To achieve load forecasting for plots with insufficient historical electric load data, the proposed method applies the principle illustrated in Figure 1.

As shown in Figure 1, there are plots in a large zone Z: {p ₁ , p ₂ , … , p _n}. For each p _i = (area, history, sld), area is the spatial area corresponding to p _i , history is the time series data of the historical electric loads, and sld is the SLD vector calculated based on history. Elements in Z can be further separated into two types: P _known and P _unknown . The difference between P _known and P _unknown is that the elements of known originate from areas that were developed a sufficiently long time ago, where rich historical load data are available; by contrast, the elements of P _unknown correspond to newly developed urban areas, for which sufficient historical data have not been accumulated. Owing to the insufficiency of historical data, a sufficiently accurate forecasting model cannot be constructed. However, we can identify plots in P _known that are highly similar to those in P _unknown and use the SLDs of these plots to construct a forecasting model jointly based on the SLD information and a small amount of historical data.

The core problem in Figure 1 is to obtain the SLD information for a given plot p _x based on a set of plots similar to p _x in P _known . The spatial structure and style of buildings in high-resolution remote sensing images can provide information to solve this problem. Thus, we can use the high-level features of ground objects to perform an approximate search and obtain the target SLD. Hence, this study proposes the SELF-HE method. The overall process of SELF-HE is depicted in Figure 2.

As shown in Figure 2, for Zone Z containing plots belonging to known and unknown, the objective is to develop an SLF model for plot p _x in P _unknown . The SELF-HE consists of three steps:

This section details the development of a compressed image patch representation model M _cmp , through which the high-level information in an image patch can be extracted. The structure of M _cmp is shown in Figure 3.

As shown in Figure 3, M _cmp consists of three components:

This section details the determination of the distance encoding model M _distance and group assignment model M _group . Plots can then be encoded using these two models.

For Zone Z, suppose that the lower left corner is positioned at the two-dimensional coordinates (0, 0), the width of Z is L _width , and the height is L _height . The distances of a plot p _i from the coordinates (0, 0) along the x and y axes are denoted by p _i .area.x and p _i .area.y, respectively. Accordingly, the following equation is used to describe the relative position of p _i in Zone Z v d i s t a n c e = ( p i . a r e a . x L w i d t h , p i . a r e a . y L h e i g h t , p i . a r e a . x L w i d t h − 0.5 , p i . a r e a . y L h e i g h t − 0.5 ) , (3) where v _distance describes the position of p _i relative to the center of Z and relative to the coordinates (0, 0). For a plot, Eq. 3 can describe its position according to the distance from the starting point and the center point of Z, and form a vector; this vector is easy to participate in the calculation process of the neural network, v _distance can assist neural network take plot’s location as important features during inference. M _distance consists of a single layer with an input of p _i .area and output of v _distance ; thus, M _distance can be used to realize end-to-end coding distance coding for a plot.

To develop M _group , we established the relationship between the SLD and the image encoding of a plot. This process is illustrated in Figure 4.

As shown in Figure 4, the process of development and training consists of two steps.

When M _cmp , M _distance , and M _group have been obtained, M _encode can be constructed. The inputs into M _encode are the image patch and area information, and the output is the high-level encoding vector v _encode . Based on v _encode , an SLF model is constructed. The corresponding process is shown in Figure 5.

As shown in Figure 5, M _encode is constructed from M _cmp , M _distance , and M _group . Moreover, M _cmp accepts image patch data and generates v _cmp , and M _distance accepts location information as an input to generate v _distance . Finally, v _cmp and v _distance are concatenated and input into M _group to generate the model output v _encode . Through this process, M _encode can realize the end-to-end capacity to encode the information of individual plots, and the resulting encoding can be further used to establish an SLF model.

Through M _encode , all plots in P _known can be processed to obtain the encoding results V _known = {v ₁ , v ₂, … , v _n }. For plot p _x , for which an SLF model should be obtained, the corresponding image patch I _x is then cut from Z in accordance with its area attribute, and p _x .area and I _x are input into M _encode to obtain v _encode . For two encoding vectors, the distance between them is as follows: d i s t a n c e ( v 1 , v 2 ) = l 1 n o r m ( v 1 − v 2 ) . (8)

Based on Eq. 8, the m nearest vectors in V _known can be identified using the k-NN algorithm; thus, the most similar plots in known, that is, similar = {p ₁ , p ₂ , … , p _m }, can be identified. The average SLD, as denoted by averageSLD, is calculated as follows: a v e r a g e S L D ( S i m i l a r ) = ∑ i m p i . S L D m . (9)

Accordingly, averageSLD represents the variation trend and fluctuation range of the electric load data of p _x . Although insufficient historical data are available for p _x , these data can provide the range of load changes within a period. Thereafter, based on the load change interval INT of p _x .history, long-term historical data can be estimated by calculating longhistory = INT × averageSLD, which can further support the development of M _forecast .

After all the above-mentioned steps, we finally obtain an end-to-end deep neural network model M _encode that can be used as a bridge from ground-building features to electrical load characteristics. Moreover, the remote sensing image data and location information of a plot are input into M _encode , which then produces high-level encoding corresponding to the image. This code can be used to identify the most similar plots with rich historical electrical load data and subsequently to obtain the average SLD. For the current plot, the average SLD can supplement the shortcomings of the insufficient data and obtain forecasting M _forecast , which is more stable and accurate than using the historical data of the plot. Finally, electrical power forecasting for developing regions or regions lacking historical load data could be realized.

We adopted Python to implement the SELF-HE method and all methods considered for comparison, and TensorFlow was used to develop the deep neural network models in SELF-HE. All experiments were performed on a computer with an Intel Core i9-9900K CPU, a GeForce RTX 2080 11 GB graphics processing unit (GPU), and 64 GB of memory.

The target area in this study corresponds to the northern area of the city of Changchun, Jilin Province, China. This area is a rapidly growing area of Changchun, and methods such as SELF-HE are required to provide decision support for SLF. This area is shown in Figure 6.

The target area and SLF Zone Z marked in Figure 6 contained various commercial, residential, educational, and manufacturing areas, all of which exhibited significantly different electrical load characteristics. The high-resolution remote sensing images of the study area were not obtained from a single remote sensing satellite sensor. In particular, we used the ArcGIS Living Atlas “World Image” web map service as the data source. For Zone Z in the study area, this service can provide detailed remote sensing image information from Level 0 to 23. We selected the 17th level, at which the resolution was 1.19 m per pixel, which was sufficient to distinguish the structural characteristics of ground objects and could support the process of SELF-HE. Different regions in Z exhibited typical differences in structure and morphology, and these differences were used as critical clues to identify plots with similar SLDs.

For the electrical load data, we selected 640 plots with dimensions of 300 × 300 m and collected historical electric load data from ammeters in the corresponding plots. The plots are shown in Figure 7.

As shown in Figure 7, these plots can be divided into three categories, the details of which are listed below.

To evaluate the load forecasting capacity of SELF-HE, the following methods were considered for comparison in this study.

The SELF-HE method comprises multiple steps. The SLD-E algorithm in Step 2 performs cluster encoding based on SLD and spatial distance, and typical clustering results are shown in Figure 8.

Figure 8 presents several examples of the typical clustering results of the SLD-E algorithm. The clustering results were obtained using SLD and spatial distance as criteria (the image content was not considered in the clustering process). However, as can be seen from the resulting clusters, plots in the same cluster exhibit similar spatial characteristics. Cluster 1 consists of residential areas that are highly similar in structural scale (size) and arrangement, and the patterns of electricity consumption in these areas are highly similar. For Cluster 2, although the sizes and directions are different, the plots correspond to the production workshops of small enterprises and exhibit similar compositions of content. The plots in Cluster 3 are from commercial areas and display similar patterns of arrangement. For the plots in Cluster 4, although their contents are not the same, they are all close to the main road. As can be seen from the results, the approximation of the SLD is correlated with the spatial characteristics of the remote sensing images. However, the mode of this correlation is not unique, and the four clusters correspond to four different correlation modes. Therefore, pure image approximation cannot describe all relevant relationships, and a more effective method, such as the GAMC algorithm of SELF-HE, is required to describe these relationships.

The average error rates of the five methods are shown in Table 1. As can be seen from this table, F-History does not use the SLD source dataset and relies only on the historical data in the test set to build a forecasting model. Moreover, given that Test set 1 contains 4 years of historical data, F-History reaches its optimal forecasting accuracy using this test set. The accuracy of this method rapidly declines as the amount of available historical data decreases, and the poorest result is obtained for Test set 3, with an average error rate of 17.12%. It can be seen that a reduction in the amount of historical data has a significant influence on the forecasting model. For Nearest-SLD and Neighbor-SLD, the spatial distance was used as the criterion for selecting the SLD information from P _known . For Test sets 1 and 2, these methods yield lower accuracies than F-History. However, for Test set 3, the results are superior to those of F-History, indicating that Nearest-SLD and Neighbor-SLD have positive influences on the load forecasting when the available historical data are limited. Similar-Structure used the similarity of image characteristics to identify plots with similar SLDs in known, and the trend of the results obtained using this method is similar to those of Nearest-SLD and Neighbor-SLD, with an accuracy slightly lower than that of Neighbor-SLD. Among all the methods, SELF-HE achieves the best results. For Test set 1, the average error rate of 4.23% is the lowest result obtained; for Test set 3, with only 1 year of historical load data, the average error rate of 8.14% is superior to those of the other methods. A comparison of the performance of the five methods is presented in Figure 9.

As shown in Figure 9, for all data sets, the SELF-HE method achieves the lowest average error rate, and Neighbor-SLD is superior to the other three methods. Moreover, F-History has the least significant influence on the test set with the smallest amount of data. Test set 1 contains 5 years of historical data, and the electricity consumption behavior of the corresponding plots is relatively stable. Based on Test set 1, using 1 year (2019), 2 years (2018 and 2019), 3 years (2017–2019), and 4 years (2016–2019) of historical data, the average error rates achieved by the five methods are listed in Table 2.

The corresponding trends of the average error rate with respect to the historical data volume shown in Table 2 are illustrated in Figure 10.

Given that the plots in Test set 1 (from the older urban areas) have the longest available history, their electricity consumption characteristics are more stable than those for the other test sets. Consequently, the 1-year results in Table 2 are superior to the results for Test set 3 in Table 1. As shown in Table 1 and Figure 10, as the amount of historical data increases, the average error rates of all the methods decrease. The decreasing trend of F-History is the most significant, indicating that this method is highly dependent on the amount of historical data. Moreover, F-History requires more historical data than other methods to develop the forecasting model and demonstrates improved performance when there are abundant historical data, and the electricity consumption behavior for the corresponding plots is stable. However, for newly developed areas in a city, sufficient historical data were not available, and the electricity consumption behavior of users corresponding to those plots was not sufficiently stable (e.g., several companies had not started running their machines). These problems prevented F-History from achieving high performance in the SLF. As observed, Nearest-SLD exhibits an unstable trend from three to 4 years, with an increase in the amount of historical data, leading to a slight increase in the average error rate; whereas the trends of Neighbor-SLD and Similar-Structure are more stable. Since the Z is located in a rapid development region of city, many plots’ corresponding supporting facilities have been built in just recent years, and some companies have undergone industrial transformation and renovation; this may lead to huge differences in the characteristics of historical data that are far apart in time. At this time, if a larger amount of data is introduced from a single neighbor (whether in distance, distribution, or structure), it may lead to the introduction of too much heterogeneity information and reduce the accuracy; so errors increase for Nearest-SLD, Neighbor-SLD, and Similar-Structure in Figure 10. Among all the methods, the trend of SELF-HE is the most gradual, and the results obtained using only 2 years of historical data are similar to the results of the other methods using 4 years of data.

Using SLDs to supplement the lack of historical data can improve the performance of an SLF model. The Nearest-SLD algorithm uses a known plot from among the neighbors of the plot of interest as the source of the SLD information. This strategy can achieve higher performance than F-History; however, due to the extensive distribution of boundaries between different land use areas in cities, the use of the plot in the nearest position may cause an increase in error. Hence, Nearest-SLD is not stable. To address this shortcoming, Neighbor-SLD uses multiple known plots from among the neighbors of the plot of interest as the SLD source, achieving higher and more stable performance than Nearest-SLD. The concept of Similar-Structure is consistent with that of SELF-HE. In particular, the similarity between the features of remote sensing images is used as the standard for identifying plots with similar SLDs. However, as can be seen from Figure 8, the spatial characteristics defining an SLD cluster do not necessarily follow a uniform rule; as distinct spatial arrangements, adjoining relationships, and content compositions may all be commonalities that define SLD clusters. Given that Similar-Structure uses only the vector distance based on v _cmp as the standard for assessing similarity, it may be suitable only for cases analogous to that of Cluster 1 in Figure 8, and it may not readily adapt to other cases. Similar-Structure exhibits no significant advantage over Nearest-SLD or Neighbor-SLD. Among all the methods, the trend of SELF-HE is the most gradual, and the results obtained using only 2 years of historical data are similar to those of the other methods using 4 years of historical data.

To analyze comprehensively the processes by which the SLF is obtained using each method, we selected a typical plot in the northeast corner of Z as the unknown plot P _x ; the process of each algorithm is shown in Figure 11.

As shown in Figure 11A, there are two types of plots in this area. The plots indicated in blue are from the training set; their SLD is stable and contains more historical data. The plots indicated in yellow are from the testing set, and they contain less historical data. Given that P _x is an unknown plot from the testing set, additional SLD data may be required to facilitate its SLF calculation. The characteristics of the five methods are shown in Figure 11B, and the error rates of the five methods on P _x are listed in Table 3.

For F-History, as it only uses limited historical data for SLF calculations, the plots of the neighbors do not participate in the SLF calculation. Moreover, due to the lack of historical data, the SLF model generated by F-History is readily fitted with specific features, which reduces its prediction accuracy. The error rate of F-History is 15.20%. For Nearest-SLD, there are four plots closest to P _x (east, south, west, and north). Given that the north and east are unknown plots, only west or east can be selected. The Nearest-SLD algorithm finally selected the south plot as the source of SLD. Although this selection mitigates the lack of historical data in F-History, this plot is located at the junction of residential and industrial areas, and its load consumption characteristic is significantly different from that of P _x , leading to the introduction of heterogeneous SLD. Thus, the forecast results obtained are lower than those of F-History, and its error rate is the highest, at 21.24%. The Nearest-SLD algorithm uses SLD to identify similar plots. As can be seen from Figure 11B, Nearest-SLD identified a plot across the main road. Although this plot can help P _x obtain the SLD and improve the accuracy of the forecast; in urban environments, several main roads divide different administrative regions, functional regions, enterprises, or residential structures in the city, which results in different policies and groups that are core driving forces of power consumption. The Nearest-SLD error rate is 13.75%. Similar-Structure selected a plot with a similar building structure and composition content near P _x . The SLD provided by this plot causes the error rate of Similar-Structure to reach 9.56%, indicating that it is feasible to use the structure of the ground building as an index to obtain the SLD. However, this method exhibits several problems. In particular, for this plot in the rapid urban development area, the electricity consumption characteristics are not sufficiently stable; thus, further improvement is required. Moreover, SELF-HE uses M _group to assign v _encode to all plots and then selects the 10 most similar plots. Based on the average SLD of these plots, the optimal result obtained by SELF-HE demonstrates an error rate of 6.79%. This result indicates that the SELF-HE electric load forecasting based on the high-level encoding of high-resolution remote sensing images is more effective than those of the other methods. Moreover, SELF-HE achieves the optimal results among the five methods, indicating that it can extract key characteristics for SLD clustering in remote sensing images and acquire SLDs that are highly similar to the SLD of a plot of interest, enabling more accurate and stable forecasting results to be obtained. The corresponding results reveal that SELF-HE can foster connections between different remote sensing image characteristics (e.g., the specific characteristics described in Figure 8) and SLD selection, which can serve as a new data source for SLF.

To more fully evaluate the spatial forecasting ability of SELF-HE under different scenarios, we introduce more regions for comparison, and the characteristics of these regions are as follows.

The separate strategy of plots has a considerable impact on SELF-HE. Smaller plots will make the SLF results more capable of reflecting the characteristics of urban regions, but it will also increase the fluctuation of the load data in the boundaries between different regions and reduce the SLF accuracy. Meanwhile, larger plots will introduce more objects and make the load data more stable, but they will confuse the content of different regions and reduce the value of the SLF result. In this study, the plot size was manually specified; this strategy may not yield the optimal solutions and may cause a longer trial-and-error experimental process. In future research, we plan to introduce more urban data sets and plot sizes to explore the relationships between different urban areas and a variety plot sizes and then explore ways to optimize the plot size automatically to make SELF-HE more efficient.