Renewable and Sustainable Energy Reviews 88 (2018) 297–325

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Renewable and Sustainable Energy Reviews

journal homepage: www.elsevier.com/locate/rser

Forecasting methods in energy planning models T

⁎
Kumar Biswajit Debnath , Monjur Mourshed
School of Engineering, Cardiff University, Cardiff CF24 3AA, United Kingdom

A R T I C L E I N F O A B S T R A C T

Keywords: Energy planning models (EPMs) play an indispensable role in policy formulation and energy sector development.
Forecasting methods The forecasting of energy demand and supply is at the heart of an EPM. Different forecasting methods, from
prediction statistical to machine learning have been applied in the past. The selection of a forecasting method is mostly
energy demand based on data availability and the objectives of the tool and planning exercise. We present a systematic and
load forecasting
critical review of forecasting methods used in 483 EPMs. The methods were analyzed for forecasting accuracy;
energy planning models
applicability for temporal and spatial predictions; and relevance to planning and policy objectives. Fifty different
forecasting methods were identified. Artificial neural network (ANN) is the most widely used method, which is
applied in 40% of the reviewed EPMs. The other popular methods, in descending order, are: support vector
machine (SVM), autoregressive integrated moving average (ARIMA), fuzzy logic (FL), linear regression (LR),
genetic algorithm (GA), particle swarm optimization (PSO), grey prediction (GM) and autoregressive moving
average (ARMA). Regarding accuracy, computational intelligence (CI) methods demonstrate better performance
than that of the statistical ones, in particular for parameters with greater variability in the source data. Moreever,
hybrid methods yield better accuracy than that of the stand-alone ones. Statistical methods are used for only
short and medium range, while CI methods are preferable for all temporal forecasting ranges (short, medium and
long). Based on objective, most EPMs focused on energy demand and load forecasting. In terms, geographical
coverage, the highest number of EPMs were developed in China. However, collectively, more models were
established for the developed countries than the developing ones. Findings would benefit researchers and
professionals in gaining an appreciation of the forecasting methods and enable them to select appropriate
method(s) to meet their needs.

1. Introduction Research indicates that CO2 emissions are negatively associated with
national expenditure on energy research; therefore, the transition away
Increasing greenhouse gases (GHGs) emission contribute to global from carbonintensive energy generation for atmospheric CO2 stabili-
warming, resulting in amplified global temperature and associated zation will require significant investments in innovative energy re-
vulnerabilities [1]. Mitigating the impacts of climate change requires search and development [8].
the reduction or at the very least the stabilization of atmospheric CO2 EPMs are essential for assisting stakeholders in making informed
concentrations, which can be achieved by decreasing global carbon decisions for future energy sector development – globally, regionally
outflow from energy and land-use sectors, the two major GHG sources. and nationally. The development of EPMs started in the 1960's [9], but
Emissions from land-use have been nearly constant, while the emissions the interest in them increased after the oil crisis in the 1970's that
from fossil fuel based energy system climbed up by 29% between 2000 highlighted the effects of dependency on conventional fuel sources on
and 2008 [2]. If current GHG concentrations remain constant, the global, regional and national economies, in particular, the role of
world will experience a few centuries of rising mean temperatures and exogenous political events on the oil market [10]. The crisis acted as a
sea levels [3–5]. Studies suggest that the current energy and transpor- catalyst for the critical assessment of fuel resources, rational use and
tation systems are likely to be responsible for significant CO2 discharges conservation of energy resources, and long-term energy planning for
over the next fifty years [6], which can increase the global mean tem- global, regional, national and sectoral utilization [11]. Also, the Rio
perature by approximately 1.1–1.4 °C between 2010 and 2060 [7]. Earth Summit in 1992 and the report of the Intergovernmental Panel on
Future initiatives on energy planning and development should, there- Climate Change (IPCC) in 1995 triggered further environmental studies
fore, focus on decarbonizing the energy generation and demand sectors. on GHG emissions [12], while cautiously concluding that CO2 emissions

⁎
Corresponding author.
E-mail address: DebnathK@cardiff.ac.uk (K.B. Debnath).

https://doi.org/10.1016/j.rser.2018.02.002
Received 24 August 2016; Received in revised form 30 September 2017; Accepted 3 February 2018
Available online 15 March 2018
1364-0321/ © 2018 Elsevier Ltd. All rights reserved.
K.B. Debnath, M. Mourshed Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Table 1 artificial intelligence not only gives an inaccurate account but also
Searched keywords and associated groups. hinders the informed comprehension of the strengths and weaknesses of
different approaches. The hybridization of methods to suit application
Model Objective Geographical extent Time
horizon areas is characterized by data incompleteness and uncertainty; tem-
poral and spatial variability; and domain features – all of which man-
Energy Forecasting Global Short dates a new classification scheme.
Electricity Projection Regional Medium
Existing reviews thus lack a comprehensive coverage regarding
Energy information Country Long
Energy economic scope, accuracy, and applicability. The objective of this review is,
Energy supply and/or therefore, to analyze the methods utilized in different EPMs to in-
demand vestigate their accuracy, objective, temporal and spatial extents with a
Emission reduction view to identifying the factors behind the choice of forecasting
Energy planning
methods. Findings of this study would benefit researchers in gaining an
appreciation of the methods, as well as enable them to select appro-
had a noticeable impact on the environment [13]. Intensive discussions priate forecasting methods for future research.
and debates followed, legislations were formulated, and GHG emission
reduction targets were set; e.g., Kyoto Protocol in 1998. Although se- 2. Methodology
parate models for the evaluation, projection, and alleviation of en-
vironmental impacts were created, EPMs played a critical role in A state-of-the-art systematic review was undertaken on published
identifying system boundaries and underlying relationships between electronic resources for the study of underlying forecasting methods in
the socio-technical parameters of energy, economy and environment. EPMs. A preliminary study was conducted to gather an overview of the
Different authors reviewed EPMs in previous years. Nguyen (2005) topics related to forecasting methods in energy planning. The identified
classified EPMs into six categories – energy information systems, mac- main topics were: energy demand and/or supply model and/or fore-
roeconomic, energy demand, energy supply, modular package and in- casting; energy planning models; emission reduction models; time
tegrated models [9]. Pfenninger et al. categorized EPMs into four types series analysis; and forecasting. These topics were used to identify re-
– energy system optimization; energy system simulation; power system levant keywords, listed in Table 1. Keywords were then utilized to
and electricity market and qualitative and mixed-method scenarios search electronic databases: Google Scholar, ScienceDirect, Scopus, Ei
[14]. Most of the reviews focused on classifying the energy planning Compendex and Web of Science, for relevant publications on fore-
models as a whole, rather than investigating and categorizing the un- casting methods of EPMs.
derlying forecasting methods. Suganthi investigated the models for An advanced search was conducted within the databases by cate-
forecasting energy demand [15], albeit only partially. Moreover, gorizing keywords into four-word groups and by combining them using
parameters for categorizing forecasting methods are not same as for the Boolean operator ‘AND.' The search was conducted in two stages.
EPMs. The choice of forecasting method can affect the accuracy and Firstly, the model, objective and geographical extent keywords were
validity of results in an EPM. used. Secondly, the model, objectives, methods, and analysis measures
Previous studies on forecasting methods of EPMs either divided the were applied. The initial search results at each stage were refined by
topic into its areas of application or the broad categories of underlying applying the following inclusion criteria:
techniques. Application areas are always evolving – through the in-
tegration of new domains and concepts, as well as by expanding the • Objective: Energy forecasting
breadth and depth of a modeled domain. The difficulty arises when • Language: English
previously categorized application areas are not flexible enough to • Sources: Publications from journals related to energy and core
accommodate a new area. For example, behavioral energy conservation forecasting and planning of energy; fossil fuel; renewable energy;
is an important environmental psychology aspect of climate and energy carbon emissions.
debate; and widely considered for the modeling of energy use in
buildings and transportation, as well as for national energy demand Abstracts of the selected publications were scrutinized. Articles
forecasting and policy making.1 On the other hand, dividing forecasting were chosen for review if the substance was within the scope of the
methods based on the underlying techniques has similar issues. For study. A further search was conducted on the recognized authors who
example, Weron classified forecasting methods into two broad cate- had contributed noticeably in related fields. 600 publications were
gories – statistical approaches and artificial intelligence (AI) based found from the search. The criteria for retention were:
techniques [16]. The developments in computing over the past decades
have enabled the use of compute-intensive methods for improved ac- • Studies covering energy demand and/or supply forecasting
curacy and reduced computation time, thereby enhancing their ap- • Studies with significant contribution in forecasting of GHG emis-
plicability. AI techniques are now widely used to tune up parameters in sions
statistical models. Moreover, some soft computing or computational • Studies on forecasting methods for energy planning
intelligence2 techniques routinely use advanced statistical concepts. • Key review articles from established authors/institutions in the area
Therefore, categorizing the forecasting methods as either statistical or of energy forecasting and planning models

Finally, 483 publications and reviews on energy forecasting and

1
Examples of the use of behavioral aspects of public energy conservation in policy planning were retained for analysis and interpretation.
making can be found in Japan's Third National Communication under the United Nations
Framework Convention on Climate Change (UNFCC) (http://unfccc.int/resource/docs/
natc/japnc3.pdf) and Energy Outlook of Vietnam through 2025 (http://open_jicareport.
3. Classification
jica.go.jp/pdf/11899796_02.pdf).
2
It can be argued that the so called AI methods used in forecasting are in fact, more Forecasting involves the predictions of the future based on the
specifically, computational intelligence (CI) techniques, also known as soft computing in analysis of trends of present and past data, comprising three major
AI. For further information on how computational intelligence branched out from general
components: input variables (past and present data), forecasting/esti-
AI, initially to distinguish neural networks from hard AI but later to incorporate fuzzy
systems and evolutionary computation, the reader is referred to the history of IEEE
mation methods (analysis of trends) and output variables (future pre-
Computational Intelligence Society (CIS) at http://ethw.org/IEEE_Computational_ dictions), as shown in Fig. 1. Based on the number of techniques used
Intelligence_Society_History. for trend analysis, the investigated methods can be broadly classified

298
K.B. Debnath, M. Mourshed Renewable and Sustainable Energy Reviews 88 (2018) 297–325

develop a hybrid method, utilized genetic algorithm and particle swarm

optimization most of the time. Also, global models utilized metaheur-
istic methods such as GA, PSO and Artificial bee colony optimization
(ABCO). Moreover, country wise forecasting models utilized a wide
range of methods both metaheuristic and MP.
In case of the temporal span, statistical methods are suitable for
short-term (Table 2), and CI methods are suitable for all temporal
(Short, medium and long) forecasting (Table 3).

4. Stand-alone methods

Most of the analyzed models adopted stand-alone methods, which

can be divided into three categories- statistical, computational in-
telligence (CI) and mathematical programming (MP) methods.
Fig. 1. Basic forecasting or estimation model structure.

4.1. Statistical methods

into two main types: stand-alone and hybrid. Stand-alone methods
apply a single technique for analyzing trends whereas hybrid methods Statistics methods investigate the accumulation, examination, elu-
integrate more than one stand-alone techniques. In most cases, the cidation, presentation, and association of data [18] and can be divided
purpose of hybridization is to rationalize or make reliable forecast into several categories from the analyzed models. For example:
output and to yield higher projection accuracy.
Based on the type of techniques, stand-alone methods are divided 4.1.1. Regression analysis
into three categories: statistical, computational intelligence (CI) and There are different regression methods for forecasting. Among, the
mathematical programming (MP). Hybrid methods are divided into regression methods six methods were utilized in the studied models.
four: statistical-statistical, statistical-CI, CI-CI and statistical-MP The methods were: Linear regression (LR), ordinary least squares (OLS),
methods. Some of the reviewed literature utilized multiple stand-alone nonlinear regression (NLR), logistic regression (LoR), nonparametric
and/or hybrid methods for comparison and critique. To obtain a com- regression (NR), partial least squares regression (PLSR) and stepwise
prehensive picture in this paper, underlying techniques in hybrid regression (SR).
methods are also separately accounted for in the stand-alone method Thirty-nine reviewed models utilized linear regression (LR) method.
categories in Tables 2, 3. LR is applied to model the relationship between two variables by fitting
The methods are also analyzed by geographical extent and fore- a linear equation to observed data [19]. Among the reviewed models
casting time frame. Geographical extent was divided into three cate- which utilized LR, 89.7% models forecasted energy and electricity de-
gories: global, regional and country. Global refers to the whole world; mand.
regional for a part of the world; e.g., Asia, Europe, G-8, and Sub- Three forecasting models utilized non-linear regression (NLR).
Saharan Africa; and country for an individual country. Models with Bilgili et al. forecasted the electricity consumptions of Turkey with NLR
geographical extent covering parts of a country are incorporated in the [20]. Ghiassi et al. proposed a dynamic artificial neural network
country category for brevity. (DAN2) model for forecasting nonlinear processes and compared to
The time frame of the forecasted models ranges from hours to 100 NLR; the method was effective for forecasting nonlinear processes [21].
years. Grubb [17] suggested five years or less for the short-term, be- Tsekouras et al. developed a nonlinear multivariable regression to
tween 3 and 15 years for the medium-term, and ten years or more for midterm energy forecasting of power systems of Greece [22]. Logistic
the long-term. However, this classification creates confusion for the or logit regression (LoR) was applied in 19 reviewed models, of which
medium- and long-term projections because of the overlapping time 68.4% models forecasted energy and electricity demand.
spans. This research, therefore, utilizes the following definitions for Three models utilized nonparametric regression (NR) method. NR
time span or modeling horizons: short- (t < 3), medium- (3 ≤ t ≤ 15) establishes model according to the data from larger sample sizes.
and long-term (t > 15), where t is time span in years. Charytoniuk et al. developed a short-time load forecasting model by
The statistical and CI & MP based classification is presented in applying NR [23]. Another study applied NR model to short-term wind
Tables 2 and 3 respectively, illustrating the techniques used, geo- power forecasting [24]. Jónsson et al. presented an analysis of how day-
graphical extent and forecasting time frame, as well as the number of ahead electricity spot prices are affected by day-ahead wind power
studies and references. forecasts. The author utilized NR to assess the wind power forecast
It is evident from the analysis of 483 studies that diversity in sta- [25].
tistical methods is more prominent than computational intelligence and Partial least squares regression (PLSR) was applied in two fore-
mathematical programming. 28 different statistical methods have been casting models. Zhang et al. forecasted China's transport energy de-
used, compared to 22 CI and one MP for forecasting. Among the sta- mand for 2010, 2015 and 2020 with PLSR method. The results de-
tistical methods in Table 2, autoregressive integrated moving average monstrated transport energy demand for 2020 will reach a level of
(ARIMA) (46 models) followed by linear regression (LR) (39 models), around 433.13 million tons of coal equivalent (Mtce) and 468.26 Mtce,
autoregressive moving average (ARMA) (22 models) and logistic re- respectively [26]. Meng et al. analyzed and forecasted China's annual
gression (LoR) (19 models). However, cointegration was widely used electricity consumption with PLSR. It showed real estate and relative
(48 models) technique to analyze the relationship among the variables. industry electricity consumption was affected by unusual development
ARIMA, LR and other statistical methods were utilized to forecast. [27].
With regard to CI techniques, ANN was used in 194 models, fol- Seven models forecasted with stepwise regression (SR) method.
lowed by SVM (58 models), FL (40 models), GA (39 models), PSO (34 Ekonomou utilized SR to estimate energy consumption of Greece for
models) and GM (29 models) (Table 3). In respect to geographical ex- 2005–2015 to compare with the results produced by LR and ANN
tent, global and regional models mostly adopt statistical methods. method [28]. Tso et al. utilized SR method to predict electricity con-
However, country-based models utilized a wide range of methods sumption in Hong Kong [29]. Rao et al. utilized SR to select the relevant
(statistical and CI) for forecasting (Tables 2 and 3). cross-products to be used in a non-homothetic Translog function to
Forecasting models, which adopted metaheuristic methods to forecast and analysis of demand for petroleum products in India [30].

299
 K.B. Debnath, M. Mourshed
Table 2
Analysis of stand-alone statistical methods utilized in forecasting models.

Methods Geographical extend Time frame of forecasting Number of References

models
Global Region Country Short Medium Long

Linear regression (LR) ■ – ■ ■ ■ ■ 39 [19,20,28,71–73,115,122,123,129,141,146,164,175,187–211]

Nonlinear regression (NLR) – – ■ ■ ■ ■ 3 [20–22]
Logistic regression (LoR) – ■ ■ ■ ■ ■ 19 [73,74,103,193,212–226]
Nonparametric regression (NR) – – ■ ■ – – 3 [23–25]
Partial least squares regression (PLSR) – – ■ – ■ – 2 [26,27]
Stepwise regression (SR) – – ■ ■ ■ – 7 [28–31,207,227,228]
Moving average (MA) – – ■ – ■ – 4 [32–35]
Autoregressive integrated moving average (ARIMA) – ■ ■ ■ ■ ■ 46 [35,36,38,40,41,43,47,62,108,117,126,128,134,136,138,139,141,143,165,229–254]
Seasonal autoregressive integrated moving average (SARIMA) – – ■ ■ ■ ■ 13 [34,36–46,255]
Autoregressive moving average model with exogenous inputs – – ■ ■ ■ – 10 [35,48–52,191,256–258]
(ARMAX)
Autoregressive moving average (ARMA) – – ■ ■ – – 22 [48,129,137,140,145,161,180,237,246,259–271]
Vector autoregression (VAR) ■ ■ ■ – ■ ■ 13 [53,75,272–282]
– – ■ ■ ■ –
300

Bayesian vector autoregression (BVAR) 4 [53–56]

Structural Time Series Model (STSM) – – ■ – ■ ■ 3 [58,59,283]
VARIMA – – ■ ■ – – 1 [57]
Generalized autoregressive conditional heteroskedasticity (GARCH) – ■ ■ ■ ■ – 14 [49,52,60,136,137,175,251,284–290]
Seasonal exponential form of generalized autoregressive – – ■ ■ – – 1 [61]
conditional heteroscedasticity (SEGARCH)
Exponential generalized autoregressive conditional – – ■ ■ – – 1 [62]
heteroscedasticity (EGARCH)
Winters model with exponential form of generalized autoregressive – – ■ ■ – – 1 [61]
conditional heteroscedasticity (WARCH)
Autoregressive distributed lag (ARDL) – ■ ■ – ■ ■ 6 [58,59,63–66]

Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Log-linear analysis (LA) – ■ ■ – ■ ■ 4 [67–70]
Geometric progression (GP) – – ■ – ■ ■ 3 [71–73]
Transcendental logarithmic (Translog) – – ■ – ■ ■ 2 [30,74]
Polynomial curve model (PCM) – – ■ – ■ – 1 [33]
Partial adjustment model (PAM) – – ■ ■ ■ – 4 [63,75,76,240]
Analysis of variance (ANOVA) – – ■ – ■ ■ 7 [32,77,78,291–294]
Unit root test and/or Cointegration ■ ■ ■ ■ ■ ■ 48 [63,66,75,76,240,273,281,283,289,295–333]
Decomposition – ■ ■ ■ ■ ■ 16 [39,58,59,334–346]
Total number 3 8 28 18 22 14
Percentage of all statistical methods (%) 11% 29% 100% 64% 79% 50%
 K.B. Debnath, M. Mourshed
Table 3
Analysis of stand-alone computational intelligence and mathematical programming methods utilized in forecasting models.

Methods Geographical extend Time frame of forecasting Number of References

models
Global Region Country Short Medium Long

Computational intelligence (CI) methods

Support vector machine (SVM) – ■ ■ ■ ■ ■ 58 [28,43,46,85,86,104,108,117,118,126–129,133,134,143,144,166,170,174,184,206,-
208,227,228,249,251,258,269–271,290,345,347–370]
Decision treea – – ■ ■ ■ – 4 [29,89,371,372]
Artificial neural network (ANN) ■ ■ ■ ■ ■ ■ 194 [20,21,28,29,32,36,37,47,61,69,77,78,83,84,87,90,95,108,115,116,126–128,131,1-
38–143,146–158,160–162,167,168,170–177,180,184,191,205,207,227,228,231,24-
6,251,253,255,256,263,268–271,280,293,294,344,349,352,354,357,360,361,365,3-
67,369,373–478]
Abductive networks – – ■ ■ – – 2 [87,88]
Expert system – – ■ ■ ■ – 7 [90–96]
Grey prediction (GM) – – ■ ■ ■ ■ 29 [43,101,115,145,164,165,167,169,184,230,248,390,479–495]
Fuzzy logic (FL) – – ■ ■ ■ ■ 40 [19,45,51,96,97,147,149–160,251,253,255,256,357,376,435,454,458,461,465,477,-
496–504]
Genetic algorithm (GA) ■ – ■ ■ ■ ■ 39 [95,96,102–108,119,122,123,126,128,156,162–165,169,171,172,247,253,268,270,-
301

351,357,465,477,505–513]
Artificial bee colony optimization (ABCO) ■ – ■ ■ – ■ 4 [116,117,270,469]
Ant colony optimization (ACO) – – ■ ■ ■ ■ 10 [95,96,109,110,118–123]
Particle swarm optimization (PSO) ■ – ■ ■ ■ ■ 34 [34,44,46,50,105,106,108–113,115,119,122,123,126,161–163,168,174,253,290,36-
4,368,452,453,461,471,493,504,514,515]
Gravitational search algorithm (GSA) – – ■ ■ – ■ 4 [85,86,130,131]
Chaotic ant swarm optimization (CAS) – – ■ ■ ■ – 2 [125,126]
Differential evolution (DE) – – ■ ■ ■ ■ 4 [127–129,464]
Harmony search (HS) – – ■ – – ■ 1 [132]
Evolutionary algorithm (EA) – – ■ ■ – – 1 [50]
Memetic algorithms (MA) – – ■ ■ – – 1 [108]

Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Immune algorithm (IA) – – ■ – ■ – 1 [133]
Simulated annealing algorithms (SA) – – ■ ■ ■ – 6 [104,108,126,128,134,359]
Firefly algorithm (FA) – ■ ■ ■ – – 4 [108,270,363,516]
Cuckoo search algorithm (CSA) – ■ ■ ■ – – 2 [251,474]
Mathematical programming (MP) methods
Nonlinear programming (NLP) – – ■ – – ■ 1 [103]
Total number 4 4 22 19 13 12
Percentage of all CI and MP methods (%) 18% 18% 100% 86% 59% 55%

a
Random forest was included under decision tree as they are collection of decision tree in the modeling.
K.B. Debnath, M. Mourshed Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Aranda et al. utilized SR to select the correct model form to predict the Table 4
annual energy consumption in the Spanish banking sector [31]. ARIMA model objectives and structures.

Objective Year ARIMA Structure Ref.

4.1.2. Univariate time series methods
Among the studied models, five univariate time series methods were p,d,q (p,d,q)
utilized. The methods were: moving average (MA), autoregressive in- (P,D,Q)s
tegrated moving average (ARIMA), seasonal autoregressive integrated
Electricity load 2005 2,2,1 – [134]
moving average (SARIMA), autoregressive moving average model with Electricity load 2013 1,1,1 – [86]
exogenous inputs (ARMAX) and autoregressive moving average Electricity demand 2003 0,1,0 – [167]
(ARMA). Wind speed 2010 1,0,0; 2,0,0 – [138]
Four forecasting models utilized moving average (MA). Azadeh Electricity demand 2006 0,1,1; 0,0,2; (0,1,1)12 [231]
3,2,0
et al. forecasted electricity consumption in Iran with moving average
Electricity demand 2008 – (0,1,1) [139]
(MA) to make the data trend-free to train the ANN. Also forecasted (0,1,1)12
electricity consumption to compare the predicted results [32]. Xu et al. Wind speed 2007 – (0,1,1) [36]
combined two statistical methods to model to forecast natural gas (0,1,1)12
Electricity demand 1997 – (1,1,0) [234]
consumption in China from 2009 to 2015. One of the methods was MA
(1,1,0)12
[33]. In another study, Zhu et al. developed an improved hybrid model Electricity load 2011 1,1,1 – [117]
(MA-C-WH) to forecast electricity demand in China, which utilized MA Electricity demand 2011 0,2,2; 1,2,1; – [141]
[34]. Li et al. applied single and double MA for forecasting power 1,1,0; 0,2,0
output of a grid-connected photovoltaic system [35]. Energy demand 1999 1,1,1; 1,2,1 – [377]
Global solar radiation 2000 – (1,0,1) [152]
The general form of Autoregressive integrated moving average
(0,1,1)
(ARIMA) is ARIMA (p,d,q) where p is the order of the auto-regressive Electricity demand 1999 – (0,1,1) [235]
part, d is the order of the differencing, and q is the order of the moving (0,1,1)
average process. Some ARIMA had the seasonal and non-seasonal part, Electricity demand 1999 – (1,1,0) [235]
(0,1,1)
and denoted as ARIMA (p,d,q) (P,D,Q)s where P, D, Q is the seasonal
Black-coal production 1999 – (1,0,1) [235]
part of the model, S the number of periods per season. Among the (0,1,1)
analyzed models, ARIMA was applied in 46 models (Tables 2 and 4). Antracite production 1999 – (0,1,1) [235]
Among the ARIMA models, 46% forecasted energy and electricity de- (0,1,1)
mand. Electricity generation 1999 – (0,1,3) [235]
(1,1,0)
Seasonal autoregressive integrated moving average (SARIMA) was
Solar radiation 2009 – (1,0,0) [243]
applied in 13 projection models (Table 2). Zhu et al. developed MA-C- (1,1,0)
WH model to forecast electricity demand in China and utilized the re- Electricity demand 2015 1,1,1 – [128]
sults from a SARIMA model to compare the accuracy of the proposed Electricity price 2002 2,1,1 – [232]
Natural gas demand 2010 36,1,0 – [233]
model [34]. Cadenas et al. forecasted wind speed with integrated
Electricity demand 2007 13,2,0 – [240]
ARIMA and ANN to compare with the results from SARIMA for Oaxaca, Power output of a grid connected 2014 1,1,1 – [35]
Mexico [36]. Jeong et al. applied SARIMA for determining the annual photovoltaic system
energy cost budget in educational facilities. In this study, models for Load forecasting 2009 2,2,1 – [126]
elementary, middle, and high schools SARIMA (13, 1, 0) (0, 1, 0), Electricity demand 2006 0,1,0 – [248]
CO2 emissions, energy demand 2012 – – [479]
SARIMA (6, 1, 1) (0, 1, 0), and SARIMA (6, 1, 1)(0, 1, 0) respectively
and economic growth
were developed [37]. Ediger et al. applied SARIMA methods to forecast Electricity price 2010 – – [136]
primary energy demand of Turkey from 2005 to 2020 [38]. Monthly Energy demand 2007 – – [38]
energy forecasting model for Thailand was developed with SARIMA (l, Electricity price 2008 – – [62]
CO2 emissions, energy demand, 2011 – – [230]
0,1)(0,1,0)12 [39]. Ediger et al. applied SARIMA to forecast production
and economic growth
of fossil fuel sources in Turkey [40]. Forecasting electricity demand Electricity load 2001 – – [238]
with SARIMA (0,1,1)(1,1,1) by Sumer et al. in [41]. Bouzerdoum et al. Electricity price 2003 – – [229]
applied SARIMA for short-term power forecasting of a small-scale grid- Fossil fuel production 2006 – – [40]
connected photovoltaic plant [42]. Guo et al. applied SARIMA for Electricity demand 2001 – – [236]
Electricity load 1987 – – [237]
forecasting wind speed in Hexi Corridor of China [43]. Wang et al.
Electricity demand 1993 – – [239]
developed electricity demand forecasting with SARIMA method for Electricity load 1995 – – [241]
China [44]. Boata et al. developed hourly solar irradiation forecasting Electricity price 2005 – – [242]
model with SARIMA (1,0,1)(1,0,1)24 [45]. Wang et al. applied SARIMA Electricity demand 2009 – – [41]
to forecast electric load in [46]. Wind speed 2009 – – [244]
Natural gas demand 1991 – – [245]
Autoregressive moving average model with exogenous inputs Electricity demand 2012 – – [165]
(ARMAX) was utilized in 10 forecasting models (Table 2). Darbellay Wind speed 2011 – – [43]
et al. applied ARMAX to forecast Czech electricity demand [47]. Li et al. Wind speed and electricity 2012 – – [143]
developed a forecasting model for the power output of a grid-connected generation
photovoltaic system with ARMAX [35]. González et al. applied
SARMAX for forecasting power prices [48]. Bakhat et al. applied
consist of two polynomials- autoregressive (AR) and moving average
ARMAX for estimation of tourism-induced electricity consumption in
(MA). Among the reviewed models, 22 utilized ARMA (Table 2), of
Balearics Islands, Spain [49]. For short-term load forecasting, Wang
which 32% and 27% were utilized for energy & electricity demand and
et al. utilized ARMAX based on an evolutionary algorithm and particle
load forecasting respectively.
swarm optimization [50]. Lira et al. utilized ARMAX for short-term
electricity prices forecasting of Colombia [51]. Hickey et al. developed
four ARMAX–GARCH models for forecasting hourly electricity prices 4.1.3. Multivariate time series methods
[52]. Vector autoregression (VAR) was applied in 13 reviewed models
Autoregressive moving average (ARMA) is a statistical method (Table 2). Among these 13 models, 77% models forecasted energy and

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electricity demand. Bayesian vector autoregression (BVAR) was applied for petroleum products in India [30]. Furtado et al. forecasted petro-
in four reviewed models (Table 2). Chandramowli et al. forecasted New leum consumption in Brazil up to 2000 with translog model along with
Jersey's electricity demand with BVAR [53]. To forecast energy con- logistic and learning model. The study demonstrated that translog
sumption in China from 2004 to 2010, Crompton et al. applied BVAR model performed better than logistic and learning model [74].
and concluded energy demand would rise at an annual average rate of Polynomial curve model (PCM) is one of the trend extrapolation
3.8% [54]. Energy consumption and projected growth were modeled methods best modeled with polynomial equations. Xu et al. combined
with BVAR for selected Caribbean countries in [55]. The Bayesian two statistical methods to forecast natural gas consumption in China
hierarchical model was developed for one-hour-ahead wind Speed from 2009 to 2015; one of the methods was PCM [33].
Prediction in [56]. Multivariate VARIMA (0,1,1) model was applied to Four reviewed models utilized partial adjustment model (PAM) for
model and forecast fossil fuels, CO2 and electricity prices and their forecasting (Table 2). Nasr et al. utilized PAM to develop an econo-
volatilities. VARIMA approach gives better results in the case of elec- metric model to estimate electricity consumption of post-war Lebanon
tricity prices. However, the time span of forecasting tends to be short [75]. Adom et al. identified the factors that affect aggregate electricity
[57]. demand in Ghana and forecasted electrical consumption from 2012 to
Structural time series model (STSM) was utilized by Dilaver et al. to 2020 with PAM and ARDL [63]. To analyze the demand for natural gas
predicted that Turkish industrial electricity demand would be some- in Kuwait, PAM was utilized in [76].
where between 97 and 148 TWh by 2020 industrial electricity demand Seven models utilized analysis of variance (ANOVA) (Table 2).
[58]. In another study, Dilaver et al. predicted Turkish aggregate ANOVA was applied to compare the selected ANN, regression and ac-
electricity demand would be somewhere between 259 TWh and tual data of forecasting electricity consumption [32,77]. ANOVA F-test
368 TWh in 2020 by utilizing STSM [59]. was applied for ANN, simulated-based ANN, time series and actual test
data for forecasting electrical energy consumption in Iran [78].
4.1.4. Autoregressive conditional heteroscedasticity (ARCH) methods Cointegration implies restrictions on multivariate time series and is
Generalized autoregressive conditional heteroskedasticity (GARCH) widely believed that it can produce better long-horizon forecasting
was applied in fourteen models. GARCH can be both univariate and [79]. Unit root test and/or Cointegration was utilized in 48 models
multivariate [60]. (Table 2). The major objective of applying cointegration method was to
Seasonal generalized autoregressive conditional heteroscedasticity find the relations among the variables of a model. Nasr et al. utilized
(SEGARCH) and Winters model with an exponential form of generalized cointegration method to develop an econometric model to estimate
autoregressive conditional heteroscedasticity (WARCH) were applied to electricity consumption of post-war Lebanon [75]. Decomposition was
forecast energy consumption in Taiwan by developing nonlinear hybrid utilized in 16 analyzed models (Table 2).
models with ANN [61]. Exponential generalized autoregressive condi-
tional heteroscedasticity (EGARCH) method was utilized by Bowden 4.2. Computational intelligence (CI) methods
et al. for short-term forecasting of electricity prices [62].
There were 22 methods utilized in the analyzed models. The real-
4.1.5. Others life problems have nonlinear characteristics while forecasting, espe-
Six analyzed model utilized autoregressive distributed lag (ARDL) cially for energy planning. Computational methods were used for pre-
(Table 2). Dilaver et al. forecasted industrial electricity demand [58] diction problems where mathematical formulae and prior data on the
and aggregate electricity demand [59] in Turkey with ARDL. In another relationship between inputs and outputs are unknown [80]. The ap-
study, Dilaver et al. predicted Turkish aggregate electricity demand plied CI methods can be divided into four categories.
would be somewhere between 259 TWh and 368 TWh in 2020 by uti-
lizing ARDL. Adom et al. utilized ARDL to forecast electricity demand in 4.2.1. Machine learning methods
Ghana to be within 20,453 and 34,867 GWh by the year 2020 for Artificial Neural Network (ANN) was highly utilized method for
analyzed three scenarios [63]. Kim et al. forecasted energy demand of various objectives. Inspired by the human brain, ANN can learn and
South Korea for 2000–2005 after reviewing the 1990s [64]. Zachariadis generalize from samples and analyses unpretentious useful connections
T. forecasted electricity consumption in Cyprus with ARDL [65]. Vita among the information regardless of the possibility that the funda-
et al. developed ARDL bounds testing approach to estimate the long-run mental connections are obscure or difficult to portray [81]. A schematic
elasticities of the Namibian energy demand [66]. diagram of feed-forward neural network architecture is shown in Fig. 2.
Among the reviewed models, four models applied log-linear analysis ANN has three layers: input, hidden and output. In Fig. 2, only one
(LA) (Table 2). Parikh et al. used the LA to project the demand for hidden layer is shown, and the number can be more than that de-
petroleum projects and natural gas in India. The study projected the pending on the complexity of the analyzed problem. Each neuron is
demand of petroleum products to be 147 and 162MT in the business as connected to every other neuron of the previous layer through adap-
usual scenario (BAU) of 6% and optimistic scenario (OS) of 8% GDP table synaptic weight. A training process is carried out to train ANN by
growth, respectively for 2011–2012 [67]. In another study, Pilli-Sihvola modifying the connection weights, and weights are adjusted to produce
utilized the log-linear econometric model to project and examine the the desired outputs as shown in Fig. 3. Description of basic ANN method
impact of gradually warming climate on the heating and cooling de- can be found in [82].
mand in five European countries form 2008–2050 [68]. Limanond et al. Among the reviewed models, 194 models applied ANN or different
project transport energy consumption in Thailand from 2010 to 2030 form of NN. The detailed analysis of ANN can be found in Table 5,
with LA [69]. Wadud et al. projected natural gas demand in Bangladesh which is demonstrating layer number, neuron number in different
from 2009 to 2025 with log-linear Cobb–Douglas method [70]. layers and neuron composition of different NN models, which differs
Geometric progression (GP) was utilized in three studied models depending on the objective. According to reviewed literature, NN
(Table 2). Mackay et al. forecasted crude oil and natural gas supplies structure with two hidden layers produced best results for the monthly
and demands from 1995 to 2010 for France [71] and Denmark [72] by load forecasting, the peak load forecasting and the daily total load
utilizing geometric progression method. In a separate study, Mackay forecasting modules [83]. However, one hidden layer is sufficient for
et al. forecasted liquid fossil fuel supplies and demands for the UK with most forecasting problems according to Zhang et al. [81]. In another
geometric progression method [73]. study, the performance of the hierarchical model on long-term peak-
Transcendental logarithmic (Translog) was applied in two fore- load forecasts outperformed the multilayer perceptron [84]. Analysis of
casting models (Table 2). Rao et al. developed a translog model on a reviewed models revealed that 83% models utilized three layer neuron
non-homothetic translog function to forecast and analyze the demand structure with one hidden layer. Only 6% and 17% models used two

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Fig. 2. ANN schematic diagram.

and four neuron layers respectively. 49%, 38%, 78% and 11% of the variables. GMDH is a learning algorithm and formalized paradigm for
neuron structures had less than five neurons respectively in the first, iterated (multi-phase) polynomial regression [87]. In another study,
second, third and fourth layer. In the case of the first and second layer, Abdel-Aal et al. utilized AIM monthly electric energy consumption in
26% and 43% of the neuron structures respectively had neuron num- eastern Saudi Arabia and demonstrated that AIM performed better than
bers between 5 and 10. Moreover, 23% and 18% neuron structures had that of regression method [88].
more than ten neurons in the first and second layers respectively. Only Decision tree develops an empirical tree which represents a seg-
8% neuron structures had more than ten neurons in the third layer, mentation of the data and able to classify and predict categorical
which is only 1% in fourth layer (Table 5). variables. The segment is developed by applying a series of simple
Support vector machine (SVM) was utilized in 58 forecasting models rules/logic. The advantage of the decision tree is that it produces a
(Table 3). Yuan et al. developed a short-term wind power prediction model which have segments of the system with interpretable rules or
model with least squares support vector machine (LSSVM) because the logic statements [29]. However, it performs poorly with nonlinear and
kernel function and the related parameters of the LSSVM influence the noisy data [80]. Tso et al. utilized decision tree method to predict
greater accuracy of the prediction [85]. Some of the models utilized electricity consumption in Hong Kong [29]. Yu et al. developed a
Support vector regression (SVR), which is SVM applied to the case of building energy demand predictive model with a decision tree and
regression. Ju et al. utilized SVR and seasonal SVR forecast electricity demonstrated high accuracy with 93% for training data and 92% for
load in Taiwan [86]. Among the reviewed models, 41.4%, 22.4%, and test data [89].
20.7% forecasted electric load, renewable energy, and energy & elec-
tricity demand.
Abductive networks is a machine learning method. It was found to 4.2.2. Knowledge-based methods
be applied in two forecasting models (Table 3). Abdel-Aal, R.E. utilized Expert systems were applied in seven models (Table 3). Most of the
AIM (abductory inductive mechanism) and GMDH (group method of models utilized expert system for short-term load forecasting [90–94].
data handling) approach for forecasting monthly energy demand. AIM Ghanbari et al. applied cooperative ant colony optimization-genetic
is a supervised inductive machine-learning tool. It automatically de- algorithm (COR-ACO-GA) for energy demand forecasting with knowl-
velops abductive network models form a database of input and output edge-based expert systems, which yielded better accuracy [95]. In an-
other study, Ghanbari et al. integrated ant colony optimization (ACO),

Fig. 3. ANN process; adopted from [82].

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Table 5
ANN model objectives and structures.

Forecasted variable Year No. of layers No. of neurons in layers Neuron composition Ref.

2 3 4 1st 2nd 3rd 4th

<5 5–10 > 10 <5 5–10 > 10 <5 5–10 > 10 <5 5–10 > 10

Electricity demand 2006 – ■ – – ■ – – ■ ■ – – – – – 5–5–1 [191]

– ■ – – ■ ■ – – – – – 5–6–1
Electricity demand 2012 – ■ – ■ – – – ■ ■ – – – – – 4–8–2 [20]
Energy demand 2010 – – ■ ■ – – – ■ – – – ■ ■ – – 4–20–17–1 [28]
Electricity load 2008 – ■ – – ■ – – – ■ ■ – – – – – 8–36–1 [146]
– ■ – – ■ – ■ – – – – – 9–10–1
– ■ – – – ■ ■ – – – – – 10–31–1
– ■ – – – ■ ■ – – – – – 8–17–1
– ■ – ■ – – ■ – – – – – 9–2–1
Electricity demand 2007 – – ■ – – ■ – – ■ – ■ – ■ – – 12–16–6–1 [32]
Energy demand 2011 – ■ ■ – ■ – – ■ – ■ – – – – – 5–5–1 [69]
– ■ – – ■ – ■ – – – – – 5–10–1
– ■ – ■ – – ■ – ■ – – 5–5–5–1
Energy demand 2008 – ■ – – – ■ ■ – – ■ – – – – – 12–4–1 [87]
– – ■ – ■ – ■ – – – – – 12–5–1
– – ■ – ■ – ■ – – – – – 12–6–1
■ – – – ■ – ■ – – – – – 3–5–1
Energy demand 2009 – ■ – ■ – – ■ – – ■ – – – – – 2–3–1 [61]
■ – – ■ – – ■ – – – – – 2–4–1
Solar radiation 1998 – ■ – ■ – – – ■ – ■ – – – – – 4–10–1 [176]
Wind speed 2010 ■ ■ – ■ – – ■ – – – – – – – – 3–1 [138]
■ – – ■ – – – – – – – – 2–1
■ – – ■ – – ■ – – – – – 3–3–1
■ – – ■ – – ■ – – – – – 3–2–1
Electricity demand 2000 – ■ – – ■ – ■ ■ – – – – – 6–6–1 [47]
Wind speed 2007 ■ – – ■ – – ■ – – – – – – – – 3–1 [36]
Electricity demand 2011 – ■ – – ■ – – ■ – ■ – – – – – 5–12–1 [77]
Electricity demand 2013 – ■ – – – ■ – – ■ – – ■ – – – 48–97–48 [344]
Electricity demand 2012 – ■ – ■ – – ■ – – ■ – – – – – 1–2–1 [184]
Time-series forecasting 2010 – ■ – – ■ – ■ – – ■ – – – – – 8–3–1 [373]
– ■ – ■ – – ■ – – – – – 8–4–1
– – ■ ■ – – ■ – – – – – 12–4–1
■ – – ■ – – ■ – – – – – 4–4–1
– ■ – – ■ – ■ – – – – – 7–5–1
Electricity demand 2007 – ■ ■ ■ – – ■ – – ■ – – – – – 2–2–1 [171]
■ – – – ■ – – ■ – ■ – – 2–10–10–1
■ – – – – ■ – – ■ ■ – – 2–20–20–1
Electricity demand 2008 – ■ – ■ – – ■ – – ■ – – – – – 3–2–1 [78]
Electricity demand 2008 – – ■ ■ – – ■ – – ■ – – ■ – – 5–3–2–1 [293]
Electricity load 2003 – ■ – ■ – – ■ – – ■ – – – – – 3–2–1 [375]
Electricity load 2005 – – ■ – ■ – – ■ – – ■ ■ – – 6–5–8–1 [83]
– ■ – – ■ – – ■ – ■ – – 9–5–8–1
Energy demand 2009 – ■ – ■ – – – ■ – ■ – – – – – 4–5–1 [294]
■ – – ■ – – ■ – – – – – 4–4–1
■ – – ■ – – ■ – – – – – 4–3–1
■ – – ■ – – ■ – – – – – 4–2–1
Electricity demand 2011 – ■ – ■ – – – ■ – ■ – – – – – 4–10–1 [141]
■ – – – ■ – ■ – – – – – 4–6–1
■ – – – ■ – ■ – – – – – 4–8–1
■ – – – ■ – ■ – – – – – 4–6–1
■ – – – ■ – ■ – – – – – 4–5–1
Energy demand 1999 – ■ – ■ – – – ■ – ■ – – – – – 2–7–1 [377]
■ – – – ■ – ■ – – – – – 3–7–1
■ – – – ■ – ■ – – – – – 4–7–1
– ■ – – ■ – ■ – – – – – 5–7–1
Electricity demand 2007 – ■ – ■ – – ■ – – ■ – – – – – 4–2–4 [379]
Energy demand 2005 – – ■ – ■ – ■ – – ■ – – ■ – – 5–4–4–1 [380]
– ■ – ■ – – ■ – – ■ – – 7–4–4–1
Energy demand 2002 – ■ – – – ■ – – ■ ■ – – – – – 55–27–1 [385]
– – ■ ■ – – ■ – – – – – 55–02–1
Electricity load 1994 – ■ – – – ■ – – ■ – – ■ – – – 77–24–24 [397]
Electricity load 1996 – ■ – – – ■ – – ■ – – ■ – – – 63–24–24 [402]
Electricity load 1993 – ■ – – – ■ – ■ – ■ – – – – – 29–8–1 [396]
– – ■ – ■ – ■ – – – – – 22–5–1
– – ■ – – ■ – – ■ – – – 39–10–24
Electricity load 1992 – ■ – – ■ – – ■ – ■ – – – – – 5–8–1 [394]
Electricity load 1996 – ■ – – – ■ – – ■ – – ■ – – – 81–81–24 [403]
Electricity load 1998 – ■ – – – ■ – – ■ ■ – – – – – 15-(7–12)*−1 [404]
– – ■ – – ■ ■ – – – – – 7-(10–16)†−1
Electricity load 2006 – ■ – – – ■ – – ■ ■ – – – – – 32–65–1 [409]
(continued on next page)

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Table 5 (continued)

Forecasted variable Year No. of layers No. of neurons in layers Neuron composition Ref.

2 3 4 1st 2nd 3rd 4th

<5 5–10 > 10 <5 5–10 > 10 <5 5–10 > 10 <5 5–10 > 10

Electricity load 2008 – ■ – ■ – – ■ – – ■ – – – – – 4–3–1 [411]

Electricity price 2007 – ■ – ■ – – – ■ – ■ – – – – – 5–7–1 [414]
Electricity load 2009 – – ■ – – ■ – – ■ – – ■ – – ■ 19–20–15–24 [417]
Electricity demand 1999 – ■ – ■ – – – ■ – ■ – – – – – 3–5–1 [420]
Electricity demand 2015 – ■ – – ■ – ■ – – ■ – – – – – 5–3–1 [162]
Solar energy potential 2005 – ■ – – ■ – – ■ – ■ – – – – – 6–6–1 [427]
Electricity demand 2001 – ■ – ■ – – – ■ – ■ – – – – – 2–6–1 [433]
■ – – – ■ – ■ – – – – – 3–9–1
■ – – – ■ – ■ – – – – – 3–5–1
■ – – ■ – – ■ – – – – – 1–3–1
Wind speed 2005 – ■ – – – ■ – – ■ ■ – – – – – 14–15–1 [437]
Wind speed 2012 – ■ – – ■ – – ■ – ■ – – – – – 5–10–1 [438]
Wind speed 2009 ■ ■ – ■ – – ■ – – – – – – – – 3–1 [441]
■ – – ■ – – – – – – – – 2–1
■ – – ■ – – ■ – – – – – 3–3–1
■ – – ■ – – ■ – – – – – 3–2–1
Electricity price 1999 – ■ – – – ■ – – ■ ■ – – – – – 15–15–1 [440]
Electricity demand 2013 – ■ – ■ – – – ■ – ■ – – – – – 4–6–1 [95]
Natural gas demand 2013 – ■ – ■ – – – ■ – ■ – – – – – 3–5–1 [95]
Oil products demand 2013 – ■ – ■ – – ■ – – ■ – – – – – 2–3–1 [95]
Energy demand 2009 – ■ – – ■ – – ■ – ■ – – – – – 7–8–1 [442]
Electricity load 2008 – – ■ – – ■ – ■ – – ■ – ■ – – 11–5–5–1 [450]
Electricity demand 1999 – ■ – ■ – – ■ – – ■ – – – – – 3–2–1 [160]
■ – – ■ – – ■ – – – – – 3–1–1
Electricity demand 2015 – ■ – – – ■ ■ – – ■ – – – – – 12–4–1 [128]
Total number 3 44 9 48 25 22 37 42 17 76 6 8 11 0 1
% 6% 83% 17% 49% 26% 23% 38% 43% 18% 78% 6% 8% 11% 0% 1%

* Number of hidden layer neurons form week 1–21 ranged from 7 to 12 for feedforward networks.
†
Number of hidden layer neurons form week 1–21 ranged from 10 to 16 for recurrent networks.

genetic algorithm (GA) and fuzzy logic to develop a load forecasting population, GDP, import, and export. Chaturvedi et al. applied GA for
expert system [96]. electric load forecasting [107]. The objective of the models, the purpose of
GA in that model and the publishing year can be found in Table 6. Among
4.2.3. Uncertainty methods the reviewed models, 27% utilized GA for parameter optimization in the
Fuzzy logic was applied in 40 models (Table 3). In the analyzed hybrid methods.
models, the fuzzy method was proved to be efficient with the in- An evolutionary algorithm (EA) was utilized in only one forecasting
complete or limited dataset. The theory of fuzzy sets is the foundation model. Wang et al. utilized a hybrid optimization method based on
of the fuzzy logic. The basic description of the method can be found in evolution algorithm and particle swarm optimization to improve the
[97]. accuracy of forecasting ARMAX model [50].
Grey prediction (GM) belongs to the family of the grey system Memetic algorithm (MA) was applied in one forecasting model. For
among which the GM (1, 1) model is the most frequently used. GM forecasting electricity load, Hu et al. applied firefly algorithm (FA)
methods adopt essential part of the grey theory (GT) which deals with based memetic algorithm (FA-MA) to determine the parameters of SVR
systems with uncertain and deficient data [98,99]. The real world model appropriately [108].
systems are modeled with the assumptions based on the inadequate Particle swarm optimization (PSO) was applied in 34 models
information [100]. GM method has been successfully adopted for (Table 3). Zhu et al. developed an improved hybrid model (MA-C-WH),
forecasting models in different disciplines. Among the reviewed models, which utilized MA and adaptive particle swarm optimization (APSO)
twenty-nine models applied GM. The basic description of the method algorithm to forecast electricity demand in China. APSO was utilized to
can be found in [101]. determine weight coefficients of the MA-C forecasting model, and the
objective function of this optimization problem was to minimize the
4.2.4. Metaheuristic methods MAPE [34]. Kiran et al. applied PSO to develop an ACO-PSO hybrid
Evolutionary methods are a subset of metaheuristic methods which method to forecast energy demand of Turkey [109]. The proposed ACO-
uses mechanisms inspired by natural biological evolution, such as re- PSO method by Kiran et al. was applied for to forecast the wind power
production, mutation, recombination, and selection. There were several output of Binaloud wind farm in Iran in [110]. Assareh et al. applied
types of metaheuristic methods applied in forecasting models- PSO for forecasting energy demand [105] and oil demand [106] in Iran
Genetic algorithm (GA) was utilized in thirty-nine forecasting models. based on based on population, GDP, import, and export. AlRashidi et al.
The basic description of the method can be found in [102]. Forouzanfar constructed long-term electric load forecasting model with PSO [111].
et al. forecasted natural gas consumption for residential and commercial Also for modeling and forecasting long-term natural gas consumption in
sectors in Iran with LoR. However, to make the process simpler, two dif- Iran PSO was utilized [112]. Abdelfatah et al. constructed a global CO2
ferent methods are proposed to estimate the logistic parameters, of which emissions forecasting model with PSO [113]. The objective of the
one was GA based [103]. Zhang et al. utilized stimulated annealing algo- models, the purpose of PSO in that model and the publishing year can
rithms with chaotic GA to develop a hybrid method to assist an SVR model be found in Table 7. Among the reviewed models, 33% utilized PSO for
in improving load forecasting performance [104]. Assareh et al. applied GA parameter optimization in the hybrid methods. The basic description of
for forecasting energy demand [105] and oil demand [106] in Iran based on the method can be found in [114,115].

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 K.B. Debnath, M. Mourshed
Table 6
The purpose of GA in the reviewed hybrid models.

Forecasted variable Purpose of GA Year Ref.

Parameter Parameter Model structure Coefficients Weighting factors Learning rate Database Estimate the Improve
tuning optimization optimization optimization value generation residual performance

Electricity demand ■ – – ■ – – – – – 2007 [171]

Electricity load – – ■ – ■ – – – – 2009 [173]
Hydro energy potential – – ■ – ■ ■ – – – 2010 [172]
Electricity demand – ■ ■ – ■ – – – – 2015 [162]
Electricity demand – – ■ – – – – – – 2015 [128]
Electricity load ■ – – – – – – – – 2013 [108]
Energy demand – – – – – – ■ – – 2013 [95]
Electricity load – – – – – – ■ – – 2011 [96]
Electricity load – ■ – – – – – – – 2009 [126]
NOx Emission – – – – ■ – – – – 2013 [119]
Energy demand – – – ■ – – – – – 2012 [122]
Energy demand – – – ■ – – – – – 2012 [123]
307

Energy demand – ■ – – – – – – – 2012 [163]

Energy demand – – – – – – – ■ – 2011 [164]
Energy demand – – – – – – – ■ – 2012 [165]
Energy distributiona – – – – – – – – ■ 2000 [505]
Energy distributiona – – ■ – – – – – – 2006 [506]
Energy demand – ■ – – – – – – – 2004 [507]
Electricity demand – – – – – – – – ■ 2005 [512]
Electricity demand – ■ – – – – – – – 2005 [508]
Petroleum exergy – – – – ■ – – – – 2004 [511]
production & demand
Transport energy demand – – – – ■ – – – – 2005 [509]

Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Oil demand – ■ – – – – – – – 2006 [510]
Electricity demand – ■ – ■ – – – – – 2007 [247]
Natural gas demand – ■ – – – – – – – 2009 [169]
Global CO2 emission – – – – ■ – – – – 2012 [513]
PV power generation – ■ – – – – – – – 2015 [268]
Total number 2 9 5 4 7 1 2 2 2
% 6% 26% 15% 12% 21% 3% 6% 6% 6%

a
Transmission network expansion planning (TNEP), Power generation expansion planning (PGEP).
K.B. Debnath, M. Mourshed Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Table 7
The purpose of PSO in the reviewed hybrid models.

Forecasted Purpose of PSO Year Ref.

variable
Parameter Parameter Model structure Coefficients Weighting Scenario Improve
tuning optimization optimization optimization factors value optimization performance

Electricity load – – – – – – – 2009 [115]

Electricity demand – ■ – – ■ – – 2015 [162]
Electricity load – – – – ■ – – 2009 [168]
Electricity demand – ■ – – – – – 2012 [44]
Electricity load – – – – – – ■ 2008 [50]
Electricity load ■ – – – – – – 2013 [108]
Electricity load – ■ – – – – – 2009 [126]
NOx emission – – – – ■ – – 2013 [119]
Energy demand – ■ – – – – – 2014 [174]
Energy demand – – – ■ – – – 2012 [122]
Energy demand – – – ■ – – – 2012 [123]
Energy demand – ■ – – – – – 2012 [163]
Economic emissions – – – – – ■ – 2013 [514]
Electricity load – – – – ■ – – 2010 [46]
Electricity demand – – – – – – ■ 2008 [161]
Electricity – – ■ – – – – 2011 [452]
consumption
Energy demand – – – – ■ – – 2014 [515]
Energy demand – ■ ■ – – – – 2012 [453]
Wind power ■ – – – – – – 2015 [461]
Electricity load – ■ – – – – – 2014 [493]
Total number of 2 7 2 2 5 1 2
models
% 10% 33% 10% 10% 24% 5% 10%

Artificial bee colony optimization (ABCO) was applied in four demand forecasting in [128]. For short -term load forecasting, Xiaobo
forecasting models among the reviewed models (Table 3). For fore- et al. developed a GRA-DE-SVR model, where DE to optimize para-
casting world CO2 emissions, BCO was utilized for finding optimal va- meters of SVR model [129].
lues of weighting factors for forecasting [116]. Chaotic artificial bee Gravitational search algorithm (GSA) was applied assist to develop
colony algorithm was applied for electric load forecasting to determine three demand estimation models to forecast oil consumption based on
suitable values of its three parameters for forecasting [117]. socio-economic indicators in [130]. GSA was utilized to forecast elec-
Ant colony optimization (ACO) was utilized in ten forecasting tricity load in Taiwan to assist the seasonal SVR model in [86]. GSA was
models (Table 3). For energy demand forecasting, Ghanbari et al. ap- applied to optimize the parameters of the LSSVM model developed by
plied Cooperative Ant Colony Optimization (COR-ACO) to learn fuzzy Yuan et al. to short-term wind power prediction model [85]. Gavrilas
linguistic rules (degree of cooperation between database and rule base), et al. proposed a model of electric load forecasting with GSA combined
which would yield better accuracy [95]. In another study, Ghanbari with regression method and Kohonen neural networks [131].
et al. applied ACO-GA to generate optimal knowledge base (KB) for an Harmony search (HS) was utilized to develop HArmony Search
expert system to forecast load [96]. Niu et al. applied ACO with SVM Transport Energy Demand Estimation (HASTEDE) model, in a study
model to forecast short-term power load, where ACO to pre-process the conducted by Ceylan et al. to project the transport sector energy con-
data which influence uncertain factors in forecasting [118]. A NOx sumption in Turkey. The results demonstrated overestimation of
emission forecasting model for Iran utilized ACO to estimate optimal transport sector energy consumption by about 26%, and linear and
values of weighting factors regarding actual data in [119]. To estimate exponential forms underestimate by about 21%, compared to Ministry
energy demand of Turkey, ACO was applied in [120]. In another study, of Energy and Natural Resources projections. The study pointed out the
to forecast energy demand of Turkey, ACO was applied to develop ACO- under, and overestimation might be the outcome of the choice of
PSO hybrid method [109]. For estimating the net electrical energy modeling parameters and procedures [132].
generation and demand of Turkey, ACO was applied based on the GDP, Immune algorithm (IA) was applied for electric load forecasting
population, import and export [121]. ACO based hybrid method was model, where IA determined the parameter selection of SVR model
applied for to forecast the wind power output of Binaloud wind farm in [133].
Iran in [110]. Yu et al. applied ACO to forecast energy demand of China Simulated annealing algorithms (SA) is an evolutionary method was
[122] and primary energy demand of China [123]. applied in six models (Table 3). Zhang et al. utilized SA with chaotic GA
Chaotic ant swarm optimization (CAS) is deterministic chaotic op- to develop a hybrid method to assist an SVR model in improving load
timization method inspired by behaviors of real ants [124], which was forecasting performance [104]. Pai et al. utilized SA algorithms were
utilized by two models (Table 3). Hong et al. for electric load fore- employed to choose the parameters of an SVM model to forecast elec-
casting. In the proposed model CAS was applied to improve the fore- tricity load in Taiwan [134]. Hong, W.-C. developed SVMSA model for
casting performance of SVR by searching its suitable parameters com- load forecasting, where SA was applied to determining appropriate
bination [125]. For electric load forecasting with SVR model, Hong W.- parameter combination for SVR model [126].
C. applied CAS to determine suitable parameter combination for the Moreover, Firefly algorithm (FA) and Cuckoo search algorithm
model [126]. (CSA) are two metaheuristic methods utilized in four and two fore-
Differential evolution (DE) was applied in three of the analyzed casting models respectively to develop a hybrid methodology in recent
models (Table 3). Wang et al. developed a load forecasting model with times (Table 3).
DE and SVR [127]. In another study, adaptive differential evolution
(ADE) was applied with BPNN for developing a method for electricity

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4.3. Mathematical programming (MP) approach on residual modification of SARIMA to develop F-S-SARIMA
model to forecast electricity demand for China [44]. Wang et al. de-
Mathematical programming or mathematical optimization pre- veloped a combined model to forecast electric load. For the model
scribes best solution/s from a set of available alternatives under some SARIMA, seasonal exponential smoothing (S-ESM) and Weighted SVM
conditions. Among the analyzed models, one mathematical program- (W-SVM) was constructed by linear combination and APSO was utilized
ming methods were found- Nonlinear programming (NLP). Forouzanfar for determining weight coefficients of combined forecasting model
et al. forecasted natural gas consumption for residential and commer- [46]. Wang et al. applied seasonal decomposition with LSSVR for hy-
cial sectors in Iran with LoR. However, to make the process simpler, two dropower consumption forecasting in China [144].
different methods are proposed to estimate the logistic parameters, of Song et al. applied fuzzy regression analysis in the short-term load
which one was GA based [103]. forecasting problem [19]. Xu et al. applied GM (1,1) with ARMA to
develop GM-ARMA model to forecast energy consumption for Guang-
5. Hybrid methods dong Province of China [145]. Amin-Naseri et al. developed a model for
daily electrical peak load forecasting (PLF) with feed-forward neural
In some models, for specific reasons (i.e., parameter tuning, ele- network (FFNN) method, where the Davies–Bouldin validity index was
vating accuracy) different stand-alone methods were combined to introduced to determine the best clusters [146]. Forouzanfar et al.
construct hybrid methods. Hybrid methods were utilized to develop the forecasted natural gas consumption for residential and commercial
assumptions and parameters in some forecasting models [135]. The sectors in Iran by utilization of LoR. However, GA based approach was
hybrid methods found in analyzed models can be divided into following proposed to estimate the logistic parameters, to make process simpler
four categories: [103]. Zhu et al. developed an improved hybrid model (MA-C-WH),
which utilized MA and adaptive particle swarm optimization algorithm
5.1. Statistical-statistical methods to forecast electricity demand in China [34]. An electric load fore-
casting model was developed with regression method combined with
Xu et al. combined MA and PCM to develop a Polynomial Curve and GSA or Kohonen neural networks [131]. GSA was applied to estimate
Moving Average Combination Projection (PCMACP) model to forecast optimal weighting factors for three demand estimation models to
natural gas consumption in China from 2009 to 2015. The model de- forecast oil consumption based on socio-economic indicators up to 2030
monstrated, the average annual growth rate will increase, and the [130].
natural gas consumption will reach 171,600 million cubic meters in
2015 in China. [33]. To estimate the long-run elasticities of the Na- 5.3. CI-CI methods
mibian energy demand, Vita et al. applied ARDL bounds testing ap-
proach to cointegration [66]. To forecast solar radiation, Chen et al. developed a fuzzy neural
Tan et al. developed a day-ahead electricity price forecasting model network (FNN) model with ANN and fuzzy logic [147]. The fuzzy
by combining Wavelet (WT)–GARCH–ARIMA [136]. Bowden et al. neural network was applied for day-ahead price forecasting of elec-
applied ARIMA-EGARCH-M for short-term forecasting of electricity tricity markets in [148]. Bazmi et al. utilized adaptive neuro-fuzzy
prices [62]. Hickey et al. developed four ARMAX–GARCH models for network (ANFIS) for electricity demand forecasting for the state of
forecasting hourly electricity prices. The four models were- GARCH Johor, Malaysia [149]. In another study, Zahedi et al. applied neuro-
(1,1), EGARCH (1,1), APARCH (1,1) and CGARCH (1,1) power ARCH fuzzy network for electricity demand forecasting for Ontario province,
(PARCH), where EGARCH is exponential GARCH; APARCH is asym- Canada [150]. Esen et al. utilized the neuro-fuzzy network for fore-
metric power ARCH, and CGARCH is Component GARCH [52]. Liu casting performances of ground-coupled heat pump system [151].
et al. developed ARMA-GARCH models (ARMA-SGARCH, ARMA- Forecasting model of mean hourly global solar radiation was developed
QGARCH, ARMA-GJRGARCH, ARMA-EGARCH, and ARMA-NGARCH) with ANFIS [152]. Akdemir et al. utilized ANFIS for long-term load
and their form of ARMA–GARCH-in-mean to forecast short-term elec- forecasting [153]. Chen et al. applied a collaborative principal com-
tricity prices [137]. ponent analysis and fuzzy feed- forward neural network (PCA-FFNN)
approach for long-term load forecasting [154]. In another study Chen,
5.2. Statistical-CI methods T. applied a collaborative fuzzy-neural approach for long-term load
forecasting [155]. Chang et al. applied weighted evolving fuzzy neural
Pao developed nonlinear hybrid models with SEGARCH and network for monthly electricity demand forecasting in Taiwan [156].
WARCH with ANN to forecast energy consumption in Taiwan [61]. For FNN was also applied for short-term load forecasting in [157–159].
wind speed forecasting Cadenas et al. developed a ARIMA-ANN model Padmakumari et al. applied FNN for long-term land use based dis-
[138]. González-Romera et al. developed an hybrid method where the tribution load forecasting [160].
periodic behavior was forecasted with a Fourier series while the trend In case of metaheuristic methods, genetic algorithm (GA), Particle
was predicted with a neural network [139]. For forecasting symbolic swarm optimization (PSO) and Ant colony optimization (ACO) were
interval time series, Maia et al. developed an ARMA-ANN model, where mostly utilized methods. El-Telbany et al. applied PSO and BP algo-
it performed better than that of ARMA [140]. Kandananond, K. devel- rithm to train NN model to forecast electricity demand in Jordan [161].
oped prediction models of the electricity demand in Thailand with Ghanbari et al. applied cooperative ant colony optimization-genetic
ANN, MLR and ARIMA methods to develop ANN-MLR and ANN-ARIMA algorithm (COR-ACO-GA) for energy demand forecasting with knowl-
hybrid methods [141]. ANN model using statistical feature parameters edge-based expert systems, which yielded better accuracy than ANFIS
(ANN-SFP) and historical data series (ANN-HDS) was applied for short- and ANN [95]. Ghanbari et al. integrated ACO, GA and fuzzy logic to
term solar irradiance forecasting (STSIF) [142]. Shi et al. applied develop a hybrid method to construct a load forecasting expert system
ARIMA with ANN and SVM to develop two hybrid models of ARIMA- for Iran in [96]. Niu et al. developed ACO-SVM model for forecasting
ANN and ARIMA-SVM for forecasting of wind speed and wind power short-term power load [118]. A NOx emission forecasting model for
generation [143]. Bouzerdoum et al. developed SARIMA-SVM model Iran, where GA, PSO, and ACO were applied to estimate optimal values
for short-term power forecasting of a small-scale grid-connected pho- of weighting factors regarding actual data in [119]. In another study, to
tovoltaic plant [42]. Guo et al. developed a hybrid Seasonal Auto-Re- forecast energy demand of Turkey, ACO-PSO based hybrid method was
gression Integrated Moving Average and Least Square Support Vector applied [109]. Hybrid ACO-PSO method was applied for to forecast the
Machine (SARIMA-LSSVM) model for forecasting wind speed in Hexi wind power output of Binaloud wind farm in Iran in [110]. To forecast
Corridor of China [43]. Wang et al. applied PSO optimal Fourier Annual electricity demand, Yu et al. utilized GA to optimizes the

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structure and PSO-GA to the parameters of the basis and weights of the 5.4. Statistical-MP methods
Radial Basis Function (RBF) neural network [162]. Yu et al. applied
PSO–GA approach for forecasting energy demand of China [122] and Forouzanfar et al. forecasted natural gas consumption for residential
primary energy demand of China [123]. In another study, Yu et al. and commercial sectors in Iran by utilization of LoR. However, NLP and
utilized improved PSO-GA to forecast energy demand for China [163]. GA based approach were proposed to estimate the logistic parameters,
Lee et al. constructed a GP-based GM(1, 1) model [164] and hybrid to make the process simpler [103].
dynamic GPGM model [165] to predict energy consumption.
Hu et al. applied firefly algorithm (FA) based memetic algorithm 6. Discussion
(FA-MA) to appropriately determine the parameters of SVR model for
load forecasting [108]. Hong, W.-C. developed IA-SVR model for elec- 6.1. Accuracy
tric load forecasting [133]. Fan et al. integrated two machine learning
techniques: Bayesian clustering by dynamics (BCD) and SVR to forecast An accurate forecasting of energy (demand and supply) and relevant
the electricity load [166]. parameters is critical to making informed decisions on energy infra-
Hsu et al. developed an improved GM (1, 1) model that combines structure for power generation and distribution. Forecasting accuracy is
residual modification with ANN sign estimations [167]. For predicting determined using different performance evaluation measures. Root
hourly load demand Bashir et al. applied ANNs and utilized PSO al- mean square error (RMSE), mean absolute error (MAE) and mean
gorithm to adjust the network's weights in the training phase of the absolute percentage forecast error (MAPE) were mostly utilized
ANNs [168]. Xie et al. constructed improved natural gas consumption [61,115,134,147,175–177]. Among other methods, mean absolute de-
GM (1, 1) model by applying GM for optimizing parameters [169]. viation (MAD), normalized root-mean-square error measure (NRMSE),
Zhang et al. utilized SA with chaotic GA to develop a chaotic genetic standard error of prediction (SEP) and absolute relative error (ARE)
algorithm-simulated annealing algorithm (CGASA), with an SVR model were also applied [44,134,145,175]. The accuracy evaluation methods
to improve load forecasting. The proposed CGASA was utilized for the were different in various models. The different choice of accuracy
internal randomness of chaotic iterations to overcome premature local methods made is hard to categorize the methods from best to worst
optimum, which yielded better accuracy [104]. SA algorithms were because the methods were not evaluated with same data or for the si-
employed to choose the parameters of an SVM model to develop SVMSA milar aim Under this circumstances, this study focused on the accuracy
method to forecast electricity load in Taiwan in [134]. Ko et al. com- results of the reviewed models and their comparisons to find out which
bined SVR, radial basis function neural network (RBFNN), and dual model performs better in specific objective (Table 8).
extended Kalamn filter (DEKF) to develop an SVR-DEKF-RBFNN model This study found that combination of statistical methods performs better
for short-term load forecasting [170]. To forecast electric load, CAS was than that of stand-alone statistical methods and [188] [61,183] [184] [184]
applied to improve the forecasting performance of SVR by searching its [60,62,136,189] [190] [175] in most of the cases, CI methods out-
suitable parameters combination in [125]. Azadeh et al. developed performed statistical methods [191]. Moreover, hybrid methods performed
electrical energy consumption forecasting models with GM-ANN superiorly in accuracy to CI methods (Table 8). In case of forecasting
method, where GA tuned parameters and the best coefficients with nonlinear and discontinuous data, machine learning methods performed
minimum error were identified for ANN [171]. Cinar et al. applied GA better than that of statistical methods [81,167,178]. When the relationship
to determine the hidden layer neuron numbers for GA-FFBPNN model between the variables is not known, or complex machine learning methods
to forecast the hydro energy potential of Turkey [172]. Xiaobo et al. can forecast the data, which is difficult to handle statistically [179]. In some
developed a GRA-DE-SVR model for short-term load forecasting with studies, authors combined machine learning methods with statistical
DE and SVR [129]. methods to increase the accuracy [88,139,143,151,180]. However, ma-
For forecasting world CO2 emissions, BCO was utilized for finding chine learning methods tend to be complex in learning and application,
optimal values of weighting factors for forecasting with ANN [116]. In while statistical methods are easy to adopt [181]. Some authors noted the
another study, chaotic artificial bee colony algorithm was applied to learning complexity of methods influence the choice of forecasting techni-
determine suitable values of its three parameters for electric load ques [103]. Data availability also affects the choice of forecasting method.
forecasting [117]. Continue genetic algorithm was applied to determine ANN is a data-driven method and requires a large amount of data for higher
the number of neurons in the hidden layer and connecting weights for forecasting accuracy [182]. In case of incomplete data sets, fuzzy logic is
ANN model to forecast short-term electricity load [173]. For accurate better. However, the accuracy level is not always satisfactory [182]. Grey
forecasting of electric load, Hong W.-C. applied CAS, CGA, CPSO, and prediction is another useful method while working with uncertainty pro-
SA with SVR model, to determine suitable parameter combination for blems with the small sample; incomplete and discrete data [183,184].
the model [126]. Significant numbers of authors advocated the utilization of hybridization
GSA was utilized to assist the seasonal SVR model to develop methods to enhance the accuracy of the forecasting models. On the other
SVRGSA and SSVRGSA for forecasting electricity load in Taiwan in hand, it would add more complexity in the model structure.
[86]. Yuan et al. developed an LSSVM-GSA model to short-term wind
power prediction model where GSA was applied to optimize the para- 6.2. Time analysis
meters of the LSSVM [85]. Niu et al. applied particle swarm optimi-
zation (PSO) as a training algorithm to obtain the weights of the fore- Based on the analysis of the previous EPMs, the research on fore-
casting methods (i.e., a method of proportional (MP), LR, GM, and casting models started in 1985, after the oil shock/crisis of 1970's
BPNN) [115]. Wang et al. developed a load forecasting model with DE (Fig. 4). At the starting period, the number of models was low. After the
and SVR, where DE algorithm was used to choose the appropriate United Nations Framework Convention on Climate Change (UNFCCC)
parameters for the SVR model [127]. Wang et al. applied ADE-BPNN committed State Parties to reduce GHG gas emission created by an-
forecasting method for developing prediction for electricity demand thropogenic CO2 emission systems, the development of forecasting
compared with different methods (i.e., ARIMA, BPNN, GA–BPNN, EPMs started to rise from 1995 because energy sector has been one of
DE–BPNN, SSVRCGASA, and TF-e-SVR-SA) [128]. Cao et al. applied the highest global emissions sources.
quantum-behaved particle swarm optimization (QPSO) to optimize the The number of models started to increase from 2005 when the
parameters for the SVR model and developed an SVR-QPSO model to Kyoto Protocol was entered into force in 2005. The number of models
forecast the energy demand of China [174]. published escalated from 12 to 25 within 2004–2005. In the last 12

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Table 8
Method-wise accuracy of the selected reviewed models.

Forecasting objective Methods Accuracya Best method Ref.

MAPE (%) MAE (-) RMSE (-) MAD (-) NRMSE (-) SEP (-) ARE (%)

Electricity price WT–GARCH–ARIMA 1.61 - - - - - - WT–GARCH–ARIMA [136]

ARIMA 10.61 - - - - - -
ARIMA–GARCH 8.65 - - - - - -
WT–ARIMA 6.37 - - - - - -
Electricity consumption AR (1)+HPF - 4.64† - - - - - AR (1)+HPF [236]
AR (1) - 7.23† - - - - -
ARIMA - 6.11† - - - - -
Power from PV system ARMAX 38.88 - 104.77 77.27 - - - ARMAX [35]
ARIMA 76.66 - 172.96 140.9 - - -
Single moving average 82.09 - 190.59 153.8 - - -
Double moving average 88.10 - 180.25 152.0 - - -
Single exponential 72.93 - 180.95 141.5 - - -
smoothing
Double exponential 72.85 - 181.04 141.5 - - -
smoothing
Holte Winter's additive 72.36 - 185.10 144.6 - - -
Holte Winter's 75.94 - 185.43 146.5 - - -
multiplicative
Electricity consumption (48 LR 8.60 1341.57 1508.96 - - - - ANN [191]
historical data) RSREGb 9.51 1489.72 1701.90 - - - -
ARMAX 4.83 764.90 931.13 - - - -
ANN 3.19 460.74 635.38 - - - -
Electricity consumption (132 LR 8.84 1376.26 1542.43 - - - -
historical data) RSREGb 7.58 1171.78 1295.43 - - - -
ARMAX 8.88 1386.99 1566.34 - - - -
ANN 4.02 598.65 709.25 - - - -
Energy consumption WARCH 2.90 - - - - - - WARCH-ANN [414]
SEGARCH 3.65 - - - - - -
WARCH-ANN 2.56 - - - - - -
SEGARCH-ANN 2.98 - - - - - -
Electricity demand PSO (training) 2.42 - - - - - - PSO [161]
PSO (test set) 2.52 - - - - - -
BP algorithm (training) 3.2 - - - - - -
BP algorithm (test set) 2.82 - - - - - -
ARMA (training) 3.98 - - - - - -
ARMA (test set) 3.93 - - - - - -
Energy consumption GPGM (1, 1) (training) 2.59 - - - - - - GPGM (1, 1) [164]
GPGM (1, 1) (test set) 20.23 - - - - - -
GM(1,1) (training) 4.13 - - - - - -
GM(1,1) (test set) 26.21 - - - - - -
LR (training) 4.20 - - - - - -
LR (test set) 27.76 - - - - - -
Energy consumption Hybrid dynamic GM 0.40 874.19 1383.11 - - - - Hybrid dynamic GM [165]
GM (1,1) 16.94 26945.07 30384.99 - - - -
NDGM(1,1) 33.33 73052.8 93230.75 - - - -
ARIMA 17.99 41890.49 59271.76 - - - -
GP 5.12 10631.51 13325.14 - - - -
Hybrid GM(1,1) 4.93 9949.13 12054.78 - - - -
Mid-term load forecasting DLS-SVM 1.082 - - - - - - DLS-SVM [350]
LS-SMV 1.101 - - - - - - [356]
SMV 2.149 - - - - - - [355]
Solar radiation FNN 6.03–9.65 - - - - - - FNN [147]
ARIMA and descriptive Around 30 - - - - - - [517]
statistics
Fuzzy logic 13.9 -20.2 - - - - - - [147]
ANN 10.9-20.3 - - - - - -
Power demand GM (1,1) 3.88 - - - - - - Improved GM (1,1) [167]
Improved GM (1,1) 1.29 - - - - - -
ARIMA 2.27 - - - - - -
CO2 emission ARIMA 2.75 9.81 11.25 - - - - GP (4 year) [230]
GP (4 year) 2.46 8.78 11.25 - - - -
GP (5 year) 4.22 15.27 17.60 - - - -
GP (6 year) 2.60 9.29 11.75 - - - -
Energy consumption ARIMA 1.75 158.11 174.36 - - - - ARIMA
GP (4 year) 4.40 427.07 627.61 - - - -
GP (5 year) 3.32 320.06 455.69 - - - -
GP (6 year) 2.45 231.23 304.28 - - - -
Economic growth (GDP) ARIMA 4.17 32.06 41.49 - - - - GP (4 year)
GP (4 year) 1.81 13.69 19.15 - - - -
GP (5 year) 3.41 26.17 36.90 - - - -
GP (6 year) 5.44 41.45 55.84 - - - -
(continued on next page)

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Table 8 (continued)

Forecasting objective Methods Accuracya Best method Ref.

MAPE (%) MAE (-) RMSE (-) MAD (-) NRMSE (-) SEP (-) ARE (%)

Energy consumption GM - - - - - - 7.17 GM-ARMA [145]

ARMA - - - - - - 7.62
GM-ARMA - - - - - - 4.39
Wind speed SARIMA-LSSVM 6.76 - - - - - - SARIMA-LSSVM [43]
ARIMA 18.08 - - - - - -
SARIMA 11.08 - - - - - -
LSSVM 8.83 - - - - - -
GM 8.93 - - - - - -
ARIMA-SVM 14.81 - - - - - -
Electric load ARIMA 6.044 - - - - - - SSVRCGA [351]
SVRCGA 3.382 - - - - - -
SSVRCGA 2.695 - - - - - -
Electric load SVRCPSO 1.61 - - - - - - SVRCPSO [126]
SVRPSO 3.14 - - - - - -
SVMSA 1.76 - - - - - -
ARIMA 10.31 - - - - - -
Electricity demand SARIMA 6.08 - - - - - - MA-C-WH [34]
MA-C-H 3.86 - - - - - -
MA-C-WH 3.69 - - - - - -
Electric load SSVRCGASA 3.73 - - - - - - SSVRCGASA [104]
TF-ε-SVR-SA 3.799 - - - - - -
ARIMA 6.04 - - - - - -
Electric load (Eastern regional) SVRCAS 2.23 - - - - - - SVRCPSO [125]
SVRCPSO 2.19 - - - - - -
SVRCGA 2.57 - - - - - -
Regression 4.1 - - - - - -
ANN 3.6 - - - - - -
Electric load ARIMA 6.04 - - - - - - SRSVRCABC [117]
TF-ε-SVR-SA 3.80 - - - - - -
SSVRCABC 3.06 - - - - - -
SRSVRCABC 2.39 - - - - - -
Electric load ARIMA 10.31 - - 13788 0.105997 - - SVMSA [134]
GRNN 5.18 - - 6758 0.054732 - -
SVMSA 1.76 - - 2,448 0.026357 - -
Electric load SSVRGSA 2.587 - - - - - - SSVRGSA [86]
ARIMA 6.044 - - - - - -
SVRGSA 3.199 - - - - - -
TF-ε-SVR-SA 3.799 - - - - - -
Electricity demand ADE-BPNN 1.725 3.0623 3.9925 - - - - ADE-BPNN [128]
ARIMA 6.044 10.6641 12.3787 - - - -
BPNN 3.341 5.9958 6.9870 - - - -
GA–BPNN 3.168 5.5618 6.9285 - - - -
DE–BPNN 3.080 5.4004 6.8622 - - - -
SSVRCGASA 1.901 3.4347 4.1822 - - - -
TF-e-SVR-SA 3.799 6.9694 8.6167 - - - -
Electric load SVM - - 12.37† - - - - GRA-DE-SVR [129]
GRA-DE-SVR - - 10.85† - - - -
ARMA - - 10.93† - - - -
LR - - 11.99† - - - -
Natural gas consumption PCMACP -3.42 - - - - - - PCMACP [33]
Polynomial Curve (2nd -10.75 - - - - - -
order)
BP neural network -10.68 - - - - - -
GM -39.61 - - - - - -
Energy consumption WARCH–ANN 2.56 404184.2 531545.14 - - - - WARCH–ANN [61]
WARCH 2.90 474189.2 643744.33 - - - -
SEGARCH 3.65 606629.3 824500.08 - - - -
SEGARCH–ANN 2.98 464632.4 596013.96 - - - -
Petroleum consumption WARCH–ANN 3.51 112542.5 134832.21 - - - - WARCH–ANN
WARCH 4.08 134300.1 165753.68 - - - -
SEGARCH 4.88 167031.1 204369.84 - - - -
SEGARCH–ANN 3.71 122320.1 148234.91 - - - -
Electricity demand F-S-SARIMAc 2.19 - 4.91 - - 2.65 - F-S-SARIMA [44]
SARIMA 3.28 - 6.67 - - 3.74 -
F-SARIMA 2.75 - 6.57 - - 3.68 -
S-SARIMA 2.91 - 6.25 - - 3.37 -
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Table 8 (continued)

Forecasting objective Methods Accuracya Best method Ref.

MAPE (%) MAE (-) RMSE (-) MAD (-) NRMSE (-) SEP (-) ARE (%)

Electricity demand COR-ACO-GA - - 1292.381 - - - - COR-ACO-GA [95]

ANFIS - - 4563.398 - - - -
ANN - - 6323.944 - - - -
Natural gas demand COR-ACO-GA - - 648.31 - - - -
ANFIS - - 1206.816 - - - -
ANN - - 2178.246 - - - -
Oil products demand COR-ACO-GA - - 3.750578 - - - -
ANFIS - - 8.795963 - - - -
ANN - - 11.05846 - - - -
Electricity price BPANN 29.46 8.5021 - - - - - DCANN [251]
FNN 22.03 6.8929 - - - - -
LSSVM 9.50 4.4632 - - - - -
ARFIMA 35.08 8.8737 - - - - -
GARCH 25.11 7.2425 - - - - -
DCANN 8.87 4.2611 - - - - -
Electric load ARMA 2.3688 34.0608 2.9198 - - - - SVR-MFA [270]
ANN 1.9569 28.8032 2.6396 - - - -
SVR-GA 1.8501 27.3499 2.1943 - - - -
SVR-HBMO 1.8375 26.5383 2.0007 - - - -
SVR-FA 1.8051 26.1718 2.5667 - - - -
SVR-PSO 1.7381 24.0145 2.1399 - - - -
SVR-MFA 1.6909 22.5423 2.0604 - - - -
Energy demand SC-SVR 2.36 3913.88 - - - - - SC-SVR [369]
LSSVR 4.77 8285.22 - - - - -
BPNN 3.61 4549.69 - - - - -
Energy demand ARMA 6.1 13.6 - - - - - FNF-SVRLP [271]
ANN 5.3 11.9 - - - - -
SVRLP 4.4 10.4 - - - - -
FNF-SVRLP 3.8 9.2 - - - - -

a
Accuracy metrics: Mean absolute percentage forecast error (MAPE), mean absolute error (MAE), root mean square error (RMSE), mean absolute deviation (MAD), normalized root-
mean-square error measure (NRMSE), standard error of prediction (SEP) and absolute relative error (ARE).
b
Response surface regression model (RSREG).
c
PSO optimal Fourier approach on residual modification of SARIMA was applied.
†
The values in the study was reported in percentage (%).

years, 76% EPMs were developed (Fig. 4). The highest number of integration of metaheuristic methods in forecasting started to grow. In
models (46) was developed in 2010. However, the number of EPMs 2015, 56 models utilized CI methods which is four times more than that
reduced to 34 in 2011 & 2012. In 2013 and 2014, the published model of the statistical ones (14 models). The CI method use is demonstrating
number reduced to 20 and 24 respectively. The EPM number elevated an exponential growth in past 12 years, where statistical methods are
to 27 in 2015. Up to June 2017, six models were published with the showing a gradual descend since 2010 (Fig. 5). A major cause of the
objective of forecasting in energy planning sector. growth may be the better accuracy of the CI methods (Table 8) and
Among the forecasting methods, statistical methods were the first to higher speed in computational capabilities [185].
rise in use from 2005. Before 1990, statistical methods were mostly
utilized (Fig. 5). After 1990's use of machine learning methods started 6.3. Geographical analysis
to rise. From 2007, the use of machine learning methods augmented
significantly as well as with statistical methods. After 2009 the Continent-wise, all the continents with human habitation developed

Fig. 4. Publishing year of the studied models.

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Fig. 5. Publishing year of the models with methods utilized in energy planning models.

EPMs. According to United Nations, there 269 countries in the world Africa has 58 countries, of which only five courtiers developed
[186]. Among these countries, forecasting models were developed for forecasting models. Namibia, Ghana, Algeria, Tunisia and South Africa
only 59 countries. Among all the countries, the highest number of established 2, 4, 2, 1 and five models respectively.
forecasting models were developed in China. Total 122 models were Among 14 countries of South America, Ecuador, Peru, Chile,
developed in China with 27 of the 50 analyzed methods of this study. Venezuela, Columbia, Argentina and Brazil adopted forecasting model
In Europe, there are 53 countries [186], but only 18 countries de- for energy planning. Brazil developed the most number of models.
veloped energy planning forecasting models. The countries were- UK, Among the studied 483 models, twelve models were developed for
Ireland, France, Netherlands, Denmark, Germany, Spain, Portugal, global forecasting (Table 2). LR, ANN, GA, ABCO, and PSO were uti-
Italy, Croatia, Romania, Russia, Czech Republic, Hungary, Poland, Cy- lized for forecasting for global geographical extent (Fig. 6).
prus, Greece, and Turkey. However, most of the models were developed However, 30 models were established for regional geographical
in the UK, Turkey, Spain, and Greece (Fig. 6). extent. The regions considered were- OECD countries, G-7 countries,
There are 41 counties in North America [186]. However, only six Europe, CIS Countries, GCC countries, BRIC country, Middle East, North
countries (Haiti, Jamaica, Trinidad and Tobago, Mexico, USA and Ca- America, South America, Asia and developing countries. Among the 30
nada) developed models for energy forecasting. Most of the models models, eight models were developed for Europe. From the analysis of
among these countries were developed in the USA (Fig. 6). the geographical extent, it is evident that developed economies have
The continent of Oceania contains 25 countries [186], of which only more EPMs than that of developing and least developed ones (Fig. 6).
Australia and New Zealand developed models. In this region other 23 Statistical methods are utilized for developed, developing and least
countries of Melanesia, Micronesia and Polynesia are considered de- developed contexts. However, CI methods are widely used in developed
veloping regions [186]. This concludes the fact that in this continent contexts (Fig. 6).
only developed countries established energy forecasting models.
In Asia, Japan, China, Hong Kong, Taiwan, South Korea, Jordan,
Lebanon, Oman, Saudi Arabia, Kuwait, Iran, Pakistan, India, Bangladesh, Sri 6.4. Objective based analysis
Lanka, Nepal, Indonesia, Singapore, Philippines, Malaysia, and Thailand
developed forecasting models for energy planning. Therefore, 21 countries The studied EPMs had different objectives. From the analysis of 483
among 50 countries [186] of the continents developed forecasting models. models, 11 objectives were identified (Table 9). These were energy and
In Asia, the only developed economy is established in Japan. Along with electricity demand, energy supply, renewable energy, GHG emissions,
Japan, other developing countries also established some models. In Asia, energy economic, socio-economic, energy and electricity price, load
China, Taiwan, Iran, and India developed a higher number of forecasting forecasting, planning and policy analysis, performance analysis and
models. model development. Among the 28 statistical forecasting methods,
ARIMA was used for nine objectives, while LR complied with seven

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K.B. Debnath, M. Mourshed Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Fig. 6. Country wise number of models utilizing different forecasting methods.

objectives, followed by ARMA (6 objectives) (Table 9). Among the 28 4% more in electric load and renewable energy forecasting models re-
statistical methods, 23 were utilized for energy and electricity demand spectively than that of statistical ones (Fig. 7).
forecasting in 53.9% of the reviewed 483 models (Table 9). Among the 50 analyzed methods, a maximum number of methods
Among the CI and MP methods, ANN was utilized for nine objec- (23 statistical, 12 CI and one MP) were utilized to develop energy and
tives, followed by GM for seven objectives. FL, SMV, PSO, and ACO electricity demand forecasting models. Second highest number of
were utilized for six objectives each. Moreover, GA was utilized for methods (8 statistical and 18 CI) were utilized to forecast electric load.
achieving five of the objectives (Table 10). Among the 22 CI and MP Third highest number of methods (7 statistical and 9 CI) were used for
methods, 13 and 18 methods were utilized for energy and electricity renewable energy forecasting (Tables 9 and 10).
demand, and electric load forecasting respectively. In the reviewed 483
models, 73%, 38%, 18% and 13% of the model objectives were energy 7. Conclusion
and electricity demand, electric load, renewable energy, and energy &
electricity price forecasting respectively. For energy and electricity Energy planning models assist stakeholders to assess the impact of
demand forecasting, statistical methods were used in 18% more models current and future energy policies. The accuracy of EPMs depends on
than that of CI and MP. However, CI methods were utilized in 28% and applying appropriate forecasting methods for demand and supply sector

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 K.B. Debnath, M. Mourshed
Table 9
Statistical method-wise objective of the reviewed models.

Objectives Energy Energy Renewable GHG Energy Socio Energy and Load Planning and/or Performance Model Total %
Methods Demand Supply energy emissions economic economic electricity price forecasting Policy analysis development

LR ■ ■ – ■ ■ – ■ ■ – – ■ 7 9.0%
NLR ■ ■ – ■ ■ – – – – – ■ 5 6.4%
LoR ■ ■ ■ ■ – – – – – – – 4 5.1%
NR – – ■ – – – – ■ – – – 2 2.6%
PLSR ■ – – – – – – – – – – 1 1.3%
GP ■ – – – – – – – – – – 1 1.3%
Log linear analysis ■ – – – ■ – – – – – – 2 2.6%
Translog ■ – – – – – – – – – – 1 1.3%
Polynomial curve model ■ – – – – – – – – – – 1 1.3%
MA ■ – – – – – – – – – – 1 1.3%
ARIMA ■ ■ ■ ■ ■ ■ ■ ■ – – ■ 9 11.5%
SARIMA ■ ■ ■ – ■ – – ■ – – – 5 6.4%
316

ARMAX – – ■ – – – ■ ■ – – – 3 3.8%
ARMA ■ – ■ ■ – – ■ ■ – – ■ 6 7.7%
ANOVA ■ – – ■ – – – – – – – 2 2.6%
SR ■ ■ – – – – – – – – – 2 2.6%
VAR ■ – – – – – ■ – – – – 2 2.6%
ARDL ■ – – – – ■ ■ – – – – 3 3.8%
PAM ■ – – – – – – – – – – 1 1.3%
GARCH ■ – – – ■ – ■ – – – – 3 3.8%
SEGARCH ■ – – – – – – – – – – 1 1.3%
EGARCH – – – – – – ■ – – – – 1 1.3%
WARCH ■ – – – – – – – – – – 1 1.3%

Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Decomposition ■ ■ – ■ – – ■ ■ – – ■ 6 7.7%
Unit root test and/or ■ – – ■ ■ ■ ■ – – – – 5 6.4%
Cointegration
BVAR ■ – ■ – – – – ■ – – – 3 3.8%
Number of methods 23 7 7 8 7 3 10 8 0 0 5
Number of models 186 11 29 29 14 15 32 23 0 0 6
Percentage of model (%) 53.9% 3.2% 8.4% 8.4% 4.1% 4.3% 9.3% 6.7% 0.0% 0.0% 1.7%
K.B. Debnath, M. Mourshed Renewable and Sustainable Energy Reviews 88 (2018) 297–325

Table 10
CI and mathematical method-wise objective of the reviewed models.

Objectives Energy Energy Renewable GHG Energy Socio Energy Load Planning Performance Model Total %
Methods Demand Supply energy emissions economic economic and forecasting and/or development
electricity Policy
price analysis

SVM ■ – ■ – ■ – ■ ■ – – ■ 6 8.8%
Decision ■ – ■ – – – – ■ – – – 3 4.4%
tree
ANN ■ ■ ■ ■ ■ – ■ ■ – ■ ■ 9 13.2%
Abductive ■ – – – – – – – – – – 1 1.5%
net-
works
Grey ■ ■ ■ ■ – ■ ■ ■ – – – 7 10.3%
predic-
tion
Fuzzy logic ■ – ■ – – – ■ ■ ■ ■ – 6 8.8%
Expert ■ – – – – – – ■ – – – 2 2.9%
system
GA ■ – – ■ – – – ■ ■ – ■ 5 7.4%
ABCO – – – ■ – – – ■ – – – 2 2.9%
ACO ■ ■ ■ ■ – – – ■ ■ – – 6 8.8%
PSO ■ – ■ ■ – – ■ ■ ■ – – 6 8.8%
GSA ■ – ■ – – – – ■ – – – 3 4.4%
CAS – – – – – – – ■ – – – 1 1.5%
DE – – – – – – – ■ – – ■ 2 2.9%
HS ■ – – – – – – – – – – 1 1.5%
EA – – – – – – – ■ – – – 1 1.5%
MA – – – – – – – ■ – – – 1 1.5%
IA – – – – – – – ■ – – – 1 1.5%
SA – – ■ – – – – ■ – – – 2 2.9%
FA – – – – – – – ■ – – – 1 1.5%
CSA – – – – – – ■ – – – – 1 1.5%
NLP ■ – – – – – – – – – – 1 1.5%
Number of 13 3 9 6 2 1 6 18 4 2 4
methods
Number of 169 5 59 17 5 1 29 162 4 3 12
models
Percentage 36.3% 1.1% 12.7% 3.6% 1.1% 0.2% 6.2% 34.8% 0.9% 0.6% 2.6%
of
model
(%)

Fig. 7. Objectives of the models.

projections. Among all the forecasting methods, choice of appropriate between 1985 and June 2017. Among the 50 identified methods, sta-
one depends on different factors. The complexity and nature, as well as, tistical, computational intelligence (CI) and mathematical program-
the objective of the research problem are one of the critical determi- ming (MP) methods were 28, 21 and one respectively. Among CI
nants of method choice. Other important factors of forecasting method methods, ANN was utilized in 194 EPMs, followed by SVM (58 models),
selection can be accuracy and estimation adaptability with incomplete FL (40 models), GA (39 models), PSO (34 models) and GM (29 models).
data-set. In the case of statistical methods, ARIMA, LR, and ARMA were utilized
The review of 483 EPMs, revealed the use of fifty different methods in 46, 39 and 22 EPMs respectively for forecasting. Evidently, CI

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