Monthly Urban Electricity Power Consumption Prediction Using Nighttime Light Remote Sensing: A Case Study of the Yangtze River Delta Urban Agglomeration

Abstract

Urban electricity power consumption (EPC) prediction plays a crucial role in urban management and sustainable development. Nighttime light (NTL) remote sensing imagery has demonstrated significant potential in estimating urban EPC due to its strong correlation with human activities and energy use. However, most existing models focus on annual-scale estimations, limiting their ability to capture month-scale EPC. To address this limitation, a novel monthly EPC prediction model that incorporates monthly average temperature, and the interaction between NTL data and temperature was proposed in this study. The proposed method was applied to cities within the Yangtze River Delta (YRD) urban agglomeration, and was validated using datasets constructed from NPP/VIIRS and SDGSAT-1 satellite imageries, respectively. For the NPP/VIIRS dataset, the proposed method achieved a Mean Absolute Relative Error (MARE) of 7.96% during the training phase (2017–2022) and of 10.38% during the prediction phase (2023), outperforming the comparative methods. Monthly EPC spatial distribution maps from VPP/VIIRS data were generated, which not only reflect the spatial patterns of EPC but also clearly illustrate the temporal evolution of EPC at the spatial level. Annual EPC estimates also showed superior accuracy compared to three comparative methods, achieving a MARE of 7.13%. For the SDGSAT-1 dataset, leave-one-out cross-validation confirmed the robustness of the model, and high-resolution (40 m) monthly EPC maps were generated, enabling the identification of power consumption zones and their spatial characteristics. The proposed method provides a timely and accurate means for capturing monthly EPC dynamics, effectively supporting the dynamic monitoring of urban EPC at the monthly scale in the YRD urban agglomeration.

1. Introduction

Electricity is a fundamental determinant of the quality of life in modern society, with its consumption showing a significant upward trend. This growth is not only closely linked to climate issues such as global warming but also has profound implications for the environment and society. The United Nations particularly emphasizes the importance of energy in its Sustainable Development Goals (SDGs), especially in SDG7, which aims to ensure access to affordable, reliable, sustainable, and modern energy for all. Therefore, accurately estimating electricity power consumption (EPC) and obtaining information about its spatial distribution is crucial for identifying the characteristics and requirements of energy consumption in different regions. It also provides solid data support for formulating scientific and reasonable sustainable development strategies and energy management policies.

EPC refers to the total amount of electricity used by residential and industrial sectors within a specific region over a given period of time. It serves as a fundamental indicator for quantitatively assessing the regional status of electricity consumption [1].However, current urban EPC data are mainly collected and reported based on administrative units, leading to relatively delayed timeliness and certain data gaps. As a result, some areas may even lack EPC statistical data entirely. Moreover, these data are unable to reflect the spatial distribution characteristics of EPC, thus failing to intuitively reflect the differences in EPC among different regions.

Nighttime light remote sensing satellites offer advantages such as regular revisit cycles, fine-resolution large-area imaging, and long-term time series data acquisition [2]. The nighttime light imagery obtained from these satellites can reflect human activities through artificial lighting [3], thereby playing a significant role in various applications including EPC estimation [4,5,6,7], electricity access assessment [8], urbanization monitoring [9,10,11], GDP estimation [12,13,14], ecological evaluation [15], population estimation [16,17,18], and disaster assessment [19,20].

In recent years, with the advancement of nighttime light remote sensing technology, the variety and availability of nighttime light remote sensing data products have significantly increased. Representative data sources include the DMSP/OLS from the United States Defense Meteorological Satellite Program [21], NPP/VIIRS [22], the Luojia-1 satellite (Luojia-01) [23], and the Sustainable Development Goals Satellite-1 (SDGSAT-1) nighttime light imagery [24]. Although early DMSP satellites provided valuable nighttime light data, their relatively low spatial resolution and signal saturation limited their applicability. The Visible Infrared Imaging Radiometer Suite (VIIRS) aboard on the Suomi National Polar-orbiting Partnership (NPP) satellite offers nighttime light data with higher spatial resolution, overcoming the limitations of DMSP/OLS data and significantly expanding the potential applications of nighttime light remote sensing. Furthermore, emerging remote sensing satellites such as Luojia-01 and SDGSAT-1 have further enhanced the utility and scope of nighttime light data [25,26,27,28,29,30].

Nightlight remote sensing can reflect the density and usage intensity of lighting infrastructure, providing a basis for spatializing EPC due to the correlation between nighttime light and actual electricity consumption [31]. Research on modeling and predicting EPC using nighttime light remote sensing data dates back to the 1980s. Welch et al. developed a multivariate model based on NTL, population, and built-up area to estimate EPC of 18 cities in the eastern United States, revealing a significant correlation between NTL and EPC [32]. Since then, numerous scholars conducted studies estimating EPC based on nightlight remote sensing data from DMSP/OLS and NPP/VIIRS, with research scales primarily covering national, regional, and urban levels.

At the national scale, existing studies on EPC prediction using nighttime light data mainly focus on Asia, America, and Africa. Shi et al. applied an improved invariant region method to inter-calibrate global DMSP-OLS nighttime stable light data from 1992 to 2013, and modeled the global EPC at a 1 km resolution, revealing that spatio-temporal changes in EPC were primarily concentrated in Europe, North America, and Asia [33]. Letu et al. proposed a saturation correction method for DMSP/OLS imagery and applied it to EPC simulations in ten Asian countries including China and Japan. The results demonstrated that the coefficient of determination for the linear regression between EPC and nighttime light data exceeded 0.6 [34]. Min et al. analyzed nightlight imagery from rural areas in Senegal and Mali, confirming the effectiveness of nighttime light remote sensing in assessing global electrification rates [35]. Gao et al. developed a denoising algorithm for nighttime light imagery in cloudy regions, using Cambodia as a case study, and the method was employed to extract the spatial distribution patterns of annual EPC in Cambodia from 2012 to 2019 [36]. Hu et al. developed a continuous 1992–2019 dataset by harmonizing DMSP-OLS and NPP-VIIRS observations, and utilized a locally adaptive selection approach to identify country-specific optimal modeling strategies to estimate EPC in different countries [37]. Zhong et al. integrated multi-source nighttime light data (DMSP-OLS and NPP-VIIRS) with GDP and other geographic data to develop an EPC estimation model for Belt and Road countries (2000–2019), followed by spatio-temporal pattern analysis [38].

At the regional scale, Guo et al. applied NPP-VIIRS data and GBRT modeling to predict EPC (2013–2022) in three Chinese provinces, revealing distribution characteristics of EPC across pixel-level to city-level scales [39]. Zhao et al. [35] incorporated demographic factors into their EPC modeling framework, developing a provincial-scale regression model to estimate EPC across Chinese provinces, and their analysis revealed a significant correlation between nighttime light intensity and EPC in highly urbanized regions [40]. Using 1992–2013 DMSP/OLS data, Xiao et al. implemented a GTWR model for spatio-temporal estimation of China’s provincial EPC [41]. By establishing a regression model linking calibrated DMSP-OLS data with provincial EPC statistical records, Xie et al. generated time-series EPC estimates and revealed the characteristics of EPC spatio-temporal patterns across China [42]. Lin et al. examined monthly EPC-NTL relationships in 14 southern Chinese provinces through comparative regression modeling of NPP/VIIRS data [43]. Previous research has predominantly concentrated on global or regional-scale EPC modeling, substantially improving the capabilities in this domain. These studies have made notable advancements in data fusion techniques, modeling methodologies, and regional applications. Despite these contributions, most existing models are limited to an annual time scale, thereby restricting their temporal resolution and limiting their utility for more detailed, fine-scale temporal analyses.

For EPC prediction at city scale, researchers account for multifactorial influences by either integrating multi-source data into models or classifying cities before modeling. Lu et al. aggregated multi-source remote sensing data, including nighttime light (NTL), enhanced vegetation index (EVI), and land surface temperature (LST) at the municipal scale, and used a random forest (RF) model to estimate city-level EPC in China from 2000 to 2020 [44]. Wang et al. utilized 2018 NPP-VIIRS nighttime light data, EPC statistical data from Chinese prefecture-level cities, and 1 km resolution land use data to model EPC using a multiscale geographically weighted regression approach [45].

Different cities have different industrial structures and other characteristics. In order to improve the accuracy of urban EPC prediction, scholars first classify cities according to their attributes, and then establish EPC models for cities in different categories according to the classified results. Classification methods such as the Boston Matrix, K-Means clustering, and modified general matrix have been widely adopted to enhance modeling accuracy. For instance, Li et al. applied the Boston Matrix to classify 182 Chinese cities into four distinct groups based on their developmental characteristics, and then constructed category-specific linear models using NTL data extracted from NPP/VIIRS data [46]. Li et al. classified 198 Chinese cities into industrial, service, and technology and education categories according to cities’ sectoral employment data, and then established category-specific regression models between NTL and EPC [47]. Cheng et al. took Shenzhen as the study area, and combined night light data, high-resolution satellite images, population data, and house price data to extract socio-economic, population density, and landscape characteristics. They constructed an EPC estimation model based on random forest regression model, and analyzed the spatio-temporal change trend of EPC in Shenzhen from 2013 to 2019 [48]. In predicting EPC at the city scale, previous studies have commonly adopted multi-source remote sensing data or city type modeling to improve estimation accuracy. However, most existing studies focus on annual EPC estimation, with limited attention given to monthly dynamic modeling that offers higher temporal resolution. Furthermore, although climatic factors such as temperature have a significant influence on electricity consumption, their role in EPC modeling remains underexplored, which limits the ability of current models to capture seasonal variations in electricity usage patterns.

Overall, significant progress has been made in EPC prediction based on nightlight remote sensing. However, most previous studies focusing on EPC prediction using nightlight remote sensing have primarily concentrated on annual timescales and spatial scales at the national, provincial, or urban level, with few studies assessing monthly urban EPC. Since EPC of cities exhibits seasonal fluctuations throughout the year, using annual timescales overlooks the variations in electricity usage within a year. This study proposed a method to predict monthly electricity consumption for city clusters based on nightlight remote sensing data. The proposed approach would enhance our understanding of energy use patterns and their dynamic changes in cities. The main contributions of this study are as follows:

(1)

A novel method for predicting monthly urban EPC was proposed. The interaction between temperature and NTL, as well as the nonlinear impact of temperature on EPC were explicitly incorporated in the proposed method. This methodological innovation enables accurate temporal and spatial variations in monthly urban EPC.

(2)

The proposed method was validated across different types of NTL remote sensing data, which were constructed from NPP/VIIRS data and SDGSAT-1. Based on NPP/VIIRS satellite imagery, the model successfully generated monthly EPC distribution maps at a spatial resolution of 400 m. Moreover, annual EPC estimates derived from the monthly predictions achieved a Mean Absolute Relative Error (MARE) of 7.13%, demonstrating the method’s effectiveness in supporting both monthly and annual EPC monitoring.

(3)

Moreover, the proposed method was further validated using the SDGSAT-1 satellite dataset, demonstrating its robustness and generalizability across diverse sensor platforms. Notably, under identical evaluation conditions, the results of SDGSAT-1 dataset exhibited higher overall accuracy compared to those obtained from the NPP/VIIRS data. This enabled the generation of high-resolution (40 m) monthly EPC spatial distribution maps, facilitating the detailed identification and analysis of EPC zones.

This paper is organized into five chapters: Section 1 introduces the research background, significance, and literature review; Section 2 describes the data and methodology, including the study area’s spatial scope, acquisition and preprocessing procedures for two nighttime light remote sensing datasets, i.e., NPP/VIIRS and SDGSAT-1, sources of auxiliary data introduction, and overall explanation of the proposed monthly EPC prediction method; Section 3 presents experimental results on both datasets, and confirms that the EPC spatial distribution mapping based on NPP/VIIRS images and SDGSAT-1 images are completed, both of which verifies the effectiveness and applicability of the proposed method; Section 4 discusses the strengths, limitations, and future research directions of the proposed method; and Section 5 summarizes the key findings and conclusions.

2. Materials and Methods

2.1. Study Area and Basic Data

2.1.1. Study Area

The Yangtze River Delta (YRD) urban agglomeration, situated along China’s eastern coast, represents one of the world’s most rapidly developing economic and urbanization zones. Comprising Shanghai Municipality and three provinces (Jiangsu, Zhejiang, and Anhui), the study area is illustrated in Figure 1 below. Rapid industrialization and urbanization have been observed in this region. The region’s electricity consumption patterns serve as a key indicator of its socioeconomic vitality. As of 2024, the area spans 225,000 km², generates a GDP of 36.2 trillion yuan, and sustains a permanent population of over 238 million people, showing its dynamic economic activities. This massive demographic scale significantly elevates residential and commercial electricity needs, making it an ideal research laboratory for power consumption studies. Furthermore, the availability of relatively complete monthly EPC statistical data across these cities provides exceptional advantages for developing nighttime light remote sensing-based analysis and electricity consumption prediction models. Therefore, cities within the YRD urban agglomeration were selected as the experimental region for developing the monthly EPC model.

2.1.2. EPC and Other Related Basic Data

Monthly statistics EPC data for 2017–2023 used in this study were obtained from statistical yearbooks. Monthly average temperature data for these cities during 2017–2023 were acquired from 1 km monthly average temperature dataset for China [49,50,51] (available at https://data.tpdc.ac.cn/en/data/71ab4677-b66c-4fd1-a004-b2a541c4d5bf (accessed on 28 June 2025)). After clipping the original temperature data to match the administrative boundaries, the raster values within each city boundary were spatially averaged to generate monthly mean temperature series for each city. Administrative boundary data were provided by National Geomatics Center of China. It should be noted that EPC statistical data are not available for every month in each city. The available amount of EPC statistical data for each city is summarized in the following table. Since the EPC data from 2017 to 2022 were used to train the model based on the NPP/VIIRS dataset, and 2023 was reserved for validation, the table separately presents the availability of EPC statistical data for the periods 2017–2022 and 2023. Since Shanghai did not publish monthly EPC data from 2017 to 2023, so it is not included in

Table 1. EPC statistical information for cities in the YRD urban agglomeration (in 104 kWh).

City	2017–2022	2023	City	2017–2022	2023	City	2017–2022	2023
Chizhou	72	12	Hangzhou	63	10	Yancheng	30	10
Tongling	72	12	Suzhou	48	10	Changzhou	68	12
Hefei	72	7	Zhoushan	20	12	Jinhua	34	12
Jiaxing	72	12	Zhenjiang	64	10	Wenzhou	33	10
Chuzhou	72	12	Huzhou	58	10	Nantong	10	0
Wuhu	72	12	Yangzhou	40	10	Wuxi	17	12
Ma’anshan	72	12	Taizhou 1	10	0	Nanjing	30	10
Xuancheng	72	12	Taizhou 2	56	12	Ningbo	54	12
Anqing	72	7	Shaoxing	21	10

Taizhou ¹ refers to Taizhou city in Jiangsu province. Taizhou ² refers to Taizhou city in Zhejiang province.

.

2.2. NPP/VIIRS Dataset

2.2.1. NPP/VIIRS Data

The 2017–2023 global monthly synthetic NPP/VIIRS data used in this study are downloaded from the National Oceanic and Atmospheric Administration, Earth Observation Group data platform (https://eogdata.mines.edu/nighttime_light/, accessed on 28 June 2025). The spatial resolution of the NPP/VIIRS low-light images is about 400 m. Since the monthly cloud-free composite data from NPP/VIIRS have not undergone filtering and therefore contain some noise, Prophet time series anomaly detection was used to recognize anomalies [52], and a neighboring-month substitution method was used to repair anomalies [43].

2.2.2. NPP/VIIRS Images Outlier Processing and NTL Extraction

The monthly composite NPP/VIIRS nighttime light data in the Northern Hemisphere is susceptible to snow cover interference during winter months and vegetation/cloud contamination in summer, potentially introducing outliers that influence the accuracy of NTL extraction and subsequent EPC estimation. It can be observed that there are distinct periodic and seasonal fluctuation patterns in urban monthly NTL time series from January to December. Consequently, this study considered monthly NTL as month-varying time series data. To address data quality issues in NTL time series, Prophet method was introduced for outlier detection [52].

Prophet is a machine learning forecasting framework based on time series decomposition principles. Its core modeling approach involves the linear superposition of several independent components, including nonlinear trend terms, yearly/weekly/daily seasonal components, and holiday effects, as shown in Equation (1). This framework can flexibly adapt to various time series characteristics and is robust to missing data and trend changes. Therefore, it is suitable for identifying anomalies in monthly city-level NTL data, which exhibits periodicity and temporal patterns.

$$y\left(t\right)=\mathrm{g}\left(\mathrm{t}\right)+\mathrm{s}\left(\mathrm{t}\right)+\mathrm{h}\left(\mathrm{t}\right)+{\mathsf{ϵ}}_{\mathrm{t}}$$

(1)

$y\left(t\right)$represents the observed value of the time series at time t; $\mathrm{g}\left(\mathrm{t}\right)$ is the trend term, which models the non-periodic changes in the time series data; $\mathrm{s}\left(\mathrm{t}\right)$ is the seasonal component; $\mathrm{h}\left(\mathrm{t}\right)$ is the holiday component, and ${\mathsf{ϵ}}_{\mathrm{t}}$ is the random error.

For identified monthly NTL anomalies, a neighboring-month substitution method was used to replace the detected anomalous NTL values. This approach is primarily motivated by the observation that a region’s economic activity and population dynamics typically exhibit gradual transitions between consecutive months, suggesting that nighttime light values should demonstrate smooth, incremental variations across adjacent monthly periods. The formula for the neighboring-month substitution method is given in Equation (2). Specifically, the process involves calculating the average pixel values from the nighttime light images of the preceding and following months and using this average to replace the pixel values at the corresponding locations in images at an anomalous month. After calibrating NPP/VIIRS imageries, monthly NTL data were extracted using Equation (3). Finally, to construct the NPP/VIIRS dataset for urban EPC estimation, these NTL data were then combined with the corresponding monthly EPC statistical data published for each city, and monthly average temperature.

$${DN}_{i,t}=({DN}_{i,t-1}+{DN}_{i,t+1})/2$$

(2)

${DN}_{i,t}$ represents the ith pixel value of a city in month t. ${DN}_{i,t-1}$ and ${DN}_{i,t+1}$ denote the ith pixel values for the same city in the month before and after month t, respectively.

$${\mathrm{N}\mathrm{T}\mathrm{L}}_j={\sum }_i^n{DN}_i$$

(3)

${\mathrm{N}\mathrm{T}\mathrm{L}}_j$ represents the total nighttime light (NTL) of the jth city, ${DN}_i$ denotes the pixel value at the ith location within the area of the jth city, and n is the total number of pixels within the jth city’s area.

2.3. SDGSAT-1 Dataset

SDGSAT-1 nightlight imageries used in this study was obtained from the International Research Center of Big Data for Sustainable Development Goals (CBAS). The SDGSAT-1 satellite was successfully launched into orbit on 5 November 2021, with the mission to provide comprehensive spatial observation datasets supporting the United Nations 2030 Agenda for Sustainable Development [24]. SDGSAT-1 carries three scientific payload systems: Glimmer Imager for Urban areas, Multispectral Imager, and Thermal Infrared Spectrometer. Specifically, the GIU payload is dedicated to monitoring nighttime light across urban and rural areas at varying intensity levels.

Three 40 m resolution color glimmer bands, i.e., red, green, and blue bands from SDGSAT-1 were used in this study. This configuration capitalizes on SDGSAT-1’s advantages in spectral coverage and spatial detail representation, thereby enhancing the precision of nighttime light information extraction. Due to the influence of clouds and other factors on the SDGSAT-1 nighttime light imagery, high-quality images that fully cover the urban areas were selected through visual interpretation. The selected SDGSAT-1 images and their corresponding months’ information are given in the following

Table 2. SDGSAT-1 dataset nightlight image time.

City	Month	City	Month
Yangzhou	October 2023	Nanjing	March 2023
Zhenjiang	October 2023	Tongling	April 2023
Changzhou	January 2023	Tongling	November 2023
Jiaxing	February 2023	Wuxi	January 2023
Jiaxing	September 202309	Hefei	January 2023

.

Furthermore, a maximum value composition method was applied to generate single-band nighttime light imagery for extracting dominant light source contributions. The specific procedure is given in Equation (4), and it involves the following: (1) pixel-by-pixel analysis of the three RGB channels, and (2) the extraction of the maximum value across all three channels for each pixel to construct a composite single-band image V(x,y). Finally, the NTL values were extracted using Equation (3). Similar to the construction process of the NPP/VIIRS dataset, the extracted NTL values were combined with the monthly EPC statistics and average temperature data of the corresponding cities to form the SDGSAT-1 dataset. Additionally, to explore the advantages of high-resolution nighttime light imagery in estimating EPC, the NTL values from NPP/VIIRS images for the same cities and months in the SDGSAT-1 dataset were also extracted for comparative analysis.

$$\mathrm{V}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{m}\mathrm{a}\mathrm{x}[\mathrm{R}\left(\mathrm{x},\mathrm{y}\right),\mathrm{G}\left(\mathrm{x},\mathrm{y}\right),\mathrm{B}\left(\mathrm{x},\mathrm{y}\right)]$$

(4)

$\mathrm{V}\left(\mathrm{x},\mathrm{y}\right)$represents the maximum value composition value from the SDGSAT-1 imagery used for EPC prediction, where $\left(\mathrm{x},\mathrm{y}\right)$ denotes the position of the pixel in the image, $\mathrm{R}\left(\mathrm{x},\mathrm{y}\right),\mathrm{G}\left(\mathrm{x},\mathrm{y}\right)$, and $\mathrm{B}\left(\mathrm{x},\mathrm{y}\right)$ represent the pixel values of the red, green, and blue bands at the position $\left(\mathrm{x},\mathrm{y}\right)$, respectively.

2.4. Method

Urban EPC exhibits distinct seasonal patterns. Existing research has demonstrated a strong correlation between urban EPC and NTL data. At the monthly timescale, urban monthly average temperature not only reflects seasonal variations but also captures the cyclical fluctuations in electricity consumption. Specifically, temperature changes associated with seasonal transitions directly affect heating and cooling demands in both residential and commercial sectors, consequently leading to corresponding adjustments in electricity consumption patterns. To more accurately characterize the complex intra-annual variations in EPC, this study incorporates monthly average temperature data as a key environmental variable, enabling better understanding of EPC seasonality and revealing its underlying influence mechanisms. The overall technique roadmap is given in Figure 2.

The overall methodology consists of four main steps. Step 1 is data collection. NTL remote sensing imageries and auxiliary data were collected. Step 2 is dataset construction. Two datasets were constructed using different sources of NTL imagery. For the NPP/VIIRS dataset, the Prophet algorithm was applied to detect anomalous values in monthly observations, and outliers were replaced using the neighboring-month substitution method. For the SDGSAT-1 dataset, high-quality images were selected, and RGB maximum value composites were used to enhance spatial representation and reduce noise. Step 3 is EPC prediction model establishment. A monthly scale EPC prediction model was established by incorporating nonlinear effects of temperature, as well as interaction between NTL and temperature, and the proposed method was validated in the two constructed datasets. Step 4 is spatial extraction and the analysis of EPC information. Using the established EPC prediction model, spatial distribution maps of EPC were generated at the city level. Temporal dynamics and spatial patterns of urban EPC were further analyzed.

2.4.1. Proposed Method

The proposed method accounts for NTL, monthly average temperature, the associated nonlinear temperature effects, and the interaction between NTL and temperature, as shown in Equation (5). Despite its simple form, the variable involved in the proposed model design accounts for multiple critical factors: (1) baseline contribution of NTL to EPC, (2) the nonlinear temperature effects on EPC, and (3) interaction effects between temperature and NTL. Temperature has a significant impact on EPC. Specifically, temperature directly affects heating and cooling demands in residential and commercial buildings. Seasonal variations lead to increased usage frequency and intensity of air conditioning systems during periods of cold or heat. Moreover, many industrial processes require specific environmental temperatures, so changes in ambient temperature may also lead to fluctuations in EPC. Given the potential nonlinearity in the relationship between temperature and EPC, the proposed model also incorporated a quadratic term for temperature to better capture this complex effect.

The proposed method includes five parameters to be estimated, namely a, b, c, d, and e. Hereinafter, the proposed method is referred to as the five-parameter model for brevity. The proposed modeling framework provided enhanced capability to represent the dynamic characteristics of urban monthly patterns of EPC.

$${\mathrm{EPC}}_{\mathrm{i},\mathrm{t}}=\mathrm{a} \times { \mathrm{NTL}}_{\mathrm{i},\mathrm{t}}+\mathrm{b}\times {\mathrm{temp}}_{\mathrm{i},\mathrm{t}}+\mathrm{c} \times {\mathrm{NTL}}_{\mathrm{i},\mathrm{t}} \times { \mathrm{temp}}_{i,t}+\mathrm{d} \times {\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}}_{i,t}^2+\mathrm{e}$$

(5)

${\mathrm{EPC}}_{\mathrm{i},\mathrm{t}}$ represents the EPC of the ith city at time t. a, b, c, d, and e represent the regression coefficients and constant terms of the model. ${\mathrm{NTL}}_{\mathrm{i},\mathrm{t}}$ represents the NTL data of the ith city at time t, and ${\mathrm{temp}}_{\mathrm{i},\mathrm{t}}$denotes the monthly average temperature of the ith city at time t.

2.4.2. Comparison Methods

Three contrastive approaches were adopted to validate the effectiveness of the proposed method. Among them, Equations (6) and (7) serve as two baseline regression models, and a random forest (RF) model constitutes the third comparative method [53]. Specifically, Equation (6) incorporates the NTL data, monthly average temperature, and their interaction, along with a constant term. Compared to Equation (5), it excludes the squared temperature term, aiming to evaluate the role of nonlinearity introduced by the squared temperature component. This model involves four parameters to be estimated, i.e., a₁, b₁, c₁, and d₁, and is simply referred to as the three-parameter model in the following. Equation (7) further simplifies the model structure by including only NTL, monthly average temperature, and a constant term, while omitting both the interaction of NTL data and temperature, and squared temperature terms. This allows for an assessment of the direct effects of these two variables on EPC. The model contains three parameters to be estimated—a₂, b₂, and c₂—and is referred to as the three-parameter model for brevity.

$${\mathrm{EPC}}_{\mathrm{i},\mathrm{t}}={\mathrm{a}}_1 \times { \mathrm{NTL}}_{\mathrm{i},\mathrm{t}}+{\mathrm{b}}_1\times {\mathrm{temp}}_{\mathrm{i},\mathrm{t}}+{\mathrm{c}}_1 \times {\mathrm{NTL}}_{\mathrm{i},\mathrm{t}} \times { \mathrm{temp}}_{i,t}+{\mathrm{d}}_1$$

(6)

a₁, b₁, c₁, and d₁ represent the regression coefficients and constant terms in the four-parameter model.

$${\mathrm{EPC}}_{\mathrm{i},\mathrm{t}}={\mathrm{a}}_2\times {\mathrm{NTL}}_{\mathrm{i},\mathrm{t}}+{\mathrm{b}}_2\times {\mathrm{temp}}_{\mathrm{i},\mathrm{t}}+{\mathrm{c}}_1$$

(7)

a₂, b₂, and c₂ represent the regression coefficients and constant terms in the three-parameter model.

The parameters in the three-parameter, four-parameter, and five-parameter models (i.e., Equations (5)–(7)) were estimated using the ordinary least squares method based on the training dataset. Given the theoretically positive relationship between NTL and EPC, non-negativity constraints (a > 0, c > 0, a₁ > 0, c₁ > 0) were imposed on the corresponding parameters in these model equations to prevent sign-reversal issues during estimation. This approach enhances the interpretability of the modeling results. The input features for the RF model included NTL, the interaction between NTL and temperature, monthly average temperature, and the squared temperature term. The hyperparameters of the RF model were optimized through five-fold cross-validation on the training set to achieve the best-performing configuration. Due to the small samples size of the SDGSAT-1 dataset, RF was employed as one of the comparative methods on the NPP/VIIRS dataset. After the training of models, the monthly average temperature and NTL data from the validation dataset were fed into Equations (5)–(7) and the trained RF model to predict the EPC of each city.

2.4.3. Experiment Settings

For the NPP/VIIRS dataset, given the availability of monthly EPC data as detailed in Table 1, models for 26 cities that had EPC statistical data from 2017 to 2022 were constructed. Model performance was assessed using training errors for each city. Additionally, predictions for 24 cities that had EPC statistical data available for 2023 were conducted to further evaluate the performance of the proposed method.

For the SDGSAT-1 dataset, due to the limited data amount, the leave-one-out cross-validation method was used in this study to handle the available SDGSAT data. Specifically, when constructing the monthly EPC model, each city’s data was selected once as the test set, while the remaining data points were used for training the model. The trained model was then used to predict the values for the withheld data point. This process was repeated for each city’s data, ensuring that every data point served as the test set exactly once. Ultimately, this resulted in a number of predictions equal to the number of available data points. By using this method, we aimed to maximize the accuracy of model evaluation given the limited data.

To evaluate model performance, three metrics were employed: Absolute Relative Error (ARE), Mean Absolute Relative Error (MARE), and Root Mean Square Error (RMSE). These complementary indicators provide multidimensional assessment of estimation accuracy by quantifying different aspects of deviation between predicted and actual values. ARE measures relative deviation for individual samples, as shown in Equation (8). MARE represents the average ARE across all samples, indicating overall prediction precision, as given in Equation (9). RMSE characterizes the magnitude of differences between predicted and observed values, as shown in Equation (10). This comprehensive evaluation framework enables systematic assessment of the proposed method’s performance in urban monthly EPC prediction.

$${ARE}_i=\left|{\displaystyle \frac{y_i-x_i}{y_i}}\right|$$

(8)

$y_i$ is the statistical EPC value of the ith city, $x_i$ is the predicted EPC value of the ith city.

$$\mathrm{M}\mathrm{A}\mathrm{R}\mathrm{E}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{ARE}_i$$

(9)

${ARE}_i$ is the absolute relative error for the ith city, and n is the total number of cities included in the computation.

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt[2]{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-x_i)}^2}$$

(10)

$y_i$ is the statistical EPC value of the ith city, and $x_i$ is the predicted EPC value of the ith city. n is the total number of cities included in the computation.

3. Results

3.1. Modeling Effects on NPP/VIIRS Dataset

The proposed method was applied to model the monthly NTL data extracted from NPP/VIIRS nighttime light imagery and the monthly EPC statistical values for 26 Yangtze River Delta cities with available monthly EPC statistics from 2017 to 2022, as described in Section 2.4. The comparison of modeling accuracy is presented in

Table 3. Comparison of monthly modeling results on NPP/VIIRS dataset.

City	3 Parameter Model		4 Parameter Model		RF Model		Proposed
	MARE (%)	RMSE (104 KWh)	MARE (%)	RMSE (104 KWh)	MARE (%)	RMSE (104 KWh)	MARE (%)	RMSE (104 KWh)
Chizhou	13.43	10,847	13.43	10,847	8.33	6726	13.40	10,744
Tongling	8.20	8505	8.20	8505	5.57	5584	7.59	7673
Hefei	14.38	56,576	14.38	56,576	6.55	24,716	9.91	38,583
Jiaxing	9.13	50,825	9.19	50,708	3.81	21,667	8.77	45,808
Chuzhou	10.78	23,312	10.55	23,026	5.38	11,611	9.15	21,646
Wuhu	10.39	22,422	10.39	22,422	6.36	13,144	8.97	19,719
Ma’anshan	8.77	19,697	8.77	19,697	5.65	12,408	8.24	18,532
Xuancheng	16.92	24,150	16.92	24,150	13.01	17,531	16.69	24,018
Anqing	10.56	13,993	10.55	13,786	4.84	5748	7.75	10,071
Changzhou	9.23	50,113	9.23	50,113	5.29	28,949	6.57	36,206
Zhenjiang	10.22	28,717	10.22	28,717	6.44	16,916	7.52	20,828
Hangzhou	11.23	101,350	11.23	101,350	2.80	25,870	6.84	61,494
Huzhou	8.39	32,681	8.39	32,647	2.85	11,977	5.94	28,068
Taizhou 1	13.39	44,436	13.39	44,436	9.39	30,700	13.00	42,933
Ningbo	9.94	81,613	9.94	81,613	3.49	33,003	8.53	71,934
Suzhou	7.36	117,596	7.36	117,596	1.17	20,089	3.18	55,868
Yangzhou	10.25	31,128	10.25	31,128	3.66	13,209	6.54	21,838
Jinhua	13.17	61,056	13.17	61,056	5.56	23,922	10.88	48,159
Wenzhou	10.12	52,375	10.12	52,375	3.52	18,098	7.76	39,561
Yancheng	11.85	47,611	11.85	47,611	6.17	26,174	8.00	32,759
Nanjing	10.37	72,499	10.37	72,499	3.71	24,848	3.66	24,533
Shaoxing	5.73	29,354	5.73	29,354	1.57	10,497	3.19	17,665
Zhoushan	6.83	11,691	6.83	11,691	5.77	9252	5.97	9780
Wuxi	8.00	68,962	8.00	68,962	2.80	23,126	3.01	24,548
Taizhou 2	7.95	25,094	7.95	25,094	6.16	21,474	2.19	6685
Nantong	7.87	38,437	7.87	38,437	7.41	38,369	2.89	14,614
Average	10.17	43,271	10.17	43,246	5.28	19,062	7.54	29,010

Taizhou ¹ refers to Taizhou City in Zhejiang province. Taizhou ² refers to Taizhou City in Jiangsu province.

. The proposed method demonstrates superior performance compared to the three-parameter and four-parameter models in terms of the Mean Absolute Relative Error (MARE) on the training dataset, with a MARE of 7.94%. Although the RF approach yields the best overall MARE on the training set, it suffers from overfitting as evidenced by its poor generalization on the validation set, which is further discussed in Section 3.2. The modeling performances of the three-parameter and four-parameter models were relatively similar across most cities. By analyzing the estimated coefficients of these two models, it can be observed that in these cities, the coefficient of the interaction term between NTL and temperature is close to zero, leading to very similar functional forms of the fitted equations for the two models. This phenomenon may be attributed to parameter compensation effects, wherein the linear temperature term, NTL term, and constant term collectively account for the majority of observed variations, thereby diminishing the statistical significance of the interaction term. This observation also highlights the importance of the squared temperature term in the five-parameter model. Its inclusion captures nonlinear EPC-temperature responses, improving the ability of the proposed model to represent EPC dynamics in the Yangtze River Delta urban areas.

For the RMSE (Root Mean Square Error) indicator, the RMSE of the proposed model was 29,010 × 10⁴ kWh, significantly outperforming the three-parameter method (43,271 × 10⁴ kWh) and the four-parameter method (43,246 × 10⁴ kWh). Further analysis revealed that, across all 26 cities in the training set, the proposed method consistently produced lower RMSE values than the three-parameter and the four-parameter methods.

3.2. Monthly Prediction on NPP/VIIRS Dataset

The 2023 monthly urban EPC prediction results are presented in

Table 4. Comparison of monthly prediction results on NPP/VIIRS dataset.

City	3 Parameter Model		4 Parameter Model		RF Model		Proposed
	MARE (%)	RMSE (104 KWh)	MARE (%)	RMSE (104 KWh)	MARE (%)	RMSE (104 KWh)	MARE (%)	RMSE (104 KWh)
Chizhou	13.52	14,034	13.49	14,010	18.89	19,433	12.81	13,536
Tongling	13.46	15,205	13.46	15,205	12.34	14,131	13.71	14,689
Hefei	8.80	68,121	8.80	68,121	9.81	62,553	10.00	62,507
Jiaxing	8.72	74,767	8.48	72,843	11.55	84,423	8.15	68,405
Chuzhou	14.12	55,000	13.94	54,055	16.81	57,532	14.29	51,665
Wuhu	8.73	29,013	8.73	29,013	8.95	28,689	7.93	24,417
Ma’anshan	13.62	33,532	13.62	33,532	14.22	33,359	13.23	32,187
Xuancheng	17.17	41,796	17.17	41,796	23.71	47,550	17.62	41,223
Anqing	8.11	17,278	9.63	19,245	12.29	18,989	10.13	18,033
Changzhou	8.89	58,355	8.89	58,355	9.30	54,065	7.88	51,600
Zhenjiang	11.03	39,626	11.03	39,626	12.01	33,602	12.36	34,573
Hangzhou	11.32	126,788	11.32	126,788	6.07	76,936	5.47	62,883
Huzhou	10.82	43,391	10.87	43,504	8.09	35,920	7.35	29,612
Taizhou 1	13.75	65,988	13.75	65,988	12.72	66,254	13.67	65,482
Ningbo	8.98	98,789	8.98	98,789	10.64	108,768	9.17	95,263
Suzhou	8.22	159,211	8.22	159,211	3.89	72,460	3.82	70,315
Yangzhou	7.54	31,387	7.54	31,387	10.98	35,265	8.40	27,084
Jinhua	16.52	92,867	16.52	92,867	18.64	93,472	15.82	77,992
Wenzhou	9.88	74,757	9.88	74,757	11.82	75,971	9.47	56,764
Yancheng	13.54	71,117	13.54	71,117	14.84	64,064	14.37	64,324
Nanjing	12.08	90,933	12.08	90,933	8.03	56,522	7.10	52,538
Shaoxing	7.21	52,886	7.21	52,886	8.18	45,637	7.07	42,465
Zhoushan	9.26	19,718	9.26	19,718	6.31	12,809	10.28	19,148
Wuxi	14.52	117,400	14.52	117,400	8.58	79,155	9.12	87,285
Average	11.24	62,165	11.29	62,131	11.61	53,232	10.38	48,500

Taizhou ¹ refers to Taizhou City in Zhejiang province.

. It is shown that the proposed method achieved a MARE of 10.38%, outperforming both the four-parameter (11.29%), three-parameter (11.24%), and RF (11.61%) methods. Although the RF model exhibited the lowest MARE on the training dataset, reflecting its strong fitting capacity, it performed suboptimally on the validation dataset, even worse than other methods, which indicated a notable overfitting issue. Despite the RF model inherently resisting overfitting, the relatively small sample size available for monthly EPC modeling limited its effectiveness. Specifically, in the NPP/VIIRS dataset, the number of monthly EPC observations per city ranges was small, as shown in Table 1, which was insufficient to fully prevent overfitting. In comparison, the structure of the proposed method is simple, and the proposed method consistently showed better generalization performance and wider applicability across most urban areas. The scatter plots of predicted versus observed EPC values across all cities is given in Figure 3. The proposed model demonstrated the best fitting performance, as indicated by both values of the coefficient of determination (R²) and the adjusted R². It is indicated that the model had stronger explanatory power and modeling capability for EPC prediction. The advantage is primarily attributed to the design of the parameter terms in the proposed model, which enables it to more effectively capture the underlying patterns of EPC variation.

For the prediction accuracy for specific cities, the proposed method achieved the best results in 14 cities, e.g., Suzhou, Hangzhou, Wuxi and Nanjing, in terms of MARE. Suzhou, Hangzhou, and Wuxi were the top three EPC cities in the study area according to the ranking of annual EPC. The performances of the proposed model for EPC prediction of these three cities were particularly outstanding; specifically, the MARE values for Suzhou, Hangzhou, and Wuxi were 3.82%, 5.47%, and 9.11%, respectively, significantly better than the values in the two comparison methods.

In addition, most cities where the proposed method achieved the best MARE had large electricity and energy consumption. It is suggested that the proposed method exhibits strong applicability and practicality in predicting EPC tasks. In terms of the RMSE indicator, the proposed method performs the best across 23 cities, which further verifies its prediction ability and stability in practical applications.

3.3. 2017–2023 Annual EPC on NPP/VIIRS Dataset

The proposed method not only enables monthly EPC prediction for the months covered in statistical yearbooks, but also allows for the estimation for the remaining months. Therefore, annual EPC could be computed by aggregating the monthly predictions in a year. To evaluate the performance of the proposed method in annual EPC prediction, this study compares the annual prediction results generated by the three-parameter and four-parameter models, and the approach proposed by Li et al. [54], (abbreviated as Year model), respectively. The annual EPC estimation performance during the training phase is summarized in

Table 5. Comparison of 2017–2022 results on NPP/VIIRS dataset.

City	Annual Model	3 Parameter Model	4 Parameter Model	RFModel	Proposed
Chizhou	4.69%	9.52%	9.52%	5.63%	9.55%
Tongling	8.11%	5.40%	5.40%	3.50%	5.29%
Hefei	14.64%	3.95%	3.95%	2.94%	3.78%
Jiaxing	4.44%	2.67%	2.73%	1.95%	2.59%
Chuzhou	5.53%	3.75%	3.59%	2.04%	3.69%
Wuhu	2.93%	5.50%	5.50%	3.59%	5.75%
Ma’anshan	28.09%	6.95%	6.95%	3.96%	6.86%
Xuancheng	9.08%	11.44%	11.44%	9.74%	11.42%
Anqing	36.96%	3.15%	3.07%	1.67%	2.35%
Hangzhou	6.59%	7.36%	7.36%	6.16%	6.71%
Suzhou	1.68%	2.02%	2.02%	4.26%	5.16%
Zhoushan	52.30%	4.23%	3.35%	71.96%	3.93%
Zhenjiang	9.09%	7.03%	7.03%	6.34%	7.47%
Huzhou	6.81%	3.69%	3.69%	5.54%	6.73%
Yangzhou	13.94%	1.54%	1.54%	6.11%	5.45%
Taizhou 1	5.42%	3.24%	3.24%	9.81%	5.88%
Taizhou 2	11.01%	2.49%	2.49%	2.91%	2.61%
Shaoxing	8.55%	11.32%	11.32%	15.43%	14.48%
Yancheng	9.81%	13.91%	13.91%	18.66%	15.92%
Changzhou	5.68%	2.08%	2.08%	2.19%	1.59%
Jinhua	6.30%	17.95%	17.95%	13.79%	13.45%
Wenzhou	8.25%	3.48%	3.48%	2.22%	3.39%
Nantong	13.48%	4.55%	4.55%	13.24%	8.82%
Wuxi	1.84%	1.89%	1.89%	9.45%	5.92%
Nanjing	2.83%	10.85%	10.85%	8.28%	5.05%
Ningbo	6.45%	6.06%	6.06%	5.45%	6.02%
MARE	10.94%	6.00%	5.96%	9.11%	6.53%
RMSE	364,147	281,084	281,062	350,473	304,378

Taizhou ¹ refers to Taizhou in Jiangsu Province. Taizhou ² refers to Taizhou in Zhejiang Province.

. As shown in Table 5, although the proposed model did not achieve optimal performance during training, its results were close to those of the best-performing model, and the RMSE was also comparable. For the prediction part in the NPP/VIIRS dataset, which was not involved in the training process, the prediction results for EPC could provide a more objective reflection of the model’s generalization capability.

The prediction performance on the test dataset is presented in

Table 6. Comparison of 2023 prediction results on NPP/VIIRS dataset.

City	Annual Model	3 Parameter Model	4 Parameter Model	RFModel	Proposed
Chizhou	2.78%	4.86%	4.83%	13.99%	4.64%
Tongling	11.15%	13.87%	13.87%	12.68%	14.00%
Hefei	16.49%	11.35%	11.35%	13.25%	10.48%
Jiaxing	12.38%	2.97%	2.78%	7.23%	2.78%
Chuzhou	16.41%	15.21%	14.95%	17.23%	15.13%
Wuhu	0.90%	4.45%	4.45%	6.51%	5.04%
Ma’anshan	30.56%	13.23%	13.23%	13.75%	13.17%
Xuancheng	20.07%	17.29%	17.29%	24.82%	17.40%
Anqing	28.12%	11.98%	11.45%	14.45%	11.31%
Hangzhou	4.53%	3.24%	3.24%	2.21%	1.11%
Suzhou	3.07%	1.64%	1.64%	0.06%	1.25%
Zhoushan	11.75%	6.01%	6.01%	2.20%	5.95%
Zhenjiang	9.24%	10.21%	10.21%	9.00%	9.06%
Huzhou	12.42%	2.51%	2.23%	4.00%	3.81%
Yangzhou	1.78%	4.39%	4.39%	8.04%	5.12%
Taizhou 1	15.47%	7.76%	7.76%	13.79%	7.57%
Taizhou 2	18.32%	6.64%	6.64%	7.13%	6.93%
Shaoxing	18.11%	2.69%	2.69%	3.29%	1.93%
Yancheng	19.72%	13.21%	13.21%	12.96%	11.51%
Changzhou	9.49%	1.60%	1.60%	2.99%	0.26%
Jinhua	20.81%	14.28%	14.28%	13.35%	8.56%
Wenzhou	2.70%	7.14%	7.14%	7.34%	4.27%
Nantong	17.66%	18.24%	18.24%	22.39%	17.57%
Wuxi	1.98%	5.09%	5.09%	0.65%	0.84%
Nanjing	3.09%	3.07%	3.07%	5.83%	4.88%
Ningbo	3.26%	1.28%	1.28%	4.83%	0.92%
MARE	12.01%	7.85%	7.80%	9.38%	7.13%
RMSE	617,072	412,490	411,589	480,417	361,064

Taizhou ¹ refers to Taizhou in Jiangsu Province. Taizhou ² refers to Taizhou in Zhejiang Province.

. It can be observed in Table 6 that the proposed method achieves a MARE of 7.13% in annual EPC prediction, outperforming all comparison methods. This highlights the advantages of the proposed method in both modeling strategy and feature integration. The performance improvement can be attributed to the effective integration of monthly EPC trends, temperature effects, and the interaction between NTL data and temperature. Furthermore, among the annual EPC predictions for the 26 cities, the RMSE of the proposed method is 361,064 × 10⁴ kWh, significantly lower than that of the four-parameter model (411,589 × 10⁴ kWh), the three-parameter model (412,490 × 10⁴ kWh), the RF model (5,958,138 × 10⁴ kWh), and the annual model (617,072 × 10⁴ kWh), further confirming its stability and superiority in annual EPC prediction.

3.4. EPC Distribution Maps and Analysis Based on NPP/VIIRS Dataset

The proposed method enables the extraction of EPC spatial distributions. Based on NPP/VIIRS imagery, monthly EPC distribution maps for Hangzhou, Hefei, and Nanjing for the months of April, June, August, and October 2023 were generated, as shown in Figure 4. It is clearly illustrated that the spatial extent of EPC, which is primarily concentrated in the central urban areas and built-up zones of these cities. These central districts, characterized by higher population density and more intense commercial activities, exhibit significantly higher EPC compared to surrounding county-level regions. Specifically, the EPC in Nanjing is mainly concentrated in the central districts, i.e., Xuanwu, Gulou, and Jianye districts. In Hefei, the high-EPC areas are primarily located in the Luyang, Shushan, Baohe, and Yaohai districts. In Hangzhou, the main EPC hotspots are found in the Gongshu, Shangcheng, Binjiang, and Xiaoshan districts. It can also be observed that the spatial distribution of EPC varies across the four months. The highest EPC occurs in August, likely due to a surge in cooling demand caused by high temperatures. In contrast, EPC levels in April and October are relatively similar, while June shows an expansion in high-consumption areas compared to April at the same intensity level. Overall, the spatial distribution of EPC exhibits significant seasonality, and it can be clearly reflected in these EPC distribution maps. This indicates that the proposed method not only helps deepen the understanding of energy consumption patterns across different regions and time periods within a city, but also provides a promising scientific data basis for optimizing energy management strategies.

3.5. Results on SDGSAT-1 Dataset

The comparison results of the proposed method, the four-parameter method, and the three-parameter method on SDGSAT-1 dataset are shown in

Table 7. Model performance on SDGSAT-1 dataset.

City	Month	SDGSAT-1			NPP/VIIRS
		3 Parameter Model	4 Parameter Model	Proposed	3 Parameter Model	4 Parameter Model	Proposed
Yangzhou	October 2023	30.36%	19.66%	12.85%	43.63%	38.97%	27.15%
Zhenjiang	October 2023	9.98%	23.86%	25.98%	18.57%	14.80%	20.59%
Changzhou	January 2023	43.55%	25.43%	14.94%	27.14%	8.10%	3.48%
Jiaxing	February 2023	9.77%	9.79%	13.94%	31.12%	22.17%	25.52%
Jiaxing	September 2023	37.12%	22.85%	7.67%	45.22%	34.43%	20.68%
Nanjing	March 2023	14.06%	21.91%	20.73%	11.42%	31.69%	23.59%
Tongling	April 2023	69.26%	10.07%	16.02%	99.84%	0.62%	17.63%
Tongling	November 2023	10.69%	98.66%	85.89%	20.11%	92.05%	70.37%
Wuxi	January 2023	13.54%	20.28%	17.38%	21.80%	24.01%	19.22%
Hefei	January 2023	44.41%	28.71%	55.56%	69.06%	50.27%	72.72%
MARE (%)		28.27%	28.12%	27.09%	38.79%	31.71%	30.09%
RMSE (104 KWh)		118,969	94,148	95,842	153,389	130,069	124,700

. As can be observed from the Table, on the NPP/VIIRS part, the proposed method outperforms the comparative methods in both the RMSE and MARE metrics. On the SDGSAT-1 part in SDGSAT-1 dataset, the MARE metric of the proposed method surpasses all comparative models, while its RMSE metric is very close to the best-performing method. In terms of the R² indicator, the proposed model demonstrated consistently superior results on both the SDGSAT-1 image subset and the NPP/VIIRS comparison image subset within the SDGSAT-1 dataset. Specifically, as shown in Figure 5, the model achieved an R² value close to the best R² on the SDGSAT-1 image subset; meanwhile it achieved the highest R² on the NPP/VIIRS comparison subset. It is indicated that the proposed model exhibited strong adaptability and consistent performance across different data sources. Overall, the proposed method exhibits superior performance on both parts, further validating its effectiveness and robustness in the EPC prediction task. It is also indicated that the proposed method is capable of more accurately capturing the complex relationships between electricity consumption, nighttime light data, temperature, and other relevant factors. Moreover, the performance of each method on the SDGSAT-1 part is better than their respective performances on the NPP/VIIRS part. This improvement is mainly attributed to the higher spatial resolution of SDGSAT-1 imagery, which allows for finer differentiation of surface light distribution characteristics and thus enables the extraction of more accurate NTL information. This advantage contributes to enhancing the model’s ability to characterize the spatial heterogeneity of electricity consumption, thereby improving prediction accuracy.

Furthermore, SDGSAT-1 images from January 2023 in Changzhou, March 2023 in Nanjing, January 2023 in Wuxi, and October 2023 in Yangzhou were used to generate 40 m spatial resolution monthly EPC distribution maps. As shown in Figure 6, the 40 m resolution imagery provides fine-grained details of EPC, clearly revealing the spatial patterns of EPC in these cities. The high-resolution EPC distribution maps effectively capture distinct electric power consumption features, with significantly higher consumption observed in city centers and industrial zones compared to suburban and rural areas. Moreover, the EPC distribution maps clearly reflect the areas of concentrated electricity consumption within different cities. For instance, in Wuxi, the consumption is concentrated in Liangxi, Xishan, Huishan, and Xinwu districts. Detailed spatial information of EPC provides valuable insights for targeted urban planning and energy distribution strategies.

4. Discussion

Existing studies have demonstrated a significant correlation between NTL data and urban EPC. Most previous research has focused on this relationship at an annual temporal scale, often overlooking the uniqueness and variations in monthly EPC patterns within cities. This lack of finer temporal resolution has, to some extent, limited the accuracy of annual prediction models. To address this research gap, this study innovatively introduces monthly temperature factors as well as their interaction with NTL, thereby establishing a novel model for predicting urban monthly electric power consumption. Compared with two baseline methods, the proposed approach demonstrates superior effectiveness. It achieved MARE of 7.96% across monthly EPC training in the YRD urban agglomeration from 2017 to 2022, and maintained a prediction accuracy of 10.38% during independent prediction in 2023, even though some monthly data were missing during the modeling process. This further confirms the model’s robustness and adaptability when dealing with incomplete datasets. In addition, the method effectively addresses, to some extent, the issue of missing monthly statistical data and enables spatial mapping of monthly EPC, thereby enhancing both the spatial detail and temporal resolution of electric power consumption analysis. The uncertainty of the proposed model primarily originates from the NTL and temperature data. First, due to the spatial resolution limitations of NTL data, it may be difficult to accurately capture fine-scale electricity consumption patterns within cities. Pixel saturations in NTL imageries are prone to occur in highly luminous areas. In addition, NTL observations may be affected by seasonal factors, e.g., vegetation cover changes, cloud cover, and atmospheric conditions. Second, the spatial resolution of the temperature data also affects the calculation accuracy of monthly average temperature at the city level, thereby introducing uncertainties into the input variables of the model. Considering that the dataset covered the period from 2020 to 2022, which overlapped with the global outbreak of COVID-19, fluctuations in human activity and economic operations could have introduced certain disturbances into electricity consumption patterns. Nevertheless, the proposed model integrated NTL data, temperature (including its quadratic and interaction terms), and a constant term, aiming to capture underlying long-term EPC trends and stable energy consumption behaviors. The proposed approach is expected to partially mitigate the impacts of COVID-19.

Despite these sources of uncertainty, the proposed model demonstrated strong stability and consistency across multiple evaluation metrics and different data sources (i.e., SDGSAT-1 and NPP/VIIRS). A comparative analysis with the three-parameter and four-parameter models further validated the practical significance of each parameter in the five-parameter model. In comparison with the RF method, the proposed method exhibited superior robustness against overfitting, enhanced interpretability, and better adaptability to small sample sizes. In annual EPC estimation tasks, the proposed method outperformed the existing annual-level prediction framework that relies on city types and historical EPC statistics [54], highlighting its ability to effectively capture and leverage monthly variation patterns. By integrating widely available NTL and temperature data, the proposed method could accurately reconstruct missing monthly EPC values, significantly improving annual prediction accuracy. Compared with EPC modeling at the provincial scale [43], the proposed method operated at the city level, offered higher spatial resolution and took the environment variable into account, making it more suitable for urban energy consumption monitoring and analysis.

Although this study improved the accuracy of urban monthly EPC prediction, there are still some limitations. Firstly, electricity consumption is not only affected by temperature, but also related to various factors within the city, such as socio-economic activities, industrial structure, and residents’ behavior patterns. For instance, the contribution of different types of land, such as industrial land, commercial land, and residential land, to the electricity demand is different.

Future research could consider integrating multi-source data, e.g., land use type, and point of interest (POI), to improve the model’s ability to describe the characteristics of urban EPC. In addition, with the development of artificial intelligence and deep learning methods, future research could explore spatio-temporal modeling methods, e.g., such as recurrent neural networks and other models, to better capture the dynamic patterns of electricity consumption and achieve higher modeling and prediction accuracy. Additionally, given the relatively short operational period of the SDGSAT-1 satellite, accumulating more long-term monthly data will be essential for improving the robustness of urban EPC modeling. This will enable a more comprehensive analysis of dynamic urban energy consumption trends. To address the issue of cloud interference in SDGSAT-1 nightlight images, spatio-temporal fusion techniques could be employed to reconstruct high-quality time series data to enhance the reliability of observations.

5. Conclusions

This study proposes a method for monthly urban EPC by integrating nighttime light remote sensing imagery with monthly temperature variables. Using the YRD urban agglomeration (2017–2023) as a case study, two datasets, NPP/VIIRS dataset and SDGSAT-1 dataset, were built to verify the performance of the proposed method. As for the NPP/VIIRS dataset, Prophet detection algorithm and a neighboring-month substitution method were used to reconstruct a continuous NTL time series. Based on this dataset, monthly EPC prediction models were established and used to forecast monthly EPC values for 2023. The results demonstrate that the proposed method outperforms two alternative approaches, i.e., one considering only the interaction between NTL and temperature, and the other incorporating only temperature variables. The proposed model achieved a MARE of 7.96% during training and 10.38% during prediction, confirming its effectiveness in capturing the dynamic changes in urban electricity consumption. In terms of annual EPC prediction, the model also exhibited strong performance, achieving a MARE of 7.13%, which surpasses the three comparison methods. Moreover, the proposed approach enables spatial mapping of urban EPC using NPP/VIIRS imagery. Through time-series EPC maps, the monthly variation patterns of EPC can be visually interpreted.

Furthermore, using SDGSAT-1 dataset and a leave-one-out cross-validation strategy, the generalization capability of the model across different data sources was also verified. Spatial distribution maps of EPC at 40 m resolution, derived from SDGSAT-1 images were generated, clearly revealing the spatial characteristics of urban EPC. These results further validate the effectiveness and practical utility of the proposed model in depicting urban monthly EPC. Although high accuracy has been achieved in EPC prediction, there is still room for improvement. For instance, incorporating additional data sources such as land use data could further explore the characteristics of urban electricity consumption. In summary, this study expands the application dimensions of nighttime light remote sensing data in urban energy modeling and provides a methodological framework for monitoring and analyzing urban EPC at high spatial and temporal resolutions.