SAGAN-ConvLSTM: Spatio-Temporal Power Load Forecasting with GAN and ConvLSTM

SAGAN
–
ConvLSTM: A novel spatio-temporal forecasting
approach combining semivariogram-enhanced GAN and
ConvLSTM for power load forecasting
Rasoul Jalalifar
a
, Mahmoud Reza Delavar
b,*
, Seyed Farid Ghaderi
c
,
Seyedeh Leyla Mansouri Alehashem
d
a
Ph.D., Geospatial Information System, School of Surveying and Geospatial Engineering, University of Tehran, Iran
b
Professor, School of Surveying and Geospatial Engineering, University of Tehran, Iran
c
Professor, Industrial Engineering, University of Tehran, Iran
d
Master of science, Geographical Information System and Remote Sensing, Kharazmi University, Iran
ARTICLE INFO
Keywords:
Power load forecasting
Deep learning
Time series
Spatial autocorrelation
Generative adversarial network
ABSTRACT
In power distribution networks, spatio-temporal load forecasting plays a crucial role in decision-
making and the development of distribution networks. Accurate forecasting models are essential
to handle the complex dependencies in power consumption across different districts of mega-
cities. However, the presence of missing values in smart meter data often caused by device
malfunctions or communication failures, can signicantly degrade model performance by
increasing complexity and reducing forecasting accuracy. To address this challenge, this paper
presents a novel forecasting approach named SAGAN
–
ConvLSTM based on Spatial Autocorre-
lation (SA) utilizing spatio-temporal semivarigram and Generative Adversarial Network (GAN) to
combine spatial statistics and deep learning to impute missing values in power load time series.
The semivariogram quanties spatial and temporal dependencies among substations and guides
the GAN to reconstruct missing data while preserving realistic spatio-temporal structures. After
imputation, the rened time series is processed by a Convolutional Long Short-Term Memory
(ConvLSTM) network to generate short-term power load forecasts.The proposed model was
evaluated using data from Tehran’s power distribution network, achieving a mean absolute error
(MAE) of 10.05 % and root mean square error (RMSE) of 15.46 %, outperforming other models
like GRU, LSTM, ConvLSTM, and SA-ConvLSTM in forecasting power load over a 20-day period.
1. Introduction
Load forecasting is necessary for power distribution network planning, and the accuracy of load forecasts can directly affect the
resource management and equipment capacities. Actually, it is crucial to maximize load forecasting accuracy in power distribution
networks [1]. Inaccurate load forecasting can result in squandered investments in distribution network development and unbalanced
growth.
Spatial load forecasting is necessary for distribution network planning and management in the short and long term. In recent years,
* Corresponding author.
E-mail address: [email protected] (M.R. Delavar).
Contents lists available at ScienceDirect
Computers and Electrical Engineering
journal homepage: www.elsevier.com/locate/compeleceng
https://doi.org/10.1016/j.compeleceng.2025.110718
Received 2 June 2025; Received in revised form 21 August 2025; Accepted 10 September 2025
Computers and Electrical Engineering 128 (2025) 110718
Available online 22 September 2025
0045-7906/© 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

notably in developing nations, the rapid urbanization and increasing demand for power distribution networks expansion have piqued
the interest of researchers. Conventional models have widely been employed for load forecasting since 1970 [2]. The conventional
models have extensively used autoregressive (AR), autoregressive integrated moving average (ARIMA) [3,4], GARCH [5] and quantile
regression with kernel-based models. In light of articial intelligence (AI) development, new load forecasting models have been
proposed in recent years [6]. Neural networks are the nonlinear models which have been widely used for load forecasting [2]. The
overtting problem of neural networks due to the increased number of layers is a major disadvantage of such models. To cope with this
disadvantage of conventional neural networks, deep learning-based models have been developed [7]. It is complicated to compute
demand patterns in a power distribution network [8] and it would be difcult to nd an efcient and effective load forecasting method,
and a particular forecasting model cannot be generalized to all power networks [8]. Deep learning-based models have been recently
used in spatio-temporal forecasting.
Recurrent neural network (RNN) models have been widely utilized in the literature on load time series forecasting [9]. Deep
learning has yielded satisfactory accuracy in time series forecasting in light of RNN development. However, an RNN may encounter a
vanishing or exploding gradient. The long short-term memory (LSTM) algorithm was developed to address this difculty [10].
Moreover, the gated recurrent unit (GRU) algorithm was devised and has demonstrated satisfactory forecasting accuracy and speed
enhancement performance [11]. GRU and LSTM have been employed in numerous researches in recent years, reporting improved
forecasting accuracy and speed. Kuster et al. [12] utilized an LSTM model for the spatio-temporal forecasting of railway transportation.
They showed that LSTM outperformed other methods. Li et al. [6] introduced an LSTM-based method for air pollution forecasting. Wen
et al. [13] proposed a GRU model to forecast the electrical loads of residential buildings and demonstrated that DRNN-GRU had been
efcient in coping with missing data and undergone a negligible accuracy decline upon an increase in missing data. Shi et al. [7]
compared an LSTM algorithm with ARIMA, RNN, and support vector regression (SR) for load forecasting. The LSTM algorithm out-
performed the other algorithms, as observed. Aseeri [14] proposed a new forecasting methodology for day-ahead electric power
demand forecasts using the European Network of Transmission System Operators for Electricity to evaluate the forecasts. To congure
the intended forecasting method, two steps were taken: Initially, a simple processing pipeline was proposed to facilitate systematic
preprocessing of raw multivariate time-discrete power data, including a stride-based sliding window approach to generate time
series-based batches suitable for the supervised learning procedure. Second, the lightweight form of recurrent neural network method,
GRU, which was trained using preprocessed multivariate time series data to generate day-ahead power load forecasts. The empirical
results demonstrate that the proposed forecasting methodology provides superior day-ahead forecasting performance for
enterprise-class measured data when compared to statistical models. Ozer et al. [15] presented a deep learning-based model for
short-term building load forecasting with limited data. They utilized cross-correlation-based transfer learning. Finding the appropriate
data for transfer learning posed the greatest difculty. For this purpose, cross-correlation was employed. They demonstrated both deep
learning and transfer learning’s benets. However, if only load data were available, the model’s forecasting performance would be
limited; additional effective data, such as meteorological data, were required to enhance the model. Meteorological data play a crucial
role in power demands and electrical discharge variations [16].
The prediction of electrical demand is dependent on spatio-temporal parameters, such as temperature [17]. Hence, convolutional
neural network (CNN) and CNN-RNN models have been employed for the spatio-temporal forecasting of load time series in recent
years (Due et al., 2020).
Despite promising performance, RNN-based techniques cannot effectively extract correlation between time series [1], as they
process time series independently and neglect correlations. Hence, a combination of CNNs and RNNs can be employed in
spatio-temporal forecasting. Wan et al. [18] developed the CTS-LSTM model to forecast correlated time series. They implemented
CTS-LSTM on air trafc time series and air pollution forecasting. It was found that CTS-LSTM outperformed the ARIMA, VAR, HA, Pre,
LSTM, and Conv-LSTM algorithms based on the root-mean-square error (RMSE) and mean absolute error (MAE). In their study, Zhou
et al. [19] introduced a novel deep network architecture that operates autonomously and utilizes fuzzy polynomial neural networks
(FPNN) in conjunction with long short-term memory (LSTM) networks and fuzzy rule-based polynomial neurons (FPNs) to address the
challenge of time-series forecasting. Lin et al. [20] adopted a Conv-LSTM methodology for air trafc forecasting. Guo and Yuan [21]
utilized a CNN model for trafc speed forecasting. Liu et al. [22] employed an autoencoder-LSTM model to forecast the wind speed.
They surpassed competing models.
Forecasting load is spatially dependent, and time series depend on meteorological parameters. Wu et al. [23] proposed a GRU-CNN
algorithm for forecasting load time series in the short term. By identifying time series characteristics, it could accurately and quickly
predict the burden. The model was shown to be effective at extracting concealed data features and had a lower RMSE and MAPE than
competing models. Hafeez et al. [24] introduced an FCRBM model for short-term load forecasting. Genetic wind-driven optimization
(GWDO) module for optimizing model parameters. The FCRBM model was found to outperform other models such as LSTM. Ouyang
et al. [25] implemented short-term load forecasting through a deep belief network (DBN) and a copula model through load time
history, price, and temperature data. Load forecasting was independently modeled for four seasons. According to the results, the model
had higher performance than other methods. Fahiman et al. [2] proposed a model based on deep learning and the k-shape clustering of
load time series data for short-term load forecasting. The clustering of load time series and the optimized number of clusters were
found to strongly enhance forecasting accuracy and reduce errors. Li et al. [6] investigated load forecasting using effective parameters
including temperature, humidity, and wind speed. They implemented a CNN to cluster input data and a neural network with three
hidden layers to predict electrical demand. Incorporating electrical load determinants into the model resulted in greater accuracy than
other techniques, such as SVM. Kim and Cho [9] proposed a CNN-LSTM model to forecast residential energy consumption. The
CNN-LSTM model demonstrated superior performance when compared to the LSTM and linear regression algorithms. The results
indicated that meteorological parameters, such as temperature, improved the model’s ability to predict time (hourly and
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Computers and Electrical Engineering 128 (2025) 110718
2

minute-by-minute, day, and week).
In their recent publication, Liu and Liang [26] presented the AC-BiLSTM model, an innovative approach to ultra-short-term power
load forecasting that combines Bidirectional LSTM (BiLSTM), CNN, and an Attention mechanism. By leveraging the capabilities of CNN
and BiLSTM, this novel methodology extracted spatio-temporal characteristics from load data. Additionally, the Attention mechanism
optimized the weights assigned to the hidden states of the BiLSTM model, which served to amplify critical historical load sequence data
and reduce information loss. To verify the effectiveness of this method, an empirical investigation employing actual load data from a
particular region was undertaken. The ndings, derived from two divergent experimental conditions, illustrate a substantial
improvement in the precision of predictions. However, the model fails to execute on a limited dataset in order to assess its accuracy.
Kim et al. [27] created a strategy for extracting electrical demand and other complementary data as multivariate time series. The
proposed system consisted of tagging and embedding procedures that extracted patterns from multivariate time series and tagged their
temporal and dimensional relations. During the embedding process, a network model with a convolutional layer and a multi-output
structure was constructed with the intention of incorporating the identiers. Mathematical analysis informed the development of this
design. In addition, the proposed framework for feature extraction was used to create an STLF model based on deep learning. The
experimental results demonstrate that the proposed method reduced the root mean square error by 5 to 12 %. In this study, a
data-driven, information-intensive algorithm has been proposed for forecasting multivariate time series. It can represent relationships
between variables such as temperature and power load, but not between variables at different locations.
Eskandari et al. [28] proposed a model for predicting electrical demand using CNN, LSTM, and GRU algorithms. In addition to load
data, they utilized temperature data independently for holidays, weekends, and workdays. The model’s short-term load forecasting
efcacy was found to be superior to that of twelve other models, including LSTM, GRU, LSTM-SVR, and bidirectional LSTM-GRU.
Fekri et al. [29] presented federated learning with smart meter data for load forecasting. Examined were two alternative federated
learning algorithms: FedSGD, which performs one step of gradient descent on the client before merging updates on the server, and
FedAVG, which performs multiple steps before merging. The results demonstrated that FedAVG was more precise than FedSGD while
requiring fewer communication cycles. FedAVG achieved comparable or superior accuracy when compared to distinct models for each
meter and a central model for all meters. This method enables the training of a singular model with all smart meters participating
without the need to share local data. This study was only concerned with analyzing FedSGD, FedAVG, and LSTM; it did not compare
methods to contemporary approaches. In addition, the models were evaluated using a modest load time series dataset. Jalali et al. [30]
proposed an innovative method for addressing load forecasting uncertainty. The optimal 1D-Convolutional neural network hyper-
parameters were determined by modifying a novel evolutionary algorithm. Combining the ower pollination algorithm (FPA) with a
convolutional neural network (CNN), this study introduced an innovative neuro-evolution technique.Minimizing the mean scaled
interval score loss function at prediction intervals of 50 %, 90 %, and 95 % yielded probabilistic forecasts. On a global energy fore-
casting competition load dataset (GEFCom-2014).It has been demonstrated that the proposed model performs better than other
benchmark models. However, their methods did not take spatial load time series dependencies into consideration. For short term load
forecasting, Yazici et al. [31] proposed a new method that employs one-dimensional CNNs based on Video Pixel Networks (VPNs) in
which the gating mechanism of Multiplicative Units of the VPNs was modied in some way. In particular, one-dimensional CNNs,
LSTM, and GRU variants were applied to actual electricity consumption data for 1-h-ahead and 24-h-ahead prediction tasks. According
to the outcomes of the comparative analyses, the proposed one-dimensional CNN model produced the best results overall, with a mean
absolute percentage error of 2.21 percent for predictions made 24 h in advance. On the other hand, there was no discernible difference
between the methods, even though the proposed one-dimensional CNN method produced the greatest results with a mean absolute
percentage error of approximately 1 % for 1-h-ahead predictions. However, the proposed method models the spatial dependence of
time series in distinct substations and predicts each series separately.
One of the major challenges in achieving high accuracy in time-series forecasting, especially in spatio-temporal domains, is the
presence of missing values due to sensor failures, data corruption, or transmission errors. These gaps signicantly degrade model
performance by introducing noise and reducing the amount of usable information for training [32,33]. In recent years, Generative
Adversarial Networks (GANs) have been increasingly utilized to address this issue in time-series forecasting and spatio-temporal
modeling. Studies such as [33], on wind power forecasting and Yang et al. [34] on trafc data imputation demonstrate that
GAN-based frameworks can effectively reconstruct missing values by learning complex data distributions across space and time.
Missing data, especially in critical infrastructure systems like power grids or transportation networks, can severely degrade model
accuracy and increase models complexity. The application of GANs mitigates these issues by providing robust data imputation, which
not only enhances model precision but also simplies the learning process by generating realistic synthetic data that preserve temporal
and spatial dependencies. These approaches have consistently outperformed traditional statistical or deep learning models, high-
lighting the potential of GANs to improve the reliability and scalability of predictive models in environments with incomplete datasets.
Ye et al. [33] propose a novel Informer-TimeGAN framework to generate day-ahead wind power scenarios with high accuracy and
temporal consistency. The model combines an auxiliary classier GAN (ACGAN), a temporal convolutional network (TCN), and the
Informer architecture to capture both dynamic error patterns and seasonal uctuations in wind power forecasting. By incorporating
forecast-conditioned error stratication and supervised learning signals, the model generates realistic scenario sets that preserve the
statistical and temporal properties of wind power uncertainty. Extensive evaluation using real datasets from two geographical regions
in China demonstrates that the proposed approach outperforms traditional GAN-based and statistical scenario generation models,
particularly in capturing ramping behavior and seasonality crucial for short-term grid operations. Yuan et al. [35] introduce STGAN, a
novel Spatio-Temporal Generative Adversarial Network designed for trafc data imputation. The model addresses the critical chal-
lenge posed by noise and missing entries in trafc datasets, which often deteriorate the performance of intelligent transportation
systems. By combining specially designed generative and center losses with a CNN-based discriminator, STGAN ensures that the
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imputed values maintain both local and global spatio-temporal consistency. Through the use of dilated convolutions and
skip-connections, the generator captures multi-scale dependencies while preserving known data. Experimental evaluations conrm
that STGAN signicantly outperforms traditional imputation methods in terms of reconstruction accuracy and temporal coherenc.
Gonzalez-Calabuig et al. [36] introduce GANFilling, a novel generative sequence-to-sequence model designed to address the challenge
of spatio-temporal gap lling in Sentinel-2 VNIR reectance data. Leveraging Convolutional LSTM networks within a GAN framework,
the model captures complex dependencies across space and time, enabling accurate reconstruction of cloud-contaminated or missing
satellite observations. Unlike previous methods requiring auxiliary data or strict quality masks, GANFilling autonomously identies
and corrects corrupted pixels while preserving unaffected regions. The approach demonstrates superior performance in both quan-
titative distortion metrics and qualitative visual assessments, particularly enhancing downstream applications such as vegetation
greenness forecasting across Europe. This work highlights the potential of generative deep learning methods to advance robust Earth
observation pipelines.
Shao et al. [37] present a multi-task spatio-temporal generative adversarial network (MTST-GAN) designed to predict travel time
reliability (TTR) during morning and evening peak hours. The model treats these two peak periods as interrelated tasks within a unied
GAN framework, enabling joint learning and mutual enhancement. By integrating multi-graph convolutional networks (MGCNs) to
capture spatial dependencies, LSTM networks for temporal modeling, and self-attention mechanisms for deeper spatio-temporal
feature extraction, the model learns complex correlations across both tasks. A feature fusion bridge is proposed to link the two
tasks, enhancing the overall prediction accuracy. Experimental evaluations using a real-world dataset show that MTST-GAN out-
performs baseline methods in terms of key reliability metrics, demonstrating its robustness and practicality for real-time trafc
management applications. Yang et al. [32] propose ST-LBAGAN, a deep generative model designed for imputing missing trafc data by
capturing complex spatio-temporal dependencies. The model utilizes a U-Net-based architecture enhanced with learnable bidirec-
tional attention maps, which separately target the encoding (forward attention) and decoding (reverse attention) processes. This
structure enables accurate modeling of both spatial relationships and temporal dynamics, even under high missing data rates. The
generator synthesizes missing values from incomplete inputs using multi-channel matrices, while the discriminator evaluates the
realism of the imputed data. A composite loss function—including masked reconstruction, perceptual, and adversarial components—is
employed to optimize performance. Experimental results on large-scale real-world GPS data demonstrate that ST-LBAGAN signi-
cantly outperforms existing methods, particularly under severe data corruption scenarios. Claeys et al. [38] introduce a novel two-step
methodology for generating high-resolution synthetic residential load proles using Generative Adversarial Networks (GANs). The
approach combines DoppelGANger (DGAN) for modeling interday and seasonal consumption dynamics with a wavelet-based
decomposition-recombination scheme to simulate realistic intraday stochastic variability and peak demands. This decoupled frame-
work captures multiscale temporal dependencies more effectively than traditional methods, addressing privacy concerns while
maintaining delity across daily and annual levels. The generated synthetic data were validated across several downstream appli-
cations, including PV and PV-BESS integration, demonstrating strong alignment with real smart meter data. The study also highlights
the importance of incorporating metadata to enhance the interday realism of synthetic proles and reduce modeling bias.
Overall, deep learning has shown satisfactory performance in electrical load forecasting. Nevertheless, the presence of null values -
caused by network issues and meter malfunctions - in the load time series data signicantly reduces forecasting accuracy. This study
aims to improve prediction performance by modeling these missing values using GANs. However, in metropolitan areas, due to
variations in climatic variables and differences in population structure across different city regions, using GANs becomes challenging,
and the modeling process involves a high level of complexity. To address these issues, we introduces a novel approach utilizing Spatial
Autocorrelation and Generative Adversarial Networks to model missing values and ConvLSTM to forecast load time series
(SAGAN
–
ConvLSTM). Proposed model rst modeled the spatio-temporal autocorrelation of the load data using spatio-temporal
semivariograms in order to reduce model complexity. Then, we used GANs to predict the missing (null) values, followed by
applying a ConvLSTM model for load forecasting. Listed below are signicant contributions to this study:
1- Enhance the accuracy of predicting power load time series in large urban areas and megacities by modeling missing (null) values
utilizing spatio-temporal autocorrelation of power load time series of dispersed substations using spatio-temporal semivariogram
and spatial statistics algorithms.
2- another objective of this study is to assess the effectiveness of incorporating a GAN within a Convolutional Long Short-Term
Memory (ConvLSTM) model, with the aim of improving its overall accuracy.
We utilize a dataset containing 81 substation load time series at 1 h intervals for 42 months in Tehran where is the capital city of
Iran, from July 2015 to January 2019.
This paper consists of 5 different sections. Section 2 describes material and methods of the spatio-temporal load forecasting model
based on spatial statistics, ConvLSTM and Self-Attention ConvLSTM. Section 3 introduces case study and of power substations. Section
4implements the proposed model on the case study of power substations in Tehran, Iran, from May 1, 2015, to January 28, 2019 and
compares the SAGAN
–
ConvLSTM model with other methodologies. Finally, Section 5 draws a research conclusion.
2. Materials and methods
This study aimed to implement a new method for spatio-temporal forecasting of electrical loads through load time series corre-
lations in megacities. The ConvLSTM and LSTM algorithms were employed to forecast each time serie. The LSTM and ConvLSTM and
GAN algorithms are described below before the description of the Spatial Autocorrelation.
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2.1. LSTM
Long Short-Term Memory (LSTM) networks are a variant of recurrent neural networks specically designed to overcome the
vanishing and exploding gradient problems [39]. They regulate information ow through input, output, and forget gates, enabling the
capture of long-range temporal dependencies in sequential data. The LSTM unit base is formulated as [40]:
ft=
σ
Wf.[ht−1,xt] + bf(1)
it=
σ
(Wi.[ht−1,xt] + bi)(2)
ct=tanh Wg.[ht−1,xt] + bg(3)
ct=ft∗ct−1+it∗gt(4)
ot=
σ
(Wo.[ht−1,xt] + bo)(5)
ht=ot∗tanh(ct)(6)
Where Wf,j,g,o is the weight matrix, bf,j,g,o is the bias vector at output gate, ct is the memory cell, and
σ and tanh represent the sigmoid
and hyperbolic tangent activation functions, respectively.Fig. 1 illustrate the LSTM architecture [41].
2.2. CNN
Having a well-known topology, CNN have been extensively utilized in numerous studies with satisfactory outcomes. Time-series
data can be sampled as a one-dimensional network at regular time intervals, whereas image data can be assumed a two-
dimensional network. Several CNN variants have been introduced with a similar structure consisting of the input layer, the con-
volutional layer, the excitation layer, the pooling layer, the fully connected layer, and the output layer.
2.3. Convolutional LSTM
The Convolutional Long Short-Term Memory (ConvLSTM) algorithm is a hybrid model that integrates both Convolutional Neural
Networks (CNNs) and Long Short-Term Memory (LSTM) networks. The ConvLSTM can be formally dened using the Eq. (7–11) [42]:
ft=
σ
Wxf ∗xt+Whf ∗Ht−1+Wcf ⊙Ct−1+bf(7)
it=
σ
(Wxi ∗xt+Whi ∗Ht−1+Wci ⊙Ct−1+bi)(8)
ct=ft⊙ct−1+it⊙tanh(Wxc ∗xt+Whc ∗Ht−1+bc)(9)
ot=
σ
(Wxo ∗xt+Who ∗Ht−1+Wco ⊙Ct+bo)(10)
ht=ot⊙tanh(ct)(11)
Where ⊙stands for the Hadamard product and * is the convolution operator. The convolution operator is used by ConvLSTM to derive
spatio-temporal information from data. The ConvLSTM algorithm can analyze complex spatio-temporal problems using spatio-
temporal information [42].
Fig. 1. LSTM architecture.
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