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Review

A Review of Auto-Regressive Methods Applications to Short-Term Demand Forecasting in Power Systems

by
Rafał Czapaj
1,*,
Jacek Kamiński
2,* and
Maciej Sołtysik
3
1
PSE Innowacje Sp.z o.o., Al. Jerozolimskie 132 a, 02-305 Warsaw, Poland
2
Mineral and Energy Economy Research Institute of the Polish Academy of Sciences, The Department of Policy and Strategic Research, The Division of Energy Economics, Wybickiego 7A, 31-261 Kraków, Poland
3
Faculty of Electrical Engineering, Częstochowa University of Technology, Armii Krajowej 17, 42-200 Częstochowa, Poland
*
Authors to whom correspondence should be addressed.
Energies 2022, 15(18), 6729; https://doi.org/10.3390/en15186729
Submission received: 10 August 2022 / Revised: 30 August 2022 / Accepted: 5 September 2022 / Published: 14 September 2022
(This article belongs to the Special Issue Intelligent Forecasting and Optimization in Electrical Power Systems)
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Abstract

:
The paper conducts a literature review of applications of autoregressive methods to short-term forecasting of power demand. This need is dictated by the advancement of modern forecasting methods and their achievement in good forecasting efficiency in particular. The annual effectiveness of forecasting power demand for the Polish National Power Grid for the next day is approx. 1%; therefore, the main objective of the review is to verify whether it is possible to improve efficiency while maintaining the minimum financial outlays and time-consuming efforts. The methods that fulfil these conditions are autoregressive methods; therefore, the paper focuses on autoregressive methods, which are less time-consuming and, as a result, cheaper in development and applications. The prepared review ranks the forecasting models in terms of the forecasting effectiveness achieved in the literature on the subject, which enables the selection of models that may improve the currently achieved effectiveness of the transmission system operator. Due to the applied approach, a transparent set of forecasting methods and models was obtained, in addition to knowledge about their potential in the context of the needs for short-term forecasting of electricity demand in the national power system. The articles in which the MAPE error was used to assess the quality of short-term forecasts were analyzed. The investigation included 47 articles, several dozen forecasting methods, and 264 forecasting models. The articles date from 1997 and, apart from the autoregressive methods, also include the methods and models that use explanatory variables (non-autoregressive ones). The input data used come from the period 1998–2014. The analysis included 25 power systems located on four continents (Asia, Europe, North America, and Australia) that were published by 44 different research teams. The results of the review show that in the autoregressive methods applied to forecasting short-term power demand, there is a potential to improve forecasting effectiveness in power systems. The most promising prognostic models using the autoregressive approach, based on the review, include Fuzzy Logic, Artificial Neural Networks, Wavelet Artificial Neural Networks, Adaptive Neurofuse Inference Systems, Genetic Algorithms, Fuzzy Regression, and Data Envelope Analysis. These methods make it possible to achieve the efficiency of short-term forecasting of electricity demand with hourly resolution at the level below 1%, which confirms the assumption made by the authors about the potential of autoregressive methods. Other forecasting models, the effectiveness of which is high, may also prove useful in forecasting by electricity system operators. The paper also discusses the classical methods of Artificial Intelligence, Data Mining, Big Data, and the state of research in short-term power demand forecasting in power systems using autoregressive and non-autoregressive methods and models.

1. Introduction

1.1. Overview

The economic development of countries is inextricably linked with the functioning of their power systems. Due to the development of power grids and the growing access to them, electricity is now indispensable for the proper functioning of the economy and the population, and the demand for it is systematically growing. Rising electricity prices in recent years and their fluctuations, in addition to insufficient development of the manufacturing sector, make it difficult to optimally meet the growing demand for electricity. Unfortunately, storage of electricity on a large scale and in the long term is a complex and very expensive issue. Thus, at any time in the operation of power systems, it is necessary to maintain a balance between the generation of electricity and its consumption, taking into account the technical limitations of electricity networks, in order to maintain continuity and security of power and electricity supplies while maintaining the optimal operating costs of the power system. In this context, forecasting the load of power systems is an essential element of planning their work in the short, medium, and long term, and is one of the greatest challenges faced by the power industry in every country. Electricity demand forecasting is a basic element of planning electricity generation, participation in electricity markets, and the development of the power grid. Short-term forecasting of the power system load, performed, inter alia, by operators of power systems, requires ensuring the highest possible accuracy for each hour of the day while maintaining the lowest computational cost at an appropriate time. Forecasting the load on systems with the use of prognostic models using explanatory variables is costly and time-consuming, in contrast to autoregressive methods which use only information about the earlier development of the analyzed parameter in the forecasting process. Thus, along with the observed trend indicating the reduction in forecast horizons from hours to minutes, and even seconds, it is necessary to search for cheap and quick forecasting methods that will allow the current forecasting effectiveness to be maintained at lower costs of their development and with a comparable or shorter development time.

1.2. Literature Survey

In short-term electrical power demand forecasting, both autoregressive methods using the properties of moving averages and exponential smoothing, and methods using machine learning [1,2,3,4,5,6]. Support Vector Machines and Particle Swarms, and artificial intelligence [7], including Artificial Neural Networks, have been used for years. Many research centers worldwide have developed more accurate forecasting methods and models, especially for short-term forecasting. Several teams have conducted research at the academic level, perfecting the methods and models they have developed. For the conducted analyses and simulations, usually, STATISTICA®, SAS/ETS, and SPSS environments [8], GRETL [9,10], and the R and Python programming languages are used, among others.
The demand for electrical power is characterized by large fluctuations [11]. In this case, the key factors exhibit daily, weekly, annual, and multi-year variability [12]. Moreover, the seasonal variability (which results in annual variability), quarterly variability (seasons), and monthly variability (part of the seasons) are distinguished. Continuity of power demand and the still “insufficient” (in the sense of high power/capacity) development of energy storage results in the inability to store it in large quantities, which makes it necessary to cover the demand for power at the time of the occurrence of this demand [13].
Other factors, apart from the passage of time (consecutive days, weeks, etc.), that influence the variability in the power system load [14,15] are the variability in weather conditions and the resulting variability in the ambient temperature, in addition to the transition from winter to summer time [16,17] and from summer to winter time (introduced to flatten the evening peak of power demand in the summer half of the year) [12]). Other weather factors influencing the level of demand in the power system include, among others, cloudiness, air humidity, and wind speed [12]. The ambient temperature significantly affects the load in the power system. The change in weather conditions directly impacts consumer behavior (municipal and industrial), consisting of increasing power consumption from lighting and heating devices (convector heating and electric heating).

1.3. Motivation and Incitement

Individual areas of the Polish Power System have a different share in shaping the domestic demand for electrical power. Naturally, areas with significant industrialization and, therefore, a significant population in Poland, translate into greater demand for electrical power (and, consequently, electrical power consumption), and thus, to a greater extent, changes in the weather (atmospheric conditions) affect these areas. The yearly demand forecasting error for the Polish National Power System is approximately 1%, which shows a high level of accuracy; thus, there is a need to search for the potential in well-known methods and models, including autoregressive models, to reduce the error below this level. In this context, this paper aims to review auto-regressive methods applied to short-term power demand forecasting in power systems.

1.4. Research Gaps

The conducted review of articles describing the methods and forecasting models used in short-term forecasting of electric power demand shows a great variety. Autoregressive methods are still an attractive and effective tool for forecasting. Their unquestionable advantage is low financial outlay and quickly obtaining forecast results. The current observation of scientific reports in the form of literature reviews is time-consuming. Therefore, it is important to develop rankings of forecasting models, taking into account their forecasting effectiveness. While preparing this review, the authors identified a gap in presenting the results of valuable research in this aspect, and thus attempted to develop such a ranking. The Mean Average Percentage Error was adopted as a measure for assessing the quality of forecasts developed with autoregressive methods. From the prepared ranking of 264 autoregressive models, a set of Top 10 models was distinguished, which can be a significant aid for researchers and scientists dealing with short-term forecasting of electricity demand in power systems.

1.5. Major Contributions

The main contribution of the authors is to present an overview of methods in the field of artificial intelligence, Data Mining (now often associated with Big Data issues), and Big Data. In addition, the state of research in short-term power demand forecasting for power systems using autoregressive and non-autoregressive methods and models is presented, along with a detailed table that describes the results of the review of 47 articles describing 264 forecasting models (Table 1, where MAPE is an ex post, and MAPE(ea) is an ex ante approach). Additionally, the authors present a new way to develop literature reviews in the context of selecting the most prospective prognostic models. In the proposed new approach (explained in the flowchart—Figure 1), ranking of forecasting models (Table 2 and Table 3 and Figure 2) was used due to the selected measure of forecast quality (Mean Average Percentage Error). The applied new approach to the development of the results of literature reviews is an excellent source of knowledge for scientists, experts, and analysts, supporting the preparation of forecasts for power system operators, with particular emphasis on transmission system operators.

2. Short-Term Forecasting Methods and Models Used for Power Systems

2.1. Classical Methods of Artificial Intelligence

There main methods are successfully used in forecasting, optimization, diagnostics, detection, and design in the power industry: artificial neural networks, evolutionary algorithms, and expert systems. Neural networks are used, among others, in optimization of tap changer settings in transformers, optimization of capacitor bank settings, and forecasting of the peak load of the power system and its daily loads using Artificial Neural Networks [13,23,40,42,43,46,49,57,62,65,66,67,68,69,70,71,72,73,74,75,76,77,78], in addition to using Deep Neural Networks [43], and autoregressive models [79], Big Data [1,80], short-circuit analyses, and transformer damage detection. Artificial Neural Networks are the most commonly used artificial intelligence methods [81] in forecasting the operating parameters of power systems and networks. Artificial Neural Networks [82,83] are an effective tool for forecasting in the power industry (not only the loads mentioned above in the power grid [84,85,86,87], but also electricity prices [88], especially in short-term forecasting [72]. In practical applications, Artificial Neural Networks are also supported by the techniques of Fuzzy Logic functions [89] and the Neuro-Fuzzy Approach [90,91,92,93].
The indication of the greater effectiveness of Artificial Neural Networks over the improvement of traditional methods in short-term forecasting of power system loads, presented in [72], does not always translate into short-term forecasting of energy prices on Polish and foreign electricity trading floors [94]. In this context, it is possible to obtain an inverse relationship. For example, the multiple regression method gives significantly greater forecasting efficiency when compared to the models of Artificial Neural Networks [95]. Artificial Neural Networks are highly effective not only in the short term, but also in long-term forecasting [96,97].
Evolutionary algorithms are used, among others in [84]: forecasting daily loads of electric power systems [46,67], optimizing the configuration of power grids, optimizing voltage levels in power grids, designing power grids, planning power plant operation, creating an economical distribution of loads, planning power grid development, supporting regulatory activities in power systems, and protection automatics [83,98]. Expert systems are used, among other things, in [99]: designing power grids and stations and reconstruction of power systems in post-emergency states [100,101].
Additional information on the application of artificial intelligence methods, taking into account the studied subject of the variability in power system loads and their forecasting, can be found in [81,84,85,102,103].

2.2. Data Mining Methods

In the literature focusing on the analysis of large data sets and forecasting using Data Mining methods, there are many definitions of these methods and ideas [104].
The main definitions of Data Mining are:
  • An interdisciplinary approach using techniques from machine learning, image recognition, statistics, databases and visualization to extract information from large databases [42,105,106];
  • An analysis of large, previously collected data sets to discover new regularities and describe the data in a new way that is understandable and useful for the data owner [107].
The first definition comes from 1998, while the second comes from 2001; thus, their evolution is noticeable.
Further definitions of Data Mining methods are:
3.
The process of searching for valuable information (knowledge) when the researcher is dealing with a large amount of data [108,109,110,111];
4.
The process of examining and analyzing large amounts of data by automated or semi-automatic methods to discover meaningful patterns and rules [112,113];
5.
Methods of broadly understood data analysis aimed at identifying previously unknown regularities occurring in large data sets, from which the results are in a form that is easy to interpret by the researcher [109].
At the beginning of their development, Data Mining methods were accused of being unscientific, assuming no theory, having no elegance or formal evidence, and being primitive and for application only [114].
The classical approach to data analysis uses the scheme [115,116] from defining the problem through creating a mathematical model, preparing the input data, and analyzing the problem, to interpreting the obtained results. The Data Mining approach uses a scheme from problem definition through preparing input data, problem analysis, and creating a mathematical model, to interpreting the obtained results. The algorithms used in the field of Data Mining are divided into supervised learning and non-supervised learning [104]. In the supervised learning methods, the main goal is to recreate the value of the examined parameter. In the non-supervised learning methods, the aim is to detect structures or hidden patterns in the analyzed data due to the lack of distinguishing a single feature. Teaching forecasting models using a supervised learning approach can be conducted as an implementation of a classification or regression problem. In classification problems, the analyzed parameter is qualitative, and in regression problems, this parameter is quantitative.
The knowledge derived from empirical research is proven, and due to the collection of larger and larger sets of data, it is beneficial for further research, both empirical and forecasting (in a certain sense speculative); it is useful to analyze these sets and draw additional conclusions. Additional research, including experimental studies, may result in obtaining a greater number of answers than the questions posed by the researcher [117,118,119]. The classification indicated in [118] of problem types and their respective Data Mining methods concerning time series analysis notes the inclusion of MultiLayer Perceptron (MLP) and Radial Basis Function (RBF) Artificial Neural Networks in this method. It must be concluded that the classifications of methods overlap and do not function as hermetic.
The group of Data Mining methods and models also includes forecasting problems, which are divided into two groups. The first group includes regression and classification trees, and the second group includes advanced machine learning methods. Classification and regression trees include Classification and Regression Trees (C&RT) and Chi-Square Automatic Interaction Detection (CHAID) trees [96,120]. The advanced machine learning group consists of the methods Multivariate Adaptive Regression Splines (MARSplines), Support Vector Machines (SVMs), k Nearest Neighbors [121,122], k—Means [123,124], Naive Bayes Classifier (only applicable to classification problems), Random Forest [125], and Boosted Trees [96]. The use of Data Mining methods in forecasting regression problems consists of evaluating many models, comparing their effectiveness results, and creating hybrid systems, due to which it is possible to maintain the smallest deviations in the forecasted values from the realized values of the analyzed parameters. The distinguishing feature of Data Mining methods is the speed of their creation. The MARSplines and Boosted Tree methods are among the most effective predictive models from the group of Data Mining methods for forecasting power demand in power systems.
The MARSplines method is in the niche of practical applications in forecasting problems in large-scale power engineering. In the MARSplines method, a non-parametric type belonging to the group of supervised learning methods, the co-variability in features is used to predict the value of a selected feature, and in classification problems [126,127]. The indicated convenience excludes from research activities the necessity to analyze the correlation between the independent variables, which in many cases may correlate with the predicted variable, but do not affect it.
The Multivariate Adaptive Regression Splines (MARSplines) method [128,129,130] uses the method of recursive division of the feature space to build a regression model in the form of spline curves [131,132,133] and is an extension of the methods of regression trees and multiple regression [105]. Due to the above properties, the MARSplines [131,132,133] is an effective tool for Big Data applications [134,135].
The MARSplines method also enables the automatic selection of explanatory variables for forecasting models. The efficiency of this selection is in many cases greater than that for classical methods of selecting variables [30,31,136,137,138]. Thus, the method can be successfully used, in addition to the multiple regression method, in selecting input variables for forecasting models and short-term forecasting of time series, including power demand in power systems. [31,32,139].
The principal components method is an alternative to those analyzing the correlations between the explanatory variables in the forecasting process. It not only allows the removal of variables that are overly correlated with each other, but also the acquisition of uncorrelated variables that are responsible for part of the variability in groups of variables or even for the variability in entire groups of variables [140]. The application of the method creates new variables, which are linear combinations of the original variables, and the following components capture as much information contained in the original data as possible. The disadvantage of the method is the difficulty in interpreting the meaning of principal components [140].

2.3. Big Data

Big Data is a term that describes, on a very general level, exceptionally large data sets. These collections are characterized by a diversified structure of high complexity. The main difficulties are data storage, real-time analysis, and data visualization and analysis results [141,142]. The process of examining massive amounts of data to reveal hidden patterns and secret correlations is called Big Data analysis. In the 1990s and the first decade of the 21st century, Big Data analysis was understood as Data Mining. Big Data sets are characterized by: high volume (Volume) [98,141,143,144], high growth rate (Velocity) [98,141,143,144], reliability and accuracy (Veracity) [141,142], great variety (Variety) [98,144], and value for decision making processes (Value) [98,141,144,145].
The use of Big Data analysis for the needs of data sets containing electrical measurements, including the load size of power systems, includes practical applications, e.g., techniques, i.e., correlation analysis and machine learning techniques (including deep learning: Multilevel Deep Learning [146], Pooling Deep Recurrent Neural Network [147], Convolutional Neural Network Based Bagging Learning Approach [148], TensorFlow Deep Learning Framework and Clustering-regression [149], Long Short—Term Memory Neural Network [150], using Scikit-Learn and TensorFlow [151], with the Keras library [152], Deep Neural Networks [43,153], and introducing Multilevel Deep Learning Methods for Big Data Analysis [146] and databases [114]). Processing of electrical measurement data includes distributed processing (data storage and processing—Distributed Computing), memory processing (data reading and processing—Memory Computing) and stream processing (real-time data processing—Stream Processing) [141,154].
The use of Big Data techniques in the energy system in the energy sector [155,156,157] and in the field of Smart Grids [1,80,154,158] includes the use of RBF Artificial Neural Networks [159] using a Convolutional Neural Network Based Bagging Learning Approach [148]. This also encompasses compatibility of aid for technical measures concerning the integration of the generating sources [160], with special regard to renewable sources [161,162] and in creating backup data sets that can be used in situations of information and communication disruptions [163].
The use of sets, techniques, and processes concerning Big Data for the power industry is inextricably linked with the security of the stored data. The security of this type of data can be increased through its location dispersion (e.g., SCOOP system) [144].
Data streams supplying Big Data sets in transmission and distribution power systems come from [164,165,166]: Supervisory Control And Data Acquisition (SCADA) systems [167], phasor measurement systems in Wide Area Management System (WAMS) technology [168], Intelligent Electronic Devices (IEDs), network asset management systems, conventional and smart meters [147,169,170,171], and information exchange systems with electricity market participants, from seismic and meteorological institutes, Global Positioning System (GPS) systems, and Geographic Information System (GIS) systems. The practical method of the similarity of days [172,173,174,175,176] allows the quality of forecasting power demand to be below 3.00% per day and the efficiency achieved by the Polish Transmission System Operator (PSE S.A.) to be approx. 1.00%. Similar days are selected based on the most recent demand factor forecasts in the first step. In the second step, the weighted average is calculated for each hour of the day, considering the historical values. In the classical approach, there is a slight variation in the values of individual weights. Due to weighting of the most similar days, it is possible to obtain minimum, maximum, and average errors for the entire day below 2% [176]. The method of self-adaptive weighing is successfully used in forecasting the demand for electric power in microgrids. Compared to the standard methods of dynamic demand profiles, multiple regression, and Artificial Neural Networks, it almost doubles forecasting effectiveness (approx. 3.5%) [177]. A similar level of effectiveness (3.99%) using the multiple regression method for the power system shows that despite the longer computation time (for a seven-day horizon), its classical version [178], using as input data (explanatory variables) forecasts of weather parameters, gives a similar quality. The use of Artificial Neural Networks in short-term forecasting of electrical power demand in power systems does not always give exceptionally effective forecasting results compared to other methods. Artificial Neural Networks require significant research experience, and the results, even using efficient network learning methods [147], rarely give effectiveness below 1.00% per day. Often, advanced Artificial Neural Networks provide forecasting efficiency expressed by the values of Mean Average Percentage Error (MAPE) from approx. 3.00% to even approx. 13.00% (in the 20-day horizon) [5]. The knowledge of electrical power quality parameters is one of the key elements of entities operating in the electricity market [179]. Cyclical measurements of these parameters (including the assessment of the condition of electrical apparatus and devices [180]), and their transmission and collection, in addition to the conducted analyses, may affect the medium-term planning of outages of individual elements of the transmission network and, thus, indirectly, short-term forecasting of power demand.

3. The State of Research in Short-Term Power Demand Forecasting for Power Systems Using Autoregressive and Non-Autoregressive Methods and Models

The study (Figure 1) was planned in such a way as to answer the question of whether the use of autoregressive methods in short-term forecasting of electricity demand in power systems can be even more effective and, at the same time, inexpensive and quick to implement. In order to answer this question, scientific articles presenting the effectiveness of autoregressive forecasting models determined by the MAPE were analyzed. The result of the review is Table 1 and a ranking of forecasting models (Table 2 and Table 3), and the Top 10 collection of the ten most effective forecasting models. As a result of the review and development of the ranking of forecasting models, it was confirmed that the use of autoregressive models may support the transmission system operator to achieve better forecasting efficiency.
The literature review (Table 1) included 47 unique items and titles, several dozen forecasting methods, and 264 forecasting models (Table 1). Scientific papers were published in the period from 1997 and concerned short-term forecasting of power demand. The source data used by the authors of the analyzed publications, constituting the input for the forecasting models, covered the period from 1998 to 2014. Diverse and international teams of authors conducted their research based on data on the functioning of power systems in 25 countries located on four continents—in the countries of the Near and the Far East, Western Europe (including the British Isles), Central Europe (including Poland), North America (USA), and Australia. The publications indicated were compiled by 44 different authors’ teams and published in 23 publishing houses. The analysis concerning the nomenclature of forecasting models covers a set of 185 unique items. Diversifying the observed relationships in individual forecasting models results in identifying 197 unique abbreviations assigned to forecasting models. The MAPE(ea) in Table 1 means that the accuracy results are measured in ex ante mode.
All the reviewed references describe the effectiveness of the presented forecasting models, in terms of the MAPE measure, to assess the accuracy of the forecasts. To analyze the collected forecasting results, 27 unique names of MAPE errors were distinguished for this analysis, reflecting the forecasting models used in the analysis. Some of the forecast results described by the MAPE index, contained in selected publications, are presented from the lowest value (MAPE min) to the highest value (MAPE max). In contrast, the remaining part of the results is described by one value.
The analysis of monovalent results was decomposed into minimum and maximum values to standardize the dominant approach used in selected publications. The lowest values of MAPE min are recorded in the range from 0.01% to 21.18%, while in the MAPE max category, the corresponding range of variability in the MAPE ranges from 0.01% to 33.45%. The MAPE min category includes 196 unique items from a set of 264 models, while the MAPE max category includes 212 unique items from the same set.
Further analysis of the results of the effectiveness of the forecasts obtained, described by the forecasting quality measure using the MAPE, concerns the MAPE category, min. A set of the ten smallest results expressed as percentages was selected in this category (Figure 2). This collection was called Top 10. The smallest values of MAPE errors min, in ascending order, in the Top 10 set (Figure 2) are obtained for the following models: Data Envelopment Analysis (DEA), Fuzzy Regression (FR), General Regression Model (GRM), Genetic Algorithm (GA), Adaptive Neuro Fuzzy Inference System (ANFIS [181,182]), Artificial Neural Network (ANN), Full General Regression Model (FGRM), Wavelet Artificial Neural Network (WANN), Artificial Neural Network (ANN), and Fuzzy Logic (FL). The values of MAPE min were: 0.01%; 0.08%; 0.10%; 0.14%; 0.15%; 0.16%; 0.20%; 0.27%; 0.28%; and 0.29%. The summary of the abbreviations used for the forecasting methods and models in the Top 10 set is as follows: DEA; FR; GRM; GA; ANFIS; ANN; FGRM; WANN; ANN; and FL.
Only analytical studies on the GRM forecasting model in the Top 10 set are performed ex ante (ea). In the case of this model, the efficiency obtained in the third position should be considered very high. The GRM model uses information about the shaping of the ambient temperature as an input variable. The second model that uses the input variables is the FGRM model, which considers both the variability in the ambient temperature and the wind speed. The FGRM model ranks seventh in the Top 10 ranking in the MAPE category, min.
The forecasting effectiveness described by the lowest value of the MAPE min has an ambiguous effect on high forecasting efficiency. The power systems subject to forecast analysis in the Top 10 list are (in ascending order) the systems of Iran (two items), USA (one item), Iran (three items), USA (one item), and Australia (three items).
The length of the analyzed period significantly affects the quality of forecasting obtained. Along with the extension of the analysis period, including the natural impact of non-working days and holidays, both cyclical and non-cyclical, there is a decline in the effectiveness of the obtained forecasts of the load on power systems. The full forecasting model ranking is presented in Table 2 and Table 3, where the column Model No. represents the model number from Table 1 (the last column on the right), and the column Ranking shows the position in the model ranking (1 equals the first position and 264 equals the last position). Table 2 consists of the models from Table 1 from 1 to 132 (in four pairs of Ranking and Model Number), and Table 3 shows the same scheme for the models from 133 to 264. Table 2 and Table 3 present four sets of Ranking and Model Number. Articles [183,184,185] from 2019 to 2021 indicate that analysis and research are being continued, including with the use of some of the analyzed methods.

4. Conclusions

The 47 publications describing 264 models published from 1997 to 2018 were analyzed in detail by applying methods that use explanatory variables to broaden the background of analyses. Some relevant publications from 2019 to 2021 were also included to determine if autoregressive methods are still of interest. The results of the review confirm the significant potential of the autoregressive approach to power demand forecasting. The analyzed methods enable very high accuracy to be achieved in short-term forecasting with the resolution of one hour (accuracy measured in terms of MAPE is below 1%). The methods whose effectiveness were classified in the top ten sets are Fuzzy Logic (LR), Artificial Neural Network (ANN), Wavelet Artificial Neural Network (WANN), Full General Regression Model (FGRM), Artificial Neural Network (ANN), Adaptive Neurofuse Inference System (ANFIS), Genetic Algorithm (GA), General Regression Model (GRM), Fuzzy Regression (FR), and Data Envelope Analysis (DEA). These methods allowed them to achieve MAPE-determined values of: 0.29%; 0.28%; 0.27%; 0.20%; 0.16%; 0.15%; 0.14%; 0.10%; 0.08%; and 0.01%. All of the Top 10 models achieved high accuracy; however, the DEA model reached the accuracy of 0.01% MAPE. Models No. 257 (FGRM) and No. 256 (GRM) of the Top 10 set use the explanatory variables, and the other eight models were autoregressive (models No.: 215—FL, 214—ANN, 213—WANN, 140—ANN, 141—ANFIS, 138—GA, 139—FR, and 142—DEA). This shows the potential of the autoregressive prediction approach used in the models for short-term power demand forecasting in power systems.

5. Critical Discussion, Major Findings and Future Scope of Research

The results of the review show that the use of short-term forecasting of electric power demand with hourly resolution enables efficiency of below 1% to be achieved. It should be borne in mind that such effectiveness should apply to the entire calendar year. In the analyzed collection of 47 articles from all over the world, the analysis period ranges from several months to several years, which indicates that the research covers significant periods of time, and the analyzed models are stable and resistant to changes in external conditions (economic and climatic conditions). The group of the most effective prognostic models includes models using artificial intelligence techniques (e.g., Artificial Neural Networks, Fuzzy Logic, and Genetic Algorithms). The effective methods also include classic forecasting methods (e.g., ARIMA, Multiple Regression, Exponential Smoothing) and methods from the Data Mining group (e.g., Support Vector Machines, Nearest Neighbors, Random Forest).
The article confirms the authors’ thesis about the enormous potential inherent in the use of the autoregressive approach for short-term forecasting of electricity demand. The results of the review (the prepared ranking of prognostic models and the knowledge from the analyzed articles) constitute an excellent starting point for further tests and pave the way for future research in this area.
The future research of the authors will focus on the first step of testing the prognostic models from the Top 10 set. The tests will take into account both the achieved effectiveness and the necessary financial costs and time consumption of the process. In the next step, the most effective prognostic methods selected in the first step will be tested, including individual testing in off-line mode. In the third step of further research, prognostic model committees will be established. The developed committees will assign weights to the participation of individual models (step 1) and test the suitability of individual models for forecasting individual hours of the day or periods of the day (step 2). The MAPE selected by the authors for the review analysis, despite the undoubted advantage of being able to be used to easily compare the effectiveness between forecasting models, has a tendency to average forecasts. Therefore, in future studies, the authors will also use other measures to assess the quality of forecasts, such as Mean Absolute Error, Mean Absolute Scaled Error, and Root Mean Square Error, and others as needed. The usefulness of the tested forecasting models will be assessed, taking into account the seasonality, periodicity, and ranges of hours during the day. The developed review encompasses an excellent range of forecasting methods and models that can be used at any time, and the usefulness of each of them may prove invaluable from the point of view of the needs of the Polish Transmission System Operator.

Author Contributions

Conceptualization, R.C., J.K. and M.S.; methodology, R.C.; data curation and data analysis, R.C.; supervision, J.K.; resources, M.S.; writing—original draft preparation, R.C., J.K. and M.S.; writing—review and editing, J.K. and M.S.; project administration, J.K.; funding acquisition, J.K. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data are available within this document.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Abbreviations

The following abbreviations are used in this manuscript:
AGGenetic Algorithm (GA)
ANFISAdaptive Neuro Fuzzy Inference System (ANFIS)
ANNArtificial Neural Network (ANN)
ARIMAAutoregressive Integrated Moving Average
C&RTClassification And Regression Trees
CHAIDChi-Square Automatic Interaction Detection
DEAData Envelopment Analysis
eaex ante
GISGeographic Information System
GPSGlobal Positioning System
IEDIntelligent Electronic Device
FLFuzzy Logic
MAPEMean Average Percentage Error
MARSplinesMultivariate Adaptive Regression Splines
MLPMultilayer Perceptron
GRMGeneral Regression Model
FGRMFull General Regression Model
NPSNational Power System
PSE S.A.Polskie Sieci Elektroenergetyczne S.A. (The Transmission System Operator in Poland)
RBFRadial Basis Function
FRFuzzy Regression
SARIMAXSeasonal Auto-Regressive Integrated Moving Average with eXogenous Factors
SCADASupervisory Control and Data Acquisition
WANNWavelet Artificial Neural Network (AWNN)
SVMSupport Vector Machines
WAMSWide Area Management System

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Figure 1. The design of the survey.
Figure 1. The design of the survey.
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Figure 2. The effectiveness of forecasting models in the Top 10 set from a group of 264 models.
Figure 2. The effectiveness of forecasting models in the Top 10 set from a group of 264 models.
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Table
Table 1. The publications’ preview results in short-term power demand forecasting methods and models used for power systems.
Table 1. The publications’ preview results in short-term power demand forecasting methods and models used for power systems.
No.Authors/Title/Publishing HouseYearAnalysis ScopeCountryMethod, ModelEffectivenessModel No.
-Years--Error, %-
1.Al-Fuhaid A.S. et al.
Neuro-Short-Term Load Forecast of the Power System
in Kuwait
Elsevier (21:215-219) [18]		19971994KuwaitANN(ea)—Artificial neural networkMAPE(ea)1.844.841
2.Almeshaiei E., Soltan H.
A Methodology for Electric Power Load Forecasting
Alexandria Engineering Journal (50) [19]		20112006–2008KuwaitMA(ea7,30)—Moving Average (7, 30)MAPE(ea)3.842
3.Al-Shobaki S., Mohsen M.
Modeling and Forecasting of Electrical Power Demands
for Capacity Planning
Elsevier Energy Conversion and Management (49) [20]		20082002–2007JordanARIMA(ea)MAPE(ea)5.253
4.Badran S.M., Abouelatta O.B.
Forecasting Electrical Load using ANN Combined with Multiple Regression Method
The Research Bulletin of Jordan ACM II(II) [21]		20131988–2006Saudi ArabiaMR—Multiple RegressionMAPE11.5814.354
ANN—Multiple RegressionMAPE2.448.045
5.Brodowski S. et al.
A Hybrid System for Forecasting 24-h Power Load Profile
for Polish Electric Grid
Elsevier B.V. Applied Soft Computing (58) [22] 		20172013, 2015Poland (NPS)HA + MR—Hierarchical Approximator + Multiple RegressionMAPE1.082.266
6.Buitrago J., Asfour S.
Short-Term Forecasting of Electric Loads Using Nonlinear Autoregressive Artificial Neural Networks with Exogenous Vector Inputs
Energies 10(40) [23]		20172005–2015USA
(New England)		ANN—Artificial Neural NetworkMAPE0.857
7.Ceperic E., Ceperic V.
A Strategy for Short-Term Load Forecasting by Support Vector Regression Machines
IEEE Transactions on Power Systems (1) [24]		20132006USAANN—Artificial Neural NetworkMAPE1.503.728
SDBWNN—Similar Day—Based Wavelet Neural NetworkMAPE1.262.709
SASVR—Seasonality—Adjusted, Support Vector RegressionMAPE0.931.8610
8.Chahkoutahi F., Khashei M.
A Seasonal Direct Optimal Hybrid Model of Computational Intelligence and Soft Computing Techniques for Electricity Load Forecasting
Energy (140) [25]		20172011.05.02–2011.07.03AustraliaARIMAMAPE0.761.0711
ANN(MLP)—Artificial Neural Network
(Multilayer Perceptron)		MAPE0.721.2312
ANFIS—Adaptive Neuro Fuzzy Inference SystemMAPE0.830.9513
DOPH—Direct Optimum Parallel HybridMAPE0.580.7114
9.Chapagain K., Kittipiyakul S.
Short-Term Electricity Load Forecasting Model and Bayesian Estimation for Thailand Data
MATEC Web of Conferences (55) [26]		20162013–2015ThailandMR—Multiple RegressionMAPE1.7533.4515
MR(Gibbs)—Multiple Regression (Gibbs Sampling)MAPE0.8523.0616
10.Chen H. et al.
ANN-Based Short-Term Load Forecasting in Electricity Markets
University of Waterloo, Department of Electrical & Computer Engineering [27]		20011999CanadaANN—Artificial Neural NetworkMAPE0.483.0017
11.Chheepa T.K., Manglani T.
A Critical Review on Employed Techniques for Short Term Load Forecasting
IRJET 04(06) [28]		20171996–1997,
2000		IranARIMAMAPE1.481.9918
12.Clements A.A. et al.
Forecasting Day-Ahead Electricity Load Using a Multiple Equation Time Series Approach
NCER Working Paper Series 103(5) [29]		20151999.07.12–2013.11.27AustraliaARIMAMAPE1.362.8919
13.Czapaj R.
Typowanie zmiennych objaśniających przy wykorzystaniu zautomatyzowanych metod statystycznych jako sposób optymalizacji wyboru metody estymacji szczytowego dobowego obciążenia KSE
Przegląd Elektrotechniczny 4(93) [30]		20162010–2014Poland (NPS)MARSplinesMAPE1.866.9920
C&RT—Classification and Regression TreesMAPE2.577.1821
C&RT—Classification and Regression TreesMAPE2.566.7722
Chi2—Automatic interaction detector using Chi2MAPE4.067.3323
CHAID—Chi2 Automatic Interaction DetectorMAPE3.699.4024
14.Czapaj R., Kamiński J., Benalcazar P.
Dobór zmiennych objaśniających z wykorzystaniem metody MARSplines
Politechnika Częstochowska, XIV Konferencja PE [31]		20182009–2014Poland (NPS)MARSplinesMAPE1.866.9925
15.Czapaj R., Kamiński J., Benalcazar P.
Prognozowanie krótkoterminowe z wykorzystaniem metody MARSplines
Politechnika Częstochowska, XIV Konferencja PE [32]		20182009–2014Poland (NPS)MARSplinesMAPE3.366.0426
MARSplines(ea)MAPE(ea)6.5727
16.Dąsal K.
Dobór zmiennych wejściowych do Modelu Rozkładu Kanonicznego
Politechnika Częstochowska, VI Konferencja PE [33]		20021993–1995Poland (NPS)MRK(Mo-Fr)
—Canonical Vector Decomposition Method from Monday till Friday		MAPE(Mo-Fr)0.649.7928
17.Dudek G.
Short-Term Load Forecasting Based on Kernel Conditional Density Estimation
Przegląd Elektrotechniczny 8(86) [34]		20102002–2006Poland (NPS)SFS(5 years)—Sequential Forward Selection MethodsMAPE1.8429
SBS(5 years)—Sequential Backward Selection MethodsMAPE1.7730
NS(5 years)—Nearest NeighborsMAPE1.9431
ANN(5 years)—Artificial Neural NetworkMAPE2.0232
FE(5 years)—Fuzzy EstimatorsMAPE1.7633
1997–2000SFS(4 years)—Sequential Forward Selection MethodsMAPE2.1934
SBS(4 years)—Sequential Backward Selection MethodsMAPE2.0635
NS(4 years)—Nearest NeighborsMAPE2.5536
ANN(4 years)—Artificial Neural NetworkMAPE2.2437
FE(4 years)—Fuzzy EstimatorsMAPE2.1438
18.Dudek G., Janicki M.
Nearest Neighbor Model with Weather Inputs for Pattern-based Electricity Demand Forecasting
Przegląd Elektrotechniczny 3(93) [35]		20172011–2014Poland (NPS)NNWISA(working days)
—Nearest Neighbors with Weather Inputs for Similarity Analysis		MAPE
(working days)		1.551.6739
BelgiumMAPE
(working days)		2.822.8840
New EnglandMAPE
(working days)		2.413.2641
USAMAPE
(working days)		3.434.8242
2011–2014Poland (NPS)NNWISA(weekends)
—Nearest Neighbors with Weather Inputs for Similarity Analysis		MAPE(weekends)1.751.7643
BelgiumMAPE(weekends)3.023.1244
New EnglandMAPE(weekends)2.923.1645
USAMAPE(weekends)4.314.9946
2011–2014Poland (NPS)NNWISA(Holidays)
—Nearest Neighbors with Weather Inputs for Similarity Analysis		MAPE(Holidays)4.3616.1747
BelgiumMAPE(Holidays)4.0512.6148
New EnglandMAPE(Holidays)6.357.0349
USAMAPE(Holidays)6.057.6250
19.Dudek G.
Pattern-Based Local Linear Regression Models for Short-Term Load Forecasting
Elsevier, Electric Power System Research (130) [36]		20162002–2004Poland (NPS)MR(January)—Multiple RegressionMAPE(January)2.3751
SR(January)—Stepwise RegressionMAPE(January)1.5252
RR(January)—Ridge RegressionMAPE(January)1.5953
Lasso(January)—Least Absolute Selection Regression and the Constriction OperatorMAPE(January)1.5154
PCR(January)—Principal Component RegressionMAPE(January)1.3655
PLSR(January)—Partial Least Squares RegressionMAPE(January)1.1856
MR(July)—Multiple RegressionMAPE(July)2.6357
SR(July)—Stepwise RegressionMAPE(July)1.1458
RR(July)—Ridge RegressionMAPE(July)1.2359
Lasso(July)—Least Absolute Selection Regression and the Constriction OperatorMAPE(July)1.0660
PCR(July)—Principal Component RegressionMAP(July)0.9461
PLSR(July)—Partial Least Squares RegressionMAPE(July)1.0062
2002–2004Poland (NPS)PCR—Principal Component RegressionMAPE1.3563
PLSR—Partial Least Squares RegressionMAPE1.3464
ARIMAMAPE1.8265
ES—Exponential SmoothingMAPE1.6666
ANN(MLP)—Artificial Neural Network
(Multilayer Perceptron)		MAPE1.4467
NWE—Nadaraya—Watson EstimatorMAPE1.3038
NM—Naive MethodMAPE3.4339
2007–2009FrancePCR—Principal Component RegressionMAPE1.7170
PLSR—Partial Least Squares RegressionMAPE1.5771
ARIMAMAPE2.3272
ES—Exponential SmoothingMAPE2.1073
ANN(MLP)—Artificial Neural Network
(Multilayer Perceptron)		MAPE1.6474
NWE—Nadaraya—Watson EstimatorMAPE1.6675
NM—Naive MethodMAPE5.0576
2007–2009Great BritainPCR—Principal Component RegressionMAPE1.6077
PLSR—Partial Least Squares RegressionMAPE1.5478
ARIMAMAPE2.0279
ES—Exponential SmoothingMAPE1.8580
ANN(MLP)—Artificial Neural Network
(Multilayer Perceptron)		MAPE1.6581
NWE—Nadaraya—Watson EstimatorMAPE1.5582
NM—Naive MethodMAPE3.5283
2006–2008AustraliaPCR—Principal Component RegressionMAPE3.0084
PLSR—Partial Least Squares RegressionMAPE2.8385
ARIMAMAPE3.6786
ES—Exponential SmoothingMAPE3.5287
ANN(MLP)—Artificial Neural Network
(Multilayer Perceptron)		MAPE2.9288
NWE—Nadaraya–Watson EstimatorMAPE2.8289
NM—Naive MethodMAPE4.8890
20.Dudek G.
Drzewa regresyjne i lasy losowe jako narzędzia predykcji szeregów czasowych z wahaniami sezonowymi
Politechnika Częstochowska [37]		20162002–2004Poland (NPS)RF(January)—Random ForestMAPE(January)1.4291
C&RT(January)—Classification and Regression TreesMAPE(January)1.7092
C&RTR(January)—Fuzzy Classification and Regression TreesMAPE(January)1.6293
ARIMA(January)MAPE(January)2.6494
ES(January)—Exponential SmoothingMAPE(January)2.3595
ANN(January)—Artificial Neural NetworkMAPE(January)1.3296
NM(January)—Naive MethodMAPE(January)6.3797
RF(July)—Random ForestMAPE(July)0.9298
C&RT(July)—Classification and Regression TreesMAPE(July)1.1699
C&RTR(July)—Fuzzy Classification and Regression TreesMAPE(July)1.13100
ARIMA(July)MAPE(July)1.21101
ES(July)—Exponential SmoothingMAPE(July)1.19102
ANN(July)—Artificial Neural NetworkMAPE(July)0.97103
NM(July)—Naive MethodMAPE(July)1.29104
21.Esener I.I., Yuskel T., Kurban M.
Short-Term Load Forecasting Without Meteorological Data Using AI-Based Structures
Turkish Journal of Electrical Engineering & Computer Sciences (23) [38]		20152009TurkeyANN—Artificial Neural NetworkMAPE3.67105
WM+ANN—WM—Wavelet Method + ANN—Artificial Neural NetworkMAPE3.73106
WM+ANN(RBF)—WM—Wavelet Method + ANN—Artificial Neural Network (Radial Basis Functions)MAPE2.89107
ED—Empirical DecompositionMAPE3.52108
2010ANN—Artificial Neural NetworkMAPE3.81109
WM+ANN—WM—Wavelet Method + ANN—Artificial Neural NetworkMAPE4.18110
WM+ANN(RBF)—WM—Wavelet Method + ANN—Artificial Neural Network (Radial Basis Functions)MAPE2.99111
ED—Empirical DecompositionMAPE3.63112
22.Fan S.
Short-Term Load Forecasting Based on a Semi-Parametric Additive Model
IEEE Transactions on Power Systems [39]		20101997–2009
(training)
2009.01.01–2009.01.31 (test)		AustraliaSPAM—Semi-Parametric Additive ModelMAPE1.412.37113
ANN—Artificial Neural NetworkMAPE1.823.90114
SPAM+ANN—Hybrid Model (Semi-Parametric Additive Model + Artificial Neural Network)MAPE1.582.79115
23.Farahat M.A.
Short Term Load Forecasting Using Neural Networks and Particle Swarm Optimization
Journal of Electrical Engineering [40]		20182011.07.01–2011.08.10
(training)
2011.08.11–2011.08.17 (test)		EgyptANN(BP)—Artificial Neural Network (Back Propagation Training)MAPE4.60116
ANN(BP)+PSO –ANN(BP)
—Artificial Neural Network (Back Propagation Training) + PSO—Particle Swarm Optimization		MAPE1.90117
24.Gorwar M.
Short Term Load Forecasting Using Time Series Analysis:
A Case Study for Karnataka, India
ResearchGate, IJESIT Conference [41]		20122011–2012IndiaAR(ea)—AutoregressionMAPE13.03118
ARMA(ea)MAPE11.73119
ARIMA(ea)MAPE6.15120
25.Hassan S., Khosravi A., Jaafar J.
Examining Performance of Aggregation Algorithms for Neural Network-Based Electricity Demand Forecasting
ScienceDirect, Electrical Power and Energy Systems (64) [42]		20152011
(30-min
Intervals)		Malaysia, Australia, PakistanANN(I)—Artificial Neural Network (Integration)MAPE(I 30 min.)7.16121
ANN(TI)—Sztuczna sieć neuronowa (Trimmed Integration)MAPE(I 30 min.)10.13122
ANN(BA)—Artificial Neural Network (Bayesian Averaging)MAPE(I 30 min.)4.34123
NM—Metoda naiwnaMAPE(I 30 min.)6.41124
26.He W.
Deep Neural Network Based Load Forecast
Computer Modelling & New Technologies 18(3) [43]		20142000.02.10–2012.11.30ChinaANN—Artificial Neural NetworkMAPE1.902.08125
27.Hong T., Wang P.
Fuzzy Interaction Regression for Short Term Load Forecasting
University of North Carolina at Charlotte 13(1) [44]		20142005–2007USAFRI(ea)—Fuzzy Regression without InteractionMAPE(ea)14.21126
FRICV(ea)—Fuzzy Regression without Interaction with Categorical VariablesMAPE(ea)5.16127
FRI(ea) + MR—FRI(ea)—Fuzzy Regression without Interaction + MR—Multiple RegressionMAPE(ea)4.63128
FRI(ea)+TV—FRI(ea)—Fuzzy Regression without Interaction + TV—Temperature VariablesMAPE(ea)3.68129
28.Janicki M.
Temperature Correction Method for Pattern Similarity-Based Short-term Electricity Demand Forecasting Models
Przegląd Elektrotechniczny 3(93) [45]		20172013–2014USAIS+TC(USA 2013)—IS—Image Similarities + TC—Temperature Correction
(USA 2013)		MAPE4.50130
USANM(USA 2013)—Naive Method
(USA 2013)		MAPE10.78131
USAIS+TC(USA 2014)—IS—Image Similarities + TC—Temperature Correction
(USA 2014)		MAPE4.86132
USANM(USA 2014)—Naive Method
(USA 2014)		MAPE10.94133
BelgiumIS+TC(BEL 2013)—IS—Image Similarities + TC—Temperature Correction
(Belgium 2013)		MAPE3.80134
BelgiumNM (BEL 2013)—Naive Method
(Belgium 2013)		MAPE8.54135
BelgiumIS+TC(BEL 2014)—IS—Image Similarities + TC—Temperature Correction
(Belgium 2014)		MAPE3.66136
BelgiumNM(BEL 2014)—Naive Method
(Belgium 2014)		MAPE9.47137
29.Kheirkhah A. et al.
Improved Estimation of Electricity Demand Function by Using of Artificial Neural Network, Principal Component Analysis and Data Envelopment Analysis
Elsevier Ltd. Computers & Industrial Engineering (64) [46]		20131992.04.01–2003.02.28Iran,
Ireland
Turkey		GA—Genetic AlgorithmMAPE0.14138
FR—Fuzzy RegressionMAPE0.08139
ANN—Artificial Neural NetworkMAPE0.16140
ANFIS—Adaptive Neuro Fuzzy Inference SystemMAPE0.15141
DEA—Data Envelopment AnalysisMAPE0.01142
30.Kolcun M., Holka L.
Daily Load Diagram Prediction of Eastern Slovakia
Politechnika Częstochowska, VI Konferencja PE [47]		20021997–1998SlovakiaANN(Koh)—Kohonen’s Artificial Neural NetworkMAPE3.50143
31.Lin Y.
An Ensemble Model Based on Machine Learning Methods and Data Preprocessing for Short-Term Electric Load Forecasting
Energies 10(1186) [48]		20172010.08.01–2011.07.31AustraliaEML—Extreme Machine LearningMAPE0.83144
EMLDE—Extreme Machine Learning (optimized by) Differential EvolutionMAPE0.77145
ARIMAMAPE0.73146
WTWTMABC—Wavelet Transform—
Wavelet Transform—Modified Artificial Bee Colony—Extreme Machine Learning		MAPE0.59147
EMDDEEML—Empirical Mode Decomposition—Differential Evolution
– Extreme Machine Learning		MAPE0.39148
VMD—Variational Mode DecompositionMAPE0.30149
32.Liu N., Babushkin V., Afshari A.
Short-Term Forecasting of Temperature Driven Electricity Load Using Time Series and Neural Network Model
Journal of Clean Energy Technologies 2(4) [49]		20142010.01.01–2011.06.30United Arab EmiratesSARIMAXMAPE1.58150
ANN—Artificial Neural NetworkMAPE2.29151
33.Magnano L., Boland J.W.
Generation of Synthetic Sequences of Electricity Demand: Application in South Australia
Elsevier Ltd. Energy (32) [50]		20062000–2001
(Summer Time)		AustraliaARMA(Summer Time)MAPE
(Summer Time)		2.40152
34.Nadtoka I.I., Al-Zihery B.M.
Mathematical Modelling and Short-Term Forecasting
of Electricity Consumption of the Power System, with Due Account of Air Temperature and Natural Illumination, Based on Support Vector machine and Particle Swarm
Elsevier Ltd. Procedia Engineering (129) [51]		20152009–2012IraqSVM+PSO—SVM
– Support Vector Machines + PSO
– Particle Swarm Optimization
(including UV)		2011.05.11.MAPE(UV; May 2011)2.65153
2011.08.31.MAPE(UV; August 2011)1.23154
2011.11.30.MAPE(UV; November 2011)2.13155
2012.01.26.MAPE(UV; January 2012)1.73156
SVM+PSO—SVM
– Support Vector Machines + PSO
– Particle Swarm Optimization
(including temperature)		2011.05.11.MAPE(Temp.;
May 2011)		2.60157
2011.08.31.MAPE(Temp.;
August 2011)		1.37158
2011.11.30.MAPE(Temp.;
November 2011)		1.94159
2012.01.26.MAPE(Temp.;
January 2012)		1.90160
SVM+PSO—SVM
– Support Vector Machines + PSO
– Particle Swarm Optimization
(including UV & Temperature)		2011.05.11.MAPE(UV; Temp.; May 2011)2.26161
2011.08.31.MAPE(UV; Temp.; August 2011)1.41162
2011.11.30.MAPE(UV; Temp.; November 2011)1.61163
2012.01.26.MAPE(UV; Temp.; January 2012)1.58164
35.Narayan A.
Long Short Term Memory Networks for Short-Term Electric Load Forecasting
IEEE International Conference on Systems, Man, and Cybernetics [52]		20172006–2016CanadaANN(January)—Artificial Neural NetworkMAPE (January)4.60165
ARIMA(May)MAPE (May)5.70166
ANN-LSTM-RNN(September)—
Long—Short—Term Memories—Recurrent Neural Network		MAPE (September)4.40167
ANN(sty.)—Artificial Neural NetworkMAPE (January)6.30168
ARIMA(May)MAPE (May)8.20169
ANN—LSTM—RNN(September)—
Long—Short—Term Memories—Recurrent Neural Network		MAPE (September)5.90170
ANN(January)—Sztuczna sieć neuronowaMAPE (January)3.80171
ARIMA(May)MAPE (May)3.90172
ANN-LSTM-RNN(September)—
Long—Short—Term Memories—Recurrent Neural Network		MAPE (September)3.80173
36.Nowicka-Zagrajek J., Weron R.
Modeling Electricity Loads in California: ARMA Models with Hyperbolic Noise
Hugo Steinhaus Center Wrocław University of Technology, KBN [53]		20021999.01.01–2000.12.31USAARMA(1,6) (January 1.—February 28.)MAPE1.66174
ARMA Adaptive (January 3.—February 28.)MAPE1.66175
ARMA(1,6) (January 1.—February 28.)MAPE1.24176
ARMA Adaptive (January 3.—February 28.)MAPE1.23177
37.Nowotarski J. et al.
Improving Short Term Load Forecast Accuracy via Combining Sister Forecasts
Hugo Steinhaus Center Wrocław University of Technology, University of North Carolina at Charlotte [54]		20152007.01.01–2011.12.31USASA—Simple Averaging(ea)MAPE(ea)2.102.82178
AT(PU—ea) (Average Trimming)MAPE(ea)2.102.82179
WA(UW—ea) (Winsor’s Averaging)MAPE(ea)2.102.83180
OLS(MNKea) (Ordinary Least Squares)MAPE(ea)2.142.82181
RMAD(ea)
(Regression of the Minimum Absolute Deviation)		MAPE(ea)2.142.83182
LSLPW(ea) (Least Squares Limited
—Positive Weights)		MAPE(ea)2.122.81183
LSL(ea) (Least Squares Limited)MAPE(ea)2.112.83184
IRMSEA(ea) (IRMSE Averaging)MAPE(ea)2.102.82185
BI—C(ea) (The Best Individual Calibration Window)MAPE(ea)2.252.93186
SM—Sister Model 1(ea)MAPE(ea)2.293.09187
SM—Sister Model 2(ea)MAPE(ea)2.243.15188
SM—Sister Model 3(ea)MAPE(ea)2.343.01189
SM—Sister Model 4(ea)MAPE(ea)2.323.17190
SM—Sister Model 5(ea)MAPE(ea)2.283.11191
SM—Sister Model 6(ea)MAPE(ea)2.303.18192
SM—Sister Model 7(ea)MAPE(ea)2.373.07193
SM—Sister Model 8(ea)MAPE(ea)2.313.21194
38.Hsiao-Ten P.
Forecast of Electricity Consumption and Economic Growth in Taiwan by State Space Modeling
Elsevier Ltd. Energy (34) [55]		20092002–2007TaiwanECSTSP
—Error—Correction State Space Model		2002–2007MAPE3.90195
2003–2007MAPE2.57196
2004–2007MAPE2.38197
2005–2007MAPE1.52198
2006–2007MAPE2.57199
2007MAPE2.04200
STSP
—State Space Model		2002–2007MAPE4.04201
2003–2007MAPE2.62202
2004–2007MAPE2.43203
2005–2007MAPE1.75204
2006–2007MAPE2.34205
2007MAPE2.39206
SARIMA2002–2007MAPE5.32207
2003–2007MAPE3.79208
2004–2007MAPE3.01209
2005–2007MAPE2.87210
2006–2007MAPE2.18211
2007MAPE1.20212
39.Rana M, Koprinska I.
Forecasting Electricity Load with Advanced Wavelet Neural Networks
Elsevier B.V. Neurocomputing (182) [56]		20162006–2007AustraliaWANN(F—Aus.)—Wavelet Artificial Neural NetworkMAPE0.27213
AustraliaANN(Aus.)—Artificial Neural NetworkMAPE0.28214
AustraliaFL(Aus.)—Fuzzy LogicMAPE0.29215
AustraliaMTR(Aus.)—Model Tree RulesMAPE0.35216
AustraliaESDS(n-1; Aus.)—Exponential Smoothing—Daily SeasonalityMAPE0.30217
AustraliaESWS(n -7; Aus.)—Exponential Smoothing—Weekly SeasonalityMAPE0.32218
AustraliaESDWS(n-1 i n -7; Aus.)—Exponential Smoothing—Daily and Weekly SeasonalityMAPE0.30219
AustraliaARIMA(n-1; Aus.) DailyMAPE0.30220
AustraliaARIMA(n -7; Aus.) WeeklyMAPE0.32221
AustraliaARIMA(n-1 i n -7; Aus.)
Daily & Weekly		MAPE0.30222
AustraliaIM(Aus.)—Industrial ModelMAPE0.31223
AustraliaNAM(Aus.)—Naive Averaged MethodMAPE13.48224
AustraliaNDM(Aus.)—Naive Delayed MethodMAPE0.47225
AustraliaNM(n-1; Aus.)—Naive Method (Previous Day)MAPE5.05226
AustraliaNM(n -7; Aus.)—Naive Method
(Previous Week)		MAPE4.94227
2010–2011SpainANN(F—Esp)—Wavelet Artificial Neural NetworkMAPE1.72228
SpainANN(Esp)—Artificial Neural NetworkMAPE2.12229
SpainFL(Esp)—Fuzzy LogicMAPE2.25230
SpainMTR(Esp)—Model Tree RulesMAPE2.24231
SpainESDS(n-1; Esp)—Exponential Smoothing—Daily SeasonalityMAPE2.54232
SpainESWS(n -7; Esp)—Exponential Smoothing—Weekly SeasonalityMAPE2.01233
SpainESDWS(n-1 i n -7; Esp)—Exponential Smoothing—Daily and Weekly SeasonalityMAPE1.95234
SpainARIMA(n-1; Esp) Daily SeasonalityMAPE2.45235
SpainARIMA(n -7; Esp) Weekly SeasonalityMAPE2.00236
SpainARIMA(n-1 i n -7; Esp) Daily & Weekly SeasonalityMAPE1.89237
SpainIM(Esp)—Industrial ModelMAPE0.31238
SpainNAM(Esp)—Naive Averaged MethodMAPE21.18239
SpainNDM(Esp)—Naive Delayed MethodMAPE5.05240
SpainNMPD(n-1; Esp)—Naïve Method (Previous Day)MAPE9.45241
SpainNMPW(D-7; Esp)—Naive Method (Previous Week)MAPE7.42242
40.Siwek K., Osowski S.
Prognozowanie obciążeń 24-godzinnych w systemie elektroenergetycznym z użyciem zespołu sieci neuronowych
Przegląd Elektrotechniczny 8(85) [57]		20092006–2008Poland (NPS)ANN(MLP)—Artificial Neural Network
(Multilayer Perceptron)		MAPE2.07243
ANN(SVM)—Artificial Neural Network
(Support Vector Machines)		MAPE2.24244
ANN(Elman)—Artificial Neural Network (Elman)MAPE2.26245
ANN(Koh)—Kohonen’s Artificial Neural NetworkMAPE2.37246
ANN(MLPZ1)—Artificial Neural Network
(Committee—Multilayer Perceptron 1)		MAPE1.48247
ANN(SVMZ)—Artificial Neural Network (Committee—Support Vector Machines)MAPE1.35248
ANN(BSSZ)—Artificial Neural Network (Committee—BSS)MAPE1.71249
41.Selivan R.A., Rajagopal R.
A Model For The Effect of Aggregation on Short Term Load Forecasting
IEEE, Stanford University [58]		2014-USAARMAMAPE2.00250
SVR (Support Vector Regression)MAPE4.00251
SSN(FF)—Artificial Neural Network
(Fast Forward Training)		MAPE2.40252
42.Sousa J.C., Neves LP., Jorge H.M.
Assessing the Relevance of Load Profiling Information in Electrical Load Forecasting Based on Neural Network Models
Elsevier Ltd. Electrical Power and Energy Systems (40) [59]		20122006.12.15–2009.11.30PortugalSSN(OK)—Artificial Neural Network
(Municipal Users)		MAPE6.1322.39253
ANN(TSDSO)—Artificial Neural Network
(Transformer Station of a Distribution System Operator)		MAPE5.145.35254
43.Wang P., Liu B., Hong T.
Electric Load Forecasting with Recency Effect: A Big Data Approach
Hugo Steinhaus Center Wrocław University of Technology [60]		20152007USAREM—Recent Effect Method
(Forecasts for each day with a year in advance)		MAPE4.274.38255
44.Wang Y., Bielecki J.M.
Acclimation and the Response of Hourly Electricity Loads
to Meteorological Variables
Elsevier Ltd. Energy (142) [61]		20181999.07.28–2007.12.31.
(Calibration Set)		USAGRM(Temp.)—General Regression Model (Temperature)MAPE
(Temp.)		~0.10~4.10256
FGRM(ea; Temperature; Wind)—Full General Regression Model (hourly delays of thermosensitivity, binary variables of historical temperatures in months, wind speed)MAPE
(ea; Temp.; Wind)		~0.20~4.30257
2008.01.01–2014.12.31.2SGRM(Temperature; Wind; Humidity)—2-Step General Regression Model
(1.—Fit to the full model; 2.—Adjustment to the model
of the influence of humidity on demand)		MAPE
(Temp.; Wind; Humid.)		1.002.00258
45.Wyrozumski T.
Prognozowanie neuronowe w energetyce
Politechnika Lubelska, Konferencja REE [62]		2005-PolandANN(ea)—Artificial Neural NetworkMAPE
(ea)		1.314.87259
46.Yang J.
Power System Short-term Load Forecasting
TU Darmstadt, Doctoral Thesis [63]		20062002ChinaC&RT—Classification and Regression TreesMAPE2.6311.64260
ANN—Artificial Neural NetworkMAPE1.514.13261
SVM—Support Vector MachinesMAPE1.513.87262
47.Yu X., Ji H.
A PSO-SVM-Based 24 h Power Load Forecasting Model
MATEC Web of Conferences (25) [64]		20152014ChinaANN(BP)—Artificial Neural Network (Back Propagation Training)MAPE3.284.13263
SVM+PSO—SVM—Support Vector Machines + PSO—Particle Swarm OptimizationMAPE2.582.68264
Table
Table 2. Forecasting model ranking for the position from 1 to 132.
Table 2. Forecasting model ranking for the position from 1 to 132.
Ranking
(1–33)		Model No.Ranking
(34–66)		Model No.Ranking
(67–99)		Model No.Ranking
(100–132)		Model No.
11423416679110043
213935986867101204
32563610691810233
413837617024710330
51413810371810465
614039627254105114
725740258732611061
821341607426210729
9214426755210880
10215431007619810920
111494458777811025
1221745997839111237
1321946567982112117
14220471028071113125
152224821281115114160
16223491018215011531
17238505983164116159
18218511548453117234
19221521778577118236
202165317686163119250
211485498793120233
2222555104887412132
23175668898112279
2414572599066123200
251475896917512435
2628596492174125243
271260639317512673
28146612489492127178
291162199570128179
30145635596249129180
31136415897228130185
321446511398156131184
337661629915132183
Table
Table 3. Forecasting model ranking for the position from 133 to 264.
Table 3. Forecasting model ranking for the position from 133 to 264.
Ranking
(133–165)		Model No.Ranking
(166–198)		Model No.Ranking
(199–231)		Model No.Ranking
(232–264)		Model No.
13322916620319987232227
134155167520010823376
13538168235201112234226
136181169232202136235240
1371821703620386236254
13821117122204105237127
13934172212051292383
1403717319620624239207
141188174199207106240166
142231175264208208241170
14324417615720913424250
144186177202210171243253
14523017857211173244120
146161179260212109245168
14724518094213224649
14819118115321417224797
14915118240215195248124
1501871838921625124927
15119218485217201250121
15219418521021848251242
1537218610721923252169
15419018745220110253135
15518918888221255254241
15620518911122246255137
1579519084223123256122
1585119120922447257131
15919319244225167258133
1602461932632261302594
16119719426227116260119
16220619542228165261118
16315219669229128262224
164252197143230132263126
165411988323190264239
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MDPI and ACS Style

Czapaj, R.; Kamiński, J.; Sołtysik, M. A Review of Auto-Regressive Methods Applications to Short-Term Demand Forecasting in Power Systems. Energies 2022, 15, 6729. https://doi.org/10.3390/en15186729

AMA Style

Czapaj R, Kamiński J, Sołtysik M. A Review of Auto-Regressive Methods Applications to Short-Term Demand Forecasting in Power Systems. Energies. 2022; 15(18):6729. https://doi.org/10.3390/en15186729

Chicago/Turabian Style

Czapaj, Rafał, Jacek Kamiński, and Maciej Sołtysik. 2022. "A Review of Auto-Regressive Methods Applications to Short-Term Demand Forecasting in Power Systems" Energies 15, no. 18: 6729. https://doi.org/10.3390/en15186729

APA Style

Czapaj, R., Kamiński, J., & Sołtysik, M. (2022). A Review of Auto-Regressive Methods Applications to Short-Term Demand Forecasting in Power Systems. Energies, 15(18), 6729. https://doi.org/10.3390/en15186729

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