Quantitative Assessment of the Impact of Extreme Events on Electricity Consumption

Abstract

Global energy consumption is growing rapidly, with the frequency and intensity of extreme events constantly increasing, posing a long-term threat to power supply and consumption. Therefore, analyzing the spatiotemporal characteristics of electricity consumption and quantitatively assessing the impact of extreme events on electricity consumption are of great significance. Based on fine-grained electricity consumption data from Europe for the years 2019–2022, this paper employs a data mining perspective and four methods including Z-score, Isolation Forest, Local Outlier Factor, and Autoencoder to detect abnormal electricity consumption during extreme events. Additionally, it combines indicators such as elastic loss, vulnerability, and duration to measure the impact of extreme events on electricity consumption. It is found that low temperatures could lead to abrupt changes in electricity consumption, with Northern Europe being more significantly affected by low temperatures. The COVID-19 pandemic had the most significant impact on electricity consumption in Europe, with the middle part of Europe being the hardest hit during the first wave of the pandemic. Electricity anomalies during the pandemic period were related to national pandemic control policies and exhibited some lag. High temperatures persisted for a longer duration in the middle part of Europe.

1. Introduction

As the global population grows and the economy develops, the rapid increase in global energy consumption, makes the energy demand and supply issues a focal point of global attention. Electricity, is a significant product of the industrial revolution and an energy resource, which has made substantial contributions to the development and prosperity of modern human society [1]. At the same time, electricity consumption, can be used as a fundamental indicator for measuring the total electricity usage across various sectors and urban and rural residents. The immediacy and sensitivity make it an important index for reflecting economic performance [2,3].

Currently, extreme events have become the norm and are on the rise. Taking recent years as an example, the number of Atlantic hurricanes reached a new high in 2020, with Central America experiencing unprecedented Category 4 hurricanes in November [4]. In the same year, the world faced large impacts from the COVID-19 pandemic [5,6]. In 2021, North America experienced unusual high temperatures, with July becoming the hottest month on record globally, while Europe faced record-breaking rainfall and flooding [7,8]. In the summer of 2022, the Northern Hemisphere was hit by exceptionally high temperatures, with a European heatwave causing over 1000 deaths, multiple countries declaring emergencies, and the UK issuing its first-ever “extreme heat” red warning [9]. The Intergovernmental Panel on Climate Change (IPCC) in its Sixth Assessment Report (AR6) points out that climate change will accelerate in all regions globally in the coming decades, with extreme heat and precipitation events becoming more frequent, and the likelihood of concurrent extreme events increasing, as well [10].

Extreme events pose a serious threat to global electricity supply and consumption, placing them in an unstable state. Extreme events could lead to sharp fluctuations in electricity consumption over short periods, such as a rapid increase in urban electricity usage during heavy rainfall seasons and a significant decrease in electricity demand during drought seasons [11]. Due to the impact of global climate change, the frequency and severity of threat are continually increasing. Countries around the world are increasingly emphasizing the resilience of their power systems, including their ability to resist and recover from extreme events, often measured as “resilience” [12,13,14]. Typically, power system resilience focuses on high-impact, low-probability extreme events [15]. In 2011, the US government released a policy framework for the 21st-century grid, emphasizing the importance of a resilient grid in addressing the impacts of increasingly frequent extreme events. The US National Research Council and the UK House of Lords have also stressed the importance of resilient energy infrastructure [16]. To address extreme events and reduce the losses they cause, it is necessary to quantitatively assess the impact of extreme events on electricity consumption.

Given the current limited quantitative assessment of the impact of extreme events on electricity consumption and the absence of established methods and metrics, this study employs anomaly detection methods to identify electricity consumption patterns in 28 European countries from 2019 to 2022. It combines indicators such as elastic loss, vulnerability, and duration to quantitatively assess the impact of extreme events on electricity consumption.

2. Related Works

As a fundamental and important comprehensive indicator of human life, electricity consumption is influenced by various factors such as the economy, society, geography, and climate. Chen constructed a regression model for global household electricity and fuel consumption. The research results indicate that global household energy consumption is significantly influenced by economic development and population growth. Climate warming will lead to an increase in household electricity consumption, while energy consumption will decrease [17]. Wenz conducted a related study on 35 European countries, and the results indicate that climate change will increase electricity consumption in some countries while decreasing it in certain cities. Extreme weather events will also cause a spatial redistribution of demand from north to south [18]. The COVID-19 pandemic has had profound effects on energy consumption. Buechler E et al. studied the impact of COVID-19 death toll, government strictness index, and individual mobility on global electricity consumption. The results show a close correlation between government restrictions, mobility, holidays, and electricity consumption [19]. Ghiani studied the effects of the COVID-19 outbreak on Italy’s electricity load, consumption, and prices. The results indicate that the pandemic led to a 37% reduction in electricity consumption and a 30% decrease in energy prices [20].

Outlier detection is one of the fundamental tasks in the field of data mining. Outliers may be caused by computational errors or operational mistakes, typically representing non-reproducible errors in normal data [21]. Furthermore, outliers may also result from the inherent variability or elasticity of the data, which holds significant value in practical production and life [22]. Currently, a large number of unsupervised algorithms have been applied to outlier detection. Donovan B, for instance, employed taxi GPS data and used Mahalanobis distance and Z-score for traffic anomaly detection, thereby identifying abnormal time periods affected by hurricanes and conducting resilience analysis [23]. Sun utilized deep autoencoder to detect anomalies in electricity consumption [24]. Li reconstructed input trajectories using autoencoder and performed trajectory anomaly detection by minimizing the difference between the reconstruction output and the original input [25]. In the power grid system, methods like wavelet analysis and autoencoder are often used for anomaly detection to discover potential anomalies in the power grid [26,27].

Theoretical and methodological approaches from resilience assessment were applied to quantitatively assess the resilience of the power system to the shock and impact of extreme events. Examples include the Elasticity Triangle Model [28] and the Elasticity Trapezoid Model [29] for measuring the cumulative disturbances in power consumption. Based upon the Elasticity Trapezoid Model, Tang proposed an elasticity index which considered the spatiotemporal characteristics of extreme events [30]. Reed D. A. characterized the effects of natural disaster events such as hurricanes and earthquakes on network infrastructure by assessing the differences between actual operational states during disaster periods and ideal operational states [31]. In the field of electricity, the focus is primarily on the resilience assessment of the power grid. Zhou calculated the resilience of a distribution network by assessing the degradation area under operational conditions [32]. Li evaluated the resilience of the power grid by combining traditional power system reliability indicators with local topology and topological data analysis methods [33]. However, there have been very few scholars who have conducted quantitative assessments of extreme events on power consumption.

In the analysis of extreme events, it is also common to measure instantaneous disturbances using metrics such as duration and the degree of deviation from normal. Zhang used indicators like vulnerability, robustness, speed, and return level to assess the impact of the COVID-19 pandemic on the subway system [34]. Liu utilized mobile signal data along with metrics like mobile population ratio, daily travel distance, and activity entropy, to measure the impact of the COVID-19 pandemic on population mobility and explored factors influencing population movement [35]. Hong utilized large-scale mobile data to quantify community-level evacuation and recovery patterns in Houston during Hurricane Harvey [36]. Based on the aforementioned research status, this paper quantitatively assesses the impact of extreme events on electricity consumption using metrics such as elasticity loss, duration, and extent of influence.

3. Study Area and Data Sources

3.1. Study Area

Europe is located in the northwest of the Eurasian continent. According to the statistics from the European Union, the total area of Europe is approximately 100,000 square kilometers, with a population of around 749 million at the end of 2022. It comprises 50 independent sovereign countries and is the third most populous continent in the world. In recent years, Europe has become an important region for global electricity consumption, accounting for 20% of the world’s total electricity consumption. However, the European region has been affected by various extreme events such as heatwaves, the Russia-Ukraine conflict, and the COVID-19 pandemic, which have had varying degrees of impact on the electricity market and consumption behavior [20,37,38,39,40,41]. In particular, in 2022, electricity prices in Europe more than doubled, maintaining a leading position in global electricity price increases [42]. Therefore, understanding the dynamic characteristics, behavioral patterns, and influencing factors of the European electricity market and consumption behavior is of significant importance for both theoretical research and practical applications. This paper quantitatively assesses the impact of extreme events on electricity consumption by collecting electricity consumption data from 28 European countries (see Figure 1) for the years 2019–2022.

3.2. Data Sources and Processing

The electricity consumption data in this study are sourced from the European Network of Transmission System Operators for Electricity (ENTSO-E), which provides real-time and historical electricity data. The original data are recorded in Coordinated Universal Time (UTC) with a time resolution of 15 min or 1 h, and are aggregated by country in terms of spatial resolution. However, as electricity consumption data require real-time recording with no gaps, missing data are not acceptable. This study selected 28 countries with data availability exceeding 80% and used forward-filling methods to input missing values in the dataset. To investigate variations in electricity consumption at different scales, this paper aggregates data from hours and minutes into hourly electricity consumption data. These preprocessing steps ensure data reliability and lay the foundation for subsequent research. Data related to the pandemic are sourced from the Our World in Data website, an open online data platform created in collaboration between the University of Oxford and global experts. It provides daily data related to the pandemic from different countries. Meteorological data are obtained from the National Oceanic and Atmospheric Administration (NOAA) in the United States, primarily used to validate the results of extreme event identification. Administrative boundary data are sourced from the Global Administrative Areas Database (GADM). Data sources and detailed processing are shown in

Table 1. Data sources and processing.

Data Name	Meaning	Time Scale	Unit	Data Preprocessing	Data Source
Temperature		1 day	0.1 F	Unit conversion	https://www.ncei.noaa.gov/ (accessed on 14 April 2022)
Precipitation		1 day	0.1 inch
Government stringency index	An indicator of the strictness of the government’s epidemic prevention policy	1 day			https://ourworldindata.org/ (accessed on 3 March 2023)
Number of new COVID-19 cases	Number of newly reported cases	1 day
The number of deaths due to COVID-19	Number of newly reported deaths	1 day
Epidemic prevention policy	The extent to which the government restricts internal movement/travel between regions and cities	1 day
Geographical base map of European administrative divisions				Projection transformation	https://gadm.org/ (accessed on 30 September 2022)
Electricity consumption		15 min/1 h	MW	Fill forward, statistical summary	https://transparency.entsoe.eu/ (accessed on 30 September 2022)

.

4. Research Methods

4.1. Anomaly Detection Methods

Anomaly detection is the process of identifying data points that are significantly different from the rest of the data within a dataset. In this paper, common anomaly detection methods, including Z-score, Isolation Forests, Local Outlier Factors, and Autoencoder, were employed for anomaly detection. These methods were then combined with anomaly duration to identify extreme events. The impact of extreme events on the power system was quantitatively assessed using metrics such as elastic loss and vulnerability.

4.1.1. Z-Score

Z-score anomaly detection is a commonly used statistical method. Its basic idea is to compare each data point with the mean of the dataset and then calculate its standard deviation, resulting in a Z-score. If the Z-score exceeds a certain threshold, the data point can be considered an outlier. The formula to calculate the Z-score is as follows:

$$Z=\frac{(X-\mu )}{\sigma }$$

(1)

In this equation, X represents the hourly electricity consumption, μ is the mean of the dataset, and σ is the standard deviation of the dataset. Considering the strong periodicity of electricity consumption, this paper simultaneously considers the division of electricity consumption data based on both the day of the week and the hour to calculate their respective means and standard deviations.

4.1.2. Isolation Forest

Isolation Forest (IF) is an anomaly detection algorithm based on a tree structure. Its basic idea is to leverage the splitting capability of random trees to randomly partition data points into different branches. Subsequently, it determines whether a data point is an outlier by calculating its depth in the tree. Normal values have a greater depth in the tree, while outliers have a smaller depth. The calculation process of the Isolation Forest is as follows:

$$s(x)=2^{-\frac{E(h(x))}{c(n)}}$$

(2)

where E(h(x)) represents the expected value of the average path length of sample point x across all trees. c(n) is a constant that can be approximated as:

$$c(n)=2H_{n-1}-\frac{2(n-1)}{n}$$

(3)

where $H_{n-1}$ is the harmonic number, defined as:

$$H(n-1)=In(n)+0.5772156649$$

(4)

where $In(n)$ is the natural logarithm base e. Through calculation, the isolation forest score for a sample point could be obtained. The score ranges from 0 to 1, with lower scores indicating that the sample point is more likely to be an outlier. In practical applications, normal points may be labeled as 1, while outliers are labeled as −1.

4.1.3. Local Outlier Factor

The Local Outlier Factor (LOF) is a density-based outlier detection algorithm that identifies outliers based on the density information of sample points. Its calculation process is as follows:

(1) For each data point, find its k-nearest neighbors (kNNs).

(2) Calculate the reachability distance for each data point, which is defined as the distance to the furthest point in its kNN, using the reachability distance formula:

$$reach-dis{t}_k(x,y)=\max \{dis{t}_k(x,y),k-dis{t}_k(y)\}$$

(5)

where $dis{t}_k(x,y)$ represents the distance between x and y at the k-th distance, where the k-th distance indicates the distance to the point that is the k-th closest to x.

(3) Calculate the local reachability density (LRD) for each data point within the kNN space, which is the reciprocal of the average reachability distance to all points in its kNN. The LRD formula is as follows:

$$LR{D}_K(x)=1/\left\{\frac{{\displaystyle \sum _{y\in N_k(x)}reach-dis{t}_k(x,y)}}{N_k(x)}\right\}$$

(6)

where k is the number of nearest neighbors, and $N_k(x)$ represents the set of k-nearest neighbors for point x.

(4) Calculate the LOF value for each data point, which represents the ratio of the density of the point relative to its neighborhood to the average density of the surrounding data points. The LOF formula is as follows:

$$LO{F}_K(X)=\frac{{\displaystyle \sum _{y\in N_k(x)}\frac{LR{D}_K(y)}{LR{D}_K(x)}}}{N_k(x)}$$

(7)

(5) Based on the computed results, data points with higher LOF values are considered outliers. In practical applications, normal points are assigned a label of 1, while outliers are assigned a label of −1.

4.1.4. Autoencoder

Autoencoder (AE) is an unsupervised learning method that primarily comprises two parts: an encoder and a decoder. The encoder projects input data into a hidden space, while the decoder reconstructs vectors from the hidden space back into the original data. An autoencoder can calculate the error between the original data and the reconstructed data, and if the error exceeds a threshold, the data are considered an anomaly. The implementation process of an autoencoder is as follows:

For a given training set X = {x₁, x₂, …, x_m}, the encoder maps X to a hidden layer, producing encoder output H = {h₁, h₂, …, h_m} as follows:

$$H=g(W_{1}X+b_1)$$

(8)

Here, W₁ is the weight matrix, b₁ is the bias vector.

Then, the hidden layer H is decoded by the decoder into a vector Z = {z₁, z₂, …, z_m} back into the original data distribution as follows:

$$Z=g(W_{2}H+b_2)$$

(9)

Here, W₂ is the weight matrix and b₂ is the bias vector.

Finally, the reconstruction error is calculated, and the backpropagation algorithm is used to optimize the network’s parameters (W₁, W₂, b₁, b₂) to minimize the error.

4.2. Extreme Event Detection

Extreme events can lead to changes in electricity consumption by affecting human behavior. This paper combines two parameters, anomaly threshold and time threshold, for the recognition of extreme events, as expressed by the following formula:

$$Event=\{s^i:s^i\ge |\theta |and(T_i-T_j)\le t\}$$

(10)

Here, $Event$ represents the recognized extreme events, $s$ indicates the anomaly score, and an event is recognized when the value of $s$ exceeds the specified anomaly threshold $\theta$. $T_i$ represents the time when an anomaly is recognized, $T_j$ represents the time when the next anomaly is recognized, and if the time difference between them exceeds the time threshold $t$, it indicates the end of this extreme event.

The anomaly threshold varies for different anomaly detection methods. This study establishes the abnormal proportion at 5% based on statistical analysis. For Z-score, it is set at 1.96, indicating that the proportion of anomalies is less than or equal to 5%. For the Isolation Forest (IF) method, 100 trees are used, and the anomaly proportion is set to 5%. In the case of the Local Outlier Factor (LOF) model, the number of local neighbors is set to 24, and the anomaly proportion is also set to 5%. As for the Autoencoder (AE) method, the anomaly proportion is set to 5%. The time threshold $t$ can be chosen based on specific requirements. In this study, to examine the impact of events such as low temperature, high temperature, and epidemics, considering their relatively long durations, the time threshold is set to 168 h, which is equivalent to one week. If no anomalies occur within one week, the event is considered to have ended.

4.3. Quantitative Assessment of Extreme Events

Once extreme events are identified, it is possible to quantitatively assess the perturbations in electricity consumption caused by these extreme events. This paper utilizes three quantitative measures, elastic loss (TLR), vulnerability (V), and duration (T), to evaluate the extent of electricity consumption’s response to extreme events. Duration is defined as the time it takes for the system to reach a new equilibrium state from the beginning of the impact, i.e., from t₀ to t₁.

The formula for calculating elastic loss (TLR) is as follows:

$$TLR={\displaystyle \underset{t_0}{\overset{t_1}{\int }}|1-Q(t)|}dt$$

(11)

where TLR represents the elastic loss, reflecting the cumulative disturbance of extreme events on electricity consumption. Q(t) represents the ratio of actual electricity consumption at time t to the average electricity consumption during that period, t₀ is the start time of the detected extreme event, and t₁ is the end time of the detected extreme event.

The formula for calculating vulnerability (V) is as follows:

$$V=\left|\frac{{\overline{E}}_t-E_t}{{\overline{E}}_t}\right|$$

(12)

where V represents vulnerability, reflecting the instantaneous disturbance of extreme events on electricity consumption. ${\overline{E}}_t$ represents the average electricity consumption at time t and $E_t$ is the actual electricity consumption at time t.

5. Result

5.1. Electricity Consumption Anomaly Detection

Anomaly detection can help quickly identify and process abnormal electricity usage data, thereby pinpointing the times when extreme events impact power consumption. During late January to early February 2019, multiple European countries experienced the impact of snowstorms and low temperatures. Subsequently, in February 2020, a pandemic broke out in Europe. Concurrently, since January 2022, tensions between Russia and Ukraine have been escalating. Therefore, this article presents selected test results from some countries during the periods from 1 January to 1 March 2019, from 20 March to 1 May 2020, and from 1 January to 1 March 2022. In the accompanying graphs, the blue curve represents actual electricity usage, while the bar chart represents model scores, with the orange bars indicating normal values and the red bars indicating identified anomalies. According to Figure 2, the LOF method seems to be not suitable for anomaly detection in the Czech region, as the anomalies it detects are uniformly distributed. Specifically, the Z-score method can only identify significant increases in electricity consumption during the period from 20 January to 26 January. In contrast, the Isolation Forest (IF) and Autoencoder (AE) methods identify more abnormal time periods, including from 7 January to 11 January and from 28 January to 1 February. In the case of electricity consumption detection in Spain (see Figure 3), the IF method first identifies an anomaly occurring at 2:00 a.m. on 22 March. The IF method and Z-score method both successfully detect abnormal time periods, while the AE method can only identify significant decreases in electricity consumption. The results of anomaly detection in Poland, as one of the countries closest to Ukraine, are illustrated in Figure 4, indicating that the IF and Z-score methods can promptly identify anomalies.

In summary, the LOF method performs poorly in detecting anomalies and cannot effectively distinguish between normal and abnormal values. This may be due to the fact that the outlier points in the electricity consumption dataset exhibit certain time series characteristics, making it difficult for the LOF algorithm to capture these outlier points. The Z-score model can only identify time periods with the most noticeable changes in electricity consumption. The AE method has lower sensitivity for countries with large fluctuations in electricity consumption. In contrast, the IF model performs relatively consistently in various situations and can accurately detect anomalies.

5.2. Extreme Event Recognition

This study aims to analyze the impact of the low temperatures in Europe in 2019, the pandemic in 2020, and the high-temperature events in 2022 on electricity consumption, utilizing data from the respective years for in-depth research. Figure 5 and Figure 6 respectively depict the anomaly detection results for the Netherlands in 2019 and Germany in 2022. The anomaly period for the Netherlands spans from 2 January 2019, at 16:00 to 15 March 2019, at 9:00, totaling 71 days. Considering the meteorological distribution in the Netherlands (Figure 7), this timeframe coincides with the lowest recorded temperatures in the Netherlands. Additionally, starting from 10 March 2019, temperatures in the Netherlands steadily increased until reaching their peak on 15 March, when electricity consumption returned to normal.

For Germany, the anomalous period during the summer of 2022 ranges from 30 April 2022, at 23:00 to 13 November 2022, at 4:00. Examining the temperature variations in Germany, it can be observed that temperatures began to rise at the end of April, started to decline in September, experienced a brief increase in October, and then resumed a decline in November. Around 13 November, a slight temperature drop occurred, coinciding with the return to normal electricity consumption. In conclusion, the results of extreme event identification can be utilized to detect extreme weather events.

Figure 8 displays the results of identifying the COVID-19 pandemic in Italy in 2020. The anomaly period spans from 15 March 2020, at 1:00 to 21 June 2020, at 4:00. The onset of the anomaly occurred approximately two weeks after Italy implemented strict lockdown measures, while the end of the anomaly period coincided with a week after the reduction in lockdown levels. This indicates that the model’s detection results align with the timing of the pandemic and can be used to characterize the pandemic event.

5.3. The Impact of Extreme Events on Electricity Consumption

In the previous section, we used the Isolation Forest (IF) model to identify the impact periods of extreme events on electricity consumption. In this section, we will use duration, elastic loss, and vulnerability indicators to quantitatively assess the impact of extreme events.

The spatial distribution map of maximum vulnerability is shown in Figure 9. From Figure 9a, it can be seen that the values of maximum vulnerability in Northern Europe and Southern Europe are much higher than in other regions. This indicates that the impact of low temperatures on Northern and Southern Europe is much greater than in other regions. Compared to other extreme events, the maximum vulnerability to low temperatures is much higher, suggesting that low temperatures are more likely to cause a sharp change in electricity consumption. During the pandemic period (Figure 9b), except for Serbia, there is no significant difference in the maximum vulnerability of other countries, indicating that the pandemic has had a significant impact on electricity consumption across the entire European region. During the 2022 heat event, the maximum vulnerability gradually decreases from south to north, indicating that the change in electricity consumption is higher in southern Europe than in the north, and northern Europe is less affected by this event.

The distribution chart of the duration of extreme events (Figure 10) reveals that the impact of the COVID-19 pandemic on Europe persists longer than other extreme events. In the central part of Europe, electricity consumption experiences an unusually extended duration of impact compared to other regions, indicating that the middle part of Europe was the primary region affected by the first wave of the pandemic. Low temperatures have a shorter duration across the nation and exhibit a relatively even distribution, with slightly longer durations in the southern regions, possibly due to the influence of cold air moving southward. High temperatures show a longer duration in the central part of Europe, which may be related to the climatic zone and topographical features of the middle part of Europe.

The distribution of elastic losses, as shown in Figure 11, indicates that the elastic losses resulting from the COVID-19 pandemic are higher than those from the other two events. This could be attributed to the prolonged duration of the pandemic. Among the countries, France stands out with the most significant losses caused by the pandemic, while the least affected countries, apart from Montenegro and Serbia, are Switzerland and the Netherlands. It is worth noting that both Montenegro and Switzerland did not implement complete lockdown measures during the pandemic. High temperatures resulted in electricity losses that are second only to those caused by the pandemic, with a greater impact on the central region of Europe compared to other areas. France experienced the most substantial losses due to high temperatures. Low temperatures caused lower electricity losses across Europe compared to the other two events. Among countries, France, Sweden, and Serbia exhibit more noticeable elastic losses due to low temperatures. In summary, it is evident from the comparison that Sweden, France, and Serbia are more sensitive to extreme events in terms of electricity consumption. Under all three extreme events, their elastic losses are higher than in other countries.

Figure 11. Spatial distribution map of elastic loss. (a) The low temperature event in 2020; (b) The COVID-19 pandemic in 2020; (c) The high temperature event in 2022.The disturbance results for electricity consumption under low temperatures, high temperatures, and the COVID-19 pandemic are presented in Table 2, Table 3 and Table 4. From Table 2, it can be observed that the onset of low temperatures is generally in early January, with Norway being the latest to experience temperature drops, starting from 12 January 2019. However, electricity consumption disruptions in Norway did not commence until 14 January, resulting in a delay of 2 days. This highlights the resilience of electricity consumption to extreme events. In comparison to other countries, Norway experienced disturbances later, possibly due to the fact that it already relies on a substantial amount of heating equipment during its cold winter seasons, indicating that electricity consumption in cold regions exhibits better stability under low-temperature conditions.

Figure 11. Spatial distribution map of elastic loss. (a) The low temperature event in 2020; (b) The COVID-19 pandemic in 2020; (c) The high temperature event in 2022.The disturbance results for electricity consumption under low temperatures, high temperatures, and the COVID-19 pandemic are presented in Table 2, Table 3 and Table 4. From Table 2, it can be observed that the onset of low temperatures is generally in early January, with Norway being the latest to experience temperature drops, starting from 12 January 2019. However, electricity consumption disruptions in Norway did not commence until 14 January, resulting in a delay of 2 days. This highlights the resilience of electricity consumption to extreme events. In comparison to other countries, Norway experienced disturbances later, possibly due to the fact that it already relies on a substantial amount of heating equipment during its cold winter seasons, indicating that electricity consumption in cold regions exhibits better stability under low-temperature conditions.

Table 2. Impact of low temperatures on electricity consumption.

Country	Start Time	End Time	Duration (Days)	Elastic Loss	Maximum Vulnerability
Austria	7 January 2019 8:00	22 February 2019 10:00	46	192.57	1.31
Belgium	3 January 2019 16:00	1 March 2019 10:00	56	204.16	1.33
Bulgaria	2 January 2019 16:00	29 January 2019 17:00	27	208.60	1.51
Croatia	3 January 2019 16:00	31 January 2019 18:00	28	86.61	1.25
Czech Republic	7 January 2019 12:00	8 February 2019 8:00	31	149.73	1.32
Denmark	3 January 2019 16:00	7 February 2019 17:00	35	78.54	1.21
Estonia	3 January 2019 14:00	13 February 2019 7:00	40	238.64	1.46
Finland	2 January 2019 10:00	7 February 2019 17:00	36	288.03	1.55
France	3 January 2019 7:00	15 February 2019 7:00	43	385.28	1.57
Germany	1 January 2019 3:00	19 February 2019 17:00	49	142.47	1.26
Greece	3 January 2019 8:00	22 January 2019 18:00	19	112.75	1.43
Hungary	1 January 2019 2:00	25 January 2019 16:00	24	71.09	1.26
Italy	1 January 2019 3:00	14 February 2019 17:00	44	120.27	1.22
Latvia	3 January 2019 8:00	12 March 2019 8:00	68	220.55	1.29
Lithuania	4 January 2019 15:00	4 February 2019 9:00	30	107.37	1.26
Luxembourg	6 January 2019 18:00	29 January 2019 7:00	22	110.64	1.65
Montenegro	3 January 2019 16:00	1 February 2019 16:00	29	203.18	1.58
Netherlands	2 January 2019 16:00	15 March 2019 9:00	71	267.62	1.41
Norway	14 January 2019 6:00	7 February 2019 16:00	24	192.94	1.45
Poland	1 January 2019 2:00	11 January 2019 16:00	10	28.40	1.16
Portugal	1 January 2019 5:00	20 February 2019 19:00	50	158.23	1.29
Romania	7 January 2019 15:00	28 February 2019 17:00	52	193.46	1.27
Serbia	3 January 2019 9:00	14 February 2019 18:00	42	347.89	1.59
Slovakia	7 January 2019 8:00	13 February 2019 11:00	37	146.84	1.25
Slovenia	1 January 2019 2:00	25 February 2019 12:00	55	193.46	1.37
Spain	1 January 2019 3:00	19 February 2019 19:00	49	159.00	1.27
Sweden	2 January 2019 16:00	12 February 2019 7:00	40	308.65	1.47
Switzerland	7 January 2019 11:00	13 February 2019 9:00	36	154.49	1.30

Table 2. Impact of low temperatures on electricity consumption.

Country	Start Time	End Time	Duration (Days)	Elastic Loss	Maximum Vulnerability
Austria	7 January 2019 8:00	22 February 2019 10:00	46	192.57	1.31
Belgium	3 January 2019 16:00	1 March 2019 10:00	56	204.16	1.33
Bulgaria	2 January 2019 16:00	29 January 2019 17:00	27	208.60	1.51
Croatia	3 January 2019 16:00	31 January 2019 18:00	28	86.61	1.25
Czech Republic	7 January 2019 12:00	8 February 2019 8:00	31	149.73	1.32
Denmark	3 January 2019 16:00	7 February 2019 17:00	35	78.54	1.21
Estonia	3 January 2019 14:00	13 February 2019 7:00	40	238.64	1.46
Finland	2 January 2019 10:00	7 February 2019 17:00	36	288.03	1.55
France	3 January 2019 7:00	15 February 2019 7:00	43	385.28	1.57
Germany	1 January 2019 3:00	19 February 2019 17:00	49	142.47	1.26
Greece	3 January 2019 8:00	22 January 2019 18:00	19	112.75	1.43
Hungary	1 January 2019 2:00	25 January 2019 16:00	24	71.09	1.26
Italy	1 January 2019 3:00	14 February 2019 17:00	44	120.27	1.22
Latvia	3 January 2019 8:00	12 March 2019 8:00	68	220.55	1.29
Lithuania	4 January 2019 15:00	4 February 2019 9:00	30	107.37	1.26
Luxembourg	6 January 2019 18:00	29 January 2019 7:00	22	110.64	1.65
Montenegro	3 January 2019 16:00	1 February 2019 16:00	29	203.18	1.58
Netherlands	2 January 2019 16:00	15 March 2019 9:00	71	267.62	1.41
Norway	14 January 2019 6:00	7 February 2019 16:00	24	192.94	1.45
Poland	1 January 2019 2:00	11 January 2019 16:00	10	28.40	1.16
Portugal	1 January 2019 5:00	20 February 2019 19:00	50	158.23	1.29
Romania	7 January 2019 15:00	28 February 2019 17:00	52	193.46	1.27
Serbia	3 January 2019 9:00	14 February 2019 18:00	42	347.89	1.59
Slovakia	7 January 2019 8:00	13 February 2019 11:00	37	146.84	1.25
Slovenia	1 January 2019 2:00	25 February 2019 12:00	55	193.46	1.37
Spain	1 January 2019 3:00	19 February 2019 19:00	49	159.00	1.27
Sweden	2 January 2019 16:00	12 February 2019 7:00	40	308.65	1.47
Switzerland	7 January 2019 11:00	13 February 2019 9:00	36	154.49	1.30

Table 3. Impact of high temperatures on electricity consumption.

Country	Start Time	End Time	Duration (Days)	Elastic Loss	Maximum Vulnerability
Austria	1 May 2022 1:00	1 November 2022 3:00	184	376.83	1.07
Belgium	29 May 2022 3:00	13 November 2022 3:00	168	287.00	1.06
Bulgaria	18 July 2022 11:00	4 August 2022 11:00	17	62.38	1.37
Croatia	8 May 2022 0:00	18 September 2022 4:00	133	386.05	0.99
Czech Republic	15 May 2022 2:00	25 September 2022 3:00	133	297.81	1.08
Denmark	5 June 2022 1:00	21 August 2022 3:00	77	280.11	1.08
Estonia	24 June 2022 0:00	2 August 2022 1:00	39	165.61	0.91
Finland	8 May 2022 2:00	1 November 2022 5:00	177	714.52	3.44
France	30 April 2022 23:00	13 November 2022 4:00	196	356.29	1.07
Germany	16 July 2022 10:00	2 August 2022 11:00	17	96.06	1.54
Greece	31 July 2022 0:00	22 August 2022 2:00	22	49.25	1.02
Hungary	21 June 2022 8:00	29 July 2022 15:00	38	162.21	1.35
Italy	28 May 2022 1:00	18 October 2022 0:00	142	424.28	1.05
Latvia	7 May 2022 22:00	26 June 2022 2:00	49	129.02	1.04
Lithuania	3 June 2022 10:00	4 August 2022 10:00	62	291.86	1.38
Luxembourg	22 July 2022 11:00	10 August 2022 12:00	19	81.59	1.42
Montenegro	9 April 2022 12:00	18 October 2022 12:00	192	596.81	1.11
Netherlands	20 July 2022 1:00	31 July 2022 4:00	11	60.96	1.08
Norway	1 May 2022 3:00	16 October 2022 2:00	167	176.18	1.11
Poland	14 August 2022 2:00	4 September 2022 4:00	21	34.80	1.02
Portugal	23 April 2022 23:00	27 June 2022 0:00	64	158.76	1.01
Romania	24 April 2022 3:00	19 July 2022 1:00	85	402.37	1.04
Serbia	15 May 2022 1:00	13 November 2022 3:00	182	505.97	1.01
Slovakia	10 July 2022 1:00	6 November 2022 4:00	119	351.50	1.08
Slovenia	12 July 2022 11:00	2 August 2022 12:00	21	53.84	1.22
Spain	24 June 2022 0:00	14 August 2022 3:00	51	280.04	0.88
Sweden	2 July 2022 21:00	28 August 2022 11:00	56	145.08	1.09

Table 3. Impact of high temperatures on electricity consumption.

Country	Start Time	End Time	Duration (Days)	Elastic Loss	Maximum Vulnerability
Austria	1 May 2022 1:00	1 November 2022 3:00	184	376.83	1.07
Belgium	29 May 2022 3:00	13 November 2022 3:00	168	287.00	1.06
Bulgaria	18 July 2022 11:00	4 August 2022 11:00	17	62.38	1.37
Croatia	8 May 2022 0:00	18 September 2022 4:00	133	386.05	0.99
Czech Republic	15 May 2022 2:00	25 September 2022 3:00	133	297.81	1.08
Denmark	5 June 2022 1:00	21 August 2022 3:00	77	280.11	1.08
Estonia	24 June 2022 0:00	2 August 2022 1:00	39	165.61	0.91
Finland	8 May 2022 2:00	1 November 2022 5:00	177	714.52	3.44
France	30 April 2022 23:00	13 November 2022 4:00	196	356.29	1.07
Germany	16 July 2022 10:00	2 August 2022 11:00	17	96.06	1.54
Greece	31 July 2022 0:00	22 August 2022 2:00	22	49.25	1.02
Hungary	21 June 2022 8:00	29 July 2022 15:00	38	162.21	1.35
Italy	28 May 2022 1:00	18 October 2022 0:00	142	424.28	1.05
Latvia	7 May 2022 22:00	26 June 2022 2:00	49	129.02	1.04
Lithuania	3 June 2022 10:00	4 August 2022 10:00	62	291.86	1.38
Luxembourg	22 July 2022 11:00	10 August 2022 12:00	19	81.59	1.42
Montenegro	9 April 2022 12:00	18 October 2022 12:00	192	596.81	1.11
Netherlands	20 July 2022 1:00	31 July 2022 4:00	11	60.96	1.08
Norway	1 May 2022 3:00	16 October 2022 2:00	167	176.18	1.11
Poland	14 August 2022 2:00	4 September 2022 4:00	21	34.80	1.02
Portugal	23 April 2022 23:00	27 June 2022 0:00	64	158.76	1.01
Romania	24 April 2022 3:00	19 July 2022 1:00	85	402.37	1.04
Serbia	15 May 2022 1:00	13 November 2022 3:00	182	505.97	1.01
Slovakia	10 July 2022 1:00	6 November 2022 4:00	119	351.50	1.08
Slovenia	12 July 2022 11:00	2 August 2022 12:00	21	53.84	1.22
Spain	24 June 2022 0:00	14 August 2022 3:00	51	280.04	0.88
Sweden	2 July 2022 21:00	28 August 2022 11:00	56	145.08	1.09

Table 4. Impact of COVID-19 pandemic on electricity consumption.

Country	Start Time	End Time	Duration (Days)	Elastic Loss	Maximum Vulnerability
Austria	5 April 2020 1:00	11 October 2020 2:00	189	488.35	1.09
Belgium	3 April 2020 1:00	3 August 2020 2:00	122	311.75	1.02
Bulgaria	16 April 2020 23:00	27 July 2020 1:00	101	416.38	1.00
Croatia	22 March 2020 1:00	31 July 2020 13:00	131	433.01	1.22
Czech Republic	10 April 2020 22:00	27 September 2020 3:00	169	517.43	1.04
Denmark	23 May 2020 2:00	9 August 2020 3:00	78	191.30	1.03
Estonia	24 May 2020 0:00	2 September 2020 0:00	101	456.08	0.94
Finland	24 May 2020 1:00	24 August 2020 0:00	91	423.42	0.92
France	11 April 2020 2:00	21 September 2020 2:00	163	740.44	0.95
Germany	5 April 2020 0:00	4 October 2020 3:00	182	386.13	1.07
Greece	5 April 2020 2:00	13 May 2020 0:00	37	189.14	1.07
Hungary	29 March 2020 2:00	5 October 2020 1:00	189	430.18	1.08
Italy	15 March 2020 1:00	21 June 2020 4:00	98	449.70	0.99
Latvia	17 May 2020 1:00	9 August 2020 3:00	84	186.41	1.05
Lithuania	5 April 2020 23:00	14 September 2020 0:00	161	382.90	1.12
Luxembourg	3 August 2020 15:00	28 November 2020 16:00	117	637.57	1.49
Montenegro	4 April 2020 11:00	27 April 2020 13:00	23	64.16	0.99
Netherlands	13 June 2020 0:00	6 July 2020 1:00	23	129.62	0.82
Norway	29 March 2020 1:00	4 October 2020 2:00	189	428.01	1.07
Poland	22 March 2020 4:00	5 July 2020 6:00	105	330.73	1.01
Portugal	12 April 2020 0:00	2 August 2020 3:00	112	318.73	1.09
Romania	9 April 2020 23:00	5 October 2020 1:00	178	450.46	1.19
Serbia	11 April 2020 0:00	4 October 2020 1:00	176	463.39	1.09
Slovakia	22 March 2020 2:00	21 June 2020 5:00	91	308.31	1.04
Slovenia	13 June 2020 2:00	23 August 2020 4:00	71	402.12	0.89
Spain	9 April 2020 3:00	9 May 2020 23:00	30	92.26	1.12

Table 4. Impact of COVID-19 pandemic on electricity consumption.

Country	Start Time	End Time	Duration (Days)	Elastic Loss	Maximum Vulnerability
Austria	5 April 2020 1:00	11 October 2020 2:00	189	488.35	1.09
Belgium	3 April 2020 1:00	3 August 2020 2:00	122	311.75	1.02
Bulgaria	16 April 2020 23:00	27 July 2020 1:00	101	416.38	1.00
Croatia	22 March 2020 1:00	31 July 2020 13:00	131	433.01	1.22
Czech Republic	10 April 2020 22:00	27 September 2020 3:00	169	517.43	1.04
Denmark	23 May 2020 2:00	9 August 2020 3:00	78	191.30	1.03
Estonia	24 May 2020 0:00	2 September 2020 0:00	101	456.08	0.94
Finland	24 May 2020 1:00	24 August 2020 0:00	91	423.42	0.92
France	11 April 2020 2:00	21 September 2020 2:00	163	740.44	0.95
Germany	5 April 2020 0:00	4 October 2020 3:00	182	386.13	1.07
Greece	5 April 2020 2:00	13 May 2020 0:00	37	189.14	1.07
Hungary	29 March 2020 2:00	5 October 2020 1:00	189	430.18	1.08
Italy	15 March 2020 1:00	21 June 2020 4:00	98	449.70	0.99
Latvia	17 May 2020 1:00	9 August 2020 3:00	84	186.41	1.05
Lithuania	5 April 2020 23:00	14 September 2020 0:00	161	382.90	1.12
Luxembourg	3 August 2020 15:00	28 November 2020 16:00	117	637.57	1.49
Montenegro	4 April 2020 11:00	27 April 2020 13:00	23	64.16	0.99
Netherlands	13 June 2020 0:00	6 July 2020 1:00	23	129.62	0.82
Norway	29 March 2020 1:00	4 October 2020 2:00	189	428.01	1.07
Poland	22 March 2020 4:00	5 July 2020 6:00	105	330.73	1.01
Portugal	12 April 2020 0:00	2 August 2020 3:00	112	318.73	1.09
Romania	9 April 2020 23:00	5 October 2020 1:00	178	450.46	1.19
Serbia	11 April 2020 0:00	4 October 2020 1:00	176	463.39	1.09
Slovakia	22 March 2020 2:00	21 June 2020 5:00	91	308.31	1.04
Slovenia	13 June 2020 2:00	23 August 2020 4:00	71	402.12	0.89
Spain	9 April 2020 3:00	9 May 2020 23:00	30	92.26	1.12

The Netherlands and Latvia were impacted by low temperatures for the longest duration. In the case of the Netherlands, the temperature began to drop from 1 January 2019, and abnormal electricity usage was identified on 2 January, causing a 1-day delay in electricity disruption. The disturbance in electricity consumption in the Netherlands ended on 15 March. Prior to this date, the temperature in the Netherlands gradually rose from 10 March, reaching its maximum value by 15 March, and electricity consumption also gradually returned to normal. This suggests that the Dutch power system was able to respond promptly to the temperature increase. The prolonged duration of electricity disruption in the Netherlands may be attributed to significant temperature fluctuations during that period, including multiple instances of sudden temperature drops and other extreme weather changes. Latvia also experienced several instances of temperature fluctuations between 3 January and 12 March 2019, indicating that abrupt temperature changes can prolong the impact of disasters.

The impact of high-temperature events on electricity consumption, as shown in Table 3, reveals that Germany experienced the longest duration of disruption. The disturbance in Germany lasted from 30 April to 13 November 2022. Germany began experiencing a continuous temperature rise from 26 April, lasting for 15 days, with the disturbance in electricity consumption lagging by 4 days. This suggests that Germany’s electricity consumption exhibits resilience to temperature changes. Germany started cooling down from 28 October, and 13 November marked the coldest day in the second wave of cooling. Electricity consumption returned to normal on that day, indicating a high sensitivity of Germany’s power system to high temperatures. The impact of high-temperature events on electricity consumption, as shown in Table 3, reveals that Germany experienced the longest duration of disruption. The disturbance in Germany lasted from 30 April to 13 November 2022. Germany began experiencing a continuous temperature rise from April 26, lasting for 15 days, with the disturbance in electricity consumption lagging by 4 days. This suggests that Germany’s electricity consumption exhibits resilience to temperature changes. Germany started cooling down from 28 October, and 13 November marked the coldest day in the second wave of cooling. Electricity consumption returned to normal on that day, indicating a high sensitivity of Germany’s power system to high temperatures.

Regarding the COVID-19 pandemic (Table 4), Italy was the first country to detect anomalies in electricity consumption, with the initial anomaly occurring on 15 March 2020, at 1:00 AM. This happened approximately two weeks after the implementation of lockdown measures. Spain, another country heavily affected by the pandemic, implemented lockdown measures from 9 March 2020 to 20 June 2020. However, disturbances in electricity consumption in Spain did not begin until 22 March 2020, which was 13 days after the lockdown measures were put in place. This indicates a lag in the impact of the initial lockdown policies on electricity consumption, and the disturbance ended on 21 June 2020, the day after the lockdown measures were lifted, highlighting the sensitivity of electricity consumption to policy changes in Spain. Sweden, one of the countries that did not enforce strict lockdown policies, experienced disturbances in electricity consumption starting on 13 June 2020. Its start time was later than that of other countries, indicating that national policies had a more noticeable impact on electricity consumption in Sweden.

6. Conclusions

The current research is based on the recognition of electricity consumption anomalies using four methods: Z-score, Isolation Forest, Local Outlier Factor, and Autoencoder. According to the results of anomaly detection, extreme events are identified and quantitatively assessed. The extent of their impact on electricity consumption is studied.

In terms of anomaly detection, the Local Outlier Factor method performs poorly and cannot accurately distinguish normal values from anomalies. Z-score can only identify periods of significantly increased electricity consumption, while Autoencoder is sensitive to low electricity values. Isolation Forest is the most stable method.

In terms of extreme event detection, electricity anomalies under low temperatures typically emerge around early January 2019, occurring frequently on the same day or the day following a temperature drop. However, the restoration of normal electricity operations usually requires several consecutive days of temperature increase. On the other hand, electricity anomalies under high temperatures started to manifest around late April 2022, and temperature fluctuations can extend the duration of the disaster’s impact. Regarding the pandemic, in countries like Italy and Spain, electricity anomalies occurred within 7–14 days following the implementation of epidemic prevention policies. Nevertheless, electricity typically returned to normal on the day of or the day after the relaxation of containment measures, and these electricity anomalies are closely associated with national pandemic prevention and control policies.

In terms of the extent of impact, low temperatures can cause a sharp change in electricity consumption, with Northern Europe being more affected. The pandemic had the greatest impact on electricity consumption in Europe, with the middle part of Europe being the main region affected by the first wave of the pandemic. High temperatures had a longer duration in the middle part of Europe. Additionally, the electricity consumption in three countries, Sweden, France, and Serbia, is most sensitive to extreme events.

This study utilizes electricity consumption data as an external representation of power usage. Taking a data mining approach, it introduces a comprehensive framework for the detection of electricity consumption anomalies, the identification of extreme events, and the quantitative assessment of these phenomena. It establishes metrics and methods for quantitatively evaluating disturbances in electricity consumption during extreme events, offering a fresh research perspective for quantifying the impact of extreme events on national power consumption.

The primary focus of this research is on the impact of extreme events on the entire power system, without dividing and analyzing the situations before, during, and after the occurrence of these events. Therefore, in future research, different analyses and assessments can be conducted based on the various stages of event occurrence. This approach will enable a more detailed and comprehensive understanding of the power system’s tolerance and response capabilities concerning different types of extreme events, thereby guiding the optimization and improvement of the resilience of the power system.