Multivariate Empirical Mode Decomposition and Recurrence Quantification for the Multiscale, Spatiotemporal Analysis of Electricity Demand—A Case Study of Japan

Abstract

In the new energy systems’ modeling paradigm with high temporal and spatial resolutions, the complexity of renewable resources and demand dynamics is a major obstacle for the scenario analysis of future energy systems and the design of sustainable solutions. Most advanced models are indeed currently restricted by past temporal energy demand data, improper for the analysis of future systems and often insufficient in terms of quantity or spatial resolution. A deeper understanding on energy demand dynamics is thus necessary to improve energy system models and expand their possibilities. The present study introduces noise-assisted multivariate empirical mode decomposition and recurrence quantification analysis for the study of this problematic variable with a case study of Japan’s electricity demand data per region. These tools are adapted to nonlinear, complex systems’ data and are already applied in a wide range of scientific fields including climate studies. The decomposition of electricity demand as well as the detection of irregularities in its dynamics allow to identify relations with temperature variations, demand sector shares, life style and local culture at different temporal scales.

1. Introduction

The optimization of energy systems is one of the great challenges of this century to mitigate climate change. To this end, researchers of the field rely on models to search for efficient alternative designs and study various evolution scenarios [1]. These models are built from our extensive knowledge of the energy supply chains and transformation technologies as their architects, and hence the most studied and accepted solutions so far are focused on the energy systems’ structure, such as sector coupling [2,3,4,5] or spatial interconnections reinforcement [3,6,7]. However, these models remain limited by parameters with high uncertainty due to the complex nature of underlying processes, such as the variations of renewable resources and energy demand with time and space, or the market behavior. Indeed, the multitude of actors distributed in social, environmental, economical and political groups makes energy systems examples of complex systems [8,9]. Such systems are known to evolve in an unpredictable, nonlinear fashion due to the adaptation and self-organization of agents from the bottom-up without centralized control, which makes them particularly difficult to study with classical linear approaches.

The strategy to manage this complexity so far has been to rely on assumptions to aggregate problematic variables at the cost of ignoring the system’s dynamics and diversity, such as the total energy production and demand per country and year, or the energy demand division in industrial, commercial and residential sectors based on social criteria. Recent data with higher resolution, especially on the supply side with weather re-analysis data, have enabled the development of models such as dynamical networks [10,11] or agents models [12,13,14], some allowing to study more complex solutions such as demand-side management [15,16], peer-to-peer energy sharing [17,18], or policy making [19,20]. However, the demand dynamics and its dependence with environmental conditions, local culture and economical situation, or the spatial distribution of consumers from different sectors is still obscure, so modelers have to rely on assumptions to estimate missing data, based, for example, on the prorated disaggregation of global demand or extrapolation from short time averages. Furthermore, scenario analysis is limited, as data are bounded to current energy systems and environmental conditions.

Analysis tools from nonlinear and complexity science could help improve our understanding of these complex parameters’ dynamics from the currently limited data samples in order to more accurately consider them for better modeling, scenario building and long-term energy planning. Nonlinear and complexity science have long benefited from their interdisciplinary dimension to establish these analysis techniques based on data, as well as experimental and numerical platforms from various fields. They are designed to extract features and patterns or detect anomalies and transitions from data containing a large amount of information and/or having underlying nonlinear processes with limited a priori knowledge. A typical example well studied in energy systems is the clustering problem of consumers with similar demand profiles [21,22], which could ultimately replace or complement energy demand sectors in the design process.

Decomposition is used to disaggregate complex signals, often by frequencies, into simpler components to interpret them separately and identify intrinsic relations. It is particularly useful and adequate for meteorological and energy demand time series, as they are signals with dynamical components at multiple scales, and has already been applied as input for machine learning forecasting and clustering models, resulting in improved prediction accuracy [23]. Seasonal decomposition [24,25], Fourier transform [26,27], and wavelet transform [28,29] have so far been the standard approaches for this purpose, but they are affected by non-negligible limitations when applied on complex signals [30]: seasonal decomposition requires the a priori selection of a single scale (or season) of interest through the moving average window length; Fourier transform considers a basis of fixed functions not suitable for the analysis of intermittent or nonstationary data; and wavelet transform relies on the choice of a wavelet. Furthermore, the integration over time results in a loss of information on the temporality of analysis results. Recently, empirical mode decomposition was suggested as an alternative due to its advantages of being data-driven and adaptative, making it suited to nonlinear and nonstationary signals [31,32]. It still, however, suffers from artificial mode mixing or splitting, and from the fact that the number and scale of the resulting intrinsic mode functions (IMFs) depend on the data. The IMFs obtained from multi-channel signals are thus not comparable. Variants of EMD have been developed to mitigate these problems, such as ensemble empirical mode decomposition (EEMD), complete ensemble empirical mode decomposition (CEEMD), and multivariate empirical mode decomposition (MEMD) [33]. The latter is capable of producing mode-aligned IMFs from multi-channels signals and efficiently prevents artificial mode mixing with the addition of noise channels as a decomposition reference (Noise-Assisted MEMD).

Recurrence plots (RPs) and recurrence quantification analysis (RQA) paired with complex network analysis tools are other analysis techniques which have rapidly drawn increasing interest over the past decade and are now widely used to study systems’ dynamical states and transitions, measure synchronization, or evaluate dynamical invariants [34,35]. They have demonstrated their usefulness in the analysis of climate data, revealing hidden periods and transitions in wind time series [36] with seasonal differences in the dynamics impacting its predictability [37], the interdependence of climate data over large periods [38], as well as in power systems stability analysis [39]. These methods have still not been applied to the analysis of energy demand time series, or the intermittent generation from renewable resources with technical considerations, such as power curves and curtailment, to our knowledge.

The present study introduces MEMD and RQA for the analysis of energy demand variations with time and differences due to regions’ characteristics with the case study of electricity demand in Japan. This country is characterized by its variety of environmental and climate conditions, having an impact on the local energy demand [40], as well as by recurrently suffering from catastrophic events, such as earthquakes and typhoons. We demonstrate here the ability of these techniques to accurately capture these features from regional electricity demand time series and use them to discover and interpret hidden demand patterns at different temporal scales that could not be obtained with the traditional statistical approach.

2. Materials and Methods

2.1. Data

We consider the electricity demand provided by the 10 major energy carriers covering the regions, shown in Figure 1 [41]. It is calculated as the sum of the output electricity from each production company’s generators adjusted by the power exchanges with other regions and does not include the self-consumption at power stations or from rooftop solar PV. The data have one hour resolution over the period from 1 April 2016 to 31 October 2020 and are shown in Figure 2. The electricity demand in Hokkaido dropped in September 2018 due the strong earthquake that caused a blackout. Although some differences can be noticed in the demand of each region, the time series appear too complex to analyze in this shape. We describe in the following sections the methodology to decompose them into simpler components.

In order to interpret the various patterns observed at different temporal scales after decomposition, we pair the results with historical temperature data impacting the heat demand, as well as the annual share of electricity demand divided in industrial, commercial, and residential sectors. The temperature data are obtained from the Japan Meteorological Agency Numerical Weather Prediction Meso-Scale Model with 5 km meshes and 1 h resolution [42]. The model provides weather forecasts every 3 h, so the data are organized in series of initial values every three hours filled with forecast values [43]. The spatial average is calculated to obtain the single temperature time series for each region. The electricity demand sectors share are obtained from the energy statistics data provided by the Japan Ministry of Economy, Trade and Industry [44]. Results are summarized in

Table 1. Annual electricity demand shares per sector for each region in 2015.

	Industrial (%)	Commercial (%)	Residential (%)
Hokkaido	18.1	43.4	38.5
Tohoku	31.1	33.8	35.2
Tokyo	24.3	45.2	30.5
Chubu	37.8	32.6	29.7
Hokuriku	35.9	26.8	37.3
Kansai	29.9	39.8	30.3
Chugoku	45.8	27.7	26.6
Shikoku	37.7	30.3	32.1
Kyushu	34.6	34.7	30.7
Okinawa	10.2	54.4	35.4

for the year 2015. These values are mostly unchanged in following years.

2.2. Empirical Mode Decomposition

Empirical mode decomposition (EMD) is a data-driven method to decompose a signal into its components at different time scales called intrinsic mode functions (IMFs). It works as a recursive nonlinear filter, which makes it adapted to nonlinear and nonstationary signals and allows for a precise definition of amplitude and frequency at the highest level of resolution, as it is not based on a temporal integration as the seasonal decomposition, Fourier transform or wavelet transform. The procedure to extract IMFs is described in Algorithm 1. Here, the stopping criterion is a critical parameter, as a too-small number of iterations for each IMF extraction (also called sifting) results in modes with artificial extrema, while a too-large number of iterations causes the smoothing of the modes amplitude. Several possibilities have been suggested for this criterion [45]. Here, we chose the standard stopping criterion specified in [46].

Algorithm 1 Empirical mode decomposition (EMD).

1: Set the initial residue of signal to decompose $x\left(t\right)$ as $r\left(t\right)=x\left(t\right)$ and $i=1$; 2: Identify the local maxima and minima of $r\left(t\right)$; 3: Evaluate the upper and lower envelopes $u\left(t\right)$ and $l\left(t\right)$ by interpolating the local maxima and minima with a cubic spline; 4: Calculate the mean of $u\left(t\right)$ and $l\left(t\right)$ as $a\left(t\right)=\left[u\right(t)+l(t\left)\right]/2$; 5: Let $r\left(t\right)=r\left(t\right)-a\left(t\right)$ and repeat 2 to 4 until a stopping criterion is reached; 6: Extract the ith IMF as $IM{F}_i=r\left(t\right)$; 7: Let $r\left(t\right)=x\left(t\right)-{\sum }_{j=1}^{i}IM{F}_j$; 8: Increment i and repeat 2 to 7 until $r\left(t\right)$ becomes a monotonic function.

Despite its advantages over other decomposition methods based on time integration and convolution, EMD suffers from several limitations, such as mode mixing or boundary distortions caused by the misidentification of end points as the local extrema. Moreover, it is not adapted to multivariate signals, as the IMFs obtained independently on different time series are not mode aligned.

2.3. Noise-Assisted Multivariate Empirical Mode Decomposition

Multivariate extensions of EMD have been proposed to extend the applications of EMD to signals with multiple channels [33]. The idea is to project the time series with p dimensions along a set of V vectors which points are on a p-dimensional hypersphere generated with a low-discrepancy Hammersley sequence. After estimating the upper and lower envelopes for each projection ${\left\{u_v\left(t\right)\right\}}_{v=1}^V$ and ${\left\{l_v\left(t\right)\right\}}_{v=1}^V$ from their local extrema, the unique mean is obtained as $a\left(t\right)=\frac{1}{2V}{\sum }_{v=1}^V{u}_v\left(t\right)+l_v\left(t\right)$. The extraction process of IMFs is then similar to standard EMD. The complete procedure is described in Algorithm 2. In order to obtain meaningful IMFs, the number of directions vectors V should be much greater than p. Adding Gaussian noise channels to the multivariate signal before decomposition (noise-assisted multivariate EMD, or NA-MEMD) also demonstrated to efficiently reduce the overlapping and mixing of modes [47].

Algorithm 2 Multivariate empirical mode decomposition (MEMD).

1: Generate V direction vectors based on a pointset on a p-dimensional hypersphere generated with a low-discrepancy Hammersley sequence; 2: Set the initial residue of p-dimensional signal to decompose $x\left(t\right)$ as $r\left(t\right)=x\left(t\right)$ and $i=1$; 3: Get the projections set ${\left\{P_v\left(t\right)\right\}}_{v=1}^V$ of $r\left(t\right)$ along each vector V; 4: Identify the local maxima and minima of ${\left\{P_v\left(t\right)\right\}}_{v=1}^V$; 5: Evaluate the upper and lower envelopes for each projection ${\left\{u_v\left(t\right)\right\}}_{v=1}^V$ and ${\left\{l_v\left(t\right)\right\}}_{v=1}^V$ by interpolating the local maxima and minima with a cubic spline; 6: Calculate the mean of $u_v\left(t\right)$ and $l_v\left(t\right)$ as $a\left(t\right)=\frac{1}{2V}{\sum }_{v=1}^V{u}_v\left(t\right)+l_v\left(t\right)$; 7: Let $r\left(t\right)=r\left(t\right)-a\left(t\right)$ and repeat 3 to 6 until a stopping criterion is reached; 8: Extract the ith IMF as $IM{F}_i=r\left(t\right)$; 9: Let $r\left(t\right)=x\left(t\right)-{\sum }_{j=1}^{i}IM{F}_j$; 10: Increment i and repeat 3 to 9 until $r\left(t\right)$ becomes a monotonic function.

2.4. Recurrence Analysis

Recurrence is an inherent property of dynamical systems and, as such, an important aspect to their study. The state of a system is said to be recurrent when its trajectory revisits a region of the phase space. One can keep track of these recurring states by building a thresholded pairwise distance matrix as

$${\mathbf{R}}_{ij}=\Theta \left(ϵ-∥{\overrightarrow{z}}_i-{\overrightarrow{z}}_j∥\right),i,j=1,\dots ,N,$$

(1)

where $\overrightarrow{z}$ is the position of each N points of the time series in the phase space, $ϵ$ is the threshold distance from which the states are close enough to be considered recurrent, and $\Theta$ is the Heaviside step function. The analysis of the structures in this binary matrix, also called recurrence plot, allows to characterize the system’s behavior qualitatively and quantitatively through recurrence quantification analysis measures (RQA) [34]. For example, diagonal recurrent lines parallel to the LOI represent a periodicity in the system of which state is recurrent at regular time intervals, while vertical and horizontal recurrent lines show a stationary state. One can then measure, for example, the systems determinism $DET$ and laminarity $LAM$ as the percentage of recurrence points forming diagonal and vertical/horizontal lines,

$$DET=\frac{{\sum }_{d=d_{min}}^{N}dP\left(d\right)}{{\sum }_{d=1}^{N}dP\left(d\right)},$$

(2)

$$LAM=\frac{{\sum }_{v=v_{min}}^{N}vP\left(v\right)}{{\sum }_{v=1}^{N}vP\left(v\right)},$$

(3)

with P, the histogram of lengths, d and v, the diagonal and vertical lines, and $d_{min}$ and $v_{min}$, the minimum lengths. Other recurrence quantifications include dynamical invariants, such as entropy or the correlation dimension, as well as measures from graph theory based on the interpretation of the recurrence matrix as the connectivity matrix of a complex network [35].

Figure 3 shows typical examples of recurrence plots for (a) a sine signal, (b) a chaotic Rössler system’s signal, and (c) a random Gaussian noise signal. In the periodic case, we observe complete diagonal lines so the system is fully deterministic. In the chaotic case, the recurrence plot shows diagonal lines with variable lengths, causing a drop in the measured determinism. The recurrence plot of the random signal only shows isolated recurrence points not forming a diagonal line, so it is non-deterministic.

Using a sliding window, one can furthermore study the time-dependent behavior of the system by computing RQA measures along the time series, allowing to identify regimes transitions and isolated events. For this purpose, some statistical testing can be employed to detect significant deviations in the RQA measure. In this study, we use the bootstrapping method, which consists in building the test distribution of the RQA measure from randomly drawn line structures in the local recurrence plots [48].

3. Results and Discussion

The following section presents the mode decomposition results for each region along with possible interpretations.

3.1. IMFs Selection

NA-MEMD is applied on the standardized time series with 26 parallel noise channels and 256 projection vectors. We first select significant IMFs to analyze from the total 16 extracted based on their amplitude and representative temporal scale. To do so, we calculate the instantaneous amplitude and frequency $IA$ and $IF$ as

$$IA=\left|H\right|,$$

(4)

$$IF=\frac{1}{2\pi }\frac{d\left(\arg \right(H\left)\right)}{dt},$$

(5)

with H being the Hilbert transform of the IMF.

Figure 4 shows the amplitude and temporal scale of extracted IMFs. For better readability, we use the instantaneous period in hours as the unit, which is given by $I{F}^{-1}$. The IMFs of all regions are included here, and the first and last 5000 h of the time series are removed to exclude the distortions at the boundaries. Except for IMFs 4 and 5, all IMFs represent a clearly distinct temporal scale. One can see that IMFs 1, 2, 10, 11, 12, 15, and 16 have a negligible amplitude. IMFs 6 and 7 show a spike in amplitude, which was later confirmed to correspond to the blackout period caused by the Hokkaido earthquake in September 2018. IMf 9 has a relatively small amplitude, and its average period of 372 h does not seem to correspond with a physically meaningful temporal scale for electricity demand. The remaining IMFs selected for the analysis have both a non-negligible amplitude and meaningful period. IMFs 3, 4 and 5 represent the semi-daily and daily variations, IMF 8 the weekly variations, and IMFs 13 and 14 the seasonal or semi-annual and annual variations in the electricity demand.

3.2. Annual Period

Figure 5 shows the IMF 14 or annual demand fluctuations for the 10 regions along with temperature profiles smoothed using a four-week sliding window. Horizontal dashed lines indicate the temperature extrema over the covered period. Only the coldest and hottest regions, Hokkaido and Tohoku in the north, Hokuriku with its mountainous area, and Okinawa in the south, show a high amplitude in demand oscillations. The oscillations seem highly correlated with annual temperature fluctuations, with peaks during winter for Hokkaido, Tohoku and Hokuriku, and during summer for Okinawa.

This can trivially be explained by the heat demand, with coldest regions having harsh winters and mild summers, while hottest regions have mild winters and very hot summers. This does not mean that other regions do not have an electricity demand in winter or summer, but rather that their difference in demand between these seasons is smaller. One can further notice that the demand oscillations amplitude decays over the year for Tohoku and Hokuriku regions, following a slight increase in the temperature, with milder winters causing a decrease in heating demand, and hotter summers causing an increase in cooling demand. Similarly, in Okinawa, the year 2018 shows the mildest summer in this region, causing a decrease in cooling demand.

3.3. Semi-Annual Period

Figure 6 shows the IMF 13 or semi-annual demand fluctuations with the smoothed temperature profiles. All regions show high amplitude oscillations with two peaks per year, in winter and summer. Hokkaido, Tohoku, and Okinawa regions show a clear difference between the peaks’ height, with a higher peak in winter for Hokkaido and Tohoku and in summer for Okinawa.

Again, this can be explained by the heat demand, with colder regions having higher heating demand in winter and hotter regions having higher cooling demand in summer. All regions, except Hokkaido and Okinawa, show a higher amplitude around the winter of year 2018, caused by the coldest recorded temperatures over the covered period.

3.4. Weekly Period

Figure 7 shows the IMF 8 representing weekly demand fluctuations. The time series for each region are organized in a days by weeks matrix for better readability. One can see that the IMF for Chubu and Hokuriku have high amplitude oscillations, with a high demand during weekdays and a lower demand during weekends, corresponding with the typical schedules of public utilities, such as schools and administrative buildings. Other regions follow the same pattern to a lesser extent, with Okinawa showing almost no fluctuations.

Some possible interpretations of the difference in amplitude between regions can be drawn from the annual electricity shares of industrial, commercial and residential sectors in Table 1. Okinawa has the highest commercial share, while having an average residential share, meaning that it has a high proportion of private businesses per capita, including entertainment, hospitality, restaurants or shops. Such businesses operate with rotating shift schedules to provide services both during weekdays and weekends, which could explain the absence of observable weekly demand fluctuation in that region. On the opposite end, Hokuriku region, showing a high contrast between the weekday and weekend demand, has the lowest commercial share for the highest residential share after Hokkaido region. Chugoku region has a low commercial share but also a low residential share caused by its high industrial share. The high demand fluctuations in Chubu cannot yet be explained this way., as it has balanced shares between all sectors. However, the industrial sector of Nagoya city, the most populated area of that region, is known to be mostly occupied by the Toyota industry, which imposes weekends as rest days to its employees.

We use recurrence quantification analysis in order to detect irregularities in the time series and possibly identify some relations with real events and further demonstrate the accuracy and physical meaningfulness of the extracted IMF. We estimate the time series determinism using $DET$ measure with a sliding window of four weeks to detect these changes. A lack of regularity in weekdays/weekends schedules should result in a lack of consistency in the weekly demand fluctuations, and thus a drop in the local $DET$ measure. The recurrence plots are computed from the phase space built, using the delay embedding method [49], and a distance threshold $ϵ$ equal to 10% of the attractor size [34]. The delay $\tau$ was set to 42 h, which corresponds to the quarter period of a week. The number of embedding dimensions m was determined using the false nearest neighbors algorithm and is equal to 3 [50]. When calculating $DET$, we first removed the LOI in the recurrence plot with a Theiler window of $(m-1)\tau$ [34]. The minimum diagonal lines length $d_{min}$ was also set to $(m-1)\tau$ [34]. We used 10,000 bootstrap resampling to estimate the variance of $DET$ for statistical significance testing [48].

Figure 8 shows the IMF 8 time series with the variations of $DET$. The horizontal dotted lines represent the lower threshold of 5% p-values. Overall, the significant drops in determinism coincide with either the new year period, Golden week which is week with several national holidays occurring between the 29th of April to early May, or Obon which is an event of several days for the commemoration of ancestors occurring in the middle of August. These periods are major national holidays followed by most of the population. Another noticeable determinism drop appears around February 2020 for most regions, yet does not seem to correspond with any holiday or cultural event. It in fact coincides with the first appearance of COVID-19 cases which caused a large-scale lock down of schools as well as disturbances in many businesses. The determinism variations for Okinawa region appear as an exception, with drops during summer caused by the cooling demand increase governed by chaotic temperature fluctuations.

3.5. Daily Period

IMFs 4 and 5 both represent the electricity demand variations with the daily period. Figure 9 shows the time series for IMF 5 organized in hours by days matrices. One can clearly see the difference between day and night demand, with typically a higher demand during daytime from 9 in the morning to 8 in the evening. There is also a difference between winter and summer for most regions, with a smaller contrast between day and night in winter. Notably, Hokkaido region shows a higher demand during winter nights than during daytime. Tokyo, Chubu, and Kansai regions appear to have a stable demand throughout the year.

The smaller demand contrast day/night in winter can be explained by either mild winters in southern regions or alternative heating solutions, such as gas and kerosene, or a combination of the two. Although electrical heaters have a high power consumption, kerosene- and gas-based heating is widely used, particularly in northern regions, such as Hokkaido, because electricity-based heating, including heat pumping, is insufficient due to the poor buildings’ insulation, as most households in Japan live in wood-framed houses. The higher demand during winter nights in Hokkaido can be explained by the necessary heating of water pipes to avoid freezing. As for Tokyo, Chubu, and Kansai regions, one might think that the stable demand can be explained by a higher industrial and commercial share, as they use the same working equipment throughout the year, but it is only the case for Tokyo and Kansai as seen in Table 1. Another possible interpretation can be drawn based on the fact that these three regions have the highest population density and regroup the largest cities in Japan, including Tokyo, Osaka, Kobe, Kyoto and Nagoya. Large cities tend to have more recent buildings, both for working places and households, equipped with heat pumps for room heating, which could explain the higher demand during winter daytime. Some households use a blanket heater in winter instead of room heating when sleeping, which can also explain the lower demand at night in these regions.

The IMF 4 for all regions is shown in Figure 10. One can see that only bursts of high amplitude are present at regular intervals in the middle of August, corresponding to the temperature peaks every year. There is no evident underlying the cause for the presence of such bursts, so we interpret for now this IMF as resulting from an artificial mode splitting with IMF 5.

3.6. Semi-Daily Period

Lastly, the electricity demand fluctuations with semi-daily period covered by IMF 3 are shown in Figure 11, again in hours by days matrices. Overall, three daily demand peaks can be observed here, one around 5 in the morning, one around 10 in the morning, and another around 8 in the evening. Hokkaido and Tohoku have both peaks at 5:00 a.m. and 8:00 p.m. with an additional small peak at 10:00 a.m. during summer. The early morning and evening peaks are more pronounced in winter. Hokuriku also has the three demand peaks but with a lower amplitude. Tokyo, Chubu and Kansai regions show similar demand patterns with peaks at 9:00 a.m. and 8:00 p.m. and a higher amplitude during winter. Chugoku, Shikoku and Kyushu regions’ demand alternates between three patterns: one during spring and fall with small peaks at 5:00 a.m. and 8:00 p.m., one during summer with small peaks at 10:00 a.m. and 8:00 p.m., and one during winter with the same peaks at 10:00 a.m. and 8:00 p.m. and a higher amplitude. Okinawa stands out with peaks at 10:00 a.m. and 8:00 p.m., with the one at 10:00 a.m. being higher during summer.

The peak at 10:00 a.m. can be associated with room heating or cooling at the start of schools, offices and businesses, which are mostly equipped with heat pumps. The demand drops in the afternoon because once the temperature has reached its desired state, it takes less energy to maintain it in a closed environment. This peak appears to be higher during winter in most regions because of the fact that the night temperature difference with comfortable room temperature (say 20 to 25 degrees) is higher in winter than summer, as well as heat pumps being less efficient for heating than cooling. It also starts later in summer because night temperatures are cooler and it takes some time in the morning for the room to heat up with rising ambient temperature. The peak is higher during summer in Okinawa because of the mild winters in this region. It is also not visible in Hokkaido during winter because of alternative fuel-based heating, notably city gas for bigger buildings.

The peak at 8:00 p.m. can be explained by room heating and cooling of households when people come back home from work, with higher heating demand during winter. We can assume that it also includes the electricity consumption of other equipment such as lighting, cooking, or televisions. The lighting demand of buildings and streets could furthermore explain the early start of this peak in winter, notably in Hokkaido, because of the days becoming dark around 5:00 to 6:00 p.m. in this period.

The peak around 5:00 a.m. can have different possible explanations. It can be interpreted as people waking up more or less early in the morning, rice cookers scheduled to heat breakfast, industries using electricity at night for cheaper prices, or even apartment blocks residences automatically switching back on outdoor lights before dawn. These interpretations yet do not explain the presence of this peak only during spring and fall for Chugoku, Shikoku, and Kyushu regions. This timing coincides with planting and harvesting schedules in the rice crop calendar and thus could also be related with seedlings and fields preparation works.

4. Summary

We studied the application of noise-assisted multivariate empirical mode decomposition (NA-MEMD) for the analysis of energy demand time series with the case of electricity demand per region in Japan. This algorithm allows to decompose the complex spatial–temporal data into intrinsic mode functions (IMFs) showing the demand dynamics at different temporal scales. The observed features in extracted IMFs could be explained by ambient temperature variations, demand sectors shares, and life style with working schedules and holidays. Recurrence quantification analysis could further accurately detect irregularities associated with cultural events, as well as prevention measures for the spread of COVID-19. These features could not properly be observed in total time series, which impairs their accurate analysis and modeling.

Time series decomposition is already used in the energy field as input for machine learning algorithms for short-term forecasting, but we advance the idea that it can also be used to fill the lack of knowledge on global energy demand dynamics to establish more accurate models for long-term scenario analysis with high temporal resolution. Future research directions thus include this modeling process, as well as analysis at smaller spatial scales, such as municipalities and the comparison between countries with different environmental conditions, economical development levels and cultures.