Spatial demand forecasting based on smart meter data for improving local energy self‐sufficiency in smart cities

JST‐Mirai Program, Grant/Award Number: JPMJMI17B5 Abstract The use of distributed energy resources (DERs) in a city contributes to the net zero CO2 of a city. However, the spatially uneven distribution of power demand and surplus electricity causes congestion in the grid system, making wide‐area operation difficult. The concept of local energy self‐sufficiency via energy management, in which batteries or electric vehicles are charged using power generated by DERs and discharged to neighbouring consumers, is expected to be a way to avoid grid conjunction while maximizing the use of DERs. For efficient local energy self‐sufficiency, it is necessary to identify where and when future power surpluses and shortages will occur within a city and optimize battery operation according to demand. Forecasts that focus only on representative points of a city may be less reproducible in diversity in the power demand transition for individual consumers in local parts of cities. Electricity smart meters that monitor power demand every 30 min from each consumer are expected to help predict the spatiotemporal distribution of power demand to achieve efficient local energy self‐ sufficiency. The significance of reflecting regional characteristics in forecasting spatiotemporal distribution of power demand is demonstrated using actual data obtained by smart meters installed in Japanese cities. The results suggest that the forecast approach, which considers the daily periodicity of power demand and weather conditions, obtains high prediction accuracy in predicting power demand in meshed local areas in the city and derives results precisely reproducing the spatiotemporal behaviours of power demand.


| INTRODUCTION
The introduction of distributed energy resources (DERs), such as solar photovoltaic (PV) generation in cities, has reduced dependence on fossil fuel power generation [1]. The mass introduction of DERs will contribute to the net zero CO 2 of a city and add new value to smart cities. However, the intensive placement of PV systems leads to a rise in voltage in local grids and a capacity constraint in electric power transmission systems. Thus, PV installation and generation must be excessively curtailed to prevent voltage deviation in grids [2]. Unplanned mass introduction of PV will impose constraints on the amount of DERs deployed.
Local self-sufficiency encourages the consumption in neighbouring areas of PV generated in a small area of a city. This can prevent an excessive rise in voltage in local distribution systems, prevent the capacity of transmission systems from being exceeded, and efficiently reduce CO 2 emissions in the city [3][4][5][6][7][8]. The idea of self-sufficiency has been welldiscussed at the building scale, where the emphasis has been on reducing CO 2 emissions and electricity costs rather than stabilizing power grids [3,4]. Several case studies have been conducted on local self-sufficiency in cities. Arcos-Vargas et al. [5] analyzed the potential for the additional introduction of PV in cities. They performed a case study and showed that the total PV generation in a city exceeds the demand of the entire city. Villa-Arrieta and Sumper [6] assumed a few typical characteristics of PV panel owners, prosumers, and consumers, and simulated the effect of long-term economic investment on PV generation and the effect of PV generation on reducing CO 2 emissions. Bartolini et al. [7] simulated the optimum electric vehicle (EV) penetration rate for the amount of PV introduced and the CO 2 reduction effect based on the actual power source ratio in a city. Jurasz et al. [8] evaluated the PV introduction potential in 1-km 2 mesh units in a city and calculated the selfsufficiency rate based on the ratio of houses and factories in each mesh. These case studies evaluated the effect of PV generation on CO 2 emission reduction and the cost of investing in solar power generation from the perspective of an entire city. These studies evaluated the effects based on power demand transition using typical demand patterns; they did not consider the diversity in the power demand transition for individual consumers in local parts of cities. Forecasts that focus only on representative points of a city may be less reproducible in the diversity in the power demand transition for individual consumers in local parts of cities and regional characteristics of power demand. A detailed spatiotemporal balance between supply and demand is required to achieve regional selfsufficiency effectively. In particular, the concept of energy management, such as charging appropriately installed storage batteries and controllable EVs using surplus PV power and discharging them in periods and regions with high power demand, will have an important role [9,10]. Thus, the ability to predict the spatiotemporally uneven distribution of PV surplus power and power demand in a city is important for efficiently realizing energy management to improve local self-sufficiency.
For the effective use of energy and the stability of power grid systems, several methods for predicting power demand and the amount of power generated spatially and temporally by PV systems have been proposed [11,12]. The amount of solar power generated in a city is significantly affected by the weather conditions of the city. The spatially fine-grained information obtained from meteorological satellites improves the accuracy of forecasting the amount of PV power generation [12]. However, power demand depends not only on weather conditions but also on the nature of consumers. Therefore, forecasts focusing on various forecast target and forecast time horizons have been studied. From the perspective of forecasting targets, these methods are divided into forecasts of individual demands of consumers [13,14] and forecasts of the total demand for a country or a power grid-scale [15,16]. Several studies [17,18] argued for the importance of forecasting the spatial distribution. From the perspective of the forecast time horizon, these methods are categorized into short-term forecasts [13,14,16], which predict power demand several hours ahead for energy management, and long-term forecasts [15,17,18], which predict power demand several years ahead for the facility planning of cities and power systems.
In particular, short-term power demand forecasting for an entire city helps achieve local energy self-sufficiency. A conventional approach to forecasting the power demand of an entire city is to estimate the average power demand by combining statistical data that represent the nature of the city, such as the population and the number of households, with typical demand transition patterns published by grid operators. This method does not consider differences in the characteristic power consumption behaviours of individual consumers. Moreover, because meteorological conditions in cities are not uniform, it is not appropriate to use the meteorological data observed only at the single point in a city for prediction. In addition to spatial differences in weather conditions, the impact of weather conditions on the dynamics of power patterns may vary in each area in a city; for example, a consumer who extensively uses air conditioning may be more sensitive to weather information for power demand compared with other consumers. Electricity smart meters that monitor power demand every 30 min from each consumer are expected to predict the spatiotemporal distribution of power demand to achieve efficient local energy self-sufficiency [19]. The analysis of meter data elucidates the various characteristics of consumers and cities [20]. The regional characteristics of power demand revealed by the meter data will contribute to a more refined forecast of the future spatiotemporal distribution of power demand. Metering observations and the data that represent the characteristics of a city, such as map data, will be able to reveal the behaviours of specific power demand in small districts within a city, and will help understand the uneven distribution of future power demand in the entire city.
The purpose of this study is to clarify the significance to consider the regional characteristics for predicting a nonuniform spatiotemporal distribution of power demand in a city. This study focuses on short-term forecasts of power demand that contribute to the optimization of energy management for achieving local energy self-sufficiency in cities. We will visualize the meshed smart meter data collected in Utsunomiya City and Haga Town in Japan and show that power demand dynamics vary by location, time of the day, and season. In this study, the spatiotemporal distribution of power demand will be predicted for each mesh based on a prediction model that is a combination of the persistence model and a regression model. In addition, a benchmark evaluation by comparison with a forecast that focuses only on the average demand trends for the entire city shows the significance of considering the regional characteristics of demand dynamics in local areas within a city.

| Overview of data use in smart cities
The equipment used in smart cities is assumed to be connected through the Internet and optimally controlled using the results of data collection and analysis to solve problems in energy and transportation infrastructure [21,22]. In Japan, smart electricity meters have been introduced for each consumer by electric power companies to automate meter readings and collect electricity charges [23]. These meters were expected to be installed for all consumers by 2024. Figure 1 shows how a smart meter collects and transmits data. The amount of power purchased from a grid and the amount of power sold to the grid are accumulated as an integrated value every 30 min. The accumulated data are transmitted to an electric power company via route A. The smart meter data are further used by providing the data to a third-party organization via route C. Grid Data Bank Lab [24] is an example of such a third-party organization in Japan. It develops services for residents using data after meshing in consideration of consumer privacy.
In addition, not only these types of smart meter data but also observation data owned by the national government and other sectors are becoming more available for the operation of smart cities because of improvements in the spatial granularity of the data. For example, the Himawari 8 Japanese meteorological satellite can observe temperature and solar radiation in 1-km 2 units [25]. The data acquired by meteorological satellites can be used to obtain spatiotemporal information about weather conditions in a city. In addition, the widespread use of personal mobile phones use human movement information based on communication history with base stations [26]. For example, Habault et al. analyzed the relation between people's movements and changes in the spatial distribution of power demand [27]. The use of data across various sectors is expected to be the key to smart city technology.

| Data use for smarter power grid systems
A power grid must be optimally controlled to maintain a constant voltage and frequency in response to changes in power demand. The power source that mainly supplies electricity to smart cities will be a distributed energy source, such as PV or renewable energy generation, rather than a conventional large-scale thermal power generator. The output of PV systems is unstable and dependent on weather conditions. In addition, PV systems are irregularly placed in cities, resulting in a rise in local voltage in power grids [28]. In smart cities, power grid systems must be optimized by collecting information from sensors in power grids. Moreover, these systems must be autonomously or remotely controlled. Several methods for power grids optimization have been proposed, such as the simulation of the power grid system characteristics of an actual city and the simulation of an energy management system at the city scale [9,10,29].
Several previous works suggest that smart meter data can replace sensors in the power grids [30,31]. It is possible to calculate the spatial voltage distribution of a power grid from power demand transition and optimally control the grid without installing an additional voltmeter. Furthermore, it was shown that using storage batteries based on power demand and PV generation contributes to the stabilization of power grids [32,33]. Figure 2 illustrates the idea of levelizing peak demand and surplus power with storage batteries and EVs. For this purpose, smart meter data can help predict power demand and surplus power several hours ahead. For example, data collected in smart cities can be used to plan route for electric buses for local energy self-sufficiency, such that surplus electricity in the area where the buses are charged in discharged to supply electricity in areas at the timings of high demand. Appropriate data use will realize the efficient use of electricity generated by DERs and contribute to improving local energy selfsufficiency without affecting the lives of citizens.
Before the widespread use of smart meters, it was impossible to collect data on the power demand of each consumer without an additional electricity meter; therefore, the popular method for estimating the power demand of an entire city was to multiply static data that represented the nature of the city, such as the population or the number of households, and a general demand transition pattern published by a power company. In addition, the forecasted power demand used for city planning emphasized monthly seasonality and peak electricity consumption and did not require the reproducibility of spatiotemporal behaviours of power demand in local areas. In contrast, the installation of smart meters for all consumers in a city make it possible to predict and use the spatial distribution of power demand in the city. The dynamics of local power demand should be accurately predicted to use surplus power appropriately without restrictions on high-voltage power grids. Smart meter data enable forecasting in all small areas of the city and are able to reproduce the regionally behaviours of power demands. Thus, understanding and predicting the spatiotemporal behaviour of power demand will bring new value to F I G U R E 1 Overview of collecting and transmitting smart meter data MIYASAWA ET AL.
smart cities, such as stabilizing the power grid and reducing urban CO 2 emissions.
We focus on the distribution of power demand based on the location data of smart meters in a city and the data for the amount of electricity purchased. The visualization of smart meter data combined with map data reveals different demand trends in each local area of a city. In particular, we focus on land use districts to characterize the difference in the behaviours of power demand in each local area. These characteristics will identify the factors required to predict future power demand. In the next section, the significance of predicting the spatiotemporal distribution of the power demand of a city will be clarified by visualizing smart meter data.

| Overview of analysis
We focus on the data of approximately 160,000 smart meters installed in low-voltage power systems in Utsunomiya City and Haga Town, Japan. The smart meters measured the amount of electricity purchased and sold every 30 min from January to December 2019. Generally, the amount of electricity purchased is obtained by subtracting the amount of power generated by consumers' PV systems from the amount of power consumed. To discuss the regional characteristics of essential demand behaviours, this study focuses on smart meter installed in houses that do not own power generation systems. Smart meter data used in this study were measured by a grid operator processed into a 250-m 2 mesh to protect the privacy of consumers. The total power consumption and the number of consumers in the mesh were provided by the power grid operator. From the perspective of discussing the regional characteristics of demand, this study focuses on the amount of electricity consumed per household, which is calculated by dividing the total amount of electricity consumed in the mesh by the number of consumers. We analyze these data from the following two perspectives. The unevenness of the spatiotemporal distribution of power demand in the city will be discussed in Section 3.2. We will also focus on typical areas from the perspective of land use districts and analyze the regional characteristics of power demand in Section 3.3. To visualize the temporal transition of power demand in the city, Figure 4 shows a heat map of the spatial distribution of power demand obtained at three different times in a day. As shown in Figure 4(a), power demand is dispersed over a wide area in the city in the morning. However, as shown in Figure 4 (b), power demand becomes concentrated at the center of the city during the day. As shown in Figure 4(c), power demand becomes dispersed again at night. This indicates that people move around the city over one day. It is presumed that the movement of people differs based on land use districts in areas such as houses, stores, and factories. The differences in power demand behaviours according to land use in the city are discussed in Section 3.3.

| Spatiotemporal unevenness of city demand
To predict the spatial distribution of power demand accurately, it is necessary to consider the spatial properties of meteorological conditions that explain the trends in power demand. We visualize the data obtained by Himawari 8, the meteorological satellite, and reveal that not only power demand but also meteorological conditions differ within the city. Figures 5 and 6 show the spatial distributions of the air temperature and total solar radiation in the city, respectively, at three different times in a day. Figure 5 shows that at a given time, the temperature of the city is high on the east side and low on the west side. Figure 6 shows that the amount of solar radiation depends on the distribution of clouds. Focusing only on a single representative point in a city indicates that we do not consider such spatial differences in the meteorological conditions, which may be an important factor in understanding the spatial distribution of urban demand.
Visualization of the spatial distribution of power demand and meteorological conditions shows that the time-series behaviour differs depending on meshes. The changes in demand behaviour in response to local weather conditions are revealed as a characteristic of area demand in terms of regiondependent demand dynamics. In the next subsection, we will discuss this region-specific characteristic from the perspective of urban land use.

| Regional characteristics of demand focusing on representative local areas
It is presumed that the difference in power demand behaviours within a city depends on the nature of the inhabitants of the city. In city planning, land use districts, which limit the use of buildings constructed for stipulating land use, are defined in advance and made open to the public by the city [34]. Figure 7 shows the land use districts of Utsunomiya City. The center of the city is a commercial area and is surrounded by residential areas. A large industrial area is located in the eastern part of the city. Three representative subareas are extracted to clarify the different characteristics of each area, as shown in Figure 7, and the power demand patterns in each subarea are compared. Table 1 shows the number of smart meters and meshes in these subareas.  Figure 8 (a) shows all power demand transitions observed in the mesh belonging to subarea 1 on weekdays in summer. The boxplot shows the minimum, median, maximum, and first and third quartiles, excluding outliers. The interquartile range (IQR), which is shown as a box in the plot, is the distance between the first and third quartiles. Observations that are larger than the third quartile +1.5 � IQR or smaller than the first quartile −1.5 � IQR are excluded as outliers. As shown in Figures 8-10, the statistical behaviours of daily power demand sequence differ depending on the season and land use districts. For example, in winter, the power demand behaviour in the morning is clearly different from that in other seasons; the power demand in winter peaks twice a day, that is, in the morning and at night. This is presumed to result from the consumption of electricity for heating during winter mornings. The IQR shows the trends of the power demand transitions observed in each mesh. In particular, the IQR in the intermediate season is smaller than that in the other seasons. This indicates that there is a negligible variation in power demand. From the perspective of land use districts, there is a large variation in power demand in industrial areas in the morning. In addition, the variances in power demand observed in commercial areas are not significant compared with the other two subareas.
It is important to understand when power demand peaks for the appropriate operation of the power grid. The peak of power demand leads to a local voltage drop and capacity -111 constraints in the power grids. Figure 11 shows histograms of the time periods in which daily demand peaks were observed for individual meshes belonging to each subarea. The peaks in residential and commercial areas are concentrated at night in all seasons except winter. In contrast, the peaks in the industrial area occur in the morning. This result suggests how to level out peak power demand in the city. For example, charging and discharging EVs at the appropriate time and place as they move between residential and industrial areas can be expected to reduce peaks in demand.
Finally, we show the daily periodicity of power demand. The time-series data of the average demand of meshes belonging to subareas for the summer, winter, and intermediate seasons are analyzed from the perspective of the autocorrelation function [35] and are shown in Figure 12. This figure suggests that the power demand trends exhibit a 24-h periodicity regardless of season or region. In the forecasting problem, the use of power demand data observed 24 h before the target forecast time may contribute to improving prediction accuracy. However, it also shows that fluctuation in demand cannot be explained solely by autocorrection with the 24 h. The trends in power demand have components that change based on external factors such as meteorological information.
These results suggest that the power demand and weather conditions in the city are spatially uneven, and imply that an analysis of typical representative demand behaviour focusing on the average demand of entire city is insufficient to reproduce the regional characteristics of power demand. The future spatiotemporal distribution obtained by the demand forecast results based on smart meter data helps to reproduce the regional characteristics.

| Prediction models
To show the significance of prediction schemes for power demand considering regional characteristics, we conducted a simulation to predict the spatial distribution of power demand in the city based on smart meter data. In this simulation, the impact of the information and assumptions used in the forecast model and the aggregation scale of forecast target are discussed in terms of the error in understanding the electricity demand per household in a mesh of smart meter data aggregated at a spatial resolution of 250 m 2 .
We focus on three forecast models: the persistence model, which shows predictive benchmarks; a non-linear regression model that learned the regional characteristics of power demand trends according to the weather for each mesh; and the modified persistence model, which considers not only the meteorological characteristics but also time-series characteristics in terms of the daily periodicity of power demand.

-
Let D n t ∈ ℝ þ [Wh/30 min] be the total power demand of mesh n ∈ f1; …; Ng observed at time t ∈ f1; …; T ; …g in a city whose area is divided into N meshes, and w n t be the weather information vector that contains a total solar radiation and temperature of mesh n observed at time t. We focus on average power demand d n t obtained by dividing total power amount D n t in a mesh by number of meters C n t in the same mesh: The purpose of the forecasting is to predict future power demandd n T þH , which will be observed after H hours at time T for each mesh. We focus on relatively short-term forecasts from 30 min ahead to 24 h ahead. We assumed that the forecasts will be updated every 30 min as new meter data are observed.
The comparison of three models is illustrated in Figure 13. In the persistence model, the prediction resultsd n T þH are derived as:d The persistence model considers the power demand at target forecast time d n T as the power demand at prediction timed n T þH . The persistence model was used as a benchmark for time-series prediction in many previous studies in terms of short-term forecasting. The persistence model does not consider information other than the latest power demand.
To clarify the effect of the regional characteristics of power demand according to the weather for each mesh on the accuracy of prediction, we focus on weather data observed by the meteorological satellite with a spatial granularity of 1 km 2 , particularly the meteorological data of the point that is spatially closest to the mesh of the aggregate demand of interest. We consider using a non-linear regression model that inputs latest power demand d n T and latest weather conditions w n T :d where ϕ n H ð⋅Þ is a pretrained regression function based on the random forest model [36], which is a machine learning approach reported in many previous studies in which high accuracy can be obtained in non-linear regression.
The proposed model that combines the persistence model and regression model is able to consider both the daily periodicity of power demand and weather conditions. Our proposed model is defined as: where d n T þH−24½h� indicates the demand at the time when it is observed 24 h before target forecast timed n T þH regardless of time H for which the model predicts demand. Separate forecast models are created for data for weekdays and holidays. The demand for Saturday is forecasted based on data from Sunday of the previous week. To consider the daily periodicity of power demand shown in Figure 12, the persistence model assuming daily periodicity is considered in the first term. The correction term Δd n T þH is predicted by the regression model as: where ψ n H ð⋅Þ is a regression function trained for each H and n individually for the purpose of explaining the discrepancy To show the significance of forecasting power demand for each mesh, we compare two spatial scales of prediction target. The first is that a 250-m 2 area is regarded as one F I G U R E 7 Land use districts map of the city

Subarea name Number of meshes Number of smart meters
Commercial (1)  35  4634 Industrial (2)  88  1195 Residential ( mesh, as previously mentioned. The second is that the entire city is regarded as one mesh as averaged power demand within the city: The forecast model training based on the entire city demand is defined as: where ψ H ð⋅Þ is regression functions trained in the same way as Equation (5). The prediction scheme shown in Equation (7) is a conventional method for forecasting demand without using high-grained observations from individual smart meters and meteorological satellites, because it considers only the typical representative demand behaviour and static distribution of consumers. To show the significance of reflecting regional characteristics in predicting the spatiotemporal distribution of power demand, we will compare the method of forecasting the power demand for each mesh with the method of predicting based on entire city demand.

| Conditions of predictive simulation
The purpose of our simulation is to discuss the impact of the information and assumptions used in the forecast models and the aggregate scale of the forecast targets. At first, three models given in Equations (2)-(4) are compared in terms of the information and assumptions used in the models. Then, two approaches given in Equations (4) and (7) In addition, in Section 4.4, we will show that the proposed method is superior in terms of the reproducibility of changes in power demand in the city, compared with the method of predicting the average power demand in the -115 city and applying it uniformly to all consumers in the city. The regional characteristics of the forecast results are compared with those of actual measurements to evaluate the regional reproducibility of the demand behaviour and the timing of demand peak that should be considered in managing regional energy to improve local energy selfsufficiency.

| Evaluation of prediction accuracy
Now, we focus on short-term forecasting whose model is trained for each forecasting target H¼ 0.5, 1, 3, 6, 12, and 24 h individually. First, we show the prediction results of 1946 meshes in the city that contain more than 10 smart meters; then, we compare the accuracy of the models to show the effectiveness of the proposed method. Figure 14 shows the accuracies of the three models in the summer, winter, and intermediate seasons. The horizontal and vertical axes represent time and RMSPE, respectively. The persistence model shows the highest accuracy in predicting the power demand 30 min ahead. In an extremely short-term forecast, such as 30 min ahead, the power demand observed immediately before the forecast can accurately express the future power demand; it is not necessary to apply corrections based on weather conditions. The persistence model shows high accuracy in predicting the power demand 24 h ahead because it considers the daily periodicity of power demand. Compared with the persistence model, the accuracy of the non-linear regression model in predicting power demand 3-12 h ahead is higher than that of the persistence model. This is considered a benefit of learning the relation between meteorological data and demand. The proposed method shows the highest and most stable accuracy in predicting the power demand several hours ahead. In winter and intermediate periods, prediction of power demand of 24 h ahead based on the proposed method gives further accurate results compared with the persistence model. This suggests that it is necessary to correct the power demand at the same time on the previous day, based on the assumption of daily periodicity, using the latest meteorological data. The result shows that using the daily periodicity of power demand and the spatial distribution of meteorological conditions effectively improves prediction accuracy. It also shows that using observed meteorological data, even 24 h before the target forecast time, contributes to an improvement in the forecast accuracy. In contrast, in summer, the meteorological data observed up to 1 day earlier are insufficient to improve forecast results.
We compare the cases of considering the entire city as one mesh and an area of 250 m 2 as one mesh using the proposed method. To analyze the reproducibility of the uneven distribution of power demand, the prediction results for the two cases are compared with the correct value of power demand observed in each 250-m 2 mesh in terms of the RMSPE. Figure 15 shows the comparison results. When power demand is averaged for all meshes, there in a loss in the reproducibility of power demand trends, which are different for each mesh. Hence, prediction accuracy is reduced. Figure 15 suggests that the spatial granularity of forecast significantly affects the reproducibility of the regional behaviours of power demand within the city. Figure 16(a) shows the distribution of the RMSPE calculated for each mesh based on the average power demand transition predicted for the entire city, and Figure 16(b) shows the distribution of the RMSPE for the power demand transition predicted for each mesh. Both figures are based on the power demand forecasted 6 h ahead. When the spatial distribution of power demand is forecasted, prediction accuracy improves for numerous meshes in the city. This result indicates that the regional behaviour of demand cannot be sufficiently represented simply by focusing on the average demand behaviour of the entire city.
Meanwhile, some meshes do not demonstrate an improvement in accuracy by the proposed approach. Figure 17 shows the power demand transition over a week observed in the meshes with and without improved prediction accuracy. It is clear that the daily periodicity of power demand does not hold in the mesh for which prediction accuracy is not improved. Such changes in power demand without daily periodicity suggest the occurrence of specific events at that point. Although it is beyond the scope of this work, the use of population staying information that indicates the movement and stay of people obtained via mobile phones [27] is expected to be effective in forecasting demand in situations in which accuracy seems to determinate owing to such specific movement events.

| Reproducibility of regional demand characteristics
Finally, we discuss the reproducibility of the prediction results based on the proposed approach in terms of the regional characteristics described in Section 3. The task of optimizing the daily operation of storage batteries to achieve local energy self-sufficiency requires the demand behaviours for the following day to be forecasted at the time of planning. A typical setup is that at 23:30 on one day, the power demand for all times ranging from 00:00 to 23:30 on the next day be forecasted. The forecast results can be represented by boxplots under the same conditions as those shown in Figures 8-10. Figure 18  shows the boxplots of the power demand on weekdays in winter to compare the average forecast results for the city and the forecast results for each mesh (Figures 8(c), 9(c), and 10(c) show the actual behaviours). In Figure 18(a), the forecast results obtained using the average power demand of the city as the input do not reproduce the different demand trends observed in various parts of the city. In contrast, the results shown in Figure 18 Figure 19 shows the frequency of the occurrence of power demand peaks versus time for the average prediction results of the city (a)-(c) and the prediction results for each mesh (d)-(f) (see Figure 11 for actual measurement trends). The forecast results for each mesh more accurately reproduce the characteristics of power demand transition compared with the average forecast results for the city. Table 2 provides a quantitative evaluation of reproducibility between the forecast result and the ground truth using the reproducibility measure: where x h andx h indicate the frequency of the occurrence of power demand peaks at time h (=0:00, 0:30, …, 23:30) derived with observation and that with estimation, focusing on D days for N meshes. Reproducibility index = 100 indicates that both histograms match perfectly, and the range of index is 0-100. The result shows that the mesh-wise forecasts reproduce the power demand peaks accurately. We showed that the proposed method is superior in terms of the reproducibility of changes in power demand in the city, compared with the method of predicting the average power demand in the city and applying it uniformly to all consumers in the city. These results demonstrate the importance of capturing regional demand characteristics in energy management to improve local energy self-sufficiency, such as daily operation plans for storage batteries that consider the occurrence of demand peaks in each region.

| CONCLUSION
The visualization of the data obtained by actual smart meters shows that power demand is not uniform within a city. Therefore, focusing only on the average demand behaviour of the entire city may compromise the reproducibility of the regional characteristics of local demand. The proposed method, which considers the daily periodicity of power demand transition, is effective for accurately predicting the temporal and spatial distribution of power demand. The forecasted distribution of power demand can be used for energy management to achieve local energy self-sufficiency. We plan to develop an energy management scheme to improve local energy self-sufficiency by using information collected in other sectors, such as population staying information that indicates the movement and stay of people, to improve the prediction accuracy of specific change in local demand that cannot be fully explained by the model examined here. -119