Information Systems
Residential Utility Meta-heuristic
technique Enhanced differential evolution ToU √ √ – – √– – –
Smart Cities 2023,115
Table 7. Comparative table of PAR and cost optimization approaches.
Ref. Year Country Journal/Conference Building Sector Energy Source Control Schemes Algorithm/Method Pricing Scheme
Optimization Objective(s)
User Comfort User Preferences Simulation Tool
PAR Cost CO2
Emission Communication Average
Waiting Time
[97] 2017 India Sustainable Cities and
Society Residential Utility Linear programming Mixed-integer linear programming ToU √ √ – – – – – GAMS/
CPLEX
[98] 2017 Pakistan
Advances on P2P,Parallel,
Grid, Cloud and Internet
Computing
Residential Utility Meta-heuristic
technique Crow search algorithm RTP √ √ – – √ √ – MATLAB
[99] 2017 Pakistan
IEEE International
Renewable and Sustainable
Energy Conference
Residential Utility RES
ESS Heuristic technique Knapsack algorithm RTP √ √ – – – – – –
[100] 2017 Pakistan
Advances in Intelligent
Networking and
Collaborative Systems
Residential Utility Meta-heuristic
technique
Enhanced differential evolution &
Strawberry Algorithm RTP √ √ – – √ √ – MATLAB
[101] 2017 UK
IEEE International
Conference on Smart
Energy Grid Engineering
Residential Utility Unnamed technique Unnamed scheduling RTP √ √ – – – – – –
[102] 2017 Pakistan
Advances on P2P,Parallel,
Grid, Cloud and Internet
Computing
Residential Utility Meta-heuristic
technique Flower pollination algorithm RTP √ √ – – √– – MATLAB
[103] 2016 India IEEE National Power
Systems Conference
Residential
Commercial
Industrial
Utility Meta-heuristic
technique Particle swarm optimization DAP √ √ – – – – – –
[104] 2016 Australia Applied Energy Elsevie Residential Utility Unnamed technique Unnamed scheduling RTP √ √ – – – – – –
[105] 2016 Pakistan Applied Sciences Residential Utility Heuristic technique Knapsack optimization ToU √ √ – – – √– MATLAB
[106] 2015 Singapore IEEE Innovative Smart Grid
Technologies
Residential
Commercial
Industrial
Utility Meta-heuristic
technique Particle swarm optimization DAP √ √ – – – – – MATLAB
[107] 2015 India
IEEE Power,
Communication and
Information Technology
Conference
Residential RES Meta-heuristic
technique 2D particle swarm optimization DAP √ √ – – – – – MATLAB
[108] 2015 Pakistan
IEEE International
Conference on
Network-Based
Information Systems
Residential
Commercial
Industrial
Utility Meta-heuristic
technique Genetic algorithm RTP √ √ – – – – – –
[109] 2015 South Africa IEEE Innovative Smart Grid
Technologies Residential Utility Evolutionary
technique Daily maximum energy scheduling ToU √ √ – – – – – MILP CPLEX
Smart Cities 2023,116
Table 8. Comparative table of PAR and cost optimization approaches.
Ref. Year Country Journal/Conference Building Sector Energy Source Control Schemes Algorithm/Method Pricing Scheme
Optimization Objective(s)
User Comfort User Preferences Simulation Tool
PAR Cost CO2
Emission Communication Average
Waiting Time
[110] 2015 Pakistan Energy Research Residential Utility Meta-heuristic technique Genetic algorithm RTP √ √ – – √– – –
[111] 2015 Italy-
france Computer Communications Residential Utility Heuristic technique Game theory RTP √ √ – – – – – –
[112] 2014 Japan
2014 International
Conference on Electronics,
Information and
Communications
Residential Utility ESS Convex optimization
technique Unnamed scheduling RTP √ √ – – – – – –
[113] 2014 China
IEEE International Joint
Conference on Neural
Networks
Residential Utility Meta-heuristic technique Stackelberg game and genetic
algorithm RTP √ √ – – – – – IBM CPLEX
[9] 2014 Singapore IEEE Journal of Selected
Topics in Signal Processing Residential Utility Distributed schemes Distributed algorithm RTP √ √ – – – – – –
[114] 2013 UK Soft Computing Residential Utility Meta-heuristic technique Stackelberg game and genetic
algorithms RTP √ √ – – – – – –
[115] 2013 Iran
2013 13th international
conference on environment
and electrical engineering
Residential Utility Meta-heuristic technique Genetic algorithm RTP √ √ – – – – – MATLAB
[116] 2013 China
2013 IEEE international
conference on
communications
workshops
Residential Utility Heuristic technique Linear programming RTP √ √ – – – – – –
Smart Cities 2023,117
4. Mapping Questions Results and Analysis
This section presents answers to the mapping questions and analyzes global trends.
In general, there has been a growth of interest in this topic, particularly since 2017 as
shown in Figure 4. The relative increase in this topic was approximately 85%: from three
selected studies in 2013 up to an average of nineteen selected studies between 2021 and
2022. This can be considered as an indicator of how electricity management and control
methods have gained importance in recent years.
Figure 4. Number of publications on the web by year and type of articles.
Moreover, the proportion of journal papers tends to increase throughout the years,
which indicates a certain maturity of the field. Pakistan (Figure 5) in particular seems very
interested in PAR and cost optimization approaches. India, Saudi Arabia, Iran, China and
South Korea follow. Most of these are Asian and emerging countries, with a strong urban
population growth. Thus, they go through a very important increase in energy demand in
a short period of time [117], which justifies the need for optimization.
Figure 5. Number of surveys per country.
The rest of the section is dedicated to answering every research question and providing
an analysis of the global trends.
RQ1. What are the most used algorithms and techniques for peak and cost reduction?
Optimization is the process of determining the state of decision variables that give
the best value for single or multi-objective functions. First of all, what is striking is the
Smart Cities 2023,118
diversity of used algorithms (Figure 6) for solving only two optimization problems: peak
and cost reduction. This can be seen in the multiple (sometimes original) names given to
heuristics: dragonfly, earth worm, lion, grey wolf, etc.
Figure 6. Algorithms used for peak and cost reduction.
This diversity could be a manifestation of Wolpert et al.’s No Free Lunch Theorem [
118
],
which states that: “Roughly speaking we show that for both static and time dependent
optimization problems the average performance of any pair of algorithms across all possible
problems is exactly identical”. The implications are that there is no optimization algorithm
that performs best for all problems. Although the problem seems the same (peak and
cost optimization), in practice, the formalization differs in the survey papers, and the
multi-objectives too (e.g., CO
2
emission, waiting time). This might justify the multiplicity
Smart Cities 2023,119
of optimization heuristics. Nevertheless, the sheer number of algorithms is still, in our
point of view, a little bit inflated. Sometimes, papers try to use ’yet another’ heuristic with a
unique name to prove the originality of the paper’s contribution with regard to the state of
the art.
The peak and cost optimization algorithms that we found can be classified into the
following categories: (1) analytical and exact algorithms; (2) heuristics (approximate algo-
rithms).
Analytical and exact algorithms were the main approach for problem optimization,
before the advent of heuristics. Some of them are based on the first and second-order
derivatives of the objective functions. They can efficiently find the exact optimum for linear
or convex problems, for example. In the works that we surveyed, these approaches are
used, but usually with another approximate algorithm. Some instances that we found
include linear programming, nonlinear programming, dynamic programming and integer
programming [
4
,
40
,
44
,
116
]. However, exact methods are inefficient and very slow in
more complex (NP-hard ones, for example) problems with many local optima, stochastic or
unknown search space, many objectives (e.g., with user preference inclusion) and renewable
sources integration. This is why their proportion in our particular case is relatively small
compared to approximate algorithms.
These are commonly called heuristics. Metaheuristics define classes of heuristics;
that is, conceptual frameworks and rules to devise a good approximate algorithm that
might converge to a global optimum [
119
]. However, metaheuristics are probabilistic in
nature and controlled by parameters such as population, elite population size, number of
generations, etc. In most of the studies, there is a concern that adjusting the parameters is
an extremely critical problem, as it can directly affect the performance of the techniques.
An incorrect setting can lead to an increase in computation time or a local optimum [
120
].
Possible taxonomies for metaheuristics are [
119
]: (1) evolution-based; (2) swarm-based;
(3) human-based; (4) physics based; (5) math-based.
Evolution-based algorithms are inspired by the Darwinian law of natural selec-
tion. They iteratively change a population of solutions using evolutionary operators
(i.e., selection, cross-over, mutation), to improve the solutions quality, hoping to con-
verge to the global optimum. genetic algorithms (GAs) and differential evolution are two
instances used for cost/peak optimization. The first ones are the most popular in our
study [
29
,
46
,
52
,
70
,
102
,
108
,
113
,
121
], perhaps because they are notoriously good for schedul-
ing tasks (our present use case), and more generally for complex discrete structures op-
timization. What is also striking is the hybridization between GAs and other types of
heuristics (e.g., genetic/ant colony hybrid optimization).
Swarm-based algorithms replicate the social interactions of certain living beings (e.g.,
bacteria, birds, wolves, lions). Usually, the social interactions considered are related to
survival (e.g., hunting, mating). Individuals from the swarm also share information, which
influences their behavior in the following iterations. Some examples that we found are:
particle swarm optimization [
103
], ant colony optimization [
76
], grey wolf optimization,
bacterial foraging [
77
], lion’s algorithm [
50
] and cuckoo search [
54
]. According to our
cumulative statistics, these types of algorithms are frequent in optimizing the PAR and
energy consumption cost. A possible reason is that they require fewer parameter tunings.
However, the specific meta-heuristic of particle swarm optimization is less used than
genetic algorithms because it is less adapted to discrete constraint problems.
Human-based metaheuristics take their inspiration from social interactions and human
behavior. We found one instance of such algorithms published in IEEE Access [
36
], mixed
with a swarm-based algorithm: teaching–learning-based optimization with ant-colony-
based heuristics. Physics-based algorithms tend to explore the search space using agents
that respect physical laws. They are practically inexistent in our study. Math-based
heuristics are only based on mathematical equations and do not obtain their inspiration
from a natural phenomenon. Few instances have been found for the peak/energy cost
optimization problem: sine–cosine [42,65] or multi-objective arithmetic optimization.
Smart Cities 2023,120
Game theory [
122
] is another mathematical model that studies the outcome and
optimal strategies for situations where agents interact with each other according to a set
of fixed rules. This theory includes four elements: players, information that they have,
their possible actions and the payoffs. Stackelberg games are an instance of this theory
where there is a leader (in our instance, the energy producer) and
n
followers (in our
instance, the consumers). The best response is called the Stackelberg–Nash equilibrium,
with the producer supplying maximum renewable energy and consumers minimizing
tariffs by appliances shifting. In our survey, these types of algorithms are used more than
10 times [
4
,
5
,
20
,
53
,
59
,
83
,
113
,
114
,
123
,
124
], which is as often as very other popular swarm-
based metaheuristics. They are also often hybridized with genetic algorithms in order to
choose the actions.
Fuzzy logic [
125
] is an interesting inference paradigm that we found when studying
papers related to peak/energy cost optimization. It manipulates variables with levels of
truth represented by a real number between 0 and 1. The inference rules from this type of
logic are used to decide when to use the appliances (shifting and scheduling).
We noticed that population-based metaheuristics are much more used for cost/peak
optimization than single-solution ones. The first type improves a set of candidate solutions
iteratively (as opposed to one candidate solution). Single-solution heuristics are preferred
when the fitness function is computationally intensive. In this case, calculating the energy
cost based on the consumption schedule is fairly straightforward, which explains what
we have.
Another important aspect is the dataset used as the input to the algorithms and its
impact on the optimization effectiveness. During our data collection, we identified three
major input categories: real-world, pre-generated and randomly generated data. Real-
world data were not popular in the 104 selected studies [
45
,
70
]. The problem might be in
the fact that a real-world dataset is often small and tied to a specific application, which is a
preferred option only in particular cases. Moreover, in certain instances, researchers seek to
prove the good performance of their proposed algorithm with adapted data. On the other
hand, artificial and randomly generated data are more popular [
49
,
61
,
84
]. They give a large
amount of data, which provides useful information on the characteristics of the compared
optimization algorithms. The difficulty is to rationalize their link with the real performance
of the algorithms.
On all these types of data, the great frequency of use of genetic algorithms and
particle swarm optimization shows their good exploration/exploitation capabilities of the
solution space. Many comparative studies [
65
,
69
,
70
] rank them amongst top algorithms
for optimizing PAR and cost. Their rank (relative to each other) varies from one study to
another, depending on the multi-objective optimization function (e.g., cost, PAR, waiting
time) and also according to the conditions and input parameters (e.g., number of users,
integration of renewable or storage systems).
In addition to the dataset impact, for the same algorithm, there are environmental
factors that influence the results: the programming language, skills of the programmer and
computer environment used to test the algorithm.
RQ2. What type of energy source has been chosen?
Energy supply source types were also studied in our paper. The utility grid supply
was large as it comprises 96% of the literature, while renewable energy occupies 35% and
storage power systems occupies 32%.
The proportion of renewable and storage energy systems are close (35% vs. 32%).
This can be explained by the fact that they are usually used together (e.g. solar panel with
battery) in an installation.
What is striking is that renewables are not used as often as we expected (a third
of the literature), although, with the current world’s climatic and energetic situation,
they are fundamental. This might be because the emerging countries (not yet mature for
generalized renewable use) are the most represented in the studies. It can also be explained
Smart Cities 2023,121
by (1) problems of integration into the system; (2) an increased difficulty in solving the
optimization problem.
Regarding the first reason, the requirement of a large area for installation and the relia-
bility of protection circuits to isolate them from the existing network whenever necessary
is a great challenge. The lack of technically qualified manpower and a poor selection of
the optimal place for the implementation will also affect the integration of this type of
energy system. The fluctuating and unpredictable nature of renewable energy sources such
as photo-voltaic solar and wind turbines require complex technologies and a deep study
starting in the site, evaluating the impacts on the network. All of this is especially true in
emerging countries, which are very well represented in our survey (Figure 5). The cost
of the batteries (although there are historical improvements [
126
]) is also sometimes a
negative factor.
Regarding the second reason, there is an increasing complexity induced by adding
intermittent renewable energy sources and battery storage systems in the optimization.
This is in part due to (a) the lack of good models; (b) the lack of accurate data sets (e.g.,
solar and wind); (c) the complexity of the resulting optimization problem [127,128].
RQ3. What type of building has been treated?
A demand response program can increase its effectiveness by taking into consideration
the types of consumers to which it applies. Typically, they are either residential,commercial
or industrial. Their needs are completely different in terms of energy, load and equipment
used. However, it is important to keep in mind that the prerequisite to energy consumption
optimization is always good energy building design [
129
] (e.g., insulation, shape, envelope
system, orientation), which can improve energy efficiency by up to 50%.
In our systematic mapping study, we noticed from (Figure 7) the predominance (96%)
of the residential building type, followed by the other two (in the same proportions: 15% vs.
13%). This could be because residential buildings are much more common than the others.
Moreover, they present very interesting challenges due to the unpredictable consumption
pattern. Industrial buildings follow because of some specific challenges linked to critical
equipment and the availability of a sensor architecture by default. Commercial buildings
also present interesting challenges due to the heating, cooling and lighting growing energy
demands. We also noticed that papers usually tackle either one type of building or all of
them at the same time.
Figure 7. Building type trends.
Smart Cities 2023,122
Regarding residential buildings, the design of an effective DR program is very com-
plicated, mainly because of the fluctuating consumption patterns, which require vigilant
modeling: individual human behavior is sometimes unpredictable. The DR program ap-
plied should not assume that all customers have the same energy consumption patterns, as
mentioned in [
130
]. In the reviewed studies, we found that all residential consumers can be
grouped into five different categories:
1.
Long-range consumers are able to shift their consumption over a wide range of time
following changes in prices;
2.
Real-world postponing consumers have a perception depending only on current and
future prices;
3.
Real-world advancing customers have a perception depending only on current and
past periods;
4.
Real-world mixed consumers are a mix of postponing and advancing consumers, taking
into account the past, present and future;
5.
Short-range consumers do not optimize their load and are only concerned and worried
about the power price at the current time.
That is why, although the residential sector constitutes the bulk of buildings, the
optimization has to be adaptive by taking into account the consumer’s profile as a variable
in the models.
Regarding industrial consumers, they are very-high-energy users. Thus, the optimiza-
tion impact is huge, if carried out correctly. However, although the infrastructure is already
equipped with sensors, measurement technologies and personal operators, the challenge
of a demand response program exists [
32
,
61
,
69
]. In our survey, we confirmed that the
implementation of DR is complicated because of the critical loads in industrial plants. A
simple service disconnection may cause a break of production, and millions of dollars of
financial loss. In fact, some manufacturing systems exhibit hard real-time constraints where
scheduling must be performed with high accuracy [
131
]. This is why the optimization
has to take into account inelastic and critical load demand and only act on non-critical
consumption loads.
Finally, regarding commercial buildings, what transpires in the works that we studied
is that commercial sectors present an important part of the total electricity consumption,
which is expected to increase. Water heating, cooling, space heating, lighting, refrigeration
and ventilation are the main electrical energy consumers. Computers, electronics and other
loads are classified as miscellaneous electrical loads, which include plug loads and all hard-
wired ones that are not responsible for cooling, lighting, water heating or space heating.
The reduction in their electrical consumption can be obtained either by the adoption
of energy-efficient construction technologies or by controlling the energy consumption
behavior of buildings thanks to the price elasticity of energy demand.
RQ4. What are the optimization objectives of the cited algorithms?
The main objectives of demand-side management algorithms studied in this paper are
to reduce the peak-to-average ratio and minimize the cost of consumption. That is why,
naturally, 100% of the papers (Figure 8) tackle these two aspects. Note that there is a natural
reduction in the cost and peak when the papers include renewable (cheaper) energy data.
However, we notice that there are other ’secondary’ optimization objectives: the
waiting time of appliances and user comfort come in second place, with around 41% and
35% each. Finally, communications, CO
2
emissions and user preferences are considered in
only very few studies.
Smart Cities 2023,123
Figure 8. Algorithms optimization objectives.
These results can be explained by the fact that the appliances waiting time and com-
fort are usually intertwined with PAR and cost optimization. Otherwise, a naive cost-
minimizing solution would consist of shifting all appliances to the moments with cheaper
electricity. In practice, the PAR and cost reduction are often constrained by time intervals
Ia
,where the appliance function can be freely shifted. Optimizing these two objectives
consists of choosing the functioning periods that minimize them in these intervals. Often,
there is a trade-off between this optimization and the delay that the appliance waits to start
functioning in Ia.
Regarding user comfort, it is usually computed using the priority of loads as defined
by the user or a set of differences elevated to a certain exponent. These differences depend
on the schedulable or non-schedulable nature of appliances. They can represent (a) the
appliance waiting time; (b) the gap between optimal appliance power and real power.
Depending on the exponent and also on a multiplication factor, discomfort can be computed
differently, influencing the optimization. However, very often, the factors and exponents
are close (e.g., 2 for the quadratic Taguchi loss function [132]).
Regarding CO
2
emissions, they are not considered very often. Since their reduction
is often a consequence of maximizing renewable energies use, this could be linked to the
smaller proportion of renewables data sets used in the works (Figure 9). The majority
of research on CO
2
emissions cited in this survey does not use data from source-specific
emission testing or continuous emission monitors. This is because they are not always
available from individual sources. They use emission factors, which are representative
values linking the quantity of the atmosphere pollutant to the type of activity (energy
production) associated with their emissions [
23
,
36
,
47
,
48
,
55
,
87
,
87
]. Usually, these are the
averages of the available data of acceptable quality. This provides sometimes approximate
results for the CO2optimization objective.
Finally, what is very surprising is the lack of explicit consideration for user preferences
as well as communications [
5
,
46
,
84
]. There are very few data documenting exchanged
information between the loads and the control system during real-time connectivity (e.g.,
the RTP case) because it requires a large frequency bandwidth and communication equip-
ment capable of encrypting the information transmitted to the control system to preserve
consumer privacy. Not taking into account preferences or communications does not allow
the user to make the compromise between payments and comfort. It impacts interactivity,
which could hinder adoption in the consumer market.
Smart Cities 2023,124
Figure 9. Building supply source trends.
RQ5. What type of energy pricing has been chosen?
Figure 10 shows the various pricing schemes (pricing scheme definitions in Section 2.3)
used in the reviewed papers. Real-time pricing (RTP) is the most used, with a proportion
of a little less than half the studies (48%). It is followed by day-ahead pricing (DAP) and
time-of-use pricing (ToU), with fairly equivalent proportions (respectively, 24% and 18 %).
Finally, critical peak pricing (CPP) has a proportion of only 10%.
Figure 10. Electricity pricing scheme.
A possible explanation is that RTP is theoretically the most efficient way to adapt
the demand to utility constraints. This is because it constantly (sometimes every 15 min)
updates the prices according to the wholesale electricity market or utility’s production
cost. However, note that it costs a large amount of communications (as well as metering
infrastructure), which is surprisingly not often taken into account in the optimization
(Figure 8). Thus, we argue that, if communication were considered in the multi-objective
optimization, the pricing schemes frequency of use would radically change in the works.
DAP is a good compromise between complexity and efficiency, which justifies the
second position. Day-ahead pricing advertises prices for the next day, making it more
Smart Cities 2023,125
relaxed (thus more realistic) than RTP. Time-of-use (ToU) pricing is more rigid, and thus
less popular in the studies: it consists of the classic attribution of fixed prices according to
particular time periods (in the day or week). Thus, it does not give any useful incentive or
information to the user during off-peak periods. Finally, critical peak pricing is an extension
of ToU with so-called ’exceptions’ where prices are increased for specific time periods.
5. Discussion
In this section, based on the comparative analysis of the 104 studies, and the answers
to the five research questions, we attempt to provide to the research community a list of
Open Issues and Recommendations for the future.
5.1. Algorithmic Hybridization
Our systematic mapping study clearly shows the need for the efficient hybridization
of two or more algorithms by taking the advantages of several strategies during a cycle,
or during each cycle in the same optimization [
3
,
35
,
90
,
133
]. For complex problems that
are often NP-hard (e.g., including energy storage systems with intermittent renewable
energy sources), a simple new generation algorithm may fail to obtain a practical and
good solution. Exact algorithms, on the other hand, are usually not adapted, as they often
impose computing first or second-order derivatives and require the linearity or convexity
of problems.
We recommend a combination of an evolution-based metaheuristic with a swarm-
based one [
52
]. They are both population-based algorithms that are adapted to our problem
because (1) with renewables integration, the problem space becomes very big, and needs
an efficient global search; (2) the fitness function is relatively easy to compute (energy cost),
which disqualifies the motivation for single-point search methods (as used in [90]).
More specifically, the motivation lies in the fact that GAs in particular are good for
exploration and less adapted to exploitation (which is quite the opposite for swarm-based
algorithms [
134
,
135
]). Indeed, from the technical point of view, GAs solutions’ (considered
as chromosomes) crossover operation provides excellent search capabilities in the solution
space [
136
]. It consists of choosing one or multiple ’points’ on both parent chromosomes
and swapping genes to the point’s left/right between the parents. However, the only
exploitation operator in GAs is the mutation, which limits the change in chromosomes
offspring. Apart from very efficient exploitation, note that swarm optimization takes into
account the interaction between solutions (considered as swarm particles). Particle swarm
optimization in particular promotes it by allowing for a faster information flow between par-
ticles: each one updates its position using its own pass experience (
pbest
in the mathematical
notations), as well as following the best particle’s movement (global interaction).
Thus, in the final model, the idea could be to alternate between GAs iterations (diverse
offspring generation for exploration) and swarm optimization iterations (offspring are
guided by the particle ’movement’ of their parents) until the maximum number of iterations
or the termination condition is met. The chromosomes generation would be initially set
to 0. A GA iteration would select parents for mating, cross them over and add them to
the population. Swarm optimization could improve the population’s fitness in the next
iteration. The best individuals would then be selected and produce the new generation
for GAs.
5.2. Interactive and Real-Time User Preference Consideration
Very few (around 6) from the 104 studied papers, (Figure 8) consider user preferences
in the optimization problem. Among the most notable works, there are those of He et al. [
5
]
and Liu et al. [
9
]. In [
5
], a distributed demand-side management control mechanism is
proposed that finds an optimal consumption/prediction routine, taking into consideration
fluctuating prices and user choice. In the surveyed works, one of the suggestions is defining
a “User Convenient” schedule and “Grid Convenient” one [
9
]. The idea is to compute
metrics quantifying the deviation between them. However, for a general adoption, most
Smart Cities 2023,126
algorithms lack real-time interactivity. This task is also a part of transitioning from research
results to consumer-market-friendly solutions, which is not always easy.
The ideal commercial system could be pictured as a control screen (or tablet)-based
system that is user interactive and optimizes in real time. The user preference has to be
the priority to enable the customer acceptance of the system, as advocated by Liu et al. [
9
].
The real-time aspect switches the optimization parameters completely as, for example,
the user no longer has a clear set of schedule intervals for their appliances, but a mere
approximate prediction of the future. The algorithm also has to involve a very fast opti-
mization heuristic.
Finally, in a commercial system, practical concerns have to be taken into account,
such as response/decision fatigue. In smart grid/user interactions, the right balance between
information sharing and communication payload has to be found to prevent overwhelming
the customer. For example, in RTP, a frequent price change every 15 min might discourage
the consumer from interacting and also bloat the communication channel between the
energy supplier and consumer.
5.3. Accurate Renewable Energy and Storage Systems Integration
Accurate renewable energy and storage systems integration in PAR and cost reduction
optimization is another open research issue. As we can see in Figure 9, less than half of the
works tackle these issues.
In reality, when the customer integrates intermittent renewables and batteries, the
optimization problem changes completely. Instead of being an appliance-shifting problem,
the customer schedules their appliances while respecting certain functioning time intervals.
They have the possibility to use battery/renewable energy, as a wildcard, to reduce the
utility energy peak [36,37,47].
This integration cannot be performed if accurate models for intermittent renewable
energy, which take into account their inherent uncertainty and unpredictability, are not
proposed. In addition to this, there is an increasing need for more datasets [
137
] that
could enable building these models. Finally, throughout our reviewing, we found that
encouraging the adoption of integrated energy systems (IESs) is also very important in this
context. An IES [
138
] incorporates renewables, storage and thermal technologies in the
grid, unifying all of them with regard to the user.
5.4. Broadening the Scope of PAR Optimization
Throughout our review, we noted a general trend in optimization objectives where
PAR and cost are considered in every study. Interest in CO
2
emissions and communications
optimization is emerging yet remains marginal (Figure 8). Most studies focus on residential
buildings as opposed to commercial and industrial plants. This highly contrasts with the
significant proportion of studies originating in emerging countries (Figure 5), with a rapid
development of industrial high-energy consumption plants. A fast transformation was
emphasized in the COP27 [
139
] (Sharm-El-Sheikh) as a contributing factor in the climate
change acceleration.
We advocate for more research effort in the direction of industrial/commercial build-
ings energy optimization, as well as taking into account ’secondary’ optimization objectives
such as communications and gas emissions. Some industries in particular (e.g., aluminium
production consumes approximately 70 GJ/tonne) are huge energy consumers. The impact
of a small algorithmic improvement can thus greatly reduce electrical consumption. In most
of the works [
32
,
61
,
69
,
131
] that tackle industrial buildings, the following four singularities
of the energy consumption make the optimization difficult: (1) HVAC and lighting are not
the most energy consuming (as opposed to residential buildings); (2) most processes run
at standard speeds with strong inter-dependencies and no possibility of interruption [
61
];
(3) safety and critical time are often hard constraints; (4) different rates from the residential
ones are applied. All these constraints can breed creativity in the design of new PAR and
cost optimization algorithms. Finally, some algorithms that successfully manage big com-
Smart Cities 2023,127
mercial buildings could be re-adapted to optimize the consumption of groups of residential
buildings (macro-scale), which exhibit some similar macro-consumption patterns.
Regarding CO
2
and communications optimization, we found that they were insuffi-
ciently addressed in the surveyed works [
37
,
46
,
47
,
74
]. Usually, researchers try to maximize
user satisfaction (represented by waiting time, comfort and, less often, preference) because
of the traditional trade-off with cost. However, in the current climate change context,
gas emissions (4.69 metric tons per capita in 2022 [
140
]) produced by fuel-based power
generators, for example, should not be considered as externalities. This goes hand in hand
with accurate renewable energy integration (see Section 5.3) because it is low in carbon
dioxide emissions. It also poses the problem of precisely quantifying the CO
2
emissions as
a function of a used energy source. In general, the electricity emission factor (CO
2
/MWh)
is used, although it is not always accurate. Finally, communications optimization is very
rare in the works that we surveyed. However, its impact is also important in our context,
regarding: (1) decision fatigue (especially in the real-time pricing scheme) due to too much
information; (2) exposing the network to potential attacks (eavesdropping, jamming, false
injection). Some original works [
36
] propose in their scheme a single-way communication
from the control center to the user to preserve confidentiality with minimal overhead.
6. Conclusions
In this paper, we conducted the first (to our knowledge) systematic mapping study
on peak-to-average-ratio and cost optimization approaches for demand-side management
in the smart grid. Reviewed works cover a decade: 1 January 2013 to 31 December 2022.
Following a systematic and reproducible methodology, we selected 104 publications defined
as “original research” from four different scientific databases, and classified them according
to 13 comparison criteria. Then, we analyzed these works according to 5 research questions
linked to algorithmic trends, energy source, building type, optimization objectives and
pricing schemes. Some main findings are: (i) the predominance of the genetic algorithm
(adequate for discrete optimization problems), but with a significant use of various swarm-
based metaheuristics; (ii) an insufficient focus on renewable and storage systems because
of their inherent unpredictability and uncertainty; (iii) a bias toward residential buildings,
although industrial ones are highly energy consuming; (iv) a preference for real-time
pricing schemes despite their communications cost.
We identified a set of recommendations for the research community: (1) a hybridiza-
tion between the strength of evolution-based heuristics in solving discrete scheduling
problems and the speed/accuracy of swarm-based heuristics; (2) developing real-time user
preference optimization mechanisms to encourage commercial adoption; (3) developing
accurate renewable (or storage) models despite their inherent uncertainty/unpredictability;
(4) broadening the scope of optimization to industrial buildings and ’secondary’ objective
minimization (e.g., CO2emissions, communications).
In future works, we intend to focus on real-time user preference considerations, as
it is a very interesting research area, with multiple challenges. This implies developing
fast parameterizable approaches with a trade-off between speed and optimality. This will
surely be the subject of a more detailed systematic literature review (SLR) by us. An SLR
details a specific area of research and answers questions related to it, while a systematic
mapping study structures the current state of the art.
Author Contributions:
All authors have participated in the conceptualization, methodology, analysis
of results and writing of the article. All authors have read and agreed to the published version of the
manuscript.
Funding:
This work was financially supported by the National Center of Scientific and Technical
Research (CNRST), Morocco.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Smart Cities 2023,128
Nomenclature
iessential appliances
sshiftable appliance
rthrottleable appliance
nconsumer
t time interval [s]
Ttotal number of time intervals in a day
et
n,i essential energy consumed by user nduring time interval t[Wh]
et
n,s shiftable energy consumed by user nduring time interval t[Wh]
et
n,r throttleable energy consumed by user nduring time interval t[Wh]
xn,t total consumed energy by user nduring time interval t[Wh]
Entotal daily energy demand of consumer n[Wh]
bn,0 battery level at the beginning of the day for consumer n[Wh]
Bnbattery capacity of user n[Wh]
rnmaximum rates of battery charge/discharge of user n[Wh]
an,t battery charging/discharging schedule for user nduring time interval t
Ln,t load demand to be purchased by user nfrom the utility during time interval t[Wh]
Onoperating time slot of consumer n
Lppeak load of the smart grid network [Wh]
Laaverage load of the smart grid network [Wh]
Ctcost function
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